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Growth, yield and silvicultural management of exotic timber species in Kenya Mathu, Winston Joshua Kamuru 1983

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GROWTH, YIELD AND SILVICULTURAL MANAGEMENT OF EXOTIC TIMBER SPECIES IN KENYA  by WINSTON JOSHUA KAMURU MATHU B.Sc.F. U n i v e r s i t y o f new Brunswick, Canada 1971 M.Sc.F. U n i v e r s i t y of Das-Es-Salaam, T a n z a n i a 1977  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY  i n the FACULTY OF GRADUATE  STUDIES  Department of F o r e s t r y  We accept t h i s t h e s i s as conforming to the r e q u i r e d s t a n d a r d  THE UNIVERSITY OF BRITISH COLUMBIA ®March, 1983  In p r e s e n t i n g  this  t h e s i s i n p a r t i a l f u l f i l m e n t of the  requirements  f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree t h a t the  library  s h a l l make i t f r e e l y  a v a i l a b l e f o r reference  I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying of the s c h o l a r l y purposes may representatives.  be  granted by  I t i s understood t h a t  thesis for financial  gains s h a l l not  permission.  Department of F o r e s t r y The U n i v e r s i t y of B r i t i s h 2357 Main M a l l Vancouver, B.C. Canada V6T 1W5 March  |g,  1983  the Head of my  Columbia  be  and  study.  thesis  Department or by  copying or p u b l i c a t i o n of allowed without my  written  for his  this  i  ABSTRACT  Supervisor:  T h i s study p r e s e n t s  D.D. MUNRO  the growth, y i e l d and the s i l v i c u l t u r a l manage-  ment o f Cupressus l u s i t a n i c a , Pinus p a t u l a and Pinus , r a d i a t a , the t h r e e most important  timber  s p e c i e s growing i n the Kenya h i g h l a n d s .  The study  Is based on 163, 176 and 164 permanent sample p l o t s f o r the t h r e e species r e s p e c t i v e l y . The  stand dominant h e i g h t development was p r e d i c t e d as a f u n c t i o n  of stand age and s i t e i n d e x , d e f i n e d as dominant h e i g h t a t r e f e r e n c e age of  15 y e a r s .  The Chapman-Richard's growth f u n c t i o n was used f o r  C_. l u s i t a n i c a and P_. r a d i a t a w h i l e a l i n e a r q u a d r a t i c equation was used t o d e s c r i b e dominant h e i g h t development f o r P^. p a t u l a by g e o g r a p h i c a l regions.  Height  development f o r the two pine s p e c i e s was found  significantly different establishment  to be  (up to age 20 y e a r s ) i n t h e Shamba and g r a s s l a n d  sites.  Stand b a s a l a r e a b e f o r e t h i n n i n g was p r e d i c t e d as a f u n c t i o n of stand age, dominant h e i g h t and number o f stems u s i n g a W e i b u l l - t y p e growth e q u a t i o n .  In t h i n n e d  stands  b a s a l a r e a was p r e d i c t e d through a  b a s a l a r e a increment n o n l i n e a r e q u a t i o n .  F o r P_. r a d i a t a , b a s a l  area  increment was p r e d i c t e d as a f u n c t i o n of b a s a l a r e a a t the beginning of the growth p e r i o d (1 y e a r ) and age.  F o r C_. l u s i t a n i c a and P. p a t u l a , a  t h i r d term-stand d e n s i t y index, d e f i n e d as the percent  r a t i o of average  s p a c i n g between t r e e s t o stand dominant h e i g h t was i n c l u d e d .  The  W e i b u l l p r o b a b i l i t y d e n s i t y f u n c t i o n was used t o c h a r a c t e r i z e stand  ii  diameter d i s t r i b u t i o n w i t h  the W e i b u l l parameters p r e d i c t e d as a  f u n c t i o n of stand parameters. volume e q u a t i o n s  f o r the r e s p e c t i v e s p e c i e s w h i l e  removed i n t h i n n i n g s was and  Stand volumes were determined from t r e e the mean DBH  p r e d i c t e d from mean stand DBH  of stems  before  thinning  weight of t h i n n i n g . Using  EXOTICS was compatible  the above f u n c t i o n s , a growth and y i e l d s i m u l a t i o n model constructed. w i t h IBM  whole-stand/distance  W r i t t e n i n FORTRAN IV G - l e v e l which i s  System/360 and  System/370, EXOTICS i s an  interactive  independent model w i t h an added c a p a b i l i t y f o r  p r o v i d i n g diameter d i s t r i b u t i o n (by 3 cm diameter c l a s s e s ) t o g i v e main stand y i e l d by s i z e c l a s s e s .  The  model i s intended  to  s i l v i c u l t u r a l management of the t h r e e s p e c i e s i n the Kenya On  v a l i d a t i o n , EXOTICS was  v a l i d a t i o n data, and  95%  final  facilitate highlands.  found to have no b i a s w i t h i n the range of  confidence  l i m i t s of 16%,  20%  and  17%  for  C_. l u s i t a n i c a , P. p a t u l a and P_. r a d i a t a r e s p e c t i v e l y . Using  EXOTICS, the c u r r e n t s i l v i c u l t u r a l management schedules  Kenya were s t u d i e d .  The  t h i n n i n g regimes were found to have marked  e f f e c t s on the c u r r e n t annual volume increment. cluded  t h a t at the present  theory  t h a t t h i n n i n g has  does not  in  I t was  t h e r e f o r e con-  l e v e l of s i l v i c u l t u r a l management, M o l l e r ' s  no a p p r e c i a b l e e f f e c t s on t o t a l volume y i e l d  h o l d f o r the t h r e e s p e c i e s i n Kenya.  p o l i c y aimed at p r o d u c t i o n  The  current thinning  of l a r g e - s i z e d sawlog crop i n as s h o r t a  r o t a t i o n as p o s s i b l e at the expense of some l o s s i n t o t a l y i e l d i s d i s c u s s e d and  found to have been overtaken  the concept of maximum volume p r o d u c t i o n  by events.  i s advocated.  A p o l i c y based A thinning  experiment ( u s i n g C. l u s i t a n i c a ) demonstrated that t o t a l merchantable  on  iii  volume c o u l d be i n c r e a s e d  by between 5 and 10% ( u s i n g 20% t h i n n i n g  i n t e n s i t y ) depending on s i t e q u a l i t y c l a s s .  Within  the range of  s t o c k i n g s m a i n t a i n e d i n p l a n t a t i o n s i n Kenya, t h i n n i n g i n t e n s i t y found t o be the most important c o n s i d e r a t i o n , w i t h t h i n n i n g having and  very  stocking  was  before  l i t t l e e f f e c t on both mean annual volume increment  t o t a l merchantable volume y i e l d up t o age 40 y e a r s .  iv  TABLE  OF  CONTENTS Page  ABSTRACT  i  TABLE OF CONTENTS LIST OF TABLES  iv v i i  LIST OF FIGURES  xi  ACKNOWLEDGEMENT  xiv  DEDICATION  xv  INTRODUCTION  CHAPTER 1:  1  BACKGROUND INFORMATION  7  1.  S p e c i e s Nomenclature and D i s t r i b u t i o n  2.  C l i m a t e and S o i l s  10  3.  S i l v i c u l t u r a l F o r e s t Management i n Kenya  16  4.  S i l v i c u l t u r a l Problems R e l a t e d t o E c o l o g i c a l F e a t u r e s of E x o t i c P l a n t a t i o n s I n Kenya  22  Permanent Sample P l o t s  27  5.1  The Permanent Sample P l o t Program i n Kenya  27  5.2  Permanent Sample P l o t s Data as a B a s i s f o r Growth and Y i e l d S t u d i e s  32  Problems A s s o c i a t e d w i t h Permanent Sample P l o t s Data  32  5.  5.3  6.  Study Methods  CHAPTER 2: 1.  STAND DEVELOPMENT AND GROWTH FUNCTIONS  7  35  38  Height Development and S i t e Index Curve C o n s t r u c t i o n ..  38  1.1  Introduction  38  1.2  S i t e Index Curve C o n s t r u c t i o n  40  V  Page  2.  M o r t a l i t y , Stand D e n s i t y Development and T h i n n i n g P r a c t i c e s i n Kenya P l a n t a t i o n s  85  2.1  Mortality  85  2.2  Stand D e n s i t y Development  86  2.3  Thinning  93  3.  B a s a l A r e a Growth B e f o r e F i r s t T h i n n i n g  104  4.  B a s a l Area Development i n Thinned  116  5.  Stand Diameter D i s t r i b u t i o n  128  6.  Stand  143  CHAPTER 3:  Stands  Volume D e t e r m i n a t i o n  YIELD MODEL CONSTRUCTION AND VALIDATION  147  1.  General P r i n c i p l e  147  2.  S i m u l a t i o n A p p l i c a t i o n t o Growth and Y i e l d Models  149  2.1  150  3.  Y i e l d Model C o n s t r u c t i o n 3.1  3.2 4.  F o r e s t Stand S i m u l a t i o n Models  E s s e n t i a l Features and Y i e l d Model  159 f o r the E n v i s a g e d  Growth  Growth and Y i e l d Model S y n t h e s i s  159 160  Model V a l i d a t i o n  173  4.1  Introduction  173  4.2  V a l i d a t i n g EXOTICS  177  4.3  Conclusion  201  CHAPTER 4:  SILVICULTURAL  MANAGEMENT MODELS FOR KENYA  203  1.  Introduction  203  2.  C u r r e n t T h i n n i n g Models f o r Sawtimber Regime i n Kenya  207  2.1  217  Summary on t h e C u r r e n t T h i n n i n g Model f o r Kenya ..  vi  Page  3.  4.  A l t e r n a t i v e T h i n n i n g Models f o r Sawtimber Crop i n Kenya  217  3.1  Thinning P o l i c y Considerations  217  3.2  T h i n n i n g Experiment f o r C_. l u s i t a n i c a  220  3.3  R e s u l t s from the t h i n n i n g experiment  224  3.4  Summary on the t h i n n i n g experiment  242  Pulpwood P r o d u c t i o n Regime f o r Kenya  CHAPTER 5:  SUMMARY: THEORETICAL AND PRACTICAL ASPECTS OF THIS STUDY, SUGGESTED FUTURE DEVELOPMENTS AND APPLICATION .,  242  249  1.  Growth and Y i e l d R e l a t i o n s h i p s  249  2.  C o n s t r u c t i o n of the Growth and Y i e l d Model  256  3.  S i l v i c u l t u r a l Management Models f o r Kenya  259  4.  F u t u r e Research and Development A r i s i n g from t h i s Study  262  5.  A p p l i c a t i o n of the R e s u l t s  263  6.  Conclusion  265  BIBLIOGRAPHY  266  vii  LIST  OF  TABLES  Table 1  2  3  4  Page D i s t r i b u t i o n of t h e s p e c i e s by area i n the major c o u n t r i e s where the s p e c i e s a r e grown  8  Summary of r a i n f a l l and a l t i t u d e f o r weather s t a t i o n s r e p r e s e n t a t i v e o f the h i g h l a n d zone  15  Seed p e r k i l o g r a m and g e r m i n a t i v e c a p a c i t y f o r C_. l u s i t a n i c a , P_. p a t u l a and P_. r a d i a t a i n Kenya  17  ....  Pruning schedules f o r C_. l u s i t a n i c a , P_. p a t u l a and P_. r a d i a t a i n Kenya as per r e l e v a n t t e c h n i c a l o r d e r s  21  B a s i c t h i n n i n g schedules f o r sawtimber and plywood crops f o r the t h r e e major p l a n t a t i o n s p e c i e s i n Kenya  23  B a s i c t h i n n i n g schedules f o r pulpwood crops f o r t h e t h r e e major p l a n t a t i o n s p e c i e s i n Kenya  24  7  Summary of the permanent sample p l o t  31  8  Coefficients equations  5  6  9  10  11  12  13  14  15  data  f o r the dominant h e i g h t over age l i n e a r 47  Comparison o f the m o d i f i e d W e i b u l l and Chapman-Richard models f o r h e i g h t over age curves  54  Asymptotic s t a n d a r d d e v i a t i o n s f o r the e s t i m a t e d c o e f f i c i e n t s of T a b l e 9  57  C o e f f i c i e n t e s t i m a t e s and o t h e r s t a t i s t i c s f o r the h e i g h t over age and s i t e index e q u a t i o n 2.13  59  Asymptotic s t a n d a r d d e v i a t i o n s f o r the e s t i m a t e d c o e f f i c i e n t s of T a b l e 11  59  D i s t r i b u t i o n o f p l o t s showing s i t e index over age c o r r e l a t i o n a t .05 p r o b a b i l i t y l e v e l f o r the t h r e e species  62  C o v a r i a n c e a n a l y s i s f o r s l o p e t e s t f o r h e i g h t over age e q u a t i o n s f o r P_. p a t u l a and P. r a d i a t a f o r d i f f e r e n t establishment s i t e s  66  C o v a r i a n c e a n a l y s i s f o r s l o p e t e s t f o r h e i g h t over age e q u a t i o n s f o r I?, p a t u l a i n d i f f e r e n t r e g i o n s i n Kenya  71  viii  Table 16  17  18  19  20  21  Page R a i n f a l l data and e l e v a t i o n f o r g e o g r a p h i c a l r e g i o n s r e c o g n i z e d f o r s e p a r a t e s i t e index curves  7 3  Height and age d a t a f o r P_. p a t u l a by g e o g r a p h i c a l regions  7 5  R e g r e s s i o n c o e f f i c i e n t s f o r s i t e index curves f o r P_. p a t u l a by g e o g r a p h i c a l r e g i o n s  7 7  D i s t r i b u t i o n of p l o t s showing s i g n i f i c a n t s i t e index over age c o r r e l a t i o n s a t . 0 5 l e v e l f o r P. p a t u l a by geographical regions  7 8  Summary o f t h i n n i n g data by s p e c i e s and r e l e v a n t variables  9 7  Mean DBH o f thinning/mean DBH b e f o r e t h i n n i n g relationship  9 8  22  B a s a l a r e a o f t h i n n i n g / b a s a l area b e f o r e t h i n n i n g r a t i o  1 0 1  23  Parameter e s t i m a t e s and other s t a t i s t i c s f o r the DBH o f t h i n n i n g equation 2 . 2 7 1 0 3  24  Parameter e s t i m a t e s and o t h e r s t a t i s t i c s thinning equation 2 . 2 8  f o r t h e DBH o f 1 0 4  25  Summary of the b a s a l a r e a b e f o r e t h i n n i n g data  1 0 6  26  Parameter e s t i m a t e s and r e l e v a n t s t a t i s t i c s area before thinning equation 2 . 2 9  1 0 9  27  f o r basal  Asymptotic s t a n d a r d d e v i a t i o n s f o r the e s t i m a t e d c o e f f i c i e n t s of T a b l e 2 6  1 1 0  28  Summary o f b a s a l a r e a increment data  1 2 0  29  Parameter e s t i m a t e s and o t h e r r e l e v a n t s t a t i s t i c s f o r the b a s a l a r e a increment e q u a t i o n f o r C_. l u s i t a n i c a , P_. p a t u l a and P. r a d i a t a (Kenya and New Zealand) ....  1 2 3  Asymptotic s t a n d a r d d e v i a t i o n s f o r the parameter on Table 2 9  1 2 3  31  Summary o f the DBH d i s t r i b u t i o n data  1 3 3  32  L i n e a r and c u r v i l i n e a r c o r r e l a t i o n of the D L and e s t i m a t e d W e i b u l l parameters w i t h o t h e r stand v a r i a b l e s  1 3 7  30  ix  Table 33  34  35  36  37  38  39  40  41  42  43  44  Page Comparison o f p r e d i c t e d and observed W e i b u l l parameters f o r the t e s t p l o t s  141  E q u a t i o n s and c o e f f i c i e n t s f o r the t r e e volume e q u a t i o n s f o r C_. l u s i t a n i c a , P_. p a t u l a and P. r a d i a t a i n Kenya  145  C o e f f i c i e n t s f o r R - f a c t o r e q u a t i o n (2.44) f o r the merchantable l i m i t s f o r the r e s p e c t i v e s p e c i e s  146  Domain of the y i e l d model EXOTICS w i t h r e s p e c t t o i n p u t variables  168  T o t a l volume y i e l d t a b l e f o r C_. l u s i t a n i c a s i t e Index 20  169  Merchantable index 20  170  volume y i e l d t a b l e f o r C_. l u s i t a n i c a  Stand t a b l e a t c l e a r f e l l f o r C_. l u s i t a n i c a index 20  site  site 171  Beta weights, mean b i a s , standard d e v i a t i o n and the 95% c o n f i d e n c e l i m i t s o f percentage d i f f e r e n c e s between observed and s i m u l a t e d t o t a l volume overbark, and the Chi-square v a l u e s f o r t h r e e h y p o t h e s i z e d l e v e l s o f accuracy: (2. l u s i t a n i c a  181  Beta w e i g h t s , mean b i a s , s t a n d a r d d e v i a t i o n and the 95% c o n f i d e n c e l i m i t s of percentage d i f f e r e n c e s between observed and s i m u l a t e d t o t a l volume overbark, and the C h i - s q u a r e v a l u e s f o r t h r e e h y p o t h e s i z e d l e v e l s of accuracy: P_. p a t u l a  182  Beta w e i g h t s , mean b i a s , standard d e v i a t i o n and the 95% c o n f i d e n c e l i m i t s o f percentage d i f f e r e n c e s between observed and s i m u l a t e d t o t a l volume overbark, and the Chi-square v a l u e s f o r t h r e e h y p o t h e s i z e d l e v e l s o f accuracy: P. r a d i a t a  183  B i a s percentage f o r dominant h e i g h t and b a s a l area f o r t e s t permanent sample p l o t s by s p e c i e s  193  Volume y i e l d and o t h e r r e l e v a n t stand parameters under the c u r r e n t sawtimber t h i n n i n g regime f o r C_. l u s i t a n i c a to a r o t a t i o n age o f 40 y e a r s : T e c h n i c a l Order No. 42 of March 1969  211  X  Table 45  46  47  48  49  50  51  52  Page Volume y i e l d and o t h e r r e l e v a n t stand parameters under the c u r r e n t sawtimber t h i n n i n g regime f o r P_. p a t u l a (Nabkoi) t o a r o t a t i o n age of 20 y e a r s : Technical Order No. 53 o f May 1981  212  Volume y i e l d and o t h e r r e l e v a n t stand parameters under the c u r r e n t sawtimber t h i n n i n g regime f o r P_. r a d i a t a t o a r o t a t i o n age of 30 y e a r s : T e c h n i c a l Order No. 44 o f March 1969  213  Basal area before t h i n n i n g regime  221  thinning  (m^/ha) f o r the a l t e r n a t i v e  Maximum MAI (nr/ha) and b i o l o g i c a l r o t a t i o n age ( c u l m i n a t i o n age) f o r d i f f e r e n t t h i n n i n g regimes f o r C. l u s i t a n i c a S.I. 18  227  Volume y i e l d (m / h a ) , i n c r e a s e % ( r e l a t i v e t o c u r r e n t t h i n n i n g regime) and o t h e r stand parameters a t 40 years r o t a t i o n age f o r d i f f e r e n t t h i n n i n g regimes f o r C. l u s i t a n i c a S . I . 18  231  Volume p r o d u c t i v i t y (m^/ha) and stand mean DBH (cm) up t o age 40 y e a r s f o r v a r i o u s t h i n n i n g l e v e l s a t 20% t h i n n i n g i n t e n s i t y by s i t e index c l a s s e s f o r C_. l u s i t a n i c a , r e l a t i v e t o the c u r r e n t t h i n n i n g regime  235  E f f e c t of i n i t i a l s t o c k i n g on y i e l d under t h i n n i n g regime C:20 f o r C. l u s i t a n i c a i . e . t h i n n i n g based on p r o p o r t i o n of b a s a l a r e a t o remove when a c r i t i c a l stand b a s a l a r e a i s e q u a l l e d o r exceeded  241  T o t a l volume y i e l d ( V ( l ) ( m / h a ) f o r P. p a t u l a (Nabkoi) by s i t e i n d e x c l a s s e s f o r v a r i o u s s t o c k i n g l e v e l s and e s t a b l i s h m e n t s i t e s up t o age 15 y e a r s ...  244  3  xi  LIST  OF  FIGURES  Figure  Page  1  Kenya f o r e s t b l o c k s and weather s t a t i o n s  11  2  Ombrothermic diagrams f o r weather s t a t i o n s r e p r e s e n t a t i v e of the h i g h l a n d zone i n Kenya  13  3  Height/age  r e l a t i o n s h i p f o r C_. l u s i t a n i c a p l o t s  43  4  Height/age  r e l a t i o n s h i p f o r P_. p a t u l a p l o t s  44  5  Height/age  r e l a t i o n s h i p f o r P_. r a d i a t a p l o t s  45  6  S i t e index e s t i m a t i o n procedure  7  Height over age ment s i t e  8  9  Height/age regions  f o r C_. l u s i t a n i c a  curves f o r d i f f e r e n t  stand  ...  49  establish67  r e l a t i o n s h i p f o r P_. p a t u l a by g e o g r a p h i c a l 72  S i t e i n d e x curves f o r C_. l u s i t a n i c a i n Kenya  ........  81  10  S i t e i n d e x curves f o r P^. r a d i a t a i n Kenya  82  11  S i t e i n d e x curves f o r P_. p a t u l a i n Kenya Nabkoi group  84  12  No. stems/height/S% r e l a t i o n s h i p by s p e c i e s and i n d e x c l a s s e s i n Kenya  92  13  14  15  16  17  18  B a s a l a r e a over age curves f o r v a r i o u s s i t e c l a s s e s a t stand d e n s i t y o f 1200 s.p.h  site  index Ill  Observed and p r e d i c t e d b a s a l a r e a f o r unthinned p l o t s not used i n f o r m u l a t i n g the b a s a l area e q u a t i o n  113  B a s a l area Increment curves (a) P_. r a d i a t a Kenya (b) P. r a d i a t a New Zealand  127  B a s a l area increment (b) P. p a t u l a  129  curves (a) C_. l u s i t a n i c a  Diameter d i s t r i b u t i o n histogram and the frequency curve r e s u l t i n g from the f i t t e d W e i b u l l p r o b a b i l i t y d e n s i t y function  135  Diameter d i s t r i b u t i o n h i s t o g r a m s , f i t t e d W e i b u l l p . d . f . and the p r e d i c t e d W e i b u l l p . d . f . f o r the 8 - t e s t p l o t s  142  xii  Figure 19  Page Overall  f o r e s t p l a n n i n g system showing the i n t e g r a t i o n  of the y i e l d model  161  20  Flowchart of the y i e l d model EXOTICS  163  21  Two s i m u l a t i o n s o f t h i n n i n g experiment 345 i n T a n z a n i a (P_. p a t u l a ) from d i f f e r e n t s t a r t i n g c o n d i t i o n s  178  Comparison o f s i m u l a t e d and observed t o t a l volume ( o v e r b a r k ) f o r two C_. l u s i t a n i c a t e s t p l o t s  180  D i s t r i b u t i o n o f £ . l u s i t a n i c a t e s t p l o t s by age and volume b i a s %  195  D i s t r i b u t i o n o f P_. p a t u l a bias %  196  22  23  24  25  26  27  28  29  30  31  32  33  D i s t r i b u t i o n o f P_. r a d i a t a bias %  t e s t p l o t s by age and volume  t e s t p l o t s by age and volume 197  D i s t r i b u t i o n of £. l u s i t a n i c a t e s t p l o t s and volume b i a s % D i s t r i b u t i o n o f P_. p a t u l a volume b i a s % D i s t r i b u t i o n o f P_. r a d i a t a volume b i a s %  test plots  by s i t e i n d e x 198  by s i t e index and 199  t e s t p l o t s by s i t e i n d e x and 200  The maximum s i z e - d e n s i t y r e l a t i o n s h i p and the n a t u r a l stand d a t a used i n p o s i t i o n i n g t h i s r e l a t i o n s h i p ....  206  Main stand b a s a l area/age r e l a t i o n s h i p under the c u r r e n t sawtimber t h i n n i n g regimes by s p e c i e s and s i t e index classes  208  Mean and c u r r e n t annual volume increment r e l a t i o n s h i p w i t h age f o r the c u r r e n t sawtimber t h i n n i n g regimes by s p e c i e s and s i t e Index c l a s s e s  209  Number o f stems and b a s a l a r e a a t d i f f e r e n t ages f o r d i f f e r e n t t h i n n i n g l e v e l s and t h i n n i n g i n t e n s i t i e s f o r C. l u s i t a n i c a S . I . 18  222  MAI and GAI o v e r age curves f o r d i f f e r e n t t h i n n i n g l e v e l s and t h i n n i n g i n t e n s i t i e s f o r C. l u s i t a n i c a S.I. 18  225  xiii  Figure 34  35  36  37  Page D i s t r i b u t i o n of merchantable volume (m^/ha) f o r d i f f e r e n t t h i n n i n g regimes f o r C. l u s i t a n i c a S.I. 18  233  Merchantable volume i n c r e a s e (%) f o r d i f f e r e n t t h i n n i n g regimes ( r e l a t i v e to c u r r e n t t h i n n i n g regime) on d i f f e r e n t s i t e index c l a s s e s  238  CAI and MAI curves f o r v a r i o u s _P. p a t u l a s i t e i n d e x c l a s s 21  245  stocking l e v e l s f o r  Diameter/age r e l a t i o n s h i p at v a r i o u s s t o c k i n g l e v e l s f o r s i t e index 21 f o r P_. p a t u l a (Nabkoi)  246  xiv  ACKNOWLEDGEMENTS  The J.P. who  a u t h o r wishes to thank h i s two  Demaerschalk who supervised  supervised  the i n i t i a l phase and  the f i n a l phase of t h i s study.  encouragement are g r e a t l y a p p r e c i a t e d . supervisory  committee members:  J . Thirgood,  C. G o u l d i n g and Mr.  Mr.  or another helped The  students  sample p l o t s data and  other  Mr.  H.L.  a l s o f o r reviewing  and  and  the t h e s i s  S p e c i a l thanks a l s o go to  i n the F a c u l t y of F o r e s t r y who  author would a l s o l i k e O.M.  Munro  author a l s o thanks h i s  the programming phase of the  make t h i s study a  F o r e s t Department Mr.  T h e i r guidance  Dr.  the  of the F o r e s t r y Department, e s p e c i a l l y  B a r r y Wong f o r h i s h e l p w i t h  A l s o to a l l s t a f f and  Dr. D.D.  P. Sanders f o r t h e i r comments  p r o v i d i n g most welcome a d v i c e .  computer programming s t a f f  The  supervisors  Drs. N. R e i d , A. Kozak, G. Weetman,  c o n s t r u c t i v e c r i t i c i s m on the r e s e a r c h , and  major r e s e a r c h  study. i n one  way  success.  to thank the C h i e f C o n s e r v a t o r of Kenya  Mburu f o r p e r m i s s i o n information  to use  the permanent  f o r t h i s study.  Also  to  Wright of the Commonwealth F o r e s t r y I n s t i t u t e , Oxford f o r  r e t r i e v i n g the data and Oxford f o r the  other relevant information  from the data bank at  author.  T h i s study was  made p o s s i b l e through f i n a n c i a l support  I n t e r n a t i o n a l Development A s s o c i a t i o n f e l l o w s h i p (through N a i r o b i ) , McPhee f e l l o w s h i p and U.B.C. F a c u l t y of F o r e s t r y ) . acknowledged. 3 y e a r study  The leave.  from  U n i v e r s i t y of  the F o r e s t P r o d u c t s f e l l o w s h i p  (through  This assistance i s g r a t e f u l l y  author a l s o thanks the U n i v e r s i t y of N a i r o b i f o r the  XV  DEDICATION  I dedicate  t h i s t h e s i s t o my w i f e - N e l l i e Muthoni Mathu.  gave up her c a r e e r In t e a c h i n g i n order d u r i n g my study  here i n Canada.  have been my main source A l s o to my  to come and m i n i s t e r to me  Her d e d i c a t e d  love and encouragement  of s t r e n g t h .  c h i l d r e n - Muthoni, Mwihaki and Mathu who  welcome d i s t r a c t i o n from the r i g o u r s of my study, evenings.  Nellie  provided  e s p e c i a l l y i n the  most  1  INTRODUCTION  The  total  f o r e s t l a n d i n Kenya c o n s i s t s o f about 2 m i l l i o n h e c t a r e s  or 3% of the t o t a l l a n d area o f the c o u n t r y , a l l of which i s p u b l i c l y owned and a d m i n i s t e r e d by the Kenya F o r e s t Department.  Of t h i s l a n d ,  about two t h i r d s i s d e s i g n a t e d p r o t e c t i o n f o r e s t , l e a v i n g about 660,000 h e c t a r e s f o r timber p r o d u c t i o n .  To date, over 150,000 h e c t a r e s have  been c o n v e r t e d t o e x o t i c softwood  p l a n t a t i o n s , mainly  Cupressus  l u s i t a n i c a M i l l e r , Pinus p a t u l a S c h l e c h t and Cham and P i n u s r a d i a t a D. Don.  These s p e c i e s a r e grown p r i m a r i l y f o r the s u p p l y o f sawtimber and  pulpwood to p r i v a t e l y owned f o r e s t The and w i l l  industries.  demand f o r timber and timber products  i n Kenya has been  c o n t i n u e t o r i s e i n the f o r e s e e a b l e f u t u r e .  r e s u l t o f two components:  rising  T h i s i s as a  i n c r e a s i n g p o p u l a t i o n e s t i m a t e d at an annual  r a t e of 4% and i n c r e a s i n g p e r c a p i t a consumption of wood and wood p r o d u c t s , a r e s u l t o f a r i s i n g standard of l i v i n g .  To meet t h i s  rising  demand f o r wood and wood p r o d u c t s w i t h i n the c o n s t r a i n t of a f i x e d forest  l a n d base, one o f the o p t i o n s open t o the government i s more  intensive  f o r e s t management t o maximize y i e l d  l a n d through  from the a v a i l a b l e  s i l v i c u l t u r a l m a n i p u l a t i o n of the s t a n d .  forest  To do t h i s  e f f e c t i v e l y r e q u i r e s a good knowledge o f the growth and y i e l d o f the c a n d i d a t e s p e c i e s under the v a r i o u s p h y s i c a l , edaphic and s i l v i c u l t u r a l c o n d i t i o n s p r e v a i l i n g i n the c o u n t r y .  When a v a i l a b l e , t h i s knowledge  forms a b a s i s f o r the f o r m u l a t i o n o f a l t e r n a t i v e management t o meet t h e d e s i r e d g o a l s and o b j e c t i v e s .  strategies  T h i s can best be achieved i f  a r e l i a b l e means o f f o r e c a s t i n g growth and y i e l d under the r e l e v a n t  2  p h y s i c a l , e d a p h i c and s i l v i c u l t u r a l c o n s t r a i n t s i s a v a i l a b l e to provide the n e c e s s a r y q u a n t i t a t i v e Since  information.  l a r g e s c a l e p l a n t a t i o n f o r e s t r y s t a r t e d i n Kenya around 1936  (C_. l u s i t a n i c a ) and 1946 (P_. p a t u l a and P_. r a d i a t a ) , s e v e r a l s t u d i e s on growth and y i e l d of p l a n t a t i o n s p e c i e s these,  have been undertaken.  Some o f  i n c l u d i n g Wimbush (1945), G r i f f i t h and Howland (1961) and  P a t e r s o n (1967) were l i m i t e d i n scope, e i t h e r because they were based on l i m i t e d d a t a o r were f o r s p e c i f i c r e g i o n s . up  However, s i n c e the s e t t i n g  of a permanent sample p l o t s program i n 1964, three  important  studies  based on d a t a from these p l o t s have been undertaken:  1.  Wanene (1975, 1976) and Wanene and W a c h i u r i (1975) c o n s t r u c t e d v a r i a b l e d e n s i t y y i e l d t a b l e s f o r P. p a t u l a , P_. r a d i a t a and C_. l u s i t a n i c a , r e s p e c t i v e l y .  These t a b l e s were of p a r t i c u l a r  s i g n i f i c a n c e as they were the f i r s t y i e l d estimation.  t a b l e s of t h e i r k i n d f o r  However, they were based on simple  r e g r e s s i o n methods and so c o u l d not represent p r o c e s s e s of stand yield 2.  growth very w e l l .  t a b l e s were d i s c u s s e d  Mathu (1977) s t u d i e d  the dynamic  Shortcomings i n these  by Mathu (1977).  the growth and y i e l d  of £ . l u s i t a n i c a i n  Kenya as p a r t requirement o f an M.Sc. study program.  This  study improved on t h e methodology used by Wanene and W a c h i u r i by c a s t i n g the p r i n c i p a l growth f u n c t i o n as a r a t e o f change of the stand it  basal area.  only considered  However, t h i s study was l i m i t e d i n t h a t  growth f o r an average s i t e i n Kenya.  major areas f o r f u t u r e r e s e a r c h were i d e n t i f i e d .  Two  3  (a)  Need f o r f u r t h e r i n v e s t i g a t i o n of b a s a l a r e a increment i n o v e r s t o c k e d and understocked stands and i n d i f f e r e n t  site  classes. (b)  Need to i n v e s t i g a t e f u r t h e r the h e i g h t development i n the different  3.  r e g i o n s i n the c o u n t r y .  S  A l d e r (1977) developed a s i n g l e stand y i e l d p r e d i c t i o n model the VYTL-2 - as a s u b r o u t i n e i n the PYMOD f o r e s t management program as p a r t of the requirements i n a Ph.D. VYTL-2 p r e s e n t s the stand s t a t e as a l i s t  study program.  o f diameters  (derived  from a diameter p r o b a b i l i t y d e n s i t y f u n c t i o n ) , stand growth i s d r i v e n by a s i t e index curve w h i l e a t r e e diameter  increment  e q u a t i o n (a f u n c t i o n of s i t e index, stand b a s a l a r e a and dominance r a t i o - a measure of c o m p e t i t i v e s t r e s s ) e f f e c t s  dia-  meter growth f o r diameter c l a s s e s as p e r c e n t i l e s of a cumulative distribution function. d i s t a n c e independent  This, therefore, i s a single  tree  model a l t h o u g h growth i s f o r diameter  c l a s s e s r a t h e r than the i n d i v i d u a l t r e e (see Chapter 3 S e c t i o n 2), The VYTL-2 was  designed to s i m u l a t e y i e l d s  f o r s i n g l e stands of  C_. l u s i t a n i c a , P_. p a t u l a and P_. r a d i a t a and, a c c o r d i n g to A l d e r (1977), it  i s a l s o capable of s i m u l a t i n g d i f f e r e n t t h i n n i n g treatments and  can be used as a s i l v i c u l t u r a l t o o l .  However, two main f a c t o r s m i t i g a t e  a g a i n s t use of t h i s model as a s i l v i c u l t u r a l 1.  tool:  On v a l i d a t i o n a t 95% c o n f i d e n c e l e v e l , the output from model ranged  this  from 40% underestimate t o 20% o v e r e s t i m a t e of  t o t a l volume y i e l d  so  ( A l d e r 1978).  A c c o r d i n g to the a u t h o r ,  4  these e r r o r s appeared to be a s s o c i a t e d w i t h a v a r i e t y of factors:  g e n e t i c , b i o t i c and  c l i m a t i c ; and  s t r u c t u r a l flaw i n the model. of these s y s t e m a t i c  not w i t h  Whatever the cause, the e f f e c t s  e r r o r s i s to reduce the  confidence  model e s p e c i a l l y as a t o o l f o r s i l v i c u l t u r a l 2.  The  thinning algorithms  which imply  the s t a n d .  practice.  t h i n n i n g , mechanical t h i n n i n g ,  a f i x e d d i s t r i b u t i o n of the removed stems i n  In a d d i t i o n , the model allows  t h i n n i n g c r i t e r i a may  the l i f e  o n l y one  The  be r e q u i r e d at d i f f e r e n t  of the stand, n e c e s s i t a t i n g use  of more than  and  PYMOD model of which VYTL-2 i s a s u b r o u t i n e  This  was  intended  as a  f e a s i b i l i t y a n a l y s i s system f o r e n t i r e  t h e i r s i t e i n d i c e s , the model s i m u l a t e s satisfying  s p e c i e s mix,  (as opposed to o p t i m i z i n g )  many stands comprising y i e l d s by v a r i o u s  a t o t a l f o r e s t e s t a t e at one  product mix  criteria.  s i m i l a r to the A u s t r a l i a n model FORSIM which s i m u l a t e s  1970).  one  For g i v e n i n i t i a l p l a n t i n g i n t e n s i t i e s , s e v e r a l p l a n t a t i o n s  y i e l d s using is  points  i s l a c k i n g i n the VYTL-2 model.  long-term f o r e c a s t i n g and forests.  thinning  In p r a c t i c e however,  t h i n n i n g o p t i o n w i t h i n a s i n g l e s i m u l a t i o n run. flexibility  the  " i d e a l " t h i n n i n g type are u n r e a l i s t i c i n  o p t i o n w i t h i n a s i n g l e s i m u l a t i o n run.  in  the  research.  These assumptions which amount to a c c e p t i n g  concept of an  different  of  i n the model are based on p u r e l y hypo-  t h e t i c a l assumptions such as low etc.  any  and  T h i s model  the growth of  time and  s i z e c l a s s e s from a l l compartments (Gibson  However, u n l i k e the A u s t r a l i a n s i t u a t i o n , the present  summarizes et a l . East  5  A f r i c a n scene f o r which PYMOD was designed l a c k s f o r e s t p l a n n i n g  systems  capable of d e f i n i n g a l l t h e c o n s t r a i n t s - economic, product mix, s p e c i e s mix, e t c . t h a t a r e r e q u i r e d  to u t i l i z e PYMOD c a p a b i l i t y .  p a r t l y e x p l a i n why the model has r e c e i v e d  so l i t t l e  T h i s may  a t t e n t i o n i n East  Africa. The growth c o n d i t i o n s Kenya vary c o n s i d e r a b l y  under which the t h r e e  species  are managed i n  i n terms o f s i t e q u a l i t i e s ( i n c l u d i n g s i t e  f a c t o r s such as r a i n f a l l d i s t r i b u t i o n and i n t e n s i t y , s o i l s , above sea l e v e l , e t c . ) , e s t a b l i s h m e n t s i t e s c u l t u r a l regimes.  From a review of past  the growth and y i e l d o f these s p e c i e s  (defined  elevation  l a t e r ) and s i l v i -  s t u d i e s , i t i s apparent t h a t  under the p r e v a i l i n g  conditions  has not been adequately addressed; n e i t h e r has the p o s s i b i l i t y of t h e a d o p t i o n o f a l t e r n a t i v e s i l v i c u l t u r a l regimes been c o n s i d e r e d of i n c r e a s i n g growth and y i e l d of the s t a n d . there  as a means  I t i s a l s o apparent t h a t  i s no r e l i a b l e means o f f o r e c a s t i n g growth and y i e l d t h a t can be  used t o f a c i l i t a t e d e s i r e d goals objectives  1.  s i l v i c u l t u r a l m a n i p u l a t i o n of the stand towards the  and o b j e c t i v e s .  These problems gave r i s e to the three  of t h i s study:  To study growth and y i e l d of t h e three  species:  £.lusitanica,  P_. p a t u l a and P_. r a d i a t a under the v a r i e t y o f s i t e s , e s t a b l i s h ment s i t e s , stand s t r u c t u r e s and s i l v i c u l t u r a l p r a c t i c e s in 2.  found  Kenya.  To c o n s t r u c t  a stand growth and y i e l d model as a means f o r  y i e l d p r e d i c t i o n and as an a i d t o s i l v i c u l t u r e of d i f f e r e n t management s t r a t e g i e s .  f o r evaluation  To e v a l u a t e the Impact o f the present and a l t e r n a t i v e management schedules objectives.  on stand development f o r d i f f e r e n t management  7  CHAPTER 1 BACKGROUND INFORMATION  1.  S p e c i e s Nomenclature and Cypressus  Portuguese  Distribution  lusitanica Miller  (1768) a l s o c a l l e d Mexican c y p r e s s ,  c y p r e s s , Cedar o f Goa  Cupressaceae  and  between l a t i t u d e  or j u s t  genus Cupressus.  cypress i s of the f a m i l y  In n a t u r e , i t occurs  15-45° North and i s widespread  naturally  i n C e n t r a l and  Southern  Mexico, Guatemala, Honduras and E l S a l v a d o r , where i t grows t o a h e i g h t of  30 meters a t 1800-2400 meters e l e v a t i o n (Dyson 1968).  n a t u r a l range, t h i s  s p e c i e s i s p l a n t e d e x t e n s i v e l y i n the South and West  of F r a n c e , Japan, P o r t u g a l , Spain and East A f r i c a . South A f r i c a Cupressus  Outside i t s  In New  Zealand,  and Malawi, i t i s p l a n t e d as a minor p l a n t a t i o n s p e c i e s .  l u s i t a n i c a was  i n t r o d u c e d t o Kenya i n 1905  p l a n t i n g d i d not b e g i n u n t i l  1936  (Wimbush 1945).  but l a r g e s c a l e  Figures for d i s t r i b u -  t i o n by area are o n l y a v a i l a b l e f o r Kenya as shown i n T a b l e  1.  P i n u s p a t u l a S c h l e c h t and Cham a l s o c a l l e d P a t u l a p i n e or s p r e a d i n g l e a v e d pine o c c u r s n a t u r a l l y i n a c o m p a r a t i v e l y r e s t r i c t e d  range i n the  S t a t e s of Queretaro, H i l d a l g o , Pueblo, Mexico and Vera Cruz i n C e n t r a l Mexico at an e l e v a t i o n of 1500-3000 meters e l e v a t i o n w i t h annual r a i n f a l l of 1200  mm  (Mirov 1967).  average  Outside i t s range, P. p a t u l a i s  p l a n t e d mostly i n A f r i c a where South A f r i c a pioneered i t s use. I t i n t r o d u c e d to Kenya i n 1910 1946  (Pudden 1957).  but  l a r g e s c a l e p l a n t i n g d i d not s t a r t  P_. p a t u l a i s grown mainly  timber but the wood can be used  was until  f o r pulpwood and saw-  f o r o t h e r purposes,  e.g. veneer  as i n  8  TABLE 1:  D i s t r i b u t i o n o f the s p e c i e s by a r e a i n t h e major c o u n t r i e s i n which the s p e c i e s a r e grown.  Country  Species  C. l u s i t a n i c a  Kenya  P. p a t u l a  South A f r i c a  P.  radiata  Source o f data  Area i n hectare  66,000  174,000  Kenya F o r e s t Department (1981) ( P e r . Comm.)  Crowe (1967)  Kenya  50,000  Kenya F o r e s t Department (1981) ( P e r . Comm.)  Malawi  23,000  M a r s h a l l and Foot  New  Zealand  307,000  Chile  261,000  Australia  185,000  Spain  173,000  South A f r i c a  35,000  Kenya  18,000  Grut  (1969)  (1970)  Kenya F o r e s t Department (1981) (Per. Comm.)  9  Kenya.  T a b l e 1 shows the d i s t r i b u t i o n o f the s p e c i e s i n South A f r i c a ,  Kenya and Malawi. P i n u s r a d i a t a D. Don a l s o known as r a d i a t a p i n e , i n s i g n i s p i n e , Monterey p i n e o r remarkable closed-cone  p i n e belongs  pines, b e l i e v e d t o have been widespread  C a l i f o r n i a In p r e h i s t o r i c times of  to a group o f p i n e s known as  (Forde 1966).  along the c o a s t of  The present  P_. r a d i a t a i s the c o a s t a l r e g i o n o f c e n t r a l C a l i f o r n i a and Mexico,  where i t grows n a t u r a l l y on some 4,050 h e c t a r e s ( S c o t t in  distribution  1960).  It exists  two v a r i e t i e s ; two n e e d l e s and t h r e e n e e d l e s . In  i t s n a t u r a l h a b i t a t , P_. r a d i a t a i s a s m a l l t o medium s i z e d bushy  t r e e which grows q u i c k l y and bears cones a t an e a r l y age - 6 y e a r s . Cones a r e hard and p e r s i s t  f o r many years on the stems and branches and  may remain c l o s e d f o r many years a f t e r m a t u r i t y . i s of l i t t l e The  I n t h i s form, the t r e e  economic v a l u e .  c l i m a t e i n c e n t r a l C a l i f o r n i a and Mexico where ]?. r a d i a t a grows  i s a s p e c i a l type o f mediterranean adequate summer moisture  climate with l i t t l e  summer r a i n but  from f r e q u e n t sea fogs and m i s t s .  I t grows on  g e n t l e to moderate s l o p e s from the c o a s t l i n e t o 10 k i l o m e t e r s i n l a n d , on deep sandy s o i l  types (sandy  500 t o 1050 mm per annum.  loam s o i l s ) w i t h r a i n f a l l ranging between  70 t o 75% o f the r a i n f a l l s i n w i n t e r .  P. r a d i a t a i s t h e most w i d e l y p l a n t e d s p e c i e s o u t s i d e i t s n a t u r a l habitat. As w i t h P^. p a t u l a , i t was i n t r o d u c e d t o Kenya i n 1910 and l a r g e s c a l e p l a n t i n g s t a r t e d i n 1946 (Pudden 1957).  The d i s t r i b u t i o n of t h i s  s p e c i e s by a r e a i n the major c o u n t r i e s where i t has been i n t r o d u c e d i s shown i n T a b l e 1.  10  2.  Climate The  and  Soils  b u l k of softwood p l a n t a t i o n s i n Kenya are found i n the Kenya  highlands  between 1800  t o 2750 meters above sea l e v e l .  l a n d zone, v a r i a t i o n s i n r e l i e f i s the Great R i f t  do o c c u r , of which the most  1.  r e s u l t s i n great v a r i a t i o n i n c l i m a t e and  vegetation.  equator.  shown on F i g u r e One  1, the h i g h l a n d  modifies  r i g h t across  would t h e r e f o r e expect an e q u a t o r i a l type  c h a r a c t e r i z e d by h i g h i n s o l a t i o n , h i g h r a i n f a l l rates.  However, the combination of a l t i t u d e and the c l i m a t e so t h a t no  in a  This v a r i a t i o n i n  zone l i e s  and  of  high  the  s i n g l e c l i m a t i c type  high-  significant  V a l l e y which t r a n s e c t s the c e n t r a l h i g h l a n d s  North/South d i r e c t i o n , as shown on F i g u r e  As  W i t h i n the  relief  the  climate  evaporation  relief  variation  can c h a r a c t e r i z e  the c l i m a t e of t h i s zone. According  t o G i l e a d and Roseman (1958), the most important  of c l i m a t e f o r p l a n t growth are warmth (temperature) and water fall).  Using  these  two  i n r e l a t i o n to p l a n t growth.  system of c l i m a t i c c l a s s i f i c a t i o n (Penman 1948)  and  utilizes  the o n l y two  water gain  from  These i n c l u d e the Thornthwaite  (Thornthwaite  1948), Penmans method  the Gaussens method (Gaussen 1954).  t h e Gaussens method has  (rain-  elements, s e v e r a l procedures have been used to  c h a r a c t e r i z e the water l o s s from e v a p o t r a n s p i r a t i o n and rainfall  elements  Of these  three,  been adopted i n t h i s study mainly because i t  c l i m a t i c data a v a i l a b l e - r a i n f a l l and  temperature  measurements. B a s i c a l l y the Gaussen procedure c o n s i s t s of c o n s t r u c t i n g ombrothermic  diagrams as  follows:  11  FIGURE 1 KENYA FOREST BLOCKS AND WEATHER STATIONS  12  1.  On  the a b s c i s s a s c a l e , p l o t  2.  On  the o r d i n a t e s c a l e , l a b e l the r i g h t  p r e c i p i t a t i o n i n mm  and  the months of the  the l e f t  year.  a x i s w i t h monthly  a x i s w i t h monthly average  temperatures i n degrees c e n t r i g r a d e to a s c a l e double t h a t of precipitation. 3.  J o i n a l l the l e v e l s of monthly temperature to get the  thermic  c u r v e , j o i n a l l the l e v e l s of monthly r a i n f a l l  the  ombrographic  curve.  When the ombrographic curve p r e c i p i t a t i o n < 2 temperature. i n d i c a t e s the d u r a t i o n and for  s i n k s below the thermic The  space e n c l o s e d  obtained  curve,  by the two  s e v e r i t y of the dry season.  dry season i s based on a r u l e of thumb but  c o n s i s t e n t w i t h those  to get  This  the r e s u l t s  u s i n g o t h e r procedures (FAO  curves criteria  are 1974).  F i g u r e 2 shows the ombrothermic diagrams f o r weather s t a t i o n s r e p r e s e n t a t i v e of the h i g h l a n d zone (see a l s o F i g u r e g i v e s the r a i n f a l l  summary, a l t i t u d e and  for  Data was  each s t a t i o n .  obtained  1) w h i l e T a b l e  2  an i n d i c a t i o n of the dry months  from the E a s t A f r i c a n M e t e o r o l o g i c a l  Department (1973, 1975). F i g u r e 2 shows t h a t of the three s t a t i o n s r e p r e s e n t i n g the lands west of the R i f t  ( E l d o r e t , Molo and K e r i c h o ) , t h e r e i s no  season as d e f i n e d by the ombrothermic diagrams. for  these  s t a t i o n s i n d i c a t e one  September and February.  one  In g e n e r a l the  highdry diagrams  l o n g r a i n y season between March to  season w i t h minimum r a i n f a l l  between October to  13  FIGURE 2 OMBROTHERMIC DIAGRAMS FOR WEATHER STATIONS REPRESENTATIVE OF THE HIGHLAND ZONE  IN KENYA Ombrographic Curve Thermic Curve  J f m a m j j a s o n d  j ( m » m j j » » o n d  15  TABLE 2:  Summary of r a i n f a l l and a l t i t u d e f o r weather s t a t i o n s r e p r e s e n t a t i v e of the h i g h l a n d zone.  Weather s t a t i o n  Elevation i n meters above sea l e a v e l  R a i n f a l l i n mm per annum  Dry season  Edoret  2084  1124 (24)  Molo  2477  1177 (28)  Kericho  2134  2081  Kimakia  2439  2288 (14)  Muguga  2096  995 (20)  September  Nanyuki  1947  759 (32)  January  (7)  Number i n b r a c k e t i n d i c a t e number of years of r e c o r d .  no dry season  M  It  & February  16  Of the t h r e e s t a t i o n s r e p r e s e n t i n g (Kimakia, Muguga and rainfall a one and  N a n y u k i ) , Kimakia has  Rift  t o t a l annual  the l e a s t .  month dry season (September) w h i l e Nanyuki has  F e b r u a r y ) of dry season.  e a s t of the  the h i g h e s t  f o l l o w e d by Muguga, w i t h Namyuki having  i n d i c a t e one and  the h i g h l a n d s  two  Muguga  has  months (January  In g e n e r a l , the diagrams f o r these s t a t i o n s  l o n g r a i n season between March and May  w i t h a peak i n A p r i l  a short r a i n y season between October to December w i t h a peak i n  November.  January/February and  July/August/September are seasons of  minimum r a i n f a l l . In g e n e r a l  the h i g h l a n d  s i t e s where p l a n t a t i o n s are e s t a b l i s h e d  o v e r l a i d w i t h v o l c a n i c loam s o i l s , u s u a l l y of great depth. u s u a l l y w e l l drained r e a c h of t r e e r o o t s .  so t h a t t h e r e i s r a r e l y any  cases a c t as b a r r i e r to t r e e r o o t p e n e t r a t i o n V o l c a n i c loams are g e n e r a l l y v e r y  3.  They are  water t a b l e w i t h i n  However, t h e r e are e x c e p t i o n s  where drainage i s impeded, pans of l a t e r i t e may  be  and  i n some p l a c e s  found which i n some  to lower s o i l  strata.  s u i t a b l e f o r t r e e growth.  S i l v i c u l t u r a l F o r e s t Management i n Kenya In d i s c u s s i n g f o r e s t management i n Kenya, t h e r e are two  approaches:  the t e c h n i c a l approach whereby the success  management a c t i v i t y e.g.  are  highest  c r i t e r i a f o r success  of a  i s measured on the b a s i s of b i o l o g i c a l  volume p r o d u c t i o n ;  and  possible given  criteria,  the economic approach whereby the  i s based on economic e v a l u a t i o n .  To date,  the  economic e v a l u a t i o n o f management p r a c t i c e s have never been attempted i n Kenya, m a i n l y because of l a c k of a b a s i s f o r a s s e s s i n g  the q u a n t i t a t i v e  17  impact of the s i l v i c u l t u r a l p r a c t i c e s . management w i l l be d i s c u s s e d  i n this  Only t e c h n i c a l a s p e c t s of f o r e s t  section.  Nursery p r a c t i c e A r t i f i c i a l regeneration i n Kenya.  through p l a n t i n g i s the standard  Nursery p r a c t i c e i s a h i g h l y developed t e c h n o l o g y .  u s u a l l y sown i n l e v e l , shaded beds which are u s u a l l y n e t t e d the s e e d l i n g s  from b i r d s and s m a l l mammals.  mostly of sand w i t h no humus m a t e r i a l . required  f o r any of the t h r e e  per k i l o g r a m  TABLE 3*:  to protect  The s o i l mixture c o n s i s t s  species.  T a b l e 3 shows the number of seed f o r each of t h e s p e c i e s  under  practice.  Seeds p e r k i l o g r a m and g e r m i n a t i v e c a p a c i t y P. p a t u l a and P_. r a d i a t a i n Kenya.  Species  Seed i s  Seed pretreatment i s not  and the g e r m i n a t i v e c a p a c i t y  normal n u r s e r y  practice  Seeds per kg  for£. lusitanica  Germinative capacity %  No. s e e d l i n g s p e r kg  C. l u s i t a n i c a  236,000  30%  70,000 t o 75,000  P. p a t u l a  180,000  30%  50,000 t o 60,000  35,000  40%  15,000 t o 20,000  P. r a d i a t a  *Data o b t a i n e d  As  from the r e s p e c t i v e t e c h n i c a l r e p o r t s .  soon as the seeds have germinated and b e f o r e  developed, the s e e d l i n g s and  any s i d e r o o t s a r e  a r e p r i c k e d out i n t o t r a y s o f s i z e 38 x 40 cm  10 cm h i g h c o n t a i n i n g s o i l t o 8 cm depth o r r a r e l y i n t o t r a n s p l a n t  beds r a i s e d 8 cm above t h e ground l e v e l .  F o r C_. l u s i t a n i c a ,  ordinary  18  . f o r e s t s o i l i s used, w h i l e p i n e s o i l i s r e q u i r e d f o r the pine s p e c i e s , as the l a t e r c o n t a i n s a mycorrhiza the p i n e s e e d l i n g s .  Each box  enjoys a p p r o x i m a t e l y  250  species necessary  c o n t a i n s 49 p l a n t s so t h a t each s e e d l i n g  cu.cm of s o i l .  nursery i s standard p r a c t i c e .  f o r the s u r v i v a l of  Use  of f e r t i l i z e r s  S e e d l i n g s are c o n s i d e r e d mature f o r  p l a n t i n g out i n the f i e l d when they are approximately P l a n t a t i o n establishment There are two 1.  i n the  20-30 cm  high.  methods  systems of p l a n t a t i o n e s t a b l i s h m e n t  Shamba System:  T h i s i s a h i g h l y developed  i n Kenya:  taungya system  whereby the land earmarked f o r t r e e p l a n t i n g Is i s s u e d to permanent f o r e s t employees f o r crop c u l t i v a t i o n . two  years of crop growing, t r e e s are p l a n t e d and  c o n t i n u e growing t h e i r crops u n t i l a g r i c u l t u r a l crops.  A f t e r one  or  the employees  the t r e e s are too t a l l  for  Under t h i s system, the employees g a i n from  the a g r i c u l t u r a l crops w h i l e the t r e e s are p l a n t e d i n c u l t i vated ground and their 2.  get f r e e weeding the f i r s t few  life.  Grassland P l a n t i n g :  F o r e s t glades and  r a r e l y s u i t a b l e f o r a g r i c u l t u r a l crops. s i t e s i s preceded strip  seasons of  ploughing  open g r a s s l a n d s  are  Tree p l a n t i n g i n these  by minimum l a n d p r e p a r a t i o n c o n s i s t i n g of  or simply d i g g i n g p i t s where the t r e e s w i l l  be  planted. E x p e r i e n c e w i t h (2. l u s i t a n i c a has  shown i t to be very i n t o l e r a n t  weed c o m p e t i t i o n , e s p e c i a l l y from g r a s s . grassland s i t e s .  As  of  such i t i s never p l a n t e d on  P i n e s p e c i e s on the other hand can be e s t a b l i s h e d  19  under e i t h e r system as t h e i r s u r v i v a l on g r a s s l a n d  sites i s quite  acceptable. Initial  s p a c i n g and e a r l y t e n d i n g  The o b j e c t i v e of stand South A f r i c a : possible.  i n plantations  establishment  i n Kenya i s s i m i l a r to t h a t of  to grow t r e e s t o merchantable s i z e i n as short a time as  Thus, the stand  establishment  i s c h a r a c t e r i z e d by wide  spacing  accompanied by heavy t h i n n i n g and pruning  stems.  P r e s e n t l y , the i n i t i a l  spacing  to i n s u r e h i g h q u a l i t y  i s 2.5 x 2.5 meters (1600 stems  per h e c t a r e ) and, as i n d i c a t e d i n the 1981 r e v i s e d T e c h n i c a l Order f o r P. p a t u l a t h e r e i s a move to even wider spacing  (3.0 x 3.0 meters =  stems per h e c t a r e ) .  T h i s i s very wide s p a c i n g  Europe where spacing  i s 1.4 x 1.4 meters = 5000 s e e d l i n g s p e r  for  compared  1110  to c e n t r a l  2+2 y e a r o l d spruce s e e d l i n g s or B r i t a i n where s p a c i n g  hectare  ranges  between 2.2 x 2.2 meters t o 2.0 x 2.0 meters (2000 t o 2300 s e e d l i n g s per h e c t a r e ) (Kuusela stand  1968).  establishment  F o r the l a t t e r c o u n t r i e s , the o b j e c t i v e s of  a r e to o b t a i n s u f f i c i e n t l y dense stands to u t i l i z e  f u l l y the s i t e p r o d u c t i v i t y and to improve the q u a l i t y of the t r e e by s e l f p r u n i n g . initial  These and the slower growth r a t e s e x p l a i n the c l o s e r  spacing.  An important  c o n s i d e r a t i o n i n adopting  a specific i n i t i a l  p o l i c y i s the c o s t of r a i s i n g the s e e d l i n g i n the n u r s e r y out  stems  i n the f i e l d .  Wide i n i t i a l  spacing  may  be j u s t i f i e d  spacing  and p l a n t i n g i n Kenya,  firstly  because i t means fewer s e e d l i n g s t o be r a i s e d and t h e r e f o r e l e s s  nursery  and p l a n t i n g expenses and, s e c o n d l y  because the i n t e n s i v e ground  20  p r e p a r a t i o n and ensures  subsequent t e n d i n g e s p e c i a l l y under the Shamba system,  h i g h e r s u r v i v a l of s e e d l i n g s .  Pruning By d e f i n i t i o n , pruning ensure p r o d u c t i o n of timber  i n v o l v e s removal of l i v e branches so as to f r e e of dead knots.  The wide  initial  spacings accompanied by heavy t h i n n i n g s as p r a c t i c e d i n Kenya imply i n c r e a s e i n s i z e of branches and d e l a y i n n a t u r a l p r u n i n g . t h e r e f o r e a standard p r a c t i c e . schedules  Table 4 shows the c u r r e n t  an  Pruning i s pruning  f o r the t h r e e s p e c i e s .  Thinning Under t r a d i t i o n a l f o r e s t r y p r a c t i c e s as p r a c t i c e d i n Europe B r i t a i n , the o b j e c t i v e of t h i n n i n g i s to h a r v e s t those be wasted as m o r t a l i t y and Thinnings  t r e e s which would  to b e t t e r the q u a l i t y of s t a n d i n g  are t h e r e f o r e v e r y l i g h t  i s kept as h i g h as i s n e c e s s a r y  and  stock.  so t h a t the d e n s i t y of s t a n d i n g  f o r maximum volume p r o d u c t i o n .  stock  The  t h i n n i n g p r a c t i c e s i n Kenya on the other hand are based on C r a i b ' s (1939, 1947)  t h i n n i n g p o l i c y which advocated  to promote t r e e diameter  growth.  very heavy t h i n n i n g s so  T h i s p o l i c y i s not c o n s i s t e n t w i t h  o b j e c t i v e of maximum volume p r o d u c t i o n but aims at p r o d u c t i o n of  as the  larger  s i z e d m a t e r i a l i n as s h o r t a r o t a t i o n as p o s s i b l e a t the expense of some loss i n total  yield.  C r a i b ' s r e v o l u t i o n a r y ideas on t h i n n i n g went a g a i n s t  traditional  t h i n n i n g p o l i c i e s , e s p e c i a l l y w i t h regard to the recommendation f o r more severe t h i n n i n g s on poor s i t e s .  As a r e s u l t t h i s p o l i c y has r e c e i v e d  v a r i e d comments, some a g a i n s t (Hawley and  Smith 1954,  Johnston  1962)  but  21  TABLE 4:  P r u n i n g schedules f o r C_. l u s i t a n i c a , P_. p a t u l a and P_. r a d i a t a i n Kenya as per r e l e v a n t t e c h n i c a l o r d e r s .  Species  Age/dominant height i n meters  Pruning h e i g h t from ground level  Number o f stems/ha to be p runed Sawtimber/ plywood  c.  lusitanica  p. p a t u l a  p. r a d i a t a  Pulpwood  2 years  1/2 h e i g h t but not over 2 meters  All  stems  All  stems  4 years  1/2 h e i g h t but not over 4 meters  All  stems  All  stems  9.25 meters  2/3 t r e e h e i g h t  533 stems  All  11.25 meters  2/3 t r e e h e i g h t  533 stems  N/A  13.75 meters  2/3 t r e e h e i g h t Minimum 9 meters Maximum 11 meters  533 stems  N/A  3 years  1/2 h e i g h t + 1 w h o r l  All  N/A  4 years  1/2 h e i g h t + 1 whorl  N/A  All  8 meters  1/2 h e i g h t + 1 w h o r l  600  N/A  12 meters  1/2 h e i g h t + 1 whorl  600  N/A  16 meters  10 meters  600  N/A  1/2 h e i g h t + 1 w h o r l  All  All  12.0 meters  1/2 h e i g h t + 1 whorl  426  All  17.5 meters  1/2 h e i g h t + 1 w h o r l  426  N/A  24.5 meters  1/2 h e i g h t + 1 w h o r l  213  N/A  3 years  22  mostly i n support Lewis 1964).  (De V i l l i e r s e t a l . ,  1961, H i l e y 1959, Fenton 1972,  Due t o changing management o b j e c t i v e s , C r a i b ' s management  recommendations have been r e v i s e d  i n South A f r i c a t o s u i t  specific  o b j e c t i v e s , such as p r o d u c t i o n o f pulpwood or to improve on timber quality. Kotze  F o r f u r t h e r d i s c u s s i o n on t h e s e , the reader i s r e f e r r e d to  (1960) and De V i l l i e r s e t a l . (1961). The  t h i n n i n g regimes adopted  South A f r i c a .  i n Kenya compare c l o s e l y w i t h those of  However, w h i l e t h i n n i n g regimes f o r the l a t t e r a r e t i e d  down t o s p e c i f i c s i t e q u a l i t y c l a s s e s , those average  f o r Kenya a r e f o r an  s i t e consequent on the l a c k o f a means o f a s s e s s i n g s i t e  classes.  quality  T h i n n i n g regimes f o r Kenya can t h e r e f o r e be c o n s i d e r e d as a  compromise between the t h i n n i n g regimes f o r the poorest and best q u a l i t y c l a s s e s i n South A f r i c a , w i t h some adjustments r a t e s o f growth i n Kenya.  site  f o r the h i g h e r  These a r e shown on Table 5 f o r sawtimber and  plywood and Table 6 f o r pulpwood. In g e n e r a l , sawtimber crop i s c o n s i d e r e d mature f o r c l e a r f e l l i n g when the mean stand DBH i s 48 cm w h i l e f o r plywood, f i n a l mean stand DBH is  51 cm.  R o t a t i o n age f o r pulpwood p l a n t a t i o n s v a r i e s but i s u s u a l l y  between 15 t o 20 y e a r s .  4.  S i l v i c u l t u r a l Problems R e l a t e d t o E c o l o g i c a l F e a t u r e s o f E x o t i c P l a n t a t i o n s i n Kenya B e f o r e the s i l v i c u l t u r a l problems o f stand management i n Kenya can  be d i s c u s s e d , i t i s worthwhile  t o mention a few e c o l o g i c a l f e a t u r e s  which a r e p e c u l i a r t o these p l a n t a t i o n s as these have a d i r e c t on the problems:  bearing  23  TABLE 5*:  B a s i c t h i n n i n g schedules f o r sawtimber and plywood crops f o r the t h r e e major p l a n t a t i o n s p e c i e s i n Kenya.  Species  Treatment  Dominant h e i g h t or age a t t h i n n i n g  Stem/ha a f t e r No.  (C. l u s i t a n i c a  P.  thinning  2nd  thinning  3rd  thinning  4th  thinning  patula Planting 1st t h i n n i n g 2nd t h i n n i n g  P_. r a d i a t a  3rd  thinning  4th  thinning  Planting 1st t h i n n i n g 2nd t h i n n i n g 3rd t h i n n i n g 4th  thinning  % of p l a n t i n g  1,600  Planting 1st  thinning  11.25 meters but not b e f o r e age 6 y e a r s 5 years a f t e r 1st t h i n n i n g 10 years a f t e r 1st t h i n n i n g 15 years a f t e r 1st t h i n n i n g  B e f o r e 1981 After 1981 16 meters 5 years a f t e r 1st t h i n n i n g 10 y e a r s a f t e r 1st t h i n n i n g 15 y e a r s a f t e r 1st t h i n n i n g (plywood p l a n t a tions only)  12 meters 17.5 meters 7 years a f t e r 2nd t h i n n i n g 13 years a f t e r 2nd t h i n n i n g  *Data from the r e s p e c t i v e t e c h n i c a l  orders.  888  55.5  533  33.3  355  22.2  266  16.6  1,600 1,110 600 400  54.0 36.0  250  22.5  170  15.3  1,600 853 426 266  53.3 26.6 16.6  213  13.3  24  TABLE 6:  B a s i c t h i n n i n g schedules f o r pulpwood crops f o r the three major p l a n t a t i o n s p e c i e s i n Kenya.  Treatment  Species  Age or dominant h e i g h t at thinning  Stems per h e c t a r e after thinning No.  £.  lusitanica  % of planting  1,322  Planting clearfelling  15-20 years  or  P.  patula  63.5  Planting: before  1981  1,322  after  1981  1,110  1st t h i n n i n g (old plantations) New  P. r a d i a t a  840  15 y e a r s  thinning  No  plantations  74.1  thinning  1,322  Planting Clearfelling  980  12 y e a r s  15-20 years  or Thinning  15 y e a r s  880  66.6  25  1.  The p l a n t a t i o n s a r e monocultures, meaning t h e r e i s o n l y one species i n a given  2.  stand.  The s p e c i e s have only r e c e n t l y been i n t r o d u c e d to Kenya, so t h a t they have not y e t f u l l y adapted themselves to the new environment.  3.  The stands  a r e even-aged, so t h a t t h e r e i s o n l y one stratum i n  terms o f s p a t i a l 4.  distribution.  The s p e c i e s a r e u s u a l l y very nutrient impoverization  f a s t growing so that the r a t e of  through t r e e h a r v e s t may be very  rapid. The are very  above e c o l o g i c a l f e a t u r e s i m p l i e s t h a t these man-made ecosystems f r a g i l e and e c o l o g i c a l l y immature so that they a r e very  s u s c e p t i b l e t o pest outbreaks. have been i d e n t i f i e d Diseases:  In p a r t i c u l a r , the f o l l o w i n g problems  i n Kenya.  Two important  f u n g a l d i s e a s e s have been i d e n t i f i e d i n  Kenya p l a n t a t i o n s : 1.  Cypress canker d i s e a s e , caused by a p a r a s i t i c  fungus  Monochaetia u n i c o r n i s (Cook and E l l i s ) Sacc.  I t i s not known  if The  t h i s fungus was present  i n Kenya or i f i t was  fungus causes l e s i o n s on the stem o f cypress  introduced. trees,  e s p e c i a l l y Cupressus macrocarpa Hartw. but has been known t o a f f e c t C_. l u s i t a n i c a to a s m a l l e r degree.  T h i s d i s e a s e was  r e s p o n s i b l e f o r stoppage of any f u r t h e r p l a n t i n g of £ . macrocarpa d e s p i t e the f a c t that i t was the more s u p e r i o r s p e c i e s i n terms of t r e e growth.  26  2.  Dothlstroma p i n t s p e c i e s , another p a r a s i t i c fungus, was ble  f o r the c e s s a t i o n of a l l p l a n t i n g o f P. r a d i a t a i n 1961  when the fungus was  d i s c o v e r e d , a p p a r e n t l y h a v i n g been  i n t r o d u c e d i n t o Kenya from elsewhere. weaken the t r e e s and sometimes k i l l 5 t o 15 y e a r s .  T h i s d i s e a s e i s known to  them at a young age between  A f t e r t h a t age,most t r e e s not a l r e a d y k i l l e d  r e c o v e r and s t a r t the  responsi-  to grow n o r m a l l y a g a i n .  d i s e a s e are s t i l l  Attempts  to c o n t r o l  i n p r o g r e s s i n Kenya.  Another fungus o f minor economic importance  i s the u n i v e r s a l  A r m i l l a r i a m e l l e a i n both C_. l u s i t a n i c a and p i n e p l a n t a t i o n s . Insect:  Among the important i n s e c t p e s t s i s the newly i n t r o d u c e d  w o o l l y a p h i d , a Pineus s p e c i e s which a t t a c k s mostly p i n e s . a t t a c k s young twigs and n e e d l e s , weakening the t r e e s and killing  them.  Another  which e n t e r s heartwood  This  insect  eventually  important i n s e c t i s the Oemida gahani D i s t a n t of l i v i n g C_. l u s i t a n i c a t r e e s through p r u n i n g o r  i n j u r y s c a r s , thus degrading the q u a l i t y of the l o g s . Rodents and b i g game damage:  Rodents,  i n c l u d i n g moles, and  f i n d the bark of the young softwood p l a n t s e s p e c i a l l y  rats  palatable.  S i m i l a r l y , b i g game such as e l e p h a n t s , b u f f a l o e s and Sykes monkeys are a continuous problem i n f o r e s t p l a n t a t i o n s , e i t h e r by pushing over the t r e e s or by f e e d i n g on the s u c c u l e n t bark. F i r e problems:  As i n d i c a t e d on the ombrothermic  diagrams  of  F i g u r e 2, January and F e b r u a r y are u s u a l l y the d r i e s t months o f the year in  most areas of the h i g h l a n d s .  Numerous f o r e s t f i r e s do o c c u r , m o s t l y  27  o r i g i n a t i n g from honey hunters and c a u s i n g  considerable  damage to f o r e s t  plantations. S o i l degradation:  A l t h o u g h no study has been done t o determine i f  s o i l f e r t i l i t y w i l l decrease i n s u c c e s s i v e  r o t a t i o n s , evidence from  Southern A u s t r a l i a on P_. r a d i a t a (Keeves 1965) and from Swaziland on P_. p a t u l a  (Evans 1975) i n d i c a t e t h a t y i e l d I n s u c c e s s i v e  r o t a t i o n s can  be expected t o be lower.  T h i s i s as expected due t o the f a c t t h a t a  large quantity of organic  matter and m i n e r a l  harvesting  n u t r i e n t s a r e removed when  the t r e e s .  A l l t h e above problems p r e s e n t s  a very  difficult  challenge to  f o r e s t management, e s p e c i a l l y as new problems a r e c o n t i n u o u s l y N o n e t h e l e s s , the advantages o f even-aged monoculture mitigate,  the problems.  plantations  In view of the l i m i t e d f o r e s t area  the very h i g h y i e l d o b t a i n a b l e  arising.  i n Kenya,  from p l a n t a t i o n s makes the investments i n  f o r e s t p r o t e c t i o n worthwhile.  5.  Permanent Sample P l o t s  5.1  The permanent sample p l o t program i n Kenya  Objective The  permanent sample p l o t s ( h e r e a f t e r r e f e r e e d  establishment species:  to as p.s.p's)  program was i n i t i a t e d i n Kenya i n 1964 f o r a l l three  C_. l u s i t a n i c a , P_. p a t u l a and P_. r a d i a t a .  of the program were:  The main o b j e c t i v e s  28  1.  To o b t a i n i n f o r m a t i o n  on growth r a t e s of these s p e c i e s  under  the c l i m a t i c and edaphic c o n d i t i o n s p r e v a i l i n g i n Kenya. 2.  To o b t a i n i n f o r m a t i o n  on the y i e l d of these s p e c i e s under the  s i l v i c u l t u r a l p r a c t i c e s o b t a i n i n g i n Kenya. 3.  To p r o v i d e  a b a s i s f o r the development o f p l a n t a t i o n management  guide. P l o t s d i s t r i b u t i o n and l a y o u t i n the f i e l d All  the p.s.p's are l o c a t e d i n the major g e o g r a p h i c a l  these s p e c i e s  are p l a n t e d  the growth p a t t e r n ,  i n Kenya.  I n order  regions  where  to g i v e a c l e a r p i c t u r e of  the o r i g i n a l p.s.p's were e s t a b l i s h e d i n 5, 10, 15,  20, 25, 30 and 35 y e a r o l d p l a n t a t i o n s .  The number of p l o t s i n each age  c l a s s was p r o p o r t i o n a l to the t o t a l area of that c l a s s so that the l a r g e r the area  f o r a given age c l a s s , the higher  S i m i l a r l y , the l a r g e r the area  f o r a given  the number of p l o t s .  s p e c i e s , the h i g h e r  the  number of p l o t s a l l o c a t e d t o i t . The whole i d e a of d i s t r i b u t i n g p l o t s i n 5 year age i n t e r v a l s was  t h a t a f t e r 5 years of continuous  measure-  ments, the growth p a t t e r n f o r the whole r o t a t i o n would be known. a given  age c l a s s , the d i s t r i b u t i o n of the p l o t s was based p r i m a r i l y on  the b a s i s of p l a n t a t i o n s t r a t i f i c a t i o n i n t o s i t e t y p e s , regions  Within  and c l i m a t i c f a c t o r s :  mainly r a i n f a l l  distribution.  Due t o t e c h n i c a l and f i n a n c i a l problems, the i n i t i a l i n t e n s i t y w i t h i n a g i v e n age c l a s s was  0.04  hectare  sampling  2 p l o t s per 50 h e c t a r e s .  the s e l e c t e d p l a n t a t i o n , the l o c a t i o n of the p l o t was p l o t s s i z e was  geographical  Within  subjective.  (.25 a c r e ) and c i r c u l a r i n shape.  The  Since the  29  I n i t i a l establishment,  many more p l o t s have been e s t a b l i s h e d u s i n g  same procedures (see Table  the  7).  I d e a l l y the p.s.p's should be marked as i n c o n s p i c u o u s l y as p o s s i b l e so t h a t they do not pruning  r e c e i v e p r e f e r e n t i a l treatments d u r i n g t h i n n i n g or  operations.  For p r a c t i c a l purposes however, and  t i o n , the p l o t s are c l e a r l y marked on the ground. possibility  t h a t the p l o t s may  the r e s t of the p l a n t a t i o n .  ease of r e l o c a -  T h i s may  be r e c e i v i n g d i f f e r e n t treatments from  However, t h i s p o s s i b i l i t y  i s minimum s i n c e  treatments i n the p l a n t a t i o n s are s u p e r v i s e d by the f o r e s t charge of the f o r e s t  officer-in-  district.  P l o t measurements and  p r e l i m i n a r y data  analyses  Two  main p l o t parameters are measured  1.  Diameter at 1.3  annually:  meters above ground, r e f e r r e d to as diameter at  b r e a s t h e i g h t or DBH. p l o t t o the n e a r e s t 2.  p o i n t to a  T h i s i s measured f o r a l l t r e e s on 0.1  cm w i t h a diameter  tape.  Stand dominant h e i g h t , d e f i n e d as the mean h e i g h t of the l a r g e s t diameter t r e e s per h e c t a r e ,  l a r g e s t diameter t r e e s on the p l o t . ments as Haga and  100  i s measured f o r each p l o t .  T h i s i s accomplished by measuring the h e i g h t of the  four  In the p a s t , such i n s t r u -  Blume-Leiss hyposometers have been used  c u r r e n t l y , the Suunto c l i n o m e t e r The  the  i s i n use.  measuring of p.s.p's i s u s u a l l y timed f o r j u s t b e f o r e the  ning operations  start.  thin-  T h i s t i m i n g i s c r u c i a l s i n c e the measurements of  t r e e s removed i n a t h i n n i n g a r e taken as those at t h e i r p r e v i o u s measurement.  but  years  30  Under an agreement between the Kenya government and the Commonwealth F o r e s t r y I n s t i t u t e , Oxford U n i v e r s i t y , a l l the b a s i c p.s.p.  data  i s sent t o t h e l a t t e r f o r f u r t h e r c a l c u l a t i o n , p r o c e s s i n g and storage on computer t a p e s .  The f o l l o w i n g i n f o r m a t i o n on p.s.p's i s a v a i l a b l e f o r  up t o and i n c l u d i n g 1979: 1.  2.  3.  F o r Main Crop: (a)  Age a t time of t h i n n i n g  (b)  Number of stems per h e c t a r e  (c)  Mean DBH o f the stand  (d)  Dominant h e i g h t of the stand  (e)  B a s a l area per h e c t a r e  (f)  Stand  (g)  Volume o f the stand i n c u b i c meters per h e c t a r e . T h i s i s o b t a i n e d u s i n g the t r e e volume equations f o r t h e r e s p e c t i v e s p e c i e s (see Chapter 3 ) .  ( i n cm) ( i n meters)  ( I n square  meters/hectare)  density indices  For Thinnings: (a)  Number of stems removed p e r h e c t a r e  (b)  B a s a l a r e a removed ( i n square  (c)  Volume removed ( i n cu.meters p e r h e c t a r e ) c a l c u l a t e d as f o r main crop.  meters/hectare)  For Total Production: (a)  T o t a l b a s a l area p r o d u c t i o n i n sq.meters p e r h e c t a r e  (b)  T o t a l volume p r o d u c t i o n i n  (c)  C u r r e n t annual  (d)  Mean annual  volume  volume  cu.meters/hectare  increment  increment.  Table 7 shows a summary of the b a s i c p.s.p. data f o r up t o 1979.  31  TABLE 7:  Summary of the permanent sample p l o t data  S P E C I E S C_. l u s i t a n i c a  P_. p a t u l a  P_. r a d i a t a  163 1,413  176 1,452  164 1,625  Minimum Mean Maximum Standard d e v i a t i o n  4.7 17.4 43.6 8.6  3.6 12.5 27.7 4.9  5.5 13.6 34.6 5.4  Dom. Height i n m.  Minimum Mean Maximum Standard d e v i a t i o n  4.3 20.2 39.4 7.2  3.8 19.0 37.3 6.7  5.3 24.2 51.2 8.8  Hart's D e n s i t y Index  Minimum Mean Maximum Standard d e v i a t i o n  12.1 21.4 74.9 5.0  8.4 20.2 57.0 6.8  7.9 16.6 168.8 9.7  No. P l o t s Remeasurements  Age i n Years  32  5.2  Permanent sample p l o t s d a t a as a b a s i s f o r growth and y i e l d In g e n e r a l , growth and y i e l d  s t u d i e s a r e based on data  studies  obtained  from e i t h e r permanent sample p l o t s ( c f . continuous f o r e s t i n v e n t o r y ) , temporary sample p l o t s , o r on a combination o f both. sample p l o t s a r e used, g r e a t e r of past  stand  i n t o account.  When temporary  e r r o r can be expected s i n c e the e f f e c t s  treatments and v a r i a t i o n i n growth over time a r e not taken In r e g i o n s  where annual growth r i n g s a r e a  standard  f e a t u r e o f t r e e growth, the problems of temporary samples a r e overcome through stem a n a l y s i s procedure.  Growth r i n g s i n the e x o t i c s p e c i e s i n  Kenya a r e u s u a l l y a r e f l e c t i o n o f seasonal  fluctuations i n r a i n f a l l  r a t h e r than annual growth and so a r e u n r e l i a b l e as a guide to past growth.  Permanent sample p l o t s a r e t h e r e f o r e t h e o n l y s u i t a b l e source  of data f o r growth and y i e l d  5.3  tree  s t u d i e s i n these p l a n t a t i o n s .  Problems a s s o c i a t e d w i t h permanent sample p l o t d a t a  G e n e r a l problems  The  problems a s s o c i a t e d w i t h p.s.p. d a t a have been d i s c u s s e d by  several authors, i n c l u d i n g Vuokila be  (1965) and A d l a r d  (1974).  These can  summarized as f o l l o w s : 1.  M e n s u r a t i o n a l e r r o r s ( a l s o common t o a l l sample p l o t systems). These i n c l u d e sampling e r r o r s i n terms of p l o t d i s t r i b u t i o n by age  c l a s s e s , s i t e c l a s s e s , e t c . and measuring e r r o r s that may  o c c u r due to use o f f a u l t y measuring equipment o r 2.  Problems a s s o c i a t e d w i t h p l o t management. failure  t o r e l o c a t e t h e p l o t s i n the f i e l d ,  These  techniques. include  to r e - i d e n t i f y  i n d i v i d u a l t r e e s i n the p l o t o r d i f f e r e n t i a l treatment of t h e  33  p l o t s I n r e l a t i o n t o the r e s t o f the p l a n t a t i o n s  (see 5.1  above). 3.  Problems  Inherent i n the p.s.p. system i t s e l f .  The main  problems i n h e r e n t i n the p.s.p. system a r i s e s from a c c i d e n t a l damage t o the p l o t o r elements i n the p l o t s e.g., damage t o i n d i v i d u a l t r e e s from game, d i s e a s e s or i n s e c t s . These problems r e s u l t s i n e r r o r s of v a r y i n g magnitude i n the f i n a l parameters e s t i m a t e d from the d a t a .  B a r r i n g the p o s s i b i l i t y of sampling  e r r o r s , the r e s u l t s of measuring e r r o r s a r e i n g e n e r a l minimal,and i n the  l o n g run,of a random n a t u r e .  r e l o c a t e p l o t s i n the f i e l d  S i m i l a r l y , p o s s i b i l i t y of f a i l u r e t o  i s very remote i n Kenya as the p l o t s a r e  c l e a r l y mapped on the p l a n t a t i o n maps, w h i l e d i f f e r e n t i a l treatment o f p.s.p's i s minimized through s t a f f  supervision.  The problem o f a u t o c o r r e l a t i o n i n p.s.p. data One o f the important assumption u n d e r l y i n g the use of r e g r e s s i o n a n a l y s i s - the p r i n c i p l e data a n a l y s i s precedure i n t h i s study - i s t h a t the  r e s i d u a l s a r e independent.  F o r example i n the u s u a l  regression  model:  Y  i  a  B  0  +  l i l  B  X  +  B  2 i2 X  +  e  x p  i  + P  H  1.1  Dependent v a r i a b l e  where X  e0,  • • •X i p e2 . . .  Bp  Independent  variables  R e g r e s s i o n parameters t o be e s t i m a t e d A n o r m a l l y d i s t r i b u t e d e r r o r w i t h mean z e r o and v a r i a n c e = a*,  34  it  i s assumed t h a t the i n d i v i d u a l e r r o r  i s independent tion.  and not p r e d i c t a b l e from the e r r o r of any o t h e r o b s e r v a -  When t h i s assumption  exist.  (e^) f o r a g i v e n o b s e r v a t i o n  i s v i o l a t e d , a u t o c o r r e l a t i o n i s s a i d to  T h i s problem o f t e n o c c u r s w i t h permanent sample p l o t s data  t o r e p e a t e d measurements b e i n g taken on the same sample  due  plot.  The g e n e r a l t h e o r y on the problem of a u t o c o r r e l a t i o n has been d i s c u s s e d i n d e t a i l by D u r b i n and Watson (1950) and Johnston  (1960).  With r e s p e c t t o a p p l i c a t i o n i n f o r e s t r y , the problem has been r e c o g n i z e d and handled i n d i f f e r e n t ways by d i f f e r e n t r e s e a r c h e r s working on growth and y i e l d  studies.  F o r example, Buckman (1962) working on growth and  y i e l d of r e d p i n e (Pinus r e s i n o s a A i t ) i n Minnesota r e c o g n i z e d the problem but went ahead and used o r d i n a r y l e a s t squares r e g r e s s i o n method i n the hope t h a t the e r r o r i n v o l v e d was  not l a r g e .  Similarly,  Curtis  (1967) r e c o g n i s e d t h i s problem w i t h D o u g l a s - f i r (Pseudotsuga m e n z i e s i i (Mirb.) F r a n c o ) volume measurements from permanent sample p l o t s .  He  went ahead and used o r d i n a r y l e a s t - s q u a r e s procedure but took care of the problem through an ad hoc procedure i n v o l v i n g t e s t i n g f o r s i g n i f i cant c o r r e l a t i o n between any two  contiguous o b s e r v a t i o n on each p l o t .  A more d e t a i l e d study on c o r r e l a t e d e r r o r s was S u l l i v a n and C l u t t e r (1972).  c a r r i e d out by  U s i n g permanent sample p l o t data f o r  L o b l o l l y p i n e (Pinus taeda L . ) , they compared two y i e l d models, one developed by the o r d i n a r y l e a s t - s q u a r e s procedure and the o t h e r by the maximum l i k e l i h o o d e s t i m a t i n g p r o c e d u r e , the l a t t e r b e i n g one of the p o s s i b l e methods of overcoming  the weaknesses of o r d i n a r y l e a s t  procedure when a u t o c o r r e l a t i o n e x i s t s .  The r e s u l t s of t h i s  squares  comparison  35  i n d i c a t e d t h a t f o r a l l p r a c t i c a l purposes, the two models were the same. Because o f the d i f f i c u l t y i n v o l v e d i n e s t i m a t i n g  parameters u s i n g t h e  maximum l i k e l i h o o d procedure ( u s i n g i t e r a t i v e p r o c e d u r e s ) , C l u t t e r wondered i f i t was worth the e f f o r t .  S u l l i v a n and  These sentiments agreed  w i t h those of Swindel (1968) who had addressed the same problem and come to the conclusion  that ordinary  least-squares  d e r a t i o n f o r parameter e s t i m a t i o n  should  be given due c o n s i -  because of i t s s i m p l i c i t y , e s p e c i a l l y  when parameter e s t i m a t e s r a t h e r than c o n f i d e n c e  i n t e r v a l s a r e the main  interest. A more r e c e n t estimators  example of t h e a p p l i c a t i o n of the maximum l i k e l i h o o d  of parameters f o r l i n e a r models when the e r r o r components a r e  c o r r e l a t e d due t o having r e p e a t e d measurement on p l o t s i s p r o v i d e d S e a g r i s t and S t a n f o r d difficulty  (1980).  involved i n using  T h i s example serves  to demonstrate the  t h i s procedure f o r parameter  estimation.  From a review of the l i t e r a t u r e , i t may be s t a t e d t h a t , to date, i s no simple procedure f o r h a n d l i n g  there  the problem o f a u t o c o r r e l a t i o n i n  l i n e a r r e g r e s s i o n models and that f u r t h e r r e s e a r c h area.  by  i s required i n t h i s  The view adopted i n t h i s study i s t h a t the problem of a u t o c o r -  r e l a t i o n may e x i s t i n the permanent sample p l o t s data but no e f f o r t  will  be expended t o r e s o l v e i t because o f the s i m p l i c i t y o f the o r d i n a r y least-squares  6.  procedure.  Study Methods The  b a s i c procedure i n growth and y i e l d  of the growth o r y i e l d f u n c t i o n . parameter e s t i m a t i o n  studies involve d e r i v a t i o n  The p r i n c i p l e t o o l adopted f o r  f o r the f u n c t i o n s  i n t h i s study i s the o r d i n a r y  36  least-squares  procedure f o r both l i n e a r and  nonlinear  regressions,  wherever p o s s i b l e , n o n l i n e a r models were p r e f e r r e d to l i n e a r models f o r reasons g i v e n  l a t e r i n Chapter 2 ) .  The  least-squares  ordinary  s i o n parameters f o r the mathematics and  method f o r the e s t i m a t i o n  l i n e a r models are d e t a i l e d i n many books  statistics.  In p a r t i c u l a r , Draper and  e d i t i o n ) have g i v e n d e t a i l e d procedures f o r f i t t i n g r e g r e s s i o n models, rigorous  l i n e a r and  a n a l y s i s are  f o r the d a t a .  shown and  on 2nd  nonlinear  study,  study o f r e s i d u a l s have been performed  t o ensure t h a t r e g r e s s i o n a n a l y s i s assumptions are met appropriate  regres-  Smith (1981,  wherever l i n e a r models are used i n t h i s  r e g r e s s i o n a n a l y s i s and  model was  of the  i n most cases,  However, not  and  that  a l l d e t a i l s of  o n l y the r e l e v a n t  the the  statistics  are  presented. In a d d i t i o n to r e g r e s s i o n a n a l y s i s , t e s t s of r e g r e s s i o n b i a s were performed and (data not  i n d i v i d u a l f u n c t i o n s v a l i d a t e d u s i n g independent d a t a  used i n d e r i v i n g the  f u n c t i o n s ) wherever p o s s i b l e .  independent data were c r e a t e d by s e t t i n g a s i d e p l o t s f o r each s p e c i e s . tabular presentation studied  choice  of the r e s u l t s from the d e r i v e d  I t should  with  be mentioned here that the major c r i t e r i a i n  b i o l o g i c a l meaning i n the  a given  f u n c t i o n was  the  t h e i r having a  function.  In t h i s study, n o n l i n e a r subroutine  or  f u n c t i o n were  f u n c t i o n performance i s c o n s i s t e n t  of v a r i a b l e s e n t e r i n g  least-squares  20 randomly s e l e c t e d  F i n a l l y , i n n e a r l y a l l cases, g r a p h i c a l  to ensure t h a t the  expectation.  These  P:3R  C a l i f o r n i a i n Los A n g e l e s .  equations were f i t t e d u s i n g  the  nonlinear  of the BMDP developed by the U n i v e r s i t y of The  r o u t i n e e s t i m a t e s the model parameters  37  i t e r a t i v e l y by m i n i m i z i n g the sums o f the squared e r r o r o f p r e d i c t i o n using  t h e Gauss-Newton i t e r a t i v e p r o c e d u r e .  t h a t t h e f u n c t i o n and the f i r s t  The s u b r o u t i n e  requires  p a r t i a l d e r i v a t i v e s (with r e s p e c t  to t h e  parameters t o be e s t i m a t e d ) be s p e c i f i e d and t h e i n i t i a l e s t i m a t e s of the parameters be s u p p l i e d . the BMDP manual. is  discussed  Further  d e t a i l s on BMDP are c o n t a i n e d i n  The s i m u l a t i o n procedure used f o r model  i n Chapter 3.  construction  38  CHAPTER  2  STAND DEVELOPMENT AND GROWTH FUNCTIONS  1.  Height  Development and S i t e Index Curve C o n s t r u c t i o n  1.1  Introduction  S i t e i n f o r e s t r y terminology  r e f e r s t o the i n t e r a c t i o n of both the  p h y s i c a l and b i o l o g i c a l f a c t o r s d e t e r m i n i n g  the p r o d u c t i v e c a p a c i t y of  an a r e a f o r a g i v e n t r e e s p e c i e s ( o r i t s provenance o r v a r i e t y ) . Because of the l a r g e number of combinations of p h y s i c a l f a c t o r s and b i o l o g i c a l f a c t o r s of a s p e c i e s , t h e r e i s t h e r e f o r e almost an i n f i n i t e number of s i t e s .  In p r a c t i c e however, s i t e s a r e r e c o g n i s e d  f o r a given  t r e e s p e c i e s (and o r i t s provenance or v a r i e t y ) w i t h i n a g i v e n w i t h i n which the environmental  area  c o n d i t i o n s a r e c o n s i d e r e d more or l e s s  homogeneous. Over t h e y e a r s , s e v e r a l methods of q u a n t i f y i n g s i t e have been developed.  Spurr  (1952), Husch e t a l . (1972) and many other  authors  have d e t a i l e d the d i f f e r e n t methods, a l l of which can be grouped i n t o two  categories: 1.  Those based on s i t e f a c t o r s c o n s i d e r e d c l o s e l y a s s o c i a t e d w i t h yield:  examples a r e the i n d i c a t o r p l a n t approach developed  Cajander i n F i n l a n d ( I l v e s s a l o  1927) and the environmental  f a c t o r s approach, u s i n g c l i m a t i c f a c t o r s , s o i l f a c t o r s , and 2.  v e g e t a t i o n (Spurr  by  fauna  (1952), Husch et^ al^. (1972) and o t h e r s ) .  Those u s i n g stand c h a r a c t e r i s t i c s as phytometers. use of volume y i e l d o r the expected  Examples a r e  mean annual volume  39  increment at a predetermined Christie without  1971)  and  r e f e r e n c e age  and  the use of stand dominant h e i g h t w i t h  r e f e r e n c e to a predetermined  In g e n e r a l , the second category  various s i t e factors affecting  used.  assumption t h a t  the  the growth of a g i v e n t r e e s p e c i e s can  q u a n t i f i e d i n t h e i r i n f l u e n c e on stand  stand c h a r a c t e r i s t i c s most w i d e l y used to q u a n t i f y  i n f o r e s t management.  and  spacing.  yield  treatments  such as t h i n n i n g and  As a r e s u l t , the most w i d e l y used procedure i n growth  s t u d i e s has  been to d e r i v e the height over age  t o t a l volume y i e l d r e l a t i o n s h i p s f o r v a r i o u s s i t e s . s h i p i s known, h e i g h t may 1967). age  The  primary  I t s main drawback i s t h a t volume y i e l d  can be i n f l u e n c e d by s i l v i c u l t u r a l initial  be  characteristics.  s i t e , volume appears the most l o g i c a l i n t h a t i t i s u s u a l l y the interest  or  age.  has been the most w i d e l y  T h i s can be a t t r i b u t e d to the w i d e l y accepted  Between the two  (Hamilton  be used to estimate  and  age  When t h i s  over  relation-  t o t a l volume y i e l d  (Crawe  o b j e c t i v e of t h i s s e c t i o n i s to i n v e s t i g a t e the h e i g h t  r e l a t i o n s h i p f o r the three s p e c i e s :  over  C_. l u s i t a n i c a , P_. p a t u l a and  P_. r a d i a t a i n Kenya. The  stand dominant h e i g h t as used i n t h i s study i s d e f i n e d as  mean h e i g h t of the 100  l a r g e s t diameter t r e e s per h e c t a r e  T h i s i s p r e f e r r e d to stand mean h e i g h t as i t i s l i t t l e treatment,  e s p e c i a l l y low t h i n n i n g .  t h i s assumption may  not  the  (Hummel 1953).  a f f e c t e d by  However, i t should be noted  always h o l d , f o r example i n the case  stand  that  of h i g h  t h i n n i n g (an e x c e p t i o n i n Kenya t h i n n i n g p r a c t i c e ) and i n s i t u a t i o n s where the dominant t r e e s might d i e of d i s e a s e or i n s e c t a t t a c k or factors.  other  40  The  b a s i c assumption u n d e r l y i n g use of dominant h e i g h t over age  r e l a t i o n s h i p f o r s i t e c l a s s i f i c a t i o n i s t h a t a stand o f a g i v e n age and h e i g h t w i l l always y i e l d the same t o t a l volume on a g i v e n s i t e i f the s i t e remains unchanged.  T h i s assumption w i l l be v a l i d p r o v i d e d t h a t the  s u p p o s i t i o n t h a t t o t a l volume y i e l d i s not a f f e c t e d by the degree o f t h i n n i n g ( M o l l e r 1947) h o l d s .  However, i t i s not known i f t h i s  supposi-  t i o n holds f o r Kenya t h i n n i n g p r a c t i c e s .  1.2  S i t e Index Curve C o n s t r u c t i o n  Procedure The  dominant h e i g h t a t t a i n e d by a g i v e n f o r e s t  stand at a p r e d e t e r -  mined r e f e r e n c e age i s the most w i d e l y used index of s i t e q u a l i t y and will  be used i n t h i s study.  To f a c i l i t a t e o b j e c t i v e a p p l i c a t i o n of t h i s  approach, a system o f h e i g h t over age c u r v e s , c a l l e d the s i t e  index  curves i s developed. Over the y e a r s , two main methods f o r c o n s t r u c t i o n of h e i g h t  over  age and s i t e index curves have e v o l v e d : 1.  Anamorphic curves procedure:  T h i s procedure  c o n s i s t s of  f i t t i n g one g u i d i n g curve t o the h e i g h t over age d a t a , e i t h e r g r a p h i c a l l y or u s i n g s t a t i s t i c a l methods, and then f i t t i n g curves above and below the guide  a f a m i l y o f anamorphic  curves a t a r b i t r a r i l y d e f i n e d i n t e r v a l s .  These curves assume: (a)  Constant and  (b)  p r o p o r t i o n a l i t y between growth curves  stand c o n d i t i o n s .  S i t e q u a l i t y i s independent of age.  for a l l sites  41  These assumptions  are c o n s i s t e n t w i t h t h e o r y which suggests t h a t  a l l o t h e r f a c t o r s b e i n g e q u a l , stands on poor s i t e s develop at a slower r a t e than those on b e t t e r s i t e s . procedure was  the f i r s t  Because of i t s s i m p l i c i t y ,  to be developed and n e a r l y a l l e a r l i e r  index curves were, based on i t .  (1963), Beck and  T h i s has g i v e n r i s e to the second  Polymorphic  polymorphic assumption  have  (1973), Spurr (1955), Powers (1972), Carmean (1956), King  (1966) and o t h e r s . 2.  site  N o n e t h e l e s s , these assumptions  been proven f a l s e f o r s e v e r a l s p e c i e s , e.g. Stage Trousdell  this  curve procedure:  procedure:  A c c o r d i n g to Stage  (1963), the  s i t e i n d e x curve approach i s a g e n e r a l i z a t i o n of the t h a t s i t e index i s independent  of age.  h e i g h t over age curves f o r a p a r t i c u l a r s p e c i e s may  I t r e c o g n i s e s that v a r y i n shape f o r  d i f f e r e n t c l i m a t i c r e g i o n s , v e g e t a t i o n t y p e s , s o i l s and o t h e r  factors.  For  example, a c c o r d i n g to Beck and T r o u s d e l l  (1973), h e i g h t growth f o r  red  p i n e (Pinus r e s i n o s a A i t ) on h i g h - q u a l i t y s i t e s i s r a p i d at  first  but the curve f l a t t e n s w h i l e stands are s t i l l young, w h i l e h e i g h t growth on l o w - q u a l i t y s i t e s i s s u s t a i n e d a t a slower r a t e f o r a l o n g e r p e r i o d , thus j u s t i f y i n g polymorphic  curves.  From the above d i s c u s s i o n i t would appear  t h a t the d i s c u s s i o n of  anamorphic curve procedure i s p u r e l y academic s i n c e i t i s now established fact  t h a t s i t e index curves are e s s e n t i a l l y  a well  polymorphic,  which v a r y i n shape from one s i t e to another (Rawat and Franz 1974). p r a c t i c e however, the i s s u e i s not so s i m p l e . dure used  For example, the p r o c e -  to e s t i m a t e the i n d i v i d u a l p l o t s i t e index i n t h i s  ( d i s c u s s e d below) d i c t a t e d  t h a t the r e s u l t i n g  In  curves would be  anamorphic, thus n e c e s s i t a t i n g f u r t h e r t e s t i n g to support the  study inherently fact.  42  T h i s was  e s p e c i a l l y n e c e s s a r y s i n c e two main f a c t o r s may  i n t r o d u c e polymorphism t o h e i g h t over age 1.  Differences i n r a i n f a l l  ( d i s t r i b u t i o n and q u a n t i t y ) i n As mentioned i n Chapter 1  p a r t of the country has one  rainy  season and one d r y season; w h i l e the E a s t o f the R i f t has  two  T h i s may 2.  r a i n y seasons  to  curves i n Kenya.  d i f f e r e n t p a r t s of the c o u n t r y . S e c t i o n 2, the western  be expected  and two  dry seasons  valley  d u r i n g the y e a r .  cause d i f f e r e n c e s i n growth r a t e s .  D i f f e r e n c e s i n s o i l types In the d i f f e r e n t p a r t s of the c o u n t r y may  cause d i f f e r e n c e s i n growth r a t e s .  E s t i m a t i n g P l o t S i t e Index The  permanent sample p l o t d a t a f o r s i t e index curve c o n s t r u c t i o n  c o n s i s t e d o f an n by 2 m a t r i x f o r each p l o t where n was p l o t remeasurements f o r the two height.  the number of  v a r i a b l e e n t r i e s , age and  stand dominant  A t h i r d v a r i a b l e , s i t e index f o r each p l o t was t h e r e f o r e  r e q u i r e d f o r the f i n a l  s i t e index curve e q u a t i o n .  shows the h e i g h t over age d a t a used i n t h i s  F i g u r e s 3, 4 and 5  study.  By d e f i n i t i o n , s i t e index r e f e r s to the dominant h e i g h t a t t a i n e d a g i v e n stand a t some a r b i t r a r i l y predetermined factors affect et^ a l .  the c h o i c e of t h i s age.  (1974), index age  r e f e r e n c e age.  by  Several  For example a c c o r d i n g to C u r t i s  should approximate  the r o t a t i o n age  s i n c e the  main i n t e r e s t i s u s u a l l y the t o t a l p r o d u c t i o n over the r o t a t i o n . A c c o r d i n g t o T r o u s d e l l e t a l . (1974) however, index age should be such t h a t the p e r i o d of r a p i d growth i s completed,  and  chosen  should p r e f e r a b l y  FIGURE HEIGHT/AGE  RELATIONSHIP  3  FOR C .  L U S I T A N I C A PLOTS  FIGURE HEIGHT/AGE  RELATIONSHIP  4 FOR P,  PATULA PLOTS  FIGURE  HEIGHT/AGE  5  RELATIONSHIP  FOR  P.  RADIATA  PLOTS  ID  a l 0  1 5  1 10 AGE  IN  1 IS YEARS  FROM  1 20 PLANTING  1 25  r 30  46  be  somewhat l e s s than the u s u a l r o t a t i o n age  recommended an index age near the average p r e d i c t e d so as t o generate  They  age of the stands to be  the most a c c u r a t e p r e d i c t i o n s .  In Kenya, the r o t a t i o n age ranges  f o r the s p e c i e s .  f o r the s p e c i e s covered i n t h i s  study  between 15. years f o r pulpwood p l a n t a t i o n s to about 30 years f o r  sawlog and p e e l e r l o g p l a n t a t i o n s .  From the p o i n t of view of management  t h e r e f o r e , c h o i c e of 15 years as r e f e r e n c e age i s l o g i c a l as i t i n c l u d e s the r o t a t i o n age  f o r pulpwood p l a n t a t i o n s .  t h i s c h o i c e are t h a t a t t h i s age, passed  the j u v e n i l e stage and  Other  f a c t o r s i n favour of  the stands are h i g h enough to have  the age  i s c e n t r a l enough to the range of  data covered i n t h i s study ( A l d e r 1977).  S i t e index i n t h i s  study  t h e r e f o r e r e f e r s t o the dominant h e i g h t a t t a i n e d by the stand at age  15  years. The was  first  step i n the e s t i m a t i o n of the i n d i v i d u a l p l o t  site  to f i t the best l i n e a r model to the dominant h e i g h t over age  index data  f o r each s p e c i e s , w i t h the dominant h e i g h t as the dependent  variable.  T a b l e 8 g i v e s the e q u a t i o n s , the estimated c o e f f i c i e n t s and  other  relevant s t a t i s t i c s The  f o r each s p e c i e s .  above e q u a t i o n s p r o v i d e d the guide curve, r e p r e s e n t i n g the  g e n e r a l growth t r e n d f o r the r e s p e c t i v e s p e c i e s . c u r v e s , the i n d i v i d u a l p l o t  s i t e index was  Using these  guide  estimated as f o l l o w s :  47  TABLE 8.  C o e f f i c i e n t s f o r the dominant h e i g h t (m) over age ( y r s ) l i n e a r equations  C_. l u s i t a n i c a H  2 r>2 r or R SEE H(15)  dom  =  b  0  +  b  l  l o  *10  P. p a t u l a A  H  dom  =  b  0  +  b  P_. r a d i a t a l  A  +  b  2 ' A  -16.0380  -1.0064  -4.5323  30.5460  1.8909  2.6424  -0.0205  -0.03337  1413  1452  1625  .90  .88  .92  2.29  2.35  2.54  19.9  22.8  27.6  48  At any g i v e n age, the p l o t  s i t e i n d e x , r e l a t i v e t o the mean  dominant h e i g h t a t age 15 y e a r s (H(15)) i s g i v e n by:  S» -  H, x ft(15) —  2.1  A.  H  i  where S' = E s t i m a t e d s i t e index c o r r e s p o n d i n g t o h e i g h t H^. Plot  dominant h e i g h t a t the g i v e n age i n meters.  Dominant h e i g h t i n meters ( c o r r e s p o n d i n g t o H^) e s t i m a t e d from the guide curve  equation.  From these e s t i m a t e s , the average as  plot  s i t e index S, i s e s t i m a t e d  follows: n S  =  i=l  2.2  S  where n = number of p l o t The  remeasurements.  r e s u l t i n g d a t a s e t f o r each p l o t  Age l a  Height  i s an n by 3 m a t r i x :  S i t e Index  h,  a  S  2  *n  n  where column 3 i s the same number f o r each p l o t . t h i s procedure  Figure 6 i l l u s t r a t e s  d i a g r a m m a t i c a l l y u s i n g the e q u a t i o n f o r C_. l u s i t a n i c a .  49  50  Choice o f the H e i g h t Over Age Model F o r e s t r y l i t e r a t u r e has numerous examples of h e i g h t over age growth models, both l i n e a r and n o n l i n e a r .  The l i n e a r models are of the g e n e r a l  form:  Y = 3Q  +  3  + B X ....  l X l  2  where Y = dependent  2  3  2  B^...3p  +  E  2.3  ±  variable.  , X ...Xp = Independent BQ,  p X p  variables.  = R e g r e s s i o n parameters  t o be e s t i m a t e d .  = A n o r m a l l y d i s t r i b u t e d e r r o r w i t h mean zero and v a r i a n c e c r 2 . The  term l i n e a r i m p l i e s t h a t the model i s l i n e a r i n parameters.  T h i s f a m i l y of models has been w i d e l y employed i n the p a s t t o d e s c r i b e height  over age r e l a t i o n s h i p s .  Examples a r e p r o v i d e d by Meyers  Schumacher (1939), T r o r e y (1932) and o t h e r s . used  f o r h e i g h t over age r e l a t i o n s h i p s  East A f r i c a  (Alder  (1940),  Schumacher's e q u a t i o n was  f o r the e x o t i c timber s p e c i e s i n  1977).  I n g e n e r a l , t h e l i n e a r models a r e easy t o develop and t o a p p l y and o f t e n f i t the data b e s t . priate.  However, they a r e not always the most  appro-  F o r example, t h e h e i g h t over age curve of an i n d i v i d u a l t r e e o r  a f o r e s t s t a n d i s known t o be a t y p i c a l b i o l o g i c a l growth curve:  Sigmoid  i n shape, s t a r t i n g a t t h e o r i g i n and i n c r e a s i n g m o n o t o n i c a l l y t o an i n f l e c t i o n p o i n t , and then a p p r o a c h i n g the asymptote,  determined  g e n e t i c c o n s t i t u t i o n o f t h e i n d i v i d u a l t r e e or stand and s i t e  by the  factors.  From a t h e o r e t i c a l s t a n d p o i n t t h e r e f o r e , l i n e a r models a r e i n a p p r o p r i a t e s i n c e they do not s a t i s f y process.  t h e b i o l o g i c a l p r i n c i p l e s o f the growth  51  One  example of n o n l i n e a r models has  P  (e0 Y  =  g e n e r a l form:  2  + BjX  +  E)  2.4  e  where 3 Q » ^1  a n c  * ^2  a  r  e  t  n  e  parameters to be  estimated.  X i s the p r e d i c t o r v a r i a b l e .  The  term n o n l i n e a r i m p l i e s t h a t the f u n c t i o n (2.4) i s n o n l i n e a r i n  parameters and  cannot be l i n e a r i z e d through t r a n s f o r m a t i o n s .  g e n e r a l , most n o n l i n e a r models used i n growth and y i e l d to the t h e o r e t i c a l laws of b i o l o g i c a l growth and p e r m i t t i n g changes i n shape, form and data of i n t e r e s t .  In  s t u d i e s conform  are f l e x i b l e ,  s c a l e of the curves  thus  to f i t the  In a d d i t i o n , they p r o v i d e a b a s i s f o r f o r m u l a t i o n of  g e n e r a l hypotheses t h a t express  the u n d e r l y i n g laws of growth.  This,  a c c o r d i n g t o P i e n a a r and T u r n b u l l (1973) p r o v i d e s a j u s t i f i c a t i o n f o r e x t r a p o l a t i o n beyond the range of c o n d i t i o n s r e p r e s e n t e d For h e i g h t over age  by the  data.  c u r v e s , the most popular n o n l i n e a r model has  been the Chapman-Richard's e q u a t i o n i n the form:  2.5  H  where H A  Stand h e i g h t . Age  of the  b^ and b  2  stand.  are the c o e f f i c i e n t s to be  estimated.  52  T h i s f u n c t i o n i s a g e n e r a l i z a t i o n of Von B e r t a l a n f f y ' s growth model (Richards  1959) where some o f the parameters have a p h y s i o l o g i c a l  i n t e r p r e t a t i o n such t h a t bg r e p r e s e n t s the b i o l o g i c a l s i t e  potential  o r maximum h e i g h t a t t a i n a b l e on a g i v e n s i t e , w h i l e b j r e p r e s e n t s the stand growth r a t e , bn i s r e l a t e d to b, value  such t h a t  = c u l m i n a t i o n age of the c u r r e n t annual  The  increment.  a p p l i c a t i o n of t h i s model t o f o r e s t r y was p o p u l a r i z e d  through  the work o f P i e n a a r and T u r n b u l l (1973), when they demonstrated i t s a p p l i c a t i o n t o b a s a l area growth. height  over age curves  I t now forms the b a s i s f o r most  i n North America.  Examples a r e Hegyi et^ a l .  (1979), T r o u s d e l l e t a l (1974), Beck (1971), B r i c k e l  (1968) and o t h e r s .  Another n o n l i n e a r model t h a t i s i n c r e a s i n g l y a t t r a c t i n g i n t e r e s t i n growth and y i e l d  H  =  s t u d i e s i s the m o d i f i e d W e i b u l l  b (l - e" Q  b l A  2  )  where H  =  Stand h e i g h t .  A  =  Age o f the stand.  bg, b j and b  The  2  f u n c t i o n i n the form:  2.6  a r e c o e f f i c i e n t s t o be e s t i m a t e d .  c o e f f i c i e n t s bg, b^ and b  as f o r Chapman-Richard's e q u a t i o n .  2  have the same i n t e r p r e t a t i o n T h i s f u n c t i o n was developed  by  W e i b u l l (1939, 1951) as a p r o b a b i l i t y d i s t r i b u t i o n f u n c t i o n of the form:  53  X F  1  2.7  where F  =  Frequency f o r a g i v e n c l a s s of  X  -  Class  a  =  A s c a l e parameter.  X  =  A shape parameter.  As  interest.  size.  a p r o b a b i l i t y d i s t r i b u t i o n f u n c t i o n , t h i s model has been used In  f o r e s t r y to model t r e e diameter d i s t r i b u t i o n , b a s a l a r e a , s u r f a c e area etc.  By  i n t r o d u c i n g an expanding f a c t o r  (1978) demonstrated t h a t the m o d i f i e d  F  (a) t o the model, Yang et a l .  form:  = a (1  2.8  performed as a h i g h l y f l e x i b l e , monotomically i n c r e a s i n g sigmoid w i t h very d e s i r a b l e growth c h a r a c t e r i s t i c s such as p a s s i n g o r i g i n when age  i s z e r o , h a v i n g an i n f l e c t i o n p o i n t and  asymptote as age  increases.  For h e i g h t over age  both the Chapman-Richard's e q u a t i o n equation  2.5  and  curves  the m o d i f i e d  through  t e n d i n g to an i n this Weibull  Models  Both equations  2.5  and  2.6  were a p p l i e d to the h e i g h t over age  f o r each of the t h r e e s p e c i e s .  1.  study,  2.6 were t e s t e d to determine the most a p p r o p r i a t e .  Comparing the Two  The  curve  r e s u l t s are g i v e n on T a b l e 9a, b and The  estimated  c which shows:  parameters f o r each model.  data  TABLE 9.  Comparison of the M o d i f i e d W e i b u l l and Chapman-Richard models f o r h e i g h t over age curves  Coefficients Equation b  o  D  l  Mean b i a s i n meters by age c l a s s e s h 2  SEE  r  <10  D  years  10-20 y e a r s  >20 y e a r s  C. l u s i t a n i c a a ) Chapman-Richards (2.5) W e i b u l l (2.6)  36.1960 36.4873  -.06092 -.03905  1.2005 1.0978  .89 .89  2.40 2.40  n = 1201  -.14 -.23  .11 .17  -.05 -.05  (802)  (448)  -.07 -.04  -.02 -.02  .37 .41  (457)  (680)  (94)  -.15 -.10  .27 .23  (451)  P. p a t u l a b) Chapman-Ri chards (2.5) W e i b u l l (2.6)  54.9478 51.1519  -.04249 -.02707  1.1650 1.1399  .89 .89  2.36 2.36  n = 1231  P. r a d i a t a c) Chapman-Richards (2.5) W e i b u l l (2.6)  55.2035 52.3892  n =  -.06871 -.01997  1.5531 1.3414  .92 .92  2.56 2.56  .14 .09  (406)  (843)  (170)  55  2.  Number of remeasurements on which the parameters a r e based.  3.  The s t a n d a r d  SEE  e r r o r of estimate  defined as:  , A "* ' ^ (  -  2  n - p  where  p  =  Number of parameters e s t i m a t e d  n  =  T o t a l number o f o b s e r v a t i o n s .  and  4.  a r e the observed  2 *  where  =  T o t a l sums of squares (H  RSS  =  5 ) 2  R e s i d u a l sums of squares  = JUi -v ,  2  and H a r e the observed,  mean of observed  5.  f o r each model, estimated as:  2  " Jl i "  where  i n the model,  TSS - RSS TSS  TSS  d e f i n e d age c l a s s e s :  <10 y e a r s , 10-20 y e a r s and >20 y e a r s . c a l c u l a t e d as:  p r e d i c t e d and the  stand dominant h e i g h t .  The mean b i a s by a r b i t r a r i l y  9  and p r e d i c t e d dominant h e i g h t s .  C o e f f i c i e n t of d e t e r m i n a t i o n  r  '  The mean b i a s was  „ , ' 1  0  n  56  n B  =  "  2  where tij = Number of o b s e r v a t i o n s i n age and  -  1 1  class j ,  are as above.  Number of remeasurements w i t h i n each age  c l a s s are shown  i n brackets. As seen from Table 9, both models gave i d e n t i c a l r e s u l t s f o r each s p e c i e s , based estimate.  on c o e f f i c i e n t of d e t e r m i n a t i o n or s t a n d a r d e r r o r of  S i m i l a r l y , mean b i a s of age  models f o r a l l t h r e e s p e c i e s .  c l a s s e s was  n e g l i g i b l e f o r both  However, a look a t the c o e f f i c i e n t  shows t h a t f o r C_. l u s i t a n i c a , both models gave i d e n t i c a l v a l u e s . i s as expected  s i n c e f o r both models t h i s parameter e s t i m a t e s  maximum a t t a i n a b l e h e i g h t f o r the s p e c i e s . however, the model gave d i f f e r e n t  bg This  the  For the two pine s p e c i e s  v a l u e s of bg, t h a t f o r Chapman-  R i c h a r d b e i n g h i g h e r than t h a t e s t i m a t e d by the W e i b u l l f u n c t i o n i n both cases.  The e x p l a n a t i o n f o r t h i s i s t h a t f o r these two  d i d not cover the asymptotic phase of growth and of bg cannot  be v e r y r e l i a b l e .  which shows the a s y m p t o t i c cients.  models.  so the e s t i m a t e d  value  T h i s i s f u r t h e r confirmed by T a b l e 1 0  s t a n d a r d d e v i a t i o n f o r the e s t i m a t e d  For C. l u s i t a n i c a , the asymptotic  i s much lower  s p e c i e s , the data  coeffi-  standard d e v i a t i o n f o r bg  compared t o t h a t f o r P. p a t u l a and P_. r a d i a t a f o r both  I t i s worth n o t i n g t h a t between the two p i n e s p e c i e s , the  asymptotic  s t a n d a r d d e v i a t i o n f o r bg i s lower  r a d i a t a whose data cover  ( f o r both models) f o r P_.  h i g h e r age c l a s s e s than t h a t f o r P. p a t u l a (35  57  y e a r s JP. r a d i a t a , 25 y e a r s P_. p a t u l a upper age l i m i t ) ; see a l s o F i g u r e s 3, 4 and 5. Table  10 a l s o shows t h a t f o r bg  model gave lower asymptotic  a  n  d  b  2'  t  h  e  Chapman-Richards  s t a n d a r d d e v i a t i o n than the W e i b u l l model,  w h i l e f o r bi» Chapman-Richards gave a s l i g h t l y h i g h e r v a l u e f o r a l l three species. equation this  Based on these r e s u l t s t h e r e f o r e , Chapman-Richards  (2.5) was s e l e c t e d f o r t h e h e i g h t over age r e l a t i o n s h i p s i n  study.  TABLE 10.  Asymptotic s t a n d a r d d e v i a t i o n s f o r the e s t i m a t e d of T a b l e 9  coefficients  Coefficient 2.6  2.5  function  2.5  2.6  2.5  2.6  C_. l u s i t a n i c a  0.5737  0.9808  0.002100  0.001827  0.007812  0.02981  P_. p a t u l a  2.7884  4.2858  0.003013  0.001032  0.004198  0.03933  P. r a d i a t a  0.9137  2.2989  0.001697  0.000047  0.005463  0.01084  2.5 2.6  = =  Chapman-Richards f u n c t i o n . Modified Weibull function.  I n t r o d u c i n g S i t e Index t o Height Over Age Model Having  d e c i d e d on t h e g e n e r a l h e i g h t over age model, the next  was t o i n t r o d u c e s i t e index as the second equation.  independent  step  v a r i a b l e i n the  From t h e o r e t i c a l c o n s i d e r a t i o n s , one would expect  that the  b e t t e r t h e s i t e q u a l i t y , the h i g h e r would be the h e i g h t growth r a t e . S i m i l a r l y , one would expect  t h a t t h e b e t t e r the s i t e q u a l i t y , the h i g h e r  58  the expected  maximum a t t a i n a b l e dominant h e i g h t .  S i t e index was t h e r e -  f o r e i n t r o d u c e d as a l i n e a r f u n c t i o n o f the c o e f f i c i e n t s bg  a  n  ^ bp  the c o e f f i c i e n t s a s s o c i a t e d w i t h maximum a t t a i n a b l e h e i g h t and growth r a t e r e s p e c t i v e l y i n e q u a t i o n 2.5.  H, = b S(l dom u n  -biA b - e ) 1  Three e q u a t i o n s were t e s t e d :  0  2.12  1  -biAS b H, = b (l - e ) dom 0 1  0  2.13  1  n  -b,AS b H  dom * V <  1  "  0  >  6  where S = p l o t s i t e index.  2  '  1  4  A l l o t h e r symbols a r e as b e f o r e .  For a l l s p e c i e s , e q u a t i o n 2.13 gave the best r e s u l t s i n terms of mean b i a s by age c l a s s e s and s t a n d a r d e r r o r of e s t i m a t e , s u g g e s t i n g t h a t s i t e q u a l i t y expressed  itself  best i n i t s e f f e c t on growth r a t e .  was unexpected s i n c e as mentioned above, one would expect quality  This  that s i t e  should a l s o be a s s o c i a t e d w i t h c o e f f i c i e n t bg f o r maximum  a t t a i n a b l e dominant h e i g h t , thus f a v o u r i n g e q u a t i o n 2.14.  This could  p a r t l y be e x p l a i n e d as being due t o l a c k of s u f f i c i e n t data i n t h e asymptotic phase of growth, more so f o r the two pine s p e c i e s , as shown on F i g u r e s 3, 4 and 5. Table 11 shows the parameter e s t i m a t e s and o t h e r r e l e v a n t statistics  ( c a l c u l a t e d as f o r T a b l e 9) from e q u a t i o n 2.13 f o r each o f  the s p e c i e s w h i l e T a b l e  12 g i v e s the asymptotic  the e s t i m a t e d parameters.  standard d e v i a t i o n s f o r  59  TABLE 11.  C o e f f i c i e n t e s t i m a t e s and o t h e r s t a t i s t i c s over age and s i t e index e q u a t i o n 2.13  Coefficients  Species  Mean b i a s by age classes  Q  b  C. l u s i t a n i a  41.9764  -0.002153  1.0481  0.97  P. p a t u l a  52.6155  -0.002038  1.2048  P. r a d i a t a  61.6871  -0.001941  1.3583  TABLE 12.  b  b„  l  f o r the height  R  SEE  <10  10-20  >20  1.24  -0.04  0.26  -0.23  0.97  1.14  -0.02  0.04  -0.31  0.98  1.22  -0.07  0.03  -0.15  2  Asymptotic standard d e v i a t i o n s f o r the estimated of T a b l e 11  coefficients  Coefficients  Species J  0  b  l  C_. l u s i t a n i c a  0.4891  0.000054  0.00253  P_. p a t u l a  1.0308  0.00010  0.00190  P. r a d i a t a  0.7352  0.000092  0.001753  The e s t i m a t e d parameters (Table 11) appear both l o g i c a l and c o n s i s tent with expectation. b^ a r e h i g h e s t f o r  F o r example, the v a l u e of c o e f f i c i e n t s bg and r a d i a t a f o l l o w e d by JP. p a t u l a and C_. l u s i t a n i c a ,  i n t h a t o r d e r as expected.  S i m i l a r l y , the magnitude of e s t i m a t e d bg  appear r e a s o n a b l e as i n d i c a t e d by the p l o t growth t r e n d s on F i g u r e s 3, 4 and 5. The e s t i m a t e d  c o e f f i c i e n t s of d e t e r m i n a t i o n a r e very h i g h f o r the  t h r e e s p e c i e s w i t h a s t a n d a r d e r r o r o f estimate i n the o r d e r o f 1.2  60  meters.  The mean b i a s by age c l a s s e s i s n e g l i g i b l e f o r P. r a d i a t a ,  w h i l e the model f o r C_. l u s i t a n i c a g i v e s a p o s i t i v e b i a s of .26 meters between ages 10-20 y e a r s and a n e g a t i v e b i a s e s of .23 meters above age 20 y e a r s .  F o r p r a c t i c a l purposes, these b i a s e s can be c o n s i d e r e d  insignificant.  F o r P^. p a t u l a , t h e b i a s up t o age 20 y e a r s  i s negligible  w h i l e above age 20 y e a r s , the model g i v e s a b i a s o f .31 meters, which c o u l d a l s o be c o n s i d e r e d i n s i g n i f i c a n t .  The o v e r a l l f i t o f e q u a t i o n  2.13 t o the data t h e r e f o r e appeared q u i t e s a t i s f a c t o r y s p e c i e s , except  f o r a l l three  f o r the minor b i a s e s .  V a l i d a t i n g the S i t e Index Model The a guide  s i t e index e s t i m a t i o n procedure used i n t h i s study was based on curve, thus presuming t h a t h e i g h t development on a g i v e n s i t e i s  p r o p o r t i o n a l t o h e i g h t development on o t h e r s i t e s .  This implied there-  f o r e t h a t the dominant h e i g h t development was i n h e r e n t l y anamorphic. In theory,  i f the s i t e index model i s c o r r e c t and the p r i n c i p l e o f  anamorphic h e i g h t development h o l d s , one would expect h e i g h t of a g i v e n stand t o develop throughout the r o t a t i o n .  the dominant  along the same s i t e index  curve  In other words, f o r a g i v e n p l o t , i f the  proposed growth model i s adequate, t h e r e should be no c o r r e l a t i o n between s i t e index and age. index may be expected  In p r a c t i c e however, random s h i f t s i n s i t e  from y e a r t o year due t o :  1.  C l i m a t i c f l u c t u a t i o n s from year t o y e a r .  2.  Measurement e r r o r s .  3.  I n t e r r u p t i o n s i n dominant h e i g h t development a r i s i n g from:  61  (a)  rare  cases of h i g h t h i n n i n g ,  dominant (b)  r e s u l t i n g i n removal of  trees.  death of dominant t r e e s  due  to d i s e a s e s , i n s e c t  attack  or  windthrow. In a d d i t i o n , v a r i e t i e s , one tive the  i f a s p e c i e s i s composed of d i f f e r e n t provenances  would expect some p l o t s  c o r r e l a t i o n of  s i t e index to age,  p a r t i c u l a r provenance or v a r i e t y  model f o r the t r e n d s to be  species.  1.  depending on  In g e n e r a l , we  The  that  Plots  and  indicated  o t h e r s nega-  growth r a t e  of  g e n e r a l growth  would expect these  the model was  l a t t e r would be  the  i n r e l a t i o n to the  random w i t h r e s p e c t to age  t r e n d s would i n d i c a t e species.  to have p o s i t i v e and  or  correlation  s i t e index, w h i l e  inadequate f o r the  systematic  particular  by:  i n s p e c i f i c s i t e classes  showing s p e c i f i c c o r r e l a t i o n  trends. 2.  Plots  i n a g i v e n age  group showing a p a r t i c u l a r  correlation  trend. 3.  Plots e.g.  from a g i v e n r e g i o n or w i t h a s p e c i f i c c h a r a c t e r i s t i c , e s t a b l i s h m e n t method or an  variety To 1.  showing a p a r t i c u l a r c o r r e l a t i o n  t e s t f o r these t r e n d s , the For  i d e n t i f i e d provenance  each p l o t , p r e d i c t e d  calculated  by  solving  following  where In r e f e r to n a t u r a l  procedure was  f o r S i n e q u a t i o n 2.13  b 2  o  trend. followed:  s i t e index at each remeasurement  S = l n ( l - (S. ) ) / - b , A b  or  1  logarithm.  to  was  get:  2.15  62  2.  For  each p l o t , a simple l i n e a r r e g r e s s i o n  s i t e index on age The are  regression  (using  b e t a weights, which are  t i o n s at  .05  TABLE 13.  standardized variables)  age.  measures of the  was  fitted.  correlation coefficient  These were s t u d i e d  the model f o r each s p e c i e s . the number and  calculated  c o e f f i c i e n t s o b t a i n e d at step 2 above f o r each p l o t  tween s i t e i n d e x and  and  of the  as  T a b l e 13 g i v e s the  the  be-  index of f i t f o r  t o t a l number of  percentage of p l o t s which showed s i g n i f i c a n t  plots correla-  level.  D i s t r i b u t i o n of p l o t s showing s i t e index over age at .05 p r o b a b i l i t y l e v e l f o r the t h r e e s p e c i e s  T o t a l no. plots  T o t a l no. p l o t s w i t h significant correlat i o n at .05 l e v e l No. %  correlation  Correlation  sign  +  -  C.  lusitanica  139  41  29.5  22  19  P.  patula  144  54  37.5  18  36  P.  radiata  148  42  28.4  19  23  Table  13 shows that  significant 19 had  correlations  of the  41  at  probability  .05  negative c o r r e l a t i o n s .  (29.5%) £ .  t h e r e f o r e these s h i f t s c o u l d be  l e v e l , 22 had  A study o f the  p l o t s w i t h r e s p e c t to s i t e i n d e x and  age  l u s i t a n i c a plots with positive  d i s t r i b u t i o n of  showed no  and  these  p a r t i c u l a r trend  c o n s i d e r e d random, a r i s i n g from any  and of  63  the  causes mentioned above.  The  s i t e i n d e x model 2.13  was  therefore;  c o n s i d e r e d s a t i s f a c t o r y f o r C_. l u s i t a n i c a . S i m i l a r l y , of the correlations,  19 had  42  (28.4%) P_. r a d i a t a p l o t s w i t h s i g n i f i c a n t  p o s i t i v e and  23 had  negative c o r r e l a t i o n s ,  a study of t h e i r d i s t r i b u t i o n showed no s i t e i n d e x or age. adequate f o r t h i s For  P_. p a t u l a  problems.  Not  significant  model.  p a r t i c u l a r trend with respect  S i t e index model 2.13  was  therefore also  to  considered  species. however, the  r e s u l t s from the  above t e s t  indicated  o n l y d i d i t have the h i g h e s t number of p l o t s  correlations;  36 n e g a t i v e .  while  54  (37.5%); but  of t h e s e , 18 were p o s i t i v e  T h i s r a i s e d doubts r e g a r d i n g the  Further i n v e s t i g a t i o n  with  of these p l o t s  a p p l i c a b i l i t y of  indicated  the  and  the  following  discrepancies. 1.  A l l the regional  plots with s i g n i f i c a n t correlations bias.  For  example, a l l p l o t s  (Nabkoi, B u r e t , Cengalo and t i o n s , while a l l p l o t s had 2.  Of  a l l the  significant  10 p l o t s  Timboroa) had  positive  correla-  Kiandongoro groups  etc.  from g r a s s l a n d p l a n t i n g  correlations,  Nabkoi group had  from Nabkoi group  from E l b u r g o n and  negative c o r r e l a t i o n s ,  showed a d e f i n i t e  s i t e s that  9 of them, a l l coming from  positive correlations.  The  had the  lone p l o t w i t h a  n e g a t i v e c o r r e l a t i o n came from the Nanyuki group. These d i s c r e p a n c i e s i n d i c a t e d h e i g h t over age and  relationships  the  i n the  d i f f e r e n t r e g i o n s of the  a c c o r d i n g t o e s t a b l i s h m e n t methods.  investigation.  p o s s i b i l i t y of v a r i a b i l i t y  This c a l l e d for  of  country  further  64  Height  Development On D i f f e r e n t E s t a b l i s h m e n t  Sites  As mentioned i n Chapter 1 S e c t i o n 3 the two e s t a b l i s h e d on e i t h e r of the two  1.  Grassland  planting.  site  pine species  are  types:  P l a n t i n g on g r a s s l a n d  s i t e s i s done w i t h  minimum l a n d p r e p a r a t i o n other than d i g g i n g p i t s i n t o which s e e d l i n g s are 2.  planted.  Shamba p l a n t i n g , a h i g h l y developed taungya system which r e s u l t s i n w e l l c u l t i v a t e d f i e l d s f o r t r e e p l a n t i n g and ensures care of the young t r e e s i n t h e i r i n i t i a l years  of l i f e  i n the  l a n d s i t e s simply  converted  Grassland  to shambas b e f o r e  s i t e s on  t r e e p l a n t i n g or  To d a t e , the e f f e c t s of  of e s t a b l i s h m e n t  y i e l d of p l a n t a t i o n s are not known although  between ages 5 to 20 y e a r s  All  ( t h e age  range covered  pine  the years  effects  species  by g r a s s l a n d  plots).  Procedure  the g r a s s l a n d p l o t s f o r P^. p a t u l a except one  and Turbo r e g i o n s . p l o t s from these  few  T h i s s e c t i o n of the study examines the  s i t e on h e i g h t development f o r the two  Data A n a l y s i s and  grass-  establishment  g e n e r a l o p i n i o n i s t h a t they a f f e c t s growth o n l y i n the f i r s t of the p l a n t a t i o n l i f e .  the  However, the c u r r e n t p r a c t i c e i s to p l a n t  as g r a s s l a n d s .  s i t e on the growth and  two  by h i g h f o r e s t , shamba p l a n t i n g i s  the o n l y method of p l a n t a t i o n e s t a b l i s h m e n t .  p l a n t e d as g r a s s l a n d s .  or  field.  On a l l s i t e s p r e v i o u s l y occupied  o t h e r hand can e i t h e r be  one  two  A n a l y s i s f o r t h i s s p e c i e s was regions.  Grassland  came from Nabkoi  therefore limited  p l o t s f o r P_. r a d i a t a were  to  65  d i s t r i b u t e d over the whole range where the s p e c i e s i s grown. number of p l o t s and shown on T a b l e  t o t a l number of remeasurements f o r each s p e c i e s are  14.  For d a t a from each e s t a b l i s h m e n t linear  H  s i t e , the best h e i g h t over  dom " 0 b  +  A  b  l  A  +  V  = Plot  2  2  computed and  6  2  from p l a n t i n g i n y e a r s .  are r e g r e s s i o n c o e f f i c i e n t s to be  estimated.  c o v a r i a n c e a n a l y s i s c a r r i e d out to determine  sites  1  e  the d i f f e r e n c e s i n the r e g r e s s i o n c o e f f i c i e n t s between the establishment  '  dominant h e i g h t i n meters,  = Stand age  bg, b j and b  c o u l d be a s c r i b e d to sampling  d i f f e r e n c e s between the e s t a b l i s h m e n t s i t e s . u s i n g the U.B.C. S:SLTEST r o u t i n e (Chinh 1980) t h a t the r e g r e s s i o n c o e f f i c i e n t s b i and b two  age  equation:  where H, dom  was  The  2  The  two  e r r o r or t o r e a l  T h i s was  accomplished  t o t e s t the h y p o t h e s i s  are i d e n t i c a l among the  e s t a b l i s h m e n t s i t e s and i f not r e j e c t e d , to t e s t  a common e q u a t i o n can be used.  whether  the h y p o t h e s i s t h a t  l a t t e r t e s t s whether the i n t e r c e p t s  (bg) a r e e q u a l , g i v e n t h a t the r e g r e s s i o n c o e f f i c i e n t s are e q u a l . T a b l e 14 g i v e s the r e s u l t s of t h i s a n a l y s i s w h i l e F i g u r e 7 shows the h e i g h t over age  curves f o r each s p e c i e s by e s t a b l i s h m e n t  site.  s t a t i s t i c a l t h e o r y on the t e s t s , the r e a d e r i s r e f e r r e d t o Chinh and Kozak  (1970).  For (1980)  66  TABLE 14. Covariance a n a l y s i s f o r s l o p e t e s t f o r h e i g h t over age equations f o r P. p a t u l a and P. r a d i a t a f o r d i f f e r e n t e s t a b l i s h m e n t s i t e s  P. p a t u l a (Nabkoi  No.  and Turbo)  P. r a d i a t a  Shamba  Grassland  0.6275 1.7560 -0.01494  -0.9087 1.8400 -0.02365  1.6420 -0.012  -3.230 2.7140 -0.03779  -4.5390 2.5940 -0.03256  137 23  145 25  282 48  532 38  878 106  plots  Common slope  Equation ^  i  o  m  = b  Shamba  (whole  Q  Grassland  + bjA + b A 2  TEST HYPOTHESIS OF A COMMON SLOPE F F(.05) DF(1) DF(2) Probability  1.92 3.00 2 276 0.1489  0.56 3.00 2 1404 0.5721  TEST HYPOTHESIS OF A COMMON EQUATION F F(.05) DF(1) DF(2) Probability  49.87 3.84 1 278 0.0000  171.37 3.84 1 1406 0.0000  country) Common slope  2.7130 -0.03800 1410 144  67  FIGURE HEIGHT  OVER STAND  — i 5  AGE  IN  FOR  ESTABLISHMENT  1 10 AGE  CURVES  7  1 IS YEARS  FROM  DIFFERENT SITES  P.  RADIATA  SHAMBA  P,  RADIATA  GRASSLAND  P.  PATULA  SHAMBA  P.  PATULA  GRASSLAND  1 20 PLANTING  — r 25  68  R e s u l t s and D i s c u s s i o n  For both s p e c i e s , the common s l o p e h y p o t h e s i s r e j e c t e d a t the  .05  (Table 14) i s not  l e v e l s i n c e the c a l c u l a t e d F-values are l e s s  the c r i t i c a l F - v a l u e s .  Thus, the r e g r e s s i o n s u r f a c e s f o r the  establishment  be assumed p a r a l l e l f o r the two  s i t e s may  than  two  species.  D e s p i t e t h i s r e s u l t , F i g u r e 7 shows t h a t w h i l e the curves f o r I>. r a d i a t a a r e a constant d i s t a n c e from one  another,  p a t u l a curves tend to i n c r e a s e w i t h The  test  the d i s t a n c e between the P_.  age.  f o r a common e q u a t i o n l e d to r e j e c t i o n of the  t h a t the i n t e r c e p t s are the same f o r both e s t a b l i s h m e n t  hypothesis  s i t e s f o r both  s p e c i e s s i n c e the c a l c u l a t e d F-values were much h i g h e r than the F-values.  T h i s meant t h a t the c o e f f i c i e n t b  be assumed equal f o r the two  establishment  0  i n e q u a t i o n 2.16  critical cannot  s i t e s , thus p r e c l u d i n g use  of  a common e q u a t i o n . The  above r e s u l t s suggest  establishment  t h a t the growth r a t e f o r the  s i t e s can be assumed to be the same.  two  For P_. r a d i a t a ,  the  growth curve f o r g r a s s l a n d s i t e s remain about 2 meters below t h a t f o r shambas f o r the whole p e r i o d covered years. for  by the data i . e . up to age  For P_. p a t u l a , the curve f o r g r a s s l a n d s i t e s remains below t h a t  shamba but the d i s t a n c e between them i n c r e a s e s w i t h age,  s i g n i f i c a n t l y so a t .05 age up  to age  The  level.  though not  T h i s d i s t a n c e worked out to be 0.156  of  20 y e a r s .  above o b s e r v a t i o n s t h a t the e f f e c t s of e s t a b l i s h m e n t  remain throughout t r e n d up to age initial  20  the l i f e of the p l a n t a t i o n (as suggested  20 y e a r s ) were unexpected.  d i f f e r e n c e s can be expected  due  sites  by the growth  For example, w h i l e  the  to the c o m p e t i t i o n f o r n u t r i e n t s  69  and moisture all  between the young t r e e s and grass on g r a s s l a n d s i t e s , i f  other f a c t o r s remained the same, one would expect  would d i m i n i s h w i t h age.  t h a t the e f f e c t s  The unexpected r e s u l t s t h e r e f o r e p o i n t t o two  p o s s i b i l i t i e s both of which c o u l d be o p e r a t i v e :  1.  G r a s s l a n d s i t e s may  be i n t r i n s i c a l l y poorer than h i g h  forest  sites. 2.  There may  be a f a c t o r of growth, e.g. m y c o r r h i z a ,  which may  be  l a c k i n g or i s l e s s e f f e c t i v e under g r a s s l a n d c o n d i t i o n s . F u r t h e r i n v e s t i g a t i o n on the t r u e cause of the d i f f e r e n c e s i n growth between the two e s t a b l i s h m e n t  s i t e s i s needed.  F o r example i f  the d i f f e r e n c e s a r e e n t i r e l y due t o the I n i t i a l c o m p e t i t i o n , i t may i n d i c a t e a need to c u l t i v a t e the g r a s s l a n d s b e f o r e t r e e p l a n t i n g and subsequent weeding.  Conclusion  The most important  f i n d i n g from t h i s i n v e s t i g a t i o n was  l a n d p l a n t i n g r e s u l t s i n slower h e i g h t development compared planting for  p a t u l a and P_. r a d i a t a .  s i t e a r e c o n t i n u e d up to age 20 y e a r s .  that grassto shamba  The e f f e c t s of e s t a b l i s h m e n t The immediate p r a c t i c a l  signifi-  cance of t h i s f i n d i n g a r e : 1.  Where the f o r e s t manager has a c h o i c e over e s t a b l i s h m e n t  site  f o r the two p i n e s p e c i e s , shamba p l a n t i n g i s to be p r e f e r r e d . 2.  Any growth and y i e l d model f o r the two p i n e s p e c i e s should have e s t a b l i s h m e n t  s i t e as one of the i n p u t v a r i a b l e s .  70  Height  Development by G e o g r a p h i c a l  Regions f o r P_. p a t u l a  F o r t h i s i n v e s t i g a t i o n , the P^. p a t u l a p l o t s were s t r a t i f i e d  into 8  groups a c c o r d i n g t o the g e o g r a p h i c a l r e g i o n s In which they a r e l o c a t e d . These r e g i o n s conform t o t h e i n v e n t o r y zones a l r e a d y r e c o g n i z e d by the Kenya F o r e s t Department.  F o r data from each r e g i o n , e q u a t i o n  computed and the c o v a r i a n c e  2.16 was  a n a l y s i s and F - t e s t s performed t o t e s t t h e  hypotheses o f common s l o p e and common e q u a t i o n , as i n the p r e v i o u s section.  Table  15 g i v e s the r e s u l t s of t h i s a n a l y s i s w h i l e F i g u r e 8  shows the r e s u l t i n g h e i g h t over age curves The  r e s u l t s on Table  s i g n i f i c a n t a t .05 l e v e l .  f o r each r e g i o n .  15 i n d i c a t e d an F v a l u e of 8.65 w h i c h i s T h i s l e d to the r e j e c t i o n o f the h y p o t h e s i s  of a common s l o p e , which i m p l i e d that a t l e a s t one of the r e g r e s s i o n s u r f a c e was not p a r a l l e l t o one o t h e r . anticipated  T h i s r e s u l t c o u l d have been  from a study of F i g u r e 8 which shows the curves  from  differ-  ent g e o g r a p h i c a l r e g i o n s c r o s s i n g each o t h e r and growing i n d i f f e r e n t directions. considered  Use of a s i n g l e s e t of s i t e index curves was t h e r e f o r e inappropriate f o r this species.  Because o f the s m a l l number  of p l o t s i n r e g i o n s 4 and 8, these r e g i o n s were e l i m i n a t e d from f u r t h e r analyses  so t h a t o n l y s i x r e g i o n s were c o n s i d e r e d .  however, t h e e q u a t i o n  f o r r e g i o n 3 (Elburgon)  growth i n r e g i o n 4 ( L i k i a ) w h i l e the equation  For the time b e i n g  can be used t o approximate f o r r e g i o n 1 (Nabkoi  r e g i o n ) can be used to approximate growth i n r e g i o n 8 (Timboroa), on g e o g r a p h i c a l p r o x i m i t y o f t h e r e g i o n s .  Table  based  16 shows the s i x  r e g i o n s , t h e i r mean annual r a i n f a l l and t h e e l e v a t i o n above sea l e v e l of the weather s t a t i o n .  TABLE 15.  Covariance a n a l y s i s f o r s l o p e t e s t f o r h e i g h t over age equations f o r P. p a t u l a i n d i f f e r e n t r e g i o n s i n Kenya  Geographical region Common slope  -7.3550  -11.6800  bl  2.5250  3.9930  b  -0.03391  b  -1.395  -2.4440  -7.6360  -1.8870  -3.9060  -5.9540  2.0180  1.9440  3.0950  2.0870  2.9160  2.2330  1.9720  -0.0.3106  -0.03127  -0.06403  -0.02598  -0.08390  -0.03160  -0.0230  0  2  n No. p l o t s  -0.1063  124  108  395  16  75  175  140  35  1072  15  9  40  2  10  22  34  4  136  Equation:  TEST HYPOTHESIS OF COMMON SLOPE F F(.05) DF(1) DF(2) Probability  =  -  8.65 1.70 14 1048 0.000  H, = b~ + b.A + b„A dom 0 1 2  where Region 1 2 3 4 5 6 7 8  Nabkoi Nanyuki Elburgon Likia Kiandongoro Kinale Turbo Timboroa  72 FIGURE  HEIGHT/AGE  S i  RELATIONSHIP GEOGRAPHICAL  8  FOR  P.  PATULA  BY  REGION  in.  10. rsi or  N A B K O I  rsi  N A N Y U K I  LU  ELBURGON L I K I A  ^ in.  KIANDONGORO  o o  K I N A L E TURBO TIMBOROA  in  - i 5  1 10 AGE  IN  YEARS  1 IS FROM  — r 20  PLANTING  73  TABLE 16.  Zone  R a i n f a l l data and e l e v a t i o n f o r g e o g r a p h i c a l r e g i o n s f o r s e p a r a t e s i t e index curves  Region  Forest district  Mean annual rainfall mm  Average elevation m  recognized  Weather station  Buret 1  Nabkoi  1160.6 (26)  2592  Nabkoi FS  908.3 (23)  2256  O n t u l i l i FS  1001.0 (25)  2317  Nanyuki FS  954.0 (10)  2287  G a t h i u r u FS  E l b u r g o n West  1093.6 (56)  2378  E l b u r g o n FS  Elburgon  1094.6 (23)  2439  N e s s u i t FS  Kiandongoro  1670.0 (24)  2378  Kiandongoro  Kabage  1373.8 (14)  2287  Kabage FS  1465.5 (14)  2591  Kamae FS  1170.0 (26)  1890  Turbo FS  Cengalo Nabkoi  Ontulili 2  Nanyuki  Nanyuki Gathiuru  3  4  Elburgon  Kiandongoro  East  Kamae 5  Kinale  Kimakia Kinale Kieni  6  Turbo  Turbo  Number i n b r a c k e t s r e f e r t o r e c o r d y e a r s . FS = F o r e s t S t a t i o n .  74  The  r e c o g n i t i o n t h a t h e i g h t development trends d i f f e r s  r e g i o n to another  i n Kenya i s a new f i n d i n g .  and Wanene (1975) developed whole c o u n t r y .  development i n the d i f f e r e n t  (1977)  curves  f o r the  16 the v a r i a b i l i t y i n h e i g h t  r e g i o n s cannot be w h o l l y a t t r i b u t e d to  d i f f e r e n c e s i n r a i n f a l l and e l e v a t i o n . Elburgon  For example A l d e r  a s i n g l e system of s i t e index  As can be seen from T a b l e  from one  F o r example Nanyuki r e g i o n and  r e g i o n a r e almost s i m i l a r i n terms of mean annual r a i n f a l l and  elevation.  Yet t h e i r h e i g h t development (curves 2 and 3 on F i g u r e 11)  are q u i t e d i f f e r e n t .  T h i s suggests  t h a t there may be o t h e r f a c t o r s  a f f e c t i n g growth, f o r example s o i l s , r a i n f a l l d i s t r i b u t i o n , i n t e r a c t i o n s of these w i t h r a i n f a l l  ( q u a n t i t y ) and a l t i t u d e and g e n e t i c s .  i n v e s t i g a t i o n s a r e needed to determine what f a c t o r s a r e most i n r e s p e c t to t h i s  Further important  variability.  S i t e Index Curves f o r P_. p a t u l a  F o r the permanent sample p l o t s from each r e g i o n , s i t e index was r e c a l c u l a t e d using equation the r e g i o n ( T a b l e fit  2.1 and 2.2 and the a p p r o p r i a t e equation f o r  15) t o o b t a i n H(15) and H^.  However, an attempt t o  the Chapman-Richards model (2.5) o r the m o d i f i e d W e i b u l l f u n c t i o n  (2.6)  t o the h e i g h t over age data  f o r each r e g i o n s e p a r a t e l y f a i l e d f o r  some, due t o the s h o r t range of ages covered Table  by the d a t a , as shown on  17 which g i v e s the range of data f o r each r e g i o n .  model f o r the d a t a , e q u a t i o n introduced:  The best  2.16 was t h e r e f o r e used and s i t e  linear  index  75  TABLE 17.  Height and age d a t a f o r ]?. p a t u l a by g e o g r a p h i c a l r e g i o n s  n  Region  Age  dom  Min.  Max.  Min.  Max.  No. of plots  No. of remeasurements  1.  Nabkoi  5.2  34.2  5.5  23.6  15  124  2.  Nanyuki  8.3  33.7  5.6  18.7  9  108  3.  Elburgon  6.4  30.5  3.6  22.6  40  394  4.  Kiandongoro  7.2  30.8  6.7  18.7  10  74  5.  Kinale  5.9  32.2  4.7  21.6  22  179  6.  Turbo  5.0  21.1  4.5  13.6  34  140  76  H  = b  + b S  Q  x  + b AS + b A 2  3  + b ^  + b^S  2.17  where v a r i a b l e l a b e l s are as b e f o r e .  F o r convenience s i o n e q u a t i o n was  and ease of r e g r e s s i o n a n a l y s i s , a n e s t e d r e g r e s -  f i t t e d , u s i n g dummy v a r i a b l e s to d i f f e r e n t i a t e between  the r e g i o n s .  Table  t i o n 2.17  the p r e d i c t e d h e i g h t s at ages 10 and  and  18 g i v e s the c o e f f i c i e n t s f o r the r e g r e s s i o n equa15 years f o r each  region. The n e s t e d r e g r e s s i o n 2.17 (.81  gave a lower  standard e r r o r of e s t i m a t e  meters) compared t o t h a t g i v e n by the n o n l i n e a r e q u a t i o n 2.13  P_. p a t u l a (1.14  meters).  Thus, s t r a t i f i c a t i o n of d a t a by g e o g r a p h i c a l  r e g i o n s l e d to h i g h e r p r e c i s i o n . 15 y e a r s f o r s i t e index 20 was 18) except expected  The p r e d i c t e d dominant h e i g h t at  f o r Turbo whose data d i d not cover t h i s age.  from the d e f i n i t i o n of s i t e i n d e x .  meters f o r Nabkoi t o 16.9  essence  of polymorphic  but have d i f f e r e n t  T h i s underscores  be of the same s i t e  the index  environmental  I t should be noted  f o r t h i s s p e c i e s shows very r a p i d  beyond the range covered by the data and avoided.  10 years v a r i e s between  growth c u r v e s , depending on the  c o n d i t i o n s under which the p l o t s are growing.  T h i s i s as  However, the p r e d i c t e d  meters f o r Turbo.  growth, t h a t p l o t s may  t h a t the q u a d r a t i c model used  age  about 20 meters f o r a l l r e g i o n s (Table  dominant h e i g h t f o r the same s i t e index at age 12.7  for  so e x t r a p o l a t i o n s h o u l d  here  decrease be  TABLE 18.  Regression C o e f f i c i e n t s  S  Region  Nabkoi  1.  Nanyuki  3.  Elburgon  4.  Kiandongoro  5.  Kinale  6.  Turbo  R^  = .98  SEE = .81 meters  AS  A  A  P r e d i c t e d values f o r S.I. 20  AS :  b  1.  f o r s i t e index curves f o r I_. p a t u l a by r e g i o n s  Q  b  x  b  2  b  3  -0.3148  b  4  b  0.01663  -0.002545  20.0  12.7  0.003034  19.8  14.8  5  H  1 5  H  1 Q  0.1831  -0.3322  0.1298  -13.0639  -0.1388  0.01763  3.1635  -0.1616  -9.5594  0.2714  0.05252  1.2761  -0.03566  -0.0005576  20.2  14.4  -21.0919  0.8502  4.2404  -0.1863  0.006048  20.5  15.6  0.2728  -0.007494  -0.0009530  19.8  13.8  -1.6231 2.2528  -0.8114  -0.03267  0.07984  -0.2011  0.1762  -1.2576  0.1199  -0.007974  -  16.9  78  Validating  S i t e Index Curves f o r ]?.  patula  A s i m i l a r procedure as used t o v a l i d a t e validate  e q u a t i o n 2.17 by s o l v i n g  e q u a t i o n 2.13 was used t o  f o r S and r e g r e s s i n g  predicted  site  i n d e x a g a i n s t age f o r each p l o t :  S = (H  d o m  - b  - b A - b A )/(b 2  Q  3  4  + b A + b A )  2.18  2  1  2  5  T a b l e 19 g i v e s the r e s u l t s .  TABLE 19.  Region  D i s t r i b u t i o n of p l o t s showing s i g n i f i c a n t s i t e index over age c o r r e l a t i o n a t .05 l e v e l f o r P. p a t u l a by geographical regions  T o t a l No. plots  Plots with s i g n i f i c a n t correlation No. %  Correlation significant + -  15  3  20.0  1  2  9  1  11.1  0  1  Elburgon  40  17  42.5  10  7  Kiandongoro  10  1  10.0  1  0  Kinele  22  5  22.7  2  3  Turbo  34  2  5.9  1  1  130  29  18.7  15  14  Nabkoi Namyuki  The  r e s u l t s of T a b l e 19 i n d i c a t e s  almost an equal number of p l o t s  showing both n e g a t i v e and p o s i t i v e c o r r e l a t i o n  f o r a l l regions.  The  79  t o t a l number of p l o t s w i t h s i g n i f i c a n t r e a s o n a b l e , the percentage  correlations i s also quite  f o r a l l r e g i o n s b e i n g lower than t h a t  o b t a i n e d on T a b l e 13, except f o r E l b u r g o n r e g i o n . index on age at  A p l o t of the  f o r the 17 p l o t s from E l b u r g o n w i t h s i g n i f i c a n t  .05 p r o b a b i l i t y l e v e l showed no apparent  t i o n s appeared  random and  trend.  site  correlation  Thus, these  correla-  t h e r e f o r e c o u l d be a t t r i b u t e d e i t h e r t o  measurement e r r o r s or i n t e r r u p t i o n of dominant h e i g h t development discussed e a r l i e r .  S i t e Index curves f o r P. p a t u l a as d e f i n e d by  e q u a t i o n (2.17) f o r each r e g i o n were t h e r e f o r e a c c e p t e d .  The F i n a l  Curves  As mentioned e a r l i e r , the d e f i n i t i o n of s i t e index r e q u i r e s t h a t a t r e f e r e n c e age,  s i t e i n d e x equals stand dominant h e i g h t .  the s t a t i s t i c a l nature of the curve f i t t i n g procedure, was  found t o be not s a t i s f i e d .  this  condition  t o 20.5  15 years as used i n t h i s  meters f o r s i t e index 20 f o r _P. p a t u l a .  S i m i l a r v a r i a t i o n e x i s t e d f o r C. l u s i t a n i c a and P_. r a d i a t a . was  to  For example T a b l e 18 above shows that  the p r e d i c t e d dominant h e i g h t at r e f e r e n c e age study v a r i e d between 19.8  However, due  This r e s u l t  not s u r p r i s i n g s i n c e the l e a s t squares procedure used t o f i t the  curves assumed dominant h e i g h t and i s not the case. guarantee  s i t e i n d e x to be independent,  In o t h e r words, t h e r e was  no b u i l t  i n procedure  which to  t h a t dominant h e i g h t w i l l equal s i t e index at r e f e r e n c e age.  To i n s u r e t h a t t h i s c o n d i t i o n was procedure was  used:  s a t i s f i e d , the f o l l o w i n g  conditioning  80  For £ . l u s i t a n i c a and ?. r a d i a t a :  At  age 15 y e a r s we r e q u i r e  that:  -biAS H  dom  where b*Q H  Thus  =  -  S  dom =  s  a  t  (1 -  —.  b  e  A  § —  where c = e  b  1 9  t h a t s a t i s f i e s the c o n d i t i o n :  S  b  —  B  s  5  '  g v A O v.— " l ) 2  (1 - C )  1  2  age 15 y e a r s .  =  _  bo  >  e  by c o e f f i c i e n t  =  b*n 0  *0<! "  b  2.20  2  l A  Thus t h e f i n a l e q u a t i o n f o r £ . l u s i t a n i c a and P_. r a d i a t a s i t e index curves was:  dom  )  f btASNb, 2 L____ ( l - e  c  =  1  o Do  (1 - c ) S  \»  2.21  J  2  where a l l v a r i a b l e s a r e as b e f o r e .  T h i s c o n d i t i o n i n g c o u l d o n l y be done n u m e r i c a l l y e q u a t i o n cannot be s o l v e d by l e a s t shows the f i n a l  squares method.  since  Figures  this 9 and 10  curves f o r C. l u s i t a n i c a and P. r a d i a t a u s i n g  equation  SITE  INDEX  CURVES  FIGURE  9  FOR  LUSITANICA  C,  IN  KENYA  FIGURE INDEX  CURVES  FOR  P.  1 10  AGE  IN  10 RADIATA  1  1  15  YEARS  IN  :  20  FROM  PLANTING  KENYA  r^5  83  F o r JP. p a t u l a :  The c o n d i t i o n i n g of e q u a t i o n 2.17 was 2.18  accomplished  through  equation  as f o l l o w s :  Let  S* be the s i t e index d e f i n e d by the model.  Let  S  be the s i t e index t h a t w i l l i n s u r e that s i t e index = dominant h e i g h t a t age 15 y e a r s .  Then at age 15 y e a r s :  H  dom  =  S  *  =  S  (  b  l  +  b  S* - ( b  2  A  +  b  5  A  2  )  +  ( b  0  +  b  3  A  +  b  4  2.22  A 2 )  + b A + b A ) 2  0  3  4  2.23  S = (b  x  + b A  S* - c  2  x  + b  A ) 2  5  where c c  = b  l  2  = b  Q  l  + b (15) + b ( 1 5 )  2  + b (15) + b ( 1 5 )  2  3  2  4  5  Thus, the c o n d i t i o n i n g of the s i t e index model f o r P. p a t u l a was through n u m e r i c a l adjustment of the s i t e index of i n t e r e s t .  F i g u r e 11  g i v e s the s i t e i n d e x curves f o r P. p a t u l a f o r Nabkoi r e g i o n o n l y .  FIGURE  SITE  INDEX  CURVES  FOR  NABKOI  11  P,  PATULA  GROUP  IN  KENYA  85  2.0  M o r t a l i t y , Stand D e n s i t y Development, and i n Kenya  2.1  Thinning Practices  Plantations  Mortality  As  defined  by Husch et a l . , 1972,  m o r t a l i t y i s the number or volume  of t r e e s p e r i o d i c a l l y rendered unusable through n a t u r a l old  age,  competition,  t i o n , two  i n s e c t and  diseases,  types of stand m o r t a l i t y can be  wind, e t c .  throws, e t c .  The  Natural studies  From t h i s d e f i n i -  and  and  the  i r r e g u l a r type  insect attack,  fire,  l a t t e r c a t e g o r y can range from i n s i g n i f i c a n t  trophic, occurring  at i n t e r m i t t e n t  i n t e r v a l s during  the  life  m o r t a l i t y i s c e n t r a l to stand dynamic and  (1980), Lee  (1974) and  others.  very l i t t l e  understood and  by  Smith and  to  catas-  of a stand.  i n growth  and  W i l l i a m s (1980), Hamilton  I r r e g u l a r m o r t a l i t y on the  very d i f f i c u l t  wind-  simulation  procedures f o r d e a l i n g w i t h t h i s type of m o r t a l i t y  y i e l d models have been d i s c u s s e d  as  i d e n t i f i e d ; t h a t a r i s i n g from  n a t u r a l m o r t a l i t y as a r e s u l t o f c o m p e t i t i o n a r i s i n g - from u n n a t u r a l causes; d i s e a s e s  causes such  to p r e d i c t .  other hand i s  A c c o r d i n g to  Lee  (1974), s t a t i s t i c a l procedures are a v a i l a b l e f o r t r e a t i n g t h i s type of m o r t a l i t y , e.g.  t r e a t i n g i t as an o v e r a l l p r o b a b i l i t y or  process f o r a given  area.  The  stochastic  major problem however Is r e l a t e d to  a v a i l a b i l i t y of adequate data needed to develop the models. example, windthrow may patterns  and  silvicultural  the  be  r e l a t e d not  r o o t systems of the  treatments t h a t the  For  o n l y to the r e g i o n a l weather species  stands have  but  a l s o to  received.  the  86  Because of the i n t e n s i v e l e v e l of p l a n t a t i o n management i n Kenya, n a t u r a l m o r t a l i t y a r i s i n g out existant after f i r s t  of c o m p e t i t i o n  thinning.  diseased,  r e m a i n i n g stems are h e a l t h y  competition  t h a t may  be  considered  T h i s i s because the  d e s i g n e d to remove dead, d y i n g , t h a t the  may  and  first  w o l f e d and therefore  non-  thinning i s  suppressed stems so  able  occur b e f o r e the next t h i n n i n g .  to w i t h s t a n d  Before  any  first  t h i n n i n g however, m o r t a l i t y might o c c u r , e s p e c i a l l y i f t h i n n i n g i s d e l a y e d beyond the p r e s c r i b e d  stage.  However, there was  no evidence of  m o r t a l i t y i n the a v a i l a b l e p.s.p. d a t a . I r r e g u l a r m o r t a l i t y on the other hand i s a constant t h r e a t  to  p l a n t a t i o n management, as mentioned e a r l i e r i n Chapter 1.  Although  of d a t a may  addressed i n  be  c i t e d as the reason why  t h i s study, the while.  t h i s problem i s not  view i s a l s o taken t h a t t h i s e f f o r t would not  T h i s i s because f o r e s t managers are  constantly  disease  c o n t r o l so t h a t any  b e f o r e i t i s ready f o r  2.2  m o r t a l i t y model may  w e l l be  insect  invalid  use.  Stand D e n s i t y Development  D e f i n i t i o n and The  Importance of Stand D e n s i t y  growth r a t e of an i n d i v i d u a l t r e e i s determined by i t s g e n e t i c  c h a r a c t e r i s t i c s , the s i t e q u a l i t y and able  be worth-  improving f o r e s t  p r o t e c t i o n procedures such as f i r e p r o t e c t i o n , game damage and and  lack  to i t .  Stand d e n s i t y  to which a given character  the amount of growing space  avail-  r e f e r s to the measure of the aggregate degree  t r e e s p e c i e s u t i l i z e s the  of an i n d i v i d u a l t r e e and  growing space.  s i t e q u a l i t y can  be  The  genetic  manipulated  87  through  t r e e b r e e d i n g t e c h n i q u e s and through use of f e r t i l i z e r s and s i t e  p r e p a r a t i o n techniques control; i n i t i a l  respectively.  However, i t i s through  s p a c i n g , t h i n n i n g and o t h e r s i l v i c u l t u r a l  density techniques  t h a t t h e f o r e s t manager has t h e best chance of d i r e c t i n g growth towards the d e s i r e d g o a l s and o b j e c t i v e s .  T h i s i s one of the reasons why the  e f f e c t s o f s t a n d d e n s i t y on stand development has been so e x t e n s i v e l y studied.  Some of t h e important  studies include:  Braathe  (1957),  Beekhuis (1966), Marsh (1957), Cromer and Pawsey (1957), A d l a r d Newnham and Mucha (1971), Baskerville  (1957),  Smith and W i l l i a m s (1980), Hummel (1947) and  (1965).  Measures o f Stand D e n s i t i e s S e v e r a l measures o f stand d e n s i t y have e v o l v e d over the y e a r s , the b a s i c ones being volume per u n i t a r e a , b a s a l area per u n i t area and number of stems p e r u n i t a r e a .  These measures have been very w i d e l y  used mainly because they a r e simple and e a s i l y understood.  However,  they a r e r e l a t e d t o age and s i t e q u a l i t y , which i s a disadvantage the s t a n d d e n s i t y i s r e q u i r e d t o express Stand to  the degree of s i t e  when  occupancy.  d e n s i t y e x p r e s s i o n s t h a t a r e independent of age and s i t e ,  referred  as stand d e n s i t y i n d i c e s ; have t h e r e f o r e come i n t o g e n e r a l u s e .  Examples o f these a r e Reineke's stand d e n s i t y index Chisman and Schumacher's t r e e area e q u a t i o n 1940)  (Reineke  1933),  (Chisman and Schumacher  and Schumacher and C o i l e ' s s t o c k i n g p e r cent (Schumacher and C o i l e  1960).  For f u l l  d e t a i l s on these, see Husch, M i l l e r and Beers (1972)  Chapter  17-2, C u r t i s (1970), Crowe (1966),  i n d i c e s mentioned above i s the  etc.  Among the stand d e n s i t y  s p a c i n g between t r e e s expressed  i n terms  88  of  stand dominant h e i g h t , r e f e r r e d  t o i n some f o r e s t r y  literature  as  Hart's d e n s i t y index and i n o t h e r s as H a r t - B e c k i n g stand d e n s i t y i n d e x (Crowe 1967,  W i l s o n 1979).  T h i s stand d e n s i t y index has been very  w i d e l y used i n t h i n n i n g r e s e a r c h i n Europe (Braathe 1957), South (Crowe 1967) interest  and N o r t h America  i n t h i s study.  (Wilson 1979)  and i s of  Africa  particular  I t i s t h e r e f o r e d i s c u s s e d below i n g r e a t e r  details.  H a r t s Stand D e n s i t y Index T h i s stand d e n s i t y index was according to Wilson  first  proposed  (1979), the concept  (1928) but  of s p a c i n g had been used i n  Denmark as f a r back as 1851 where I t may  R e l a t i v e d i s t a n c e of t r e e s =  by Hart  have been f o r m u l a t e d a s :  Height  The p r e s e n t d e f i n i t i o n of t h i s index can take any of the two  1.  forms:  F o r square s p a c i n g :  S%  -  H  100 dom  2.25  89  2.  For t r i a n g u l a r  spacing: f  S%  10.000 x S i n 60 No. t r e e s / h a  c  -  . 100  2.26  dom where S% = Stand  d e n s i t y index.  Between these two forms, the square much wider acceptance,  s p a c i n g formula has r e c e i v e d a  mainly because i t i s f r e e of the c o n s t a n t ( S i n  60°) and t h e r e f o r e much e a s i e r t o a p p l y .  However, one problem a s s o c i a t e d  w i t h use of t h i s index i s t h a t i t assumes a r e g u l a r s p a c i n g i n t h e s t a n d , even a f t e r r e p e a t e d t h i n n i n g .  T h i s may not always be t r u e . I t s  main advantages a r e t h a t i t i s l a r g e l y Independent of stand age, s i t e q u a l i t y and s p e c i e s , b e s i d e s b e i n g simple and easy t o a p p l y . One of the d e s i r a b l e c h a r a c t e r i s t i c s of a stand d e n s i t y  index  e x p r e s s i o n i s t h a t i t should g i v e an i d e a o f the degree t o which an a r e a i s b e i n g u t i l i z e d by t r e e s . f u l l y account two  As i t s t a n d s , H a r t s d e n s i t y index does n o t  f o r t h e degree of s i t e u t i l i z a t i o n .  F o r example, c o n s i d e r  stands o f the same stand dominant height and the same s p a c i n g .  A c c o r d i n g t o t h i s index, the two would have t h e same d e n s i t y index. if  one had been t h i n n e d t o the present d e n s i t y e a r l i e r  I t would have a c o n s i d e r a b l y h i g h e r b a s a l a r e a . e s p e c i a l l y important  than the o t h e r ,  T h i s shortcoming i s  i n i n t e n s i v e l y managed p l a n t a t i o n s where the  h i s t o r y of stand treatment y i e l d determination.  Yet  i s an important  c o n s i d e r a t i o n i n growth and  I t s h o u l d a l s o be noted t h a t stand dominant h e i g h t  i s used i n s t e a d of stand mean h e i g h t , because the former i s l i t t l e a f f e c t e d by stand t r e a t m e n t s ,  especially thinning.  90  Stand D e n s i t y Development f o r t h e P l a n t a t i o n S p e c i e s i n Kenya (based on H a r t s D e n s i t y Index) The  o p i n i o n over whether stands  should be managed a t constant  d e n s i t y index o r not d i f f e r s among f o r e s t e r s .  F o r example, Hummel and  C h r i s t i e (1953) favoured maintenance of constant r o t a t i o n p e r i o d , w h i l e Becking  index throughout  ( a c c o r d i n g to Braathe  t h i n n i n g t o a constant  the .  1957) recommended  c o n s t a n t index f o r D o u g l a s - f i r and p o p l a r s and a d e c r e a s i n g index f o r beech and l a r c h i n H o l l a n d .  stand  ( w i t h age)  Another s t r o n g proponent o f  stand d e n s i t y index i s W i l s o n  (1979) who recom-  mended l e a v i n g a s p a c i n g o f 20.6% o f dominant h e i g h t a f t e r each t h i n n i n g at  S t a r Lake, Minnesota.  S%, t h i n n i n g schedules New Zealand  Although  not e x p l i c i t l y d e f i n e d i n terms of  f o r P_. p a t u l a and P_. r a d i a t a i n South A f r i c a and  r e s p e c t i v e l y a r e d e f i n e d i n terms of number of stems p e r  h e c t a r e t o be l e f t  a t a g i v e n stand dominant h e i g h t (Crowe 1967, Fenton  1972), which t r a n s l a t e s to t h i n n i n g to a constant  d e n s i t y index.  In  g e n e r a l , t h i n n i n g to a c o n s t a n t d e n s i t y index i s f a v o u r e d , i f o n l y because i t p r o v i d e s an o b j e c t i v e c r i t e r i a f o r d e c i d i n g when a stand i s due  forthinning. As  shown on T a b l e 5 of Chapter  1 on s i l v i c u l t u r e , the f i r s t  thin-  n i n g f o r a l l t h e three s p e c i e s i n Kenya i s d e f i n e d i n terms o f number o f stems t o be l e f t to  at a s p e c i f i e d  stand dominant h e i g h t .  This translates  an S% o f about 30%, 25.5% and 27.7% f o r C_. l u s i t a n i c a , P_. p a t u l a and  P_. r a d i a t a r e s p e c t i v e l y a f t e r f i r s t  thinning.  F o r 1?. r a d i a t a , 2nd  t h i n n i n g i s d e f i n e d s i m i l a r l y and t r a n s l a t e s t o the same S% a f t e r  91  thinning.  The  P_. p a t u l a and  2nd  and  subsequent t h i n n i n g  a l s o subsequent t h i n n i n g s  terms of number of stems to be thinnings  are  f o r C_. l u s i t a n i c a and  f o r P_. r a d i a t a are d e f i n e d  l e f t a f t e r each t h i n n i n g w h i l e  spaced at constant time i n t e r v a l s .  The  in  the  e f f e c t s of t h i s  p r a c t i c e on S% development i n the d i f f e r e n t s i t e index c l a s s e s are shown on F i g u r e  12a,b  and  respectively. 1.  The  c f o r C_. l u s i t a n i c a , P_. p a t u l a and f i g u r e shows:  F o r C_. l u s i t a n i c a S% v a r i e s between 18-30% w h i l e f o r P. and  2.  Stand d e n s i t y  index (S%) v a r i e s f o r the d i f f e r e n t s i t e  f o r each s p e c i e s , w i t h wide s p a c i n g  poor s i t e and  overcrowing on good s i t e s .  C_. l u s i t a n i c a , S% while that  t h a t the  full  f o r s i t e index 24 i s  s i t e capacity  thus d e p r i v i n g  on poor s i t e s i s not  the e f f e c t s o f s p a c i n g  t r e e diameter development. t i o n p o i n t of view.  To  y i e l d are not  For example f o r  fully  (S%) on  exploited In  while  addition,  stand development,  of the b a s i c t o o l s f o r c o n t r o l of  This i s e s p e c i a l l y c r i t i c a l  from a  utiliza-  d a t e , the e f f e c t s of the present schedules known and  30%  that i t i s l i k e l y  be a f f e c t i n g growth.  the management o f one  on  20%.  of t h i s p r a c t i c e are  overcrowding on v e r y good s i t e s may t h i s p r a c t i c e ignores  developing  f o r f i n a l t h i n n i n g on s i t e index 12 i s  p r a c t i c a l implications  growth and  patula  P_. r a d i a t a , i t v a r i e s between 15-25%.  qualities  The  P_. r a d i a t a  on  i t i s hoped t h a t r e s u l t s from t h i s  study w i l l p r o v i d e some knowledge on the magnitude of these e f f e c t s .  92 FIGURE 12 NO. STEMS/HEIGHT/S% RELATIONSHIP BY SPECIES AND  (A) C. LUSITANICA  Ul z  o  s  5  P. PATULA (Nabkoi) SITE  SITE  o. in S.77  SITE INDEX CLASSES IN KENYA  .200  4  t h  3'  thinning  INDEX  12  15  18  r  I  I  IS  S%  21 24 T__ff  I  30 25 20 18  _T— "  5.77. 2 0 0  3  r d  408-600  7  3.16-1000'  2.89-1200  2.67-1400  2.5-1600  / / //  //  / / / / / /  3.16*1000  /  / /  2.89.1200^  '//  /  1 ,  600\  3 . 5 4 . 800  7 7  2.67.1400  10  ! '  1600  —I— DOMINANT  HEIGHT  1  20  10  30  •/-——  IN  METER  Cc ) P. RADIATA 3 z z  SITE  o  21  r  INDEX 24  27  30  T i l l  33  sr. - 20  5.77-200  — 15  4 ' thinning rd n  3  5.00-400  «nd  /A  4.08-600  3.54-800'  3.16-1000  2.89-1200  2.67-1400'  2.5-1600  1»«  / / /  n  7 1 I  I  n 1 ; 10 DOMINANT  20 HEIGHT  S  ^  -  4  orrd 4.08.  24 27  1 I 1 l__30 — _**.—. 25  thinning  2nd  5-00. 4 0 0  5 0 0 . 400  / / /  18 21  •  d  3.54-800  INDEX  >° IN  METER  40  *  15  93  2.3  Thinning Definition:  Braathe (1957) d e f i n e d  some of the stems i n an immature stand remaining t r e e s b e t t e r c o n d i t i o n s quality.  of t r e e s i n order  f o r growing and  to g i v e  the  p r o d u c i n g wood of  However, t h i s d e f i n i t i o n i s inadequate without f u r t h e r  f i c a t i o n as 1.  t h i n n i n g as the a c t of removing  quali-  to:  Type of  thinning  This q u a l i f i c a t i o n describes  the t r e e s to be removed; based  the p o s i t i o n of the t r e e s w i t h r e s p e c t t i o n or tree s i z e s .  For example low  removal of the s m a l l e s t  to e i t h e r s p a t i a l  codominant The  t h i n n i n g which i d e a l l y  implies  t r e e s , s t a r t i n g w i t h the suppressed ones or  d e f i n i t i o n of types of t h i n n i n g s  i s w e l l documented i n  Smith (1962) pages 90-94.  be noted t h a t i n p r a c t i c e , most t h i n n i n g s  t i o n of two  or t h r e e  changes and  the i n d i v i d u a l stand  However,  are a combina-  types at the same time o r i n sequence.  i s because the t h i n n i n g o b j e c t i v e s change as the  2.  and  categories.  most t e x t s on s i l v i c u l t u r e e.g. should  on  distribu-  h i g h t h i n n i n g , which i d e a l l y removes t r e e s from the dominant  it  high  stand  This  structure  develops.  Thinning i n t e n s i t y T h i s r e f e r s to the p r o p o r t i o n t h i n n i n g as a f u n c t i o n of the stand  of the stand before  removed i n  thinning.  measures of t h i n n i n g i n t e n s i t y have been used.  Several  94  The r a t i o d/D a t t r i b u t e d t o E i d e and L a n g s a e t e r (Braathe 1957) where: d  =  Mean DBH o f t r e e s removed i n a t h i n n i n g  D  =  Mean DBH of t r e e s b e f o r e  thinning.  T h i s r a t i o b a s i c a l l y measures the type of t h i n n i n g c a r r i e d out.  Thus a c c o r d i n g  to the above a u t h o r s ,  t h i n n i n g types can be d e f i n e d the r a t i o  according  to the value of  d/D:  £0.70  =  Low  thinning  0.70 to .85  =  No d e f i n i t e low or crown t h i n n i n g  0.85 to 1.0  =  Crown  > 1  =  Selection thinning  thinning  T h i s r a t i o has been used by Reukema and Bruce (1977) to d e f i n e the recommended  t h i n n i n g type f o r D o u g l a s - f i r .  The number of t r e e s to be removed at each t h i n n i n g , expressed e i t h e r as a pure number or as a p r o p o r t i o n o f initial  stand  d e n s i t y ; such as i s p r e s e n t l y p r a c t i c e d i n  Kenya. Basal area area and  ( o r volume) removed as a p r o p o r t i o n  ( o r volume) before Bruce (1977) d e f i n e d  thinning.  For example Reukema  the i n t e n s i t y of t h i n n i n g f o r  D o u g l a s - f i r i n terms o f the minimum recommended b a s a l a r e a to be maintained i n the stand thinning.  of b a s a l  residual  a f t e r each  The F o r e s t Management T a b l e s ( M e t r i c ) f o r  Great B r i t a i n use the same p r i n c i p l e by d e f i n i n g the  95  m a r g i n a l t h i n n i n g i n t e n s i t y i n terms o f t h e annual r a t e o f volume removal e q u i v a l e n t annual increment.  t o 70% o f the maximum mean  This proportion represents  the maximum  t h i n n i n g i n t e n s i t y which can be maintained without l o s s of volume p r o d u c t i o n  3.  Thinning  cycle:  (Hamilton and C h r i s t i e  1971).  which r e f e r s t o the p e r i o d i c i t y o f t h i n n i n g .  Choice o f t h i n n i n g c y c l e i s a f u n c t i o n of both economic and b i o logical  considerations.  F o r example, frequent  but l i g h t  thinnings  are p r e f e r r e d from y i e l d and b i o l o g i c a l c o n s i d e r a t i o n s while ( l o n g e r c y c l e s ) but h e a v i e r economic p o i n t o f view.  fewer  t h i n n i n g s a r e a t t r a c t i v e from an  The b i o l o g i c a l c o n s i d e r a t i o n s  often  o v e r r i d e the economic c o n s i d e r a t i o n s m a i n l y because the main concern i s the growth c o n d i t i o n s o f the remaining stand.  Thus,  a l t h o u g h not i m p l i c i t l y s t a t e d , the t h i n n i n g c y c l e f o r D o u g l a s - f i r (Reukema and Bruce 1977) i s d e f i n e d by the growth r a t e of the stand,  the time i t takes f o r the b a s a l area t o grow from the recom-  mended r e s i d u a l l e v e l t o the maximum b a s a l a r e a , where maximum i s defined  as the approximate maximum b a s a l a r e a t o which a g i v e n  number o f merchantable t r e e s should The  be grown i n a managed  stand.  concept of maximum s i z e - d e n s i t y advocated by Drew and  F l e w e l l i n g (1979) f o r c o n t r o l o f p l a n t a t i o n d e n s i t y f o r D o u g l a s - f i r i n New Zealand r e i n f o r c e s t h e importance o f b i o l o g i c a l t i o n i n determining  the t h i n n i n g c y c l e .  t h a t t h e t h i n n i n g type,  I t should  considera-  however be noted  t h i n n i n g i n t e n s i t y and t h i n n i n g c y c l e a r e  v e r y c l o s e l y i n t e r r e l a t e d and c h o i c e o f one i n f l u e n c e s the o t h e r .  96  Thus the f o r e s t manager has  to compromise between the  d e s i r a b i l i t y of a t h i n n i n g and determining  the economic c o n s i d e r a t i o n s when  both the t h i n n i n g i n t e n s i t y and  c h o i c e of one a f f e c t s the  biological  thinning cycles, since  other.  T h i n n i n g Type and I n t e n s i t y f o r P l a n t a t i o n S p e c i e s i n Kenya So f a r , the t h i n n i n g schedules  f o r the t h r e e s p e c i e s have been  d e s c r i b e d i n terms of t h i n n i n g c y c l e (time i n t e r v a l s between t h i n n i n g s ) and  i n t e n s i t y ( i n terms of number of stems and  t o d e s c r i b e the t h i n n i n g type and will  r e v e a l both the s i z e and  terms of mean D B H and  spacing  (S%).  I t remains  the t h i n n i n g i n t e n s i t y i n terms t h a t  the p r o p o r t i o n of the stand removed i n  b a s a l area of stand b e f o r e t h i n n i n g .  of data f o r t h i s study i s shown on T a b l e 20 by s p e c i e s and v a r i a b l e s as measured on the permanent sample p l o t s .  The  summary  basic  From these  v a r i a b l e s , o t h e r d e s c r i p t i v e v a r i a b l e s , the r a t i o s of the b a s a l a r e a , D B H and number of stems were d e r i v e d . c a t e g o r i z e d as precommercial y e a r s ) or 1.  In a d d i t i o n , each t h i n n i n g  (those which took p l a c e at ages <  was  13.5  commercial.  Mean D B H of thinning/mean D B H b e f o r e t h i n n i n g r a t i o T a b l e 21 shows the r a t i o s of the mean D B H o f t h i n n i n g s to mean D B H  of stand b e f o r e t h i n n i n g f o r precommercial,  commercial and  combined  t h i n n i n g s f o r each s p e c i e s . The  f o l l o w i n g o b s e r v a t i o n s can be noted 1.  That and  from t h i s  table.  DBH(T)  f o r a l l three s p e c i e s the r a t i o T J B H ( B T ) commercial t h i n n i n g s are almost  ^  ,  precommercial  equal a l t h o u g h those f o r  97  TABLE 20.  Variable  Summary of t h i n n i n g d a t a by s p e c i e s  Species  and r e l e v a n t  Mean  Mininum  Maximum  variables  Standard deviation  Age of thinning (years)  C. l u s i t a n i c a P. p a t u l a P. r a d i a t a  117 139 121  12.1 11.0 11.5  5.6 5.7 5.5  30.4 24.5 30.4  5.6 4.2 4.8  Dominant height (m)  £. l u s i t a n i c a P. p a t u l a P. r a d i a t a  117 139 121  16.0 17.2 20.6  7.6 8.0 5.9  30.2 35.4 44.2  5.6 6.5 8.3  No. stems thinned  C. l u s i t a n i c a P. p a t u l a P. r a d i a t a  117 139 121  289 278 2706  74 74 49  791 1161 988  195 185 196  No. stems before thinning  C. l u s i t a n i c a P. p a t u l a P. r a d i a t a  117 139 121  1007 908 959  198 222 99  1631 1680 2001  400 347 422  DBH of thinning (cm)  C. l u s i t a n i c a P. p a t u l a P. r a d i a t a  117 139 121  18.4 17.5 15.5  6.2 7.2 3.2  51.0 35.7 45.8  8.4 5.8 8.1  DBH before thinning  C. l u s i t a n i c a P. p a t u l a P. r a d i a t a  117 139 121  21.3 19.9 18.9  10.2 8.6 7.6  45.1 37.0 47.9  8.4 5.9 7.9  Basal a r e a of thinning  C. l u s i t a n i c a P. p a t u l a P. r a d i a t a  117 139 121  6.5 6.3 4.6  0.3 0.4 0.1  22.5 21.5 15.1  4.2 4.2 3.4  Basal area before thinning  £• l u s i t a n i c a P. p a t u l a P. r a d i a t a  117 139 121  29.9 25.9 22.5  7.6 2.4 7.4  53.0 57.4 45.8  10.0 9.7 9.1  98  TABLE 21.  Mean DBH o f thinning/mean DBH b e f o r e t h i n n i n g  Mean D  B  5 5 5  m (BT) H  Minimum  Maximum  relationship  Standard deviation  Precommercial C. l u s i t a n i c a  .84  ,53  1.0  .11  75  P_. p a t u l a  .87  .59  1.1  .09  91  P. r a d i a t a  .77  .30  1.0  .15  82  Commercial £. l u s i t a n i c a  .88  .54  1.13  .11  42  P. p a t u l a  .89  .66  1.05  .07  48  P. r a d i a t a  .86  .45  1.10  .14  39  Combined C. l u s i t a n i c a  .85  .53  1.13  .11  117  P.  .88  .59  1.10  .09  139  .80  .30  1.10  .15  121  patula  P. r a d i a t a  99  precommercial are s l i g h t l y lower. d i f f e r e n c e was  expected between these two  s i n c e w i t h commercial t h i n n i n g s , systematic  there  to o f f s e t  types of  thinnings  i s a tendency towards a  cost of t h i n n i n g , w h i l e precommercial  are aimed at stand  h y g i e n e , removing t r e e s mostly  from the lower diameter c l a s s e s . been p a r t l y reduced by  T h i s d i f f e r e n c e may  have  the presence of wolfed t r e e s which are  u s u a l l y removed d u r i n g precommercial The  bigger  type of t h i n n i n g so as to remove some stems of  economic v a l u e thinnings  In g e n e r a l , a  thinnings.  combined r a t i o f o r C_. l u s i t a n i c a and  that  f o r P.  patula  are almost equal w h i l e t h a t f o r P_. r a d i a t a i s s l i g h t l y T h i s may  reflect  the e f f e c t s of d o t h i s t r o m a pine  lower.  disease  mentioned i n Chapter 1 s i n c e t h i n n i n g , e s p e c i a l l y precommerc i a l , removes d i s e a s e d  t r e e s as a  priority.  Based on the c l a s s i f i c a t i o n of E i d e t o Braathe  1957)  corresponds to no  the r a t i o  QBH(BT)  F  O  R  Langsaeter -  R  A  D  I  A  T  A  (according (°« °) 8  d e f i n i t e low or crown t h i n n i n g w h i l e  f o r C_. l u s i t a n i c a and P_. p a t u l a borders on the  and  ( 0 . 8 5 and  that  0 . 8 8 respectively)  lower s i d e of crown t h i n n i n g .  100  2.  B a s a l area o f t h i n n i n g / b a s a l a r e a b e f o r e t h i n n i n g r a t i o and number of stems thinned/number o f stems b e f o r e t h i n n i n g r a t i o  Both of these r a t i o s f o l l o w e d e x a c t l y t h e same p a t t e r n as f o r t h e DBH(BT)  Tat  -^°>  except  f°  r  t h e magnitude.  Table  f o r t h e b a s a l a r e a r a t i o f o r t h e precommercial, data by s p e c i e s .  22 shows the magnitude commercial and combined  The t a b l e i n d i c a t e s t h a t the average l e v e l of b a s a l  a r e a removal i s between 20-25% o f the b a s a l a r e a b e f o r e t h i n n i n g although  3.  i t can be as low as 1% and as h i g h as 70%.  Mean DBH o f t h i n n i n g The mean DBH o f stems removed i n a t h i n n i n g can be expected  t o be a  function of: (1)  Mean diameter  (2)  T h i n n i n g type:  of stand b e f o r e t h i n n i n g . F o r example, mean DBH of t h i n n i n g s i n low-  t h i n n i n g can be expected  t o be lower  than mean stand DBH  b e f o r e t h i n n i n g , mean DBH o f t h i n n i n g s i n s e l e c t i o n t h i n n i n g would be h i g h e r than mean stand DBH b e f o r e t h i n n i n g . (3)  Weight of t h i n n i n g s :  In low, crown or i n s e l e c t i o n t h i n n i n g ,  t h e h e a v i e r the t h i n n i n g , the c l o s e r would t h e i r mean DBH approach t h e mean stand DBH b e f o r e t h i n n i n g . Other v a r i a b l e s t h a t can a f f e c t the mean DBH o f t h i n n i n g s i n c l u d e s t a n d dominant h e i g h t and age.  P r e l i m i n a r y i n v e s t i g a t i o n s however  i n d i c a t e d the stand mean DBH b e f o r e t h i n n i n g as the v a r i a b l e best c o r r e l a t e d w i t h mean DBH of t h i n n i n g s .  101  TABLE 22.  B a s a l a r e a of t h i n n i n g / b a s a l a r e a b e f o r e  Mean ratio  Minimum  Maximum  thinning  ratios  Standard deviation  Precommercial Cypress  .22  .02  .56  .12  75  P.  patula  .24  .03  .70  .12  91  P.  radiate  .19  .01  .56  .13  82  Commercial Cypress  .22  .06  .61  .11  42  P.  patula  .25.  .05  .71  • 14  48  P.  radiate  .23  .02  .68  .13  39  Combined Cypress  .22  .02  .61  .12  117  P.  patula  .24  .03  .71  .13  139  P.  radiata  .20  .01  .68  .13  121  102  BA ( T ) As a measure o f weight o f t h i n n i n g the r a t i o g ^ g ^ ) was b e t t e r  c o r r e l a t e d t o mean DBH of t h i n n i n g s expected s i n c e b a s a l area number o f stems. probability  i s a b e t t e r measure of stand  Both r a t i o s  showed s i g n i f i c a n t  This density  correlation  i s as than  a t .05  l e v e l except f o r the r a t i o o f number of stems f o r  C. l u s i t a n i c a .  F o r t h i s s t u d y , one t h i n n i n g o p t i o n i n the e n v i s a g e d  y i e l d model r e q u i r e d stems t o be l e f t appropriate  than the r a t i o ^jjjfy  t h a t t h i n n i n g s be d e f i n e d  after  the t h i n n i n g .  i n terms of number of  For t h i s option t h e r e f o r e , the  measure of weight of t h i n n i n g i n the DBH o f t h i n n i n g  e q u a t i o n was ^ g j ) •  The f o l l o w i n g m u l t i p l e l i n e a r e q u a t i o n was  formulated:  DBH(T) = b  Q  + b  1  DBH(BT) + b  9 97  N(T)  l  2  T a b l e 23 shows the e s t i m a t e d parameters and other statistics  relevant  f o r t h e r e s p e c t i v e e q u a t i o n s f o r each s p e c i e s .  independent v a r i a b l e s were s i g n i f i c a n t  '^>  at .05 p r o b a b i l i t y  A l l the level,  i n c l u d i n g those f o r £ . l u s i t a n i c a w h i l e the study of r e s i d u a l s i n d i c a t e d no  systematic  trends.  103  TABLE  Parameter e s t i m a t e s and o t h e r thinning equation 2.27  23.  s t a t i s t i c s f o r the.DBH of  Species -  . C.  b  0  b  l  b  2  n R  2  radiata  -2.1596  -4.5192  .9508  .9262  .9637  5.2153  4.0669  6.1003  121  117  139  .92  .92  .91  1.64  2.42  cm  cm  o t h e r t h i n n i n g o p t i o n i n the envisaged  cm  (15.6%)  (9.4%)  (12.9%)  The  P.  patula  -3.3840  2.37  SEE  P.  lusitanica  model r e q u i r e d t h a t  t h i n n i n g be d e f i n e d i n terms of p r o p o r t i o n of b a s a l area to be removed at each t h i n n i n g .  Thus i f b a s a l a r e a b e f o r e t h i n n i n g i s known, b a s a l  a r e a to be removed i s completely procedure was  how  defined.  The  problem w i t h  to determine the number of stems removed i n t h i n n i n g  s i n c e o n l y b a s a l area removed i s known.  T h i s was  c a l c u l a t i n g the mean diameter of t h i n n e d  stems u s i n g the  DBH(T) = b  Table equation  Q  + b j DBH(BT) + b  24 shows the e s t i m a t e d  2.28  this  f o r each s p e c i e s .  £  accomplished by equation:  ff^y  parameters and  first  2-28  other s t a t i s t i c s  for  104  TABLE 24.  Parameter e s t i m a t e s and o t h e r s t a t i s t i c s f o r the DBH t h i n n i n g e q u a t i o n 2.28  of  Species C. l u s i t a n i c a  b  -4.0099  P.  radiata  -2.4008  -4.4723  0  .9316  °1 b  P. p a t u l a  11.6300  .9129  .9274  7.2044  11.9780  2  n  117  139  121  R2  .94  .94  .93  2.06  SEE  All  (11.2%)  1.46  (8.3%)  2.14  the independent v a r i a b l e s were s i g n i f i c a n t at .05  l e v e l and  (13.8%)  probability  the study o f r e s i d u a l s i n d i c a t e d no s y s t e m a t i c t r e n d s .  3.  B a s a l Area Growth b e f o r e F i r s t  3.1  Introduction B a s a l a r e a i s one  t h a t i t i s one  Thinning  of the most important  stand c h a r a c t e r i s t i c s i n  of the d i r e c t l y measurable independent v a r i a b l e i n the  stand volume e q u a t i o n .  There i s a l s o no doubt t h a t b a s a l a r e a i s the  s i m p l e s t and most w i d e l y accepted measure of s t o c k i n g d e n s i t y (Rawal and Franz  1973).  Thus, i n i n t e n s i v e l y managed p l a n t a t i o n s , b a s a l a r e a i s  o f t e n used as one for f i r s t  and  of the c r i t e r i o n f o r d e t e r m i n i n g when the stand i s due  subsequent t h i n n i n g s .  I t i s a l s o one  of the v a r i a b l e s  105  o f t e n used f o r i n i t i a l i z i n g s t a n d , diameter  the stand f o r growth and y i e l d i n whole  f r e e models (Smith and W i l l i a m s , 1980).  B a s a l area development i n managed stands phases, b e f o r e and a f t e r f i r s t development i s mostly stand age.  After f i r s t  first  t h i n n i n g the and  t h i n n i n g , the b a s a l a r e a o f the stand i s a  of t h i n n i n g s .  f a c t o r s but a l s o of the i n t e n s i t y  Data f o r B a s a l Area  and  T h i s s e c t i o n o f the study i n v e s t i g a t e s the  development of b a s a l a r e a b e f o r e f i r s t  3.2  Before  c o n s i d e r e d i n two  a f u n c t i o n of stand d e n s i t y , s i t e q u a l i t y  f u n c t i o n of not o n l y these frequency  thinning.  can be  t h i n n i n g f o r the t h r e e s p e c i e s .  Development  Data f o r b a s a l a r e a development were d e r i v e d from p l o t s e s t a b l i s h e d when stands were 3 to 8 y e a r s o l d and 1,000  stems per h e c t a r e .  had number of stems h i g h e r  Table 25 shows a summary of the d a t a .  p r e l i m i n a r y study of the b a s a l area growth f o r P_. p a t u l a had for  K i n a l e r e g i o n , b a s a l a r e a development was  t h a t of the r e s t of the c o u n t r y . age 7 y e a r s was  28.6  m  2  T h i s e x p l a i n s why  different  groups.  3.3  A  shown t h a t  markedly d i f f e r e n t  from  F o r example, the mean b a s a l area at  compared to 19.7  country.  than  m  2  f o r the r e s t of the  data f o r t h i s s p e c i e s were t r e a t e d as  two  Choice of the R e g r e s s i o n Model The  (1952).  growth of the i n d i v i d u a l t r e e b a s a l area i s d e s c r i b e d by He  f u r t h e r s t a t e d t h a t the growth curve  Spurr  f o r b a s a l area of the  106  TABLE 25.  Summary o f the b a s a l a r e a b e f o r e t h i n n i n g data  n  Variable  Species  Mean  Standard deviation  Mininum  Maximun  112  7.1  1.29  4.7  11.5  No. stems/ha  112  1337  177.28  1013  1656  Height  (dom) m 2 Basal area m  112  10.2  2.32  5.0  15.8  112  19.5  6.66  4.2  38.2  Age  (years)  172  7.2  2.02  3.6  16.5  P. p a t u l a  No. stem/ha  172  1300  162.22  1012  1631  r e s t of country  Height  172  11.9  3.47  3.8  26.3  172  19.7  8.52  1.1  49.1  45  7.0  .87  5.5  8.5  1038  1532  Age C. l u s i t a n i c a  (years)  (dom) m  Basal area m Age P. p a t u l a K i n a l e Group  P. r a d i a t a  (years)  No. stem/ha  46  1296  119.71  Height  (dom) m o B a s a l area m  46  12.0  1.86  8.2  16.4  46  28.6  5.81  14.7  40.8  Age  (years)  95  7.2  1.10  5.5  9.5  No. stem/ha  95  1342  178.29  1038  1705  95  12.8  2.89  6.1  20.0  95  15.3  3.84  5.7  24.4  Height  (dom) m  2 Basal area m  107  stand i s s i m i l a r , e s p e c i a l l y f o r managed stands where m o r t a l i t y i s negligible.  Spurr was  r e f e r r i n g to the sigmoid growth c u r v e .  P i e n a a r and T u r n b u l l (1973) used Chapman-Richards growth model f o r b a s a l a r e a growth of a stand f o r d i f f e r e n t study, the authors  fitted  worked upon by Marsh ( 1 9 5 7 ) ) . the asymptote parameter may  i n South A f r i c a (CCT  experiments  They demonstrated t h a t the magnitude of  be d e n s i t y dependent, but w i t h i n c e r t a i n  considered constant f o r d i f f e r e n t d e n s i t i e s ,  s u p p o r t i n g the h y p o t h e s i s o f c o n s t a n t The  In t h e i r  t h i s e q u a t i o n t o d a t a from d i f f e r e n t s t o c k i n g  d e n s i t i e s from c o n t r o l l e d experiments  l i m i t s c o u l d be  stand d e n s i t i e s .  thus  yield.  above study i n d i c a t e d t h a t the b a s a l area growth curve i s  s i g m o i d , s t a r t i n g a t the o r i g i n and increases.  t e n d i n g to an asymptote as  However, i n t h e i r study of asympotic  age  growth c u r v e s , Rawat  and F r a n z (1973) n o t i c e d t h a t f o r some s p e c i e s l i k e p i n e (Pinus s i l v e s t r i s , L . ) , b a s a l a r e a per a c r e over age  curves were not  but bend downwards a f t e r r e a c h i n g the maximum v a l u e . t h i s as due  asymptotic  They e x p l a i n e d  to the f a c t t h a t the s i t e i s not capable of s u p p o r t i n g  optimum number of stems per u n i t a r e a at h i g h e r ages.  They t h e r e f o r e  recommended d e r i v a t i o n of stand b a s a l a r e a from b a s a l a r e a over curve o f mean t r e e and number of t r e e s per u n i t area over age  age  curves.  F o r t h i s study however, the d a t a d i d not cover the h i g h e r ages. a r e a per h e c t a r e was v a r i a b l e of d i r e c t  Basal  r e t a i n e d as the dependent v a r i a b l e as i t i s the interest.  From e x p e r i m e n t a t i o n w i t h the Chapman-Richard's and m o d i f i e d W e i b u l l f u n c t i o n ; the l a t t e r was  s e l e c t e d as most s u i t e d to the d a t a :  108  BA . „ ( l - .-VW*) 0  2  . , 2  2 Where  BA = Stand b a s a l area i n m  /ha  A H  = Stand age i n y e a r s = Stand dominant h e i g h t ( i n c l u d e s e f f e c t s of s i t e  N  = Number of stems per h e c t a r e  bo; b j . - . b ^ are c o e f f i c i e n t s to be where bg b^ = The b2»  =  The  quality)  estimated  asymptote.  r a t e a t which b a s a l a r e a approaches the asymptote  b^ and b^ a r e s c a l e  parameters.  T h i s model assumed constant asymptote f o r a l l s i t e q u a l i t i e s stand d e n s i t i e s .  and  Both assumptions appear j u s t i f i e d because of the  narrow range of d e n s i t i e s covered by the data and because the data does not  cover the asymptotic  phase of growth.  In other words, the estimated  asymptotes are mainly a r e f l e c t i o n of the r a t e a t which the p l o t s are growing i n the e a r l y ages.  Table 26 shows the estimated parameters  o t h e r r e l e v a n t s t a t i s t i c s from e q u a t i o n 2.29 and R  f o r a l l the s p e c i e s .  v a l u e s were e s t i m a t e d u s i n g equations 2.9 and 2.10  w i t h BA s u b s t i t u t e d f o r H.  T a b l e 27 g i v e s the asymptotic  and SEE  respectively standard  d e v i a t i o n s f o r the e s t i m a t e d c o e f f i c i e n t s of T a b l e 26 w h i l e F i g u r e  13  shows the b a s a l a r e a over age curves f o r v a r i o u s s i t e index c l a s s e s a t stand d e n s i t y of 1200  stems per h e c t a r e .  109  TABLE 26.  Parameter e s t i m a t e s and r e l e v a n t s t a t i s t i c s b e f o r e t h i n n i n g : E q u a t i o n 2.29  f o r basal  area  Species C. l u s i t a n i c a  P. p a t u l a ( k )  P. r a d i a t a  b  0  39.6342  53.1844  87.7894  22.1194  b  x  -0.00001426  -0.0000003329  -0.000006209  -0.00000727  b  2  1.2418  0.9381  1.2788  0.2540  b  3  1.1797  1.1033  0.5626  1.7142  b  4  0.7807  1.3367  112  172  46  95  2  .85  .91  .91  .63  SEE  2.61 m 13.35%  n R  *  P. p a t u l a *  2  or  2.58 m 13.1%  P_. p a t u l a r e s t of the country,  (k) P. p a t u l a K i n a l e  region.  2  or  1.79 m 6.26%  2  or  2.36 m 15.4%  2  or  no  TABLE 27.  Asymptotic s t a n d a r d d e v i a t i o n s of the e s t i m a t e d of T a b l e 26  Species  0  b  l  b  2  b  3  b  4  c. l u s i t a n i c a  4.6935  0.000000  0.2540  0.1662  0.1657  p. p a t u l a *  4.6404  0.000000  0.1292  0.1082  0.1394  38.8152  0.000000  0.2091  0.1311  2.1430  0.000000  0.4698  0.3400  p. p a t u l a ( k ) p. r a d i a t a  *  b  coefficients  P. p a t u l a r e s t o f the c o u n t r y ,  (k) P. p a t u l a from K i n a l e group.  -  Ill FIGURE 13 BASAL AREA OVER AGE CURVES FOR VARIOUS SITE  IH  O E X CLASSES AT STAND DENSITY  OF 1200 S.P.H. C  .L U S I T A N I C A  P  AGE IN YEARS FROM PLANTING  RADIATA  112  3.4  V a l i d a t i o n and Equation  D i s c u s s i o n of the B a s a l Area b e f o r e  Thinning  2.29  E q u a t i o n 2.29 d e t e r m i n a t i o n and  was  accepted  on the b a s i s of the h i g h c o e f f i c i e n t  the good f i t i n d i c a t e d by a study o f the r e s i d u a l s  f o r the i n d i v i d u a l s p e c i e s e q u a t i o n s . w e l l these e q u a t i o n s  However i t remained to see  the e q u a t i o n s .  Unthinned p l o t s from  the 20 permanent sample p l o t s set a s i d e f o r each s p e c i e s as t e s t were used f o r t h i s .  F i g u r e 14a,b,c,d shows the observed  c o u n t r y ) and P_. p a t u l a ( K i n a l e ) p l o t s  P.  data  and p r e d i c t e d  b a s a l area f o r C_. l u s i t a n i c a , P_. r a d i a t a , P_. p a t u l a ( r e s t o f  the  respectively.  f i g u r e i n d i c a t e s v e r y a c c u r a t e p r e d i c t i o n f o r some of  p l o t s , e.g. p l o t s 348  how  p r e d i c t e d b a s a l area development of permanent  sample p l o t s not used to formulate  The  of  f o r C.. l u s i t a n i c a , and p l o t s 391  p a t u l a from the r e s t of the country and  the  and 276  for  from K i n a l e r e s p e c t i v e l y .  F o r the o t h e r p l o t s , the growth r a t e appears very a c c u r a t e l y modeled but the p r e d i c t e d curves are s h i f t e d e i t h e r above or below the curve.  The  w i t h i n +2 The at age  shift  f o r C_. l u s i t a n i c a and P_. p a t u l a (both groups) i s  s q . meters of b a s a l a r e a , w i t h no i n d i c a t i o n of b i a s .  shift 8.5  For plot  observed  for  radiata plot  years but t h i s reduces  164,  the s h i f t i s almost  d i v e r g e s towards age  9.5  years.  In g e n e r a l , the v a r i a b i l i t y  289  i s of the order of 4 s q . meters  to 2.5  sq. meters a t age  n i l at age 7.5  11.5  y e a r s but the  years. curves  This trend i s reversed f o r plot  i s expected  to be h i g h e r f o r t h i s s p e c i e s  as i n d i c a t e d by the lower c o e f f i c i e n t of d e t e r m i n a t i o n (.63) t o t h a t of the o t h e r s p e c i e s ( T a b l e 26).  373.  compared  T h i s c o u l d be the e f f e c t s of  113 FIGURE 14 OBSERVED AND PREDICTED BASAL AREA FOR UNTHINNED PLOTS NOT USED IN FORMULATING THE BASAL AREA EQUATION  C . LUSITANICA (a)  348  -40  3 0  25  20  < <! 1 0 pa  0«-i-^-  8  9  10  8  9  10  Observed Predicted  II  12  FIGURE 14  con't  P . PATULA  (Rest of the country)  AGE IN YEARS FROM PLANTING  115  dothistroma  p i n e d i s e a s e which a t t a c k s t h i s s p e c i e s i n the e a r l y  between 3 to 15 y e a r s . f o r height  S u r p r i s i n g l y , t h i s v a r i a b i l i t y was  development, which would suggest t h a t p r o b a b l y  of t h i s d i s e a s e development.  on stand  not  age,  noticed  the e f f e c t s  development are expressed mainly on b a s a l  There i s however no  i n d i c a t i o n of b i a s or  area  inconsistency  i n these p r e d i c t i o n s . The  higher  r a t e of b a s a l a r e a development f o r P. p a t u l a p l o t s from  K i n a l e r e g i o n was  unexpected.  development, there was  no  q u a l i t y than the o t h e r s we  i n d i c a t i o n t h a t t h i s r e g i o n had  (see F i g u r e 8 curve No.  see t h a t t h i s r e g i o n has  region, while Table  For example from the study on  the second h i g h e s t  6)  better  site  A l s o from Table  16  r a i n f a l l to Kiandongoro  25 f o r the b a s a l a r e a data does not i n d i c a t e  d i f f e r e n c e s i n stand d e n s i t y f o r p l o t s from K i n a l e and r e s t of the country. 1.  height  This leaves  two  possible  those from  the  explanation:  That t h e r e are s i t e f a c t o r s p o s s i b l y a s s o c i a t e d w i t h  soils  which expresses themselves through b a s a l a r e a development f o r P_. p a t u l a .  T h i s would be  theory which holds  c o n t r a r y to the g e n e r a l  t h a t e f f e c t s of s i t e f a c t o r are  mainly through stand h e i g h t 2.  growth expressed  development.  That the P_. p a t u l a grown In K i n a l e r e g i o n i s of a  different  provenance o r v a r i e t y from t h a t grown i n the r e s t of country.  To date,  t h e r e has  been no  evidence of  the  this  possibilty. The  i m p l i c a t i o n here i s t h a t P. p a t u l a t r e e s from K i n a l e r e g i o n  of d i f f e r e n t form from t h a t of t r e e s from the r e s t of the  country.  are  116  T h i s phenomenon needs f u r t h e r i n v e s t i g a t i o n as the f i n d i n g s a r e of both economic and b i o l o g i c a l  importance.  4.  B a s a l Area Development i n Thinned  4.1  Introduction  Stands  As mentioned i n t h e p r e v i o u s s e c t i o n , b a s a l area development i n p l a n t a t i o n s can be viewed i n two phases, b e f o r e and a f t e r thinning. of  first  T h i s s e c t i o n d e a l s w i t h the second phase i n which t h e e f f e c t s  thinning are a factor. T h i n n i n g i n f l u e n c e s stand development through  two changes i n stand  conditions: 1.  I t reduces  the s t a n d i n g b a s a l area by removing some of the  t r e e s , the b a s i c u n i t s on which growth o c c u r . 2.  I t reduces  c o m p e t i t i o n f o r l i g h t and n u t r i e n t s , thus c r e a t i n g  c o n d i t i o n s condusive  t o f a s t e r r a t e of growth of the remaining  t r e e s i n the stand. The  first  e f f e c t r e s u l t s i n an i n s t a n t r e d u c t i o n i n t o t a l b a s a l  a r e a per u n i t a r e a and an i n s t a n t change i n mean stand DBH, whose magnitudes depend on type of t h i n n i n g .  F o r example t h i n n i n g (as  p r a c t i c e d i n Kenya) r e s u l t s i n the remaining DBH than b e f o r e t h i n n i n g .  stand h a v i n g a h i g h e r mean  T h i s e f f e c t has been termed mechanical o r  s t a t i s t i c a l growth (Grut 1970). The  second e f f e c t a f f e c t s the subsequent r a t e o f stand b a s a l a r e a  growth or mean s t a n d DBH increment.  Most s t u d i e s on b a s a l a r e a  117  development i n t h i n n e d  stands have c o n s i d e r e d  b a s a l a r e a increment  the v a r i a b l e of i n t e r e s t r a t h e r than b a s a l area i t s e l f .  Examples  as are  Crowe (1967), Grut (1970), C u r t i s 91967), C l u t t e r (1963), S u l l i v a n and C l u t t e r (1972), C l u t t e r and A l l i s o n  (1974) and  others.  I n s t u d y i n g b a s a l a r e a increment of a stand, an important d e r a t i o n i s the p e r i o d of growth. or  10 y e a r s  variations.  has  consi-  In g e n e r a l , a l o n g e r p e r i o d , e.g.  5  the advantage of evening out the year to y e a r c l i m a t i c  T h i s would r e s u l t i n an apparent h i g h e r  p r e d i c t i o n equation.  p r e c i s i o n i n the  In p r e d i c t i n g p e r i o d i c growth however, an assump-  t i o n i s made t h a t w i t h i n t h a t p e r i o d , annual growth r a t e s are the same. This could r e s u l t species  i n s e r i o u s e r r o r s e s p e c i a l l y f o r f a s t growing  such as are the s u b j e c t of t h i s study.  For t h i s reason  because permanent sample p l o t s i n Kenya are measured a n n u a l l y , growth i n t e r v a l was  4.2  and annual  used.  Choice of Dependent and  Independent V a r i a b l e s  As mentioned above, the v a r i a b l e of I n t e r e s t i n b a s a l area ment a f t e r f i r s t  tropical  t h i n n i n g i s u s u a l l y b a s a l area Increment.  develop-  The  p o s s i b i l i t y e x i s t e d of u s i n g e i t h e r b a s a l a r e a increment per h e c t a r e b a s a l a r e a increment of the t r e e of mean b a s a l a r e a i n the s t a n d . former was one  s e l e c t e d as i t i s more d i r e c t l y r e l a t e d t o stand b a s a l  of the main d r i v i n g v a r i a b l e s of the envisaged growth and  or The  area,  yield  model. For  independent v a r i a b l e s i n the b a s a l a r e a increment e q u a t i o n ,  f o l l o w i n g v a r i a b l e s were  considered:  the  118  1.  B a s a l area i n square meters per h e c t a r e at the b e g i n n i n g the growth p e r i o d .  T h i s v a r i a b l e forms the b a s i c u n i t  which b a s a l a r e a increment accumulated.  B a s a l a r e a i s a l s o one of the most e a s i l y  t h e r e f o r e an obvious  measure of s t o c k i n g d e n s i t y .  candidate as an  v a r i a b l e i n the b a s a l area increment 2.  Stand  age:  independent  equation.  For a g i v e n s t a n d i n g b a s a l a r e a , one would  t h a t the o l d e r the stand, the lower 3.  the b a s a l a r e a  I n t e r a c t i o n of number of stems per h e c t a r e and height.  from  i s formed and on which i t i s  o b t a i n a b l e and w i d e l y accepted I t was  The  of  expect  increment.  stand dominant  e f f e c t s of number of stems on b a s a l area  Increment are accounted  f o r l a r g e l y by b a s a l a r e a .  some of the e f f e c t s of s i t e q u a l i t y are absorbed  Similarly,  by the b a s a l  area s i n c e the b e t t e r the s i t e q u a l i t y , the h i g h e r the b a s a l a r e a , p r o v i d e d c o m p e t i t i o n i s not l i m i t i n g . be noted  However i t should  t h a t the b e t t e r the s i t e q u a l i t y , the h i g h e r  dominant h e i g h t of the stand and  t h e r e f o r e f o r a f i x e d number  of stems per h e c t a r e , the h i g h e r the c o m p e t i t i o n and lower b a s a l area  therefore  increment.  In the p r e l i m i n a r y study of the b a s a l area increment t h i r d independent v a r i a b l e ( i n t e r a c t i o n ) was d e n s i t y index - S%,  the  calculated  from e q u a t i o n  e q u a t i o n , the  i n t r o d u c e d as the 2.25:  stand  119  / 10,100 \/No. t r e e s / h a S%  =  . H  S  =  Harts  100  dom  stand d e n s i t y index  (see a l s o S e c t i o n  2.2).  Thus, t h i s stand d e n s i t y index a c t e d as a measure of the a c t i o n between number o f stems and of  s t a n d dominant h e i g h t , an  equivalent  c o m p e t i t i o n index measuring the e f f e c t of average s p a c i n g on b a s a l  a r e a increment on a per u n i t area b a s i s .  F o r C_. l u s i t a n i c a  P^. p a t u l a , t h i s v a r i a b l e proved s i g n i f i c a n t at the .05 significant  and  l e v e l but non-  f o r P_. r a d i a t a i n the p r e l i m i n a r y l i n e a r e q u a t i o n s .  28 g i v e s the summary of data used f o r b a s a l area increment  4.3  inter-  B a s a l Area Increment  Table  study.  Equation  In the p r e l i m i n a r y study of the r e l a t i o n s h i p of the b a s a l area Increment to the independent v a r i a b l e s , the f o l l o w i n g curve  shapes were  observed: 1.  With age:  an e x p o n e n t i a l decay curve; a l l t h r e e s p e c i e s .  2.  With i n i t i a l approximating  3.  With S%:  basal area: a hyperbola:  a l s o an e x p o n e n t i a l decay  curve,  a l l three s p e c i e s .  an approximate l i n e a r r e l a t i o n s h i p f o r £ .  lusitanica  and P_. p a t u l a ; no r e l a t i o n s h i p i n d i c a t e d f o r P. r a d i a t a . From l i t e r a t u r e review  and p r e l i m i n a r y t r i a l w i t h n o n l i n e a r models,  the f i n a l e q u a t i o n adopted was  an e x t e n s i o n and more g e n e r a l i z e d model  120  TABLE 28.  Species  C.  lusitanica  P. p a t u l a  P. r a d i a t a  Summary o f b a s a l area increment  Variable  Mean  Standard deviation  Maximum  7.5 8.5 12.6 0.1  43.6 67.9 35.9 5.9  4.56 10.64 5.70 1.29  7.4 5.2 8.4 0.1  27.7 62.2 57.0 7.7  5.44 10.15  7.5 4.7  34.6 57.0  -  -  Age BA S BAI  20.3 34.6 21.2 2.2  8.43 10.34 3.95 1.10  Age BA S BAI  14.3 28.0 19.6 2.4  Age BA S BAI  15.2 25.6  -2.1  Minimum  data  0.79  0.2  —  4.7  n  658  638  723  121  for  b a s a l a r e a increment  Allison  ( C l u t t e r and  1974):  . _ (MA  BAI  Where:  f o r P. r a d i a t a i n New Zealand  b 2  + b B 4) b  3  2  A  = I n i t i a l age  B  = I n i t i a l p e r acre b a s a l area  BAI  = P r e d i c t e d b a s a l a r e a increment  bp  b , b 2  3  d u r i n g the next  >  3  0  year  and b^ a r e r e g r e s s i o n c o e f f i c i e n t s .  I n t h e i r e q u a t i o n , C l u t t e r and A l l i s o n had b4=-l which was g e n e r a l i z e d i n t h i s study.  The e x t e n s i o n c o n s i s t e d of i n c l u s i o n of a  t h i r d independent v a r i a b l e , S% (Hart's stand d e n s i t y index), t o account for  the i n t e r a c t i o n between s t o c k i n g and stand dominant h e i g h t .  P r e l i m i n a r y i n v e s t i g a t i o n s w i t h t h i s v a r i a b l e however proved  nonsignifi-  cant f o r P_. r a d i a t a and so the extended form o f the e q u a t i o n was used o n l y f o r C_. l u s i t a n i c a and P_. p a t u l a :  BAI = e  Where:  +  ^  +  b  5 )  BAI = B a s a l a r e a increment  S  2.31  i n nr/ha  B  = B a s a l area i n m /ha a t b e g i n n i n g of the growth p e r i o d  A  = Age a t end o f growth p e r i o d  S  = H a r t s stand d e n s i t y index a t end of growth p e r i o d  bp  b ...bij are regression c o e f f i c i e n t s .  2  2  E q u a t i o n 2.31 (and s i m i l a r l y 2.30) can be r e w r i t t e n a s :  122  b B . e  b  3  BAI  4  b S . e  2.32  5  b i i n d i c a t e the r a t e o f growth of the b a s a l area so t h a t e due  t o the r e s p e c t i v e independent  s c a l e parameters r e l a t e d  v a r i a b l e , while b  2  and b  increment  4  are  to the shape o f the r e l a t i o n s h i p o f the r e s p e c -  t i v e v a r i a b l e s t o b a s a l area increment.  Table 29 g i v e s the estimated  parameters from e q u a t i o n 2.31 (C_. l u s i t a n i c a and P_. p a t u l a ) and e q u a t i o n 2.30 (P. r a d i a t a ) and t h e i r r e l e v a n t s t a t i s t i c s .  The parameters f o r the  New Zealand P. r a d i a t a e q u a t i o n are a l s o given f o r comparison T a b l e 30 g i v e s the asymptotic meters from equations  4.5  purposes.  standard d e v i a t i o n s of the estimated  para-  2.30 and 2.31.  R e s u l t s and D i s c u s s i o n The  equations  f o r a l l t h r e e s p e c i e s show moderate t o low c o e f f i -  cient of determination:  0.61, 0.69 and 0.31 f o r C_. l u s i t a n i c a ,  P_. p a t u l a and P_. r a d i a t a r e s p e c t i v e l y .  The c o e f f i c i e n t  i s e s p e c i a l l y low compared t o t h a t f o r New Zealand. be noted t h a t the data f o r New Zealand  f o r P. r a d i a t a  However i t should  came from a r e l a t i v e l y  restricted  a r e a - the New Zealand F o r e s t Products L i m i t e d f o r e s t s , w h i l e t h a t f o r Kenya came from the whole country.  T h i s and the dothistroma d i s e a s e  problem i n Kenya may p a r t l y e x p l a i n the h i g h v a r i a b i l i t y i n Kenya d a t a . In g e n e r a l , h i g h v a r i a b i l i t y expected  s i n c e the increment  i n b a s a l area increment  i s a f u n c t i o n o f s e v e r a l other f a c t o r s not  i n c l u d e d i n the model:  1.  may be  C l i m a t i c v a r i a t i o n from y e a r to y e a r .  123  TABLE 29.  Parameter e s t i m a t e s and o t h e r r e l e v a n t s t a t i s t i c s f o r the b a s a l a r e a increment e q u a t i o n f o r £ . l u s i t a n i c e , IP. p a t u l a and P. r a d i a t a (Kenya and New Zealand)  Coefficients  b  2  b  3  b  4  C. l u s i t a n i c a  -0.3836  -0.2327  -0.6218  -4.7451  -7.1706  -11.1983  -0.2227  -0.07970  .61  .69  SEE  .68 m or 31% 1  Asymptotic  2  b  3  b  4  b5  -0.2941 -21.663 -1  -1.0632  0.01282  R  b  5.978  5.9090  638  Coefficients  P. r a d i a t a (N.Z.)  11.1362  658  TABLE 30.  P. r a d i a t a (Kenya)  7.7226  0.01653  ^5  P. p a t u l a  723 .76  .31 .66 m or 32%  .72 m or 30%  2  2  18.2%  s t a n d a r d d e v i a t i o n s f o r the parameters on T a b l e 29  C. l u s i t a n i c a  P. p a t u l a  P_. r a d i a t a (Kenya)  0.2864  3.5863  0.5602  0.1362  0.1691  0.05722  0.8785  4.4411  5.3622  0.0948  0.0666  0.2440  0.0043  0.0036  124  2.  Stand d i s t u r b a n c e s a study  during c u l t u r a l operations.  For example i n  of b a s a l a r e a Increment f o r P_. r a d i a t a , Grut  found t h a t d u r i n g approximately t h i n n i n g , the Increment was p a r t i c u l a r age,  the f i r s t  (1970)  year a f t e r a  lower than t h a t normal f o r the  s i t e q u a l i t y and number of stems.  This,  he  s t a t e d , c o u l d p a r t l y be e x p l a i n e d by the f a c t t h a t a p o r t i o n of the growing s t o c k had had not yet a d j u s t e d year,  been removed and  itself  to the new  the remaining  conditions.  crop  After a  the b a s a l a r e a increment rose above t h a t which i s normal  f o r the p a r t i c u l a r age,  s i t e q u a l i t y and  T h i s c o u l d p a r t l y be e x p l a i n e d of the r e l e a s e d s l a s h and  as due  roots l e f t  number of stems.  to the manurial  effects  In the ground.  A l t h o u g h c l i m a t i c f a c t o r s can be measured f o r i n c l u s i o n i n the b a s a l a r e a increment e q u a t i o n ,  they are not u s e f u l f o r p r a c t i c a l  pur-  poses s i n c e i t i s not p o s s i b l e to p r o j e c t a c c u r a t e l y what these f a c t o r s w i l l be i n f u t u r e .  The  e f f e c t s of s i l v i c u l t u r a l d i s t u r b a n c e s  o t h e r hand can o n l y be measured f o r c o n t r o l l e d experiments: t h a t was The theory.  not a v a i l a b l e f o r t h i s  on  information  study.  s i g n s f o r a l l the p r e d i c t e d parameters are c o n s i s t e n t F o r example, the p o s i t i v e s i g n a s s o c i a t e d w i t h by f o r  i m p l i e s t h a t b a s a l a r e a increment w i l l be d e c r e a s i n g because of the n e g a t i v e associated with b  3  the  v a l u e of b£» while  as age  the n e g a t i v e  with age  increases  sign  f o r b a s a l area i m p l i e s t h a t b a s a l area  increment  w i l l be i n c r e a s i n g as b a s a l a r e a i n c r e a s e s , a l l other f a c t o r s b e i n g c o n s t a n t , because of the n e g a t i v e  value a s s o c i a t e d w i t h b4«  The  held  125  positive sign associated with coefficient  f o r d e n s i t y index f o r  C. l u s i t a n i c a and P. p a t u l a means t h a t b a s a l a r e a increment i n c r e a s e as d e n s i t y index of the stand i n c r e a s e s .  will  T h i s can r e s u l t  1.  I n c r e a s i n g s p a c i n g as a r e s u l t of h e a v i e r t h i n n i n g s .  2.  F o r f i x e d s p a c i n g , lower density  s i t e q u a l i t y means h i g h e r stand  index.  In e i t h e r case, the r e s u l t i s l e s s crowding  o f the remaining  l e s s c o m p e t i t i o n and t h e r e f o r e h i g h e r b a s a l area increment remaining stand.  from:  stand,  f o r the  S i m i l a r l y , stands w i t h a h i g h e r number of stems p e r  u n i t a r e a or on h i g h q u a l i t y s i t e s means h i g h e r crowding: t i o n and t h e r e f o r e lower b a s a l a r e a increment.  more  competi-  Thus t h i s s i g n i s con-  s i s t e n t w i t h growth t h e o r y . An important  o b s e r v a t i o n i n Table 29 i s t h a t t h e parameter b j  which i s a s s o c i a t e d w i t h growth r a t e w i t h r e s p e c t t o age i s almost the same f o r both t h e Kenyan e q u a t i o n and the New Zealand e q u a t i o n f o r _?. radiata.  The parameter b  increment  t o b a s a l a r e a r e l a t i o n s h i p i s a l s o almost  4  a s s o c i a t e d w i t h shape of t h e b a s a l a r e a the same; thus  c o n f i r m i n g the h y p e r b o l i c r e l a t i o n s h i p , w h i l e the other parameters d i f f e r by almost  twice each o t h e r .  However, the comparison of the  magnitude o f these parameters i s i n v a l i d a t e d by the f a c t t h a t t h e e q u a t i o n s a r e not based  on the same u n i t s .  I t i s a l s o s i g n i f i c a n t t h a t f o r P. r a d i a t a i n Kenya, the i n t e r a c t i o n between number o f stems and stand dominant h e i g h t as measured by s t a n d d e n s i t y index (S%) f a i l e d t o be s i g n i f i c a n t .  As mentioned  e a r l i e r , t h i s v a r i a b l e measures the e f f e c t s of c o m p e t i t i o n on b a s a l area  126  increment p e r u n i t a r e a .  Thus f o r t h i s s p e c i e s , stand d e n s i t y  w i t h i n the range maintained  index,  i n p l a n t a t i o n s i n Kenya, has no s i g n i f i c a n t  e f f e c t on b a s a l a r e a increment on a u n i t area b a s i s . e x p l a i n why C l u t t e r and A l l i s o n  T h i s may w e l l  (1973) used o n l y b a s a l area and age i n  t h e i r b a s a l area increment e q u a t i o n  f o r t h i s s p e c i e s i n New  Zealand.  F i g u r e 15a and b shows the p r e d i c t e d b a s a l increment f o r v a r i o u s densities f o r 2.30.  r a d i a t a i n Kenya and New Zealand,  using  The range o f d e n s i t i e s i s w i t h i n the range covered  f o r Kenya. 1.  Two main o b s e r v a t i o n s  by the data  are worth of note:  F o r any g i v e n b a s a l a r e a , b a s a l a r e a increment i s much h i g h e r f o r Kenya than f o r New Zealand.  T h i s c o u l d be a r e s u l t o f  s i t e f a c t o r s i n Kenya b e i n g more f a v o u r a b l e this 2.  equation  t o the growth of  species.  F o r Kenya, b a s a l area increment i s much more a f f e c t e d by stand d e n s i t y (as measured by b a s a l a r e a ) than i n New e s p e c i a l l y f o r b a s a l a r e a under 30 m /ha.  Zealand,  Thus, the theory  t h a t b a s a l area increment i s not a f f e c t e d by changes i n stand d e n s i t y does not h o l d f o r Kenya a t the present densities.  F o r P. r a d i a t a i n New Zealand,  to hold closely.  range of  the theory  appears  T h i s may be a r e f l e c t i o n o f the d i f f e r e n c e  i n s i t e q u a l i t y , suggesting  t h a t f o r Kenya, s i t e q u a l i t y i s  much h i g h e r so t h a t t h e present  stand d e n s i t i e s do not  e n t i r e l y u t i l i z e t h e s i t e p o t e n t i a l , e s p e c i a l l y below 30 m per  hectare.  127  FIGURE 1 5 BASAL AREA INCREMENT CURVES  128  F i g u r e 16a and b shows t h e p r e d i c t e d b a s a l area increment f o r v a r i o u s stand d e n s i t i e s f o r C_. l u s i t a n i c a and P. p a t u l a , u s i n g 2.31. 19.6  These curves a r e f o r t h e average stand d e n s i t y index r e s p e c t i v e l y ) w i t h i n the range o f d e n s i t i e s covered  equation  (21.2 and  by the d a t a .  F o r a g i v e n b a s a l a r e a , the curve would be h i g h e r f o r h i g h e r v a l u e o f S% and  vice versa.  radiata.  The f i g u r e i n d i c a t e s the same p a t t e r n as f o r F_.  Thus, b a s a l area increment  f o r these s p e c i e s v a r i e s w i t h  d e n s i t y w i t h i n the range o f d e n s i t i e s maintained  5.  stand  i n Kenya p l a n t a t i o n s .  Stand Diameter D i s t r i b u t i o n The  i n f o r m a t i o n on stand s t r u c t u r e and diameter  c e n t r a l to f o r e s t s t a n d management.  Besides  distribution i s  forming the b a s i s f o r the  stand t a b l e c o n s t r u c t i o n , t h i s knowledge i s e s p e c i a l l y important i n stands managed f o r sawtimber and veneer p r o d u c t i o n s i n c e the f i n a l  yield  i n these p l a n t a t i o n s i s c l o s e l y r e l a t e d t o the s i z e of the l o g s . Knowledge of the volume d i s t r i b u t i o n by s i z e c l a s s e s forms the b a s i s f o r d e c i s i o n making as t o when a stand can be e c o n o m i c a l l y h a r v e s t e d f o r a g i v e n end p r o d u c t . A c c o r d i n g t o Hyink (1980),  t h r e e b a s i c approaches have been  employed i n m o d e l l i n g growth and y i e l d a t t r i b u t e s by s i z e c l a s s e s : 1.  Approaches employing Markov chains and systems o f d i f f e r e n t i a l equations.  A c c o r d i n g t o Moser (1980), t h i s approach uses a  square m a t r i x o f c o n d i t i o n a l p r o b a b i l i t i e s t h a t correspond t o the p r o b a b i l i t y o f going from s t a t e i t o s t a t e j a f t e r one  FIGURE 16 BASAL AREA INCREMENT CURVES  130  step or t r a n s i t i o n .  In p r a c t i c e , t h i s approach corresponds to  the u p d a t i n g of a s t a n d t a b l e . 2.  I n d i v i d u a l t r e e model approach:  By t h e i r n a t u r e , i n d i v i d u a l  t r e e models, p i o n e e r e d by Newnham (1964^ p r o v i d e yield attributes for individual 3.  growth and  trees.  Diameter d i s t r i b u t i o n approach based on p r o b a b i l i t y t h e o r y .  The f i r s t  two approaches p l a c e  no r e s t r i c t i o n on the form or shape  of the u n d e r l y i n g diameter d i s t r i b u t i o n the t h i r d approach.  (Hyink 1980), an advantage  over  I t s h o u l d however be noted t h a t these approaches  a r e i n h e r e n t t o the m o d e l l i n g s t r a t e g y and so a r e not a l t e r n a t i v e s f o r the t h i r d approach i n the whole s t a n d , diameter f r e e models. t h i r d approach which i s of i n t e r e s t  5.1  Theoretical  It i s this  i n t h i s study.  Considerations  The b a s i c assumption u n d e r l y i n g the p r o b a b i l i t y  distribution  approach to s t a n d diameter d i s t r i b u t i o n i s that the l a t t e r can be a d e q u a t e l y c h a r a c t e r i z e d by a g i v e n p r o b a b i l i t y d e n s i t y f u n c t i o n In p a r t i c u l a r , e v e n - a g e d stands tend to have unimodal shape and which has l e a d t o the wide use of continuous unimodal  form,  probability  d e n s i t y f u n c t i o n to c h a r a c t e r i z e t h e i r diameter d i s t r i b u t i o n .  (pdf).  131  In g e n e r a l , the p r o b a b i l i t y d e n s i t y f u n c t i o n has the p r o p e r t y :  f ( x ; 6 ) dx = 1  Where  6 =  2.3  a v e c t o r c o n t a i n i n g the parameters of the p a r t i c u l a r pdf.  Put i n a n o t h e r form: x p(x  x  < X <x ) 2  2  -  f ( x ; 6 ) dx x  2.34  l  which reads t h a t the p r o b a b i l i t y of the random v a r i a b l e X assuming a v a l u e between x^ and x  2  i s g i v e n by the i n t e g r a l of the p r o b a b i l i t y  d e n s i t y f u n c t i o n between the two v a l u e s (x^ and x ) . 2  The problem  t h e r e f o r e i n a p p l y i n g t h i s t h e o r y t o f o r e s t r y i s one of f i n d i n g the a p p r o p r i a t e pdf and e s t i m a t i n g i t s parameters.  5.2  Choosing the A p p r o p r i a t e pdf As mentioned above, even-aged  stands i n g e n e r a l have diameter d i s -  t r i b u t i o n w i t h unimodal shape and form.  Over the y e a r s , s e v e r a l mathe-  m a t i c a l f u n c t i o n s have been used to model t h i s d i s t r i b u t i o n .  Examples  i n c l u d i n g the normal curve ( e . g . Crowe 1967), G r a m - c h a r l i e r S e r i e s ( e . g . Meyer 1930, Crowe 1967), P e a r l - R e e d p o p u l a t i o n growth curve (Osborne and Schumacher 1935, Nelson 1964, Crowe 1967), Beta d i s t r i b u t i o n  (Clutter  and Bennett 1965, McGee and D e l i a B i a n c a 1967, Lenhart and C l u t t e r 1971), t h e Gamma d i s t r i b u t i o n  (Nelson 1964) and the W e i b u l l  (e.g. B a i l e y and D e l l 1973, C l u t t e r and A l l i s o n  1974, A l d e r  function 1977,  132  R u s t a g i 1978 and Hyink of  1980, Schreuder  and Swank 1974).  I n an a n a l y s e s  the s u i t a b i l i t y of most of these f u n c t i o n f o r c h a r a c t e r i z i n g  d i s t r i b u t i o n , B a i l e y and D e l l  (1973) concluded t h a t no o t h e r  diameter  diameter  d i s t r i b u t i o n f u n c t i o n e x h i b i t s as many d e s i r a b l e f e a t u r e s as the W e i b u l l function.  These i n c l u d e the s i m p l i c i t y o f a l g e b r a i c m a n i p u l a t i o n and  its ability of  t o assume a v a r i e t y of curve shapes.  T h i s e x p l a i n s why most  the r e c e n t work on diameter d i s t r i b u t i o n and stand s t r u c t u r e has used  t h i s f u n c t i o n , as evidenced by the examples quoted was chosen  above.  This function  f o r t h i s study f o r the above reasons and because p r e l i m i n a r y  i n v e s t i g a t i o n s i n d i c a t e d t h a t i t would adequately c h a r a c t e r i z e the diameter d i s t r i b u t i o n o f the permanent sample p l o t s a v a i l a b l e  for this  study. The W e i b u l l p r o b a b i l i t y d e n s i t y f u n c t i o n has a l r e a d y been d i s c u s s e d i n S e c t i o n 1.2 o f t h i s c h a p t e r i n c o n n e c t i o n w i t h h e i g h t over age growth function.  F o r diameter  d i s t r i b u t i o n , the u s u a l procedure  w i t h the cumulative d i s t r i b u t i o n  F(x) = 1 - e  i s to work  form o f the f u n c t i o n , d e f i n e d a s :  x-x. - ( b  2.35  f o r x > x. 0 0 < F(x) < 1  where F ( x ) measures the a r e a under the curve between X = x X = x.  Thus i n terms o f diameter  distribution,  0  and  133  F ( x ) = p (X < d)  or  p(d  < X < d ) - F ( d ) - F ( d ) -.-  2.36  T h i s e q u a t i o n i s e q u i v a l e n t t o e q u a t i o n 2.34.  5.3  F i t t i n g the W e i b u l l Model t o Diameter  The  Distribution  Data  data f o r the diameter d i s t r i b u t i o n study c o n s i s t e d of 58  permanent sample p l o t s made up o f a l l t h r e e s p e c i e s : 18 of £ . l u s i t a n i c a and 10 of P_. r a d i a t a .  30 f o r P_. p a t u l a ,  The number of stems p e r p l o t  ranged between 4 t o 70 stems on which t r e e DBH had been measured t o one d e c i m a l p l a c e of a cm.  F o r c o n s i s t e n c y w i t h timber measurement  p r a c t i c e s i n Kenya, the t r e e diameters i n t o 3 cm diameter and  classes.  s e t a s i d e as t e s t d a t a .  f o r each p l o t were s t r a t i f i e d  Of the 58 p l o t s , 8 were s e l e c t e d a t random Data summary  f o r the 50 remaining p l o t s are  g i v e n on T a b l e 31.  TABLE 31.  Summary of the DBH d i s t r i b u t i o n  data  Standard deviation  Variable  n  Minimum  Maximum  Mean  Age  50  9.700  41.700  18.568  6.5781  Height  50  16.100  39.000  24.754  6.0117  Stems  50  74.000  1160.0  523.08  278.37  The  first  step was to f i t t h e W e i b u l l cumulative  f u n c t i o n to the 50 diameter d i s t r i b u t i o n histograms e s t i m a t e of the parameter:  distribution  to o b t a i n an  134  F(D) = 1 - e-b*D*  where  b* =  ^  2.37  c  c  D* = D - (DL + 3) DL = Minimum diameter c l a s s on the histogram D  = A g i v e n diameter c l a s s  b and c a r e W e i b u l l parameters F(D) = Observed p r o b a b i l i t y o f t r e e s having a DBH < D.  The parameters b and c were e s t i m a t e d u s i n g BMDP:3R n o n l i n e a r routine.  F i g u r e 17 shows the h i s t o g r a m f o r p l o t  sub-  135 and the curve  r e s u l t i n g from the e s t i m a t e d parameters. The next s t e p was t o t e s t how w e l l the W e i b u l l f u n c t i o n ized  the diameter frequency d i s t r i b u t i o n of t h e 50 p l o t s .  character-  F o r each  p l o t , the expected f r e q u e n c y p e r diameter c l a s s was c a l c u l a t e d u s i n g the e s t i m a t e d parameters and a C h i - s q u a r e t e s t of goodness of f i t  performed  u s i n g the f o l l o w i n g e q u a t i o n :  x  where  a  .  K  Wj - V  i=l  N  2 2  .  38  = Observed number of t r e e s i n a diameter c l a s s i = Expected number of t r e e s i n a diameter c l a s s i p r e d i c t e d u s i n g the e s t i m a t e d parameters k X  = T o t a l number of diameter c l a s s e s 2  = C a l c u l a t e d Chi-square v a l u e .  135  FIGURE 17 DIAMETER DISTRIBUTION HISTOGRAM AND THE FREQUENCY CURVE RESULTING FROM THE FITTED WEIBULL PROBABILITY DENSITY FUNCTION  Plot no 135 N = 716 Sph n s 39 D _ = 18 b= 10.6246 C si.9257  18  21  24 27  30  33  36  DIAMETER CLASSES  136  The X  9  calculated x  v a l u e s were then compared w i t h the t a b u l a t e d  v a l u e s f o r .05 p r o b a b i l i t y l e v e l of s i g n i f i c a n c e and k-3  degrees of  freedom. Out  of the 50 p l o t s , x  p l o t s as they had  v a l u e s c o u l d not be c a l c u l a t e d  3 or fewer diameter  p l o t s , o n l y 4 showed a l a c k of f i t , t a i l s or had  d i s t r i b u t i o n was  5.4  Of the remaining  e i t h e r because they had  sharply truncated data.  the h y p o t h e s i s t h a t the diameter  classes.  for 8 42  very long  On b a s i s of t h i s t e s t t h e r e f o r e ,  d i s t r i b u t i o n f o l l o w s the W e i b u l l  accepted.  E s t i m a t i n g the Parameters and V a l i d a t i o n of the E s t i m a t i n g Model  The W e i b u l l parameters estimated the shape and  form of the frequency  the p a r t i c u l a r p l o t . to p l o t due  As  f o r each i n d i v i d u a l p l o t  d i s t r i b u t i o n by diameter  i s expected,  these parameters d i f f e r  to d i f f e r i n g stand c o n d i t i o n s .  define  c l a s s e s of from p l o t  In o r d e r to be a b l e to  p r e d i c t the a p p r o p r i a t e I > L and W e i b u l l f u n c t i o n parameters f o r g i v e n stand c o n d i t i o n s , the l i n e a r and estimated  c u r v i l i n e a r c o r r e l a t i o n of  parameters w i t h stand v a r i a b l e s was  s t u d i e d (Table  Table 32 i n d i c a t e s t h a t the minimum diameter c o r r e l a t e d w i t h the stand mean dbh,  age,  due  w i t h age  and  i n a stand i s best  The  high  v a r i a b l e without  so any  the  correla-  dominant h e i g h t c o u l d be e x p l a i n e d as  to the h i g h c o r r e l a t i o n between the stand mean dbh,  dominant h e i g h t and  the  32).  stand dominant h e i g h t and  log^Q number of stems per h e c t a r e i n t h a t o r d e r . t i o n of  and  largely  age and  stand  one of these c o u l d be used as the p r e d i c t o r  l o s s of p r e c i s i o n i n the e s t i m a t i o n of t h i s  variable.  137  TABLE 32.  L i n e a r and c u r v i l i n e a r c o r r e l a t i o n of the D^ and e s t i m a t e d W e i b u l l parameters w i t h o t h e r stand v a r i a b l e s  n = 50  Stand  r @ .01 = 0.36  r @ .05 = 0.28  DF = 48  variables  Age  0.92  0.34  -0.46  Height  0.80  0.28  -0.43  No. stem  -0.76  -0.10  0.40  DBH  0.94  0.37  -0.43  DL  1.00  0.04  -0.43  -0.02 DBH -  0.94  0.13  DL  0.66  -0.54  -0.44  1 No. stem  0.77  -0.04  -0.42  Log Age  0.91  0.29  -0.50  Log  0.76  0.26  -0.44  °L DBH  Height  Log No. stems Log  (DBH-DL)  °L  Log  -0.81 -0.14 0.63  -0.07 0.90 -0.50  0.42 0.15 -0.42  DBH Log  DBH  0.93  0.35  -0.46  Log  DL  0.95  0.01  -0.52  DBH  =  Mean stand DBH i n cm (D)  Height  = Stand dominant h e i g h t i n meters  DL  = Minimum stand DBH i n cm  No. stems = Number o f stems p e r h e c t a r e b & c  =  Estimated W e i b u l l  parameters.  138  On  the o t h e r hand, the number of stems per h e c t a r e i s not so  c o r r e l a t e d w i t h the stand mean DBH.  These two  v a r i a b l e s were t h e r e f o r e  s e l e c t e d as p r e d i c t o r s of the minimum stand diameter parameter.  The  Inverse of number of stems was  used  o r the xg i n s t e a d of the  of the number of stems because the former r e g r e s s i o n equation with a higher c o e f f i c i e n t f i n a l equation  D  L  where  Minimum stand  N  = Number of stem/ha  n  =  50  =  .90  SEE = 3.1 all  2.39  cm = 15% of the mean  the p r e d i c t o r v a r i a b l e s were s i g n i f i c a n t at .05 The  The  dbh  = Stand mean dbh  2  of d e t e r m i n a t i o n .  691.14(i) N  D  R  resulted i n a  was:  = -3.2048 + .7472D +  D_  closely  s c a l e parameter b was  level.  v e r y s t r o n g l y c o r r e l a t e d w i t h the  differ-  ence between the stand mean DBH  and the minimum s t a n d DBH,  the r a t i o of the two.  not s u r p r i s i n g s i n c e t h i s parameter i s  T h i s was  f o l l o w e d by  d e f i n e d i n terms of i t s p o s i t i o n on the x - a x i s , on which both D_ D are l o c a t e d ( B a i l e y and D e l l 1973). meter w i t h these two equation:  A regression for this  and  para-  v a r i a b l e s as p r e d i c t o r s gave the f o l l o w i n g  139  b = -3.6207 + 1.2263(5 - D. ) + 5 . 7 9 1 0 ( — ) D  2.40  L  n R  2  =  50  =  .91  SE = 1.24  = 11%  of mean  Both p r e d i c t o r v a r i a b l e s were s i g n i f i c a n t at .05 The  parameter c on the  w i t h which i t was of p r e d i c t o r  strongly  other hand d i d not correlated.  v a r i a b l e s produced the  probability  have any  stand a t t r i b u t e  T r i a l s with several  f o l l o w i n g best  level.  combinations  equation:  \  c = 4.6585 - 2 . 0 6 3 5 ( — ) - .02360D D  n R  2  =  50  =  .27  SE = .68  = 27%  2.41  of mean  Both p r e d i c t o r v a r i a b l e s were s i g n i f i c a n t at  5.5  .05  probability  level.  Model V a l i d a t i o n E q u a t i o n s 2.39  and  2.40  proved q u i t e  c o e f f i c i e n t of d e t e r m i n a t i o n and against  the p r e d i c t e d  values.  the  s a t i s f a c t o r y based on  study of t h e i r r e s i d u a l s  E q u a t i o n 2.41  w i t h s a t i s f a c t o r y d i s t r i b u t i o n of r e s i d u a l s . t o see  how  proved the best  plotted possible  However, i t s t i l l  w e l l these equations would p r e d i c t the  respective  their  remained  Weibull  140  parameters f o r independent d e r i v e the e q u a t i o n s . observed  d a t a from the same p o p u l a t i o n as used  Table 33 g i v e s the p r e d i c t e d parameters and  parameter o b t a i n e d by f i t t i n g  terms of mean b i a s the equations  for  S i m i l a r l y , the e q u a t i o n f o r c i n d i c a t e s , no model i s o n l y moderately  purpose.  i n d i c a t e no overall bias.  bias. However, the  s e n s i t i v e to changes i n stand a t t r i b u t e s ,  t h a t h i g h v a l u e s of c are a s s o c i a t e d w i t h p o s i t i v e r e s i d u a l s and values with negative r e s i d u a l s .  the  the W e i b u l l f u n c t i o n to the  frequency d i s t r i b u t i o n s of the 8 p l o t s set a s i d e f o r t h i s In  to  so  low  Parameter b, on the o t h e r hand, has  one  l a r g e p o s i t i v e r e s i d u a l , t h a t of p l o t 327, which has l a r g e l y c o n t r i b u t e d to  the p o s i t i v e b i a s f o r t h i s parameter.  range between +3.6,  which i s w i t h i n the expected  i n d i c a t e d by e q u a t i o n 2.40. unbiased In  Otherwise,  E q u a t i o n 2.40  the o t h e r  variability  residuals  as  can t h e r e f o r e be c o n s i d e r e d  s i n c e , as seen from F i g u r e 18, p l o t  327  r e p r e s e n t s an  outlier.  terms of p r e c i s i o n , the standard e r r o r s of estimate f o r a l l  parameters,  a r e i n g e n e r a l h i g h e r than those obtained i n the  of  t h e i r equations.  of  freedom a s s o c i a t e d w i t h the t e s t sample.  derivation  T h i s can be e x p l a i n e d p a r t l y by the lower  e r r o r f o r parameters b and  c can be expected  degrees  In a d d i t i o n the s t a n d a r d to depart even f a r t h e r  from  t h a t of t h e i r e q u a t i o n s i n c e t h e i r v a r i a b i l i t y  i n c l u d e s the  in  a predicted variable).  (as a p r e d i c t o r v a r i a b l e which i s i t s e l f F i g u r e 18 shows the histograms  of the diameter  t i o n s of the t e s t p l o t s , the observed ed by f i t t i n g  frequency  distribution (solid  distribu-  curve) o b t a i n -  the W e i b u l l f u n c t i o n to the i n d i v i d u a l p l o t  p r o b a b i l i t y d a t a , and  variability  cumulative  the p r e d i c t e d d i s t r i b u t i o n ( d o t t e d curve) o b t a i n e d  from W e i b u l l parameters p r e d i c t e d from equations 2.39,  2.40  and  2.41.  TABLE 33.  Comparison  of p r e d i c t e d and observed W e i b u l l  parameters f o r the t e s t  plots  Plot #  Observed  Predicted  Predicted  Residual  Observed  210  11.7  14.8  -3.1  13.6583  10.0550  3.6033  3.6882  2.7844  0.8538  327  26.6  33.3  -6.7  21.5330  14.1089  7.4241  3.3244  2.0608  1.2636  128  18.4  19.9  -1.5  14.2300  11.2948  2.9352  2.4216  2.5530  -0.1314  147  19.3  16.4  2.9  8.7052  10.4026  -1.6974  2.8789  2.7055  0.1734  189  26.8  23.2  3.6  9.0294  12.7995  -3.7701  1.7225  2.4350  -0.7125  202  14.8  15.1  -0.3  10.4126  9.7630  0.6496  4.0712  2.7574  1.3138  221  25.1  23.6  1.5  10.4964  11.1698  -0.6734  1.4104  2.3862  -0.9758  238  18.8  14.7  4.1  5.9215  9.5166  -3.5951  1.8959  2.7720  -0.8761  SE = 4.41 cm or 21.8%  Mean b i a s = 0.0625  Residual  Observed  SE = 4.64 cm o r 39%  Mean b i a s = 0.6095  Predicted  Residual  SE = 1.1248 o r 42%  Mean b i a s = 0.1136  142  FIGURE 18 DIAMETER DISTRIBUTION HISTOGRAMS, FITTED WEIBULL P.D.F. AND THE PREDICTED WEIBULL P.D.F. FOR THE EIGHT TEST PLOTS PLOT  PLOT  2I0 34  N=  /  (0)  327  PLOT  = 8  N  I28  N =19  (b)  (c)  pdf f i t t e d d i r e c t l y t o p l o t data pdf p r e d i c t e d from equations 10 8 6  .4 .3  4  .2  2  .1  12  15  18 21  PLOT  24  27  30  27  39 42 45 4B  54  16  21  24  27  30 33 36 39  202  N = 23  N = 23  (d)  51  PLOT  PLOT I 8 9  I47  N = 24 10  3 0 33 38  (f)  (e)  .5  8  .2  18  21  24  27  27  30  30  33  36 39 42  PLOT 221 N =12 ig)  •s .4 .3 •2  0 24  27  3 0 33  36  39 42  18 21  DIAMETER  CLASSES  24  27  IN Cm  30  15  18  21  24  27  143  I n g e n e r a l , the histograms  I n d i c a t e the range  of diameter  frequency  d i s t r i b u t i o n s t h a t can be expected  i n p l a n t a t i o n s where t h i n n i n g i s a  standard p r a c t i c e .  r e p r e s e n t s an extreme case t e n d i n g  Thus, p l o t  327  towards a u n i f o r m d i s t r i b u t i o n w h i l e most of the o t h e r p l o t s w i t h multimodal 189 and  d i s t r i b u t i o n s can be expected  221.  as d e p i c t e d by p l o t s 327,  A l l these cases u n d e r l i n e the problem  128,  a s s o c i a t e d w i t h the  use of any one p r o b a b i l i t y d i s t r i b u t i o n f u n c t i o n t o c h a r a c t e r i z e a l l these  shapes. Assuming the unimodal  teristic, terize  shape and  form to be the predominant  the f i t t e d W e i b u l l f u n c t i o n ( s o l i d  curve) appears  this distribution quite s a t i s f a c t o r i l y .  from the p r e d i c t e d parameters that f i t t e d  charac-  to c h a r a c -  S i m i l a r l y , the curves  ( d o t t e d ) f o l l o w s i m i l a r shape and form to  from the d a t a , w i t h no i n d i c a t i o n of b i a s or i n c o n s i s t e n c y .  Thus, the W e i b u l l parameter p r e d i c t i o n equations were accepted f o r the diameter  6.0  frequency d i s t r i b u t i o n modeling  in this  study.  Volume D e t e r m i n a t i o n  Tree volume equations f o r C_. l u s i t a n i c a , P. p a t u l a and P_. r a d i a t a i n Kenya were developed  by Wright  i n 1969  (Wright  these volume equations have been very w i d e l y used p r a c t i c e s and  tests. study.  Since then,  i n management  form the b a s i s f o r the t r e e volume t a b l e s f o r these  s p e c i e s (Wright Wanene 1975,  1977).  1974)  1976).  and  the y i e l d t a b l e s (Wanene and W a c h i u r i  They can t h e r e f o r e be s a i d to have passed  These equations were used t o determine  1975, the  field  the stand volumes i n t h i s  144  The  t r e e volume e q u a t i o n s p r o v i d e  volume from the t r e e DBH  f o r the d e t e r m i n a t i o n of t r e e  and e i t h e r the i n d i v i d u a l t r e e h e i g h t o r the  t r e e dominant h e i g h t , o b t a i n e d from d e t e r m i n i n g the dominant h e i g h t of the s t a n d .  Only e q u a t i o n s based  on t r e e dominant h e i g h t a r e of i n t e r e s t  i n t h i s study s i n c e i n d i v i d u a l t r e e h e i g h t s are not a v a i l a b l e . g i v e s the e q u a t i o n s and species.  Table  34  the r e s p e c t i v e c o e f f i c i e n t s f o r each o f the  These equations g i v e t o t a l overbark  volume.  F o r a l l s p e c i e s , the c o n v e r s i o n of the t o t a l volume to merchantable volume i s a c h i e v e d through m u l t i p l i c a t i o n by a f a c t o r R which i s dependent on the t r e e  DBH: bD 0  R = b  0  + bi e  2.44  2  T a b l e 35 g i v e s the r e l e v a n t c o e f f i c i e n t s f o r each of the s p e c i e s f o r the merchantable standards i n Kenya: 15 cm and 20 cm top diameter P. p a t u l a and P. r a d i a t a ,  15 cm o n l y f o r C;. l u s i t a n i c a .  limits for  145  TABLE 34.  1. 2. l o g  1 ( )  E q u a t i o n s and c o e f f i c i e n t s f o r the t r e e volume e q u a t i o n s f o r C. l u s i t a n i c a , P. p a t u l a and P_. r a d i a t a i n Kenya  V -  b  o  V =  b  o  + b D  + b DH + b D H  2  2  x  2  + t^log^D +  C.  3  b logH 2  lusitanica  -0.01733  t>0  P. p a t u l a  -0.0072  P. r a d i a t a  -4.2643  bl  0.0001937  0.00002887  2.0598  b  2  0.00005069  0.00002077  0.7875  b  3  0.00002296  0.00003276  E q u a t i o n 2.47 i s f o r £ . l u s i t a n i c a  and P_. p a t u l a  E q u a t i o n 2.48 i s f o r P_. r a d i a t a V = D = H =  Tree volume i n cu.meters Tree DBH i n cm Stand dominant h e i g h t i n meters.  146  TABLE 35.  C o e f f i c i e n t s f o r R-factor equation l i m i t s f o r the r e s p e c t i v e s p e c i e s  (2.44) f o r the merchantable  20 cm  15 cm b  b.  l  C. l u s i t a n i c a  0.9870  -11.1577  -0.1742  -  P. p a t u l a  0.98471  -8.6658  -0.16135  0.97352  -21.9737  -0.15407  P. r a d i a t a  0.98348  -14.7231  -0.17505  0.97622  -18.7751  -0.13971  147  CHAPTER  3  YIELD MODEL CONSTRUCTION AND VALIDATION  1.0  General The  Principle  general p r i n c i p l e  on which growth and y i e l d models a r e based  can be d e r i v e d d i r e c t l y from t h e d e f i n i t i o n o f these two terms. F o r example i n t h e simple  case of an even-aged stand w i t h a s t a n d i n g volume,  V, growth r a t e may be expressed  as a f u n c t i o n o f age, A, i n terms of  d i f f e r e n t i a l notation:  dA  where  — d  = f(A)  =  r a t e of change of stand volume w i t h r e s p e c t t o stand age.  A  f(A)  3.1  =  a f u n c t i o n o f stand age.  When t h e age i s expressed  i n y e a r s , the r a t e of change as g i v e n i n  e q u a t i o n 3.1 i s r e f e r r e d t o as annual  growth o r annual  increment i n  age A Q t o a f u t u r e  volume.  From t h i s , volume y i e l d from an i n i t i a l  age A Q  can be o b t a i n e d as t h e summation o f t h e growth r a t e s w i t h i n  + t  t h i s time p e r i o d . age  Analytically,  f u n c t i o n w i t h i n the l i m i t s  Y  = ^ °  +  t  f(A)dA  y i e l d i s o b t a i n e d by i n t e g r a t i n g t h e  AQ  to  =  A Q  +  T  F(A)  ;  : -  3.2  148.  where  Y  =  Stand y i e l d  or the summation  of the annual growth  increments between the i n i t i a l  stand age A Q , and a  f u t u r e stand age, A Q ^ . F(A)  =  Yield the  f u n c t i o n o b t a i n e d by m a t h e m a t i c a l l y growth-rate e q u a t i o n , f ( A ) .  The essence o f t h i s and  principle  h e l p s put the whole concept o f growth  y i e l d into i t s h i s t o r i c a l perspective.  models r e p r e s e n t e d by normal y i e l d  Thus, the e a r l i e r  ( d e r i v e d u s i n g g r a p h i c a l and  l a t e r by r e g r e s s i o n t e c h n i q u e s ) as a f u n c t i o n of stand discrete variables.  c l a s s o f models:  Forest l i t e r a t u r e  Plonski  a result  characteristics  has numerous examples of t h i s  (1956), Barnes (1962), e t c .  models i s d e s c r i b e d as S t a t i c  yield  t a b l e s and l a t e r by the v a r i a b l e  d e n s i t y y i e l d t a b l e s p r e s e n t e d stand y i e l d  as  Integrating  T h i s c a t e g o r y of  models i n growth and y i e l d  literature.  As  of r e c e n t advances i n computational techniques and computer  t e c h n o l o g y , r e c e n t y i e l d models p r e s e n t s stand y i e l d d e r i v e d from stand parameters which a r e r a t e s o f change (growth r a t e s ) .  This category of  models i s termed Dynamic where one ( o r more) of the independent v a r i a b l e i s an i n t e g r a l  o f the dependent v a r i a b l e .  The e a r l i e s t  example of a  dynamic model appears to be the growth and y i e l d model f o r ponderosa p i n e stands by Lemraon and Schumacher as  (1963) which e s t i m a t e d t r e e growth  a f u n c t i o n of diameter growth a f t e r The t r a n s i t i o n  thinning.  between the s t a t i c models and dynamic models  p r e s e n t e d problems t o the m e n s u r a t i o n i s t s , s i n c e most models tended to treat was  growth and y i e l d as e s s e n t i a l l y  independent phenomena.  The  t h a t y i e l d d e r i v e d from c o n v e n t i o n a l ( s t a t i c ) models d i f f e r e d  result from  149  y i e l d d e r i v e d from dynamic models.  T h i s c o n t r a d i c t e d the b a s i c  p r i n c i p l e of growth and y i e l d which r e q u i r e d t h a t t o t a l growth  (yield)  be synonymous w i t h the summation of continuous growth i n c r e m e n t s . problem of i n c o m p a t i b i l i t y between the two r e c o g n i s e d by C l u t t e r  c a t e g o r i e s of models  was  (1963) when he developed compatible growth  y i e l d models f o r L o b l o l l y p i n e .  This  and  T h i s he d i d by d i f f e r e n t i a t i n g  already  a c c e p t e d y i e l d models ( w i t h r e s p e c t t o age) t o produce c u b i c - f o o t b a s a l a r e a growth f u n c t i o n s .  and  He d e f i n e d as compatible those y i e l d  models whose a l g e b r a i c form can be d e r i v e d by mathematical  integration  of t h e i r growth model.  2.  S i m u l a t i o n A p p l i c a t i o n t o Growth and Y i e l d  Models  By f a r , the most w i d e l y used method f o r growth and y i e l d i s s i m u l a t i o n t e c h n i q u e (Lee 1967).  modeling  B a s i c a l l y , the term r e f e r s t o any  model t h a t e x h i b i t s a behaviour s i m i l a r to the r e a l system.  Because  the complex n a t u r e of a f o r e s t stand and the need f o r a f l e x i b l e comprehensive  of  and  t e c h n i q u e t o handle a l l the component i n t e r a c t i o n s w i t h as  few r e s t r i c t i v e assumptions the s t a n d a r d t o o l .  as p o s s i b l e , s i m u l a t i o n has become almost  I t s a p p l i c a t i o n has been s t i m u l a t e d by the  i n programming languages and a c c e s s to h i g h speed computers. i n s i m u l a t i n g stand growth and the b i o l o g i c a l and economic  advances Its role  assumptions  u n d e r l y i n g i t s a p p l i c a t i o n were d i s c u s s e d by Smith (1966), w h i l e Gould and O'regan (1965) d i s c u s s e d i t s r o l e to b e t t e r f o r e s t p l a n n i n g .  Among  i t s main advantages are the time compression e f f e c t s whereby the t e c h n i que accomplishes i n seconds what might otherwise take s e v e r a l y e a r s of  150  a c t u a l e x p e r i m e n t a t i o n and the f a c i l i t y system r a t h e r than the a c t u a l system.  to experiment w i t h the s i m u l a t e d I t should however be s t a t e d here  t h a t s i m u l a t i o n i s not a p e r f e c t t o o l as i t only p r o v i d e s e s t i m a t e s of the  model s t a t e r e s u l t i n g from predetermined d e c i s i o n v a r i a b l e s .  according to H i l l i e r  and Lieberman  (1980), i t o n l y compares a l t e r n a t i v e s  r a t h e r than g e n e r a t i n g the o p t i m a l one. comprehensiveness  and f l e x i b i l i t y  Thus,  B e s i d e s t h i s , o n e pays f o r the  of s i m u l a t i o n i n terms of a n a l y t i c  intractibility. The g e n e r a l approach t o f o r e s t s t a n d s i m u l a t i o n I n v o l v e s the development  of the i n d i v i d u a l growth r e l a t i o n s h i p s and f u n c t i o n s t o  d e s c r i b e the i n d i v i d u a l i n t e r a c t i o n s . of  the system.  sequence the  These form the elements  (blocks)  These a r e then put t o g e t h e r i n a s y s t e m a t i c and  (as a computer  logical  programme) t o form the mathematical s i m u l a t o r of  f o r e s t s t a n d system.  T h i s i s the g e n e r a l approach adopted to t h i s  study.  2.1  F o r e s t Stand S i m u l a t i o n Computer based f o r e s t  early  Models  stand s i m u l a t i o n models f i r s t  appeared i n the  1960's, h e r a l d e d by the p i o n e e r i n g work of Newnham (1964).  then, t h e i r development  has been very r a p i d so t h a t as of 1980,  and W i l l i a m s (1980) counted not l e s s than 26 p u b l i s h e d models. t h i s development for  Since Smith  Most o f  has been mainly i n response t o f o r e s t management  p l a n n i n g t o o l s , academic endeavours  f o r e s t stand modeling,or both.  needs  to broaden the knowledge of  The l e v e l of d e t a i l o b t a i n a b l e from  151  each model depends on the type of model and which i t s e l f  the s i m u l a t i o n approach,  i s l a r g e l y governed by the a v a i l a b l e data w i t h i n the  p r e v a i l i n g f i n a n c i a l and  t e c h n i c a l c o n s t r a i n t s . Although s e v e r a l  r e s e a r c h e r s have attempted to c l a s s i f y stand s i m u l a t i o n models: M i t c h e l l (1980), terminology  Smith and W i l l i a m s (1980), Munro (1974):  by Munro (1974) w i l l be adopted here  firstly  the because i t i s  comprehensive and because i t encompasses the p h i l o s o p h y on which models are based.  these  Munro's c l a s s i f i c a t i o n r e c o g n i s e s t h r e e c a t e g o r i e s of  models, based on i n t e r - t r e e dependence s t a t u s and primary  u n i t parameter  requirements:  1.  S i n g l e t r e e - d i s t a n c e dependent f o r e s t stand models: Newnham's (1964) y i e l d model f o r D o u g l a s - f i r was  computer based y i e l d model but a l s o i n t r o d u c e d a new  not o n l y the g e n e r a t i o n of  f o r e s t stand models based on the i n d i v i d u a l t r e e i n the stand as b a s i c u n i t , and  c h a r a c t e r i z e d by the requirement  p o s i t i o n i n the stand be known. butes  that i n d i v i d u a l tree  o b t a i n i n g the p o t e n t i a l growth f o r  then r e d u c i n g t h i s by a f a c t o r dependent on  degree of c o m p e t i t i o n to which the t r e e i s s u b j e c t e d . T h i s p o p u l a r i z e d the concept  the  These models grow the p h y s i c a l a t t r i -  of the i n d i v i d u a l t r e e by f i r s t  a f r e e growing t r e e and  first  the  procedure  o f a c o m p e t i t i o n index which can be d e f i n e d as a  r e l a t i v e measure of the degree of c o m p e t i t i o n .  Different  stand  attri-  butes have been used as c o m p e t i t i o n i n d i c e s i n c l u d i n g mean d i s t a n c e of s u b j e c t t r e e to a predetermined  number of competing neighbours  (Adlard  1974), angle count d e n s i t y (Lowe 1971), crown o v e r l a p (Newnham 1964, 1967)  s i z e - d i s t a n c e of competing neighbours  r e l a t i v e to s u b j e c t t r e e ,  etc.  For f u r t h e r d i s c u s s i o n on c o m p e t i t i o n i n d i c e s , the reader i s  Lee  152  r e f e r r e d to A d l a r d (1974), Newnham and Mucha (1971), G e r r a r d (1968) and Opie  (1968). S i n c e Newnham's (1964) model, s e v e r a l models based on s i m i l a r  concept but d i f f e r i n g i n c o m p l e x i t y and l e v e l o f a t t r i b u t e d e t a i l have been developed. Arney's  Examples of some of those w i t h unique  (1972) D o u g l a s - f i r model improved  features  follow:  on Newnham's model by  s i m u l a t i n g t h e t r e e diameter growth a t each whorl up the t r e e so that' t r e e form was a r e f l e c t i o n o f d i f f e r e n t i a l growth r a t e s a t d i f f e r e n t s e c t i o n s up the t r e e .  T h i s f e a t u r e was p a r t i c u l a r l y s i g n i f i c a n t i n  p e r m i t i n g modeling t r e e responses to such s i l v i c u l t u r a l p r u n i n g , t h i n n i n g and f e r t i l i z a t i o n .  Hegyi's (1974) BUSH model f o r j a c k  p i n e (Pinus banksiana Lamb.) used Arney's M i t c h e l l ' s (1969,  treatments as  approach.  1975) TASS I (white spruce, D o u g l a s - f i r and  hemlock) and TASS I I ( D o u g l a s - f i r ) models r e s p e c t i v e l y r e p r e s e n t the h i g h e s t development  I n the s i n g l e - t r e e d i s t a n c e dependent  on the l e v e l o f d e t a i l o f s t a n d a t t r i b u t e s modeled.  models based  The unique  feature  of these models i s t h a t t h e crown of the s i m u l a t e d t r e e i s modelled e x p l i c i t l y w i t h the growth o f i n d i v i d u a l branches responding to such f a c t o r s as c o m p e t i t i o n from o t h e r branches e i t h e r of t h e same s u b j e c t t r e e or from a d j a c e n t t r e e s .  A f t e r c a l c u l a t i n g I n d i v i d u a l branch  size  and f o l i a r volume, t h e n e t p r o d u c t i o n of photosynthates i s then p r e d i c t e d and p r o p o r t i o n a t e l y d i s t r i b u t e d i n c r e a s e s i n diameter a c c o r d i n g l y .  to the stem b o l e which  Thus, these models come c l o s e s t to  modeling t h e whole t r e e biomass based on the p h o t o s y n t h e t i c a c t i v i t y o f the f o l i a g e .  They a r e t h e r e f o r e t h e o r e t i c a l l y capable of m o d e l l i n g t r e e  responses to c u l t u r a l treatments ( p r u n i n g , t h i n n i n g and f e r t i l i z e r s )  153  and t o i n s e c t s and tree  d i s e a s e s which a f f e c t  the q u a n t i t y and  q u a l i t y of  foliage. Ek and Monserud's (1974) FOREST model i s a l s o a s i n g l e - t r e e  d i s t a n c e dependent model but i s unique  i n t h a t w h i l e most of the o t h e r  models i n t h i s category a r e f o r even-aged stands of a s i n g l e s p e c i e s , FOREST s i m u l a t e s growth and species f o r e s t stands.  r e p r o d u c t i o n of even- or uneven-aged mixed  T h i s i s accomplished  r e p r o d u c t i o n ( r e g e n e r a t i o n ) and the s p a t i a l p a t t e r n of the new  through modeling  the  u n d e r s t o r y development e x p l i c i t l y , stems determined  by the p r i o r  with  stand  conditions. As  i n d i c a t e d by the few examples quoted  above, t h i s category of  models i s capable of p r o v i d i n g v e r y d e t a i l e d i n f o r m a t i o n on t r e e growth i n response  to s i l v i c u l t u r a l  treatments  and  d i s e a s e a t t a c k s , depending on the l e v e l of complexity.  individual  insect  and  They are  also  capable of s i m u l a t i n g the development of heterogenous stands ( i n terms of age,  s p e c i e s and  spatial distribution).  l i m i t e d by t h e i r complexity and  the requirement  each i n d i v i d u a l t r e e i n the stand be known. (1974) makes them very expensive  However, t h e i r use i s t h a t the c o o r d i n a t e s of  T h i s , a c c o r d i n g to Munro  i n terms of time r e q u i r e d to  them and the e x c e s s i v e computer time r e q u i r e d to execute f o r s t o r a g e of t r e e p o s i t i o n r e c o r d s . these models can be, M i t c h e l l 17 y e a r s f o r development and Canadian.  Nonetheless,  f o r e s t s i l v i c u l t u r e and  develop  the e x t r a  As an example of how  space  expensive  (1980) s t a t e d t h a t TASS system had  taken  t e s t i n g a t a c o s t of about $1,000,000  t h e i r p o t e n t i a l v a l u e as a r e s e a r c h t o o l i n economics of s i n g l e f o r e s t stands may  j u s t i f y the commitment i n time and funds.  more than  For t h i s study, however, t r e e  154  p o s i t i o n d a t a were not a v a i l a b l e and so t h i s c a t e g o r y of models was not applicable.  2.  Single tree - distance Conceptually,  independent stand  models:  t h i s term r e f e r s to the c l a s s of stand  models which r e c o g n i s e  the i n d i v i d u a l t r e e i n the stand  simulation  as the b a s i c  production  u n i t but do not r e q u i r e t h a t the i n d i v i d u a l t r e e p o s i t i o n s be  provided.  In a p p l i c a t i o n however, i t i s not c l e a r what c o n s t i t u t e s a  single tree - distance  independent model.  Munro (1974), i t Includes  F o r example, a c c o r d i n g to  models where t r e e s a r e grown i n dimensions  i n d i v i d u a l l y o r i n groupings o f s i m i l a r d i a m e t e r s . is  a c c e p t e d , then a c c o r d i n g  c a t e g o r y c o u l d be c o n s i d e r e d  If this  to Moser (1980), most of the models i n t h i s as s i m i l a r to the t r a d i t i o n a l stand  p r o j e c t i o n approach p r e s e n t e d i n most mensuration t e x t s . should  definition  table  However, i t  be noted t h a t t h e concept o f the s i n g l e t r e e as the b a s i c  production  u n i t i s c o n t r a d i c t e d when growth i s a p p l i e d to a group of  trees of s i m i l a r diameters. A common f e a t u r e of a l l s i n g l e t r e e - d i s t a n c e  independent  models i s t h a t the i n i t i a l model s t a t e c o n s i s t s of a l i s t diameters o r t r e e diameter c l a s s e s . from i n v e n t o r y  This l i s t  of tree  can be s p e c i f i e d e i t h e r  data o r from diameter p r o b a b i l i t y d e n s i t y  Beyond t h i s stage however, two g e n e r a l  stand  functions.  s t r a t e g i e s f o r modeling  stand  growth appear: 1.  F o r some models, the p o t e n t i a l growth i s computed f o r the aggregate s t a n d , list.  and then a l l o c a t e d among the t r e e s i n the DBH  Stand l e v e l c o m p e t i t i v e  s t r e s s i s thus i n c o r p o r a t e d i n  155  the growth e q u a t i o n .  Growth i s then a l l o c a t e d among the  i n d i v i d u a l t r e e s o r diameter c l a s s e s a c c o r d i n g t o t h e i r p o s i t i o n i n the ordered diameter of  list.  Examples o f t h i s  model a r e STANDSIM (Opie 1970), C l u t t e r and A l l i s o n s  type (1974)  model f o r P. r a d i a t a i n New Zealand, FORSIM (Gibson e t a l . , 1969, 2.  1970), e t c .  Other models p r e d i c t each diameter  the diameter increment  class e x p l i c i t l y  of each t r e e o r  as a f u n c t i o n of o t h e r s t a t e  v a r i a b l e s , i n c l u d i n g a t l e a s t one t h a t i s t r e e diameter ( o r c l a s s d i a m e t e r ) dependent t o g i v e d i f f e r e n t i a l growth r a t e s between the c l a s s e s .  Examples of these are TOPSY ( G o u l d i n g  1973), P r o g n o s i s (Stage 1973), PYMOD ( A l d e r 1977), e t c . In  g e n e r a l , these models do have appeal t o f o r e s t managers mainly  because they a r e c o m p u t a t i o n a l l y e f f i c i e n t t o r y d a t a as i n p u t .  and use c o n v e n t i o n a l i n v e n -  I n a d d i t i o n the t r e e diameter  list  i s an i n v a l u a b l e  f e a t u r e , e s p e c i a l l y i n e v a l u a t i n g the r e t u r n s from management d e c i s i o n s in  terms of product  important  s i z e and diameter  Thus, a c c o r d i n g t o Munro (1974), they cannot  models  be used  examine i n d i v i d u a l t r e e s f o r crown shape and growth, b o l e shape  changes o r d e f o l i a t i o n . to  of s i n g l e t r e e - d i s t a n c e independent  t h a t they cannot p r e d i c t the growth o f a s p e c i f i c s i n g l e t r e e w i t h  any r e l i a b i l i t y . to  This i s especially  f o r p l a n n i n g purposes.  A s e r i o u s shortcoming is  distribution.  Nonetheless,models  w i t h c a p a b i l i t y t o respond  t h i n n i n g , s p a c i n g and i n some cases f e r t i l i z a t i o n i n t e r v e n t i o n s have  been developed.  These models a r e o f i n t e r e s t I n t h i s study and so a  d i s c u s s i o n of some of them i s germane.  156  STANDSIM  (Opie 1970) i s a s i n g l e t r e e - d i s t a n c e  developed t o s i m u l a t e  preferred s i l v i c u l t u r a l  Mountain Ash ( E u c a l y p t u s a s i l v i c u l t u r a l rather  regnans F. M u e l l ) . than a p l a n n i n g  growth o f a s i n g l e stand o n l y porated i n t o a planning  (Alder  independent model  treatments f o r A u s t r a l i a n The model i s c o n s i d e r e d  model i n t h a t i t s i m u l a t e s  1977).  as  the  However, i t has been i n c o r -  and management system MARSH, f o r p r e d i c t i o n of  growth under a l t e r n a t i v e s i l v i c u l t u r a l schedules (Weir 1972). state c o n s i s t s of a l i s t  Model  o f i n d i v i d u a l t r e e diameters, w h i l e growth i s  accomplished by c a l c u l a t i n g the gross b a s a l area increment p e r u n i t area.  Thus c o m p e t i t i o n  i s implicitly  included.  I n d i v i d u a l t r e e growth  I s e f f e c t e d by d i s t r i b u t i n g the gross b a s a l a r e a increment p r o p o r t i o n a t e l y according  t o the i n d i v i d u a l t r e e s i z e .  C l u t t e r and A l l i s o n  (1974) developed a s i n g l e t r e e - d i s t a n c e  independent model f o r P_. r a d i a t a i n New Zealand. initial  stand s t a t e c o n s i s t e d  Unlike  STANDISM, the  of a f i x e d number of diameter c l a s s e s of  e q u a l p r o b a b i l i t y i n s t e a d o f the s i n g l e t r e e diameter l i s t .  Tree  diameter d i s t r i b u t i o n from which the diameter c l a s s e s are d e r i v e d i s o b t a i n e d from a W e i b u l l  p r o b a b i l i t y density  function.  Annual growth i s  accomplished by p r e d i c t i n g gross annual b a s a l area Increment and then d i s t r i b u t i n g t h i s t o the diameter c l a s s medians as a f u n c t i o n o f stand age,  current  current  median diameter, c u r r e n t  and p r o j e c t e d  mortality  i s predicted  and p r o j e c t e d  number o f t r e e s per a c r e .  b a s a l a r e a , and  S i m i l a r l y , gross  and d i s t r i b u t e d among the diameter c l a s s medians  as a f u n c t i o n of c l a s s b a s a l area r e l a t i v e to stand b a s a l a r e a . model i s designed f o r s i n g l e s p e c i e s  even-age stands.  This  157  PROGNOSIS model f o r stand development (Stage  1973)  represents a  v e r y h i g h l e v e l of development i n t h i s c l a s s of models i n t h a t i t can s i m u l a t e growth of mixed stands i n terms of s p e c i e s , age c l a s s e s and size classes.  The  h i g h l e v e l of r e s o l u t i o n i n the model i s  by r e c o r d i n g not o n l y the DBH dimensions.  list  but a l s o t r e e h e i g h t and  The key growth component i s annual b a s a l a r e a  computed from DBH,  accomplished crown increment  s i t e , h a b i t a t t y p e , crown r a t i o , r e l a t i v e  d e n s i t y , and the p e r c e n t i l e of the t r e e i n the b a s a l area  stand  distribution.  In a d d i t i o n , the b a s a l area growth f u n c t i o n i n c o r p o r a t e s a s t o c h a s t i c element a l t h o u g h the t o t a l growth process remains e s s e n t i a l l y ministic.  I n d i v i d u a l t r e e s are incremented  i n DBH  deter-  (as a f u n c t i o n of  p o s i t i o n of the p a r t i c u l a r t r e e i n the b a s a l area d i s t r i b u t i o n ) , (as a f u n c t i o n o f DBH  growth, h a b i t a t type, DBH  and h e i g h t ) and  height crown  l e n g t h or c l e a r bole l e n g t h (as a f u n c t i o n of r e l a t i v e stand d e n s i t y , b a s a l a r e a p e r c e n t i l e and DBH).  Thus, the model has a v a r i e t y of t r e e  c h a r a c t e r i s t i c s which a l l o w s i m u l a t i o n of a wide range of prescriptions.  silvicultural  Stage (1973) has demonstrated use of t h i s model to  prognose lodgepole p i n e stand development i n the presence  of an  t i o n of mountain p i n e b e e t l e (Dendroctonus ponderosae H o p k i n s ) . used as a s u b r o u t i n e i n PYMOD f o r e s t p l a n n i n g programme ( A l d e r ( d i s c u s s e d i n the I n t r o d u c t i o n ) f a l l s  3.  i n this  infestaVYTL-2 1977)  class.  Whole stand - d i s t a n c e independent models: T h i s category of models i s based on the same p h i l o s o p h y as  conventional y i e l d  the  t a b l e s , normal or v a r i a b l e d e n s i t y , i n t h a t the b a s i c  u n i t of p r o d u c t i o n i s the whole stand.  However, c o n v e n t i o n a l y i e l d  158  t a b l e s d i f f e r from computer-based s i m u l a t i o n are dynamic w h i l e the  former are  later  static.  From a p h i l o s o p h i c a l p o i n t j u s t i f i e d as  models i n t h a t the  of view, t h i s c l a s s of models cannot  the concept o f the whole stand as the b a s i c p r o d u c t i o n  c o n t r a d i c t s the bionomic ( e c o l o g i c a l ) t h e o r y of i n d i v i d u a l i s t i c (such as the i n d i v i d u a l t r e e i n the  be unit  systems  s t a n d ) as s t a t e d by Boyce (1978):  "Each l i v i n g organism and i t s environment forms an i n d i v i d u a l i s t i c system w i t h n e g a t i v e feedback loops g u i d i n g behaviour i n accordance w i t h the g o a l of s u r v i v a l . Behaviour i s d i r e c t e d by d e c i s i o n mechanisms. These mechanisms are g e n e t i c a l l y and e n v i r o n m e n t a l l y determined and are p h y s i o l o g i c a l , a n a t o m i c a l and m o r p h o l o g i c a l s t r u c t u r e of the i n d i v i d u a l i s t i c system. Each i n d i v i d u a l i s t i c system senses and r e a c t s to i t s own s t a t e . Past a c t i o n s i n f l u e n c e f u t u r e a c t i o n s to a c h i e v e the g o a l of s u r v i v a l . "  The  s i n g l e t r e e approach to growth and  t h i s theory.  On  the  other hand, the whole stand concept i s  w i t h the management o b j e c t i v e of o r d e r i n g t h a t make up  the  t h i s concept t h e r e f o r e  and  have r e c e i v e d  l e s s expensive and  i n d i v i d u a l tree information  is  Models based  on  usually  as computation of  eliminated. independent models, whole stand -  independent models take c o n v e n t i o n a l  inventory  The  major d i f f e r e n c e between the  two  the  output i n f o r m a t i o n  l a t t e r does not  information.  systems  suitable  a t t e n t i o n s i n c e they are  efficient  As w i t h s i n g l e t r e e - d i s t a n c e distance  objectives.  with  consistent  the i n d i v i d u a l i s t i c  f o r e s t i n t o a f o r e s t community w i t h the  s t r u c t u r e to achieve s p e c i f i c goals  computationally  y i e l d i s consistent  s i n c e the  I t should however be  classes therefore  pointed  out  data as  input.  appears to be  in  provide i n d i v i d u a l tree  t h a t whole stand  159  s i m u l a t i o n models can r e c a p t u r e some o f the i n d i v i d u a l t r e e i n f o r m a t i o n by i n c o r p o r a t i n g diameter frequency  d i s t r i b u t i o n models.  d i s t r i b u t i o n o f the t r e e s by diameter  This w i l l  provide  c l a s s e s i n t o which  growth o r y i e l d can be d i s t r i b u t e d whenever t h i s i n f o r m a t i o n i s r e q u i r e d . T h i s approach i s more economical  from the programming and  computational  p o i n t o f view and t h e r e f o r e has been adopted f o r t h i s study. example simulator  An  of the models i n t h i s c l a s s i s the D o u g l a s - f i r managed y i e l d (DFIT) o f Bruce, De Mars and Reukema (1977).  Stand  state i s  r e p r e s e n t e d as the number o f t r e e s per a c r e , stand b a s a l area and the mean stand DBH.  Height  growth i s o b t a i n e d from a s i t e index  equation  w h i l e stand volume growth (a f u n c t i o n of s t a t e v a r i a b l e s ) i s m o d i f i e d by a d e n s i t y dependent f a c t o r , the r a t i o of average stand b a s a l a r e a t o the maximum l i m i t i n g b a s a l area o f the stand.  3.  Y i e l d Model C o n s t r u c t i o n  3.1  E s s e n t i a l F e a t u r e s f o r the Envisaged The  Growth and Y i e l d Model  o v e r r i d i n g o b j e c t i v e o f t h i s study i s t o extend  the under-  s t a n d i n g of the t h e o r e t i c a l and p r a c t i c a l aspects of growth and y i e l d of the t h r e e r e s p e c t i v e s p e c i e s under the c l i m a t i c , edaphic t u r a l c o n d i t i o n s o b t a i n i n g i n Kenya.  Consequently,  and s i l v i c u l -  the t h r e e major  q u e s t i o n s t h a t the e n v i s i o n e d model must answer a r e : 1.  What i s the expected  y i e l d under p r e s e n t  silvicultural  practices? 2.  What i s the impact stand development?  of the present  s i l v i c u l t u r a l p r a c t i c e s on  160  3.  What i s the impact  of a d o p t i n g a l t e r n a t i v e  p r a c t i c e s on the f u t u r e development of the  silvicultural stand?  Answers to these q u e s t i o n s w i l l depend on the q u a n t i t a t i v e i n f o r m a t i o n p r o v i d e d by the growth and y i e l d model.  To do t h i s  effectively,  the model must c o n t a i n the f o l l o w i n g e s s e n t i a l f e a t u r e s : 1.  The  model should permit  practices 2.  The  s p e c i f i c a t i o n s of the management  ( d e c i s i o n v a r i a b l e s ) as i n p u t .  model output  s h o u l d p r o v i d e not o n l y t o t a l volume but a l s o  volume to d i f f e r e n t merchantable l i m i t s and by s i z e c l a s s e s . 3.  The model should be a b l e to e v a l u a t e d i f f e r e n t  l e v e l s of stand  management. 4.  The  f i n a l model should be i n t e g r a t a b l e i n t o the o v e r a l l  forest  p l a n n i n g system. W i t h i n the data and  resource  above f e a t u r e s c o u l d be b u i l t model w i t h s u f f i c i e n t r e s e a r c h purposes.  l i m i t a t i o n s , i t was  felt  t h a t a l l the  i n t o an i n t e r a c t i v e stand l e v e l s i m u l a t i o n  d e t a i l f o r management, p l a n n i n g and  silvicultural  F i g u r e 19 shows the p o s i t i o n of the envisaged  model  i n the o v e r a l l p l a n n i n g system and a l s o serves to show the sequence of the present  3.2  research project ( s o l i d  lines).  Growth and Y i e l d Model S y n t h e s i s The  growth and y i e l d  f u n c t i o n s developed  i n Chapter  2 form the  b u i l d i n g b l o c k s of the y i e l d model EXOTICS; an acronym f o r E x o t i c Species.  These f u n c t i o n s were coded as FORTRAN s u b r o u t i n e s and  o r g a n i z e d i n t o a l o g i c a l sequence (programme) capable  then  of s i m u l a t i n g the  Figure  PSP Data System  191.  O v e r a l l f o r e s t p l a n n i n g system showing  ->  Data  Analysis  the i n t e g r a t i o n of the y i e l d  Y i e l d Model Construction  model.  Model T e s t i n g & Validation  K f I I IMPLEMENTATION  HYPOTHESES  <-  SIMULATION Y i e l d predications under v a r i o u s management s c h e d u l e s  FIELD TRIALS  W  POLICY FORMULATION <r  -ANALYSIS & EVALUATION  Economic Criteria  Technical) Criteria )  Bioliogical  Design model adopted from Munro (1974). Broken l i n e s i n d i c a t e the stages of the o v e r a l l sequence not covered i n t h i s study.  162  growth and y i e l d of a s i n g l e , even-aged m o n o s p e c i f i c s t a n d . shows the f l o w c h a r t o f the f i n a l program c o n f i g u r a t i o n .  F i g u r e 20  Documentation  and v a r i a b l e d e s c r i p t i o n f o r the main and a u x i l i a r y s u b r o u t i n e s i s g i v e n at  the b e g i n n i n g of each s u b r o u t i n e on the program l i s t i n g  from t h e author on r e q u e s t . the main f u n c t i o n a l MAIN:  available  The f o l l o w i n g i s a d e t a i l e d d e s c r i p t i o n of  subprogrammes:  T h i s programme i n i t i a l i z e s  and d e f i n e s v a r i a b l e s which a r e  s p e c i f i c t o i t o r a r e common o r shared w i t h o t h e r subprogramme.  I t i s a l s o r e s p o n s i b l e f o r c o n t r o l of the sequence  i n which v a r i o u s subprogrammes a r e c a l l e d and b a s i c a l l y d i r e c t s the whole programme i n c l u d i n g i n i t i a l i z a t i o n , and HDSTDC:  input  output.  C a l c u l a t e s stand dominant h e i g h t as a f u n c t i o n o f stand age and s i t e index u s i n g e q u a t i o n 2.21 f o r C_. l u s i t a n i c a and P_. r a d i a t a and e q u a t i o n 2.22 f o r P_. p a t u l a .  Correction f o r  e s t a b l i s h m e n t s i t e i s accomplished by d e d u c t i n g 2 meters and (0.156 x Age) meters from dominant h e i g h t f o r P_. r a d i a t a and P_. p a t u l a r e s p e c t i v e l y .  BACALC:  C a l c u l a t e s the stand b a s a l area b e f o r e f i r s t e q u a t i o n 2.29 f o r a l l t h r e e s p e c i e s . called i f i n i t i a l  thinning using  This subroutine i s only  stand b a s a l area i s not p r o v i d e d  (indicated  by e n t e r i n g a n e g a t i v e v a l u e o f b a s a l area when u s i n g the model) and stand i n i t i a l i z a t i o n  age i s 5 y e a r s .  163  FIGURE 20 FLOWCHART OF THI YIELD MODEL EXOTICS  GENERATE INITIAL STAND STATE 1. DOMINANT HEIGHT-F(A.SI,ESTAB.)  INPUT VARIABLES 1-C. LUSITANICA 2'P. RADIATA 3-B-P. PATULA  I.SPECIES  2. BA/HA. F(A.H.N) a  1-SHAMBA  2.ESTABLISHMENT  3.MEAN STAND 08H-F(BA..N)  2'GRASSLANO  4.STAND DENSITY INOEX-F(H.M)  3.A0E-5-40 YEARS  CALCULATE THINNING OUTPUT 1.NO.STEMS REMOVED 3.BA. REMOVEO 3.VOLUME REMOVEO TOTAL AND MERCHANTABLE  3. STOCKING. 100-1«00 I F AQE>S YEARS OR -1000-1600 IF AGE'S YEARS  (AGE  -VE  OR  XBA.TO BE REMOVED 3. THINNING CRITERIA (WHEN THE SPECIFIED AGE.DOMINANT HEIGHT OR BASAL AREA ISREACHEO OREXCEEDEp)  IS.STAND VOLUME/HA"F(DBH.H,N) (TOTAL AND MERCHANTABLE)  4.SITE INDEX-10-3S  6.BASAL AREA  SIMULATE THINNING BY S P E C I F Y I N G t.THINNING OPTION 2. NO.STEMS TO BE LEFT  IF BA. IS UNKNOWN  •VE IF BA. IS SIVEN MUST BE 9 YEARS IF BA. UNKNOWN)  T.THINNING 0- NO 1- BY 2- BY  SPECIFICATIONS (OPTIONS) THINNING NO. OF STEMS TO BE REMOVED BASAL AREA TO BE REMOVED  <  STORE THINNING OUTPUT  8.CLEARFELLING OPTIONS 1- IF DBH>SPECIFIEO VALUE 2- IF AGE>SPECIFIED VALUE CALCULATE RESIDUAL STAND STATE 1 NO. STEMS/HA 2.BA/HA  _NO_  2  CALCULATE 1. WEIBULL PARAMETERS 1.X FROM DBH AND STOCKING 3.b FROM DBH AND X 3 C FROM DBH AND X 2. NO.STEMS BY OBH CLASSES USING WEIBULL DISTRIBUTION FUNCTION 3. TOTAL AND MERCHANTABLE VOLUME BY OBH CLASSES  OUTPUT  RESULTS  2.STI» VAlI  (  " * " " > " « »  THINNINGS)  UPDATE STAND STATE 1.STAND DOMINANT HEIGHT 2.STAND DENSITY INDEX 3.STAND BA. VIA BASAL AREA INCREMENT EOUATION: BAI«F(A,BA.) FOR P.RADIATA BAI-F(A.BA.SX) FOR C.LUSITANICA AND P.PATULA 4.STAND DBH STANO VOLUME  164  BABAI:  This subroutine  updates the stand b a s a l area i n thinned  u s i n g b a s a l area a t the b e g i n n i n g at and  o f the growth p e r i o d and age  the end of the growth p e r i o d ( e q u a t i o n 2.30 f o r P^. r a d i a t a ) S% ( e q u a t i o n  2.31 f o r C_. l u s i t a n i c a and P_. p a t u l a ) t o  c a l c u l a t e the b a s a l a r e a increment. b a s a l area at beginning end  data.  T h i s i s then added to the  o f growth p e r i o d to g i v e b a s a l a r e a a t  of the growth p e r i o d .  initial  This subroutine  i s called i f  stand b a s a l area i s known, f o r example from i n v e n t o r y Initializing  stand  s i m u l a t i o n a t an age >5 y e a r s  a u t o m a t i c a l l y c a l l s t h i s r o u t i n e and so i n i t i a l a r e a must be g i v e n .  I t allows  g i v e n age, an important using f i e l d  VOLCAL:  data  Calculates total equations for  f o r stand  stand  basal  s i m u l a t i o n from any  f e a t u r e when v a l i d a t i n g the model  ( c f . p.s.p.s').  overbark stand volume u s i n g t r e e volume  2.42 and 2.43 and the number o f stems per h e c t a r e  the r e s p e c t i v e s p e c i e s .  able volume by f i r s t  I t a l s o c a l c u l a t e s the merchant-  c a l c u l a t i n g the r e l e v a n t R - f a c t o r  r e s p e c t i v e s p e c i e s and merchantable l i m i t  THIN:  stands  Controls thinning operations  (equation  f o r the  2.44).  of which t h e r e a r e t h r e e  options: 0  =  No t h i n n i n g  1  =  Thinning  based on number o f stems t o be l e f t  when a  predetermined age i n t e r v a l or stand dominant h e i g h t i s e q u a l l e d or exeeded.  165 2  =  Thinning based on proportion of basal area to be removed when a c r i t i c a l predetermined basal area i s equalled or exceeded.  This subroutine allows f o r the use of any one option or a combination of two or a l l three options i n one simulation run, thus allowing f o r a change of management decision (with regard to thinning c r i t e r i a ) at any age within the l i f e of the plantation. THNCAL:  This subroutine calculates thinning variables:  DBH(T)  or DBH(T) N(T) or N(T) BA(T) or BA(T)  f[DBH(BT), N(T), N(BT)] i f thinning option = 1  equation 2.27  f[DBH(BT), BA(T), BA(BT)] i f thinning option = 2  equation 2.28  f[N(BT), N(AT)]  i f thinning option  1  f[BA(T), DBH(T)]  i f thinning option  2  f[DBH(T), N(T)]  i f thinning option  1  a specified proportion of BA(BT) i f thinning option = 2  V(T)  f[DBH(T), H, N(T)]  Where  N(T)  =  No. stems removed i n a thinning/ha  N(BT)  =  No. stems before  N(AT)  =  No. stems after thinning/ha  DBH(T)  =  Mean DBH of thinnings i n cm  thinning/ha  DBH(BT) = Mean DBH of stand before thinning i n cm BA(T)  =  Basal area of thinnings i n m ^  BA(BT)  =  Basal area of stand before thinning i n m /ha  V(T)  =  Volume of thinnings i n m3. "  2  ha  2  166  CHKCLF:  Checks i f stand i s due f o r c l e a r f e l l i n g by checking i f the predetermined Clearfelling  c l e a r f e l l age o r DBH i s e q u a l l e d o r exceeded. has p r i o r i t y  over t h i n n i n g o p e r a t i o n ( c f .  F i g u r e 20). CLRFEL:  Calculates total y i e l d 1.  classes:  C a l c u l a t e s W e i b u l l parameters XQ = f  2.  a t c l e a r f e l l by diameter  (DBH, N)  e q u a t i o n 2.39  b  = f(DBH, D_)  e q u a t i o n 2.40  c  = f(DBH, D_)  e q u a t i o n 2.41  C a l c u l a t e s number o f t r e e s per diameter number o f t r e e s / h a and t h e cumulative function  c l a s s from  total  distribution  ( e q u a t i o n 2.42) u s i n g the W e i b u l l parameters  c a l c u l a t e d above. 3.  C a l c u l a t e s volume y i e l d by diameter V_ = f ( D , H, 1  classes:  N ) ±  V£ r e f e r t o volume c o r r e s p o n d i n g t o diameter  class (at  b r e a s t h e i g h t ) D_» H I s stand dominant h e i g h t at c l e a r fell  and N_ i s number of stems/ha a t c l e a r f e l l i n  diameter  c l a s s D_«  Input v a r i a b l e s f o r EXOTICS At t h e b e g i n n i n g of each s i m u l a t i o n r u n , the programme c a l l s f o r several input v a r i a b l e s : State variables:  Species, establishment  s i t e , age, s i t e  s t o c k i n g and b a s a l a r e a .  index,  167  Decision variables:  T h i n n i n g o p t i o n and and how  c o n t r o l i n p u t s (when to t h i n  much t o remove) and  clearfelling  criteria.  These v a r i a b l e s are g i v e n on F i g u r e 20, w h i l e T a b l e 36 g i v e s domain or the range w i t h i n which t h e i r v a l u e s should be. i n g the v a r i a b l e domain, the main g u i d i n g f a c t o r was  their  In e s t a b l i s h -  the range of the  d a t a used i n d e v e l o p i n g the v a r i o u s growth and y i e l d f u n c t i o n s .  It  s h o u l d be noted t h a t the t h i n n i n g v a r i a b l e s entered at the b e g i n n i n g of the s i m u l a t i o n run a p p l y to f i r s t  thinning only.  The  programme  calls  f o r f u r t h e r t h i n n i n g s t r u c t i o n s at the end of each t h i n n i n g .  Output from EXOTICS I n c o n f o r m i t y w i t h the b a s a l area Increment e q u a t i o n whose i n c r e ment p e r i o d i s one y e a r , the s i m u l a t i o n c y c l e f o r EXOTICS Is one At each c y c l e , s e v e r a l main stand s t a t e parameters are namely age, No.  the stand d e n s i t y Index, S%.  meters No.  stems, DBH,  lated.  calculated,  stems, dominant h e i g h t , mean s t a n d DBH,  volume and  year.  basal area,  At each t h i n n i n g , the p a r a -  b a s a l a r e a and volume of t h i n n i n g s are  calcu-  Both main stand y i e l d and y i e l d of t h i n n i n g are combined t o give  t o t a l stand p r o d u c t i o n : (CAI) and mean annual  b a s a l a r e a , volume, c u r r e n t annual  increment  (MAI).  A l l these v a r i a b l e s are s t o r e d  i n an a r r a y f o r output at the end of the s i m u l a t i o n run. (output as T a b l e  Table  1 i n the programme) i s an example u s i n g C.  sawtimber regime f o r s i t e index In a d d i t i o n t o T a b l e  1, two  increment  37  lusitanica  20. o t h e r t a b l e s are output:  T a b l e 2 which  g i v e s the merchantable volume t o the r e s p e c t i v e merchantable l i m i t s T a b l e 3 which g i v e s the main stand f i n a l volume ( t o t a l and  and  merchantable)  TABLE 36.  Species  Domain of the y i e l d model EXOTICS w i t h r e s p e c t to i n p u t v a r i a b l e s  1  code  2  4  3  5  6  7  8  1 only  1 or 2  1 or 2  1 or 2  1 or 2  1 or 2  1 or 2  1 or 2  5-40  5-35  5-20  5-20  5-20  5-20  5-20  5-12  12-24  21-33  15-27  15-27  15-27  15-27  15-27  21-30  1000-1600  1000-1600  1000-1600  1000-1600  1000-1600  1000-1600  1000-1600  1000-1600  Basal area m  10-60  10-60  10-60  10-60  10-60  10-60  10-60  10-60  No. stems t o remove  10-50%  10-50%  10-50%  10-50%  10-50%  10-50%  10-50%  10-50%  B a s a l a r e a to remove  10-50%  10-50%  10-60%  10-50%  10-50%  10-50%  10-50%  10-50%  Establishment  code  Age i n year Site  index  Initial  Species  stocking  code:  Establishment  code:  1 = C. l u s i t a n i c a  1 = Shamba  2 = P. r a d i a t a  2 = Grassland  3 = P_. p a t u l a  Nabkoi  4 = P. p a t u l a  Nanyuki  5 = P_. p a t u l a  Elburgon  6 = P. p a t u l a  Kiandongoro  7 = P_. p a t u l a 8 = P_. p a t u l a  Kinale Turbo  No. stems and b a s a l area to remove are given as percent  of v a l u e s before t h i n n i n g .  Table  EXAMPLE OF OUTPUT FROM EXOTICS  37  TABLE 1 TOTAL VOLUME YIELD SPECIES: CUPRESSUS LUSITANICA I N I T I A L S I T E INDEX: ESTABLISHMENT: SHAMBA  AGE YEARS 5.0 G.0 7.0 8.0  NO. OF STEMS  TABLE  20.0  STANDING CROP HDOM DBH(1) BA(1)  V(1)  cu M  S%  1200 1200 1200 1200  0 0 0 0  7 9 10 12  M 8 2 6 0  CM 10 4 12 5 14 2 15 8  SO 10 14 19 23  M 3 6 1 4  32 61 94 130  9 6 7 1  37 31 27 24  1 3 2 2  9.0 10.0 11 .0 12.0 13.0  888 888 888 888 888  0 0 0 0 0  13 14 15 16 17  2 5 7 8 9  18 19 20 21 22  1 4 5 5 4  22 26 29 32 35  9 3 4 3 1  140 173 206 239 272  6 3 3 6 9  25 23 21 20 18  3 2 4 0 7  14.0 15.0 16.0 17 .0 18.0  533 533 533 533 533  0 0 0 0 0  19 20 21 21 22  0 0 0 9 8  25 26 27 27 28  0 1 0 9 7  26 28 30 32 34  2 4 6 6 6  213 241 268 296 324  7 2 9 7 4  22 21 20 19 19  8 7 6 8 0  19.0 20.0 21 .0 22.0 23.0  355 355 355 355 355  0 O 0 0 0  23 24 25 26 26  7 5 3 1 8  31 32 33 33 34  2 1 1 9 7  27 28 30 32 33  1 8 5 1 6  261 285 309 333 357  6 4 3 3 3  22 21 21 20 19  4 7 0 4 8  24.0 25.0 26.0 27.0 28.0 29.0 30.0 31 .O 32.0 33.0 34 .0 35.0  266 266 266 266 266 266 266 266 266 266 266 266  0 0 0 0 0 0 0 0 0 0 0 o  27 28 28 29 30 30 31 31 32 32 33 33  5 2 8 5 0 6 2 7 2 7 1 6  36 37 38 39 40 41 41 42 43 44 44 45  9 8 7 5 3 1 9 6 3 0 7 3  28 29 31 32 34 35 36 37 39 40 41 42  .4 8 2 6 0 3 6 9 2 4 7 9  307 329 350 372 393 415 436 458 479 501 522 543  5 0 6 2 8 3 8 3 7 0 2 3  22 21 21 20 20 20 19 19 19 18 18 18  3 8 3 8 4 0 7 3 0 8 5 3  NO. OF STEMS  THINNING DBH(2) BA(2)  TOTAL Pf JODUCTIOf'•1  V(2)  BA(3) SO 10 14 19 23  M 3 6 1 4  CU 32 61 94 130  27 30 33 36 39  0 4 5 4 2  41 43 45 47 49  CM  SO.M  CU.M  312.0  13.0  4. 1  21.5  355.0  20.0  11.2  86.4  178.0  25.7  9.2  86.5  89.0  31.0  6.7  71.2  V(3)  CAI  MAI  M 9 6 7 1  cu M  CU.M  0 28 33 35  0 7 1 4  6.6 10.3 13.5 16.3  162 194 227 261 294  1 8 9 1 5  32 32 33 33 33  0 7 1 2 3  18.0 19.5 20.7 21.8 22.7  5 7 9 9 9  321 349 376 404 432  7 2 9 6 4  27 27 27 27 27  2 5 7 8 8  23.0 23.3 23.6 23.8 24.0  51 53 55 56 58  6 3 0 6 2  456 479 503 527 551  1 9 8 7 7  23 23 23 23 24  7 8 9 9 0  24.0 24.0 24.0 24 .0 24.0  59 61 62 63 65 66 67 69 70 71 72 74  6 0 4 8 2 5 8 1 4 7 9 1  573 594 616 637 659 681 702 723 745 766 787 808  1 7 3 8 4 0 5 9 3 6 8 9  21 21 21 21 21 21 21 21 21 21 21 21  4 5 6 6 6 5 5 4 4 3 2 1  23.9 23.8 . 23.7 23.6 23.6 23.5 23.4 23.4 23.3 23.2 23.2 23. 1  Table  38  EXAMPLE OF OUTPUT FROM EXOTICS TABLE 2  MERCHANTABLE VOLUME YIELD SPECIES: CUPRESSUS LUSITANICA I N I T I A L S I T E INDEX: ESTABLISHMENT: SHAMBA  AGE YEARS 5.0 6.0 7.0 8.0  MAIN 0 O 0 0 4 91 35 10  V( 15) CU.M THINNING  9.0 72 10.0 105 1 1 . 0 139 12.0 173 13.0 208  OS 29 28 63 1 1  14.0 15.0 16.0 17.0 18.0  180 209 238 267 295  44 37 31 20 99  19.0 20.0 21.0 22 . 0 23.0  245 269 294 318 343  44 94 42 85 22  24.0 25.0 26.0 27 . 0 28 . 0 29.0 30.0 31.0 32 . 0 33.0 34 . 0 35.0  297 319 341 363 384 406 427 449 470 491 512 533  93 68 41 10 74 33 83 26 59 83 95 97  0.0  55.82  74.35  66 .65  TABLE  20.0  TOTAL 0 0 0 0 4 91 35 10 72 105 139 173 208  03 29 28 63 1 1  236 265 294 323 351  27 20 13 02 82  375 400 424 449 473  61 1 1 59 03 39  494 516 538 559 581 603 624 646 667 688 709 730  76 51 23 93 57 15 66 09 42 66 78 80  MAIN  V ( 2 0 ) CU.M THINNING  TOTAL  Table  39  EXAMPLE OF OUTPUT FROM  EXOTICS  TABLE 3 STAND TABLE AT CLEARFELL SPECIES: CUPRESSUS LUSITANICA I N I T I A L S I T E INDEX: ESTABLISHMENT: SHAMBA  DIAMETER CLASS CM 33.0 36.0 39.0 42.0 45.0 48.0 51.0 54 . 0 57.0 60.0 63.0 66.0 TOTALS 1  NO. OF TREES  V(1) CU.M 9.81 33 .66 5 9 . 15 79.03 86.57 82.35 69.64 51 . 9 9 35.36 21 . 35 1 1 .76 4.30  9.00 26 . 0 0 39.00 45.00 43.00 36.00 27 . 0 0 18.00 1 1 .00 6.00 3.00 1 .00 264.001  544.95 I  FINAL AGE AT CLEARFELL=  V( 15) CU.M 9.33 32.51 57.64 77.42 85 . 0 6 81 . 0 6 68.62 51 . 2 6 34.88 2 1 .07 1 1 .60 4.24 534.71 I  V(20) CU.M  I  172  distributed  by diameter  classes.  Table 38 and Table 39 are examples  from the same s i m u l a t i o n run as f o r Table 37.  A f t e r these o u t p u t s ,  programme r e t u r n s to the b e g i n n i n g f o r f u r t h e r i n s t r u c t i o n :  the  to stop or  to b e g i n another s i m u l a t i o n . As expected,  the f i n a l number of stems i n T a b l e 37 i s the same as  those on T a b l e 39, except S i m i l a r l y , we  f o r a r o u n d i n g - o f f e r r o r of +2  would expect  t h a t the f i n a l main stand volume on T a b l e  s h o u l d be the same as t o t a l volume ( V ( l ) ) i n Table 39. volume V(15)  and V(20)  diameter lower  stand dominant h e i g h t and  on the DBH  thus assumes a normal  distribu-  However, the volume as c a l c u l a t e d f o r  depend very much on the d i s t r i b u t i o n of the t r e e s by  classes.  Thus, d i s t r i b u t i o n s skewed to the l e f t w i l l  t o t a l volume and  T a b l e 37.  result i n  those skewed to the r i g h t w i l l r e s u l t i n h i g h e r  One  (V(l))  p o s s i b l e s o l u t i o n to t h i s problem would be to c a l c u l a t e  volumes a t each c y c l e as the sum  of the volumes c a l c u l a t e d through  diameter  However, i t was  distribution function.  s t u d y , the diameter  f e l t that f o r t h i s  t h i n n i n g and  so the  d i s t r i b u t i o n f u n c t i o n would not be v a l i d i n unthinned moment, the d i s c r e p a n c y appears and  the  d i s t r i b u t i o n d a t a d i d not cover the young stand ages  adequately, e s p e c i a l l y before f i r s t  +5%  may  of t r e e of mean  t o t a l volume i n T a b l e 39 compared to the f i n a l main stand volume of  V(20)  The main cause of the d i s c r e p a n c y i s t h a t the  t i o n o f the t r e e s by b a s a l a r e a . T a b l e 39 w i l l  37  final  However, as Tables 37 and 39 show, t h i s  volume as c a l c u l a t e d i n T a b l e 37 i s based b a s a l a r e a and  A l s o the  of T a b l e 38 should be the same as V(15) and  r e s p e c t i v e l y of T a b l e 39. not always be the c a s e .  stems.  diameter  stands.  At  the  to be of the order of not more than  so can be c o n s i d e r e d i n s i g n i f i c a n t  for practical  purposes.  173  4.0  Model V a l i d a t i o n  4.1  Introduction Model v a l i d a t i o n i s the p r o c e s s of b u i l d i n g an a c c e p t a b l e l e v e l of  c o n f i d e n c e t h a t an i n f e r e n c e about a s i m u l a t e d p r o c e s s i s a c o r r e c t o r valid  i n f e r e n c e about a s i m u l a t e d p r o c e s s (Van Horn 1968).  e s s e n t i a l accompaniment  I t i s an  f o r any s i m u l a t i o n model as a t e s t t h a t both the  component p a r t s of the model and the performance of the model as a whole are i n agreement w i t h the behaviour fails  o f the r e a l system.  I f the model  to pass t h i s t e s t , then changes must be made i n e i t h e r the  v a r i a b l e s , parameters e s t i m a t e s , o r the s t r u c t u r e o f the model.  This  p r o c e s s s e r v e s two purposes: 1.  I t b u i l d s c o n f i d e n c e of p r o s p e c t i v e model users i n the model.  2.  I t h e l p s d e l i n e a t e the l i m i t s t o model v a l i d i t y .  The knowledge of the l i m i t s to model v a l i d i t y , e s p e c i a l l y w i t h r e s p e c t t o a c c u r a c y and p r e c i s i o n i s v e r y important  to the user when  choosing between a l t e r n a t i v e models. The problems and procedures  f o r model v a l i d a t i o n have been  d i s c u s s e d by s e v e r a l r e s e a r c h e r s I n c l u d i n g N a y l o r and F i n g e r (1967) and Van Horn (1968) w i t h a d e t a i l e d summary by G o u l d i n g F i n g e r (1967) suggested 1.  (1972).  N a y l o r and  a t h r e e stage approach:  C o n s t r u c t a s e t o f hypotheses and p o s t u l a t e s f o r the process using a l l available information:  observations, general  knowledge, r e l e v a n t t h e o r y , and i n t u i t i o n . 2.  Attempt to v e r i f y  the assumptions of the model by s u b j e c t i n g  them t o e m p i r i c a l t e s t i n g .  174  3.  Compare the i n p u t / o u t p u t  transformations  model to those  by the r e a l  Steps one  and  two  generated  of t h i s approach e n t a i l  i n d i v i d u a l model components and  generated  the  system. d e t a i l e d t e s t i n g of  the u n d e r l y i n g assumptions w h i l e  t h i r d step v a l i d a t e s the performance of the whole model. t e s t i n g was  by  The  the  order of  j u s t i f i e d on the grounds t h a t t e s t i n g of assumptions  and  components ( b e f o r e s y n t h e s i s of the model) i s cheaper than t e s t i n g  the  predictions. Van Horn (1968) summed up the problems of v a l i d a t i n g s i m u l a t i o n s  as  s i m i l a r to the s t a n d a r d problems of e m p i r i c a l r e s e a r c h :  He  1.  Small samples due  2.  Too  3.  Data whose own  suggested  aggregate  to h i g h c o s t of  data.  data. validity  i s questionable.  the f o l l o w i n g p o s s i b l e v a l i d a t i o n a c t i o n s - i n rough order  of d e c r e a s i n g v a l u e - c o s t  ratio:  1.  F i n d models w i t h h i g h f a c e  2.  Make use  validity.  of e x i s t i n g r e s e a r c h , e x p e r i e n c e , o b s e r v a t i o n s and  any  o t h e r a v a i l a b l e knowledge to supplement models. 3.  Conduct simple e m p i r i c a l t e s t s of means, v a r i a n c e s ,  and  d i s t r i b u t i o n s using a v a i l a b l e data. 4.  Run  " T u r i n g " type  5.  Apply  tests.  complex s t a t i s t i c a l t e s t s on a v a i l a b l e data e.g.  analysis, Theil's inequality coefficient (1967)).  (Naylor and  spectral  Finger  175  6.  Engage i n s p e c i a l data c o l l e c t i o n .  7.  Run p r o t o t y p e and f i e l d  8.  Implement  tests.  the r e s u l t s w i t h l i t t l e  or no v a l i d a t i o n .  The a p p r o p r i a t e v a l i d a t i o n a c t i o n w i l l depend on s e v e r a l including the  a v a i l a b i l i t y of data ( i n c l u d i n g  type of model.  available  F o r example, complex s t a t i s t i c a l  time and funds) and t e s t s may  a p p r o p r i a t e f o r s t o c h a s t i c models but not f o r d e t e r m i n i s t i c s h o u l d be noted here t h a t process constitute  a l l the s t a t i s t i c a l  n u l l hypotheses.  w i l l not be a "proof" t h a t  factors  be  models.  It  t e s t s i n the v a l i d a t i o n  Acceptance of the n u l l h y p o t h e s i s  the model i s c o r r e c t  but simply  indicates  acceptance o f the model as an a c c e p t a b l e a p p r o x i m a t i o n o f the s i m u l a t e d system a t the r e q u i r e d  Validation  l e v e l of d e t a i l .  of F o r e s t Growth and Y i e l d Models  The v a l i d a t i o n of most growth and y i e l d models i n f o r e s t r y to f o l l o w  c l o s e l y the approach proposed by N a y l o r and F i n g e r  However, l e v e l of model accuracy and p r e c i s i o n has i n g e n e r a l little  attention  1.  T h i s may  (1967). received  i n s p i t e o f concern r a i s e d by some r e s e a r c h e r s  i n c l u d i n g Munro (1974), Row (1980).  appears  and N o r c r o s s (1978) and Smith and W i l l i a m s  be a t t r i b u t e d  to among o t h e r s :  F o r management and p l a n n i n g purposes ( t h e o b j e c t of most growth and  y i e l d models), the r e q u i r e d  l e v e l of accuracy i s o f t e n not  v e r y h i g h so t h a t m o d e l l e r s have tended to downplay the process o f model v a l i d a t i o n .  176  2.  Most growth and y i e l d models are d e t e r m i n i s t i c so t h a t v a l i d a t i o n has been r e s t r i c t e d to simple t e s t s of comparison of o u t p u t s from the model w i t h the r e a l system.  3.  F i e l d t e s t s , which should be e s s e n t i a l f o r any g i v e n model, are u s u a l l y v e r y expensive and time consuming and so a r e o f t e n not conducted.  With r e s p e c t t o the t h i r d problem, the g e n e r a l t r e n d has been t o use long-terra study samples o r permanent sample p l o t s data not used i n the c o n s t r u c t i o n of the model t o t e s t how w e l l the model performs.  This  approach was advocated by Munro (1974a) and has been e f f e c t i v e l y employed by Ek and Mouserud (1977).  (1979), Moser e t a l .  (1979) and A l d e r  Ek and Mouserud (1979) used remeasured p l o t  d a t a to compare  the performance of two models, FOREST and SHAFT (both c a l i b r a t e d f o r n o r t h e r n hardwood stands i n W i s c o n s i n ) w i t h r e s p e c t t o accuracy and precision.  They found the former to be more a c c u r a t e .  Moser e t a l .  (1979) used long-term study ( c u t t i n g c y c l e ) data to v a l i d a t e a s i m u l a t i o n model of uneven-aged n o r t h e r n hardwoods  forest.  They observed  that  b a s a l area and volume were more a c c u r a t e l y p r e d i c t e d than number of stems a l t h o u g h the a c c u r a c y of the l a t t e r was a c c e p t a b l e f o r management and p l a n n i n g purposes.  A l d e r (1977) used psp data to v a l i d a t e PYMOD  a l t h o u g h i t was not c l e a r whether the data had been used i n the cons t r u c t i o n of the model. A more p r e s s i n g concern i n growth and y i e l d model v a l i d a t i o n i s the l e n g t h o f p e r i o d over which the t e s t p l o t s are remeasured. t i o n models a r e designed to "grow" the stand f o r the whole  Most  simula-  rotation.  177  Unfortunately,  any  rotation period.  one  t e s t p l o t u s u a l l y covers  o n l y a f r a c t i o n of  I t i s t h e r e f o r e obvious that t e s t s of accuracy  p r e c i s i o n based on data from these  Put  i n o t h e r words, the  of the s i m u l a t i o n , run governs the p r e c i s i o n of e s t i m a t e s  a  length  obtained  s i m u l a t i o n j u s t as sample s i z e determines the p r e c i s i o n of  by  real-life  T h i s problem i s demonstrated on F i g u r e 21 from A l d e r  (1977), which shows two Tanzania  and  short p e r i o d t e s t p l o t s cannot be  t r u e r e f l e c t i o n o f the model a c c u r a c y .  experiment.  the  s i m u l a t i o n s of t h i n n i n g experiment 345  (P_. p a t u l a ) from d i f f e r e n t  starting conditions.  i n d i c a t e s t h a t i n g e n e r a l , the t o t a l volume simulated diameter d i s t r i b u t i o n at age volume than the  8 years  figure  from the a c t u a l  i s c l o s e r to the a c t u a l measured  t o t a l volume s i m u l a t e d  of the model u s i n g the e x p e r i m e n t a l  The  in  from age  zero.  Thus, v a l i d a t i o n  p l o t s between ages 8 to 15 does not  t e l l the t r u e p i c t u r e o f model v a l i d i t y between ages 0 t o 15. f i g u r e i l l u s t r a t e s i n general  the problem of v a l i d a t i n g  This  the growth and  y i e l d model u s i n g permanent sample p l o t data or o t h e r data whose remeasurement p e r i o d covers  o n l y a f r a c t i o n of the r o t a t i o n p e r i o d over  which the model w i l l be used.  Any  quoted measures of accuracy  or  p r e c i s i o n w i l l appear much b e t t e r than they a c t u a l l y are when the model i s used f o r long-term p r e d i c t i o n s .  T h i s problem w i l l be p a r t l y  resolved  when permanent sample p l o t s c o v e r i n g the whole r o t a t i o n become a v a i l a b l e .  4.2  V a l i d a t i n g EXOTICS U s i n g Independent Permanent Sample P l o t Data  The  data a v a i l a b l e f o r model v a l i d a t i o n i n t h i s study  c o n s i s t e d of  20 permanent sample p l o t s f o r each s p e c i e s (see Chapter 1 S e c t i o n 6)  and  F i g u r e 2 1 t Two S i m u l a t i o n s o f T h i n n i n g Experiment 3 U 5 i n T a n z a n i a ( P . p a t u l a ) from d i f f e r e n t s t a r t i n g c o n d i t i o n s . (from Alder  1977)  T o t a l Volume ( m A a ) 700 n 3  « A c t u a l measurements Simulated  from age 0  S i m u l a t e d from a c t u a l d i a m e t e r d i s t r i b u t i o n a t age 8 600  i  Treatments A  B  C 500  H  300  i  200  H  D E  1 3 9 0 stemsAa 9 8 7  6 9 U 3U7 1 2 0  100  T~  8  ~1—  —1—  10  12  Age from P l a n t i n g  11*  (years)  179  t h e r e f o r e c o n s t i t u t e d an independent s e t of data coming from the same p o p u l a t i o n as those  used t o c o n s t r u c t the model.  the b a s i c v a r i a b l e s :  The data c o n s i s t e d of  age, dominant h e i g h t , b a s a l a r e a and t o t a l  bark volume, w i t h some p l o t s h a v i n g  over-  r e c e i v e d one or more t h i n n i n g s  d u r i n g t h e i r remeasurement p e r i o d . The i n i t i a l  remeasurement age f o r most t e s t p l o t s was  from 5 y e a r s , the i n i t i a l i z a t i o n age f o r the model. problems when s i m u l a t i n g b a s a l a r e a s i n c e p r i o r stand known.  F o r these  This  different presented  s t a t e was not  p l o t s , the i n i t i a l observed b a s a l a r e a was assumed t o  be the same as the p r e d i c t e d b a s a l a r e a and the s i m u l a t i o n s t a r t e d on the second year  of measurement.  stems per h e c t a r e  Where p l o t s t o c k i n g was l e s s than  1000  at age 5 y e a r s , t h i n n i n g was assumed to have a l r e a d y  been c a r r i e d out and s i m u l a t i o n done as f o r p l o t s i n i t i a l i z e d a t ages other  than 5 y e a r s .  For each p l o t , the stand  dominant h e i g h t ,  basal  a r e a , and the b a s a l a r e a removed i n t h i n n i n g ( i f a n y ) , a l l c o r r e s p o n d i n g to  the observed measurements were s i m u l a t e d  and from t h e s e ,  ponding stand t o t a l volume overbark was c a l c u l a t e d .  the c o r r e s -  F i g u r e 22 shows the  r e s u l t s of t h i s procedure f o r two C_. l u s i t a n i c a p l o t s , one i n i t i a t e d a t age 5.5 y e a r s , the o t h e r a t age 21.5 Of the many output  years.  v a r i a b l e s from the s i m u l a t i o n model, t o t a l  volume overbark was s e l e c t e d as the p r i n c i p l e v a r i a b l e to be v a l i d a t e d s i n c e i t i s the primary i n t e r e s t i n f o r e s t management.  Several  t i c s were computed f o r comparing the observed and s i m u l a t e d are p r e s e n t e d  on T a b l e s  statis-  volume and  40, 41 and 42 f o r C_. l u s i t a n i c a , P_. p a t u l a and  P. r a d i a t a r e s p e c t i v e l y .  These s t a t i s t i c s were computed as f o l l o w s :  FIGURE 22  i 8  i 10  12  14  i 16  • 18  i 20  i 22  AGE IN YEARS FROM PLANTING  i 24  i 26  i 28  i 30  i 32  i 34  TABLE 40:  Beta weights, mean b i a s , standard d e v i a t i o n and the 95% c o n f i d e n c e l i m i t s of percentage d i f f e r e n c e s between observed and simulated t o t a l volume overbark, and the Chi-square v a l u e s f o r three h y p o t h e s i z e d l e v e l s of accuracy. C.  Plot  No.  N  Beta-weight  %  Mean b i a s %  lusitanica  Standard deviation %  95% confidence limits  X  15  4 37 54 116 117 121 181 190 202 233 246 261 279 288 295 331 336 348 379 388  Chi-square  10 12 12 5 11 11 11 11 12 13 10 10 11 11 10 9 9 10 9 7  -0.84* 0.64* 0.27 0.89* 0.95* -0.88* -9.60* 0.55 -0.94* -0.77* -0.85* 0.50 0.42 0.95* -0.36 -0.88* -0.95* 0.88* 0.60 -0.68  -0.40 -6.42 -1.25 -0.28 -5.30 -7.65 1.32 4.92 -18.18 -9.39 -7.76 8.57 17.83 -1.39 3.03 -4.65 -4.21 2.32 0.36 -14.63  4.42 5.03 2.25 4.16 9.12 8.10 4.83 5.44 9.95 8.57 3.51 5.08 8.40 4.34 8.05 5.31 2.40 13.93 3.98 12.11  3.16 3.20 1.43 5.17 3.85 5.37 3.24 3.66 6.32 5.18 2.51 3.63 5.64 2.92 5.76 4.08 1.85 9.97 3.06 11.20  B = -2.21  S.D.= 7.93  6.36  v a l u e at the .05 p r o b a b i l i t y  l e v e l of 204 degrees  3.41 17.09 1.33 1.27 27.65* 30.86* 4.20 8.10 164.24* 56.53 15.11 13.56 47.86 3.86 7.87 8.83 3.97 33.73* 2.09 66.02*  of freedom = 238.04.  value  20  25  1.92 9.61 0.75 0.72 15.55 17.36 2.36 4.56 92.38* 31.80* 8.50 7.63 26.92* 2.17 4.43 4.97 2.23 18.97* 1.18 37.14*  1.23 6.15 0.48 0.46 9.95 11.11 1.51 2.92 59.12* 20.35 5.44 4.88 17.23 1.39 2.84 3.18 1.43 12.14 0.75 23.77*  291.1*  186.335  TABLE 41:  Beta weights, mean b i a s , standard d e v i a t i o n and t h e 95% c o n f i d e n c e l i m i t s of percentage d i f f e r e n c e s between observed and simulated t o t a l volume overbark, and the Chi-square v a l u e s f o r three hypothesized l e v e l s of accuracy. P. p a t u l a  P l o t No.  N  Beta-weight %  Mean b i a s %  Standard deviation %  95% confidence limits  X  15 2 12 34 59 123 126 144 147 154 167 203 209 252 270 276 312 315 324 342 391  Chi-square  9 11 12 11 10 10 8 12 11 12 12 13 11 11 11 10 10 9 10 8  0.91* -0.02 -0.72* 0.77* -0.92* -0.02 -0.45 -0.90* -0.18 -0.86* -0.68* -0.86* -0.82* 0.64 -0.25 -0.71* 0.24 -0.89* -0.84* -0.81*  2.46 -1.21 5.37 22.68 -15.42 -1.01 0.54 -5.40 -8.10 -22.82 0.04 -9.51 12.84 3.88 3.31 -8.53 -0.88 -13.20 4.68 -0.28  19.83 3.39 14.20 13.47 14.87 4.19 6.86 15.22 4.71 8.40 11.84 11.99 10.61 2.56 6.53 4.25 4.46 3.96 3.97 11.43  15.24 2.28 9.02 9.05 10.63 3.03 5.74 9.67 3.16 5.33 7.52 7.24 7.13 1.72 4.39 3.04 3.19 3.05 2.84 9.56  B = -1.53  S.D.= 10.02  10.10  v a l u e at the .05 p r o b a b i l i t y l e v e l o f 207 degrees  101.65 2.32 26.20* 74.44* 106.95* 3.24 5.13 58.93 20.71 232.31* 25.30* 69.24 33.91* 3.55 7.87 19.63* 3.39 40.00* 4.20 15.05  o f freedom = 241.28.  2  value  20 57.18* 1.30 14.74 41.87* 60.16* 1.82 2.89 33.15 11.65 130.67* 14.23 38.95* 19.08* 2.00 4.42 11.04 1.91 22.52* 2.36 8.46  25 36.60* 0.83 9.43 26.80* 38.50* 1.16 1.85 21.22* 7.46 83.63* 9.11 24.93* 12.21 1.28 2.83 7.06 1.22 14.41 1.51 5.41 307^33*  TABLE 42:  Beta weights, mean b i a s , standard d e v i a t i o n and the 95% c o n f i d e n c e l i m i t s of percentage d i f f e r e n c e s between observed and simulated t o t a l volume overbark, and the Chi-square v a l u e s f o r three hypothesized l e v e l s of accuracy. P. r a d i a t a  P l o t No.  N  Beta-weight %  Mean b i a s %  Standard deviation %  95% confidence limits  X  15 6 18 31 91 96 99 103 112 134 138 164 177 238 256 289 340 373 383 400 402  14 11 11 6 13 13 9 9 8 12 11 10 13 10 8 8 9 9 7 8  0.48 0.44 0.63* -0.88* -0.84* -0.93* 0.34 0.44 0.72* -0.48 0.59 0.25 -0.46 -0.94* 0.36 -0.62 0.19 0.44 0.77* -0.68 B =  Chi-square  -7.17 2.58 11.92 -7.67 14.29 6.88 6.52 -0.10 -2.71 20.22 3.69 -8.19 -8.43 -1.31 -2.13 -2.00 -1.22 16.07 8.86 -3.32  11.24 3.55 12.00 5.62 18.50 20.16 3.62 2.22 5.22 6.45 10.21 3.10 10.56 5.39 3.73 3.69 3.40 8.19 6.42 3.84  6.49 2.38 8.06 5.89 11.18 12.18 2.78 1.71 4.37 4.10 6.86 2.22 6.38 3.85 3.12 3.08 2.62 6.30 5.94 3.21  2.34  S.D. = 8.50  10.14  value at the .05 p r o b a b i l i t y l e v e l of 199 degrees  57.91* 3.07 33.08* 11.13 61.36* 64.69* 7.06 0.70 5.00 60.29* 16.52 16.06 53.75* 5.30 2.54 2.42 1.99 34.50* 10.49 3.77  of freedom = 232.64.  2  value  20  25  32.57* 1.73 18.61 6.26 34.51* 36.39* 3.97 0.40 2.81 33.91* 9.29 9.03 30.23* 2.98 1.43 1.36 1.12 19.41* 5.90 2.12  20.84 1.11 11.91 4.01 22.09 23.29* 2.54 0.26 1.80 21.70* 5.94 5.78 19.35 1.91 0.92 0.87 0.72 12.42 .3.78 1,36  254.02*  162.58  184  Beta-weight the r e s i d u a l s  %:  (express as p e r c e n t of s i m u l a t e d  -V  E =  E  =  VQ V  3.3  s  R e s i d u a l c o r r e s p o n d i n g to each remeasurement Observed volume  =  S  of  value):  i . 100 V  Where  were o b t a i n e d from the s t a n d a r d i z e d r e g r e s s i o n  = Simulated  on remeasurement age.  volume  The p o s i t i v e values i n d i c a t e p o s i t i v e  correlation  of r e s i d u a l s w i t h r e s p e c t to age and v i c e v e r s a f o r n e g a t i v e v a l u e s , w h i l e the magnitude of the b e t a weight i n d i c a t e the degree of c o r r e l a tion.  I d e a l l y , the c o r r e l a t i o n should be z e r o .  Significant correla-  t i o n s at the .05 p r o b a b i l i t y l e v e l are shown i n a s t e r i s k s on T a b l e s 40, 41 and 42.  Mean b i a s  %:  t h i s was  calculated  as the mean r e s i d u a l f o r each  plot:  B = •?  Where  3.4  ±  E  =  n  = T o t a l number of remeasurements per p l o t .  Standard residuals  E /n  As i n 3.3 above  deviation  i n percent:  %:  computed as the standard d e v i a t i o n  of the  185  s.d. =  £ (E. - B ) / n 1=1 2  - 1  3.5  1  Where  E  =  As i n  3.3  B  =  As i n  3.4  s.d.  =  Standard  deviation.  95% c o n f i d e n c e l i m i t s :  * *  C  Where  L  =  t  ( . 0 5 , n-1)'  S  CL.  -  Confidence  S.j  =  Standard each  Chi-square accuracy: of  computed as:  3  ,  6  limits  e r r o r of the r e s i d u a l s i n percent f o r  plot.  values:  15, 20 and  d  c o r r e s p o n d i n g to t h r e e h y p o t h e s i z e d  25%.  l e v e l s of  These were computed u s i n g F r e e s e ' s 1960  test  accuracy:  X  2,  \  .  ("'P)  Where  a  2 z  _  1  i  1.96 P  =  Z  a  p  2  2  =  V  0  V  2  p e r c e n t of the t r u e value u n l e s s a l - i n - 2 0  occurred  S p e c i f i e d a l l o w a b l e e r r o r as percent of the t r u e  and V  G  3.7  2  (observed) v a l u e VQ,  2  2 196^  Hypothesized chance has  E^ =  -  i-1  E  =  » •  are as above.  186  The  c a l c u l a t e d Chi-square  c r i t i c a l Chi-square freedom.  v a l u e f o r each p l o t was  compared w i t h  v a l u e f o r .05 p r o b a b i l i t y l e v e l and n-degrees of  I f the c a l c u l a t e d C h i - s q u a r e  value exceeded the  critical  v a l u e , then the s i m u l a t e d volume d i d not meet our accuracy and  requirement  the n u l l h y p o t h e s i s of a common d i s t r i b u t i o n of the observed  s i m u l a t e d volumes r e j e c t e d . 41 and  the  and  These are shown i n a s t e r i s k s on T a b l e s  40,  42.  R e s u l t s and D i s c u s s i o n 1.  Beta-weight The  test:  expected  However, due  c o r r e l a t i o n between the r e s i d u a l s  to both random and  negative correlations  and age  i s zero.  s y s t e m a t i c e r r o r s , both p o s i t i v e  are expected.  The  and  t r u e value of t h i s t e s t  t h e r e f o r e i s t o d e t e c t s y s t e m a t i c t r e n d s i n the model by r e v e a l i n g i f t h e r e i s a preponderance of e i t h e r p o s i t i v e or n e g a t i v e s i g n s and i f these a r e s i g n i f i c a n t at the .05 p r o b a b i l i t y T a b l e 40 f o r C_. l u s i t a n i c a shows that n e g a t i v e beta-weights, whose beta-weights  level.  t h e r e were 10 p o s i t i v e and  an i n d i c a t i o n of l a c k of b i a s .  Of the 13  plots  were s i g n i f i c a n t , 5 were p o s i t i v e and 8 n e g a t i v e ,  which would i n d i c a t e a s l i g h t tendency  to o v e r e s t i m a t e .  T a b l e 41 f o r P_. p a t u l a i n d i c a t e t h a t  16 p l o t s had  negative  c o r r e l a t i o n s and o n l y 4 were p o s i t i v e i n d i c a t i n g o v e r e s t i m a t i o n by model.  Of the 13 p l o t s w i t h s i g n i f i c a n t c o r r e l a t i o n s , o n l y 2 were  p o s i t i v e , again p o i n t i n g  to overestimation.  the  10  187  T a b l e 42 f o r P_. r a d i a t a i n d i c a t e s 8 n e g a t i v e and 12 p o s i t i v e weights, a s l i g h t  underestimate.  Of the 7 p l o t s w i t h  beta-  significant  c o r r e l a t i o n s , 3 were p o s i t i v e and 4 n e g a t i v e , i n d i c a t i n g l a c k of b i a s i n the model. From t h i s t e s t , the models f o r C_. l u s i t a n i c a and P_. r a d i a t a cate no apparent  indi-  s y s t e m a t i c t r e n d s w h i l e t h a t f o r P_. p a t u l a p o i n t t o a  p o s s i b l e tendence f o r the r e s i d u a l s t o i n c r e a s e w i t h age.  2.  Mean b i a s t e s t : The mean b i a s measured as p e r c e n t of the p r e d i c t e d v a l u e i s i d e a l l y  expected cannot  t o be z e r o .  F o r reasons  mentioned above, however, t h i s  situation  be r e a l i z e d and the best one can hope f o r i s t h a t over a l a r g e  number of s i m u l a t i o n s , the o v e r a l l mean b i a s w i l l be zero o r c l o s e t o zero. T a b l e 40 f o r C_. l u s i t a n i c a i n d i c a t e s p l o t mean b i a s r a n g i n g +0.3% t o +18% w i t h a mean of -2.21%.  from  Table 41 f o r P^. p a t u l a shows  a range of ±0.5 t o ± 2 3 % w i t h a mean of -1.53% w h i l e T a b l e 42 f o r P. r a d i a t a shows a range of ± 0 . 1 % t o ± 2 0 % w i t h a mean of 2.34%. all  For  t h r e e s p e c i e s , the mean b i a s can be c o n s i d e r e d as n e g l i g i b l e .  It i s  worth n o t i n g t h a t i n s p i t e of the h i g h e r v a r i a b i l i t y i n t h e mean b i a s f o r P. p a t u l a (measured by the r a n g e ) , i t has a s l i g h t l y lower mean b i a s than the o t h e r two s p e c i e s . and  I t i s a l s o worth n o t i n g t h a t p l o t No. 59  167 (P. p a t u l a ) r e p r e s e n t s o u t l i e r s .  each other so t h a t t h e i r e f f e c t  However, the two compensate  on t h e mean b i a s i s almost  nil.  188  3.  Standard  d e v i a t i o n and  standard e r r o r of the r e s i d u a l s as  percentage of s i m u l a t e d volume: The  standard  d e v i a t i o n f o r the £ . l u s i t a n i c a p l o t s i s f a i r l y  homogeneous, r a n g i n g between 2 to 14% w i t h a standard e r r o r of 7.93%. The  variability  f o r V_. p a t u l a and P_. r a d i a t a i s h i g h e r , r a n g i n g between  1 to 20% w i t h a standard e r r o r o f 10% and t r u e d i f f e r e n c e between the observed g e n e r a l l i e w i t h i n ±16% +17%  and  8.50%  respectively.  simulated volume w i l l i n  f o r C_. l u s i t a n i c a , +20%  f o r P_. p a t u l a and  f o r _P. r a d i a t a u n l e s s l - i n - 2 0 chance o c c u r s .  T h i s i s an  improvement on VYTL2 whose 95% c o n f i d e n c e l i m i t s ranged between underestimation  4.  The  Thus, the  40%  and 20% o v e r e s t i m a t i o n ( A l d e r 1978).  i n d i v i d u a l p l o t 95% c o n f i d e n c e  limits:  These i n d i c a t e the range w i t h i n which the t r u e d i f f e r e n c e between the observed  and  s i m u l a t e d volume would be expected  to be u n l e s s a  l - i n - 2 0 chance o c c u r r e d - j u s t as the standard e r r o r i n 3 above.  Thus, i f  the r e s u l t s of 3 above are c o r r e c t , no more than one  be  expected  to have a 95%  e r r o r c a l c u l a t e d i n 3.  confidence  p l o t would  l i m i t g r e a t e r than twice the  standard  As i t turned out none of the t h r e e s p e c i e s  any p l o t w i t h 95% c o n f i d e n c e  l i m i t s g r e a t e r than twice the  had  standard  e r r o r , which c o u l d be c o n s i d e r e d very s a t i s f a c t o r y r e s u l t c o n s i d e r i n g o n l y twenty sample p l o t s were a v a i l a b l e .  5.  Chi-square Freese  square t e s t  t e s t of  accuracy:  (1960) d i s c u s s e d the use of both the t - t e s t and f o r t e s t s of a c c u r a c y .  the C h i -  In regard to the t - t e s t he  t h a t i t i s not s u i t a b l e as i t uses one  form of a c c u r a c y  concluded  (precision) to  189  test  f o r the o t h e r form  results.  He  (freedom  from b i a s ) , f r e q u e n t l y w i t h anomalous  t h e r e f o r e recommended use of C h i - s q u a r e t e s t as i t w i l l  r e j e c t i n a c c u r a t e r e s u l t s , r e g a r d l e s s of the source of i n a c c u r a c y . To use the t e s t as proposed  by Freese (1960), t h r e e statements  are  required: 1.  Statement of a c c u r a c y r e q u i r e d  2.  A measure o f a c c u r a c y  3.  An o b j e c t i v e method of d e c i d i n g whether the a c c u r a c y  attained attained  i s e q u a l t o the a c c u r a c y r e q u i r e d . For t h i s study, the statement  of the r e q u i r e d a c c u r a c y c o n s i s t e d of  three hypothesized l e v e l s of accuracy: v a l u e s , w h i l e the observed  each s p e c i e s .  25% of the  observed  a c c u r a c y c o n s i s t e d of the c a l c u l a t e d C h i -  square v a l u e s by e q u a t i o n 3.7. for  15, 20 and  These are shown i n the r e s p e c t i v e t a b l e  The a s t e r i s k s i n d i c a t e p l o t s where the s i m u l a t e d  volume d i d not meet the r e q u i r e d l e v e l of a c c u r a c y .  T h i s c o n c l u s i o n was  reached by comparing the c a l c u l a t e d C h i - s q u a r e value w i t h the  critical  Chi-square v a l u e f o r n-degrees of freedom at .05 p r o b a b i l i t y l e v e l .  For  the o v e r a l l model, a l l the measurements f o r each s p e c i e s were c o n s i d e r e d t o g e t h e r and the o v e r a l l Chi-square value c a l c u l a t e d . w i t h the c r i t i c a l C h i - s q u a r e v a l u e approximated  x 2  (V)df  =  °*  8 5 3  + V + 1.645  T h i s was  by:  72V - 1  3.8  (From Freese Where  V  =  Degrees of freedom.  compared  (1969))  190  T a b l e 40 f o r C. l u s i t a n i c a i n d i c a t e s t h a t a t a 15% l e v e l of a c c u r a c y , the model gave 7 u n a c c e p t a b l e  r e s u l t s out o f 20.  unacceptable  S i m i l a r l y , a 20% l e v e l of  at .05 p r o b a b i l i t y l e v e l .  a c c u r a c y gave 5 out of 20 unacceptable able.  However, a t 25% l e v e l  This i s  r e s u l t s , which again i s unaccept-  of accuracy o n l y two p l o t s were  unaccept-  a b l e and the o v e r a l l model i s accepted as meeting the s t a t e d l e v e l o f accuracy. lies  Thus, the t r u e l e v e l of a c c u r a c y f o r the C_. l u s i t a n i c a model  somewhere between 20 and 25%.  These r e s u l t s a p p l y a l s o t o the  P. r a d i a t a model as shown on T a b l e 42.  I t can t h e r e f o r e be s t a t e d t h a t  b a r r i n g a l - l n - 2 0 chance, the models f o r these two s p e c i e s are a c c u r a t e if  the r e q u i r e d l e v e l of accuracy i s 20% or l e s s . The model f o r P. p a t u l a (Table 41) on the other hand had a s l i g h t l y  lower  l e v e l of accuracy compared to the other two s p e c i e s .  of  a c c u r a c y , 11 p l o t s out of 20 were u n a c c e p t a b l e , 8 were  at  20% and 6 were unacceptable  at 25%.  At 15% l e v e l unacceptable  The o v e r a l l model was  unaccept-  a b l e a t the r e q u i r e d a c c u r a c y l e v e l o f 25% but was a c c e p t a b l e at 30% (X  2  = 213.42 compared to c r i t i c a l X  2  = 241.28).  Thus, the t r u e  a c c u r a c y l e v e l f o r t h i s s p e c i e s a t .05 p r o b a b i l i t y l e v e l l i e s between 25 and 30%. to  somewhere  T h i s lower l e v e l of accuracy i s seen from the t a b l e  be a s s o c i a t e d w i t h the l a r g e r b i a s e s and/or standard d e v i a t i o n s . The above l e v e l s of accuracy a r e comparable w i t h the accuracy of  two models a l r e a d y i n o p e r a t i o n - FOREST and SHAFT (Ek and Monserud 1979).  F o r example both models were found t o p r e d i c t b a s a l area w i t h  approximately  a l - i n - 2 0 chance of a 20% or g r e a t e r e r r o r .  Number o f  stems f o r t r e e s w i t h DBH > 12.7 cm were p r e d i c t e d w i t h 22 and 39% or  191  greater  e r r o r by FOREST AND  SHAFT r e s p e c t i v e l y .  t h a t FOREST i s a s i n g l e - t r e e , d i s t a n c e  I t should be noted here  dependent model w h i l e SHAFT i s a  whole s t a n d , diameter d i s t r i b u t i o n model.  EXOTICS i s a whole  stand  diameter f r e e model a l t h o u g h diameter d i s t r i b u t i o n i s a v a i l a b l e i n the f i n a l output.  I t i s therefore  o f i n t e r e s t to note how d i f f e r e n t types  of models can have c l a i m to the same l e v e l of a c c u r a c y . For  purposes of a p p l i c a t i o n i t should be noted t h a t the l e v e l s o f  a c c u r a c y c a l c u l a t e d above f o r EXOTICS a r e based on a .05 p r o b a b i l i t y level.  I f a u s e r i s prepared t o t o l e r a t e lower l e v e l s , the models  appear a c c e p t a b l e down to 15% a c c e p t a b l e e r r o r f o r £ . l u s i t a n i c a and P_. r a d i a t a and 20% f o r P. p a t u l a .  Indeed Ek and Monserud  (1979)  c o n s i d e r e d FOREST s u i t a b l e f o r development of management guides and a n a l y s i s o f s i l v i c u l t u r a l a l t e r n a t i v e s i n d e t a i l a t these l e v e l s o f accuracy.  I t i s therefore  c o n c e i v a b l e t h a t EXOTICS w i l l be a v e r y  u s e f u l t o o l f o r t h a t purpose, i n a d d i t i o n t o y i e l d p r e d i c t i o n s f o r management and p l a n n i n g p u r p o s e s .  6.  Sources o f E r r o r s : The l a r g e b i a s and s t a n d a r d d e v i a t i o n e x h i b i t e d  p l o t s on T a b l e s 40, 41 and 42 c o u l d have a r i s e n  by some of the  from t h r e e  possible  sources: 1.  From model  2.  B i a s from age c l a s s o r s i t e index d i s t r i b u t i o n .  3.  Errors  In EXOTICS,  components.  from exogenous f a c t o r s . two major components c o u l d  dominant h e i g h t and b a s a l a r e a f u n c t i o n s .  give r i s e to e r r o r s : The b i a s e s f o r  192  dominant h e i g h t and b a s a l a r e a (as p e r c e n t of p r e d i c t e d v a l u e s ) f o r a l l t h r e e s p e c i e s a r e shown on T a b l e 43.  In g e n e r a l , the o v e r a l l mean b i a s  f o r both dominant h e i g h t and b a s a l a r e a was almost s p e c i e s , except  negligible for a l l  the mean b i a s f o r P_. r a d i a t a b a s a l a r e a w i t h an under-  e s t i m a t e of 2.74%.  T h i s may be the cause of the volume underestimate of  2.34%  I t s h o u l d be noted here t h a t the mean b i a s  on T a b l e 42.  from  volume i n t h i s case i s lower than mean b i a s from b a s a l area because the mean b i a s from dominant h e i g h t i s n e g a t i v e . volume i s a p p r o x i m a t e l y  In g e n e r a l the e r r o r i n  the sum of the component  errors.  For a l l s p e c i e s , the p l o t s h e i g h t b i a s e s a r e v e r y low, r a n g i n g almost  zero t o 5%.  estimate:  from  T h i s i s confirmed by the low s t a n d a r d e r r o r of  1.38, 3.07 and 1.04 f o r C_. l u s i t a n i c a , P. p a t u l a and  P_. r a d i a t a r e s p e c t i v e l y .  P l o t No. 324 f o r P_. p a t u l a appears  o u t l i e r w i t h a -10.45% b i a s .  t o be an  T h i s was because the p l o t age extended t o  28 y e a r s which i s beyond the range covered by the h e i g h t over age data f o r P_. p a t u l a . which i s s t i l l  E x c l u d i n g t h i s p l o t gave a standard e r r o r o f 2.12%, h i g h e r than t h a t f o r the other two s p e c i e s .  The p l o t b a s a l a r e a b i a s e s on the other hand a r e v e r y v a r i a b l e as i n d i c a t e d by the s t a n d a r d e r r o r of e s t i m a t e :  7.94, 6.66 and 8.52 f o r  C_. l u s i t a n i c a , P_. p a t u l a and P. r a d i a t a r e s p e c t i v e l y . appears  I t therefore  t h a t n e a r l y a l l o f t h e v a r i a b i l i t y i n the _C. l u s i t a n i c a and  P. r a d i a t a models i s a r e s u l t o f t h i s component w h i l e v a r i a b i l i t y i n the P_. p a t u l a model can be a p p o r t i o n e d t o both dominant h e i g h t and b a s a l a r e a f u n c t i o n s i n the r a t i o o f 1:2. variability noted  I n a d d i t i o n t o the sources o f  i n b a s a l a r e a e s t i m a t e d i s c u s s e d i n Chapter  2, i t should be  t h a t i n t h e s i m u l a t i o n model, e r r o r s c o u l d a r i s e from  three  TABLE 43:  B i a s percentage f o r dominant h e i g h t and b a s a l a r e a f o r t e s t sample p l o t s by s p e c i e s .  £. l u s i t a n i c a  P_. p a t u l a  Height  Basal area  4 37 54 116 117 121 181 190 202 233 246 261 279 288 295 331 336 348 379 388  -0.08 -1.12 -1.91 -4.04 -1.06 -1.36 -1.81 -2.14 -0.29 -1.20 -3.41 -2.98 -0.93 -0.64 -0.34 -2.02 -1.79 0.79 -0.61 1.82  -0.30 -5.04 0.26 3.03 -4.09 -6.61 2.85 6.54 -17.36 -8.38 -5.25 11.48 17.21 -0.83 3.19 -3.21 -2.83 1.47 1.04 -14.72  Means S.D.  -1.26 1.38  -1.08 7.94  P l o t No.  E x c l u d i n g p l o t 348 f o r P. p a t u l a :  P l o t No.  2 12 34 59 123 126 144 157 154 167 203 209 252 270 276 312 315 324 342 391  Mean ) S.D. )  P. r a d i a t a  Height  Basal area  -1.87 0.30 -.190 -1.04 1.40 -0.53 -0.42 -0.05 -0.90 -0.74 0.55 -0.42 2.55 2.77 2.59 -5.81 -3.14 -10.45 -3.58 0.57  5.23 -1.49 6.71 23.78 -16.96 -0.45 0.87 -6.14 -7.01 -21.92 -0.69 -9.60 9.60 1.16 0.69 -2.59 2.25 -3.35 8.17 -1.34  -1.01 3.07  -0.65 6.66  -0.48 2.12  permanent  P l o t No.  6 18 31 91 96 99 103 112 134 138 164 177 238 256 289 340 373 383 400 402  Height  Basal area  -0.49 0.10 -0.73 -2.55 -1.55 -1.75 -0.33 -0.84 0.12 -1.83 -0.98 -1.66 2.33 -0.14 -0.45 0.40 -0.10 -0.55 -0.10 -0.35  -6.52 2.41 12.27 -5.65 15.08 7.67 6.68 0.56 -2.72 21.29 4.41 -6.59 -9.62 -1.15 -1.76 -2.18 -1.11 16.02 8.69 -2.93  -0.57 1.04  2.74 8.52  194  sub-components:  b a s a l area  f u n c t i o n before  first  increment e q u a t i o n and the t h i n n i n g f u n c t i o n .  thinning, basal  In g e n e r a l  area  however, the  v a r i a b i l i t y appears t o be of a random nature except f o r the tendency f o r the P_. r a d i a t a model t o s l i g h t l y underestimate the b a s a l area  component.  T h i s may r e q u i r e f u r t h e r refinement i n f u t u r e work. Figures age  23, 24 and 25 show the d i s t r i b u t i o n o f the t e s t p l o t s by  and p l o t mean b i a s % f o r C_. l u s i t a n i c a , P_. p a t u l a and P_. r a d i a t a  respectively.  I n a l l cases,  there i s no evidence of b i a s i n the  d i s t r i b u t i o n of the b i a s w i t h r e s p e c t and  S i m i l a r l y , Figures  26, 27  28 show the d i s t r i b u t i o n o f the t e s t p l o t s by s i t e index and p l o t  mean b i a s and a g a i n index.  i s no evidence of b i a s w i t h r e s p e c t  to s i t e  P l o t No. 238 f o r P_. r a d i a t a appears t o be an o u t l i e r .  It i s  worth n o t i n g belonged: and  t o age.  there  t h e range of the s i t e i n d i c e s w i t h i n which the t e s t p l o t s  17 t o 23, 18 t o 28 and 24 t o 31 f o r C. l u s i t a n i c a , P. p a t u l a  P_. r a d i a t a r e s p e c t i v e l y .  S i m i l a r l y , the age range f o r t e s t p l o t s  was 5 t o 43, 5 t o 20 and 5 t o 30 f o r C_. l u s i t a n i c a , P_. p a t u l a and P_. r a d i a t a r e s p e c t i v e l y . F i n a l l y but not l e a s t , there a r e s e v e r a l exogenous f a c t o r s t h a t may introduce  e r r o r i n the model.  1.  Measurement e r r o r s .  2.  Biotic factors:  These i n c l u d e :  i n c l u d i n g game damage, i n s e c t and d i s e a s e ,  etc. 3.  C l i m a t i c and e d a p h i c f a c t o r s some of which may not have been covered i n the study.  These i n c l u d e annual weather f l u c t u a -  t i o n s and cumulative drought e f f e c t s , s o i l f a c t o r s , e t c .  FIGURE 23 DISTRIBUTION OF C. LUSITANICA TEST PLOTS 3Y AGE AND VOLUME BIAS Z  , 279  • 116 54 -336 -117 •37  . 121  246  • 233  1 1 I In  , 30 «  14  16  18  20  22  24  26  • 32  1 34  . 36  • 38  1 40  1— 42  28  AGE IN YEARS FROM PLANTING VO  FIGURE 24 DISTRIBUTION OF P. PATULA TEST PLOTS BY AGE AND VOLUME BIAS %  -34 270 -2 144  VO 2  4  6  8  10  12  14  16  18  20  22  24  AGE IN YEARS FROM PLANTING  26  28  30  32  34  FIGURE 25 DISTRIBUTION OF P^ RADIATA TEST PLOTS BY AGE AND VOLUME BIAS %  • 400 99  -103  373-  238-  12  16  20  AG!' IN YEARS FROM PLANTING  24  FIGURE 26 DISTRIBUTION OF C. LUSITANICA TEST PLOTS BY SITE INDEX AND VOLUME BIAS %  •  279  • 190  • 181 •116  *4  288»  ,  S  4  • 336 • 117 • 37 •246  »121 • 233  • 388 •  -I 10  1  r — — i 12  • 14  1  1 16  1  1 1 8  202  •  PLOT SITE INDEX IN METERS  . 20  .  — 22  .  r24  FIGURE 27 DISTRIBUTION OF P. PATULA TEST PLOTS BY SITE INDEX AND VOLUME BIAS %  20'  •  •  252  • 34  342  • 2 .203  • 270  • 276 «144  391  '  *126  «12  • 209  • 312  •  324  • 123  17  18  19  167 "• ' 20  21  22  23  24  PLOT SITE INDEX IN METERS  25  26  27  FIGURE 28 DISTRIBUTION OF P. RADIATA TEST PLOTS BY SITE INDEX AND VOLUME BIAS %  • 138  • 383 • 98 • 31  • 400 • 103  • 164 • 18  .373 •256 *  3  4  8,34  0  " \  •• •  y\  'l8  . 20  ..  2  402  »177  238  19  " "  -91  (S3 21  22  23  24  25  26  27  PLOT SITE INDEX IN METERS  28  29  30  31  O  201  The  e f f e c t s of these  f a c t o r s i s to i n t r o d u c e e r r a t i c behaviour  some p l o t s so t h a t t h e i r observed simulated values.  The  in  v a l u e s w i l l d i f f e r markedly from the  q u e s t i o n of how  to d e a l w i t h these f a c t o r s i s  more p h i l o s o p h i c a l than p r a c t i c a l s i n c e these problems are f o r the most p a r t t h e r e to s t a y . (outliers) call  Thus, i n my  view, p l o t s showing e r r a t i c  behaviour  f o r s p e c i a l a t t e n t i o n to determine the cause but  not be e l i m i n a t e d u n l e s s t h e r e Is c l e a r evidence  should  that they a r e from  o u t s i d e the p o p u l a t i o n of I n t e r e s t .  4.3  Conclusion The  o v e r a l l c o n c l u s i o n from the v a l i d a t i o n process  model i s unbiased  f o r a l l s p e c i e s except  e s t i m a t i o n f o r P. r a d i a t a . between simulated +20%  and  The  observed  f o r _P. p a t u l a and +17%  95%  confidence  volume was  occurred. . up to 15%  25 to 30%  ±16%  f o r P. r a d i a t a .  a t an e r r o r s p e c i f i c a t i o n between 20 and P_. r a d i a t a ) and  for a slight  25%  tendency to under-  l i m i t s f o r the d i f f e r e n c e f o r C_.  The  lusitanica  model i s a c c e p t a b l e  (C_. l u s i t a n i c a  I f the lower p r o b a b i l i t y l e v e l i s a c c e p t a b l e . of e r r o r f o r £ .  has  for error s p e c i f i c a t i o n  f o r C_. l u s i t a n i c a and P_. r a d i a t a and up to 20%  Both dominant h e i g h t and  and  f o r .P. p a t u l a , u n l e s s a l - i n - 2 0 chance  However, the model i s f a i r l y a c c u r a t e  as the main source  i s t h a t the  f o r P_. p a t u l a  B a s a l area was  l u s i t a n i c a and P.  identified  r a d i a t a models.  b a s a l area c o n t r i b u t e d to the e r r o r f o r  P_. p a t u l a model i n the r a t i o of 1:2.  Thus f u t u r e refinement  to the  model should be d i r e c t e d at b a s a l a r e a components f o r a l l s p e c i e s . Dominant h e i g h t f u n c t i o n f o r P. p a t u l a may  a l s o need f u r t h e r  refinement.  202  The 24 to 31 t o 43,  t e s t p l o t s covered s i t e index ranges of 17 to 23, f o r 0,  l u s i t a n i c a , P_. p a t u l a and  5 t o 20 and  P.  r a d i a t a and  5 to 30 years f o r the same s p e c i e s  a c c u r a c y l e v e l s mentioned above apply  18 to 28  age  ranges of 5  respectively.  to these ranges.  I t should  be noted t h a t i n d i v i d u a l p l o t runs were l i m i t e d to an average of years.  It i s l i k e l y that longer  simulations  w i l l not  and  The  also 10  r e s u l t i n the same  l e v e l of accuracy. From the above d i s c u s s i o n , i t i s c l e a r t h a t EXOTICS i s capable of accurately simulating  stand  l i m i t a t i o n s s t a t e d above.  growth f o r the three Its u t i l i t y  species within  f o r p r e d i c t i n g stand  the  y i e l d and  as  a management guide i n a n a l y z i n g d i f f e r e n t s i l v i c u l t u r a l a l t e r n a t i v e s i s the  subject  of the next c h a p t e r .  test with respect  This w i l l  to i n p u t v a r i a b l e s .  serve  as the  sensitivity  203  CHAPTER  4  SILVICULTURAL MANAGEMENT MODELS FOR KENYA  1.  Introduction  As mentioned i n t h e i n t r o d u c t i o n (Chapter  1) a thorough knowledge  of t h e growth and y i e l d o f t h e f o r e s t r e s o u r c e s under d i f f e r e n t p h y s i c a l and b i o l o g i c a l c o n d i t i o n s i s b a s i c t o f o r m u l a t i o n o f sound  forest  management p l a n s , i n c l u d i n g s i l v i c u l t u r a l management s c h e d u l e s .  Forest  i n v e n t o r y systems, o f which the permanent sample p l o t programme f o r Kenya forms a p a r t , a r e t h e main source o f t h i s i n f o r m a t i o n , w h i l e growth and y i e l d models a r e i n v a l u a b l e t o o l s f o r p l a n n i n g and experiment a t i o n with a l t e r n a t i v e schedules.  T h i s chapter I s devoted  to the study  of t h e growth and y i e l d of t h e three s p e c i e s under the p r e s e n t management schedules  and the f o r m u l a t i o n of a l t e r n a t i v e schedules u s i n g t h e  y i e l d model EXOTICS developed  i n the previous chapter.  In t h i s  regard,  t h i n n i n g i s s i n g l e d out as t h e p r i n c i p a l s i l v i c u l t u r a l means f o r stand manipulation  towards t h e d e s i r e d g o a l s and o b j e c t i v e s .  Fundamentally, t h i n n i n g i n v o l v e s the p e r i o d i c removal o f some o f the t r e e s , w i t h t h e main o b j e c t i v e being to p r o v i d e the remaining w i t h adequate growing c o n d i t i o n s .  trees  In p r i n c i p l e , t h e r e f o r e , the whole  p r o c e s s amounts t o stand d e n s i t y c o n t r o l to achieve t h e d e s i r e d o b j e c tives.  The main concern  t o f o r e s t e r s has been to d e c i d e what measures  of stand d e n s i t y t o employ and t h e l e v e l of stand d e n s i t y c o n t r o l to apply. Since t h i n n i n g c o n s i s t s of removal of some of t h e t r e e s i n the s t a n d , i t seems obvious  t h a t stem count  should be the l o g i c a l means o f  204  density  control.  r o t a t i o n , the  However, as the number of t r e e s d i m i n i s h e s over  s i z e of the  i n d i v i d u a l trees increases.  Thus,  according  to W i l s o n (1979), stem count must be q u a l i f i e d by some measure of s i z e i f i t i s to have meaning.  W i l s o n proposed the use  f u n c t i o n of stand dominant h e i g h t , discussed  under the  s e c t i o n on  W i l s o n ' s (1946) p r o p o s a l several other countries disadvantage a l r e a d y that  the  stand has  as  already  been  index.  research  in  In a d d i t i o n to i t s  i t i s demonstrated l a t e r i n t h i s s e c t i o n same stand d e n s i t y  index w i l l  have  areas per h e c t a r e f o r d i f f e r e n t s i t e index c l a s s e s .  these s p e c i e s  t h i s index i s inadequate as a measure of the degree to  which a given  species  A more recent by Drew and  is utilizing  the  (1977, 1979).  any  density  c o n t r o l has  p r i n c i p l e of p l a n t  can be determined by a r e l a t i o n s h i p known as the -3/2  where v = mean t r e e volume constant  P = stand d e n s i t y expressed as number of  trees.  the  popula-  In pure stands, the maximum mean t r e e s i z e a t t a i n a b l e  law:  a = a  been proposed  B a s i c a l l y the approach employs  concept of maximum s i z e - d e n s i t y as a g e n e r a l tion biology:  For  site.  approach to stand d e n s i t y  Flewelling  a  density.  been a p p l i e d i n t h i n n i n g  f o r some s p e c i e s , stands o f the  d i f f e r e n t basal  tree  of s p a c i n g  concept of which has  as H a r t ' s d e n s i t y  discussed,  the  for  power  205  The  above law  can be r e w r i t t e n  as:  I n v = a' - — lnp 2 So t h a t -3/2  4.2  represents  the s l o p e of the maximum s i z e - d e n s i t y  r e l a t i o n s h i p as shown on F i g u r e Washington and  29  for coastal Douglas-fir  from  Oregon (adopted from Drew and F l e w e l l i n g 1979).  e m p i r i c a l determination  of t h i s law and  The  i t s t h e o r e t i c a l d e r i v a t i o n were  developed by Yoda et a l . ( 1 9 6 3 ) w h i l e I t s a p p l i c a t i o n to f o r e s t r y has been demonstrated by Yoda et a l . (1963) and 1979).  According  power law The initial  t o Harper (1977), t h e r e  Drew and  i s evidence that t h i s  h o l d s t r u e f o r f o r e s t t r e e s as w e l l as p r a c t i c a l i m p l i c a t i o n of t h i s law  density  F l e w e l l i n g (1977, -3/2  f o r annual p l a n t s .  i s t h a t a stand  of a  given  ( i n terms of number of t r e e s per u n i t a r e a ) w i l l  main-  t a i n volume growth u n t i l the mean t r e e volume (or s i z e ) reaches maximum s i z e f o r that d e n s i t y g i v e n  by e q u a t i o n 4.1.  s i z e - d e n s i t y a t which s e l f - t h i n n i n g ( c o m p e t i t i o n i n and  i n d i c a t e s the p o i n t at which the  stand  This indicates  induced) m o r t a l i t y  i s due  for thinning.  problem f o r the f o r e s t manager then i s to determine that t h i s a p p l i e s to the s p e c i e s he 4.1)  i s d e a l i n g w i t h and  which w i l l depend on the  bility  species  of t h i s r e l a t i o n s h i p i s best  ments, e s p e c i a l l y the constant The principle  and  the  the  The  sets The  law  relationship  site factors.  the  (equation  applica-  determined from c o n t r o l l e d e x p e r i -  stocking  trials.  approach of Reukema and Bruce (1977) u t i l i z e s a s i m i l a r to t h a t of Drew and F l e w e l l i n g (1977, 1979)  used maximum s t o c k i n g l e v e l when a stand  i s due  except t h a t they  ( b a s a l a r e a ) per u n i t area as a guide to  for thinning.  B e s i d e s p r o v i d i n g the f o r e s t manager  206  Mean Tree Volume  (m»)  (ff)  300  500  (trees/acre)  1000  1500 2000  (trees /hectare)  3000  5000  Density  Figure 29  The maximum size-density relationship and the natural stand data used in positioning this relationship.  (from Drew and F l e w e l l i n g 1979)  207  w i t h an o b j e c t i v e guide (maximum b a s a l a r e a ) t o t h i n n i n g , t h i s approach has  the advantage of e n s u r i n g  e f f i c i e n t u t i l i z a t i o n of s i t e by a s p e c i e s .  In a d d i t i o n , i t p r o v i d e s  a c o n t i n u o u s mechanism f o r t r e e dimension  c o n t r o l s i n c e mean stand  DBH can be d e r i v e d  time.  I t s main drawback r e s t s I n d e f i n i n g q u a n t i t a t i v e l y the maximum  stocking  level.  In a d d i t i o n t o d e c i d i n g when a stand other the  from the b a s a l area a t any  v a r i a b l e s enter a t h i n n i n g model:  l e n g t h of time between t h i n n i n g s .  i s due f o r a t h i n n i n g , two the i n t e n s i t y o f t h i n n i n g and  As mentioned e a r l i e r i n Chapter  2, these two are i n t e r r e l a t e d , s i n c e the higher longer  the t h i n n i n g i n t e r v a l and v i c e v e r s a .  the i n t e n s i t y , the  Thus, i f the b a s a l  area  a f t e r t h i n n i n g and b a s a l area growth r a t e a r e known, then the time i t takes b e f o r e  the stand  i s due f o r the next t h i n n i n g i s known.  Both  these v a r i a b l e s a r e f u n c t i o n s o f the economics o f t h i n n i n g and the b i o l o g i c a l f a c t o r s , as mentioned elsewhere. mics o f t h i n n i n g I s not c o n s i d e r e d w i l l be d i s c u s s e d . quantity the  2.  Current Figure  and t h e r e f o r e o n l y b i o l o g i c a l  factors  The problem reduces to one of determining the  o f the stand  current  In t h i s study, the econo-  to be removed a t each t h i n n i n g .  In t h i s  respect,  t h i n n i n g i n t e n s i t y used i n Kenya was used as a guide.  T h i n n i n g Models f o r Sawtimber Regimes i n Kenya 30a,b, and c, i l l u s t r a t e the c u r r e n t b a s a l area  thinning  model f o r £ . l u s i t a n i c a , P_. p a t u l a and P_. r a d i a t a r e s p e c t i v e l y while Figure the  31a,b, and c, i l l u s t r a t e  respective  species  the MAI and CAI (smoothed) curves f o r  under the c u r r e n t  sawtimber t h i n n i n g regimes.  208 FIGURE 30 MAIN STAND BASAL AREA/AGE RELATIONSHIP UNDER THE CURRENT SAWTIMBER THINNING REGIMES BY SPECIES AND S.I. CLASSES  4  8  12  1 6  2 0  AGE IN YEARS FROM PLANTING  2 4  2 8  3 2  209  FIGURE 31 MEAN AND CURRENT ANNUAL VOLUME INCREMENT RELATIONSHIP WITH AGE FOR THE CURRENT SAWTIMBER THINNING REGIME BY SPECIES AND S.I. CLASSES M.A.I, and C.A.I, m a)  50  C.A.I, m  (smoothed out)  (unsmoothed)  C . LUSITANICA.  <40  24-  P3 en  230  2 1 ' /v---*r _V.%  18'x  .20  oio > 10  20  30  40  10  20  30  40  210  Unsmoothed CAI curves  a r e a l s o shown on F i g u r e 31 f o r each s p e c i e s to  i l l u s t r a t e the e f f e c t s o f t h i n n i n g on the c u r r e n t annual volume i n c r e ment development. stand  Tables  44, 45 and 46 give the volume y i e l d and other  c h a r a c t e r i s t i c s f o r C_. l u s i t a n i c a , P_. p a t u l a and P_. r a d i a t a  respectively.  The f o l l o w i n g f e a t u r e s c h a r a c t e r i s t i c o f the present  sawtimber t h i n n i n g model a r e worth n o t i n g : (a)  F o r £ . l u s i t a n i c a t h i n n i n g model 1.  At f i r s t  t h i n n i n g , c a r r i e d out when stands  on a l l s i t e  classes  have the same stand d e n s i t y index o f 25%, stand b a s a l areas are 32.2,  28.5, 25.3, 24.3 and 17.7 m  2 p  e  r  hectare  for site  c l a s s e s 12, 15, 18, 21 and 24 r e s p e c t i v l e y (see Table t h i s s p e c i e s t h e r e f o r e , t h i n n i n g t o a common stand index r e s u l t s i n d i f f e r e n t  index  44).  For  density  l e v e l s of s i t e u t i l i z a t i o n , w i t h the  poor s i t e s c a r r y i n g a much h e a v i e r b a s a l area than the good sites. and  T h i s i s the o p p o s i t e  demonstrates the weakness, a l r e a d y mentioned, i n h e r e n t i n  using Hart's this 2.  to what the s i t u a t i o n should be  stand d e n s i t y index as a guide to t h i n n i n g f o r  species.  Except f o r f i r s t before  t h i n n i n g , the average maximum b a s a l  t h i n n i n g i s 33 m  area  p e r h e c t a r e , and the average b a s a l  a r e a a f t e r t h i n n i n g i s 26 m  per h e c t a r e .  Thus, t h e r e i s an  i m p l i e d maximum b a s a l a r e a which, j u d g i n g from the b a s a l curve  area  t r e n d s , appear to be w e l l below the maximum c o n s i s t e n t  w i t h maximum b a s a l a r e a y i e l d , e s p e c i a l l y f o r s i t e c l a s s e s >18.  211  TABLE 44.  Volume y i e l d and o t h e r r e l e v a n t stand parameters under the c u r r e n t sawtimber t h i n n i n g r e g i me f o r C. l u s i t a n i c a t o a r o t a t i o n age of 40 y e a r s : T e c h n i c a l Order No. 42 of March 1969.  12  S i t e Index  15  11.25  11.25  Age a t l s t t h i n n i n g  14  11  2 BA (m ) b e f o r e  32.2  28.5  C u l m i n a t i o n age (approx.)  30  MAI max  (m )  CAI max  (m )  H  dom  a  t  l  s  t  thinning  l s t thinning  3  DBH a t age 40 y e a r s Total V ( l ) m  J  a t age 40 y e a r s  T h i n n i n g volume as % T o t a l V(15) nr a t age 40 y e a r s T h i n n i n g V(15) m  No. i n b r a c ket  3  as %  18  11.25  21  11.25  24  11.25  8  6  25.3  24.3  17.7  26  24  21  19  16.0  19.0  22.0  25.2  28.1  23(12)  27(11)  32(10)  37(9)  40(7)  43.7  46.1  47.6  48.3  50.1  637.5  749.3  849.7  943.0  1037.7  37.3  33.0  30.3  29.7  28.1  771.4  860.6  961.8  24.4  24.2  21.6  567.3 30.8  i n d i c a t e age o f max. CAI.  674.2 , 26.7  9  212  TABLE 45.  Volume y i e l d and o t h e r r e l e v a n t stand parameters under the c u r r e n t sawtimber t h i n n i n g regime f o r P_. p a t u l a (Nabkoi) t o a r o t a t i o n of 20 y e a r s : T e c h n i c a l Order No. 53 of May 1981  P. p a t u l a (Nabkoi) Shamba 21  24  27  16.8  16.8  17.5  17.7  17  14  12  11  10  40.1  36.6  33.7  33.0  31.5  18  21  24  27  30  33(14)  40(13)  48(12)  55(11) 61(10)  15  18  16.9  Age a t l s t t h i n n i n g BA (m ) b e f o r e  S i t e Index  H  dom  a  t  l  s  t  thinning  2  MAI max CAI max  l s tthinning  (m ) a t age 20 y e a r (m ) 3  Total V ( l ) m  3  a t age 20 y e a r  T h i n n i n g volume as % T o t a l V(15) m  3  a t age 20 y e a r  T h i n n i n g V(15) m T o t a l V(20) m  3  3  as %  a t age 20 y e a r  T h i n n i n g volume as %  358.9 35  416.2 45  472.0 39  542.6 35  261.0  312.8  364.3  428.8  28  37  29  26  101.9 0  No. i n b r a c k e t i n d i c a t e age o f max. CAI.  642.0 32 520.7 22  160.5  218.0  277.0  374.3  12.0  8.0  8.0  7.0  213  TABLE 46.  Volume y i e l d and o t h e r r e l e v a n t stand parameters under the c u r r e n t sawtimber t h i n n i n g regime f o r P_. r a d i a t a t o a r o t a t i o n age of 30 y e a r s : T e c h n i c a l Order No. 44 o f March 1969.  P. r a d i a t a Shamba 21  24  12.2  12.5  S i t e Index  H  dom  a  t  l  s  t  t  h  i  n  n  i  n  g  Age a t l s t t h i n n i n g o BA n r a t l s t t h i n n i n g 2 BA n r a t 2nd t h i n n i n g 3 MAI max m up t o age 35 CAI max m  3  DBH t o age 30 y e a r s Total V ( l ) m  a t age 30 y e a r s  T h i n n i n g volume as % T o t a l V(15) m  3 a  t age 30 y e a r s  T h i n n i n g V(15) as % 3 T o t a l V(20) nr a t age 30 y e a r s T h i n n i n g volume as %  9  8  27  30  33  12.4  14.1  13.5  7  7  6  14.9  14.9  14.5  16.3  15.4.  21.0  19.5  19.8  19.1  18.9  22  25  28  31  34  32(35)  35(35) . 38(35)  40(17)  44(16)  41.6  44.3  46.2  47.7  49.5  655.8  751.8  855.8  946.9  1052.8  33.1  28.7  27.2  25.8  24.2  542.8  642.6  743.4  831.0  939.1  21.4  18.5  18.0  17.1  16.7  471.3  573.6  713.4  760.9  869.5  14.4  12.4  11.9  12.0  12.0  No. i n b r a c k e t i n d i c a t e age o f max. CAI.  214  3.  The CAI c u r v e s (unsmoothed) i n d i c a t e that except f o r f i r s t t h i n n i n g , a l l o t h e r t h i n n i n g s have a marked e f f e c t on the c u r r e n t annual volume increment, i n d i c a t e d by the drop i n CAI after thinning.  T h i s i n e v i t a b l y has an e f f e c t on t o t a l volume  y i e l d which i n d i c a t e s t h a t f o r t h i s s p e c i e s , M o l l e r ' s theory t h a t t h i n n i n g has no e f f e c t on t o t a l volume y i e l d does not h o l d under the present t h i n n i n g regime 4.  Important  f i g u r e s to note i n T a b l e 44 are the volume of  n i n g ( t o t a l and merchantable) yield to  (b)  which on the average works out These p e r c e n t a g e s , along w i t h the  a t age 40 y e a r s are important i n comparing  alternative  thin-  as a percentage of the volume  ( t o t a l and merchantable)  30% and 24% r e s p e c t i v e l y .  DBH  i n Kenya.  outputs  from  schedules.  F o r P_. p a t u l a t h i n n i n g model 1.  At f i r s t  t h i n n i n g which i s c a r r i e d out at the common stand  d e n s i t y index o f 17%, 33.0  and 31.5  m  stand b a s a l areas are 40.1,  36.6,  per h e c t a r e f o r s i t e index c l a s s e s 15,  21, 24 and 27 r e s p e c t i v e l y .  The  first  18,  Thus, as f o r C_. l u s i t a n i c a , H a r t ' s  d e n s i t y i n d e x i s i n a p p r o p r i a t e as a measure of s i t e 2.  33.7,  t h i n n i n g appears very severe, removing  42% of the b a s a l area b e f o r e t h i n n i n g .  occupancy.  an average  of  T h i s i s confirmed by  F i g u r e 31b which shows a v e r y d r a s t i c drop i n c u r r e n t annual increment a f t e r t h i s t h i n n i n g f o r a l l s i t e c l a s s e s . t h i n n i n g s a l s o appear to have an e f f e c t  on CAI.  Subsequent  I t i s evident  215  t h e r e f o r e t h a t f o r t h i s s p e c i e s , M o l l e r ' s theory does not h o l d at 3.  t h e present  l e v e l of thinning i n t e n s i t y .  Except f o r t h e f i r s t  t h i n n i n g , subsequent t h i n n i n g s appear  l i m i t e d t o an average maximum b a s a l a r e a b e f o r e t h i n n i n g o f o 30 xsr p e r h e c t a r e t h i n n i n g o f 22.5 m  and an average minimum b a s a l a r e a per hectare.  after  The maximum appears w e l l  s h o r t of the maximum c o n s i s t e n t w i t h maximum b a s a l a r e a for 4.  yield  a l l site classes.  T a b l e 45 shows t h a t t h i n n i n g volume c o n s t i t u t e s a very  high  percentage o f the t o t a l volume y i e l d up to age 20 y e a r s , a result 5.  of the heavy t h i n n i n g s f o r t h i s  A t the present  species.  l e v e l of thinning i n t e n s i t y , culmination of  growth does not occur  b e f o r e age 20 y e a r s  From the smoothed CAI and MAI curves  on any s i t e  ( F i g u r e 31b) i t would  appear from e x t r a p o l a t i o n t h a t c u l m i n a t i o n would occur same age on a l l s i t e c l a s s e s : However i t should  class.  a t the  between age 20 and 21 y e a r s .  be noted t h a t t h i s may be due t o the heavy  t h i n n i n g s a f f e c t i n g the stand development o r t o the smoothing out of curves u s i n g s u b j e c t i v e judgement. F o r _P. r a d i a t a t h i n n i n g model 1.  F o r t h i s s p e c i e s , b a s a l area a t f i r s t  and second t h i n n i n g a r e  2 an average 15.2 and 19.7 m s i t e c l a s s e s (see T a b l e at  46).  per hectare  r e s p e c t i v e l y on a l l  These t h i n n i n g s a r e c a r r i e d out  a common stand d e n s i t y index of 23% and 18% r e s p e c t i v e l y on  216  all  site classes.  H a r t ' s stand  I t t h e r e f o r e appears t h a t f o r t h i s  d e n s i t y i n d e x i s a good a p p r o x i m a t i o n of  degree to which the be  species,  an a p p r o p r i a t e  species  is utilizing  the  site.  b a s i s f o r t i m i n g when a stand  the  I t would  i s due  for a  thinning for this p a r t i c u l a r species. 2.  In g e n e r a l  the t h i n n i n g model i n d i c a t e s t h a t the l e v e l of  area b e f o r e  thinning increases  31c  (unsraoothed) shows t h a t the  f o r CAI  s i t e index c l a s s e s has volume increment. appreciable  w i t h age  ( F i g u r e 30c). first  basal  Figure  t h i n n i n g on a l l  no marked e f f e c t on c u r r e n t  However, subsequent t h i n n i n g s  annual  do have an  e f f e c t as i n d i c a t e d by the drop i n CAI  a f t e r each  thinning. 3.  From e x t r a p o l a t i o n , i t would appear t h a t c u l m i n a t i o n  age  P_. r a d i a t a would o c c u r w e l l beyond the range covered by d a t a i n t h i s study (see F i g u r e be s t i l l 21,  a c c e l e r a t i n g up  24 and  27.  4.  the  appears to  35 years f o r s i t e index c l a s s e s  t h a t the r o t a t i o n (up  to age  higher  35 y e a r s ) does  exploit this potential fully.  At age  30 y e a r s ,  27.2%, 18.0% volume to DBH  to age  Indeed the CAI  T h i s suggests t h a t t h i s s p e c i e s has  y i e l d p o t e n t i a l and not  31c).  for  and  15 cm  t h i n n i n g volume on the average c o n s t i t u t e s 11.9% top DBH  r e s p e c t i v e l y (Table  of t o t a l volume y i e l d , merchantable and 46).  merchantable volume to 20 cm Thus, the t h i n n i n g s are  a b l y l i g h t e r than those f o r P. p a t u l a and £ .  top  consider-  lusitanica.  217  2.1  Summary on the C u r r e n t  1.  Hart'8  T h i n n i n g Model f o r Kenya  stand d e n s i t y index  i s Inadequate as a guide t o t h i n n i n g f o r  C_. l u s i t a n i c a and P_. p a t u l a as i t r e s u l t s i n h i g h e r  site  on poor s i t e s than on good s i t e s , based on b a s a l a r e a .  occupancy  For  P_. r a d i a t a t h e index appears q u i t e s a t i s f a c t o r y as a measure o f the degree o f s i t e u t i l i z a t i o n by t h e s p e c i e s . 2.  F o r £ . l u s i t a n i c a and _P. r a d i a t a , f i r s t marked e f f e c t  on CAI.  t h i n n i n g appears t o have no  However, subsequent t h i n n i n g s do appear t o  have an a p p r e c i a b l e e f f e c t , r e s u l t i n g i n lowering annual volume increment.  3.  of the c u r r e n t  F o r P_. p a t u l a , both f i r s t  and subsequent  t h i n n i n g s do have a d r a s t i c e f f e c t  on CAI.  As a f o l l o w - u p  on 2 above, i t i s i n f e r r e d  that  sawtimber t h i n n i n g regimes, M o l l e r ' s theory  that  t o the o b s e r v a t i o n s  under the c u r r e n t  t h i n n i n g has no a p p r e c i a b l e e f f e c t not  on t o t a l volume p r o d u c t i o n  h o l d f o r the t h r e e s p e c i e s i n Kenya.  3.  A l t e r n a t i v e t h i n n i n g model f o r sawtimber crop i n Kenya  3.1  Thinning P o l i c y Considerations As  does  mentioned i n Chapter 1 S e c t i o n 3, the t h i n n i n g p o l i c y  aims a t p r o d u c t i o n  f o r Kenya  of l a r g e - s i z e d m a t e r i a l i n as s h o r t a r o t a t i o n as  p o s s i b l e a t t h e expense of some l o s s i n t o t a l y i e l d . p o l i c y was adopted i n the f i f t i e s  At the time  this  and e a r l y s i x t i e s and documented i n  the r e l e v a n t T e c h n i c a l Orders i n 1969, the predominant purpose of p l a n t a t i o n management was p r o d u c t i o n  o f sawlogs as q u i c k l y as p o s s i b l e  218  as the shortage of sawtimber from indigenous felt.  f o r e s t s was  a l r e a d y being  At t h a t time, t h e r e were no o t h e r major wood-using i n d u s t r i e s ,  n e i t h e r was  the p r e s s u r e on the l i m i t e d f o r e s t r e s o u r c e acute as the  p o p u l a t i o n was  s t i l l v e r y low w i t h low per c a p i t a consumption of wood.  S i n c e then, s e v e r a l developments have o c c u r r e d : 1.  The 1950  p o p u l a t i o n has  i n c r e a s e d from an e s t i m a t e d 6 m i l l i o n i n  t o 8 m i l l i o n i n 1960  and  p o p u l a t i o n growth r a t e of 4%, the world  to 15 m i l l i o n i n 1980,  with a  e s t i m a t e d t o be the h i g h e s t i n  ( a c c o r d i n g to Kenya Bureau of S t a t i s t i c s  1982).  This  has put a l o t of p r e s s u r e on the f o r e s t s f o r the supply of sawtimber, f i r e w o o d , g e n e r a l purpose wood, p u l p and  paper  products, e t c . 2.  There has been a very r a p i d i n c r e a s e i n f o r e s t r a n g i n g from modern s a w m i l l s , p a r t i c l e board  industries,  manufacturing  i n d u s t r i e s , plywood i n d u s t r i e s and a modern p u l p m i l l , which came i n t o p r o d u c t i o n i n 1972.  The  i m p l i c a t i o n of  development i s t h a t w h i l e a few p l a n t a t i o n s may managed e x c l u s i v e l y  f o r s u p p l y of o n l y one  this  still  be  end product,  the  m a j o r i t y of p l a n t a t i o n s w i l l be managed f o r supply of m u l t i p l e end p r o d u c t s .  Thus even i n a predominantly  management zone, t h e r e w i l l p a r t i c l e board and 3.  sawtimber  be a component f o r pulpwood,  plywood.  There has been a r a p i d I n c r e a s e i n standard of  living,  r e s u l t i n g i n an i n c r e a s e i n consumption of wood and wood products.  For example, the per c a p i t a l roundwood consumption  219  f o r Kenya i n 1950 1979  was  0.1  m. 3  T h i s had  r i s e n to 1.8  (F.A.O. Yearbook of f o r e s t products  F.A.O. Yearbook of f o r e s t products i n c r e a s e has  1979).  m  statistics Most of  by  3  1947-1951, this  been a r e s u l t of i n c r e a s e d l i t e r a c y l e v e l ,  ing i n higher  consumption of pulp and paper p r o d u c t s ,  and  change to modern s t y l e s of b u i l d i n g which r e q u i r e more All  these  result-  timber.  f a c t o r s p o i n t to a need f o r a change i n t h i n n i n g p o l i c y  i n f a v o u r of the o b j e c t i v e of maximum volume p r o d u c t i o n .  The  develop-  ment of i n t e g r a t e d f o r e s t i n d u s t r i e s which can u t i l i z e both s m a l l l o g s from t h i n n i n g s and policy.  wood p r o d u c t s  favour  t h e r e f o r e the mounting p o p u l a t i o n and  can o n l y favour  available forest The  l a r g e s i z e l o g s from f i n a l f e l l i n g s  size this  I t should a l s o be noted t h a t f o r e s t s i n Kenya c o n s t i t u t e o n l y  3% of the l a n d area and  any  the  the a d o p t i o n  demand f o r  of maximum volume y i e l d  on  land.  need f o r changing the t h i n n i n g p o l i c y to accommodate the  changes i n the f o r e s t r y i n d u s t r i a l s e c t o r appear a l r e a d y to have been a p p r e c i a t e d by the Kenya F o r e s t r y Department. 1981 No.  r e v i s i o n o f the management schedule 53 of May  1981).  The  T h i s i s evidenced  changes i n t h i s T e c h n i c a l  Order a r e i n regard to the d e l a y and heaviness  of the f i r s t  These changes appear to have been i n s t i t u t e d to p r o v i d e of l a r g e r - s i z e d t h i n n i n g s to go to the p u l p m i l l .  schedule  i s not  thinning.  a higher  Unfortunately,  volume as  has  section, this thinning  c o n s i s t e n t w i t h the concept of maximum volume y i e l d  the whole r o t a t i o n .  the  f o r P. p a t u l a ( T e c h n i c a l Order  most s i g n i f i c a n t  a l r e a d y been demonstrated i n the p r e v i o u s  by  over  220  3.2  T h i n n i n g Experiment f o r C_. l u s i t a n i c a  In o r d e r to i n v e s t i g a t e the p o s s i b i l i t y of a l t e r n a t i v e t h i n n i n g regimes f o r the e x o t i c timber was  s p e c i e s i n Kenya, a t h i n n i n g experiment  designed w i t h the f o l l o w i n g o b j e c t i v e s : 1.  To i n v e s t i g a t e the e f f e c t s of d i f f e r e n t t h i n n i n g l e v e l s t h i n n i n g i n t e n s i t i e s on growth and y i e l d on d i f f e r e n t  and  site  index c l a s s e s . 2.  Based on r e s u l t s from (1) above, t o i d e n t i f y the a p p r o p r i a t e t h i n n i n g regime based on the c r i t e r i a of h i g h e s t merchantable yield.  In o r d e r to draw reasonable C_. l u s i t a n i c a was counts;  considered.  bounds to the study, o n l y one  T h i s s p e c i e s was  s i n g l e d out on  (1) i t i s the p r e f e r r e d s p e c i e s f o r sawtimber, and  domain covered management  species, two  (2) i t s model  the whole range of i t s r o t a t i o n under the c u r r e n t  schedules.  Experimental  design:  F i v e t h i n n i n g l e v e l s A,  B, C, D and E were  a r b i t r a r i l y s e l e c t e d i n o r d e r of i n c r e a s i n g b a s a l a r e a b e f o r e t h i n n i n g . These l e v e l s are g i v e n on Table 47.  W i t h i n each t h i n n i n g l e v e l , four  t h i n n i n g i n t e n s i t i e s were s e l e c t e d based on the p r o p o r t i o n of b a s a l area t o be removed as a percentage 10, 20, 30 and 40%.  of b a s a l area b e f o r e t h i n n i n g .  These treatments  were repeated  index c l a s s e s f o r C_. l u s i t a n i c a i . e . 12, of 100  treatment  combinations.  15,  These were  over the f i v e  site  18, 21 and 24 f o r a t o t a l  A l l the experiments were conducted  the y i e l d model EXOTICS t o s i m u l a t e r e s u l t s .  F i g u r e 32 shows how  t h i n n i n g regimes t r a n s l a t e s i n terms of b a s a l a r e a b e f o r e and  using these  after  221  TABLE 47.  Thinning  B a s a l area b e f o r e t h i n n i n g regimes  level  t h i n n i n g (M /ha) f o r the a l t e r n a t i v e  l s t thinning  A B C D E  z  2nd t h i n n i n g  3rd t h i n n i n g  4th t h i n n i n g  35 35 35 40 40  35 40 45 45 50  35 40 45 45 50  . 2 5 25 25 25 25  t h i n n i n g and number o f stems ( i n i t i a l at  d i f f e r e n t ages f o r s i t e index  s t o c k i n g o f 1200 s.p.h. assumed)  c l a s s 18.  A major concern i n s e l e c t i n g the t h i n n i n g l e v e l s was whether  these  exceeded t h e maximum b a s a l a r e a p o t e n t i a l f o r each s i t e q u a l i t y c l a s s . A p r e l i m i n a r y attempt  to f i n d  these maxima u s i n g the -3/2 power law  (Drew and F l e w e l l i n g 1977, 1979) f a i l e d , s u g g e s t i n g  t h a t the p l a n t a t i o n s  from which the data was drawn were managed below the maximum potential. for  these  site  Faced w i t h the problem of d e f i n i n g the maximum b a s a l stands, Alder  (1977) had f i t t e d hand-drawn curves  area  over t h e  maximum b a s a l area observed on the p.s.p.s. and then q u a n t i f i e d these curves  G  using a nonlinear  equation:  (-b,H).b, - b (1 - e ) max 0 ' 1  4.3  2  n  v  where  = Maximum b a s a l a r e a i n m2/h . a  H  = Stand dominant h e i g h t  ( r e p r e s e n t s e f f e c t s of age and s i t e ) .  FIGURE 32 NUMBER OF STEMS AND BASAL AREA AT DIFFERENT AGES FOR DIFFERENT THINNING LEVELS AND THINNING INTENSITIES FOR C. LUSITANICA S.I. CLASS 18  40 %  400  rO ho ho  O-  10  20  30  40  SO  AGE  O  10  IN  20  30  YEARS  40  FROM  50  0  10  PLANTING  20  30  40  50  STEMS  PER  HA  224  bg, b^ and  b  2  are the r e g r e s s i o n c o e f f i c i e n t s .  l u s i t a n i c a i n Kenya, he o b t a i n e d b2  = 2.551.  equation  No  criteria  as i t was  f o r goodness of f i t was  b^ = 0.1219 and  given f o r t h i s and  used to determine the G  m a x  hence such  criteria  curves  shown on  32.  3.3  R e s u l t s from the Simulated  (a)  E f f e c t s of a l t e r n a t i v e t h i n n i n g regimes on MAI r o t a t i o n age:  F i g u r e 33 g i v e s the MAI l e v e l s and Table  £.  F o r l a c k of b e t t e r means of guidance i n t h i s  t h i s e q u a t i o n was  Figure  bg = 63.9,  based upon a hand-drawn curve  would be meaningless. study,  the v a l u e s :  For  and  thinning intensities  T h i n n i n g Experiment  CAI  curves  f o r £ . l u s i t a n i c a s i t e index  ( c u l m i n a t i o n age)  t h i n n i n g i n t e n s i t y f o r the the c u l m i n a t i o n age  the age  class.  The  f o r the c u r r e n t t h i n n i n g regime and 48 as c o n t r o l .  be noted from both F i g u r e 33 and 1.  and  Table  For a l l t h i n n i n g l e v e l s , MAI of t h i n n i n g .  thinning 18  while  at which t h i s  f o r each t h i n n i n g l e v e l  same s i t e index  c l a s s are a l s o shown on Table  biological  f o r the d i f f e r e n t  48 g i v e s a summary of the maximum MAI  maximum i s o b t a i n e d  and  and  maximum MAI  and  some s i t e  index  Several observations  48. decreases w i t h i n c r e a s i n g s e v e r i t y  F o r example under 10% t h i n n i n g i n t e n s i t y ,  the  e f f e c t s of t h i n n i n g are minimal so t h a t growth can almost considered  as f o r unthinned stands.  expected to be a t maximum and  can  MAI  can t h e r e f o r e  be  be  to decrease w i t h i n c r e a s i n g  s e v e r i t y o f t h i n n i n g so t h a t i t i s minimum at 40%  intensity.  227  TABLE 48.  Maximum MAI (m /ha) and b i o l o g i c a l r o t a t i o n age ( c u l m i n a t i o n age) f o r d i f f e r e n t t h i n n i n g regimes f o r C_. l u s i t a n i c a S.I. 18 J  Intensity  Level  10  20  30  40  Control  MAI  Age  MAI  Age  MAI  Age  MAI  Age  A  24.2  36  22.6  22  22.0  22  21.0  26  B  24.2  34  22.9  25  22.2  25  21.0  26  C  24.3  32  23.3  26  22.4  28  21.1  32  D  24.4  32  23.5  27  22.6  28  21.7  24  E  24.6  30  23.8  28  22.7  32.  21.7  20  Control  i  MAI  Age  22.0  24  228  T h i s confirms  the e a r l i e r o b s e r v a t i o n  that M o l l e r ' s theory with respect  (Chapter  to e f f e c t s  4 S e c t i o n 2)  o f t h i n n i n g on  volume y i e l d does not h o l d f o r C_. l u s i t a n i c a w i t h i n the thinning i n t e n s i t i e s considered Within  i n this  study.  a g i v e n t h i n n i n g i n t e n s i t y , MAI i n c r e a s e s w i t h i n c r e a s i n g  l e v e l o f t h i n n i n g i . e . i n c r e a s e s from t h i n n i n g l e v e l A t o E. T h i s i s as expected s i n c e MAI i s a f u n c t i o n of b a s a l increment which i n t u r n i s a f u n c t i o n o f b a s a l area thinning.  considered  from changes In t h i n n i n g i n t e n s i t y  unimportant  for practical  C_. l u s i t a n i c a , t h i n n i n g i n t e n s i t y (measured by b a s a l area before c o n s i d e r a t i o n w i t h regard  and may  purposes.  From the above o b s e r v a t i o n s , i t i s concluded  For  before  T h i s i n c r e a s e however i s very s m a l l compared to the  increase resulting be  area  that f o r  r a t h e r than t h i n n i n g l e v e l  t h i n n i n g ) i s the more c r i t i c a l  to MAI.  10% t h i n n i n g i n t e n s i t y ,  the c u l m i n a t i o n age decreases  i n c r e a s i n g l e v e l o f b a s a l area b e f o r e that t h i s t h i n n i n g i n t e n s i t y i s a s f o r unthinned s t a n d .  thinning.  This indicates  i s so l i g h t t h a t stand I n c r e a s i n g b a s a l area  t h i n n i n g t h e r e f o r e has same e f f e c t as improving  with  development  before  site  quality.  F o r 20 and 30% t h i n n i n g i n t e n s i t i e s , c u l m i n a t i o n age i n c r e a s e s w i t h i n c r e a s i n g b a s a l area b e f o r e t h i n n i n g i . e . from t h i n n i n g l e v e l s A to E. curves  being  shifted  T h i s i s mainly a r e s u l t o f the CAI  f u r t h e r t o the r i g h t as the b a s a l  area  229  before while  t h i n n i n g i s r a i s e d ( r e s u l t i n g i n delay i n t h i n n i n g s ) the MAI curves  are l i t t l e  a f f e c t e d (see F i g u r e 3 3 ) .  r a i s i n g l e v e l of basal area before  t h i n n i n g when t h i n n i n g  i n t e n s i t i e s a r e heavy has the same e f f e c t s as d e c r e a s i n g quality.  This effect  s i t y but i s r e v e r s e d  site  i s a l s o apparent f o r 40% t h i n n i n g i n t e n f o r t h i n n i n g l e v e l s D and E as t h e e f f e c t s  of the t h i r d t h i n n i n g on MAI and CAI curves 5.  Thus  diminishes.  W i t h i n a g i v e n t h i n n i n g l e v e l , t h e c u l m i n a t i o n age i s expected to i n c r e a s e w i t h i n c r e a s i n g t h i n n i n g i n t e n s i t y . manifest 20,  This i s  i n t h i n n i n g l e v e l s C, D and E f o r t h i n n i n g i n t e n s i t i e s  30 and 40% ( l e v e l s A, B and C o n l y ) .  Based on MAI and c u l m i n a t i o n age, the most promising regimes a r e those w i t h 20 and 30% t h i n n i n g i n t e n s i t y .  thinning  The 10% t h i n n i n g  i n t e n s i t y g i v e s h i g h c u l m i n a t i o n age i n s p i t e of the h i g h e r MAI.  Besides  t h i s , the l i g h t t h i n n i n g s a r e accompanied by s h o r t t h i n n i n g c y c l e s and t h e r e f o r e are u n a t t r a c t i v e e c o n o m i c a l l y .  The 40% t h i n n i n g i n t e n s i t y  r e s u l t s i n low MAI compared t o the c u r r e n t t h i n n i n g schedule, t h a t i t i s probably  suggesting  too s e v e r e .  Between the 20 and 30% t h i n n i n g i n t e n s i t i e s , the former has an edge i n both MAI and c u l m i n a t i o n age.  Thinning  regime A:20 appears t o  be t h e best w i t h a h i g h e r MAI and lower c u l m i n a t i o n age than the c u r r e n t t h i n n i n g regime. regime.  T h i s however does n o t mean t h a t t h i s i s the optimum  A l l the o t h e r t h i n n i n g regimes under 20% t h i n n i n g i n t e n s i t y  have h i g h e r MAI but l o n g e r r o t a t i o n age than the c u r r e n t t h i n n i n g regime. without  I t i s t h e r e f o r e not p o s s i b l e t o determine t h e best an economic a n a l y s i s .  regime  230  The provides  b i o l o g i c a l r o t a t i o n of a p l a n t a t i o n (as d i s c u s s e d the r o t a t i o n of h i g h e s t  t o t a l volume y i e l d .  For  above) sawtimber  production  however, the main I n t e r e s t i s the t o t a l merchantable volume  production  f o r a g i v e n end  product.  As a r e s u l t , b i o l o g i c a l r o t a t i o n i s  h a r d l y ever used i n sawtimber p r o d u c t i o n the  current  which a DBH  As mentioned  earlier,  r o t a t i o n f o r sawtimber p l a n t a t i o n s i n Kenya i s the age o f 48  cm i s a t t a i n e d .  a r o t a t i o n s i n c e the 48  cm DBH  I t t h e r e f o r e does not  stocking  and  thinning  intensi-  A commonly used  method i n f o r e s t r y i s to c a l c u l a t e the economic r o t a t i o n , d e f i n e d  r a t e of r e t u r n (Crowe 1967, such i n f o r m a t i o n assortments and  economic land value  Grut  1970,  others).  a c l e a r d e f i n i t i o n of product mix,  because i t i s the average age under the c u r r e n t  either  highest  T h i s would  require log class  a l l of which were not  For purposes of y i e l d a n a l y s i s under d i f f e r e n t  t h i n n i n g regimes, a common r o t a t i o n age  (b)  and  or of the  as the economics of p l a n t a t i o n e s t a b l i s h m e n t ,  a v a i l a b l e to t h i s study.  for  can be a t t a i n e d i n a p l a n t a t i o n at  r e l a t e to volume y i e l d .  as the r o t a t i o n of the h i g h e s t  at  T h i s however i s a gpoor c r i t e r i a  d i f f e r e n t ages depending on the i n i t i a l ties.  regimes.  of 40 y e a r s was  adopted, m a i n l y  at which sawtimber crop a t t a i n s 48  cm  DBH  t h i n n i n g regime i n Kenya.  E f f e c t s of a l t e r n a t i v e t h i n n i n g regimes on p r o d u c t i v i t y T a b l e 49 shows v a r i o u s measures of p r o d u c t i v i t y up to age  f o r C_. l u s i t a n i c a s i t e Index 18 f o r the v a r i o u s i n c l u d i n g the c u r r e n t  thinning  40  years  t h i n n i n g regimes,  regime as c o n t r o l .  The  table also  gives  the i n c r e a s e i n y i e l d of the a l t e r n a t i v e t h i n n i n g regimes (expressed p e r c e n t a g e ) r e l a t i v e to the y i e l d under the c u r r e n t  thinning  regime.  as  TABLE 49.  ll^TZ^t^li^'  l n  at 40 year r o t a t i o n  V(l) total Stand  parameter  T h i n n i n g regime control  A  B  C  D  E  "  f  r M  2?«  (  r  e  l  a  age f o r d i f f e r e n t  Increase *  V(15) t o t a l m  849.7  3  "  t h i n n i n g regime) and other stand parameters t h i n n i n g regimes f o r C. l u s i t a n i c a S.I. 18 v  e  t  0  c  u  r  Increase  X  771.4  r  e  n  t  V(15) T h i n n i n g 3  ra  Increase X  188.5  V(15) main m  Increase  DBH(40)  3  582.9  47.6  10 20 30 40  966.1 883.0 821.5 784.9  13.7 3.9 -3.3 -7.6  894.1 806.1 744.1 709.2  15.9 4.5 -3.5 -8.1  45.9 152.1 282.9 309.6  -75.6 -19.3 50.1 64.2  848.2 654.0 461.2 399.6  45.5 12.2 -20.9 -31.4  38.3 44.7 48.9 49.1  10 20 30 *40  966.8 888.2 839.6 801.0  13.8 4.5 -1.2 -5.7  895.0 812.3 763.2 726.1  16.0 5.3 -1.1 -5.9  67.0 177.3 332.4 289.8  -64.4 -5.9 76.3 53.7  834.0 635.0 430.8 436.3  43.1 8.9 -26.1 -25.2  37.9 44.0 47.2 45.7  10 20 30 *40  969.7 899.1 861.3 816.4  14.1 5.8 1.4 -3.9  898.2 824.3 785.7 741.9  16.4 6.8 1.8 -3.8  75.9 211.9 380.7 324.5  -59.7 12.4 102.0 72.1  822.3 612.4 405.0 417.4  41.1 5.1 -30.5 -28.4  37.5 43.1 45.8 44.7  10 20 *30 *40  969.9 903.9 869.3 836.8  14.1 6.4 2.3 -2.7  897.2 829.3 794.5 753.3  16.3 7.5 3.0 -2.3  83.4 230.7 236.3 356.9  -55.8 22.4 25.4 89.3  813.8 598.6 558.2 396.4  39.6 2.7 -4.2 -32.0  37.2 42.5 43.1 43.6  10 20 *30 **40  974.4 917.7 878.5 847.9  14.7 8.0 3.4 -0.2  902.7 844.0 804.1 774.9  17.0 9.4 4.2 0.4  98.7 263.8 257.7 147.9  -47.6 39.9 36.7 -21.5  804.0 580.2 546.4 627.0  37.9 -0.5 -6.3 7.6  37.0 41.8 42.7 40.9  * Received only three t h i n n i n g s . **Received only two t h i n n i n g s .  232  F i g u r e 34 shows the d i s t r i b u t i o n  o f the merchantable volume f o r the same  t h i n n i n g regimes between t h i n n i n g s and f i n a l crop. observations 1.  The f o l l o w i n g  may be noted:  The d i f f e r e n c e i n y i e l d between the d i f f e r e n t  thinning  intensi-  t i e s i s c o n s i d e r a b l y g r e a t e r than the d i f f e r e n c e between the different  thinning l e v e l s w i t h i n a given thinning  T h i s confirms  the e a r l i e r o b s e r v a t i o n t h a t t h i n n i n g  i s a more c r i t i c a l c o n s i d e r a t i o n i n choosing I t a l s o confirms  the o b s e r v a t i o n  thinning i n t e n s i t i e s  considered  t h a t t h i n n i n g has l i t t l e e f f e c t f o r C_. l u s i t a n i c a 2.  intensity  a t h i n n i n g regime.  t h a t w i t h i n the range o f i n t h i s study, M o l l e r s  theory  on volume y i e l d does not h o l d  i n Kenya.  The 10% t h i n n i n g i n t e n s i t y  has the h i g h e s t  able volume y i e l d up t o age 40 y e a r s . at  intensity.  t o t a l and merchant-  Most of t h i s y i e l d comes  f i n a l h a r v e s t , w i t h o n l y about 5-10% (depending on t h i n n i n g  l e v e l ) recovered  as t h i n n i n g volume.  a l r e a d y mentioned r e g a r d i n g noted on T a b l e a result  Besides  the shortcomings  t h i s regime, i t should a l s o be  49 t h a t i t a l s o r e s u l t s  i n the lowest  o f the l a r g e number of stems a t r o t a t i o n  stand  DBH,  age (see  F i g u r e 32). 3.  Of the r e s t  of the t h i n n i n g i n t e n s i t i e s , 20% r e s u l t e d i n the  h i g h e s t percent  i n c r e a s e i n both t o t a l volume and t o t a l  merchantable volume.  The t o t a l merchantable volume i n c r e a s e  ranged from 4.5% f o r t h i n n i n g regime A:20 t o 9.4% f o r t h i n n i n g regime E:20.  233 FIGURE 34 DISTRIBUTION OF MERCHANTABLE VOLUME (M /HA) FOR DIFFERENT THINNING REGIMES FOR C. LUSITANICA S.I. 18 3  Thinning Level  Thinning Volume Final Stand Merchantable Volume to 15 cm top dbh Thinning L e v e l B  A  1000-  I  IZZ  800-  600'  n  A A  E  a E  « E  200  3  200  O >  o >  C  10  20  30  C  40  20  30  40  Intensity  Intensity  Thinning  10  Level  Thinning  C  Level  1000-  i  m ^  400  I  200  V?7 600'  n  E 0)  E 3  200  "o >  o >  C  10  20  C  30 4 0  10  20 30  Intensity  Intensity  Thinning  Level  E  40  234  4.  Within  a given  t h i n n i n g i n t e n s i t y , mean stand  w i t h i n c r e a s i n g l e v e l o f b a s a l area before decreases from t h i n n i n g  l e v e l A t o E.  s i n c e r a i s i n g the b a s a l area the  DBH d e c r e a s e s  thinning i . e .  T h i s i s as expected  l e v e l has the e f f e c t o f i n c r e a s i n g  l e n g t h of the t h i n n i n g c y c l e and so the stand  higher  stocking  i s at a  level.  A l l the t h i n n i n g regimes under the 20% t h i n n i n g i n t e n s i t y c o u l d be considered  f o r a d o p t i o n depending on the p r o d u c t i o n  example i f the f i n a l highest  crop i s the p r i o r i t y ,  priority.  For  t h i n n i n g regime A:20 w i t h  f i n a l c r o p merchantable volume i n c r e a s e f 12.2% and h i g h e s t  (among those c o n s i d e r e d ) would be p r e f e r r e d .  DBH  I f on the other hand the  d i s t r i b u t i o n o f y i e l d over the r o t a t i o n i s a p r i o r i t y , t h i n n i n g regime E:20  w i t h merchantable volume o f t h i n n i n g i n c r e a s e o f 39.9% would be  preferred.  The optimum regime however cannot be i d e n t i f i e d  economic i n p u t s , as a l r e a d y mentioned I t should  elsewhere.  be noted here t h a t the above o b s e r v a t i o n s  p r o d u c t i v i t y on s i t e index 18.  without  apply  o n l y to  P o s s i b i l i t y t h e r e f o r e e x i s t e d t h a t the  e f f e c t s o f these a l t e r n a t i v e regimes on p r o d u c t i v i t y may be d i f f e r e n t on different  site quality classes.  T h i s p o s s i b i l i t y i s explored  i n the  f o l l o w i n g s e c t i o n , u s i n g t h i n n i n g regimes under the 20% t h i n n i n g intensity (c)  only.  E f f e c t s o f the new t h i n n i n g regimes on p r o d u c t i v i t y on d i f f e r e n t site quality classes T a b l e 50 g i v e s the p r o d u c t i v i t y and stand  years f o r the v a r i o u s  mean DBH up t o age 40  s i t e index c l a s s e s f o r C_. l u s i t a n i c a under the  TABLE 50.  Volume p r o d u c t i v i t y (m /ha) and stand mean DBH (cm) up t o age 40 y e a r s f o r v a r i o u s t h i n n i n g l e v e l s a t 20% t h i n n i n g i n t e n s i t y f o r v a r i o u s s i t e index c l a s s e s f o r £ . l u s i t a n i c a r e l a t i v e to the c u r r e n t t h i n n i n g regime  Thinning  Site  regime  3  index  V ( l )total 3 m  Increase %  V(15) t o t a l 3 m  Increase %  V(15) t h i n n i n g 3 m  Increase %  175.0 180.2 188.5 208.1 207.3  Increase %  392.3 494.0 582.9 652.5 754.5  DBH(40) c  m  12 15 18 21 24  637.5 749.3 849.7 943.0 1037.7  A: 20  12 15 18 21 24  671.0 781.2 883.0 977.9 1075.6  5.2 4.2 3.9 3.7 3.6  604.3 710.3 806.1 891.1 983.8  6.5 5.4 4.5 3.5 2.3  122.7 134.1 152.1 166.5 178.9  -29.9 -25.6 -19.3 -20.0 -13.7  481.6 576.2 654.0 724.6 804.9  22.8 16.6 12.2 11.0 6.7  42.9 44.1 44.7 45.1 45.9  B:20  12 15 18 21 24  675.6 787.1 888.2 984.3 1083.1  6.0 5.0 4.5 4.4 4.4  610.0 717.4 812.3 898.6 992.6  7.5 6.4 5.3 4.4 3.2  150.1 165.6 177.3 194.3 209.7  -14.2 -8.1 -5.9 -6.6 1.2  459.9 551.8 635.0 704.3 782.9  17.2 11.7 8.9 7.9 3.8  41.3 43.1 44.0 44.3 45.1  Current regime  567.3 674.2 771.4 860.6 961.8  V(15) main 3 . m  43.7 46.1 47.6 48.3 50.1  tsJ  Table 50 (cont'd)  Thinning  Site  V ( l ) total  Increase  V(15) t o t a l  regime  index  m  %  m  C:20  12 15 18 21 24  684.0 797.1 899.1 966.7 1097.1  7.3 6.4 5.8 5.7 5.7  D:20  12 15 18 21 24  685.7 797.4 903.9 1002.4 1099.2  E:20  12 15 18 21 24  698.4 811.6 917.7 1017.5 1115.2  3  Increase  V(15) t h i n n i n g  Increase  %  m  619.2 728.3 824.3 912.3 1008.0  9.1 8.0 6.8 6.0 4.8  177.3 196.6 211.9 232.1 251.2  1.3 9.1 12.4 11.5 21.2  7.6 6.4 6.4 6.3 5.9  621.0 728.7 829.3 918.2 1010.1  9.5 8.1 7.1 6.7 5.0  187.7 204.4 230.7 253.0 263.1  9.6 8.3 8.0 7.9 7.5  634.3 743.7 844.0 934.3 1027.2  11.8 10.3 9.4 8.6 6.8  218.1 238.8 263.8 288.7 302.2  3  3  %  V(15) main m  Increase  DBH(40)  %  cm  441.9 531.7 612.4 680.2 756.8  12.6 7.6 5.1 4.2 0.3  40.9 42.2 43.1 43.5 44.3  7.2 13.4 22.4 21.6 26.9  433.3 524.3 598.6 665.2 747.0  10.4 6.1 2.7 1.9 -1.0  40.5 41.9 42.5 42.9 43.9  24.6 32.5 39.9 38.7 45.8  416.2 504.9 580.2 645.6 725.0  6.1 2.2 -0.5 -1.1 -3.9  39.6 41.0 41.8 42.2 43.2  CO  237  c u r r e n t and  a l t e r n a t i v e t h i n n i n g regimes at 20%  F i g u r e 35a,b and V(15)  c shows the percent  main stand and V(15)  thinning intensity.  increase i n productivity ( v ( l ) ,  thinning r e s p e c t i v e l y ) r e l a t i v e to  the  c u r r e n t t h i n n i n g regime on the d i f f e r e n t s i t e index c l a s s e s f o r the same t h i n n i n g regimes. 1.  The  F i g u r e 35a  following observations  may  be noted:  shows t h a t a l l the t h i n n i n g regimes r e s u l t e d i n an  i n c r e a s e i n the t o t a l merchantable volume, w i t h h i g h e s t on regime E:20. index 6.8%  The  c l a s s ranging  i n c r e a s e decreased between 11.8%  f o r s i t e index c l a s s 24.  response to the new which confirms  with i n c r e a s i n g s i t e  f o r s i t e index  T h i s suggests the  f u l l y u t i l i z e d under the c u r r e n t F i g u r e 35b  highest sites,  i n Chapter 2 S e c t i o n  t h a t the f u l l s i t e c a p a c i t y on poor s i t e s may  2.  c l a s s 12 to  t h i n n i n g regimes i s on the poor  the s u s p i c i o n expressed  increase  not  be g e t t i n g  t h i n n i n g regimes i n Kenya.  shows the i n c r e a s e i n f i n a l crop merchantable volume  d e c r e a s i n g w i t h i n c r e a s i n g s i t e index c l a s s . of the g r e a t e r d i f f e r e n c e i n DBH  This i s a  between the c u r r e n t  result  and  a l t e r n a t i v e t h i n n i n g regime as s i t e index c l a s s i n c r e a s e s Table  50).  regime A:20  2.3  (see  The  response i n t h i s case i s h i g h e s t on t h i n n i n g  and  lowest  on E:20.  T h i s i s as expected s i n c e , as  p o i n t e d above, the h i g h e s t b a s a l area l e v e l s imply t h i n n i n g s and  consequently  delaying  lower f i n a l crop mean DBH  lower f i n a l crop merchantable volume.  This effect  to produce  i s reversed  f o r the merchantable volume of t h i n n i n g s ( F i g u r e 34c) which shows t h i n n i n g regime E:20  w i t h h i g h e s t response because of  the  FIGURE  35  MERCHANTABLE VOLUME INCREASE (%) FOR DIFFERENT THINNING REGIMES (RELATIVE TO CURRENT THINNING REGIME) ON DIFFERENT SITE INDEX CLASSES  239  l a r g e r - s i z e d t h i n n i n g s r e s u l t i n g from the d e l a y . a l s o shows the response  F i g u r e 35c  increasing with increasing s i t e  c l a s s w i t h i n each t h i n n i n g regime.  Thus the h i g h e s t  w i t h r e s p e c t to t h i n n i n g volume o c c u r s on the best  The r e s u l t s from t h i s s e c t i o n complement previous final  index  response  sites.  the o b s e r v a t i o n s of the  s e c t i o n t h a t t h i n n i n g model A:20 would be p r e f e r a b l e i f t h e  crop i s the p r i o r i t y , w h i l e E:20 would be p r e f e r r e d i f d i s t r i b u -  t i o n o f y i e l d over the whole r o t a t i o n i s a major concern. average,  On the  t h i n n i n g model C:20 would be a good compromise as i t r e s u l t s i n  p o s i t i v e i n c r e a s e of both merchantable f i n a l crop volume and volume of t h i n n i n g s (see F i g u r e 35b and c ) . q u a l i t y c l a s s , the poorest  The response  s i t e s responding  i s dependent on the s i t e  best to the f i n a l  merchantable volume (12.6% on S.I. 12 compared to almost  crop  zero on S.I.  24) w h i l e the best s i t e s responds best to the merchantable volume of thinning (d)  (21.2% on S.I. 24 compared to 1.3% on S.I. 12).  E f f e c t s of i n i t i a l regime  s t o c k i n g on y i e l d under a s p e c i f i c t h i n n i n g  Under the c u r r e n t t h i n n i n g model f o r C. l u s i t a n i c a (and f o r P. p a t u l a and P_. r a d i a t a as w e l l ) , the emphasis i s on the number of stems to  be l e f t  after thinning.  I n c r e a s i n g the i n i t i a l  number of stems say  from 1200 t o 1600 stems per h e c t a r e (sph) w i l l have v e r y l i t t l e on the y i e l d of the stand w i t h r e s p e c t to volume p r o d u c t i o n . s l i g h t decrease  i n DBH may r e s u l t .  However, a  F o r example f o r s i t e Index 18 under  the c u r r e n t t h i n n i n g regime, C. l u s i t a n i c a DBH from 47.6 cm to 46.6 cm when i n i t i a l  effect  ( t o 40 y e a r s )  decreased  number of stems were i n c r e a s e d from  240  1200  to 1600  having  sph.  T h i s decrease i s a r e s u l t  a lower DBH  forward  to age  40  at time of f i r s t  t h i n n i n g , an e f f e c t  the number, of stems to be removed at each t h i n n i n g i s a f u n c t i o n  (see e q u a t i o n  2.28).  I n c r e a s i n g the i n i t i a l  b o t h the b a s a l a r e a b e f o r e t h i n n i n g and removed c o n s t a n t  be maintained  after  results  each t h i n n i n g .  t h e r e f o r e a lower mean stand DBH.  DBH  to age  This effect  1600  The  i s demonstrated on T a b l e  The  results  net r e s u l t  a f t e r each t h i n n i n g , DBH 40 y e a r s  under the two  decrease of 4.7  under the  and  level.  i s quite appreciable.  site  s t o c k i n g s of 1200 40 y e a r s  s t o c k i n g s , mainly because  1600  model, t h i s e f f e c t must be taken i n t o  area  fixed  merchantable  and  does the  sph s t o c k i n g i s almost made up  f o r by the l a r g e r number of stems removed i n t h i n n i n g s .  that t h i s e f f e c t  stocking  f o r C_. l u s i t a n i c a  at the two  not appear much d i f f e r e n t  decrease i n DBH  in a  i s a decrease i n  d i f f e r e n c e i n merchantable volume to age  cm i n DBH  to  51, which shows the number of stems  18 under the t h i n n i n g regime C:20 sph.  holding  among the h i g h e r number of stems  volume ( t o 15 cm top diameter) a t age index  thinnings  i n the l e v e l o f s t o c k i n g to  s i n c e the stand w i l l be at a h i g h e r  b a s a l area b e f o r e and  of  s t o c k i n g , while  This inevitably  and  40 years  the mean DBH  the p r o p o r t i o n of b a s a l a r e a  i n an Increase  amount of b a s a l area b e i n g a l l o c a t e d  and  that i s c a r r i e d  t h i n n i n g model proposed f o r C_. l u s i t a n i c a i n t h i s  of the b a s a l a r e a removed i n the t h i n n i n g and  be  stems  years.  Under the new study,  of the i n d i v i d u a l  However, t h i s  Thus, i n u s i n g t h i s consideration.  thinning  I t should be noted  can be minimized by a d j u s t i n g the p r o p o r t i o n of b a s a l  to be removed at f i r s t  t h i n n i n g so as to leave a reasonably  lower  241  TABLE 51.  E f f e c t of i n i t i a l s t o c k i n g on y i e l d under t h i n n i n g regime C:20 f o r £ . l u s i t a n i c a i . e . t h i n n i n g based on p r o p o r t i o n of b a s a l area to remove when a c r i t i c a l stand b a s a l area i s e q u a l l e d o r exceeded.  Stocking  1200  1600  Before  After  Before  After  1st t h i n n i n g  1200 (25.0)  850 (20.0)  1600 (25.0)  1124 (20.0)  2nd t h i n n i n g  850 (35.0)  621 (28.0)  1124 (35.0)  813 (28.0)  3rd t h i n n i n g  621 (45.0)  459 (36.0)  813 (45.0)  597 (36.0)  459 (45.0)  342 (36.0)  597 (45.0)  442 (36.0)  4th t h i n n i n g  DBH  (40*) cm  V(15) (40*) m  3  43.1  38.4  824.3  812.6  SI = 18. o  No. i n b r a c k e t s a r e b a s a l area i n m . 40* = age 40 y e a r s .  .  242  number of stems. higher f i n a l  3.4  crop  Lowering the i n i t i a l number of stems would r e s u l t i n DBH.  Summary on the S i m u l a t e d  The  T h i n n i n g Experiment  p r e c e d i n g a n a l y s i s of the p r o d u c t i v i t y under the  different  t h i n n i n g regimes served to demonstrate the a b i l i t y of the y i e l d model EXOTICS as a v e r s a t i l e t o o l f o r stand m a n i p u l a t i o n to study development under v a r i o u s s i l v i c u l t u r a l was  i d e n t i f i e d as the most c r i t i c a l  schedules.  stand  Thinning  intensity  c o n s i d e r a t i o n when f o r m u l a t i n g a  t h i n n i n g p o l i c y , w i t h l e v e l of s t o c k i n g b e f o r e t h i n n i n g having little up  e f f e c t on t o t a l and  to age  40  merchantable volume y i e l d f o r C.  very  lusitanica  years.  From a p r a c t i c a l p e r s p e c t i v e , the a n a l y s i s demonstrated t h a t by a d o p t i n g t h i n n i n g regime C:20  f o r C_. l u s i t a n i c a , t o t a l merchantable  t h i n n i n g volume c o u l d be i n c r e a s e d by between 1 t o 21% f o r s i t e  index  c l a s s e s 12 to 24 r e s p e c t i v e l y w h i l e a t the same time i n c r e a s i n g the final  crop merchantable volume by between zero and  c l a s s e s 24 to 12 r e s p e c t i v e l y . o p t i m a l and  i s but one  minimum DBH  utilize  4.  T h i s t h i n n i n g schedule  for site  formulated  economic c o n s t r a i n t s , i n c l u d i n g  a t c l e a r f e l l age and  index  i s not n e c e s s a r i l y  of s e v e r a l a l t e r n a t i v e s t h a t can be  f o r v a r i o u s s i l v i c u l t u r a l and mix,  12.6%  product  the a v a i l a b i l i t y of f a c i l i t i e s  to  t h i n n i n g volume.  Pulpwood P r o d u c t i o n Regime f o r Kenya  F o r primary p o l i c y i s not  pulpwood p r o d u c t i o n p l a n t a t i o n s , the b a s i c management  to t h i n but  to manipulate  the i n i t i a l  stand d e n s i t y  243  t o maximize t o t a l volume p r o d u c t i o n .  1?. p a t u l a i s the favoured s p e c i e s  f o r pulpwood p l a n t a t i o n s and so i t i s not s u r p r i s i n g t h a t f o r t h i s s p e c i e s , d a t a f o r unthinned  stands covered up t o age 16.5 y e a r s ( s e e  T a b l e 25 - P_. p a t u l a , r e s t o f the country which i n c l u d e s Nabkoi, the zone f o r pulpwood p r o d u c t i o n ) . study volume y i e l d and  _P. p a t u l a (Nabkoi) was t h e r e f o r e used t o  f o r pulpwood p r o d u c t i o n under v a r i o u s s t o c k i n g l e v e l s  establishment s i t e s  a t a 15 y e a r r o t a t i o n age.  T a b l e 52 g i v e s the t o t a l y i e l d a t age 15 years f o r the v a r i o u s stocking levels, percentage  s i t e index c l a s s e s and e s t a b l i s h m e n t s i t e s .  decreases  also given.  i n volume under g r a s s l a n d e s t a b l i s h m e n t  The s i t e s are .  F i g u r e 36a and b shows the CAI and MAI curves f o r the  v a r i o u s s t o c k i n g l e v e l s a t the two e s t a b l i s h m e n t s i t e s  for site  index  c l a s s 21 w h i l e F i g u r e 37 shows the DBH development under shamba establishment  site  f o r s i t e index 21 (average  s i t e index c l a s s f o r  P. p a t u l a ) . As expected, T a b l e 52 shows t h a t volume y i e l d  i n c r e a s e s as s i t e  i n d e x c l a s s i n c r e a s e s and w i t h i n c r e a s e i n number o f stems f o r both Shamba s i t e s  and g r a s s l a n d s i t e s , w i t h t h e y i e l d  l i s h m e n t s i t e b e i n g lower than the former The  percentage  decrease  of the l a t t e r  estab-  f o r a g i v e n s i t e index  class.  on g r a s s l a n d s a l s o decreases w i t h i n c r e a s i n g  s i t e index c l a s s and i n c r e a s i n g s t o c k i n g .  T h i s i s an e f f e c t o f the  c o n s t a n t r e d u c t i o n i n h e i g h t being expressed  as a percentage  of an  i n c r e a s i n g h e i g h t as s i t e index c l a s s i n c r e a s e s or as b a s a l area i n c r e a s e s ( a s a r e s u l t o f i n c r e a s e i n number o f stems).  The important  p o i n t t o note however i s t h a t y i e l d under g r a s s l a n d e s t a b l i s h m e n t i s on t h e average  about 16% lower  than on shamba e s t a b l i s h m e n t  sites  sites for  TABLE 52.  T o t a l volume y i e l d V ( l ) f o r P. p a t u l a (Nabkoi) by s i t e index c l a s s e s f o r v a r i o u s s t o c k i n g l e v e l s and e s t a b l i s h m e n t s i t e s up t o age 15 y e a r s .  27  24  21  18  15  S.I. s.p.h.  1000  201.8  150.6 (25.4)  272.8  217.0 (20.4)  347.8  289.0 (16.9)  425.4  364.7 (14.3)  504.5  442.7 (12.2)  1200  233.0  176.3 (24.3)  309.5  249.5 (19.4)  388.5  326.8 (15.9)  468.6  406.1 (13.3)  548.6  486.2 (11.4)  1400  258.7  198.5 (23.3)  338.3  276.0 (18.4)  418.7  355.9 (15.0)  498.8  436.4 (12.5)  577.9  516.3 (10.6)  1600  279.4  217.1 (22.3)  360.1  297.1 (17.5)  440.4  377.9 (14.2)  519.3  457.8 (11.8)  596.6  536.4 (10.0)  No. i n bracket i n d i c a t e % decrease S = Shamba  sites.  G = Grassland  sites.  i n y i e l d under g r a s s l a n d r e l a t i v e  t o Shamba  yield.  FIGURE 36 C.A.I. AND M.A.I. CURVES FOR VARIOUS STOCKING LEVELS FOR P. PATULA SITE INDEX 21  S3  FIGURE  37  DIAMETER/AGE RELATIONSHIP AT VARIOUS STOCKING LEVELS FOR SITE INDEX 21 FOR P. PATULA (NABKOI)  AGE IN YEARS FROM PLANTING  247  a s t o c k i n g o f 1200  sph.  T h i s i s an important  f i n d i n g h i t h e r t o not  r e c o g n i z e d by the f o r e s t managers i n Kenya. F i g u r e 36a and b shows the CAI and MAI l e v e l s being h i g h e r than f o r the lower  curves f o r h i g h e r s t o c k i n g  l e v e l s , w i t h those f o r g r a s s l a n d  s i t e s being lower than f o r Shamba s i t e s , a g a i n as expected.  However, at  some p o i n t s i n time, the CAI  curves f o r h i g h e r s t o c k i n g l e v e l s are  to  curves.  f a l l below those of lower  competition.  seen  T h i s i n d i c a t e s the e f f e c t s of  T h i s i s confirmed on F i g u r e 37 which shows the  development on a l l s t o c k i n g l e v e l s b e i n g almost  DBH  the same a t the  lower  ages ( i n absence of c o m p e t i t i o n ) but w i t h the curves f o r the h i g h e r stocking levels f a l l i n g earlier:  9,  tively.  10 and  below those of lower s t o c k i n g l e v e l s much  11 y e a r s f o r s t o c k i n g s 1600,  T h i s i s as expected  of  at which CAI  the next  stems.  at which t h a t  above t h a t of the next  to  competi-  lower s t o c k i n g l e v e l  t o the h i g h e r number of stems u n t i l a c r i t i c a l DBH  i s reached  which the h i g h e r number of stems do not compensate the CAI The  This i s  but a l s o of the number of  development s t a r t s s l o w i n g down due  t i o n , the CAI i s maintained due  below t h a t  below the g e n e r a l growth t r e n d curve.  i s not o n l y a f r u n c t i o n of DBH  Thus when DBH  respec-  to set i n  curves of a g i v e n s t o c k i n g l e v e l f a l l s  curve f a l l s  because the CAI  1200  I t should however be noted t h a t  lower s t o c k i n g l e v e l i s l a t e r than the age  s t o c k i n g s DBH  and  s i n c e c o m p e t i t i o n i s expected  e a r l i e r on stands w i t h h i g h e r s t o c k i n g . the age  1400  below  sufficiently.  t r u e onset of c o m p e t i t i o n t h e r e f o r e i s marked not by the age at  which CAI  starts falling  the age a t which DBH  below t h a t of the lower  development s t a r t s  s t o c k i n g l e v e l but  slowing down due  by  to c o m p e t i t i o n .  248  The  c o n c e p t u a l b a s i s f o r the use of DBH development as a c r i t e r i a  f o r stand d e n s i t y c o n t r o l i s s i m i l a r t o t h a t of the maximum s i z e - d e n s i t y proposed  by Drew and F l e w e l l i n g  c o n s t a n t s t o c k i n g experiments  (1977, 1979).  I t t h e r e f o r e r e l i e s on  t o p r o v i d e the c r i t i c a l  v a l u e s a t which stands s h o u l d be t h i n n e d .  size-density  As has j u s t been demon-  s t r a t e d , EXOTICS p r o v i d e s a u s e f u l t o o l f o r conducting constant s t o c k i n g experiments,  p r o v i d e d d a t a from unthinned  c a l i b r a t i n g the model and f o r v a l i d a t i o n . f o r constant s t o c k i n g experiments  stands i s a v a i l a b l e , both f o r As i t i s , the model i s v a l i d  f o r up to 10 y e a r s ( f o r C_. l u s i t a n i c a  and P_. r a d i a t a ) and 15 y e a r s ( f o r P_. p a t u l a ) and f o r s t o c k i n g between 1000  t o 1600 sph f o r a l l s p e c i e s .  249  CHAPTER SUMMARY:  THEORETICAL AND  5  PRACTICAL ASPECTS OF THIS STUDY,  SUGGESTED FUTURE DEVELOPMENTS AND  As s t a t e d i n the i n t r o d u c t o r y  chapter,  APPLICATION  the main o b j e c t i v e of t h i s  study was  t o advance our knowledge  of the growth and y i e l d of the three  species:  C_. l u s i t a n i c a , P_. p a t u l a and P_. r a d i a t a under the p r e v a i l i n g  c l i m a t i c , e d a p h i c and s i l v i c u l t u r a l regimes i n Kenya. was  This  objective  pursued i n three phases: 1.  A study of the growth and y i e l d r e l a t i o n s h i p and d e r i v a t i o n of the a p p r o p r i a t e  2.  Construction  growth f u n c t i o n s .  of a growth and y i e l d model as a means of  p r e d i c t i n g growth and y i e l d under v a r i o u s  physical, biological  and management c o n s t r a i n t s . 3.  An a n l y s i s of the growth and y i e l d of these s p e c i e s under the present  and a l t e r n a t i v e s i l v i c u l t u r a l management regimes.  T h i s chapter summarizes  the accomplishments of the study, i t s  t h e o r e t i c a l and p r a c t i c a l i m p l i c a t i o n s and suggests areas f o r f u t u r e development and a p p l i c a t i o n .  The summary i s presented by phases as they  o c c u r i n the study.  1.  Growth and Y i e l d R e l a t i o n s h i p s D i f f e r e n t a s p e c t s of stand  development were s t u d i e d and r e l e v a n t  growth f u n c t i o n s d e r i v e d as f o l l o w s :  250  Dominant h e i g h t  development:  Stand dominant h e i g h t  ( d e f i n e d as the mean h e i g h t o f the 100  l a r g e s t diameter t r e s p e r h e c t a r e ) was s t u d i e d as a f u n c t i o n o f age from p l a n t i n g and s i t e index stand a t age 15 y e a r s ) . Richards  ( d e f i n e d as dominant h e i g h t of the  Two n o n l i n e a r f u n c t i o n s , the Chapman-  ( e q u a t i o n 2.5) and the m o d i f i e d W e i b u l l f u n c t i o n ( e q u a t i o n  2.6) were c o n s i d e r e d and the former found based on the asymptotic  standard  to be more a p p r o p r i a t e ,  deviation.  The f i n a l e q u a t i o n was  of the form:  Hdom - b o d  where A  b  A S I  ) 2 b  = Age of stand from p l a n t i n g  SI H  - e- l  = Site  dom  bQ»  =  ^  t a n c  index  * dominant h e i g h t i n meters  b j and b£ a r e r e g r e s s i o n c o n s t a n t s .  On v a l i d a t i o n , t h i s f u n c t i o n was accepted and P_. r a d i a t a .  F o r P. p a t u l a , h e i g h t development was found t o  d i f f e r from one r e g i o n t o another, ment was polymorphic. curves  f o r C_. l u s i t a n i c a  Covariance  suggesting  that height  develop-  a n a l y s i s f o r the development  f o r each r e g i o n i n d i c a t e d t h a t f o r a t l e a s t  some of the  r e g i o n s , the growth curves were s i g n i f i c a n t l y d i f f e r e n t a t the .05 significance level. edaphic  T h i s phenomenon was suspected  d i f f e r e n c e s i n the d i f f e r e n t  required i n t h i s regard.  t o be due t o  r e g i o n s but more r e s e a r c h i s  Data f o r t h i s s p e c i e s was s t r a t i f i e d by  g e o g r a p h i c a l r e g i o n s and a l i n e a r q u a d r a t i c model ( e q u a t i o n 2.17) fitted:  251  H  dom  =  b  0  +  b  l  S  I  +  b  2  A  +  b  3  A 2  +  b  4  A S I  +  b A SI 2  5  where v a r i a b l e names a r e as above. The  f i n d i n g t h a t h e i g h t development f o r P_. p a t u l a i s p o l y -  morphic i s unique t o t h i s study.  A l l p r e v i o u s s t u d i e s on t h i s  s p e c i e s have used one s e t of s i t e index curves country.  f o r the whole  The p r a c t i c a l i m p l i c a t i o n o f t h i s f i n d i n g i s t h a t p l a n t a -  t i o n s may be of the same s i t e index c l a s s a t a g i v e n p o i n t i n time but t h a t the development curves may be d i f f e r e n t . for different  s i t e index curves f o r d i f f e r e n t  Hence the need  geographical regions.  F o r b o t h P. p a t u l a and P_. r a d i a t a , two types of e s t a b l i s h m e n t s i t e s a r e used - Shamba and g r a s s l a n d .  Dominant h e i g h t under each  type o f e s t a b l i s h m e n t was s t u d i e d , a g a i n u s i n g c o v a r i a n c e The  c o n c l u s i o n was t h a t up t o age 20 y e a r s , h e i g h t development  under g r a s s l a n d was s i g n i f i c a n t l y Shamba. two (1)  analysis.  ( a t .05 l e v e l ) lower  than under  T h i s f i n d i n g , which h i t h e r t o had not been r e c o g n i s e d , has  important  practical  significance:  Where the f o r e s t manager has a c h o i c e , Shamba p l a n t i n g i s t o be p r e f e r r e d .  (2)  Any growth and y i e l d model f o r t h e two pine s p e c i e s should have e s t a b l i s h m e n t  (b)  s i t e as one of the i n p u t v a r i a b l e s .  M o r t a l i t y , stand d e n s i t y development and t h i n n i n g p r a c t i c e s i n Kenya: Due t o t h e i n t e n s i v e nature of stand management, i n c l u d i n g  t h i n n i n g , m o r t a l i t y was not c o n s i d e r e d i n t h i s study.  Stand  density  252  development and t h i n n i n g p r a c t i c e s were i n t e n s i v e l y s t u d i e d  and the  f o l l o w i n g important f i n d i n g s noted: (1)  Under the present s i l v i c u l t u r a l density  p r e s c r i p t i o n s , the stand  Index (S%) v a r i e s between 18-30% f o r C_. l u s i t a n i c a and  15-25% f o r JP. p a t u l a and P_. r a d i a t a . (2)  Stand d e n s i t y  index v a r i e s f o r d i f f e r e n t s i t e c l a s s e s  s p e c i e s , w i t h wide spacing crowding on good  d e v e l o p i n g on poor s i t e s and o v e r -  sites.  The second o b s e r v a t i o n productivity.  for a l l  was  suspected to have an i n f l u e n c e  T h i s p o s s i b i l i t y was e x p l o r e d  on  f u r t h e r i n Chapter 4.  T h i n n i n g types f o r Kenya, based on the c l a s s i f i c a t i o n of E i d e  and  L a n g s a e t e r (Braathe 1957) (based on  be 0.80 and  DBH(T) DB  TJ('B'J.)  r a t i o ) was  found to  f o r P_. r a d i a t a (no d e f i n i t e low or crown t h i n n i n g ) ,  0.88 f o r C_. l u s i t a n i c a and P_. p a t u l a  b o r d e r s on the lower s i d e o f crown  0.85  r e s p e c t i v e l y , which  thinning.  DBH o f t h i n n i n g was expressed as a f u n c t i o n of DBH  before  t h i n n i n g and i n t e n s i t y o f t h i n n i n g , measured as a r a t i o e i t h e r of the number of stems thinned as b a s a l area thinned  over number of stems b e f o r e t h i n n i n g or  over b a s a l  area b e f o r e t h i n n i n g .  f u n c t i o n s were n e c e s s a r y f o r the s i m u l a t i o n l a t t e r p a r t of the study.  of t h i n n i n g s  These i n the  253  B a s a l a r e a development b e f o r e f i r s t  thinning:  B a s a l a r e a b e f o r e t h i n n i n g was d e s c r i b e d as a f u n c t i o n of stand age,  stand dominant h e i g h t  (which i n c l u d e s e f f e c t s of s i t e q u a l i t y )  and number of stems u s i n g n o n l i n e a r e q u a t i o n  where BA  =  B a s a l a r e a i n m^/ha  A  =  Age i n y e a r s  H  =  Stand dominant h e i g h t i n meters  N  =  No. stems/ha-.  2.29 as f o l l o w s :  from p l a n t i n g  An unexpected f i n d i n g from t h i s study was that b a s a l area development f o r P_. p a t u l a from K i n a l e r e g i o n d i f f e r e d the r e s t of the country,  from that f o r  a phenomenon t h a t c o u l d not be e x p l a i n e d  from any o f the b i o l o g i c a l o r c l i m a t i c f a c t o r s a v a i l a b l e t o t h i s study.  More i n v e s t i g a t i o n w i l l be r e q u i r e d t o determine the under-  l y i n g f a c t o r or f a c t o r s :  B a s a l a r e a development i n t h i n n e d  stands:  B a s a l a r e a increment r a t h e r than b a s a l a r e a per se was s t u d i e d i n t h i n n e d stands thinning.  as i t i s r e l a t i v e l y independent o f the e f f e c t s of  Nonlinear  equation  2.31 which i s an e x t e n s i o n and more  g e n e r a l i z e d form o f the b a s a l area increment equation f o r New Zealand  BAI  = ( l b  e  ( C l u t t e r and A l l i s o n  b BA 4 + _ b  A  3  b s) 5  f o r P_. r a d i a t a  1974) was used i n t h i s  study:  254  where  A  =  Age  i n y e a r s a t the end of growth p e r i o d  BA  =  Stand b a s a l a r e a a t b e g i n n i n g of growth p e r i o d i n  m  2  per ha S  =  Stand d e n s i t y index, c a l c u l a t e d  S = H  §_ dorn  x  as:  100  /l0,000 a = /— V N  where  1  N  =  No.  stems per h e c t a r e  For P_. r a d i a t a , the term S% was level.  T h i s term was  found n o n - s i g n i f i c a n t at  a l s o not i n c l u d e d i n the New  Zealand  which suggests t h a t i t s e f f e c t s on b a s a l area increment species  Diameter  equation be  specific.  distribution:  The W e i b u l l p r o b a b i l i t y d e n s i t y f u n c t i o n was diameter  may  .05  distribution  for several  s e l e c t e d to model  reasons:  (1)  I t i s simple and m a t h e m a t i c a l l y handy.  (2)  Its ability  (3)  On f i t t i n g t h i s model t o 58 diameter d i s t r i b u t i o n  t o assume a v a r i e t y of curve  shapes. histograms,  o n l y f o u r p l o t s ( w i t h a multimodal h i s t o g r a m ) were r e j e c t e d  as  not having a W e i b u l l d i s t r i b u t i o n , based on a goodness of f i t test. The  cumulative form of t h i s d i s t r i b u t i o n  f i t t e d t o the d a t a :  ( e q u a t i o n 2.35)  was  255  F(x) = 1 for  x > xg 0 < F(x) < 1  where x x  = observed  diameter  = minimum observed  0  class diameter  b and c a r e the W e i b u l l  constants.  The estimated parameters f o r each p l o t were then w i t h stand parameters.  F i n a l equations  correlated  f o r the p r e d i c t i o n o f  these parameters were:  x  Q  = b + b5 + b Q  b  = b  Q  c  = b  0  x  I  2  + b (x - x ) + b x  Q  2  Ji  + b1  where x = Mean stand DBH i n cm. XQ = Mininum stand DBH i n cm. b and c a r e p r e d i c t e d W e i b u l l parameters.  Stand volume  calculations:  Tree volume equations  f o r the t h r e e s p e c i e s d i s c u s s e d i n t h i s  study have been i n e x i s t e n c e i n Kenya s i n c e 1969.  These have been  the b a s i s f o r t h e volume t a b l e s and the y i e l d t a b l e s and so were deemed t o have passed  the t e s t o f time i n the f i e l d .  they were used i n t h i s study t o d e r i v e stand volume.  Therefore  256  In the study of the dominant h e i g h t development, the adopted i m p l i c i t l y  i m p l i e d t h a t the s i t e index curves f o r the  s p e c i e s were anamorphic.  T h e r e f o r e the v a l i d a t i o n procedure  a t e s t of the n u l l h y p o t h e s i s anamorphic.  procedure  amounted to  t h a t dominant h e i g h t development i s  T h i s h y p o t h e s i s was  Another important  three  r e j e c t e d f o r P. p a t u l a o n l y .  t h e o r e t i c a l c o n s i d e r a t i o n i n t h i s study  to b a s a l a r e a development i n t h i n n e d s t a n d s .  related  A g e n e r a l l y accepted  s u p p o s i t i o n i n f o r e s t r y l i t e r a t u r e i s t h a t b a s a l area increment  i s not  a f f e c t e d by changes i n stand d e n s i t y over a wide range of d e n s i t i e s , a t h e o r y t h a t has  come to be known as M o l l e r ' s t h e o r y ( B a s k e r v i l l e  T h i s t h e o r y i s c o n s i s t e n t w i t h i n t u i t i o n s i n c e a decrease  i n number of  stems on a u n i t area b a s i s i s compensated f o r by an i n c r e a s e i n growth of the remaining v a r y very l i t t l e .  t r e e s and  thus increment  1965).  i n basal area  In t h i s study however, b a s a l area increment  diameter should  was  found  to be a f u n c t i o n of the b a s a l of the stand at the b e g i n n i n g of the growth p e r i o d f o r a l l t h r e e s p e c i e s . measure of s t a n d d e n s i t y , i t was the p r e s e n t  2.  Inasmuch as b a s a l area i s a  concluded  t h a t f o r these s p e c i e s and  at  l e v e l of stand d e n s i t i e s , M o l l e r ' s theory does not h o l d .  C o n s t r u c t i o n of the Growth and Y i e l d Model A growth and y i e l d model EXOTICS was  o b j e c t i v e b e i n g to p r o v i d e a p l a n n i n g and  c o n s t r u c t e d w i t h the main s i l v i c u l t u r a l management t o o l  t h a t would a l l o w m a n i p u l a t i o n of a s i n g l e stand to meet f o r e s t management o b j e c t i v e s . IBM  System/360 and  W r i t t e n i n FORTRAN IV G l e v e l which I s compatible  with  System/370, EXOTICS i s an i n t e r a c t i v e whole-stand/  d i s t a n c e independent model designed  to handle  a s i n g l e even-aged  257  monospecific  stand a t a time.  d i s t r i b u t i o n by 3 cm diameter  The model a l s o p r o v i d e s  c l a s s e s which allows output  main stand y i e l d by s i z e c l a s s e s . model unique i n the Kenya 1.  o f the f i n a l  The f o l l o w i n g f e a t u r e s make t h i s  scene:  Refinement of t h e s i t e index curves through establishment  diameter  i n c l u s i o n of  s i t e as an i n p u t v a r i a b l e , and the polymorphic  growth p a t t e r n f o r P_. p a t u l a .  These a r e new f i n d i n g s from  this  study. 2.  The model allows f o r t h r e e t h i n n i n g o p t i o n s , a l l of which can be addressed  i n the same s i m u l a t i o n run:  0  =  No t h i n n i n g .  1  =  T h i n n i n g based on number of stems t o leave t h i n n i n g when a predetermined  after  age o r stand dominant  h e i g h t i s e q u a l l e d or exceeded. 2  =  T h i n n i n g based on a p r o p o r t i o n of b a s a l a r e a t o remove when a predetermined  basal area i s equalled  or exceeded. T h i s feature allows f o r f l e x i b i l i t y  i n t h i n n i n g d e c i s i o n and  f o r use of d i f f e r e n t o p t i o n s a t d i f f e r e n t stages of stand development. 3.  The i n t e r a c t i v e aspect of the model makes i t a very handy t o o l for s i l v i c u l t u r a l research.  On v a l i d a t i o n , EXOTICS was found following  limitations:  t o be a c c e p t a b l e w i t h i n the  258  1.  The model was found t o have no apparent  b i a s f o r a l l three  species. 2.  95% c o n f i d e n c e l i m i t s f o r the d i f f e r e n c e between observed and s i m u l a t e d volumes were C. l u s i t a n i c a  :  ± 16%  P. p a t u l a  :  ± 20%  P. r a d i a t a  :  ±17%  T h i s was a l o t o f improvement on VYTL-2 which had an average 95% c o n f i d e n c e l i m i t s of ± 3 0 % ( A l d e r 1977). 3.  The model was found a c c e p t a b l e f o r e r r o r s p e c i f i c a t i o n of between 20-25% (C. l u s i t a n i c a and P. r a d i a t a ) and 25-30% f o r P_. p a t u l a u n l e s s a l - i n - 2 0 chance has o c c u r r e d .  T h i s compared  w e l l w i t h the a c c u r a c y o f some models a l r e a d y i n o p e r a t i o n : FOREST and SHAFT (Ek and Monserud 1979). 4.  N e a r l y a l l v a r i a b i l i t y f o r C_. l u s i t a n i c a and P_. r a d i a t a was from the b a s a l a r e a component. f u t u r e refinement component.  Thus, f o r these two s p e c i e s ,  of the model should be d i r e c t e d t o t h i s  F o r P_. p a t u l a , t o t a l v a r i a b i l i t y i n the p r e d i c t e d  volume was c o n t r i b u t e d t o by dominant h e i g h t and b a s a l area components i n the r a t i o s o f 1:2. refinement  should be addressed  For t h i s species future  t o both  components.  As noted e a r l i e r i n the study, the v a l i d a t i o n  process c o n s t i t u t e d a  t e s t o f the n u l l h y p o t h e s i s t h a t the model i s an a c c e p t a b l e approximat i o n o f t h e r e a l system. w i t h i n the above s t a t e d  I n t h i s case the n u l l h y p o t h e s i s was accepted limitations.  259  3.  S i l v i c u l t u r a l Management Models f o r Kenya The  c u r r e n t t h i n n i n g p o l i c y f o r Kenya aimed at p r o d u c t i o n  of l a r g e -  s i z e d sawlog crop i n as s h o r t a r o t a t i o n as p o s s i b l e at the expense of some l o s s i n t o t a l y i e l d was by events.  A new  p r o d u c t i o n was forest  d i s c u s s e d and  found to have been  t h i n n i n g p o l i c y based on the concept of maximum volume  proposed as more a p p r o p r i a t e  i n the presence of  l a n d , i n c r e a s i n g demand f o r wood products  t i o n of the f o r e s t r y i n d u s t r i a l Using  overtaken  and  limited  increased i n t e g r a -  sector.  the y i e l d model EXOTICS, growth and y i e l d under the  t h i n n i n g p r e s c r i p t i o n s was  s t u d i e d and  the f o l l o w i n g main  current  observations  noted: 1.  Hart's  stand d e n s i t y Index was  guide to when a stand i s due  found to be inadequate as  f o r t h i n n i n g f o r C_. l u s i t a n i c a  P_. p a t u l a as t h i s l e d to development of d i f f e r e n t s i t e occupancy ( w i t h r e s p e c t quality  classes.  a  levels  to b a s a l a r e a ) on d i f f e r e n t  However t h i s index was  found to be  and  of site  appro-  p r i a t e f o r P_. r a d i a t a . 2.  For C_. l u s i t a n i c a and P_. r a d i a t a , f i r s t  t h i n n i n g was  have no apparent e f f e c t on volume CAI.  Subsequent  were found to have marked e f f e c t s on CAI. t h i n n i n g had 3.  marked e f f e c t s on volume  Consequent to 2 above, i t was ( M o l l e r 1947)  found to thinnings  For P_. p a t u l a , a l l  CAI.  concluded  that M o l l e r ' s  theory  t h a t t h i n n i n g has no a p p r e c i a b l e e f f e c t s on  volume y i e l d does not h o l d f o r these l e v e l of s i l v i c u l t u r a l management.  s p e c i e s at the  total  present  260  U s i n g C_. l u s i t a n i c a , a t h i n n i n g experiment  was  designed  to i n v e s t i -  gate the e f f e c t s of a l t e r n a t i v e t h i n n i n g regimes on growth and Five thinning levels arbitrarily sities:  yield.  (based on b a s a l a r e a l e v e l s b e f o r e t h i n n i n g ) were  s e l e c t e d f o r study.  W i t h i n each l e v e l , f o u r t h i n n i n g i n t e n -  10, 20, 30 and 40% of the stand b a s a l area t o be removed were  i n v e s t i g a t e d over the range of s i t e index c l a s s e s f o r C_. l u s i t a n i c a . S e v e r a l important 1.  f i n d i n g s were  observed:  W i t h i n the range of t h i n n i n g l e v e l s and  thinning intensities  c o n s i d e r e d , t h i n n i n g I n t e n s i t y i s the most important t i o n w i t h r e s p e c t to volume y i e l d . l i t t l e e f f e c t on both the MAI a b l e volume up to age 2.  The  T h i n n i n g l e v e l has  very  the t o t a l y i e l d of merchant-  40 y e a r .  t h i n n i n g i n t e n s i t y of 20% was  on b i o l o g i c a l r o t a t i o n age. was  and  considera-  the most a p p r o p r i a t e , based  Without economic data however, i t  not p o s s i b l e t o i d e n t i f y the optimum t h i n n i n g l e v e l under  this thinning intensity.  B i o l o g i c a l r o t a t i o n age ranged  be-  tween 22 t o 28 years f o r s i t e index c l a s s 18 depending on t h i n n i n g l e v e l , s h o r t e s t r o t a t i o n a s s o c i a t e d w i t h the  lower  l e v e l s of b a s a l a r e a b e f o r e t h i n n i n g . 3.  By a d o p t i n g t h i n n i n g model C:20,  i t was  p o s s i b l e to increase  the t o t a l merchantable y i e l d f o r C_. l u s i t a n i c a  (up to age  y e a r s ) by between 5 t o 10% depending on the s i t e q u a l i t y The  poorest s i t e q u a l i t y c l a s s (12) responded  best to  40 class.  final  crop merchantable volume (12.6% i n c r e a s e compared to 0.3%  for  261  S.I. 24) w h i l e the best s i t e q u a l i t y c l a s s (24) responded to merchantable volume of t h i n n i n g (21.2% compared t o 1.3% S.I. 12).  T h i s model was  not n e c e s s a r i l y the optimum but  best for one  of the p o s s i b l e a l t e r n a t i v e s depending on both the economic and biological 4.  c o n s t r a i n t s t h a t may  Using the t h i n n i n g model C:20, the i n i t i a l but had  be  imposed.  i t was  observed  that increasing  s t o c k i n g r e s u l t e d i n l o w e r i n g the f i n a l stand  very l i t t l e  effect  DBH  on t o t a l merchantable volume up to  age 40 y e a r s . Using P_. p a t u l a ( N a b k o i ) , y i e l d f o r pulpwood p r o d u c t i o n regimes under d i f f e r e n t sites.  stand d e n s i t i e s was  s t u d i e d under the two  Y i e l d under g r a s s l a n d s i t e s was  found  establishment  to be between 10-25% lower  than t h a t on shamba s i t e s depending on s i t e index c l a s s and  the s t o c k i n g .  High s t o c k i n g and b e t t e r s i t e q u a l i t i e s were a s s o c i a t e d w i t h percentage  decrease.  E f f e c t s of c o m p e t i t i o n on DBH  lower  and CAI development  were a l s o s t u d i e d u s i n g s i m u l a t e d r e s u l t s from these pulpwood  regimes.  B e s i d e s i n d i c a t i n g p o s s i b l e a l t e r n a t i v e management s t r a t e g i e s f o r i n c r e a s i n g y i e l d , r e s u l t s from t h i s phase o f the study served t o demonstrate the use of EXOTICS as a s i l v i c u l t u r a l  r e s e a r c h t o o l w i t h the  s i l v i c u l t u r a l models as the framework w i t h i n which the y i e l d model must operate.  The model appears  to p r o v i d e both r e a l i s t i c and  reliable  r e s u l t s w i t h r e s p e c t to stand development, thus p r o v i d i n g the framework on which economic a n a l y s i s can be  based.  262  4.  F u t u r e R e s e a r c h and Development A r i s i n g from t h i s One  Study  o f the c h a r a c t e r i s t i c s of most r e s e a r c h u n d e r t a k i n g s i s t h a t  they tend t o u n e a r t h areas t h a t r e q u i r e f u r t h e r r e s e a r c h and/or r e f i n e ment.  S i n c e most r e s e a r c h i s p r o s c r i b e d w i t h i n s p e c i f i e d time,  finan-  c i a l o r o t h e r l i m i t a t i o n s , i t i s not always p o s s i b l e t o address areas i n the p a r t i c u l a r are a n t i c i p a t e d 1.  study.  these  The f o l l o w i n g areas were i d e n t i f i e d or  f o r improvement on the present  study:  More data a r e r e q u i r e d on the mature phase of p l a n t a t i o n development f o r a l l s p e c i e s and, i n p a r t i c u l a r , those f o r P_. p a t u l a a r e u r g e n t l y r e q u i r e d . c o u l d be o b t a i n e d from temporary run, permanent sample p l o t  Immediately,  these data  sample p l o t s but i n the l o n g  data w i l l be more a p p r o p r i a t e .  This information i s necessary to provide a b a s i s f o r estimat i o n of the asymptotes i n the s i t e index curve and b a s a l area development 2.  Constant range  functions.  s t o c k i n g experiments  a r e r e q u i r e d c o v e r i n g a wide  o f d e n s i t i e s and r e p l i c a t e d  qualities.  over a wide range o f s i t e  T h i s w i l l p r o v i d e a b a s i s f o r the study o f e f f e c t s  of d e n s i t y and s i t e q u a l i t y on b a s a l area development, maximum b a s a l a r e a and maximum s i z e - d e n s i t y concept: n e c e s s a r y f o r stand d e n s i t y c o n t r o l .  a l l of which a r e  263  3.  More d e t a i l e d s t u d i e s on f a c t o r s a f f e c t i n g b a s a l ment are needed.  In p a r t i c u l a r , c l i m a t i c f a c t o r s and  of t h i n n i n g need to be the b a s a l 4.  a r e a develop-  investigated  area increment  Refinement of the of d a t a c o v e r i n g  for possible inclusion i n  function.  diameter d i s t r i b u t i o n model through i n c l u s i o n the e a r l y phase of p l a n t a t i o n development.  a l t e r n a t i v e t o the procedure used i n t h i s study may i n c l u d e modeling b a s a l a r e a frequency by diameter r a t h e r than stem f r e q u e n c y . basal 5.  This requires  chosen s i l v i c u l t u r a l  classes  d e t a i l e d study of  optimization  treatment.  In t h i s  t e c h n i q u e s such as network a n a l y s i s  c r i t i c a l pathway a n a l y s i s should be of s i l v i c u l t u r a l  investigated  to a l l o w  treatments f o r g i v e n  T h i s r e q u i r e s more i n v o l v e d  and  Immediately  t h e r e f o r e may  Future studies  not  be  should be  A p p l i c a t i o n of the  research  subsequent  yield.  Results  r e s u l t s from t h i s study w i l l be  main a r e a s :  and  tenable.  addressed to the e f f e c t s of  stand growth and  or  for  economic  biological constraints.  r o t a t i o n s on  The  also  I n c l u s i o n of an economic a n a l y s i s model to p r o v i d e economic  connection, optimization  5,  An  a r e a development over the whole r o t a t i o n .  a n a l y s i s o f any  6.  effects  immediately a p p l i c a b l e i n  three  264  Production  of up-to-date y i e l d  t a b l e s f o r any  c u l t u r a l treatment, s i t e index and  specified  establishment  silvi-  site:  These  t a b l e s a r e r e q u i r e d by the Kenya F o r e s t Department f o r day-today  planning  and  management purposes.  F o r r e s e a r c h i n f o r m u l a t i o n of a l t e r n a t i v e s i l v i c u l t u r a l treatments. provide  The  r o l e of the y i e l d model EXOTICS w i l l be  q u a n t i t a t i v e i n f o r m a t i o n on stand  treatments.  response to  to  various  T h i s a p p l i c a t i o n w i l l be u s e f u l to the F o r e s t  Research S e c t i o n of the Kenya F o r e s t Department, the Kenya A g r i c u l t u r a l Research I n s t i t u t e and  the s t a f f at the  Forest  Department of the U n i v e r s i t y of N a i r o b i . For t e a c h i n g purposes at the U n i v e r s i t y of N a i r o b i F o r e s t r y Department: experience  The  r e s u l t s from t h i s study  and  the  author's  on growth and y i e l d w i l l be t r a n s f e r r e d to  U n i v e r s i t y of N a i r o b i to the b e n e f i t of the students interested parties. on  For the f i r s t  time, r e l i a b l e  the and  other  information  stand development f o r the three s p e c i e s w i l l be a v a i l a b l e as  a b a s i s f o r t e a c h i n g and growth and student's  yield.  f u r t h e r r e s e a r c h i n the f i e l d  of  In a d d i t i o n , EXOTICS c o u l d form a b a s i s f o r  experiments, p a r t i c u l a r l y i n s i l v i c u l t u r e  mensuration experiments.  and  265  6.  Conclusion A growth and y i e l d  study on (3. l u s i t a n i c a , P_. p a t u l a and P. r a d i a t a  under t h e p r e v a i l i n g c l i m a t i c , edaphic regimes i n Kenya has been p r e s e n t e d .  and s i l v i c u l t u r a l management T h i s study r e p r e s e n t s a s i g n i f i -  cant e x t e n s i o n o f our knowledge o f the development o f these e s p e c i a l l y w i t h r e s p e c t t o y i e l d under d i f f e r e n t s i l v i c u l t u r a l regimes, i n c l u d i n g e s t a b l i s h m e n t  s i t e q u a l i t i e s and  site.  A growth and y i e l d model EXOTICS was developed s i l v i c u l t u r a l research t o o l .  species,  as a p l a n n i n g and  T h i s model r e p r e s e n t s an improvement on an  e a r l i e r model VYTL-2, both i n terms o f p r e c i s i o n and i n f l e x i b i l i t y i n h a n d l i n g t h i n n i n g d e c i s i o n models.  I t i s t h e r e f o r e hoped t h a t  this  model w i l l be an i n v a l u a b l e a i d to f o r e s t management ( p r o d u c i n g t a b l e s ) , s i l v i c u l t u r a l r e s e a r c h ( i n f o r m u l a t i n g and m o n i t o r i n g response t o v a r i o u s treatments) The  present  proposed.  stand  and as a t e a c h i n g a i d .  t h i n n i n g p o l i c y i s d i s c u s s e d and found  t e n t w i t h the c u r r e n t c o n d i t i o n s i n the c o u n t r y . the concept  yield  t o be i n c o n s i s -  A new p o l i c y based on  o f maximum volume p r o d u c t i o n on a v a i l a b l e f o r e s t l a n d i s A l t e r n a t i v e management schedules  a r e proposed which demon-  s t r a t e t h e p o s s i b i l i t y o f i n c r e a s i n g merchantable volume y i e l d over the whole r o t a t i o n . F i n a l l y , areas  f o r f u r t h e r r e s e a r c h and development a r e d i s c u s s e d .  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