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A least squares analysis of inventory data to compare yields of pure and mixed stands in British Columbia… Yang, Richard C. 1978

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A LEAST SQUARES ANALYSIS OF  INVENTORY DATA TO COMPARE YIELDS OF PURE AND  MIXED STANDS IN BRITISH COLUMBIA FOREST ZONES  by  Richard  C. Yang  B.S.A., N a t i o n a l Taiwan U n i v e r s i t y , 1963 M.S.,  L o u i s i a n a S t a t e U n i v e r s i t y , 1972  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE  REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in  THE  FACULTY OF GRADUATE STUDIES (Forestry)  We accept  t h i s t h e s i s as conforming  to t h e r e q u i r e d  THE  standard  UNIVERSITY OF BRITISH COLUMBIA September, 1978  (c)  Richard  C. Yang  In p r e s e n t i n g t h i s  thesis  in p a r t i a l  fulfilment of  an advanced degree at the U n i v e r s i t y of B r i t i s h the L i b r a r y I  further  for  this  freely  available  representatives. thesis for  Department of  It  financial  i s understood that gain s h a l l  Forestry ________________  The U n i v e r s i t y o f B r i t i s h 2075 Wesbrook P l a c e V a n c o u v e r , Canada V6T 1W5  a  t  e  requirements  Columbia,  I agree  reference and copying o f  this  October 19, 1978  Columbia  not  copying or  for  that  study. thesis  purposes may be granted by the Head of my Department  written permission.  D  for  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  scholarly  by h i s of  s h a l l make it  the  or  publication  be allowed without my  - i iSupervisor:  Dr. A. Kozak  ABSTRACT  The author.developed i r r e g u l a r , unbalanced  a s t a t i s t i c a l procedure  to analyze  i n v e n t o r y data by the l e a s t squares  principle.  The method i s found u s e f u l i n f o r e s t r y where d a t a c o l l e c t e d o f t e n unbalanced  i n nature.  are  I t p r o v i d e s a unique means to i n c o r p o r a t e  q u a l i t a t i v e as w e l l as q u a n t i t a t i v e v a r i a b l e s i n f o r e s t y i e l d a n a l y s e s . Inventory data f o r t h r e e major s p e c i e s — and  D o u g l a s - f i r , spruce,  l o d g e p o l e p i n e were analyzed i n c o n n e c t i o n w i t h the study of growth  and y i e l d  of pure (81% or more of the o v e r s t o r y i s of a s i n g l e s p e c i e s )  and mixed stands i n up t o 12 B.C. occurred.  f o r e s t i n v e n t o r y zones i n which they  More than 50% of D o u g l a s - f i r , spruce, and l o d g e p o l e p i n e  stands occur n a t u r a l l y i n pure s t a n d s .  I f t h e r e are any adverse  effects  on the e s t a b l i s h m e n t of pure s t a n d s , these should have been w e l l r e f l e c t e d q u a n t i t a t i v e l y i n the data p r o v i d e d by the B.C.  Forest Service.  E s t i m a t e s of s i t e index from the i n v e n t o r y data might support t h a t pure stands d e t e r i o r a t e s o i l c o n d i t i o n s ; however, the h i g h e r s i t e i n d i c e s i n mixed stands may  be a t t r i b u t e d to the b e t t e r s i t e c o n d i t i o n s when the  stands  were o r i g i n a l l y e s t a b l i s h e d . Mixed c o n i f e r stands tend to grow more t r e e s per a c r e  than  pure or hardwood mixed type s t a n d s . Among the t h r e e s p e c i e s i n v e s t i g a t e d , D o u g l a s - f i r r e q u i r e d more growing space stand d e n s i t y based  than the o t h e r s .  The  relative  on b a s a l area per a c r e a l s o i n d i c a t e s t h a t stand  d e n s i t y i s h i g h e r i n c o n i f e r mixed stands than i n pure or hardwood mixed type  stands.  - iii  -  The mean annual increment  i s higher  stands than i n pure o r c o n i f e r mixed ones. mixed types i s much l e s s .  i n hardwood mixed  But stand age i n hardwood  The mean annual b a s a l a r e a increment o f  c o n i f e r mixed stands i s c o n s i s t e n t l y h i g h e r than two  types.  t h a t o f the o t h e r  Z o n a l v a r i a t i o n s i n the mean annual b a s a l a r e a growth  are apparent.  The mean annual volume increment  s i m i l a r t o t h a t o f the mean annual b a s a l area  follows a trend increment.  D o u g l a s - f i r stands growing on the Coast and i n the I n t e r i o r were compared. f o r t h e Coast  Mean annual volume growth i s 84.00 c u b i c f e e t per a c r e stands and 25.53 c u b i c f e e t f o r the I n t e r i o r  stands.  The e f f e c t o f s p e c i e s c o m p o s i t i o n on n e t volume y i e l d i s s i g n i f i c a n t i n I n t e r i o r D o u g l a s - f i r s t a n d s , but n o n - s i g n i f i c a n t i n Coast D o u g l a s - f i r , I n t e r i o r spruce, and I n t e r i o r l o d g e p o l e p i n e s t a n d s . That the e f f e c t o f f o r e s t  i n v e n t o r y zones i s h i g h l y s i g n i f i c a n t  i n the  I n t e r i o r D o u g l a s - f i r , spruce, and l o d g e p o l e pine stands j u s t i f i e s the z o n a t i o n u n l e s s adjustments  a r e made f o r stand d e n s i t y .  f o r types and zones a r e s i g n i f i c a n t  Interactions  i n the Coast D o u g l a s - f i r , the  I n t e r i o r s p r u c e , and the I n t e r i o r l o d g e p o l e p i n e stands but a r e nonsignificant  i n the I n t e r i o r D o u g l a s - f i r s t a n d s .  The d i f f e r e n c e i n  y i e l d i n the I n t e r i o r D o u g l a s - f i r stands i s a t t r i b u t a b l e t o s p e c i e s c o m p o s i t i o n types and f o r e s t i n v e n t o r y zones alone.  The e s t a b l i s h m e n t  of D o u g l a s - f i r c o n i f e r mixed type stands i n t h e I n t e r i o r i n c r e a s e s f o r e s t p r o d u c t i v i t y by 21%.  effectively  - iv -  I n t e r p r e t a t i o n s of the i n t e r a c t i o n s l e a d t o the c o n c l u s i o n t h a t the advantages of m o n o c u l t u r a l o r m u l t i c u l t u r a l cannot be o v e r - g e n e r a l i z e d .  Pure type stands a r e more p r o d u c t i v e i n  some zones but l e s s i n the o t h e r s . practices.  The  same i s t r u e f o r m u l t i c u l t u r a l  Growth of f o r e s t t r e e s i s e s s e n t i a l l y  B e f o r e a d e c i s i o n i s reached  practices  site-dependent.  on what s p e c i e s c o m p o s i t i o n type t o  e s t a b l i s h , , f o r e s t e r s should c a r e f u l l y i n v e s t i g a t e the l o c a l s i t e  quality  and past y i e l d h i s t o r y of v a r i o u s f o r e s t types t o ensure t h a t the maximum p o t e n t i a l p r o d u c t i v i t y of a p a r t i c u l a r s i t e can be F u r t h e r a n a l y s e s t o t e s t the h y p o t h e s i s t h a t no  realized. differences  i n volume y i e l d e x i s t among t h r e e s p e c i e s c o m p o s i t i o n types f o r stands growing on same s i t e c o n d i t i o n s r e v e a l t h a t the e f f e c t s f o r s p e c i e s types and  i n v e n t o r y zones as w e l l as i n t e r a c t i o n s t h e r e o f a r e not  s i g n i f i c a n t f o r Coast D o u g l a s - f i r , however, f o r I n t e r i o r D o u g l a s - f i r s t a n d s , the e f f e c t of s p e c i e s c o m p o s i t i o n i s s i g n i f i c a n t .  I t i s shown  t h a t on s i m i l a r s i t e c o n d i t i o n s , D o u g l a s - f i r c o n i f e r mixed stands s u b s t a n t i a l l y more than pure or hardwood mixed stands i n the The  Interior.  s p e c i e s c o m p o s i t i o n e f f e c t i s not s i g n i f i c a n t i n I n t e r i o r  spruce stands w h i l e z o n a l e f f e c t s and are s i g n i f i c a n t . composition  yield  i n t e r a c t i o n s f o r types and  zones  In I n t e r i o r l o d g e p o l e p i n e stands, e f f e c t s of  types, zones, and  interactions thereof d i f f e r  significantly.  In a l l t h r e e s p e c i e s groups i n v e s t i g a t e d , t h a t the e f f e c t s of hardwood mixed type c o n s i s t e n t l y shows  n e g a t i v e 'values i m p l i e s t h a t hardwood  mixed type stands a r e the l e a s t d e s i r a b l e stand composition s t r u c t u r e  - v -  f o r these s p e c i e s i n the I n t e r i o r .  D i f f e r e n c e s i n volume between  pure and mixed type stands r e s u l t p r i m a r i l y from the i n e q u a l i t y i n b a s a l area per a c r e . The v a r i a b l e s , h e i g h t x b a s a l area and b a s a l a r e a are most important  in yield  b a s a l a r e a , and  table analyses.  forest  In a d d i t i o n , stand age,  relative  i n v e n t o r y zone a r e a l l h i g h l y s i g n i f i c a n t i n  c o n t r i b u t i n g to the v a r i a t i o n s i n volume y i e l d of the Coast D o u g l a s - f i r stands.  For I n t e r i o r D o u g l a s - f i r , the most s i g n i f i c a n t v a r i a b l e s a r e ,  i n a d d i t i o n to the above two v a r i a b l e s , stand age, density.  E f f e c t s of s p e c i e s c o m p o s i t i o n type and  are n o n - s i g n i f i c a n t .  and r e l a t i v e  stand  f o r e s t i n v e n t o r y zones  For I n t e r i o r spruce, the prominent v a r i a b l e s i n  y i e l d t a b l e a n a l y s i s are h e i g h t x b a s a l a r e a , b a s a l a r e a , s p e c i e s c o m p o s i t i o n , s t a n d age, h e i g h t , and  r e l a t i v e stand d e n s i t y .  v a r i a b l e s b e i n g e q u a l , pure spruce stands o u t y i e l d spruce-hardwood and mixed s p r u c e - c o n i f e r . evidence  The  All  stands of mixed  r e s u l t s p r o v i d e good  t h a t e s t a b l i s h m e n t of pure spruce stands i s more d e s i r a b l e  than of spruce and  c o n i f e r s or hardwood mixed  stands.  F o r l o d g e p o l e p i n e , the most s i g n i f i c a n t v a r i a b l e s i n y i e l d t a b l e s a n a l y s i s are h e i g h t x b a s a l a r e a , s p e c i e s c o m p o s i t i o n and  f o r e s t i n v e n t o r y zones.  suggests  and  The h i g h s i g n i f i c a n c e of z o n a l e f f e c t s  that a separate y i e l d  i s warranted,  t a b l e f o r l o d g e p o l e p i n e i n each zone  u n l e s s a p p r o p r i a t e adjustments  stand d e n s i t y .  are made f o r s i t e  index  Y i e l d of pure l o d g e p o l e p i n e stands exceeds those  of l o d g e p o l e p i n e c o n i f e r mixed type and mixed t y p e s .  types,  l o d g e p o l e p i n e hardwood  T h e r e f o r e , f o r h i g h y i e l d s the e s t a b l i s h m e n t of pure  l o d g e p o l e p i n e type stands i s p r e f e r r e d .  - vi -  A p p l i c a t i o n o f t h e s e methods to the temporary sample p l o t data has c l e a r l y demonstrated the widespread d i s t r i b u t i o n o f pure stands and l a c k of s u b s t a n t i a l e f f e c t s of monocultures on y i e l d . N e v e r t h e l e s s , the f a c t t h a t h i g h e r y i e l d s may  r e s u l t from some  m u l t i c u l t u r e s s h o u l d encourage e s t a b l i s h m e n t of l o n g term s t u d i e s of s p a c i n g and m i x t u r e s of s p e c i e s .  - vii -  TABLE OF CONTENTS  Page  ABSTRACT  i i  TABLE OF CONTENTS  v i i  LIST OF TABLES  xi  LIST OF FIGURES  xv  LIST OF MAPS  xvii  ACKNOWLEDGEMENTS  xviii  1.0  INTRODUCTION  1  2.0  REVIEW AND BACKGROUND INFORMATION  6  2.1  A n a l y s i s o f Unbalanced Data  6  2.2  Pure V e r s u s Mixed Stands  19  2.2.1  Definition  19  2.2.2  Silvicultural  C o n s i d e r a t i o n s o f Pure  and Mixed Stands 2.2.3  20  Comparison o f Growth and Y i e l d o f Pure and Mixed Stands  2.3  F o r e s t I n v e n t o r y Zones  29  2.3.1  Definition  29  2.3.2  R e g i o n a l P r o d u c t i v i t y o f F o r e s t S t a n d s . . 31  2.3.3  R e g i o n a l i t y and B i o c l i m a t i c S t u d i e s i n Other Regions  2.4 3.0  25  Chapter Summary  Zones 36 39  METHODOLOGY  41  3.1  L i n e a r Model  41  3.2  Normal E q u a t i o n s  43  - viii  4.0  5.0  -  3.3  Imposing R e s t r i c t i o n s  47  3.4  Absorption Process  48  3.5  E s t i m a t i o n o f Constants  50  3.6  P a r t i t i o n i n g t h e T o t a l Sum o f Squares  56  3.7  L e a s t Squares Means, Variances, and H y p o t h e s i s Tests  58  3.8  Computer Program  62  3.9  Chapter Summary  65  DATA BASE  66  4.1  69  Chapter Summary  RESULTS AND DISCUSSIONS 5.1  72  Occurrence o f D o u g l a s - f i r - , Spruce-, and Lodgepole Pine-dominated F o r e s t Types i n B r i t i s h Columbia.  . 72  5.2  S i t e D e t e r i o r a t i o n and Pure Stands  . 76  5.3  Number o f T r e e s P e r Acre  79  5.4  R e l a t i v e Stand D e n s i t y  81  5.5  Average  Stand Age, Mean Annual H e i g h t , B a s a l Area,  and Volume Growth  5.6  83  5.5.1  Average  Stand Age  83  5.5.2  Mean Annual Height Growth  88  5.5.3  Mean Annual B a s a l Area Growth  92  5.5.4  Mean Annual Volume Growth  97  D i f f e r e n c e i n Growth and Y i e l d Between Coast and I n t e r i o r D o u g l a s - f i r Stands  97  - ix-  5.7  Comparison o f Volume Y i e l d by Species Types and F o r e s t Inventory  Zones  103  5.7.1  Douglas-fir  104  5.7.2  Spruce  119  5.7.3  Lodgepole P i n e  122  5.7.4  Summary o f Volume Y i e l d by Species Composition and Inventory  5.8  Composition  Influence o f Species  Zones  Composition Types on Volume  Yield  5.9  127  5.8.1  Douglas-fir  136  5.8.2  Spruce  136  5.8.3  Lodgepole P i n e  137  Y i e l d o f D o u g l a s - f i r and C o n i f e r Mixed Type Stands i n the I n t e r i o r  5.10  125  . .,  138  Y i e l d Table Construction  152  5.10.1  Douglas-fir  162  5.10.2  Spruce  164  5.10.3  Lodgepole P i n e  166  5.11  T e s t o f Homogeneity o f V a r i a n c e  167  5.12  Least  171  5.13  Chapter Summary  Squares A n a l y s i s  174  6.0  SUMMARY AND CONCLUSIONS  177  7.0  LITERATURE CITED  188  APPENDICES  196  1.  B.C. F o r e s t Inventory  2.  Computer Program  Zones  197 201  -  3.  X  -  L e a s t Squares E q u a t i o n s  212  3.1  Coast D o u g l a s - f i r  212  3.2  Interior Douglas-fir  213  3.3  Interior  215  3.4  I n t e r i o r Lodgepole  Spruce Pine  217  - xi -  LIST OF TABLES Table 2-1  2- 2  3- 1  3-2  3-3  3-4  3-5  3-6  3-7  3- 8  4- 1  Page Y i e l d s o f pure hemlock and hemlock-spruce stands (Eidman, 1952) .  admixed 27  C l a s s i f i c a t i o n o f f o r e s t r e g i o n s of B r i t i s h Columbia (Stanek, 1966.)  3.0  Western hemlock i n v e n t o r y d a t a c l a s s i f i e d by s p e c i e s types and i n v e n t o r y zones ( F . I . Z . )  45  The l e a s t squares equations western hemlock d a t a  46  f o r m u l a t e d from  the  The reduced s e t of l e a s t squares e q u a t i o n s f o r the western hemlock d a t a  51  M a t r i x i n v e r s e to the complete v a r i a n c e - c o v a r i a n c e m a t r i x f o r western hemlock d a t a  .53  E s t i m a t e d c o n s t a n t s f o r western hemlock mean annual growth d a t a  54  Complete s e t o f e s t i m a t e d c o n s t a n t s f o r western hemlock mean annual growth d a t a  35  A n a l y s i s of v a r i a n c e t a b l e f o r western hemlock mean annual growth data  59  Comparison o f the i n c i d e n c e m a t r i x between the program and BMDP g e n e r a l l i n e a r h y p o t h e s i s program  63  The number o f sample p l o t s by s p e c i e s f o r d a t a p r o v i d e d by B.C. F o r e s t S e r v i c e I n v e n t o r y D i v i s i o n  .  .  .68  4-2  Comparison o f s p e c i e s types and f o r e s t type groups  .  .  .70  5-1  Numbers o f sample p l o t s by s p e c i e s and f o r e s t s p e c i e s type  73  The frequency of sample p l o t s by f o r e s t f o r e s t i n v e n t o r y zones  75  5-2  5-3  5-4  types  Averages o f s i t e index by s p e c i e s types and i n v e n t o r y zones  and  forest  Averaged numbers of t r e e s per a c r e i n v a r i o u s s p e c i e s types and f o r e s t i n v e n t o r y zones  78  80  - xii-  0  5-5  5-6  R e l a t i v e stand d e n s i t y f o r v a r i o u s s p e c i e s and f o r e s t i n v e n t o r y zone combinations  type 82  Age, mean annual h e i g h t , b a s a l a r e a , and volume growth by s p e c i e s types and f o r e s t i n v e n t o r y zones . . .84  5-7  5-8  5-9  Mean h e i g h t o f dominant and codominant t r e e s by types and i n v e n t o r y zones  85  Mean b a s a l a r e a p e r a c r e o f D o u g l a s - f i r , spruce, and l o d g e p o l e p i n e by s p e c i e s types and i n v e n t o r y zones  86  Mean n e t volume o f D o u g l a s - f i r , spruce, and l o d g e p o l e p i n e by s p e c i e s types and i n v e n t o r y zones.  5-10  Comparison o f D o u g l a s - f i r stands and  . .87  grown on t h e Coast  i n the I n t e r i o r  102  5-11  Estimated  constants  f o r Coast  D o u g l a s - f i r volume y i e l d . 105  5-12  Estimated yield  constants  f o r I n t e r i o r D o u g l a s - f i r volume 106  5-13  A n a l y s i s o f v a r i a n c e f o r t h e Coast D o u g l a s - f i r net volume y i e l d by s p e c i e s types and i n v e n t o r y zones . . . 107  5-14  A n a l y s i s o f v a r i a n c e f o r t h e I n t e r i o r D o u g l a s - f i r net volume y i e l d by s p e c i e s types and i n v e n t o r y zones . . . 108  5-15  P o t e n t i a l y i e l d o f D o u g l a s - f i r a t age 100 i n B.C. F o r e s t Inventory Zones  109  Estimated constants volume y i e l d  110  5-16  5-17  5-18  5-19  5-20  f o r I n t e r i o r spruce net  A n a l y s i s o f v a r i a n c e f o r n e t volume y i e l d s o f I n t e r i o r spruce stands by s p e c i e s types and i n v e n t o r y zones . . P o t e n t i a l y i e l d o f I n t e r i o r spruce stands by f o r e s t i n v e n t o r y zones and types  I l l  a t age 100 112  E s t i m a t e d c o n s t a n t s f o r l o d g e p o l e p i n e net volume y i e l d by s p e c i e s types and i n v e n t o r y zones  113  A n a l y s i s o f v a r i a n c e f o r l o d g e p o l e p i n e n e t volume y i e l d by s p e c i e s types and i n v e n t o r y zones  114  - xiii  5-21  5-22  5-23  5-24  5-25  5-26  5-27  5-28  5-29  5-30  5-31  5-32  5-33  5-34  5-35  -  P o t e n t i a l y i e l d s of I n t e r i o r l o d g e p o l e p i n e a t age 100 by s p e c i e s types and f o r e s t i n v e n t o r y zones . .  115  A n a l y s i s of v a r i a n c e f o r net volume y i e l d of the Coast D o u g l a s - f i r stands a d j u s t e d f o r s i t e index and stand age  128  E s t i m a t e d c o n s t a n t s from volume y i e l d d a t a of Coast D o u g l a s - f i r stands  129  A n a l y s i s o f v a r i a n c e f o r n e t volume y i e l d o f the I n t e r i o r D o u g l a s - f i r stands a d j u s t e d f o r s i t e index and stand age  130  E s t i m a t e d c o n s t a n t s f o r n e t volume y i e l d s of I n t e r i o r D o u g l a s - f i r stands  131  A n a l y s i s of v a r i a n c e f o r n e t volume y i e l d s of the I n t e r i o r spruce stands a d j u s t e d f o r s i t e index and stand age  132  E s t i m a t e d c o n s t a n t s from volume d a t a of the I n t e r i o r spruce stands .  133  A n a l y s i s o f v a r i a n c e f o r net volume y i e l d s of I n t e r i o r l o d g e p o l e p i n e stands a d j u s t e d f o r s i t e index and stand age  134  E s t i m a t e d c o n s t a n t s f o r net volume y i e l d s o f I n t e r i o r l o d g e p o l e p i n e stands  135  Comparison o f h e i g h t , number o f t r e e s , b a s a l a r e a , and volume per a c r e f o r pure D o u g l a s - f i r and D o u g l a s - f i r c o n i f e r mixture stands grown I n t e r i o r on s i t e , c l a s s I  139  Comparison of h e i g h t , number o f t r e e s , b a s a l a r e a , and volume p e r a c r e f o r pure D o u g l a s - f i r and D o u g l a s - f i r c o n i f e r m i x t u r e stands grown on Interior site class II  140  Comparison of h e i g h t , number of t r e e s , b a s a l a r e a , and volume per a c r e f o r pure D o u g l a s - f i r and D o u g l a s - f i r c o n i f e r m i x t u r e stands grown on Interior site class III  141  A n a l y s i s o f v a r i a n c e f o r the net volume y i e l d of Coast D o u g l a s - f i r stands  154  A n a l y s i s of v a r i a n c e f o r n e t volume y i e l d s of I n t e r i o r D o u g l a s - f i r stands  155  A n a l y s i s of v a r i a n c e f o r net volume y i e l d d a t a of I n t e r i o r spruce stands  156  - xiv -  5-36  5-37  5-38  5-39  5-40  5-41  5-42  A n a l y s i s of v a r i a n c e f o r net volume y i e l d I n t e r i o r l o d g e p o l e p i n e stands  158  Comparison of F - v a l u e s i n I n t e r i o r D o u g l a s - f i r yield analysis  159  Comparison of F-values i n I n t e r i o r spruce analysis  160  yield  Comparison of F - v a l u e s i n I n t e r i o r l o d g e p o l e p i n e yield analysis  161  Y i e l d f u n c t i o n s f o r D o u g l a s - f i r , spruce, lodgepole pine  165  Standard  and  d e v i a t i o n s of D o u g l a s - f i r volume y i e l d f o r e s t i n v e n t o r y zones . . . .  Standard d e v i a t i o n s of spruce volume y i e l d by s p e c i e s composition types and  5-44  157  Comparison of F - v a l u e s i n Coast D o u g l a s - f i r yield analysis  d a t a by s p e c i e s types and 5-43  of  168  data  i n v e n t o r y zones . . . .  Standard d e v i a t i o n s o f l o d g e p o l e p i n e volume y i e l d d a t a by s p e c i e s c o m p o s i t i o n types and i n v e n t o r y zones .  169  .170  -  XV  -  LIST OF FIGURES Figure  5-1  5-2  5-3  5-4  5-5  5-6  5-7  5-8  5-9  5-10  Page  Comparison o f the mean h e i g h t increments o f dominant and codominant t r e e s o f D o u g l a s ^ f i r stands by types and zones .  89  Comparison o f the mean annual h e i g h t increments o f dominant and codominant t r e e s by types and zones o f I n t e r i o r spruce  90  Comparison o f t h e mean annual h e i g h t increments o f dominant and codominant t r e e s o f l o d g e p o l e p i n e i n I n t e r i o r zones  91  Comparison o f t h e mean b a s a l a r e a increments o f D o u g l a s - f i r stands by types and zones  93  Comparison o f the mean b a s a l a r e a increment of spruce stands by types and f o r e s t i n v e n t o r y zones  94  Comparison of the mean annual b a s a l a r e a increments of l o d g e p o l e p i n e stands by types and i n v e n t o r y zones.  . .95  Comparison o f t h e mean volume increments o f D o u g l a s - f i r by types and zones  98  Comparison o f t h e mean annual volume increments o f spruce by types and zones  99  Comparison o f the mean annual volume increments of l o d g e p o l e p i n e by types and zones •  100  P o t e n t i a l y i e l d o f D o u g l a s - f i r a t age 100 by types and i n v e n t o r y zones  117  5-11  P o t e n t i a l y i e l d s o f I n t e r i o r spruce a t age 100 by s p e c i e s types and i n v e n t o r y zones 120  5-12  P o t e n t i a l y i e l d s o f I n t e r i o r l o d g e p o l e p i n e stands at age 100  123  5-13  H e i g h t growth o f I n t e r i o r D o u g l a s - f i r on s i t e c l a s s I . . 142  5-14  Height growth o f I n t e r i o r D o u g l a s - f i r on s i t e c l a s s I I . . 143  5-15  H e i g h t growth o f I n t e r i o r D o u g l a s - f i r on s i t e c l a s s I I I . .144  - xvi -  5-16  B a s a l a r e a growth of I n t e r i o r D o u g l a s - f i r on s i t e c l a s s I . .'.146  5-17  B a s a l a r e a growth of I n t e r i o r D o u g l a s - f i r on s i t e c l a s s II.".;. 147  5-18  B a s a l a r e a growth o f I n t e r i o r D o u g l a s - f i r on s i t e c l a s s I I I . .148  5-19  Volume growth of I n t e r i o r D o u g l a s - f i r on s i t e c l a s s I  5-20  Volume growth o f I n t e r i o r D o u g l a s - f i r on s i t e c l a s s I I . . .  5-21  Volume growth o f I n t e r i o r D o u g l a s - f i r on s i t e C l a s s I I I . . . . 151  .149 . .150  - xvii -  LIST OF MAPS  Map 1  Page Forest Inventory Zones i n B r i t i s h Columbia  32  - xviii  -  ACKNOWLEDGEMENT S  Without  the e f f o r t , encouragement, and guidance  p e o p l e , t h i s t h e s i s would not have been p o s s i b l e . my  s i n c e r e thanks  to my  of s e v e r a l  I wish  to extend  s u p e r v i s o r , Dr. A. Kozak ( F o r e s t r y ) , f o r  s h a r i n g h i s time, wisdom, and e x p e r i e n c e i n h i s r o l e as an academic advisor.  The moral support he gave me  guidance, u n d e r s t a n d i n g , p a t i e n c e and to  make my  throughout  the s t u d y , h i s  the a d d i t i o n a l e f f o r t he made  s t u d i e s a warm and rewarding  e x p e r i e n c e are h e a r t i l y  acknowledged. I am i n d e b t e d to Dr. J.H.G. Smith to  undertake  who  suggested  the study, p r o v i d e d v a l u a b l e a d v i c e i n the c o u r s e o f d a t a  a n a l y s i s and reviewed  c o n s t r u c t i v e l y and c r i t i c a l l y  S p e c i a l thanks Dr. S. W.  (Forestry)  are extended  to my  Nash (Mathematics), Dr. D.D.  the  manuscript.  Committee Members:  Munro ( F o r e s t r y ) , and Dr.  J.P.  Demaerschalk ( F o r e s t r y ) f o r t h e i r i n v a l u a b l e s u g g e s t i o n s and a d v i c e . E d i t o r i a l a s s i s t a n c e p r o v i d e d by, and some e q u a t i o n s d e r i v e d from Dr. Nash a r e c o r d i a l l y acknowledged. Nokoe, a former of  f e l l o w graduate  G r a t e f u l thanks  go to Dr.  student, f o r h i s help i n t r a n s c r i p t  the o r i g i n a l d a t a . I wish a l s o to thank the B.C.  D i v i s i o n and  the B.C.  F o r e s t S e r v i c e Inventory  F o r e s t S e r v i c e P r o d u c t i v i t y Committee f o r  p r o v i d i n g the data f o r t h i s  Sagary  study.  - xix -  F i n a n c i a l a s s i s t a n c e was g i v e n i n t h e form o f F a c u l t y of F o r e s t r y Teaching/Research G r a n t s , t h e McPhee F o r e s t  Fellowship,  and  o f B.C.  t h e Youth Summer Employment Program o f the P r o v i n c e  I am g r a t e f u l t o a l l those who made these p o s s i b l e . Thanks a r e due t o Dr. J.W. W i l s o n ( F o r e s t r y ) who supported my t r a n s f e r from Wood Science  to Biometrics.  I owe my deepest g r a t i t u d e  to my f a m i l y , my w i f e Judy, my c h i l d r e n John and M a r j o r i e , who have undergone many s a c r i f i c e s t o make i t a l l p o s s i b l e .  - 1 -  1.0  INTRODUCTION  Forest  i n v e n t o r i e s , one  manager to d e s c r i b e a f o r e s t and out  to a s s e s s the q u a n t i t y and  of the b a s i c t o o l s of the f o r e s t c o n t r o l managed stands, are c a r r i e d  q u a l i t y of f o r e s t t r e e s and many  c h a r a c t e r i s t i c s of the l a n d a r e a upon which t r e e s grow. without s a y i n g  that well-designed  i n v e n t o r i e s always c o n t a i n  accumulation of m a t e r i a l p r o v i d i n g a s u i t a b l e b a s i s f o r specialized studies. of f o r e s t i n v e n t o r y  By a p p r o p r i a t e d a t a one  can  I t goes  analyses  and  an  various  correct interpretations  g a i n i n s i d e knowledge of  stand  characteristics. H i s t o r i c a l l y , d a t a c o l l e c t e d f o r growth and from permanent or temporary p l o t s were analyzed methods b e f o r e  e a r l y t h i s century.  methods, r e g r e s s i o n a n a l y s i s has g r a p h i c a l method. an i n d i s p e n s a b l e  by  yield  graphical  With the advances of  gradually replaced  Forest mensurationists t e c h n i q u e i n growth and  studies  the  statistical traditional  have found r e g r e s s i o n y i e l d studies.  Indeed, i t i s  a p o w e r f u l t o o l i n e x p l o i t i n g d a t a i f f a c t o r s of i n t e r e s t are i n n a t u r e e.g.  volume, b a s a l a r e a , h e i g h t ,  and  age.  or  analyzed  by  quantitative  If factors  i n v o l v e d are q u a l i t a t i v e i n n a t u r e , such as f o r e s t types, zones, the d a t a are c o n v e n t i o n a l l y  analysis  inventory  the a n a l y s i s of  variance  covariance. However, comparing d a t a from f o r e s t i n v e n t o r y  from w e l l - d e s i g n e d  surveys to those  experiments, the former are f r e q u e n t l y n o t o r i o u s  t h e i r i r r e g u l a r i t y : the numbers of sample p l o t s surveyed o f t e n  for  differ  - 2 -  i n main c l a s s e s as w e l l as i n s u b c l a s s e s . v a r i a n c e methods, i n terms of w e l l - d e s i g n e d a p p l i c a b l e o n l y to b a l a n c e d p a t t e r n s of L a t i n square  data  experiments,  ( e x c e p t i o n s are the  d e s i g n s , balanced  and d e r i v a t i v e s t h e r e o f ) .  T r a d i t i o n a l a n a l y s i s of  incomplete  are g e n e r a l l y  specified block designs,  Hence f o r i r r e g u l a r unbalanced  forest  i n v e n t o r y d a t a , a n a l y s i s of v a r i a n c e i n i t s t r a d i t i o n a l framework i s inapplicable.  T h e r e f o r e , the f i r s t  s e a r c h f o r and develop,  o b j e c t i v e of t h i s study was  i f necessary,  to  a methodology of a n a l y z i n g and  t e s t i n g d a t a c o l l e c t e d from f o r e s t i n v e n t o r y surveys. The  second o b j e c t i v e of t h i s t h e s i s was  to t e s t the  t h a t no d i f f e r e n c e i n net volume y i e l d e x i s t s among pure, mixed, and  conifer-hardwood  mixed type stands.  hypothesis  conifer  Advantages and  dis-  advantages of pure and mixed stands have been the s u b j e c t of many c o n t r o v e r s i a l arguments s i n c e the l a s t c e n t u r y .  The  problem of  mono- and m u l t i - c u l t u r e i s not o n l y of academic i n t e r e s t but a l s o of p r a c t i c a l importance i n B r i t i s h Columbia.  Y i e l d s of pure and mixed  f o r e s t types a r e o f t e n compared on a v e r y l i m i t e d number of p l o t s . In t h i s study,  the aforementioned  set of data c o l l e c t e d a c r o s s B.C.,  hypotheses w i l l be t e s t e d by a l a r g e which i s e s s e n t i a l to draw a  g e n e r a l i z e d c o n c l u s i o n on the c o n t r o v e r s i a l problem. The  t h i r d o b j e c t i v e was  s i g n i f i c a n c e of any than through  to determine the  statistical  i n f l u e n c e of i n v e n t o r y zones on stand y i e l d s  d i f f e r e n c e i n average s i t e and  Columbia, f o r e s t e d a r e a  stand d e n s i t y .  In  other  British  ( P u b l i c S u s t a i n e d Y i e l d U n i t s and T r e e Farm  L i c e n c e s ) has been grouped i n t o twelve  i n v e n t o r y zones as a b a s i s f o r  - 3 -  planning  growth and y i e l d and  volume and,age curves f o r e s t types and  (VAC)  loss factor studies.  have been c o n s t r u c t e d  Although i n B.C.  determining  the y i e l d of a f o r e s t type d i f f e r s from  zone to the other has not y e t been t e s t e d s t a t i s t i c a l l y . of the z o n a l growth changes i s n e c e s s a r y example, i t may  for various  employed f o r p r e d i c t i n g volume y i e l d s and  annual a l l o w a b l e c u t , how  zonal  Knowledge  f o r v a r i o u s reasons.  For  be h e l p f u l f o r managing f o r e s t e r s i n t e r e s t e d i n  a s s e s s i n g the p r o f i t a b i l i t y of f o r e s t c u l t i v a t i o n on d i f f e r e n t and  i n various climatic  sites  regions.  In the f o l l o w i n g c h a p t e r  the background i n f o r m a t i o n on  a n a l y s i s methods f o r unbalanced d a t a , the s i l v i c u l t u r a l and aspects  one  of pure and mixed type stands,  and  the  mensurational  i n v e n t o r y zones a r e c o n c i s e l y  reviewed. The  b a s i c problem t a c k l e d i s to develop a s t a t i s t i c a l l y  method f o r a n a l y z i n g i n v e n t o r y p l o t s . i s t h e i r l a r g e number. i n c l a s s e s and  The  valid  s t r e n g t h of i n v e n t o r y p l o t s  T h e i r weakness, however, i s the l a c k of  l a c k of r e p r e s e n t a t i o n i n some s u b c l a s s e s .  The  balance strength  has been g r a d u a l l y r e c o g n i z e d by r e s e a r c h f o r e s t e r s as i l l u s t r a t e d an i n c r e a s i n g number of s t u d i e s based on d a t a from i n v e n t o r y The  s t a t i s t i c a l methods used i n those  A f t e r a long process  of t r i a l and  Therefore,  e r r o r , i t was  found t h a t the  Chapter 3 d e s c r i b e s the procedures of the  squares a n a l y s i s and  plots.  s t u d i e s are mainly r e g r e s s i o n .  squares a n a l y s i s i s a procedure which s u i t s to the p r e s e n t best.  by  least  objectives least  the development of a computing program which  handles problems w i t h empty c e l l s i n s u b c l a s s e s .  - 4 -  Sources i n Chapter  4.  o f the i n v e n t o r y d a t a used  i n the study a r e b r i e f e d  I n the f o l l o w i n g c h a p t e r s , t h r e e major B.C. commercial  s p e c i e s , 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 ) , spruce  ^  ( P i c e a s p p . ) , and l o d g e p o l e p i n e (Pinus c o n t o r t a Dougl.) were chosen and a n a l y z e d t o i l l u s t r a t e the a p p l i c a t i o n o f the method developed i n Chapter  3 i n c o n n e c t i o n w i t h the s i l v i c u l t u r a l and m e n s u r a t i o n a l  o b j e c t i v e s s e t f o r t h above.  S p e c i e s other than the t h r e e c o u l d have  been i n c l u d e d ; however, time and space do n o t a l l o w f o r e x t e n s i v e study on a l l s p e c i e s p r e s e n t l y growing i n B.C. p r e s e n t e d i n Chapter composition and  R e s u l t s and d i s c u s s i o n s a r e  5 where means o f stand c h a r a c t e r i s t i c s i n s p e c i e s  type and i n v e n t o r y zone combinations  then the l e a s t squares method developed  are f i r s t l y  i n Chapter  3 i s applied to  the i n v e n t o r y d a t a t o a s c e r t a i n the e f f e c t s o f s p e c i e s types and f o r e s t i n v e n t o r y zones.  F i n a l l y a l l stand  composition  parameters,  q u a l i t a t i v e as w e l l as q u a n t i t a t i v e , a r e i n c l u d e d i n y i e l d to a s s e s s t h e i r r e l a t i v e importance Chapter  i n yield  examined  table  analyses  table construction.  6 summarizes t h e r e s u l t s and c o n c l u s i o n s . A d m i t t e d l y , t h e o n l y way i n which one can o b t a i n d e f i n i t i v e  r e s u l t s t o s a t i s f y t h e l a s t two o b j e c t i v e s s e t f o r t h above i s t o e s t a b l i s h p l a n t a t i o n s i n which s p e c i e s a r e a p p r o p r i a t e l y t e s t e d over a range o f s p a c i n g and p l a n t i n g c o n f i g u r a t i o n s . We a r e f o r c e d i n t o s t u d i e s such as t h i s t h e s i s because d a t a a r e n o t a v a i l a b l e but many s p e c u l a t i o n s have been made and t h e r e has been much p u b l i c concern about the problem o f monocultures.  I t i s b e l i e v e d t h a t the a n a l y s e s o f i n v e n t o r y d a t a w i l l  - 5 -  shed some light on the issue in the absence of direct experimental data.  - 6 -  2.0  REVIEW AND BACKGROUND INFORMATION  2.1  A n a l y s i s of Unbalanced Data  F o r e s t i n v e n t o r y data c o n t a i n much i n f o r m a t i o n f o r v a r i o u s specialized studies. and  But, when the data a r e c l a s s i f i e d  subclasses designated  plots  f o r a s p e c i f i e d study,  into classes  the numbers o f sample  ( o b s e r v a t i o n s ) i n main c l a s s e s and s u b c l a s s e s a r e o f t e n found to  differ.  I n s t a t i s t i c a l a n a l y s i s , two d a t a s t r u c t u r e s a r e g e n e r a l l y  recognized:  balanced  (complete) and unbalanced  (incomplete).  Data  where these numbers a r e t h e same a r e known as equal-numbers d a t a , o r more f r e q u e n t l y , as balanced to  data.  the case where the numbers i n v a r i o u s s u b c l a s s e s a r e e q u a l i s simple,  andihas been v e r y f u l l y developed. of  The s t a t i s t i c a l procedure a p p r o p r i a t e  I n c o n t r a s t , data w i t h unequal numbers  o b s e r v a t i o n s i n s u b c l a s s e s , i n c l u d i n g perhaps some t h a t c o n t a i n no  o b s e r v a t i o n s a t a l l (empty s u b c l a s s e s , o r empty c e l l s ) a r e c a l l e d  unequal-  numbers d a t a , o r u s u a l l y , unbalanced d a t a , o r sometimes "messy d a t a " ( S e a r l e , 1971). The  e v i l of l a c k o f b a l a n c e  i s most f r e q u e n t l y encountered  with  data r o u t i n e l y c o l l e c t e d as p a r t o f c u r r e n t l y o p e r a t i v e i n f o r m a t i o n systems such as, f o r example, w i t h those p r o v i d i n g " o f f i c i a l based on censuses and s u r v e y s .  However, l a c k of b a l a n c e  i n d a t a c o l l e c t i n g a c t i v i t i e s which were designed r e c o r d s as i n b a l a n c e d occurrence  experiments  of incomplete  statistics"  a l s o can a r i s e  to g i v e complete  ( J e f f e r s , 1965).  So f r e q u e n t i s the  d a t a t h a t i t has become one of the more  - 7 -  important problems i n s t a t i s t i c a l a n a l y s i s . o c c u r r e n c e o f the incomplete d a t a problem may  While the  widespread  be regarded as a  "necessary e v i l " r e a l i s t i c a l l y a s s o c i a t e d with data c o l l e c t i o n ,  the  l i t e r a t u r e p r o v i d e s ample e v i d e n c e t h a t s t a t i s t i c i a n s have expended c o n s i d e r a b l e e f f o r t s t o "make a v i r t u e o f the v i c e " Hocking,  (Hartley  and  1971). Brandt  (1933) was  the f i r s t  s t a t i s t i c i a n to treat  the  a n a l y s i s of v a r i a n c e i n a 2 x S t a b l e with d i s p r o p o r t i o n a t e frequencies. Yates  (1934) c o n s i d e r e d  the more g e n e r a l case of a p x q t a b l e ,  and  suggested  c e r t a i n c o r r e c t i o n s which appear t o be n e c e s s a r y i n Brandt's  methods.  He proposed  unbalanced  data:  two procedures  f o r analyzing multiple c l a s s i f i e d  (1) a method of f i t t i n g c o n s t a n t s f o r the cases i n  which i n t e r a c t i o n s do not e x i s t ; and  (2) a method of weighted  squares  of means f o r the cases w i t h i n t e r a c t i o n s p r e s e n t .  (1)  Method o f f i t t i n g  constants  In the g e n e r a l p x q t a b l e the o r d i n a r y procedure o f the method o f l e a s t squares g i v e s the f o l l o w i n g e q u a t i o n s f o r m, the e s t i m a t e s o f  y , a.,  (3 . .  a^, b^  - 8 -  Leading Term m  Nm +N  a  +N  a  x* x  a  l  a  N  l .  m  +  N^m  2  l .  N  +  +N  z• z  l  a  +  + N ^  b  l  N  ..I  m +  b  2  N  . 2  m  n  +  n  l l l a  1 2  a  +  +  n  l  +  21 2 a  n  2 2  b  +N  .xx  •'•  +  a  2  +  b a  + . ..  y•  n  l l l  +  n  12 2 -''  n  21 l  +  n  22 2 '• '  b  b  N  . l  b  +  =SS  Z'Z  b  +  b  +  l  =  S  S  =  S  S  =  +  N  .2 2 b  The r u l e f o r f o r m a t i o n i s as f o l l o w s .  S S  y l .  y2  y.l  = S S  y.2  Write N equations f o r  the N observed v a l u e s o f the form  Y. = y + a. + 13k I  where ^^y_ i e  l e a d i n g term,  s  a  n  8.3  + e. ljk  e r r o r term.  (2-1)  To form the e q u a t i o n i n which m i s the  sum t h e squares o f t h e c o e f f i c i e n t s  o f y i n the N e q u a t i o n s  and the p r o d u c t s o f these c o e f f i c i e n t s w i t h the c o r r e s p o n d i n g of  a^, (X^J  ...8^5  ••• i - t u r n .  i s always u n i t y so the f i r s t in  the N^  elsewhere,  n  coefficients  In t h i s case the c o e f f i c i e n t f o r y  sum i s N.  The c o e f f i c i e n t of  i s unity  e q u a t i o n s f o r the o b s e r v a t i o n s i n a l l a^ c l a s s e s and zero so t h a t the sum o f the p r o d u c t s i s N^ , and so on.  These  - 9 -  sums g i v e t h e c o e f f i c i e n t s o f m, a^, a^, first  equation.  ..., b^, b^, ...  The SS i s t h e sum o f p r o d u c t s of each y..  i n the observed  v a l u e w i t h t h e c o e f f i c i e n t o f y i n the c o r r e s p o n d i n g e q u a t i o n The other e q u a t i o n s a r e formed i n the same manner.  (2-1).  The whole s e t of  e q u a t i o n s g i v e s t h e v a l u e s o f y, t h e a's and the B's which make t h e sum o f the squares o f t h e e r r o r terms ^y e  a i  minimum.  Only p + q - 1 o f the above p + q + 1 equations a r e independent, the e q u a t i o n w i t h l e a d i n g term m b e i n g the same as the sum o f a l l the e q u a t i o n s w i t h an 'a' as l e a d i n g terms, and o f a l l the equations a,  with  'b' as l e a d i n g term. Methodologies  t o s o l v e the l i n e a r e q u a t i o n s a r e many.  After  the v a l u e s o f t h e a's, b's and m have been o b t a i n e d , the r e d u c t i o n i n the sum o f squares due t o f i t t i n g  the c o n s t a n t s can be c a l c u l a t e d as the  sum of the p r o d u c t s of each c o n s t a n t w i t h the n u m e r i c a l term of t h e e q u a t i o n of which i t i s t h e l e a d i n g term. Yates  (1934) p o i n t e d out t h a t t h e g e n e r a l r u l e a p p l i c a b l e t o  any groups o f f i t t e d accounted  c o n s t a n t s i s t o f i n d t h e p a r t o f t h e sum o f squares  f o r by f i t t i n g the c o n s t a n t s and deduct  the sum of squares accounted  from i t the p a r t of  f o r by f i t t i n g a l l t h e c o n s t a n t s  except  those to be t e s t e d .  (2)  Method of weighted  squares o f mean  F o r a two-way a n a l y s i s o f v a r i a n c e model, when i n t e r a c t i o n i s  - 10 -  p r e s e n t , Y a t e s (1934) d e s c r i b e d the method o f weighted squares of mean which f u r n i s h e d u n b i a s e d e s t i m a t e s of the main e f f e c t s .  Assume the model  y .  ., = y + a.i + B. + (aB) x.j . J  + e.  xjk  3  2 j = l , 2 , . . . s ; k=l,2,.. .n. .; and e. ., »>_/NID(0,O' ) .  i=l,2,...r;  xj  y'.  x. .  and y  (2-2)  xjk  .  1  .j•  as the unweighted row and column means,  y.. = £ —^x.. s  y' .  and  Define  i j k  y'  3  y.. . = E .j. . r 1  respectively,  "  1  i  On the b a s i s o f t h e assumption of v a r i a n c e homogeneity o f the c e l l s , v a r i a n c e o f y!  x..  is  ii ) = Var(Z - ^ ) j s Y  Var(y!^  the  2  _ - -  1  •2  . n. .  s  J  a2  xj  1 = \ s  S Var(y j  )  2  - 2 _  2  s  s  1 . n. . j  xj  (2-3)  N. x  v, where  1 — N.  _ =  x  1 —z 2 s  y  1 h . n.. x  xj  These weights 1SL w i l l be used i n c a l c u l a t i n g the A main sum of squares.  effect  - 11 -  The  sums o f squares f o r A i s d e f i n e d as  SS  = E  A  (y^  - C)  (2-4)  2  j . N. y' .  Z  where  C =  Z- N. x  1  1 2 I t can be shown t h a t — - r EN.(y! -C) has e x p e c t a t i o n r-1 . x •'x.. x 2 , 0  1 _ r ^ l i i M  E  a  ,2 '  where E N. . 1 x ^w. a  a  l  =  i"  a  . X X  The  sums o f squares f o r t h e B e f f e c t  SS  =  "  where  — J  1 = — r  analogously;  E N (y' -D) , 3 •3• 3 2  E  1  i s defined  1 Z — j xj  j and  N J  y ' ' 3  D =  A l s o , under t h e assumed model,  j  1 — r S  J-  j  .  J  EN. I  (y' .  • "1 •  2 -D)  -  has  12  -  expectation E N. a2  +  2 N.  s-1  •  B' 2 ,  3  where 8'.  3  = 6.  3  3  -  J  ^ v  6.  3  S  3  .T N  3  Both main e f f e c t mean squares a r e t e s t e d by comparing them a g a i n s t the e r r o r ( w i t h i n ) mean square.  F o r c a l c u l a t i o n purposes  the  f o l l o w i n g i d e n t i t i e s are u s e f u l :  a E N.(y! _ 1  - C)  m  = E N ( y j / x  2  .2  y  N.y-  ^  "  (2-5)  . 1  and  EN.  (y'. i . j .  .2  - D)  . „  =  x2  EN.(y' ) . 1 -3-  3  -  (E N.y'. ) J j -J'  2  .  J  (2-6)  EN.  3  , 3  F o l l o w i n g Y a t e s ' p u b l i c a t i o n on the a n a l y s i s of v a r i a n c e for  unequal f r e q u e n c i e s i n s u b c l a s s e s , Snedecor and  (1941),  Cochran  (1943),  Rao  (1946),  and Henderson ( 1 9 5 3 ) p r e s e n t e d unbalanced c l a s s i f i c a t i o n s . Hazel  1957),  (1946),  Rao  (1946),  Snedecor  (1956),  Cox  (1935),  Stevens  (1948),  a n a l y s i s of v a r i a n c e procedures  Day  and F i s h e r ( 1 9 3 7 ) , W i l k s  Henderson  (1953),  Das  (1953),  Nair  for  (1938),  Federer  (1955,  and H a r t l e y ( 1 9 6 7 ) , d i s c u s s e d c o v a r i a n c e a n a l y s i s f o r unbalanced  classifications.  Bartlett  (1936, 1937),  ( 1 9 5 5 ) and Outhwarte and Ruther  Quenouille  (1948),  Federer  ( 1 9 5 5 ) , among o t h e r s , have d i s c u s s e d  - 13 -  the use of a dummy c o v a r i a b l e t o remove the e f f e c t in particular  of d i s p r o p o r t i o n  unbalanced c l a s s i f i c a t i o n s .  G o s s l e e and Lucas  (1965) i n v e s t i g a t e d  the analysis of  v a r i a n c e o f d i s p r o p o r t i o n a t e d a t a when i n t e r a c t i o n According to the authors, the analysis  o f v a r i a n c e of d i s p r o p o r t i o n a t e  d a t a can be computed by s e v e r a l methods which f a l l groupings, namely, a d d i t i v e  i s present.  i n t o two major  sums o f squares method and l e a s t  squares  methods. A d d i t i v e sums o f squares methods produce sums o f squares for effects variation  and i n t e r a c t i o n s  t h a t add t o the sum o f squares r e p r e s e n t i n g  among the c e l l means.  But each sum o f squares does n o t , i n  g e n e r a l , f o l l o w a c h i - s q u a r e d i s t r i b u t i o n under t h e n u l l h y p o t h e s i s n o r a n o n c e n t r a l c h i - s q u a r e d i s t r i b u t i o n under the n u l l h y p o t h e s i s . the  Thus,  r a t i o s o f mean squares used t o t e s t hypotheses do not, i n g e n e r a l ,  f o l l o w the F d i s t r i b u t i o n . L e a s t squares methods d e f i n e t e s t s  o f hypotheses which  follow  an F d i s t r i b u t i o n under the n u l l h y p o t h e s i s , and thus have a c t u a l of  significance  equal t o t h e i r normal l e v e l s .  A l s o each t e s t  f o l l o w s a n o n c e n t r a l F d i s t r i b u t i o n under the a l t e r n a t i v e so t h a t t h e power o f t h e t e s t can be o b t a i n e d r e a d i l y .  levels  statistic  hypothesis  However, t h e  computed sums o f squares a r e g e n e r a l l y n o t a d d i t i v e . Examples o f l e a s t  squares methods a r e the method o f f i t t i n g  c o n s t a n t s (Yates, 1934), the method o f weighted squares o f means (Yates, 1934;  Snedecor and Cox, 1935), and the m o d i f i e d method o f  weighted squares o f means (Kramer,  1955).  Examples o f the a d d i t i v e  - 14 -  sums o f squares methods a r e t h e method o f unweighted means (Yates, 1934; Snedecor and Cox, 1935) and t h e method of expected s u b c l a s s e s numbers (Snedecor, 1934). When i n t e r a c t i o n e x i s t s i n d i s p r o p o r t i o n a t e d a t a t h e sums of squares c a l c u l a t e d t o t e s t main e f f e c t depend on the parameters i n the model. Thus, when i n t e r a c t i o n i s assumed t o e x i s t a method should be chosen which uses a p p r o p r i a t e r e s t r i c t i o n s even though i t may not be the s i m p l e s t  o r the most e f f i c i e n t method ( G o s s l e e and Lucas, 1965).  In t h e absence o f i n t e r a c t i o n s a method o f a n a l y s i s can be chosen on the b a s i s o f i t s e f f i c i e n c y a l o n e (Finney, 1948). Bancroft  (1968) t r e a t e d t h e a n a l y s i s o f v a r i a n c e and c o v a r i a n c e  f o r unequal s u b c l a s s f r e q u e n c i e s i n g r e a t d e t a i l .  He examined  methods and approximate methods f o r two-way and three-way  exact  classifications,  and extended the exact and approximate methods t o n-way c l a s s i f i c a t i o n w i t h unequal and d i s p r o p o r t i o n a t e s u b c l a s s numbers. Computational p r o c e d u r e s f o r unbalanced d i s p r o p o r t i o n a t e d a t a a r e more c o m p l i c a t e d than f o r t h e b a l a n c e d d a t a , so t h a t p r i o r t o the p r e s e n t e r a o f computers, approximate methods such as unweighted means were g e n e r a l l y p r e f e r r e d t o exact l e a s t squares methods.  With  the appearance o f high-speed e l e c t r o n i c computers, t h e a n a l y s e s o f d a t a w i t h unequal numbers o f o b s e r v a t i o n have been f a c i l i t a t e d . l e a s t squares methods have been g e n e r a l l y f a v o r e d because o f the advantages p r e v i o u s l y mentioned as w e l l as s i m p l i c i t y i n m a t r i x expression.  The  - 15  The of v a r i a n c e  -  a p p l i c a t i o n of l e a s t squares t h e o r y to the  has  analysis  l o n g been known to s t a t i s t i c i a n s under the name  " l i n e a r s t a t i s t i c a l models" or " g e n e r a l l i n e a r h y p o t h e s i s " . r e s e a r c h e r s i n f o r e s t r y are applies  f a m i l i a r with regression  Most  a n a l y s i s which  the l e a s t squares p r i n c i p l e to o b t a i n unbiased e s t i m a t e s of  parameters i n q u e s t i o n .  In r e g r e s s i o n  analysis  the  variables  concerned are p r i m a r i l y c o n t i n u o u s or q u a n t i t a t i v e v a r i a b l e s . l e a s t squares t h e o r y a p p l i e s e q u a l l y w e l l  The  to " c o u n t e r " or q u a l i t a t i v e  v a r i a b l e s such as the a n a l y s i s of v a r i a n c e .  In f a c t , under the  normal  d i s t r i b u t i o n assumption, the r e s u l t from maximum l i k e l i h o o d method i s i d e n t i c a l t o t h a t from the l e a s t squares methods. In d e f i n i n g the a n a l y s i s of v a r i a n c e , and  the a n a l y s i s of c o v a r i a n c e , S c h e f f e  variance  regression  analysis  (1959) s a i d the a n a l y s i s  of  i s a body of s t a t i s t i c a l methods of a n a l y s i s measurements  assumed to be  Y  i  of the  =  X  l i  3  l  structure,  +  X  2i 2 3  •••  +  where the c o e f f i c i e n t s a n a l y s i s of v a r i a n c e  the  a  r  ^j-j^  +  X  e p  l  p  +  integers  e  a  r  e  t  n  e  e  i (i=l>2,...,n)  u s u a l l y 0 or 1.  (2-7)  In  the  v a l u e s of " c o u n t e r " v a r i a b l e s  or " i n d i c a t o r " v a r i a b l e s which r e f e r to the presence or absence of effect X..  3  j  i n the c o n d i t i o n s  i s the number of times 8.  i s u s u a l l y 0 or 1.  I f the  under which the o b s e r v a t i o n s are o c c u r s i n the i - t h o b s e r v a t i o n ,  {X..}  a r e v a l u e s taken on i n the  the  taken; and  this  observations  - 16  -  not by c o u n t e r v a r i a b l e but by a continuous v a r i a b l e , we have a case of r e g r e s s i o n a n a l y s i s . k i n d s , we  have an a n a l y s i s of The  i s well-supported K e n d a l l and Searle  I f t h e r e are some {X  l e a s t squares  i n t e r v a l e s t i m a t i o n and  } of b o t h  G r a y b i l l , 1961;  (1971) began w i t h a simple  theory,  t e s t s of hypotheses,  by r i g o r o u s mathematical theory  S t u a r t , 1966;  we  covariance.  a n a l y s i s of l i n e a r models by  i n c l u d i n g p o i n t and  say  Rao,  (Scheff£,  1965;  explanation  1959;  S e a r l e , 1971).  of r e g r e s s i o n  and  proceeded to m u l t i p l e r e g r e s s i o n , t o g i v e a u n i f i e d treatment f o r t e s t i n g a general  l i n e a r hypothesis.  He  i n t r o d u c e d models not of  rank by d i s c u s s i n g r e g r e s s i o n on dummy (0,1) equivalence  t o l i n e a r models.  He  v a r i a b l e s and  then t r e a t e d the  full  showing i t s  non-full-rank  model i n g r e a t d e t a i l , u t i l i z i n g g e n e r a l i z e d i n v e r s e m a t r i c e s  and  g i v i n g a u n i f i e d procedure f o r e v a l u a t i n g any  hypothesis.  testable linear  Three methods to compute the a n a l y s i s of v a r i a n c e  from view-  p o i n t s o f m u l t i p l e r e g r e s s i o n have been examined by Freeman and J e f f e r s (1962):  (1) the d i r e c t s o l u t i o n of normal e q u a t i o n s or use  of  based on them, (2) the i t e r a t i v e s o l u t i o n u s i n g the language of space, and  (3) the approach through the v a r i a n c e - c o v a r i a n c e  formulae vector  matrix.  A l l of the methods r e q u i r e , at l e a s t i m p l i c i t l y , the s o l u t i o n of a s e t of normal  equations. The  of v a r i a n c e general  sums of squares i n the g e n e r a l unequal numbers a n a l y s i s  f o r an n-way or n - f a c t o r c l a s s i f i c a t i o n can be o b t a i n e d  terms from standard  r e g r e s s i o n theory.  formulas u s i n g the u s u a l normal e q u a t i o n  and  However, the  in  computing  s o l u t i o n procedures become  - 17 -  unmanageable even w i t h t h e l a r g e s t computers whenever t h e number o f f a c t o r s and/or the number o f l e v e l s become moderately  large.  With  the use o f t h e c a l c u l u s o f f a c t o r i a l s developed by K u r k j i a n and Zelen  (1962)  , F e d e r e r and Z e l e n  r e l a t i v e l y simple computational squares  procedures  f o r o b t a i n i n g sums o f  i n t h e a n a l y s i s o f v a r i a n c e f o r any e f f e c t w h i l e  a l l other e f f e c t s . two,  (1966) were a b l e t o s e t f o r t h  eliminating  F o r sums o f squares o f i n t e r a c t i o n t o the o r d e r  t h e computations  may be performed  on an o r d i n a r y c a l c u l a t o r .  As l i n e a r models have become more w i d e l y u t i l i z e d , have s i m u l t a n e o u s l y become l e s s w e l l s p e c i f i e d .  Urquhard e t a l .  (1973) r e c o n s i d e r e d the d e f i n i t i o n o f a l i n e a r model w i t h  special  reference t o i t s a s s o c i a t i o n with the experimental content. proposed  They  an a l t e r n a t e k i n d o f l i n e a r model which i s c l o s e l y  with the experimental context.  identified  The means o f t h e p o p u l a t i o n s sampled  i n t h e e x p e r i m e n t a l c o n t e x t s e r v e as i t s parameters. was echoed by Hocking  they  and Speed (1975) who found  The p r o p o s a l  i t e l i m i n a t e d much  of t h e c o n f u s i o n , p a r t i c u l a r l y i n t h e a r e a o f h y p o t h e s i s t e s t i n g w i t h unbalanced  data. There a r e many procedures  of l i n e a r models.  t o o b t a i n e s t i m a t e s f o r parameters  Rao (1965) and S e a r l e (1971) used  i n v e r s e method t o s o l v e t h e simultaneous  a generalized  e q u a t i o n system.  A  g e n e r a l i z e d i n v e r s e i s c h a r a c t e r i z e d by t h e f o l l o w i n g p r o p e r t i e s ( S e a r l e , 1971):  - 18  (1)  -  when G i s a g e n e r a l i z e d i n v e r s e of X'X. a l s o a g e n e r a l i z e d i n v e r s e of  X'X;  (2)  y&X'X  (3)  XGX'  i s i n v a r i a n t t o G;  (A)  XGX'  i s symmetric, whether G_ i s or n o t .  = X; i . e . GX'  i s a g e n e r a l i n v e r s e of X; and  The g e n e r a l i z e d i n v e r s e technique p r o v i d e s a procedure  then G' i s  convenient  i n the a n a l y s i s of v a r i a n c e f o r l i n e a r models.  But, i f the  i n v e s t i g a t o r i s i n t e r e s t e d i n the e s t i m a t e of a p a r t i c u l a r the q u e s t i o n o f e s t i m a b i l i t y a r i s e s A unique  ( S e a r l e , 1971).  s o l u t i o n to the l e a s t squares e q u a t i o n cannot  o b t a i n e d u n t i l they a r e reduced degrees  effect,  of freedom.  be  i n number to equal the number of  Although numerous r e s t r i c t i o n s may  be  imposed  i n o r d e r t o a c c o m p l i s h t h i s , the r e s t r i c t i o n t h a t the c o n s t a n t s f o r the main e f f e c t s sum most s a t i s f a c t o r y  t o zero over each row  (Harvey,  1960).  and  column i s p r o b a b l y  The l i n e a r mathematical  suggests t h i s s e t o f r e s t r i c t i o n s s i n c e the main e f f e c t s , e f f e c t s , and the e r r o r term e..,  a r e expressed  model  the itself  interaction  as d e v i a t i o n s from  the  i l k  mean y. U s i n g the r e s t r i c t i o n which r e q u i r e s the s e t t i n g of one the c o n s t a n t s i n each s e t of main e f f e c t s equal t o zero suggests t h a t the  (say, a  P  (ab). , the (ab) . and the (ab) interaction iq P3 pq  of  and b ) q constants  c o u l d be a l s o s e t e q u a l t o z e r o , thereby, a l l o w i n g the d e l e t i o n of a l l these e q u a t i o n s .  Although a unique  s o l u t i o n t o the e q u a t i o n can  be  o b t a i n e d when t h i s i s done, the e s t i m a t e s f o r the c o n s t a n t s a r e not satisfactory  (Harvey,  1960).  - 19  Freeman and J e f f e r s e s t i m a t e means and  standard  -  (1962) d e s c r i b e d an a l g o r i t h m to  e r r o r s i n the a n a l y s i s of non-orthogonal  experiments. Mulet and Walsh (1974) r e p o r t e d a g e n e r a l i z e d i n v e r s e algorithm.  R e c e n t l y , Hemmerle (1974, 1976)  developed  a method f o r  h a n d l i n g a non-orthogonal a n a l y s i s o f v a r i a n c e r e s i d u a l . a n d e x p e c t a t i o n operators.  In p r a c t i c e , the g e n e r a l l i n e a r h y p o t h e s i s  B i o m e d i c a l Computing Programs (Dixon, The program e s t i m a t e s e f f e c t s and  the  enjoys wide p o p u l a r i t y .  the parameters by imposing  interactions.  s u b c l a s s e s i s one  1971)  of  r e s t r i c t i o n s on main  That the program handles no empty c e l l s i n  of i t s severe  drawbacks.  2.2  Pure V e r s u s Mixed Stands  2.2.1  Definition  A f o r e s t can be s i l v i c u l t u r a l l y c l a s s i f i e d as a "pure" o r a "mixed" stand a c c o r d i n g to i t s s p e c i e s composition.  The  former c o n s i s t s  of a s i n g l e t r e e s p e c i e s of s i l v i c u l t u r a l o r economic importance, whereas the l a t t e r has  two  or more s p e c i e s .  The  theoretical  concept  i s s t r a i g h t f o r w a r d , but i n p r a c t i c e the d e f i n i t i o n of a " s i n g l e " o r a "pure" stand i s vague. when 90 p e r c e n t 1950).  Stands a r e c u s t o m a r i l y d e s i g n a t e d as "pure"  or more of the canopy i s of a s i n g l e s p e c i e s  Tourney and K o r s t i a n  species  (1947) m a i n t a i n e d  (Baker,  that i n e s t i m a t i n g  timber  f o r commercial purposes a stand i s u s u a l l y c l a s s i f i e d as pure when 80  - 20 -  percent o r more of the o v e r s t o r y i s of a s i n g l e s p e c i e s and p r a c t i c a l l y a l l of the commercial The  forms  product.  S o c i e t y o f American F o r e s t e r s d e f i n e d a pure stand as  " o f a f o r e s t , crop or stand, composed p r i n c i p a l l y of one s p e c i e s : by c o n v e n t i o n , g e n e r a l l y t o the e x t e n t of g r e a t e r than 80% of the s p e c i e s , based  on numbers, b a s a l a r e a or volume", and mixed  a r e "of a f o r e s t , c r o p ' o r stand, composed o f two  stands  o r more s p e c i e s by  c o n v e n t i o n , g e n e r a l l y t o the extent of l e s s than 20% of s p e c i e s o t h e r than the p r i n c i p a l one, (Ford-Robertson,  based  on numbers, b a s a l a r e a o r volume"  1971).  A c c o r d i n g t o the B . C . F o r e s t S e r v i c e , i n pure f o r e s t  types  major s p e c i e s must be 81 p e r c e n t o r g r e a t e r by volume of l i v e t r e e s i n the main s t a n d .  V e t e r a n s a r e not i n c l u d e d i n t h i s c a l c u l a t i o n .  mixed stand a second  In  s p e c i e s must be 20 p e r c e n t or more (B.C. F o r e s t  S e r v i c e , F o r e s t I n v e n t o r y D i v i s i o n C l a s s i f i c a t i o n and  Sampling  Manual,  1972).  2.2.2  S i l v i c u l t u r a l C o n s i d e r a t i o n s of Pure and Mixed Stands  The  l i t e r a t u r e on s i l v i c u l t u r a l a s p e c t s of pure  and mixed stands reviewed h e r e . the l a s t two  ( m u l t i c u l t u r e s ) i s too voluminous t o be  (monoculture) thoroughly  A comprehensive review of l i t e r a t u r e p u b l i s h e d w i t h i n  decades has been prepared by Haddock  (1974).  - 21  In Europe, I t has establishment  -  been r e p o r t e d  that large c l e a r c u t s  of even-aged monocultures d e t e r i o r a t e d f o r e s t h a b i t s  to such a degree t h a t the extent  of changes of the t r e e  c o m p o s i t i o n sometimes r e q u i r e s a r t i f i c i a l a m e l i o r a t i o n Scholz,  and  1974).  species (Klinka  and  Others observed t h a t c a l a m i t i e s e x p e r i e n c e d i n even-  aged c o n i f e r o u s monocultures were caused by v a r i o u s damaging agents which would u l t i m a t e l y r e s u l t i n d i s c o n t i n u i t y of wood l o s s e s o f investment, and  y i e l d s t h a t c o u l d not be  production,  sustained.  In s p i t e of c a l a m i t i e s e x p e r i e n c e d i n some pure stands, Hiley  (1959) advocated f o r B r i t i s h f o r e s t s the use  of c e r t a i n crop  tending, p r a c t i c e s used i n South A f r i c a monocultures, e s p e c i a l l y those of p i n e s .  Keets  (1966) argued the need f o r r e s e a r c h  s o i l data required  to grow s u c c e s s i v e  to p r o v i d e  the  crops of P i n u s p a t u l a i n South  Africa. Keeves (1966) and Whyte (1973) have p r e s e n t e d evidence of a d e c l i n e i n growth of second r o t a t i o n crops of Monterey p i n e r a d i a t a D. Don) respectively. and  on c e r t a i n s o i l s i n South A u s t r a l i a and  q u a n t i t a t i v e s t u d i e s have been made.  through c r o p p i n g , Florence some v a l u a b l e focused  others  In some  suspected reasons f o r observed d e c l i n e i n p r o d u c t i v i t y  i n c l u d e the m a r g i n a l c h a r a c t e r  He  Zealand,  Bunn (1967) reviewed the work of Keeves (1966) and  concluded t h a t few  instances,  New  (Pinus  of s h a l l o w s o i l s , l o s s of n u t r i e n t s  or l o s s of n u t r i e n t s by means of s l a s h b u r n i n g . (1967) p r o v i d e d  an e x c e l l e n t b i b l i o g r a p h y and  gave  s u g g e s t i o n s f o r r e s e a r c h , w i t h emphasis on edaphic f a c t o r s .  on the s i t u a t i o n f a c e d  i n South A u s t r a l i a where the  decline  - 22 -  i n p r o d u c t i v i t y o f Monterey p i n e on c e r t a i n s o i l s i s o f a s e r i o u s magnitude.  He observed t h a t a monoculture p l a n t a t i o n i s regarded  as a simple system and i n comparison t o n a t u r a l communities,  lacks  t h e i r dynamic v e g e t a t i o n a l and s o i l b i o l o g i c a l p r o c e s s e s n e c e s s a r y for s t a b i l i t y .  He expressed the need f o r g r e a t e r u n d e r s t a n d i n g o f  these p r o c e s s e s i n n a t u r a l f o r e s t s i n o r d e r problems i n t o b e t t e r p e r s p e c t i v e .  t o put t h e p l a n t a t i o n  He a l s o reviewed t h e i n f l u e n c e  of s p e c i e s and s p e c i e s m i x t u r e s on s o i l s ,  l i t t e r decomposition, and  n u t r i e n t r e t u r n , and changes i n the r e l a t i o n s h i p i n f o r e s t - s o i l microflora. In s p i t e o f t h e c o n t r o v e r s i e s and  other  America.  about monoculture i n Europe  countries, monocultural p r a c t i c e s are prevalent  i n North  I n 1950, Baker s a i d " i t i s o n l y human n a t u r e t o take a  chance and gamble on h i g h p r o f i t s r a t h e r than t o p l a y s a f e when i t i s obvious t h a t i t w i l l c o s t money t o do so". the concept o f monocultures, p o i n t e d i d e a o f growing s o u t h e r n p i n e s l i k e l y t o be uncommon. s p e c i e s was of i t s e l f  Smith (1962) i n d i s c u s s i n g  out t h a t " d e p a r t u r e s from t h e b a s i c  i n pure, even-aged stand  I f the e x i s t e n c e  a r e , however,  o f such stands o f these  i n v i t a t i o n to calamity,  t h i s would have become  obvious i n the e x i s t i n g n a t u r a l stands o f t h i s s o r t " . The  p o i n t t h a t pure stands a r e s u s c e p t i b l e t o a t t a c k s by  i n s e c t s and f u n g i has been argued by f o r e s t e r s . where l o s s e s r e s u l t i n g from i n s e c t and d i s e a s e s  Cases can be c i t e d a t t a c k have o c c u r r e d t o  b o t h mixed and pure stands ( B a s k e r v i l l e , 1965; McSwain, 1970).  - 23 -  The  s i t u a t i o n r e g a r d i n g monocultures i n B r i t i s h  i s a c o m p l i c a t e d one.  Columbia  I n B.C. c l e a r - c u t t i n g has developed  consequence o f s e v e r a l c o n v e r g i n g i n f l u e n c e s .  Among these a r e  i n c r e a s e d u t i l i z a t i o n as a r e s u l t o f improved s a w m i l l i n g  techniques  and t h e c o n s t r u c t i o n of a number o f pulp m i l l s , r e s t r i c t e d development, r i s i n g p r i c e s , i n c r e a s e d m e c h a n i z a t i o n , and  as a  road  shortage o f l a b o r  the o p i n i o n on t h e p a r t o f some f o r e s t e r s t h a t p l a n t i n g c o u l d  e f f e c t i v e l y s o l v e the r e g e n e r a t i o n problem c r e a t e d by l a r g e area c l e a r - c u t t i n g and sometimes n e c e s s a r y s l a s h b u r n i n g }  t  (Haddock, 1974).  On the o t h e r hand, the a b i l i t y o f l o d g e p o l e p i n e and many o t h e r s p e c i e s t o e x i s t n a t u r a l l y i n extremely areas i s w e l l known (Horton, 1956).  dense stands over v a s t  Thousands o f t r e e s p e r a c r e may  become e s t a b l i s h e d a f t e r f i r e and t h e h i g h s u r v i v a l r a t e can l e a d t o extreme s t a g n a t i o n . requirements,  Lodgepole  pine i s not exacting i n i t s s o i l  grows on a wide v a r i e t y o f s o i l types, and reaches i t s  b e s t developments on moist but w e l l - d r a i n e d sandy o r g r a v e l l y loam (Duffy, 1964).  N a t u r a l monocultures o f l o d g e p o l e p i n e occur w i d e l y  i n the Northern  I n t e r i o r on areas a s s o c i a t e d w i t h major n a t u r a l  disturbance  ( f i r e , wind throw, e t c . ) .  I n a d d i t i o n , l o d g e p o l e p i n e may  occur e x t e n s i v e l y on lower q u a l i t y s i t e s , sometimes as an uneven-aged open stand as an " e d a p h i c " c l i m a x  (Haddock, 1974).  One way o r t h e o t h e r , t h e pure stands w i l l c o n t i n u e t o e x i s t i n B r i t i s h Columbia as w e l l as elsewhere  i n North America.  Advocates  f o r m u l t i c u l t u r e s o f t e n c l a i m t h a t mixed stands a r e s u p e r i o r t o pure ones based  on t h e assumptions t h a t pure stands:  - 24 -  (1)  may f a i l to u t i l i z e the s i t e f u l l y ;  (2)  make excessively heavy demands on s o i l nutrients;  (3)  may cause a slow deterioration of upper s o i l layers by fostering the formation of some sort of acid raw humus; and  (4)  are susceptible to attacks by insects and fungi.  In managing commercial forests, the productivity of stands is  of major concern.  The above-mentioned disadvantages w i l l  r e f l e c t on the growth and y i e l d of pure stands d i r e c t l y or i n d i r e c t l y . Therefore, to some extent the potential impact of monoculture can be quantitatively assessed by comparing natural y i e l d s of pure and mixed stand types. In h i s recent report, Haddock (1974) has extensively reviewed the environmental impact of monocultures i n second-growth forests i n the Interior of B r i t i s h Columbia.  He defended monocultural practices  by i l l u s t r a t i n g nutrient cycling and insect attacks i n even-aged pure stands.  In h i s report, quantitative evidence i s lacking, however. Scattered published information on comparisons of growth and  y i e l d of pure and mixed stands can be found. r e s t r i c t e d to l o c a l conditions.  But most examples are  In view of the increasing concern  expressed by foresters about the impact of monoculture practices i n B r i t i s h Columbia, there i s a pressing need to provide information on the effects of pure stands on growth and y i e l d i n comparison to that of mixed stands.  - 25 -  2.2.3  Comparison of Growth and Y i e l d  Turnbull  of Pure and Mixed Stands  (1963) gave a comprehensive review of  literature  on growth and y i e l d , w i t h emphasis on stand s t r u c t u r e , f o r pure and mixed stands up t o 1960. shift  Recent s t u d i e s on t h i s s u b j e c t seems to  from comparison of y i e l d to f a c t o r s c o n t r i b u t i n g to the d i f f e r e n c e  i n growth and y i e l d between pure and mixed In Europe, V a c o v s k i f r e s h or f r e s h t o moist of pure beech was  stands.  (1967) p r e s e n t e d d a t a showing t h a t , on  s i t e s w i t h r i c h t o v e r y r i c h s o i l s , the performance  s l i g h t l y s u p e r i o r to mixed stands or t o pure  oak.  On f r e s h s i t e s w i t h r i c h s o i l s , the m i x t u r e s were more p r o d u c t i v e than pure stands of e i t h e r s p e c i e s .  On f r e s h s i t e s w i t h r i c h t o  moderately  r i c h s o i l s , stand p r o d u c t i v i t y i n c r e a s e d w i t h i n c r e a s i n g p r o p o r t i o n of oak. Hegre and Langhammer (1967) d e s c r i b e d the e s t a b l i s h m e n t treatments  of a mixed stand e s t a b l i s h e d i n 1947  (2+0  aspen and  spruce, p l a n t e d as a l t e r n a t e t r e e s ) , and gave graphs and h e i g h t s , d.b.h., volume, increment, Comparison w i t h increments  2+2  t a b l e s showing  s p a c i n g , e t c . i n p e r i o d up to  from y i e l d t a b l e s f o r the two  pure stands shows t h a t the m i x t u r e has developed  very  and  1966.  species i n  satisfactorily,  but i t seems l i k e l y t h a t s i t e q u a l i t y i s b e t t e r than u s u a l f o r good spruce and aspen stands. In 1971,  Langhammer d i s c u s s e d the advantages and  a s s o c i a t e d w i t h mixed c o n i f e r o u s and particularly  problems  coniferous/broad-leaved stands,  as r e g a r d s h e i g h t i n c r e a s e s and forms of v a r i o u s s p e c i e s  - 26 -  and t h e i r r e l a t i o n to the success of mixtures, effect on the s o i l , and the e f f e c t on growth of thinning or of removing one of the species i n a mixture. From studies on 13 t r i a l plots i n Czechoslovakia over a period of 30 years, Zakopal and Mares (1968) presented evidence to support the growing of Picea abies i n mixture with oak on FagetoQuercetum s i t e s .  The admixtures of spruce not only result i n increased  volume production but also i n a substantial improvement i n oak value production.  The best results are obtained with an admixture of 30%  spruce i n the top story. Tarrant (1961) investigated stand development and  soil  f e r t i l i t y i n a D o u g l a s - f i r — r e d alder (Alnus rubra Bong.) plantation i n the Wind River Experimental Forest i n south western Washington and found that planted Douglas-fir mixed  with  " o f f s i t e " alder i n  comparison with Douglas-fir growing alone showed no r e a l difference i n either height or diameter growth.  Tarrant also found that when f i r  and alder measurements are combined, more than twice the cubic volume of wood was produced i n the mixed stand than i n the pure Douglas-fir stand.  The b e n e f i c i a l r e s u l t s of mixture of alder with Douglas-fir  continued to 1976 when the experiment was e f f e c t i v e l y destroyed by bear damage. In natural stands, Eidmann (1952) reported some very i n s t r u c t i v e figures on the Sitka spruce (Picea sitchensis (Bong.) Carr.) —  western hemlock (Tsuga heterophylla Sarg.) stands of the  Cascade Head Experiment Forest.  Data from four plots are given i n  Table 2-1. One plot had approximately the same number of trees of both  Plot  Table 2-1. Yields of pure hemlock and hemlock-spruce admixed stands (Eidmann, 1952). Species Number Averaqe Average Volume Total of Trees Height Diameter Volume per acre m cm cu. m/ha cu. m/ha HEMLOCK  193  45.1  48.8  651  SPRUCE  173  50.3  68.8  1110  HEMLOCK  161  32.9  39.3  274  SPHUCE  289  45. 1  61.7  13 43  HEMLOCK  383  42. 1  48.5  1212  77  47.6  65.5  4 18  1630  781  39.6  40.1  1686  1686  SPRUCE HEMLOCK  m  1761  1617  - 28 -  species, a second plot had a higher percentage of spruce, a t h i r d plot was mainly hemlock and the l a s t plot was pure hemlock. Irrespective of the individual share of each of the species, the t o t a l volume for both i s approximately the same i n a l l four cases.  Eidmann  argued that t h i s was one example out of thousands which have shown that one species can replace another and that they can then grow together and prosper with advantage to the whole stand.  From these  impressions, the author concluded that mixed conifer stands are preferable to pure stands i n Europe. Several Nelder plantations for spacing t r i a l s and for assessing species competition effects have been established at the Research Forest of the University of B r i t i s h Columbia  (Walters and Smith, 1973).  Four  species, Douglas-fir, western hemlock, western redcedar (Thuja p l i c a t a Donn.), and Sitka spruce were planted.  Results on the species effects  are not yet available because the stands are i n their early developing stages, but Douglas-fir has survived and grown best to-date'. Based on data collected from forest inventories, Smith (1976) compared average y i e l d s of pure and mixed species stands for Douglas-fir, "balsam" f i r , lodgepole pine, and spruce i n Interior, B.C.  The  averages indicate a difference i n y i e l d between pure and mixed stands i n Douglas-fir and "balsam" f i r , but no differences i n lodgepole pine and spruce were observed.  Based on the same data, Smith (1977)  developed y i e l d estimates and preliminary guides f o r spacing and thinning B r i t i s h Columbia  forests.  - 29  -  2.3  F o r e s t I n v e n t o r y Zones  2.3.1  Definition  The species, first  f a c t o r s d i r e c t l y r e s p o n s i b l e f o r the  the  f o r e s t t y p e s , and  p l a c e , the  geographic l o c a t i o n and  c l i m a t e as w e l l as r e l a t e d w i t h the The been the the  growth of f o r e s t  the geology and  resulting  the  related inter-  soils.  specialized  studies.  T a b l e 2.2  by W h i t f o r d and and  Ruggles  has  compares Craig  (1956),  (1965) (from Stanek, 1966).  The  z o n a l c l a s s i f i c a t i o n system i n t h i s study d i f f e r s  s l i g h t l y from K r a j i n a ' s The  the  in  c l a s s i f i c a t i o n of f o r e s t types i n B r i t i s h Columbia  c l a s s i f i c a t i o n of f o r e s t r e g i o n s of B.C.  basis.  the  b i o t i c f a c t o r s , which are  s o i l forming p r o c e s s e s and  s u b j e c t of s e v e r a l  Krajina  stands are,  topography and  (1918), Rowe (1959), Chapman, T u r n e r , F a r l e y and  d i s t r i b u t i o n of  B.C.  which c l a s s i f i e s B.C.  F o r e s t S e r v i c e I n v e n t o r y D i v i s i o n has  f o r e s t a r e a s i n t o twelve " f o r e s t zoning system has  f o r e s t s on an  i n v e n t o r y zones".  been expressed i n the  The  ecological  grouped  B.C.  need f o r  this  "Growth Manual" (B.C.F.S., 1966).  "Because of the l a r g e number of Crown U n i t s p r e s e n t l y i n e x i s t e n c e , i t i s o b v i o u s t h a t we cannot hope, i n a r e a s o n a b l e p e r i o d , t o e s t a b l i s h enough permanent p l o t s to p r o v i d e r e l i a b l e growth e s t i m a t e s f o r a l l growth types, age c l a s s e s , and s i t e s i n each u n i t . Therefore, we have combined a l l of the e x i s t i n g U n i t s i n t o twelve groups, t h r e e on the Coast and n i n e i n the I n t e r i o r . "  Table 2-2. Whitford and Craig (1918) FOREST TYPES COASTAL BELT Douglas-fir - Western Red Cedar Western Red Cedar - Bestern Hemlock Western Hemlock - Sitka Spruce Western Hemlock - Amabilis Fir Subalplne INTERIOR TREELESS AND SEMITREELESS Sage Brush— Artemisia Tridentata Grass and Semlopen * Agropyron Splcatum Yellow Pine (or Ponderosa Pine) Interior Douglas-fir INTERIOR WET BELT Douglas-fir - Western Larch Int. West. Red Cedar - West. Hemlock West. Red Cedar - Engelmann Spruce Western Hemlock - Alpine Fir  ZONES  Classifications of forest regions of British Columbia  |  Krajina (1965) SUBZONES  SPRUCE - ALPINE FIR OF THE INTERIOR PLATEAUS AND MOUNTAIN REGIONS Engelmann Spruce - Alpine Fir or Lodgepole Pine Subalplne  White Spruce - Alpine Fir  Treeless (teste Land  Rove (1959) SECTIONS  I. PACIFIC COASTAL MESOTHERMAL FOREST REGION COAST FOREST REGION Coastal -JSarryJDak.j:. Douglas-fir(drler) CI [ Strait of Georgia Douglas-fir C2 | Southern Pacific Coast Madrono - Douglas-fir "(wetter) Coastal JeSSAJL?;!*.*!* Western Hemlock (drier) "C3~ j Northern Pacific Coast Pacific Silver Fir "-Wes tern Hemlock' Western Hemlock C4 Queen Charlotte Islands ' (wetter) II. PACIFIC COASTAL SUBALPINE REGION SUBALPINE FOREST REGION Mountain | Subalpine ForeBt (lower) SA3 Coastal Subalpine Hemlock PSubalpine Parkland (upper) IV. CORDILLERAN COLD STEPPE AND SAVANNA FOREST REGION MONTANE FOREST REGION j Bunch Grass (drier) G Grassland Ponderosa Pine Bunch Grass Ponderosa Pine (wetter) Ml Ponderosa Pine - Douglas-fir III. CANADIAN CORDILLERAN FOREST REGION Interior Douglas_Pine Grass (drier) fir False Bojcwood (wetter)  M2  Central Douglas-fir  —  Chapman et al. (1956) BIOTIC REGION Gulf Islands and Puget Sound Lovland Coast Forest  Subalplne Forest  O f l o v o o s Ari  A  Dry Forest  COLUMBIA FOREST REGION Interior Western Hemlock  Western Larch (drier) Western Hemlock (wetter)  Cariboo Aspen Lodgepole Pine Douglas-fir Parkland  Subzones not proposed  CL1 CL2  INTERIOR TREELESS AND SEMITREELESS Crass and Semiopen Agropyron Splcatum  (Stanek, 1966) .  •  M3 M4 M5  V. CANADIAN CORDILLERAN SUBALPINE FOREST REGION Engelmann Spruce - j Subzones not proposed Subalpine Fir ' i VI. CANADIAN BOREAL FOREST REGION Sub-boreal Spruce Subzones not proposed (mainly white spruce vlth some Engelmann spruce) Boreal White and Black Spruce VII. ALPINE TUNDRA REGION a) Coastal b) Interior Subzones  j  Southern Columbia Northern Columbia MONTANE FOREST REGION Northern Aspen Montane Transition Douglas-fir - Lodgepole Pine  Columbia Forest  Cariboo Parklands  SUBALPINE FOREST REGION SA1 | East Slope Rockies SA2 jInterior Subalpine BOREAL FOREST REGION Aspen Grove a) Mixed Wood . b) Hay River a) b") c) Lower-Nbrth-Upper Foothills a) Lower Mackenzie Upper Liard Stikine Plateau B26'j a)bawson b)Centr. Yukon c)East.Yukon  B17 B18 -fil9~ ~ B23" "B24" "B2S  Tundra  Subalpine Forest  Peace River Parklands and Boreal Forest  Alpine - Arctic .  - 31 -  Map 1 shows g e o g r a p h i c a l l y t h e boundary o f the twelve f o r e s t i n v e n t o r y zones i n B.C.; the z o n a l d e f i n i t i o n Y i e l d U n i t s and T r e e Farm L i c e n s e s ) classification i s essentially  2.3.2  Regional  (Public Sustained  i s g i v e n i n Appendix 1.  The z o n a l  geographical.  P r o d u c t i v i t y of Forest  Stands  Most f o r e s t growth s t u d i e s , i n B.C. and elsewhere, have been based on m a t e r i a l s c o l l e c t e d over r e l a t i v e l y l i m i t e d a r e a s .  Comparisons  of t h e r e s u l t s o f growth and y i e l d s i n v a r i o u s r e g i o n s o r b i o c l i m a t i c zones n a t u r a l l y show t h e changes i n growth on t r a n s i t i o n from f a v o r a b l e to l e s s f a v o r a b l e c l i m a t i c c o n d i t i o n s .  T r a d i t i o n a l l y the zonal  d i f f e r e n c e s i n growth and y i e l d have been a t t r i b u t e d by f o r e s t e r s t o differences i n site quality.  Indeed, f o r e s t s i t e has been d e f i n e d by  the S o c i e t y o f American F o r e s t e r s as "an a r e a , c o n s i d e r e d e c o l o g i c a l f a c t o r s w i t h r e f e r e n c e to c a p a c i t y t o p r o v i d e v e g e t a t i o n " , o r as " t h e combination o f b i o t i c , c o n d i t i o n s o f an a r e a "  (Ford-Robertson,  y i e l d t a b l e s f o r even-aged stands  f o r e s t or o t h e r  c l i m a t i c and s o i l  1971).  D i f f e r e n c e s i n stand y i e l d caused by v a r i o u s l o c a t i o n s have been w e l l r e c o g n i z e d  as t o i t s  by f o r e s t e r s .  o f S i t k a spruce  geographical  In compiling  normal  and western hemlock,  Meyer (1937) used t h e b a s i c data c o l l e c t e d over t h e e n t i r e c o a s t a l range of the s p e c i e s , extending  from Southern Oregon through Washington and  B r i t i s h Columbia t o Southeastern  A l a s k a and analyzed  t h e data  without  Map  1. F o r e s t i n v e n t o r y zones i n B r i t i s h C o l u m b i a . Numbered F o r e s t i n v e n t o r y Zones a r e d e f i n e d i n the Appendix I .  - 33 -  regard to species composition or geographical l o c a t i o n . subsequently found t h a t these f a c t o r s a f f e c t y i e l d and p r o v i d e d supplementary  Meyer  b o t h s i t e index and  tables f o r correcting  yields.  F u r t h e r a n a l y s e s by Barnes (1962) on t h e d a t a used by Meyer i n d i c a t e d t h a t many y i e l d v a r i a b l e s d i f f e r e d regions.  markedly among  Stands o f t h e same age and s i t e index had much, s m a l l e r average  diameters i n A l a s k a and B r i t i s h Columbia  than i n Oregon and Washington.  The d i f f e r e n c e i n average diameter amounted t o about  20 p e r c e n t , and  the c o r r e s p o n d i n g d i f f e r e n c e i n volume was even g r e a t e r .  These  d i f f e r e n c e s a r e a t t r i b u t e d t o denser stands a t e a r l y ages i n t h e n o r t h e r n latitudes, closure. earlier  which r e s u l t e d i n more severe c o m p e t i t i o n and e a r l i e r  crown  C o o l e r and w e t t e r summers t o n o r t h p r o b a b l y c o n t r i b u t e t o and more complete r e s t o c k i n g . The average h e i g h t o f stands o f t h e same age and s i t e  also d i f f e r s .  index  Average h e i g h t s i n Oregon, Washington, and B r i t i s h  were about e q u a l , but average h e i g h t i n A l a s k a was about  Columbia  15 p e r c e n t  less.  T h i s i n d i c a t e s a l a r g e r number o f s h o r t e r t r e e s i n t h e subdominant p a r t of  the A l a s k a s t a n d s .  Barnes (1962) concluded "some r e c o g n i t i o n o f  g e o g r a p h i c a l l o c a t i o n , seemed n e c e s s a r y " . y i e l d t a b l e s f o r (1) Oregon—Washington,  Therefore, separate r e g i o n a l l y  (2) B r i t i s h Columbia,  and (3)  A l a s k a were c o n s t r u c t e d f o r stands i n which 40 p e r c e n t o r more o f t o t a l b a s a l a r e a was i n western  hemlock.  I f t h e r e a r e v a r i a t i o n s i n growth and y i e l d w i t h i n t h e Northwestern  Pacific  Coast, they must a l s o occur w i t h i n B r i t i s h  Columbia.  - 34  Andody (1968) d e s c r i b e d  Columbia.  Her  of c u l m i n a t i o n  of mean annual increment  to the C e n t r a l I n t e r i o r r e g i o n of  between z o n a l and  suggested the d e s i r a b i l i t y  the B.C.  age  British  a n a l y s i s demonstrated average d i f f e r e n c e s i n the  of 25 to 30 percent  inventory  yield,  g r a p h i c a l methods f o r d e t e r m i n i n g  mean annual increment, and with s p e c i a l reference  -  l o c a l curve averages.  She  of c o n s t r u c t i n g curves f o r twelve f o r e s t  zones r a t h e r than the seven Forest  inventory  zones then used  f o r e s t stands a c r o s s  B r i t i s h Columbia.  y i e l d t a b l e s were p u b l i s h e d  i n 1958.  i n d i c a t i o n o f the growth r a t e of any b a s i s f o r the t a b l e s was  f o u r dbh  Seven i n v e n t o r y l i m i t s , and  The  first  comprehensive e m p i r i c a l  f o r e s t stand  zones, e l e v e n  i n the p r o v i n c e .  c l a s s and  (Fligg,  constructed  p l o t t i n g them over  t a b l e s prepared by  1960).  T a b l e s were  s i t e was  the B.C.  A d d i t i o n a l samples were  reported,  In a d d i t i o n to the y i e l d  a l s o addressed i t s e l f  and  age.  limit. Forest  Service  included,  type groups were expanded to s i x t e e n , the b a s i s of sampling by  clarified.  The  g r o s s c u b i c - f o o t volumes i n l i v i n g merchantable  empirical y i e l d  growth type and  an  type groups, f o u r s i t e c l a s s e s ,  Balanced freehand curves were drawn f o r each dbh  and  of  11,500 samples each c o n s i s t i n g of f o u r or more  by a v e r a g i n g volumes f o r each age  were r e v i s e d l a t e r  yield  They were developed to g i v e  t r e e s of a l l commercial s p e c i e s were i n v o l v e d .  The  by  Service.  Many e f f o r t s have been made t o e s t i m a t e growth and  plots.  order  zone  d e t a i l s of c a l c u l a t i o n  t a b l e s , the B.C.  t o the problem of l o c a l i z i n g  Forest  Service  e s t i m a t e s of  yield.  - 35  -  Young (1966) I l l u s t r a t e d an approach i n which volumes were p l o t t e d over age  f o r two  utilization limits.  volumes per a c r e i n c u b i c f e e t u t i l i z a t i o n stands.  continuing  (net a l l o w i n g  Volume over age  r e v i s e d or withdrawn as new inventory  Y i e l d s were expressed as f o r decay o n l y ) to  Each VAC  became a v a i l a b l e from was  drawn to g i v e a  Yield Unit.  and  the  zonal  summary f o r a type group or t o r e p r e s e n t the y i e l d t h a t c o u l d be from a p a r t i c u l a r P u b l i c S u s t a i n e d  close  curves (VAC's) were numbered  information  program.  average  expected  The VAC's were used to  d e f i n e the p o i n t at which maximum mean annual increment i n volume o c c u r r e d and t h e y e a r s c o r r e s p o n d i n g to t h i s set The  volume over age  drawn freehand and being  tested.  curves of the B.C.  Forest  S e r v i c e were  the p o s s i b i l i t y of combining t h e i r curves was  However, Richmond (1969) found no  P u b l i c Sustained poor, and  the r o t a t i o n .  d i f f e r e n c e s i n many  Y i e l d U n i t s when the rough c l a s s e s of good, medium,  low were r e p l a c e d w i t h approximate s i t e index.  found t h a t s e v e r a l types c o u l d be (1973) a n a l y z e d  not  grouped.  d a t a on volumes by age  On  h i g h l y s i g n i f i c a n t and  zones and  c o e f f i c i e n t s r e s u l t e d i n l a r g e v a r i a t i o n s i n standard  He  reported  a l s o showed t h a t use  estimates w i t h i n species  groups.  that  regression  e r r o r s of  When u s i n g o n l y zone, type group, and  c l a s s , l a r g e d i f f e r e n c e s remained among zones and i n t e r i o r regions.  summaries  important d i f f e r e n c e s i n i n t e r c e p t and  among the s t r a t a s t u d i e d .  also  the o t h e r hand, Smith  c l a s s e s from VAC  f o r type groups w i t h i n seven major i n v e n t o r y  He  between c o a s t  estimate site and  of z o n a l curves improved  - 36  -  In the same study, Smith (1973) i n v e s t i g a t e d volume y i e l d of I n t e r i o r l o d g e p o l e  pine  f o r 22  separate sustained  concluded t h a t t h e r e were l a r g e and  and  extend the c o n c l u s i o n s  In d i s c u s s i n g s o i l ,  and  of Andody  s i t e , and  strata.  These r e s u l t s  (1968).  l a n d c l a s s i f i c a t i o n , Rowe (1962)  i n d i c a t e d t h a t a geographic s t r a t i f i c a t i o n of l a n d i s needed to a framework w i t h i n which r e l i a b l e s o i l - s i t e and can be  established.  regardless  The  of i t s t h e o r e t i c a l shortcomings, was  2.3.3  R e g i o n a l i t y and  classification,  a step i n the r i g h t  i s concerned.  B i o c l i m a t i c Zone S t u d i e s  i n Other Regions  In Europe, r e f o r e s t a t i o n , m a i n l y w i t h e x o t i c t r e e has  been c a r r i e d out  i n the B r i t i s h I s l e s f o r some time.  species,  To  facilitate  the s e l e c t i o n of t r e e s p e c i e s , F a i r b a i r n (1968) d i v i d e d Great i n t o zones on the b a s i s of the l e n g t h o f the growing season precipitation. proposal  Sweden has  provide  growth r e l a t i o n s h i p s  o l d z o n a l i t y concept i n s o i l  d i r e c t i o n so f a r as s o i l use  and  important d i f f e r e n c e s from u n i t  to u n i t i n volume per a c r e f o r a g i v e n age confirm  yield units  Britain  and  been d i v i d e d i n t o s i x growth r e g i o n s ,  and  has been made f o r t h e i r f u r t h e r d i v i s i o n i n t o s u b - r e g i o n s  the b a s i s of the r a d i a l growth r e v e a l e d by national forest inventories  the m a t e r i a l o b t a i n e d  (Hagberg, 1959).  on  from  a  - 37 -  In F i n l a n d , country was d i v i d e d  f o r t h e purposes o f f o r e s t  into 9 forest taxation  into 5 s i t e q u a l i t y or tax classes. for taxation taxation  A s o - c a l l e d mean volume u n i t  1971).  Lukkala  of the n a t i o n a l  (1938) d i v i d e d  r e g i o n s f o r f o r e s t d r a i n a g e purposes. basis  r e g i o n s and these a g a i n  has been determined f o r each t a x c l a s s o f each f o r e s t  r e g i o n on t h e b a s i s  (Koivisto,  taxation, the  forest  Finland  into 5 climatic  H e i k u r a i n e n (1959, 1973) on t h e  o f t h e annual increment e s t i m a t e d from m a t e r i a l  swamp f o r e s t s  i n various parts of Finland,  i n t o zones which d i f f e r  inventories  collected  also divided  the country  s l i g h t l y from those proposed by L u k k a l a .  Some e f f o r t s have been made i n Europe t o p r e d i c t forest productivity  from  regional  by c l i m a t i c c o e f f i c i e n t s . . Week (1955) i n h i s book  " F o r e s t Increment and Y i e l d " proposed t h e composite c l i m a t i c  N T + 10  x  n 92  index  Z - 60 100  x  i n which N r e p r e s e n t e d p r e c i p i t a t i o n , T the mean temperature d u r i n g t h e period  May t o J u l y , n t h e number o f days on which t h e r e was a t l e a s t  0.1 mm o f r a i n , and Z t h e number o f f r o s t - f r e e days i n t h e y e a r . average annual increment was  (dry-weight) f o r each o f t h e 25  When  growth-districts  compared w i t h t h e c o r r e s p o n d i n g c l i m a t i c index, a c o r r e l a t i o n o f  0.743 + 0 . 0 9 was o b t a i n e d .  v  - 38  Paterson  (1956) has  -  attempted s i m i l a r c o r r e l a t i o n s on  a  more ambitious i n t e r c o n t i n e n t a l s c a l e , u s i n g d a t a on p r o d u c t i v i t y of mature, u n d i s t u r b e d  h i g h f o r e s t , which he  P a t e r s o n ' s c l i m a t i c index i n c o r p o r a t e d of the h o t t e s t and  s t a t i s t i c s f o r mean temperature  the c o l d e s t months, mean annual p r e c i p i t a t i o n ,  p r e c i p i t a t i o n e f f e c t i v e n e s s , and logarithm  called "ideal site class".  a solar radiation factor.  of t h i s index p l o t t e d a g a i n s t  The  " i d e a l s i t e c l a s s " was  reported  to be a s t r a i g h t l i n e . However, Week (1957) q u i t e p r o p e r l y p o i n t e d  out  t h a t p r o d u c t i v i t y should have been expressed i n terms of dry-weight production,  and  a l s o t h a t wood-volume comprised o n l y a p a r t of  total  production. Koivisto  (1971)  d e r i v e d volume increment f u n c t i o n s  and  f o r e s t growth i n F i n l a n d to o b t a i n a p r e c i s e i d e a of the changes i n f o r e s t growth from the south coast  o f F i n l a n d to the N o r t h e r n timber  l i n e , and  to d i v i d e the c o u n t r y on t h i s b a s i s i n t o homogeneous growth  regions.  He  concluded t h a t a l t h o u g h the growth o f f o r e s t i n the  p l a c e depends on c l i m a t e and  the f e r t i l i t y  r e l a t i v e increment were b e t t e r e x p l a i n e d  of s o i l ,  logarithmic  of the  accounted f o r 69 to 75 percent  of  stand.  the  to K o i v i s t o (1971), the e f f e c t i v e temperature  the most p r o m i s i n g c l i m a t i c f a c t o r .  growing season, however, was in  the age  variance.  According seemed to be  variations in  by more a c c u r a t e l y measurable  secondary growth f a c t o r s , the most important b e i n g Depending on the s p e c i e s , age  first  The  l e n g t h of t h e r m a l  the v a r i a b l e s e l e c t e d f o r the  stands dominated by p i n e or spruce, and  sum  l a t i t u d e f o r the  function function  -  i n birch-dominated  stands.  3 9 -  Spruce and b i r c h seem t o r e a c t t o  c l i m a t i c changes more r e a d i l y than does p i n e , f o r the f a c t o r was  climatic  the f o u r t h i n sequence t o be i n c l u d e d i n the f u n c t i o n  of p i n e stands, but the t h i r d i n the f u n c t i o n s of the o t h e r t h r e e species. Koivisto  (1971) a l s o observed  another, the mean volume increment volume increment southernmost  f a l l s by about  t h a t from one growth r e g i o n t o  d u r i n g the r o t a t i o n o f maximum  24 p e r c e n t .  r e g i o n i s g i v e n a r a t i n g o f 100,  I f the increment  the mean wood p r o d u c t i o n  c a p a c i t i e s of the growth r e g i o n s f o l l o w the sequence 100 — The wood p r o d u c t i o n c a p a c i t y , t h e r e f o r e , does not d e c l i n e towards the n o r t h e r l y r e g i o n s .  Chapter  82 —  56 —  36.  rectilinearly  The d e c l i n e i s slow a t the b e g i n n i n g ,  and i t s r a t e i n c r e a s e s as i t n e a r s the timber  2.4  of the  line.  Summary  In t h i s c h a p t e r p u b l i c a t i o n s concerned w i t h s t a t i s t i c a l methods f o r the a n a l y s i s o f e x p e r i m e n t a l d a t a w i t h unequal  c e l l frequencies,  s i l v i c u l t u r a l and m e n s u r a t i o n a l problems a s s o c i a t e d w i t h mono- and m u l t i c u l t u r a l p r a c t i c e s i n f o r e s t r y , and r e g i o n a l p r o d u c t i v i t y of f o r e s t stands were s e p a r a t e l y reviewed.  The l e a s t squares t h e o r y which  i s w i d e l y r e c o g n i z e d i n r e g r e s s i o n a n a l y s i s has been a p p l i e d t o the a n a l y s i s of unbalanced  d a t a s i n c e 1934.  Techniques  involving  the  employment o f l e a s t squares t h e o r y i n the a n a l y s i s of unbalanced  data  a r e more c o m p l i c a t e d than i n r e g r e s s i o n a n a l y s i s because the m a t r i x  - 40 -  formulated i n the former unbiased  i s not of f u l l rank.  Methods t o compute  e s t i m a t e s f o r parameters have been proposed;  computational  procedures  t o o b t a i n unique  however,  estimates f o r data with  empty c e l l s which a r e common i n f o r e s t i n v e n t o r y d a t a a r e l a c k i n g . S i l v i c u l t u r a l and m e n s u r a t i o n a l problems w i t h r e g a r d t o pure and mixed stands have been s t u d i e d .  S i l v i c u l t u r a l s t u d i e s on  t h i s s u b j e c t are o f t e n l a c k i n g i n q u a n t i t a t i v e support mensurational experimental  while  i n v e s t i g a t i o n s a r e f r e q u e n t l y r e s t r i c t e d to v e r y  limited  plots.  The need to s u b d i v i d e the f o r e s t a r e a i n B.C. I n v e n t o r y Zones" was  explained.  p r o d u c t i v i t y of f o r e s t were d i s c u s s e d .  into "Forest  L i t e r a t u r e on z o n a l and r e g i o n a l  stands i n B.C.  as w e l l as i n o t h e r r e g i o n s  - 41 -  3.0  METHODOLOGY  3.1  L i n e a r Model  The complete model f o r a two-way c l a s s i f i c a t i o n w i t h unequal o b s e r v a t i o n s i n t h e s u b c l a s s e s i s  Y... = u + a.  xjk  I  + B. + (aB). . + e... J i j ijk  (3-1)  for i = l , . . . . , r J 1,...«,s k l,....,n ^< #  where  Y  .  =  t h e k - t h o b s e r v a t i o n i n t h e i - t h a c l a s s and j-th 8 class;  y  = t h e o v e r a l l mean w i t h e q u a l s u b c l a s s numbers; = e f f e c t of the i - t h a c l a s s ;  Bj (aB)^j  = e f f e c t of the j - t h B c l a s s ; =  e f f e c t o f t h e i j - t h aB c l a s s a f t e r t h e average e f f e c t s o f a and B have been removed these a r e the i n d i v i d u a l i n t e r a c t i o n e f f e c t s expressed as d e v i a t i o n s from t h e mean u + a, + g.  i  e.., ij k  2 = random e r r o r s , assumed t o be N(0,a ).  The l i n e a r model (3-1) c a n be notation:  j;  expressed : i n  matrix  - 42  -  Y = Xb + e  (3-2)  where Y i s N x l v e c t o r of o b s e r v a t i o n s X i s an NxP  matrix  i s an  of random terms; e can be d e f i n e d  Nxl  of known v a l u e s  Y; b i s p x l v e c t o r of parameters;  ( i n most cases  O's  and  l ' s ) and  as  e = y - E(y).  (3-3)  The v e c t o r b i n Y  = Xb + e i s a  v e c t o r of parameters; i t i s  the v e c t o r of a l l elements of the model. b will  e  In the above model the  vector  have  b' = {u.o^.o^,... ,a ,3 ,8 ,... , 3 , a 6 , a 6 , . . . , a B , r  1  2  a 8 , a 3 , . •. > & s' ''' > a  2 1  as i t s elements.  2 2  2  s  a e  n  12  lg  i> ^ 2" ** ' ^ r s * a  r  r  I t i n c l u d e s the t e r m y , the terms r e p r e s e n t i n g  species  e f f e c t a,the terms r e p r e s e n t i n g F o r e s t Inventory Zone e f f e c t s 3, and r e p r e s e n t i n g i n t e r a c t i o n e f f e c t s between s p e i e s a and For r s p e c i e s and  i n v e n t o r y zones  s zones, i t can have as many as  p = l + r + s + rs  elements.  I f t h e r e are empty s u b c l a s s e s , p i s equal  p = l + r + s + r s - m  where m i s the number of empty  cells.  the terms  to  8-  - 43 -  The m a t r i x X i n (3-2) i s c a l l e d t h e i n c i d e n c e m a t r i x , o r more commonly, t h e d e s i g n m a t r i x , because t h e presence o f the O's and l ' s throughout i t s elements r e p r e s e n t i n g the i n c i d e n c e o f terms of the model among t h e o b s e r v a t i o n s .  3.2  Normal  Equation  The normal e q u a t i o n c o r r e s p o n d i n g + e can be d e r i v e d by the l e a s t  t o t h e model (3-2) Y = Xb  squares p r i n c i p l e s .  The expected  value  2 and v a r i a n c e o f the e v e c t o r a r e 0 and a I  ( I i s an i d e n t i t y m a t r i x ) ,  r e s p e c t i v e l y ; that i s , E(e) = 0  (3-4)  Var(e) = E  {e - E ( e ) }  {e - E ( e ) } *  = E(ee') =  The  a I.  least  (3-5)  2  squares e s t i m a t e  o f b i s d e r i v e d by m i n i m i z i n g  the sum o f squares o f the o b s e r v a t i o n s from t h e i r expected The  values.  e x p e c t a t i o n o f Eq. (3-2) equals  E(y) = E(Xb) + E ( e ) = Xb,  (3-6)  - 44 -  s i n c e E(e) = 0. The sum of squares o f the e v e c t o r i s as f o l l o w s ,  e'e = (Y - E ( y ) ) ' ( Y - E ( y ) ) = (Y - Xb) ' (Y - Xb) = Y'Y - 2b'X'Y + b'X'Xb.  (3-7)  Choosing as the l e a s t squares e s t i m a t e b t h a t v a l u e o f b which minimizes elements  e'e i n v o l v e s d i f f e r e n t i a t i n g e'e w i t h r e s p e c t t o the  o f b. E q u a t i n g  6(e'e)/6b  to zero and w r i t i n g the r e s u l t i n g  e q u a t i o n s i n terms o f b, the normal e q u a t i o n s  X'Xb = X'Y  (3-8)  are derived. The p r i n c i p l e used t o d e r i v e  t h e normal e q u a t i o n s f o r t h e  l e a s t squares a n a l y s i s i s i d e n t i c a l t o t h a t t o d e r i v e the normal equations i n m u l t i p l e r e g r e s s i o n a n a l y s i s . The d i f f e r e n c e between these two methods lies  i n the f a c t t h a t the elements  i n the X m a t r i x a r e e i t h e r  continuous  or d i s c r e t e c o n s t a n t s i n the r e g r e s s i o n a n a l y s i s w h i l e they a r e e i t h e r 1 o r 0 i n the l e a s t squares  analysis.  T a b l e 3-2 shows the l e a s t squares e q u a t i o n f o r the f o r e s t i n v e n t o r y d a t a c l a s s i f i e d by type group and f o r e s t i n v e n t o r y zones i n T a b l e 3-1.  I t can be seen from t h i s T a b l e 3-2 t h a t the r e s u l t i n g m a t r i x  of X'X i s symmetrical.  The d i a g o n a l elements  of the m a t r i x  indicate  the numbers o f o b s e r v a t i o n s c o n t r i b u t i n g to the e f f e c t b e i n g c o n s i d e r e d .  Table  3-1.  Western  hemlock i n v e n t o r y d a t a c l a s s i f i e d by s p e c i e s t y p e s and i n v e n t o r y z o n e s ( F . I . Z.) (Unit: cubic feet/acre/year)  F. I . Z  SPECIES a 1. '  1 NO. PLOT MEAN  8 58.43  TYPES  H+ F 2  H+C 3  H+B 4  H+S 5  H+hA 6  12 65. 91  7 81 .85  11 77.79  6 69. 73  2 39. 93  46 69. 24  SOBTOTAL  2  26 NO. PLOT MEAN 121.52  16 79.91  14 73. 35  18 109.73  2 89. 11  3 56. 46  79 98. 58  3  NO. PLOT MEAN  10 49.27  22 39.01  19 45. 16  3 54.48  1 80. 28  3 29. 00  58 43. 79  7 NO. PLOT MEAN  26 30. 39  17 22 .94  35 27. 9 1  4 17.82  5 42. 95  1 41.33  88 28. 23  'OTAL PLOT MEAN  70 70. 14  67 49.52  75 45. 80  36 85.1 5  14 63. 69  9 41.95  271 42. 95  R e m a r k s : H : p u r e ]tiemlock t ype; H+F: hemlock and f i r mixed t y p e H + C : hemlock and c e d a r mixed t y p e ; H+B: h e m l o c k and b a l s a m mixed t y p e ; H+S: hemlock and s p r u c e mixed t y p e ; H+HA: h e m l o c k and hardwood mixed t y p e .  Table 3-2. The least squares equations f c r i u l a t e d fcon the western healoci data  S? 1 S? 2 SP 3 -,1 " ' 7  57 ,,  67 ~  1*  3= 1= 9 6 79 e  26 10 26 12 16 •22  S? U 3  6  ,_ 7  3  SP 5 SP 6 ! 2 1 rz 2 ?Z 3 t ! I S211 SZ1 2 SZ13 SZ1« SZ21 SZ22 SZ23 SZ20 SZ31 SZ32 SZ33 SZ31 SZ41 SZ02 SZ43 \ ? " 03 8 26 10 26 12 16 22 17 7 14 19 35 11 18 3 « 26 10 26 8 26 10 26 12 16 22 17 " " 12 16 22 17 i " 19 35 ,„ io «35 9  6  7  7  36 3 10 26 26 8 26 1C 26  12 22 16 17  7 19 18 35  11 3 13 «  11  5 2 3 3 1  6 1 2 S  11 6 2 06  16 2 3  7S  3  3  1  a. 5 1  8  1 2  26  Ifi  7  .  12 16 22.  19 35 11 13 3  19 35 11 18 3  " 6  SZ»» SZ51 SZ52 SZS3 SZ50 SZ61 SZ62 SZ63 S Z 6 0 7C1C-8 6 2 1 5 2 3 3 1 15557.C 30 ,,,, , le3e.E3 306?.. 55 6 2 1 5 891.525 2 3 3 1 377.578 6 2 3155.15 2 3 7737.71 1 3 2535.80 5 1 2U56.35 567.sci 3155.eS 352.72.3 7 90.2 22 7 90.8 33 1275.50 858.258 365.507 572.565 1026.93 868.071 • 976.861 355.til f  4  6 2 1 5  2 1  S  2 3 3  71.2710 e16.385 178.210 50. 2 = 00 210.75s 79.6760 165.373 86.S960 1 S1.333C 0.100225E.07  2 3 3  1  1  Absorption processes Step - .+  +  +  +  +  --  + + + - + + +  - + + +  -  + + + - + +  + -  + + +  +  + + + - + + +  1 Step  -  - -  + + +  + +  + +  + + +  2 Remarks: S P l = s p e c i e s type 1; F Z l = f o r e s t i n v e n t o r y zone 1; and S Z l l = i n t e r a c t i o n term f o r SP1 and FZ1. Other symbols a r e s i m i l a r l y d e f i n e d .  . !  - 47 -  At  t h e r i g h t hand s i d e o f t h e l e a s t  squares e q u a t i o n s a r e p r o d u c t s  of XY, which a r e t o t a l s and s u b t o t a l s o f c l a s s e s and s u b c l a s s e s . The l a s t of  column o f t h e t a b l e i s t h e t o t a l unadjusted sum .  squares, t h a t i s X'Y. A simultaneous c o n s i d e r a t i o n of t h e l e a s t  i n T a b l e 3-2 w i l l produce unbiased l e a s t effects  3.3  . -  i n q u e s t i o n , which a r e f r e e from  Imposing  squares e q u a t i o n s  squares e s t i m a t e s b f o r t h e entanglement.  Restrictions  U n f o r t u n a t e l y , one cannot s o l v e t h e e q u a t i o n s f o r m u l a t e d above w i t h o u t f u r t h e r m a n i p u l a t i o n o f the m a t r i x , because i s not of f u l l  the matrix  itself  rank.  Examining  the c o e f f i c i e n t s  of t h e e q u a t i o n s i n T a b l e 3-2  r e v e a l s t h a t some e q u a t i o n s a r e l i n e a r combination o f the o t h e r s .  The  g e n e r a l mean U, f o r example, i s a l i n e a r combination o f the e q u a t i o n s for species effects,  or a c l a s s ;  i t a l s o i s a l i n e a r combination f o r  growth zone e f f e c t s , o r 3 c l a s s .  A g a i n the e q u a t i o n f o r any one i n  the s p e c i e s o r growth zone e f f e c t  i s a l s o a l i n e a r combination of the  interaction  e f f e c t e q u a t i o n s t h a t c o n t a i n the p a r t i c u l a r  species 3 e f f e c t  effect.  The  i n T a b l e 3-2, f o r example, i s a l i n e a r combination o f  the e q u a t i o n SZ31, SZ32, SZ33, and SZ34. In f a c t , t h e r e a r e p l e a s t but a c t u a l l y  squares e q u a t i o n s i n t h e system,  o n l y q e q u a t i o n s a r e independent,  that i s ,  q = 1 + ( r - 1) + (s - 1) + ( r - 1) (s - 1) - m = r s - m  - 48 -  where m,  as p r e v i o u s l y d e f i n e d , i s the number of empty c e l l s .  T a b l e 3-2,  In  m e q u a l s t o 0. A unique s o l u t i o n  t o the l e a s t squares e q u a t i o n s can be  o b t a i n e d o n l y i f they a r e reduced i n number to the number of of freedom, t h a t i s , q.  degrees  A l t h o u g h numerous r e s t r i c t i o n s can be  imposed  i n o r d e r t o a c c o m p l i s h t h i s , the r e s t r i c t i o n t h a t the c o n s t a n t s f o r the main e f f e c t s ( a 8 ) . . sum  sum  to zero w i t h i n a s e t and t h a t the c o n s t a n t s f o r the  to zero over each row and over each column i s the most  satisfactory  (Harvey, 1960).  The l i n e a r mathematical model (3-1)  suggests t h i s s e t o f r e s t r i c t i o n s s i n c e the e f f e c t s o f a^,  itself (aB)^  8..»  and t h e e a r e expressed as d e v i a t i o n s from the mean.  3.4  Absorption Process  The method of o b t a i n i n g e s t i m a t e s o f the e f f e c t s from the mean i s t o impose the r e s t r i c t i o n on the l e a s t  as d e v i a t i o n s  squares e q u a t i o n s  E a. =0, E 8. =0, E(aB).. = E(aB).. =0. Because of these i j i j r e s t r i c t i o n s , the e f f e c t of a l e v e l w i t h i n a c l a s s can be d e r i v e d from the that  1  J  1 3  1 J  e f f e c t s of the r e s t of the l e v e l s w i t h i n t h i s c l a s s and thus e l i m i n a t e d .  The  same p r i n c i p l e a p p l i e s . t o e q u a t i o n s f o r i n t e r a c t i o n e f f e c t s as w e l l as main e f f e c t s . In p r a c t i c e , of  the a b s o r p t i o n p r o c e s s i s c a r r i e d  s u b t r a c t i o n s and a d d i t i o n s w i t h i n the c o e f f i c i e n t m a t r i x and  r i g h t hand s i d e members. of the a^,  a.'s.  say a^,  When t h i s i s done the c o e f f i c i e n t s  must be s u b t r a c t e d f o r the c o e f f i c i e n t s  The s u b t r a c t i o n s are r e q u i r e d w i t h i n the  i  E(aB)..« j  out by a number  1 J  After  of  J  ±  one  o f the o t h e r  a., B.5 E(aB).. i  the  i l  and  these changes have been made by column the same procedure  - 49 -  i s f o l l o w e d by row w i t h the m o d i f i e d c o e f f i c i e n t s f o r the  (aB)^  e q u a t i o n s and f o r the r i g h t hand s i d e members. In T a b l e 3-2, the bottom p a r t , shows a p r a c t i c a l example o f the  t e c h n i q u e o f the a b s o r p t i o n p r o c e s s .  main e f f e c t s and primary i n t e r a c t i o n are needed.  S i n c e the model i n v o l v e s  e f f e c t s , two a b s o r p t i o n s t e p s  I n Step 1, e q u a t i o n s f o r SP1 and FZ1 e f f e c t s a r e  t o be absorbed and e l i m i n a t e d as i n d i c a t e d  A  6  s a t i s f y the r e s t r i c t i o n s  by a "-" s i g n .  4  selected  T h i s i s to  A  ^  E SP. = 0 and E FZ. = 0. i-1 3=1  Because SP1 and  3  FZ1 a r e e l e c t e d  t o be absorbed, t h e i r i n t e r a c t i o n s  a l s o have t o absorbed  by the e q u a t i o n s f o r the e f f e c t s w i t h i n the c l a s s e s .  The n e g a t i v e  s i g n s under t h e e s t i m a t e SZ11, SZ21, SZ31, SZ41, SZ51, SZ61, SZ12, SZ13, and  SZ14 i n Steps 1 and 2 of T a b l e 3-2 demonstrate the i m p o s i t i o n of  the  restrictions  E  (<xB) . . 1 3 i  . = E (aB) . . =  The a c t u a l  • 3  13  0  a b s o r p t i o n procedures a r e c a r r i e d out by sub-  t r a c t i n g the c o e f f i c i e n t s of the columns w i t h "-" s i g n of the columns w i t h "+" s i g n w i t h i n a c l a s s .  from the c o e f f i c i e n t s  F o r the s p e c i e s  effects,  f o r example, the c o e f f i c i e n t s i n column 2 a r e s u b t r a c t e d and then added to those i n columns 3 t o 7; the c o e f f i c i e n t s i n column 8 a r e s u b t r a c t e d and then added t o those i n 9, 10, and 11; and column 12 from columns 13, 14 and 15, e t c . i s done by s u b t r a c t i n g  The second step o f the a b s o r p t i o n p r o c e s s  t h e c o e f f i c i e n t s i n column f o r t h e e s t i m a t e  SZ12 and then added t o columns f o r the e s t i m a t e s SZ22, SZ32, SZ42, SZ52, and SZ62. /v SZ13 and SZ14.  Similarly,  t h e s u b t r a c t i o n s a r e c a r r i e d out f o r columns  - 50  -  There i s no r e s t r i c t i o n on s e l e c t i n g the to be absorbed  and subsequently e l i m i n a t e d .  within a class  However, i t has to be  kept i n mind that e f f e c t s w i t h empty c e l l s should not be s e l e c t e d . A reduced c o e f f i c i e n t m a t r i x i s thus o b t a i n e d a f t e r the a d d i t i o n and s u b t r a c t i o n procedures on column and row and the columns and rows w i t h n e g a t i v e s i g n i n Steps 1 and absorption process.  completing eliminating  2 of the  The f a c t t h a t the o f f - d i a g o n a l elements of reduced  c o e f f i c i e n t m a t r i x must be symmetrical about the main d i a g o n a l p r o v i d e s a check f o r computational T a b l e 3-3  correctness.  shows the reduced  c o e f f i c i e n t m a t r i x d e r i v e d from  the l e a s t squares e q u a t i o n s i n T a b l e 3-2 p r e s c r i b e d on the bottom of T a b l e 3-2.  u s i n g the a b s o r p t i o n p r o c e s s e s I t shows o n l y the t r i a n g u l a r  elements. I f the numbers of o b s e r v a t i o n s i n s u b c l a s s e s a r e a l l e q u a l , the o f f - d i a g o n a l elements i n the reduced all  be  z e r o ; i n o t h e r words, the e x p e r i m e n t a l d a t a are o r t h o g o n a l .  3.5  E s t i m a t i o n of  Constants  From the reduced unique  s e t of the l e a s t squares e q u a t i o n s , a  s o l u t i o n f o r the e f f e c t s can be r e a d i l y d e r i v e d .  employed t o s o l v e the simultaneous most  c o e f f i c i e n t matrix w i l l  satisfactory.  Of the methods  e q u a t i o n s , the m a t r i x i n v e r s i o n i s  Table 3-3. The reduced s e t of l e a s t squares e q u a t i o n s f o r the western  1EAN SP 2 SP 3 SP 4 SP 5 SP 6 FZ 2 271 -3 137 70 145 5 70 106 70 -34 84 70 70 70 -56 79 70 70 70 70 -61 125 33 -14 -11 -11 -22 -17 -1 46 -7 10 -10 8 12 46 10 -25 -19 -19 42 -13 13 18 -6 18 18 -14 22 . 2 4 • 2 2 2 12 8 18 4 18 18 18 23 -13 19 -13 18 18 25 18 -1 1 2 -1 2 2 14 2 10 18 18 -1 18 18 ' 46 10 18 18 -5 25 18 18 - 11 2 3 2 -6 2 2 -10 18 18 3 11 18 18 -25 14 / 18 -26 18 18 18 -22 2 -2 -3 2 2 2 -7 18 -2 17 18 18 18 -19 19 -29 18 18 18 18 -17 -6 3 2 2 2 2 -1 -6 18 . 17 18 18 18 -19  Remarks:  SZ42 SZ43 SZ44 SZ52 SZ53 SZ54  3 F2 4 SZ22 SZ23 SZ24 SZ32 SZ33  104 46 4 16 4 -1 8 -1 3 -4 3 -2 -11 -2 -6 -13 -6  134 4 4 -5 -1 -1  a  3 3 -19 -2 -2 -23 -6 -6 -31  62 20 20 34 8 8 34 8 8 34 8 8 34  e  8  52 20 8 18 8 8 18 8 8 18 8 8 18 8  63 8 55 15 8 15 34 8 • 34 8 8 34 8 8 34 8 8 34 8 8 34 8 8 e 34  44 15 8 18 8 8 18 8 8 18 8  76 8 8 34 8 8 34 8 . 8 34  Symbols SP2. FZ2, and SZ22 etc. are defined i n Table 3-2.  63 19 19 34 8 8 34 8 3  32 19 8 13 8 8 18 8  49 8 8 34 8 8 34  42 14 14 34 8 8  25 14 8 18 8  45 8 8 34  SZ63 SZ64 VOLtf«E 15997.0 - 1592. 17 -1474.97 -1844.24 -4013. 17 -4532. 22 4602.56 -645.349 -70C.800 -2204. 39 42.0930 -723.797 -2233.CE 259.784 81.0750 -1572.49 -717.529 -1107. 19 -2932. 23 -363.427 -526.452 -2602. 55 39 -18.2020 23 10 37 -361. 364 10 10 0.144229E+C7  Ui  - 52 -  Equation  (3-8) suggests  t h a t the s o l u t i o n o f e s t i m a t e v e c t o r  b is  b = (X'X)  1  (3-9)  X'Y  which i s a w e l l r e c o g n i z e d formula f o r d e r i v i n g r e g r e s s i o n c o e f f i c i e n t s in regression analysis.  In E q u a t i o n  (3-9), X'X i s the c o e f f i c i e n t  matrix,  the t r i a n g u l a r p o r t i o n o f T a b l e 3-3 and X'Y the r i g h t hand s i d e v e c t o r on T a b l e 3-3. The unique s o l u t i o n f o r b v e c t o r  i s r e a d i l y o b t a i n e d by  m u l t i p l y i n g X'Y , t h e r i g h t hand s i d e member, on t h e l e f t by the i n v e r s e of X'X m a t r i x . and  The i n v e r s e o f X'X m a t r i x i s shown i n T a b l e 3-4  t h e e s t i m a t e d b v e c t o r i n T a b l e 3-5.  The complete s e t o f e s t i m a t e d  c o e f f i c i e n t s , as shown i n T a b l e 3-6 i s d e r i v e d by r e v e r s i n g t h e r e s t r i c t i o n s on t h e e f f e c t s p r e v i o u s l y imposed.  The e s t i m a t e o f SP1,  f o r example, i s  SP1 = - E SP. = 6.3912. i=2  The i n v e r s e further explanation. the m a t r i x r e f l e c t  c o v a r i a n c e m a t r i x shown i n T a b l e 3-4 needs The magnitudes o f the o f f - d i a g o n a l elements i n  t h e confounding  among e f f e c t s b e i n g c o n s i d e r e d .  In t h e s p e c i a l case t h a t a l l numbers o f o b s e r v a t i o n i n s u b c l a s s e s a r e e q u a l , t h e o f f - d i a g o n a l elements w i l l be z e r o , then t h e t r a d i t i o n a l a n a l y s i s o f v a r i a n c e can be used.  Table  R O  1  3-4.  Hatrlx  Inverse to the complete vnrlance-covarlance matrix  for  western  hemlock  data.  KEAN  C.97407ZE-02 R O 3 SP7 -C.7I 2539E-C2 ROV. 4 SP 3 -0.666271E-C2 ROW ; S P 4  0.2016206-01  C.4057386-02 0.220)276-01  -0.213e6«E-C2 -C.4666706-03 -0.939330E-0.3 0.4C149CE-01 6SP 5 / 0.97G372E-02 -0.1230916-01 -0.1278176-01 -0.I73CS86-0I 0.8791856-01 ROW 7 SP 6 0 . 12E287E-01 -0.I54341E -01 -0.159067E -01 -0.2C43C66-01 -0.322732E -01 ROW  RCW 9 f? ? -0.237C73E-C2 0.2369576 -C2 0.2268916-02 -0.291652E-02 ROW 10 FZ 3 c.32CE95F-02 -0.3920346-02 -C.4C9396E-02 O.307787E-02 ROW II F M 0. 12C273E-C2 -0.1357086 -02 -0.3090266-02 0.1611666-02 ROW 17 SZ22 a.2365576-02 -0.2375376-C2 -0.2267136-C2 0.29176(6-02 0.5?7353E-01 ROV If S223 - 0 . 3920346-02 0.3634016 -03 0.4805376-02 -0.2366496-02 - 0 . 1815C1E-01 0.6121296 -01 ROW 19 SZ24 - 0 . 1357CEE-02 0.5853416 -03 0.3244616-02 -0.1457336-02 - 0 . 1F372CE-CI -0.2111086 -01 0.6165686-01 RCW 2 1 J73 2 0.726R91E-C2 -0.226775E -02 -0.277799E-02 0.3018346-02 0 . 7t3f.c6E-C2 -0.6595006 -02 -0.5034246-02 0.6060236-01 pnw 2 2 S733 - 0 . 4C935BE-02 0.4805376 -02 -0.33I14E6-03 -0.2192856-02 - o . 6595CCE-C2 0.2I7E29F -CI -C. 1210746-01 -0.1894366- -01 RCW 23 SZ34 - 0 . 309076E-C2 0.3244616 -02 -0.634 7406-02 0.2756556-03 - 0 . 503424E-CZ -0.121C74E -01 0.1866146-01 -0.1292746 -01 RCW ?'. S742 - 0 . 7916 57F-C2 0.2917686 -02 0.3018346-02 -0.235I97E -01 o . 443515F-C2 -0.0452526 -04 -C.9934826 -03 0.3218636 -02 P O  71 7F-C2 S743 -0.736<49F -02 0 . 30776 -0. B45752F-04 -0.613258F -02 " O 7 7 S74 4 0 . 16 1 1 BOE-0? -0.145753F -02 -0. 9 ' » 3 ' i n ? E - C 3 0.429C69E -02 RCW 75 S752 0. 375<:ft2E-0? -0.375P45E -02 -0 . 0. 343694E -01 c . 2f E<;25 3C S7! 3 0 . 190133F-01 -0.183019E -01 c . 343f.94E-Cl -0.735309E -01 - c . 1B2P01 C.4467M ROW 31 5 254 - 0 . 12313PE-01 0.1246e2E -CI 0 . 359937F-0? 0.1B 1477E -01 - 0 . 474E16F-CI -0.136375 P O 33 S762 - 0 . 63C5e3F-C2 0.631C59F--02 - 0 . 336FC2F-0I -0.3477P3E -02 Bfc977cE-Cl C.376649E -01 -c. RCW 34 SJE3 - 0 . 11PP5SE-01 0. 1260C9F-01 - 0 . 3'.7783f-C? -0.211004E-01 c.37<i e<.9E-C 1-0.117465 35 S764 ROW 0 . 17B945E-01 -O.177401E--01 0 . 2tt<: 32E-C1 0.205733F- - CI 0 . 34l35«r-Cl C.491B93F--CI  -0.2192856 -C2 0.4290696 -02  0.1C0018  0.3755626 -02 -0.630983E -02  0.2448076 -01  0.1901336 -01 -0.1188956 -01 -0.1057896 -01  0.356401E- 01  -0.123138E-01  0.1789456 -01 -0.8572726 -02 -0.141524E- 01  0.316776F -01  -0.3736456-02  0.631099E -02 -0.1666706 -01  0.868617E-•02 0.868617E-  O.612290E -07  0.8686176- -02 -0.292469E- 01  0.124128E -01  -0.IR3019E  -01  0.126009E -01  0.1246826 -01 -0.1T740IE -01 -0.3657806  -02  0.6411656-02  -0.1812826 -01 0.6545606 -01  0.1277456 -01  0.1420146 -01 -0.160070E -01 -0.1537426 -01 0.534635E -01  0.612290E -02 -0.1545036 -01  0.8487786- 02  0.748406E -02  0.84877BE -02 -0.281761E- 01  0.138469E -01  0.740406E -07  0.152763E -0 2 O . l I5971E -01 -0.1224906 -01 O . l 138616 -0 3 -0.2 35464E -02 0.734075E -01  0.2B3 563E -01 -0.253CC1F -01 0.1 I3861F -03 -0.720375E -0?  0.124128E- 01 -O.241203F -01  0.13B46TE-•01 -0.76U.B 7E -01 0.1 977306- 02  0.344330F -07  0.5602686 -02 0.197730E -02 -0.Z60224F-•03 -0.755I09F -07 0.2B5654E -02 -0.449855E -0 1 0.177159  0.275655E -C3 0.12461 IE -01 -0.431507E -02 -0.2354646 -02  0.949523E -02 -0.207091F -01 0.344330E -02 -0.755109E-•0? - 0 . 3 197776 -07 0.2B5654E -02 -0.226674C -02 -0.290904E -01 -0.B09664E- 01 0.145369  0.1527636 -02 -C.3«578C6 -C2 0.359932E-02 -0.4566086 -01  0.3I84B3E -02 0.34567BE -01  0.492094E -02 0 . 36f.304E -01 -0. 324 766E-•0 1 -0.1 149-iCE -C? 0.223816F. -02 -0.48862 IE -0 1 0.4107R3E- 01 0.677B97E -07  -0.1812826-01 -O.253001E-01 0 .1814776 -01  0.1420146-01 -0.1199086 -01 C.176072  0.920578E -01 -0.103327E -01 -0.324766E -01 0.671377E-•01 -0.164037E -01 0.167086E -01 0.4107B3E -01 - 0 . 10251 B 0.331066E -01 0.3456786 -01 -0.746017E -01 0.9499236 -02 -0.432417E -01 -0.67B338E -02 -0.114950E -0? -0.164032E- 01 0.44835OE -02 0.167C86E -01 -0.994246E -02 0.627892E -02 0.33I066E- •01 -0.379139E -01 0.2238I6E -02  0.6411656-02 0.1 I597IF-01 C.26A632E-01 -0.348969F-01 C.34|35«6-CI 0.22567C  0.4920546 -02 -0.370929E -01 0.75B665F -01 -0.3279456 -02 0.255020F -01 -0.7809B2E--01  C.127745E-01 0. 560266E-02 - 0 . 103327E--01 -0.315I3JE -01 0.205737F-01 -0.327945E-02 -0.221711E -01 0.191392E -01 C.4938936-01 -0.314123E-01 0.237C29 -O.I6007C6--01 -C.ei78256-•01 -C.l 1C3B6  -0.20709IF-01  0.25502CE-01 14051 7  -0.  0.537061E- 02 -0.744 1 3 E-01 0.323IO3E- 02 0.79547 BE -01  0.537061E- -02 0. 147077E- 01 -O.I 8833 7C -01 0.323103E- -02 -0.50J870E- 01 0.355377E -01  -0.67833BE-O2 0. 775916E--01 -0.244 1 34E-01 -0.1B8337F- 01 0.747757E- -01 0.I91392F-01 -0.797341F -01 o.2954?nn0.355377E- 0 1 - 0 . 1 027 1 1 -01 -C.I46C9 7 0.4557 39  Table  3- 5. E s t i m a t e d data  c o n s t a n t s f o r w e s t e r n hemlock mean a n n u a l ( U n i t : c u b i c f e e t / a c r e year)  SPECIES MEAN 58.51C8  SP 2 •6. 56956  F.I.Z.  qcowth  TYPES  SP 3 -1.44166  SP 4  SP 5  SP 6  6. 44312  1 2. 0059  -16.8290  INTERACTIONS  2  29.8350  1.86749  -13.5517  14.9447  -11.2467  -15.0592  3  -8. 9767  •3. 95092  -2. 93073  -1. 4992  18.7401  -3.70639  7 -27.9539  •1.05164  -1.20493 -19.1815  0.38802  27.6050  Remarks: SP 2: hemlock a n l f i r mixed; SP 3:hemlock and c e d a r mixed; SP 4: hemlock and balsam mixed; SP 5: h e m l o c k and s p r u c e m i x e i ; SP 6: hemlock and hardwood mixed.  Table  3-6. C o m p l e t e s e t o f e s t i m a t e d c o n s t a n t s f o r w e s t e r n mean a n n u a l qrowth d a t a (Unit; cubic feet/acre/year) SPECIES  MEAN  SP 1  58.5108  6.3912  TYPES  SP 2  SP 3  SP 4  -6.5696  -1.4417  6.4431  F.I.Z. 1  hemlock  SP 5  SP 6  12.0059  -16.8290  INTERACTIONS  7.0957 -13.5726  6.8701  17.6874  5.7359  -7.8814  -8.8394  2  29.8350  26.7804  -1.8675  -13.5517  14.9447  -11.2467  -15.0592  3  -8.9768  -6.6529  -3.9509  -2.9307  -1.4992  18.7401  -3.7064  7-27.9539  -6.5549  -1.0514  -1.2049 -19.1815  0.3880  27.6050  Remarks: SP 1: pure hemlock  type;  other  symbols see remarks i n T a b l e  3-5  - 56 -  3.6  P a r t i t i o n i n g the T o t a l Sum of Squares  The t o t a l u n a d j u s t e d sum of squares e q u a l YY and the reduction  i n t h e sum of squares due t o f i t t i n g model (3-1) a r e  d e s i g n a t e d as R(fi, a ,  B> aB) > where y, a ,  B> aB a r e the b v e c t o r  as i n t h e p r e v i o u s s e c t i o n and, r e s p e c t i v e l y , the e s t i m a t e s of S\  A  y, a ,  B> aB i n the model. R(y, a ,  R(y, a ,  3, aB)  = yY.. +  ^  3» aB)  i s computed as f o l l o w s ,  £ a . Y . . + E3.Y.. x j 1  This formula i s equivalent  1  2  2  + E (aB)..Y.. ij 1 J  (3-10)  1 3  t o t h a t i n the c a l c u l a t i o n o f  sum o f squares due t o r e g r e s s i o n i n r e g r e s s i o n a n a l y s i s .  I t can  be shown t h a t the Y's i n Eq. (3-10) a r e the r i g h t hand s i d e members of the reduced s e t of l e a s t squares e q u a t i o n s . The sum o f squares f o r e r r o r i s computed by  SS  error  =  ,Y'Y  - R(y, a ,  £ , OB)  (3-11)  which i s the d i f f e r e n c e between the t o t a l u n a d j u s t e d sum of squares and the sum o f squares due t o f i t t i n g the model. Two methods may be used t o compute the sum of squares f o r each source o f v a r i a t i o n . in reduction  differences  i n sums o f squares due t o f i t t i n g d i f f e r e n t models.  The sum of squares f o r a ,  SS  An i n d i r e c t procedure i n v o l v e s  a  = R(y, a ,  f o r instance,  3, aB)  - R(y,  i s computed by  aB).  (3-12)  - 57 -  S i m i l a r l y , t h e sum o f squares due t o 8 and aB  SS  = R (y,  0  a,  8, aB) - R (y,  a,aB)  (3-13)  and  A  A  S S = = R (y, a, ag  A  A  6,  a£  - R (y,  a,8)  (3-14)  In a p p l i e d r e g r e s s i o n a n a l y s i s t e r m i n o l o g y ,  the sum o f squares  f o r each source o f v a r i a t i o n i n v o l v e s computing t h e d i f f e r e n c e o f sums ^  /\  of squares between a maximum model, f o r i n s t a n c e , R(y, a, reduced  model, R(y, B,  model except The  aB)  A  8J aB)  and a  which i n c l u d e s a l l v a r i a b l e s i n t h e maximum  t h e one classa,whose sum o f squares i s b e i n g  considered.  i n d i r e c t method , i n v o l v i n g f i t t i n g v a r i o u s models,  t h e r e f o r e , i s t e d i o u s and time consuming.  The sum o f squares f o r each  source o f v a r i a t i o n may a l s o be computed by a d i r e c t method which employs the segments o f t h e m a t r i x the c o n s t a n t The  i n v e r s e t o t h e v a r i a n c e - c o v a r i a n c e m a t r i x and  estimated. d i r e c t method computes t h e sums o f squares as f o l l o w s ,  SS = b ' Z b ,  (3-15)  _ 1  where b' i s a row v e c t o r o f t h e c o n s t a n t  estimates  f o r a given set;  i s t h e i n v e r s e o f t h e segment o f t h e i n v e r s e of t h e v a r i a n c e - c o v a r i a n c e matrix  corresponding,  by row and column, t o t h i s s e t o f c o n s t a n t s ; and  - 58 -  b i s a column v e c t o r of the s e t of c o n s t a n t s .  The  sum  of squares  o b t a i n e d i n t h i s manner i s e q u a l to the r e d u c t i o n i n the sum  of  squares due  to f i t t i n g  a l l c o n s t a n t s minus the r e d u c t i o n i n sum  squares due  to f i t t i n g  a l l c o n s t a n t s except  In the g i v e n example, the sum i s computed by the constant 3-5  estimates  m u l t i p l y i n g the m a t r i x  column and  row,  of squares f o r s p e c i e s  f o r SP2,  SP3,  2 to 7 i n T a b l e 3-4.  The  i n Table  of squares f o r  respectively.  3-7.  Hypothesis  l e a s t squares mean f o r c l a s s of a  and y +  types  the complete a n a l y s i s of v a r i a n c e t a b l e  L e a s t Squares Means, V a r i a n c e s , a n d  The  SP6  computed sum  the g i v e n i n v e n t o r y data a r e shown i n T a b l e  3.7  considered.  i n v e r s e of the submatrix w i t h elements i n ,  each source of v a r i a t i o n and for  the s e t b e i n g  of  a n  d  Tests  c l a s s e s 3 are y  The v a r i a n c e f o r y , y +  a r e computed from the a p p r o p r i a t e i n v e r s e elements and  a n  d y +  estimate  +  8..  of  2 a  from the e r r o r l i n e of the a n a l y s i s of v a r i a n c e . e  The v a r i a n c e f o r SP2,  S  2 0  u+sp2  where  = (c  1 1  + c  2  2  f o r i n s t a n c e , i s computed  + 2c 1 2 )  as  (3-16)  2 a  e  i s the i j " t h element of the reduced  (X'X)  Table  3-7.  Source o f Variation  Species  D.F.  type  F. I.Z.  Interactions Error  Analysis of variance table annual growth data  Mean Squares  5  1853.5  3  16509.0  15  1761. 1  247  * S i g n i f i c a n t a t 5% l e v e l . * * S i g n i f i c a n t a t 1% l e v e l .  917.46  f o r western  F-value  2. 02  hemlock  mean  Tabulated F-value (5% l e v e l )  2. 24  17.99**  2. 63  1. 92*  1. 70  - 60 -  If the i n t e r a c t i o n i n t h e aB  i s more i n t e r e s t e d means.  s u b c l a s s means r a t h e r than t h e c l a s s  The l e a s t squares s u b c l a s s mean i s  = y + a. + "3. + (aB).. i 3 13  aB..  ij  and  e f f e c t s a r e s i g n i f i c a n t , the i n v e s t i g a t o r  (3-17)  t h e v a r i a n c e may be computed from the i n v e r s e m a t r i x and as f o l l o w s :  S%  = { C  aB±j  + C i i + C j j + C  W  a  yB.  2C  2C j 3  The  a  + 2c  ( a 3 )  6  u(aB)..  ij  } a  B  +  2c  a  a.B.  ij  3  +  a  6  ij  + 2C  a.(aB)..  2c  U a  i +  +  (3-18)  2 &  l e a s t squares means f o r these e f f e c t s b e i n g absorbed by  o t h e r e f f e c t s a r e computed as Eq. (3-19) i f the complete s e t o f e s t i m a t e c o e f f i c i e n t s , as i n T a b l e 3-6, i s a v a i l a b l e . by  r e c o g n i z i n g the means as l i n e a r combinations o f t h e absorbent  I f , f o r instance,  y + a  and  The v a r i a n c e s a r e d e r i v e d  n  the a- e f f e c t has been absorbed, t h e c l a s s mean i s  A ^ y  A A + a - y  A  6  - E a., 1=2  (3-19)  v a r i a n c e f o r t h e c l a s s mean i s  g  2 u  _  =  h  x  l  effects.  {  c  yy  +  E  6 ^ . a ._ i=2  2  E  c  6 ya. _ i=2  2  E  c  6 a.a  j }  ( 3  _  2 Q )  - 61 -  S i m i l a r l y , t h e l e a s t squares means and v a r i a n c e s f o r s u b c l a s s e s b e i n g absorbed can a l s o be d e r i v e d .  L e t 0^C_ = a  2  ( C ^ ) (q x q)  denote the c o v a r i a n c e m a t r i x o f b (q x 1 ) , where b i s the reduced vector of estimators.  The absorbed e f f e c t s can be expressed a s ,  say, y = c'b and z = d'b, where c and d a r e (q x 1) v e c t o r s . present  I n the  s i t u a t i o n c and d have components -1 and 0.  q  Var(y) = O  E  (c'C c) = 0  E  i=l j=l  i i2  H  =o  C V  E 1=1  + 21  E  C^c.c. i J  C  1 3  c.C i J  (3-21)  l^i<j=q  1  S i m i l a r l y f o r Var(z),  Cov(y,z)  a ( c ' C d) = a 2  =  a  q q Z E C c.d i 3 i=l j = l 1 J  2  q .. . E C c.d. i=l 1:L  1  1  +  E E l=i<j=q  C (c.d. 1 J  1  2  + c.d.) 3  1  (3-22)  I f t h e assumptions f o r a n a l y s i s a r e met, t h a t i s , data a r e n o r m a l l y - d i s t r i b u t e d and e q u a l l y - d i s p e r s e d , t h e v a r i a n c e - c o v a r i a n c e m a t r i x o f T a b l e 3-3 p r o v i d e s a handy way f o r v a r i o u s h y p o t h e s i s M u l t i p l e range tests can a l s o be c a r r i e d out f o r t h e l e a s t means (Kramer, 1956, 1957).  tests.  squares  - 62 -  3.8  Computer Program  The  l e a s t squares t e c h n i q u e i s v e r y v e r s a t i l e ;  a p p l y t o d a t a w i t h e q u a l f r e q u e n c i e s as w e l l as unequal subclasses.  i t can frequencies i n  As d e s c r i b e d i n p r e v i o u s s e c t i o n s , i t a n a l y z e s  a l l kinds o f data s t r u c t u r e s :  b a l a n c e d , unbalanced,  practically  and d a t a w i t h  empty c e l l s i n some s u b c l a s s e s . Computer programs which employ t h e l e a s t squares to a n a l y s i s o f v a r i a n c e can be found i n some s t a t i s t i c a l  principle  computing  packages such as B i o m e d i c a l Computer Programs Package (BMDP) (Dixon, 1971). A  severe r e s t r i c t i o n f o r u s i n g the e x i s t i n g l e a s t squares  analysis  programs i s t h a t they a r e i n c a p a b l e o f a n a l y z i n g d a t a w i t h empty  cells  i n s u b c l a s s e s when i n t e r a c t i o n s must be i n c l u d e d i n t h e model. A computer program, i n F o r t r a n language, m u l t i p l e c l a s s i f i c a t i o n unbalanced  data  (unequal and without  i n some s u b c l a s s e s ) f o l l o w i n g t h e procedures developed  by t h e w r i t e r .  to analyze generalized observations  d e s c r i b e d above has been  The a l g o r i t h m t o compute the e s t i m a t e d  c o n s t a n t s and the sum o f squares  f o r a source o f v a r i a t i o n i n t h e program  i s e s s e n t i a l l y s i m i l a r t o t h a t o f t h e g e n e r a l l i n e a r h y p o t h e s i s program of t h e B i o m e d i c a l Computer Programs Package ; however, i t d i f f e r s from the l a t t e r i n t h e f o r m u l a t i o n o f t h e i n c i d e n c e m a t r i x  (design matrix).  T a b l e 3-8 p r e s e n t s two i n c i d e n c e m a t r i c e s f o r t h e main f a c t s i l l u s t r a t e d i n t h i s Chapter.  Two main f a c t o r s a r e c o n s i d e r e d :  species  types and growth zones. As shown i n T a b l e 3-8, t h e BMDP program uses l ' s and O's t o i n d i c a t e the presence  and absence o f t h e f i r s t  5 effects  3-8.  Table  C o m p a r i s o n o f t h e i n c i d e n c e m a t r i x between t h e proqram and BMDP g e n e r a l l i n e a r h y p o t h e s i s proqram MAIN  I AN'G  SP2  SP3  SP4  SP5  A  A  SP6  FZ1  1  1  0  0  0  0  0  1  0  1  0  0  0  1  0  0  1  0  1  0  0  0  1  0  0  0  1  A  A  A  A  A  A  A  FZ2  FZ3  1  0  0  0  0  0  1  0  0  0  0  0  0  1  0  1  0  0  0  0  0  1  0  0  1  0  1  0  0  0  0  0  0  0  1  0  1  0  0  1  0  0  0  0  1  0  0  1  0  1  0  0  0  0  1  0  1  0  0  1  0  0  0  0  1  1  0  0  0  1  0  -1  -1  1  0  0  0  0  1  1  0  0  1  0  1  0  1  BMDP  FACTORS  SP 1  MEAN  A  1  Remarks:  -1  -1  A  A  SP 1,SP2 A  A  -1  A  -1  A  A  ,SP2, SP4,SP5, and  A  ,  A  FZ1 ,FZ2 ,FZ3, and FZ4 a r e  -1  FZ  -  A SP6 a r e s p e c i e s t y p e s ; Forest Inventory  Zones  - 64 -  of t h e s p e c i e s type f a c t o r 6th e f f e c t  (e.g. SP6).  and  to i n d i c a t e  t h e presence o f t h e  Similarly,  i t uses l ' s and O's f o r t h e f i r s t  3 e f f e c t s i n t h e z o n a l f a c t o r and  f o r t h e presence o f t h e 4 t h  zonal e f f e c t .  I f interactions  between these two main f a c t o r s a r e  t o be i n c l u d e d , t h e c o e f f i c i e n t s a r e computed from these two main factors.  The c o e f f i c i e n t s f o r t h e i n t e r a c t i o n between SP1 and FZ1, f o r  example, are the product of t h e c o e f f i c i e n t s i n SP1 and FZ1 columns. In s h o r t , t h e BMDP program does t h e a b s o r p t i o n p r o c e s s e s , s-1 r-1 t h a t i s , a = - £ a. and 8 = £ 8.> i n t h e course of f o r m u l a t i n g t h e s . , I r • i J i=l 3=1 incidence matrix  (X).  The l a s t e f f e c t i n a main c l a s s thus i s absorbed  and e l i m i n a t e d .  The product X'X  formed from t h e i n c i d e n c e m a t r i x X  i s a reduced m a t r i x e q u i v a l e n t t o t h a t shown i n T a b l e 3-3. A d m i t t e d l y , the procedure which combines t h e a b s o r p t i o n processes with the formation of the incidence matrix e f f e c t i v e l y the computational complex.  However, i f t h e r e i s an empty c e l l i n t h e  s u b c l a s s and t h e i n t e r a c t i o n s the procedure  fails.  a r e needed t o be c o n s i d e r e d i n the model,  The BMDP program assumes t h a t the number of degrees  freedom f o r the primary i n t e r a c t i o n s o n l y i f o b s e r v a t i o n s occur are empty c e l l s , (r-1)  reduces  i s (s - 1) ( r - 1) which i s t r u e  i na l l cells.  the number o f degrees  I n t h e cases where t h e r e  o f freedom equals t o (s - 1)  - m, where m i s the number o f empty  cells.  The program a s s i g n s l ' s and O's i n t h e i n c i d e n c e m a t r i x t o indicate  the presence and absence o f an e f f e c t i n a y i e l d  ( T a b l e 3-8).  Once t h e l e a s t squares equations  variable  (matrix) i s formed  from the i n c i d e n c e m a t r i x , a b s o r p t i o n p r o c e s s e s a p p r o p r i a t e t o t h e  - 65 -  the e f f e c t s c o n s i d e r e d a r e s e l e c t e d t o reduce the m a t r i x t o a form t h a t a unique s o l u t i o n f o r t h e e f f e c t s can be computed.  such  I t goes  without s a y i n g t h a t i t takes more computer time t o r u n t h i s program than the BMDP program; however, t h i s i s a p r i c e t h a t one has t o pay for  a n a l y z i n g more g e n e r a l i z e d unbalanced  data.  The F o r t r a n source program i s l i s t e d i n Appendix 2.  3.9  Chapter  Summary  T h i s chapter c o n s i d e r s t h e computational procedures f o r a n a l y s i s o f unbalanced c l a s s i f i e d model.  d a t a w i t h s p e c i a l r e f e r e n c e t o a two-way  The procedures d e s c r i b e d i n t h i s c h a p t e r are more  c o m p l i c a t e d than these commonly found i n textbooks, b u t they a r e methods a p p r o p r i a t e t o t h e a n a l y s i s o f unbalanced  d a t a w i t h no o b s e r v a t i o n s  i n some s u b c l a s s e s , such as d a t a which are f r e q u e n t l y observed  i n forest  i n v e n t o r i e s . Because no e x i s t i n g computer program handles d a t a w i t h empty c e l l s i n s u b c l a s s e s , a program i n F o r t r a n language was developed by t h e w r i t e r to a n a l y z e t h e f o r e s t i n v e n t o r y d a t a .  D i f f e r e n c e i n computational  a s p e c t s between the BMDP g e n e r a l l i n e a r program and the program a r e illustrated.  - 66 -  4.0  DATA BASE  A total the B.C. of  of 20,458 temporary  p l o t s has been p r o v i d e d by  F o r e s t S e r v i c e Inventory D i v i s i o n f o r a n a l y s i s .  sample p l o t s by s p e c i e s i s shown i n T a b l e 4-1.  The number  The t a b l e  indicates  t h a t D o u g l a s - f i r , spruce, and l o d g e p o l e p i n e d a t a which a r e the b u l k of  the d a t a s e t p r o v i d e e x c e l l e n t bases f o r the p u r s u i t of the  o b j e c t i v e s s e t f o r t h i n Chapter  1.  In a d d i t i o n , d a t a of western  (Tsuga h e t e r o p h y l l a S a r g . ) , " b a l s a m ' f i r (Abies s p p . ) , and aspen t r e m u l o i d e s Michx) can a l s o be used i n t h i s study.  hemlock (Populus  However, a f u r t h e r  grouping o f these p l o t s by pure, c o n i f e r mixed, and hardwood mixed types r e v e a l e d t h a t t h e r e i s no p l o t f o r the"balsam hardwood type and the pure L  aspen type.  Consequently,  d a t a for"balsam"and  aspen were e x c l u d e d .  The  western hemlock p l o t s which have been used to i l l u s t r a t e the a n a l y s i s procedures  i n Chapter 3 were a l s o excluded because p l o t s a v a i l a b l e f o r  a n a l y s i s were r e s t r i c t e d t o o n l y a few i n v e n t o r y zones. Methods used i n c o l l e c t i n g and summarizing  the d a t a made  a v a i l a b l e f o r t h i s study have been r e p o r t e d i n the F o r e s t Survey Manual and Growth Manual p u b l i s h e d by the F o r e s t I n v e n t o r y D i v i s i o n of the B.C.  Forest Service.  Only the r e c e n t c o m p i l a t i o n s were s u i t a b l e s i n c e  e a r l y summaries of p l o t s d i d not i n c l u d e i n f o r m a t i o n on numbers of t r e e s , b a s a l a r e a , and average been summarized t o 7.1, utilization  standard.  9.1,  stand dbh  11.1,  (Smith, 1973).  and 13.1  Douglas-fir.  utilization  the study because they p r o v i d e d more sample  p l o t s than the o t h e r s and they f a c i l i t a t e d Interior  i n c h e s dbh t o a c l o s e  The d a t a f o r 7.1-inch dbh and c l o s e  were a n a l y z e d throughout  and  Data have  comparisons  between Coast  - 67 -  Data were made a v a i l a b l e by u n i t name, type group, class,  s i t e index^  site  age c l a s s * numbers o f r e g i o n s , compartment,  and sample p l o t , n e t c u b i c f o o t volume w i t h d e d u c t i o n f o r decay o n l y  '  to a c l o s e u t i l i z a t i o n s t a n d a r d , b a s a l a r e a , and number o f t r e e s p e r a c r e , age i n 10's and h e i g h t o f dominant and codominant t r e e s i n 10's, f o r e s t i n v e n t o r y zone, volume over age curve number.  A l l d a t a were  measured and r e c o r d e d i n the I m p e r i a l system, t h e r e f o r e , t h e r e s u l t s were r e p o r t e d here i n t h e o r i g i n a l u n i t s .  Should  t h e need a r i s e , the  r e s u l t s can be c o n v e r t e d i n t o m e t r i c u n i t s . In r e t r i e v i n g d a t a , which were s t o r e d i n a magnetic tape, the v a l u e s f o r overmature stands were f i r s t  (stand age g r e a t e r than 150 y e a r s )  d e l e t e d because t h e r e i s l i k e l y t o be l i t t l e  interest i n  managing stands i n t e n s i v e l y once they become o l d e r than about 130 y e a r s (Smith-, 1973).  Furthermore,  estimates of e f f e c t s .  t h e overmature stands might l e a d t o b i a s e d  The p l o t s w i t h zero v a l u e s f o r volume, b a s a l  a r e a , and number o f t r e e s because e i t h e r they a r e below t h e dbh l i m i t or measurements f o r t h i s dbh l i m i t and c l o s e u t i l i z a t i o n standard were not a v a i l a b l e a l s o were e l i m i n a t e d . of  A f t e r the d e l e t i o n s the f i n a l number  p l o t s o f these t h r e e s p e c i e s a v a i l a b l e f o r a n a l y s e s i s l i s t e d i n  T a b l e 4-1. The f a c t t h a t d i f f e r e n t a species, growing i n d i f f e r e n t  s t a n d a r d volume t a b l e s were used f o r  zones needs f u r t h e r e x p l a n a t i o n .  Coast, a stand i s i d e n t i f i e d as mature a p p r o p r i a t e t o t h e stand s t a t u s i s used  On t h e  or immature and a volume t a b l e i n volume computation.  In the  I n t e r i o r , however, o n l y one s t a n d a r d volume t a b l e f o r a s p e c i e s i s used  Table  4-1.  The  n u m b e r o f s a m p l e p l o t s by s p e c i e s f o r d a t a p r o v i d e d b y B. C. F o r e s t S e r v i c e I n v e n t o r y Division  Species  Type Group  Do u g l a s - f i r  1 —  Yellow  27  151  32  21 1  3 3 , 34  279  pine  Western  white  pine  Larch Western  hemlock  Total Plots 8  7. 1 - i n c h DBH < 150 Years  4790  2967  --  12  --  17  1914  271  Balsam  18  --  20  1764  --  S pruce  21  26  5523  2615  31  5 154  4199  Lodgepole ' P opulus :  (  Red  pine spp.  21,  alder  white  28  -36  43  birch  50  4 1 , 42  TOTAL  Remarks:  1  40  Aspen  ----  135  1 38 5  —  20458  type  group  codes defined  by  B.C.  10052  Forest  Service.  - 69 -  throughout are used  except  i n Zone 11 and 12 where . s e p a r a t e volume t a b l e s  f o r mature and immature spruce and l o d g e p o l e p i n e r e s p e c t i v e l y . To pursue t h e o b j e c t i v e s s e t f o r t h i n Chapter  1 and t o  f a c i l i t a t e a n a l y s e s , d a t a were f u r t h e r grouped by s p e c i e s type ( s p e c i e s composition) hardwood mixed  (HMIX).  such as pure, c o n i f e r s mixed  (CMIX), and  A comparison o f t h e s p e c i e s types and t h e  i n c l u d e d type groups ( d e s i g n a t e d by t h e B.C. F o r e s t S e r v i c e ) i s p r e s e n t e d i n T a b l e 4-2. S e v e r a l a d d i t i o n a l stand parameters were computed from the o r i g i n a l data.  Mean annual h e i g h t , b a s a l a r e a , and volume  increments  were o b t a i n e d d i r e c t l y from t h e p l o t v a l u e s d i v i d e d by i t s stand age. R e l a t i v e stand d e n s i t y (RSD) f o r each sample p l o t was computed  from  the b a s a l a r e a of t h e p l o t d i v i d e d by t h e mean b a s a l a r e a o f t h e age class.  The mean b a s a l a r e a o f an age c l a s s i n t u r n i s t h e average  a r e a f o r a l l p l o t s a t t h e age c l a s s , i g n o r i n g t h e s p e c i e s t y p e s .  basal The  r e l a t i v e stand d e n s i t y was computed s e p a r a t e l y f o r each s p e c i e s ; f o r D o u g l a s - f i r i t was computed i n d e p e n d e n t l y  f o r the Coast and t h e I n t e r i o r  zones.  4.1  Chapter  Summary  In t h i s chapter, t h e d a t a source and t h e sample p l o t s f o r each s p e c i e s a v a i l a b l e f o r a n a l y s i s were i d e n t i f i e d .  The reasons f o r  s e l e c t i n g D o u g l a s - f i r , spruce and l o d g e p o l e p i n e f o r subsequent a n a l y s e s and  c h o o s i n g t h e 7.1-inch dbh l i m i t were e x p l a i n e d , b r i e f l y .  Table  4-2.  Comparison  of s p e c i e s types  and f o r e s t  type  S pecies  S pecie s Ty pe  Inventory  Douglas-fir  PURE  1 IF)  CMIX  5 (FP1) ,2 (FC,FCy) ,3 (FH) 4 ( F S ) , 6 (FPy)  HMIX  8  (FDecid)  PURE  21  (S)  CMI X  22 (SF) , 23 25 (SP1)  HMIX  26  PURE  26 (PI)  CMIX  29  (P1F),  HMIX  31  (PlDecid)  S pruce  Lodgepole  Pine  Type  groups  Groups  (SH,SC) , 24 (SB)  (SDecid)  30  (P1S,P1B)  Remarks: PURE: p u r e D o u g l a s - f i r t y p e , e t c . CMIX: D o u g l a s - f i r - c o n i f e r s mixed t j j p e ; HMIX: Do u g l a s - f i r - h a rdwood mixed t y p e . F: D o u g l a s - f i r ; P i : L o d g e p o l e p i n e ; C : C e d a r ; C y : Y e l l o w Cedar H: Hemlock; P y : Y e l l o w p i n e ; D e c i d : D e d i d o u s s p e c i e s ; S : S p r u c e ; B:Balsam.  - 71  -  For a s e l e c t e d s p e c i e s , not the B.C.  Forest  a l l sample p l o t s p r o v i d e d  S e r v i c e were s u i t a b l e f o r a n a l y s i s i n the  of the o b j e c t i v e s mentioned i n Chapter 1, because they are overmature or below the dbh  limit.  The  by  pursuit either  f a c t t h a t d i f f e r e n t volume  t a b l e s were used f o r a s p e c i e s because of d i f f e r e n c e s i n growing zones and  stand age was  also explained.  The  and the f o r e s t type groups d e s i g n a t e d by compared.  species the B.C.  types used i n the Forest  study  S e r v i c e were  - 72 -  5.0  RESULTS AND  5.1  Occurrence  DISCUSIONS  of D o u g l a s - f i r - ,  Spruce-,  dominated F o r e s t Types i n B r i t i s h  and Lodgepole  Pine-  Columbia  Numbers o f sampled p l o t s f o r D o u g l a s - f i r ,  spruce,  and  l o d g e p o l e p i n e c l a s s i f i e d by pure type (PURE) (81% or more of the leading  s p e c i e s by  volume-  per a c r e ) , pure and c o n i f e r mixed  (CMIX), and pure and hardwood mixed type  (HMIX) are l i s t e d  type  i n Table  S i n c e these p l o t s were randomly sampled from f o r e s t a r e a a c r o s s it  5-1.  B.C.,  i s l o g i c a l to i n f e r t h a t r e l a t i v e frequency of the p l o t s i s a  u s e f u l i n d i c a t o r of the frequency w i t h which the v a r i o u s types occur i n nature. T a b l e 5-1  i n d i c a t e s t h a t more than 50 p e r c e n t of  Douglas-fir,  spruce, and l o d g e p o l e p i n e o c c u r n a t u r a l l y as pure type stands. Because these p l o t s spread a l l a c r o s s B.C., that  i f t h e r e a r e any adverse e f f e c t s o f e s t a b l i s h i n g pure f o r e s t  i n B.C., On  i t i s r e a s o n a b l e t o say crops  these e f f e c t s should have been w e l l r e f l e c t e d i n these s t a n d s .  the o t h e r hand, the t a b l e shows t h a t about  45 p e r c e n t of these  stands  a r e grown n a t u r a l l y i n m i x t u r e w i t h e i t h e r o t h e r c o n i f e r o u s or hardwood species.  The growth b e h a v i o r o f mixed stands not o n l y i s more c o m p l i c a t e d  than but a l s o d i f f e r s from pure stands Barnes,  1962;  Turnbull,  (Meyer, 1937;  M u l l o y , 1944,  1963); i t i s of m e n s u r a t i o n a l and  1947;  managerial  s i g n i f i c a n c e t o examine the extent o f d i f f e r e n c e i n y i e l d between pure and mixed type s t a n d s .  Table  5-1  Numbers o f ' s a m p l e  p l o t s by s p e c i e s and f o r e s t  species  type  SPECIES "YPE  DF COAST  . DF INTERIOR  %  404 63.6  1450 62.2  CMIX %  172 27.1  798 34.2  HMIX  59 9.3  84 3.6  PORE  TOTAL  635  2332  Remarks: D F - - D o u g l a s - f i r ;  SP  1144 43. 7  PL  2356 5354 56. 1 54 .7  1190 1010 45.5 • 24.1 281 10.7 2615  SP--Spruce  TOTAL  3170 32.4  833 1257 19.8 12.9 41 99  9781  spp; PL--Lodqepole  PURS--pure t y p e s t a n d ; C M I X — p u r e and c o n i f e r s HMIX--pure and hardwoods mixed t y p e s t a n d .  Pine mixed t y p e  stand;  - 74 -  The degree of s p e c i e s mixture v a r i e s w i t h i n t h r e e s p e c i e s studied.  As shown i n T a b l e 5-1,  type p l o t s i s 62.2 and 43.7%  to 63.6%  f o r D o u g l a s - f i r , 56.1%  f o r lodgepole pine  f o r spruce; o f the c o n i f e r mixed type i s 24.1%  p i n e , 27.1  t o 34.2%  f o r D o u g l a s - f i r and 45.5%  hardwood mixed type i s 3.6 and 19.8%  the r e l a t i v e frequency o f the pure  t o 9.3%  f o r lodgepole pine.  f o r lodgepole  f o r spruce; o f the  f o r D o u g l a s - f i r , 10.7%  f o r spruce,  D o u g l a s - f i r which o c c u r s m a i n l y  as  pure type (62.3 t o 63.6%) mixes p r e d o m i n a t e l y w i t h o t h e r c o n i f e r s p e c i e s (27.1 t o 34.2%) and r a r e l y w i t h hardwood s p e c i e s (3.6 t o 9.3%). i s grown e i t h e r as pure species  (43.7%) o r i n m i x t u r e w i t h o t h e r c o n i f e r o u s  (45.5%) and hardwood s p e c i e s (10.7%).  f r e q u e n t l y grows as pure types  Lodgepole  s p e c i e s (19.8%).  a r e of e c o l o g i c a l s i g n i f i c a n c e which w i l l not be pursued  either The f r e q u e n c i e s  f u r t h e r here.  shows the frequency o f the sampled p l o t s  by s p e c i e s c o m p o s i t i o n type and f o r e s t i n v e n t o r y zone. distributed  p i n e which  (56.1%) mixes commonly w i t h  c o n i f e r o u s s p e c i e s (24.1%) or deciduous  T a b l e 5-2  Spruce  from Zone 2 to Zone 8.  classified  Douglas-fir i s  The reasons t h a t no D o u g l a s - f i r  stands grow i n Zones 9 t o 12 a r e e i t h e r t h a t D o u g l a s - f i r stands grown i n t h e s e zones were not sampled or t h a t they were sampled but have been c l a s s i f i e d under o t h e r s p e c i e s types as they were not dominant s p e c i e s . The  same arguments a p p l y t o spruce and l o d g e p o l e p i n e as w e l l . The r e l a t i v e f r e q u e n c i e s i n T a b l e 5-2  agreement w i t h K r a j i n a ' s c l a s s i f i c a t i o n  are g e n e r a l l y i n  ( K r a j i n a , 1969).  F o r e s t Inventory  Zone 2, f o r example, f a l l s i n the Coast D o u g l a s - f i r Zone (CDF) where the D o u g l a s - f i r type o c c u r s predominately;  Zone 4 i s the I n t e r i o r D o u g l a s - f i r  Table  5-2 The f i e q u e n c y  o f sample  inventory  plots  by f o r e s t  8  DF,P UK E  347 69. 2  57 42. 5  691 74. 2  164 71.3  44 33. 8  320 40. 6  DF+CMIX  107 21.4  65 48.5  232 ' 24.9  62 27.0  83 63.9  400 50. 7  47 9. 4  12 9.0  8 0. 9  4 1.7  3 2.3  69 8. 7 45 16. 4  SP,PUHE  52 26. 0  84 65. 1  1 6 20.3  SP+CHIX  144 72. 0  44 34. 1  59 74. 7  223 80.3  SP+HMIX  4 2.0  4 5. 0  9 3. 3  •  %  PL,PURE *  " ~  "  PL+CMIX  -  -  P  L  *  H  K  I  ~  %  s:  5  " ."  X  642 6  250 22. 1 238 «1 2 1  1 0.8  1 8  5  3  1  4  2  55. 0  5 1. 8  49 17. 6  132 48. 2  76 27.4  forast  ZONE  TYPE  DF+HMIX  and  zones  FOREST INV2NT0BY  %  types  -  15 4.9  1 1  12  292 35.0  37 46.3  522 66. 4  439 52. 6  24  146 1 3. 6  231 91.7 21 I.3  96 41.2 114 48.9 23 9. 9  137 964 44. 8 67.2 154 50. 3  1 0  30.0  1 03 12. 4  19 23.7  2 13 40. 0  27 57. 5  138 9.6  2 17 40.7  1 2.1  332 23. 2  103 1 9. 3  1 9. 40. 4  -  118 15. 0 78 39.6 69 35. 0  -  1. DF,PUEE - - D o u g l a s - f i r p u r e t y p e s t a n d ; DF + C M I X — D o u q l a s - f i r - C D n i f mixed t y p e ; DF+HMIX-- D o u q l a s - f i r - h a r d w o o d mixed t y p e S P , P U R E — p u r e s p r u c e t y p e ; SP + C M I X — s p r u c e - c o n i f e r s mixed t y p e s ; PL, P U R E - - p u r e l o d g e p o l e p i n e t y p e ; PL + CHIX — l o d q e p o l e pine-conif•=» mixed t y p e ; P L + H M I X — l o d q e p o l e p i n e - h a r d w o o d s m i x e d t y p e . 2. % I n d i c a t e s t h e p e r c e n t a g e o f a s p e c i e s t y p e w i t h i n a n i n v e n t o r y zone f o r t h i s s p e c i e s .  50 23.4  - 76 -  Zone (IDF) where D o u g l a s - f i r and ponderosa p i n e major s p e c i e s i n the d r i e r subzone (IDFa) and f r e q u e n t l y i n the w e t t e r subzone (IDFb). where l o d g e p o l e p i n e dominates f a l l s D o u g l a s - f i r Zone (CALPDF).  (Pinus ponderosa)  lodgepole pine occurs  The F o r e s t I n v e n t o r y Zone 8  i n the Cariboo Aspen-lodgepole  the dry and  f a i r l y warm summer.  D o u g l a s - f i r o c c u r here most o f t e n . m o i s t e r and  pine-  A c c o r d i n g t o K r a j i n a , the number of  c o n i f e r o u s t r e e s growing i n the CALPDF i s v e r y l i m i t e d , due severe w i n t e r and  are  t o the  Lodgepole  pine  and  Spruce becomes f r e q u e n t m a i n l y  c o o l e r s i t e s , e s p e c i a l l y those f l o o d e d i n the s p r i n g .  o c c u r r e n c e of Populus  on The  t r e m u l o i d e s which i s a f r e q u e n t t r e e i n the Zone  becomes even more common i n the secondary loamy s o i l s as i s well-shown i n T a b l e A c c o r d i n g t o K r a j i n a (1969), a r e the Engelmann Spruce-Subalpine B l a c k Spruce Zone (BWBS), and  stands e s p e c i a l l y on  rich  5-2. the F o r e s t I n v e n t o r y Zones 9 to  F i r Zone (ESSF), B o r e a l White and  Sub-boreal  Spruce Zone (SBS).  The major  c o n i f e r o u s s p e c i e s a r e P i c e a g l a u c a , P i c e a mariana, P i n u s c o n t o r t a , L a r i x l a r i c i n a , and A b i e s l a s i o c a r p a and deciduous such as Populus  angiospermous t r e e s  t r e m u l o i d e s , P_. b a l s a m i f e r a , B e t u l a p a p y r i f e r a ,  J3. r e s i n i f e r a , Alnus t e n u i f o l i a and A. c r i s p a f r e q u e n t l y o c c u r . r e l a t i v e f r e q u e n c i e s i n T a b l e 5-2  The  are i n l i n e with K r a j i n a ' s f i e l d  observations.  5.2  S i t e D e t e r i o r a t i o n and Pure Stands  Some pure f o r e s t s , n o t a b l y of c o n i f e r s , may  cause a slow  d e t e r i o r a t i o n of the upper s o i l l a y e r s by f o s t e r i n g the f o r m a t i o n of a c i d and raw humus (Baker, 1950).  The n e e d l e s of p i n e and  spruce i n  12  - 77 -  p a r t i c u l a r decompose v e r y s l o w l y and tend t o form deep l a y e r s of the p o o r l y decomposed raw humus m a t e r i a l i n which s e e d l i n g s f i n d i t difficult —  t o grow.  I f t r e e s w i t h l e a v e s which decompose r e a d i l y  u s u a l l y hardwoods —  improve  a r e mixed w i t h the c o n i f e r s , they n o t o n l y  t h e humus l a y e r s d i r e c t l y , b u t they a l s o tend t o develop  c o n d i t i o n s i n which t h e decomposition o f t h e c o n i f e r n e e d l e s  themselves  i s considerably accelerated. The average  s i t e i n d i c e s f o r pure, c o n i f e r mixed, and  hardwood mixed type stands o f D o u g l a s - f i r , spruce, and l o d g e p o l e p i n e i n v a r i o u s f o r e s t i n v e n t o r y zones a r e l i s t e d  i n T a b l e 5-3.  The above  statements made by Baker may g a i n s t r o n g support by t h e f i g u r e s o b t a i n e d from t h e i n v e n t o r y d a t a .  I n most o f t h e cases t h e c o n i f e r mixed and  hardwood mixed stands have h i g h e r s i t e index than t h e i r c o u n t e r p a r t pure type s t a n d s .  The improvement i n s i t e q u a l i t y by m i x i n g c o n i f e r o u s  o r deciduous s p e c i e s i s more s i g n i f i c a n t fertility  i n t h e zones where s o i l  i s poor, e.g. Zone 4 and t h e N o r t h e r n I n t e r i o r Zones. However, t h e b e n e f i c i a l e f f e c t o f mixed stands on s o i l  f e r t i l i t y cannot be accepted w i t h o u t r e a s o n a b l e doubts.  I t has been  f r e q u e n t l y observed by f o r e s t e r s t h a t hardwood s p e c i e s such as Populus, A l n u s , and B e t u l a o c c u r h a b i t u a l l y on f e r t i l e s o i l and r a r e l y on poor s i t e s w h i l e spruce and l o d g e p o l e p i n e pure stands a r e o f t e n found growing  on poor s i t e s .  T h e r e f o r e , t h e h i g h e r s i t e i n d i c e s shown i n  T a b l e 5-3 f o r c o n i f e r mixed and hardwood mixed stands cannot be f u l l y i n t e r p r e t e d as t h e b e n e f i c i a l e f f e c t o f mixed stands on s o i l  improvement;  Table  5-3  Avera qes o f  s i t e i n d a x by s pec i e s t y p e s and i n v e n t o r y zonas  forest  FOHES T INVENTOfiY. ZONE  2  TYPE  3  A veraye h e i g h t s  a of  5 dominant  6  7  8  and c o d o m i n a n t t r e e s a t  9  10  aqe  100, f t .  -  -  11  12  -  -  DF,PUHE  125. 2  103.0  73. 5  82. 3  70.6  83. 4  73. 1  DF+CMIX  116.6  107. 2  75. 0  81.6  73. 9  84. 7  69.3  DF+KMIX  129.4  126.7  88. 1  80.0  ' 70.0  86. 0  -  SP,PURE  -  80. 9  85 . 4  80.2  86. 6  84. 4  82. 7  -  59. 0  77. 2  SP+CMIX  -  -  79. 8  37. 4  78. 4  84. 5  79.8  84.4  -  61.3  67. 0  85.5  96. 0  90. 8  81.8  79.4  86.0  -  62. 3  79. 7  -  63. 1  79.0  76.7  82. 7  70. 8  86. 2  86. 3  PL+CMIX  -  -  68.0  84.3  73.3  86. 1  73.3  87.2  PL+HMIX  -  -  78. 8  79. 2  -  83. 3  75. 0  83.8  SP+HMIX  PL,PUSE  Bemarks:  -  -  70. 0  -  64. 5  90. 0  -  68. 8  DF,PUS2, D F + C a i X , DF+HMIX; SP,PURE, SP+CMIX, SP+HHIX;PL,PURE, PL+CHIX, a n d PL+HMIX s e e T a b l e 5 - 2 .  60. 3  - 79 -  the h i g h e r s i t e i n d i c e s i n mixed stands might simply be e x p l a i n e d by the f a c t t h a t these stands were e s t a b l i s h e d on b e t t e r s i t e conditions. The i d e a l experiments  t o assess the e f f e c t of f o r e s t  on s o i l d e t e r i o r a t i o n a r e t o e s t a b l i s h s p e c i e s w i t h v a r i o u s of  mixture on t h e same s i t e c o n d i t i o n and observe  w i t h the development o f s t a n d s .  types  degrees  any changes of s i t e  U n t i l such e x p e r i m e n t a l d a t a become  a v a i l a b l e , f o r e s t e r s a r e f o r c e d t o s p e c u l a t e on the e f f e c t o f stand types on s o i l  5.3  from d a t a such as used  i n this  study.  Number o f Trees P e r Acre  One of t h e advantages c l a i m e d f o r e s t a b l i s h i n g mixed has been t h a t t h e l i m i t e d f o r e s t l a n d can be more e c o n o m i c a l l y  stands utilized,  t h a t i s , more f o r e s t t r e e s p e r u n i t can grow i n mixed stands than i n pure stands. for  T a b l e 5-4 which shows t h e average  number o f t r e e s p e r a c r e  t h r e e type groups i n B.C. f o r e s t i n v e n t o r y zones demonstrates  c l e a r l y t h e advantages o f mixed c o n i f e r stands over pure ones. With t h e e x c e p t i o n o f t h r e e cases, c o n i f e r mixed stands grow c o n s i d e r a b l y more t r e e s p e r a c r e than pure stands do.  However, T a b l e  5-4 shows no d e f i n i t e advantages o f hardwood mixed stands over pure type stands i n number o f t r e e s p e r a c r e .  The compensative e f f e c t o f  d i f f e r e n t c o n i f e r o u s s p e c i e s growing on t h e same a r e a has been r e c o g n i z e d by f o r e s t e r s as w e l l by e c o l o g i s t s . deciduous  F o r hardwood mixed stands, because  s p e c i e s u s u a l l y have l a r g e r crowns and more requirement f o r  s u n l i g h t , t h e number o f t r e e s p e r a c r e i s , i n g e n e r a l , l e s s than of  c o n i f e r mixed and pure type  stands.  those  Table  5-4  A v e r a g e d numbers o f t r e e s p e r a=re and f o r e s t i n v e n t o r y z o n e s ( U n i t : T r e e s / A c r e ) ( 7 . 1 i n c h e s DBH  FOREST INVENTORY TY PE  2  3  DF+PURE  197  1 85  DF+CMIX •  159  DF+HMIX  164  SP,PURE  -  4  5  6  i n various  species  types  and l a r g e r )  ZONE  7  8  9  10  1 1  12  -  -  -  -  -'  -  -  -  150  190  154  -  177  138  162  159  210  177  215  200  16 4  132  184  191  179  200  91  115  108  137  208  120  141  130  . 174  152  84  106  100  147  206  172  153  180  190  174  288  . 89 92  -  -  -  P L , PURE  -  -  1 48  166  17 1  229  187  199  208  -  150  PL+CMIX  -  -  176  180  178  1 94  206  218  226  -  220  PL+KMIX  -  -  179  172  -  1 52  163  218  156  SP+CMIX SP+HMIX  Remark:  DF,PURE; DF+CMIX;  and DF+HMIX ETC. s e e  Table  5-2.  -  co o  241  - 81  -  The number of t r e e s per a c r e v a r i e s w i t h i n t h r e e investigated. T a b l e 5-4  Comparing the Southern and  species  C e n t r a l I n t e r i o r Zones i n  where data on a l l t h r e e s p e c i e s a r e a v a i l a b l e , one  can  c l e a r l y r e c o g n i z e t h a t the numbers of t r e e s per a c r e i n D o u g l a s - f i r stands a r e s u b s t a n t i a l l y l e s s than those i n spruce- or l o d g e p o l e dominated s t a n d s .  Being a shade i n t o l e r a n t  pine-  species Douglas-fir requires  more growing space and thus reduces i t s number of t r e e s per a c r e , or gaps i n s t o c k i n g may The The  r e s u l t s a r e of p r a c t i c a l i m p l i c a t i o n f o r s p a c i n g  optimum s p a c i n g i s species-dependent,  s p a c i n g f o r one species. possible  5.4  occur. trials.  t h a t i s , the most p r o d u c t i v e  s p e c i e s i s n o t n e c e s s a r i l y the one a p p r o p r i a t e to o t h e r  Well-planned  experiments a r e needed t o demonstrate such  relationships.  R e l a t i v e Stand D e n s i t y  Stand d e n s i t y i s much l e s s r e a d i l y d e f i n e d and q u a n t i f i e d ( C u r t i s , 1967); f o r e s t e r s are of d i f f e r e n t o p i n i o n s as t o theprop'er b a s i s f o r computing stand d e n s i t y .  In t h i s study, r e l a t i v e stand d e n s i t y  computed f o r each sample p l o t by a formula The  d e s c r i b e d i n Chapter  average r e l a t i v e stand density:£or v a r i o u s f o r e s t type and  zone combinations i s shown i n T a b l e  4.  inventory  5-5.  I f c o n i f e r mixed type stands per a c r e , i t goes without  was  a r e capable  of growing more t r e e s  s a y i n g t h a t the r e l a t i v e stand d e n s i t y i n the  stand i s h i g h e r than i n pure stands.  With a few e x c e p t i o n s  i n Table  5-5,  Table  5-5 R e l a t i v e  stand forest  density  for various  inventory  zone  3  2  4  5  6  t y p e and  combinations  FOREST INVENTORY TYPE  species  7  ZONE 8  9  DF,PURE  1.05  0. 95  0.77  1. 05  0.88  1. 22  0.77  DF+CHIX  0.87  1. 03  0. 87  1. 07  0.93  1. 41  0.67  DF+HMIX  0.96  1. 07  0.70  0. 83  0.71  1. 25  -  1.12  1. 08  0.93  1.01  1.01  0. 98  SP,P0RE SP+CMIX SP+HMIX  PL,PURE PL+CMIX PL+HMIX  -  -  10  12  -  -  0.75  0. 93  1.00  0. 84  0.76  0. 92  —  -  -  -  0.98  1. 22  0.95  1.09  -  1 .07  1. 08  0.79  1. 87  0.99  1. 04  0.85  1. 13  -  -  0. 74  1. 06  0.99  1. 15  0. 95  1. 28  1.38  1. 00  1. 23  1.05  1.24  1. 14  1. 36  0.75  1. 00  0. 95  1. 17  0.87  1. 29  1.11  -  11  -  Bemarks:DF, SP. PL, PURE, CMIX, and HMIX as d e f i n e d i n T a b l e 5-2. D i m e n s i o n l e s s u n i t ; based on t h e mean b a s a l a r e a of an a q e c l a s s .  0. 60  _  1. 11 1.02  - 83  -  the r e l a t i v e stand d e n s i t y i n c o n i f e r mixed stands i s c o n s i s t e n t l y h i g h e r than t h a t i n pure s t a n d s .  However, the c o n c l u s i o n cannot  be  g e n e r a l i z e d t o hardwood mixed stands f o r which no d e f i n i t e t r e n d has been shown.  5.5  Average Stand Age,  Mean Annual Height, B a s a l Area,  and  Volume Growth.  5.5.1  Average Stand  T a b l e 5-6  Age  p r e s e n t s average  stand age, mean annual  increments  f o r h e i g h t of dominant and codominant t r e e s , b a s a l a r e a per a c r e , and volume.per a c r e f o r D o u g l a s - f i r , spruce, and c o r r e s p o n d i n g averages are l i s t e d  The  f o r the h e i g h t , b a s a l a r e a , and volume y i e l d  i n t a b l e s 5-7, The average  lodgepole pine.  5-8,  stand age  younger than f o r pure type and  and 5-9,  respectively.  f o r hardwood mixed type stands i s much c o n i f e r mixed type stands.  Deciduous  s p e c i e s such as aspen, r e d a l d e r , cottonwood and b i r c h have been c o n s i d e r e d as " p i o n e e r " s p e c i e s ( T u r n b u l l , 1963) e s t a b l i s h immediately forest f i r e s occurred.  and  a r e ready  a f t e r areas have been logged or l a r g e s c a l e The hardwood s p e c i e s e s t a b l i s h r a p i d l y  i n l a r g e numbers on f r e s h l y opened a r e a s .  Characteristically,  t r e e s grow r a p i d l y from the time of e s t a b l i s h m e n t and short  lived.  to  and those  are r e l a t i v e l y  Table  5-6  Aqe, mean a n n u a l h e i q h t , by s p e c i e s t y p e s  b a s a l a r s a , and volume qrowth and f o r e s t i n v e n t o r y zor.es  FOREST INVENTORY ZONE TYPE  2  3  4  5  6  7  8  9  DF,PURE AGE 47 HT 1.83 BA 2.83 VOL 91.00  80 1.23 2.17 74.33  93 0.72 0.76 18.56  95 0.84 0.95 25.64  92 0.70 0.87 21.23  77 0.98 1.25 32.79  10 1 0.68 0.73 17.58  -  DF+CMIX  AGE 52 HT 1.58 EA 2.27 VOL 73.99  91 1.16 2.41 83.06  94 0.75 0.88 22.95  94 0.87 1.11 29.32  92 0.75 ' 0.96 25.79  80 0.99 1.49 40.45  87 0.70 . 0.73 17.99  -  AGE 45 HT 1.86 3A 2.52 VOL 79.40  53 1.78 2.63 90.10  68 1.09 0.68 15.72  78 0.97 0.89 23.94  78 0.85 0.81 18.63  65 1.15 1.36 35.52  DF+HMIX  SP,PURE A G E HT BA VOL  10  11  12  -  -  -  -  -  -  116 114 138 118 0.76 0.81 0.71 0.79 1.36 1.30 1.04 1.14 41.96 38.97 35.97 37.97  112 112 0.78 0.78 1.25 1.19 38.27 35.51  -  111 0.57 0.97 24.20  SP+CMIX AGE HT BA VOL  -  -  108 0.77 1.24 35.84  101 103 0.80 0.81 1.37 1.31 39.92 39.51  -  116 102 0.60 0.66 1.22 1.12 31.29 28.73  SP+HHIX  AGE HT BA VOL  -  -  85 0.94 1.29 36.72  75 1.33 2.67 73.40  78 1.03 1.41 36.50  62 1.03 1.53 38.17  88 0.84 1.19 30.96  93 0.92 1.52 43.19  -  116 100 0.62 0.83 0.97 1.25 23.40 32.89  AGE KT BA VOL  -  -  90 0.67 0.81 21.50  87 0.88 1.15 34.06  73 0.91 1.15 32.7£  76 0.98 1.31 39.17  92 0.75 1.06 30.56  90 100 0. 88 0. 90 1.36 1.53 41. 54 48. 53  PL+CMIX AGE HT EA VOL  -  -  91 0.73 1.11 29.63  85 0.93 1.28 35.95  87 0.79 1.14 31.25  76 1.01 1.41 40.74  FL+HMIX AGE HT 3A VOL  -  -  73 0.91 1.11 32.96  78 0.92 1.09 33.05  PL,PURE  103 114 109 0.84 0.73 0.83 1.20 1.13 1.29 34.16 32.31 38.27  -  63 1.07 1.14 29.63  104 145 102 0. 86 0. 55 0.74 1 . 44 0. 69 1.21 45.93 18.88 35.20 33 0.83 0.99 28.76  81 67 0.94 1.15 1 . 40 1. 29 42.10 35.91  Remarks: 1. DF, SP, PL, PURE, CMIX, and HMIX as d e f i n e d i n Table 5-2. 2. H T : h e i q h t ( f t / y e a r ) : B A : b a s a l a r e a (sq. f t / a c r e / y e a r ) VOL: volume ( c u b i c f t / a c r e / y e a r ) .  109 0.74 1.21 34.77  -  92 0. 66 0.73 18. 35  -  95 0. 69 1. 24 30.94  -  99 0.73 1. 17 31.82  -  Table  5-7  Mean._height o f d o m i n a n t and c o n d o m i n a n t by t y p e s and i n v e n t o r y z o n e s . ( U n i t : Foot) FOREST INVENTORY  TYPE  2  3  4  5  67 . 6  79 . 5  64. 3  76 .0  105.4  70 .7  81 . 9  68. 6  95.0  73 . 8  75 . 0  -  87 . 5  -  -  PL,PURE  6  trees  ZONE  7  8  9  10  67. 9  -  -  79 .2  6 1. 0  -  66. 7  75 .2  •  • -  -  92 . 1  98. 1  93 .3  88. 0  86.8  -  63. 5  81.2  83 . 3  90 . 0  82. 7  90 .4  80. 8  87.0  -  70.0  6 7. 4  -  80 . 0  100 . 0  80. 0  66 .7  73. 9  85.3  -  71. 6  79. 9  -  -  60 . 5  76 . 3  65. 8  75 .0  68. 5  79.8  90. 0  PL+CMIX  -  66 , . 6  79,. 4  68. 6  76 .4  74. 8  88.9  80. 0  PL+HMIX  -  -  71 , . 0  71 , .7  67.. 3  68. 3  76. 6  77. 4  DF,PURE  83.7  DF+CJilX  82. 1  DF+HMIX  83.6  SP,PURE  -  SP+CMIX SP+HMIX  98. 8  -  Remarks: DF, SP, PL, PURE, CMIX, and HI* IX a s d e f i n e d  i n T a b l e . 5-2.  1 1  12  -  60.7  —  -  65.2 71.5  ' a b l e 5-  Hean b a s a l a r e a p e r a c r e o f D o u q l a s - f i r , s p r u c e , l o d q e p o l e p i n e by s p e c i e s t y p e s a n d i n v e n t o r y zones ( U n i t : Sq. f t . / a c r e ) FOSSST INVENTORY  TYPE  ZONE  2  3  4  DF,PUHE  129. 2  174.7  71. 2  90. 2  80 .7  96.5  DF+CBIX  118. 0  218.1  83. 2  104. 6  88 .2 ,  119.3  DF+HMIX  113. 2  140. 5  45. 9  69. 0  63,.3  89.0  SP,PURE  -  -  156. 9  148. 0  1 42 ,, 6  134. 1  1 40.3  133.2  -  -  134. 1  160. 1  128. , 5  140. 9  138. 6  140. 9  -  109. 5  200. 0  109, .5  97,3  1 04.4  140.42  PL,PURE  -  -  72. 9  100. 4  8 3 . .2  100. 2  96. 8  12 3.0  PL+CMIX  -  -  101. 3  10 8. 9  98. 6  106. 3  1 2 2 .8  PL+HMIX  -  -  87. 3  84.6  72. 1  81. 3  SP+CMIX SP+HMIX  Remarks:  5  6  7  and  8  9  10  72., 9  -  63. 6  -  1 1  12  -  -  -  -  -  -  - •  -  oo  DF, S P , P L , PURE, CH I X ,  -  a n d HMIX  -  107. 7  132. 1  141. 5  115. 1  11 1. 5  125. 3  152. 8  -  66. 7  149. 4  100. 0  -  117. 7  114. 1  86. 4  _  115.5  as d e f i n e d i n Table  -  5-2.  Table  5-9.  Mean n e t volume of D o u q l a s - f i r , s p r u c e , and l o d q e p o l e by s p e c i e s t y p e s and i n v e n t o r y z o n e s (Unit: cubic f o o t / a c r e ) FOREST  TYPE  INVENTORY  pine  ZONE  2  3  4  5  6  7  8  9  10  1 1  12  DF,PURE  4158  5983  1731  2430  1959  2537  1767  -  3855  7520  216 1  2762  2363  3238  1572  -  -  DF+HMIX  3573  4805  106 1  1855  1459  2319  -  -  -  -  -  DF+CMIX  -  -  SP,PUR E  -  -  48 50  4426  4946  4468  43 02  3 97 7  -  2679  3793  SP+CMIX  -  -  3880  4772  3672  4 189  4041  4250  -  3638  2940  SP+HMIX  -  -  3121  5880  2829  2354  2726  3998  -  2703  3300  PL,PUfiE  -  -  1940  2971  2381  2989  2796  3757  4834  -  -  2701  3056  2704  3 077  3576  4757  2737  2583  2566  .1 86 5  23 73  3419  2410  PL+CMIX PL+HMIX  _  Remarks: DF, SP, PL, PURE, CMIX, and HMIX as d e f i n e d i n T a b l e  5-2.  _  1733 2930 3137  - 88 -  The concerns  f u t u r e c o m p o s i t i o n o f any stand i s one o f the prime  i n f o r e s t management.  part, intolerant  The hardwood s p e c i e s a r e , f o r a l a r g e  s p e c i e s which can be expected  t o d i e out l o n g b e f o r e  the admixed c o n i f e r o u s s p e c i e s have reached m a t u r i t y . Mulloy  (1947) i l l u s t r a t e d  c o m p o s i t i o n w i t h r e s p e c t t o age.  i n d e t a i l t h e change o f hardwood  I n p r e p a r i n g y i e l d t a b l e s , he i n d i c a t e d  t h a t a stand w i t h 90% hardwoods a t age 30 reduces to 17% a t age 80 and 9% a t age 100.  The average  i n hardwood  composition  stand age l i s t e d i n  T a b l e 5-6 bears no d i r e c t evidence on t h e dynamic change i n s p e c i e s c o m p o s i t i o n o f hardwood stands; however, i t s lower age than those o f pure type and c o n i f e r mixed type stands suggests t h e dynamic n a t u r e o f hardwood mixed stand  5.5.2  structure.  Mean Annual Height Growth  T a b l e 5-6 and F i g u r e s 5-1, 5-2, and 5-3 show t h a t t h e mean annual h e i g h t increment  o f dominant and codominant t r e e s i s h i g h e r i n  hardwood mixed type stands than i n pure and c o n i f e r mixed type  stands.  The reason f o r t h e h i g h e r mean annual h e i g h t growth o f hardwood mixed type stands can be e x p l a i n e d i n p a r t by t h e f a c t t h a t they a r e younger i n age than t h e o t h e r stands.  Among the t h r e e s p e c i e s s t u d i e d , the  s u p e r i o r i t y o f hardwood stands i n h e i g h t growth i s more i n D o u g l a s - f i r than i n spruce and l o d g e p o l e p i n e .  conspicuous  Douglas-fir i s  i n t o l e r a n t with other coniferous species, but i n mixture with s p e c i e s t h e s p a t i a l c o n f i g u r a t i o n o f stands d i f f e r s c o m p l e t e l y those o f pure o r c o n i f e r mixed type s t a n d s .  deciduous from  F i q u r e 5-1. Comparison of the mean heiqht increments of dominant and codominant t r e e s of D o u q l a s - f i r stands by types and zones . 2.0 + H  I H  1.0  0.0 +•  I H I+H I+H I+H I +H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H ONE 2  H H H H H H I+H I+H H I+H • H I+H H I+H +H I + H I+H I+H I+H I + H I+H I+ H I+H I+H I+H I+H I+H I+H I+H ZONE 3  ZONE U  I : PORE +: CMIX H: HMIX  Ii +H +H I+ H I+H I+H I+H I+H I+H I +H ZONE 5  H +H I+H I+H I+H I+H I+H I+H I+H ZONE 6  H H I+H I+H I+H I+H I+ H I+H I+H I+H I+H I+ H ZONE 7  oo  Vi5  1+ 1+ 1+ 1+ 1+ 1+ 1+ ZONE 8  Remarks: PURE--pure type;CMIX--conifer  ZONE 9  ZONE 10  ZONE 11  ZONE 12  mixed type;HMIX—hardwood  mixed type.  Figure 5-2. Comparison of the mean annual heiqht increments o f dominant and codominant t r e e s by types and zones of I n t e r i o r spruce 2.0 + I: PUKE + ; CMIX H: HMIX  H  1.0 H I+H I +H I +H I+H I+H I +H I+H I+H  O M W  0.0 ZONE 2  ZONE 3  ZONE 4  H H H H H I+H I+H I+ H I+H I+H I+H I+H I+H ZONE 5  H H H I+H I+H I+H I+H I+H I+H I+H ZONE 6  H H H I+H I +H I+H I+H I+H I+H I+H I+H ZONE 7  I +H I+H I+H I+H I+H I+H I+H I+H ZONE 8  Remarks: PURE—pure type;CMIX--conifer  H H I+H I+H I+H I+H I+H I+H I+H ZONE 9  I+H I+H I+H I+H I+H I+H ZONE 10  ZONE 11  o  H I+H I+H I+H I+H I+H I+H ZONE 12  mixed type;HMIX—hardwood  mixed type.  Figure  5 -3. Comparison of the mean annual h e i g h t increments of dominant and codominant t r e e s of l o d g e p o l e pine' i n I n t e r i o r zones  I : PURE • : CMIX H: HMIX  a  H B I +H I + II I +H I+H I+H I+H I+U  ZONE 2  ZONE 3  ZONE 4  I+li I+H I+H I +H I+H I+H I+H I+H I+H  ZONE 5  I 1+ 1+ 1+ 1+ 1+ 1+ 1+ 1+  ZONE 6  I +H I +H I+H I+H I +H I+H I+H I+H I +H I+H  ZG NE 7  I I I I I I I  H +H +H +H +H +H +H +H  ZONE 8  I+H I+H 1+ H I +H I+H I+H I+H I+H I+H  ZONE 9  H H H I H I H I H I +H I+H I +H I +H I +H I+H  ZONE 10  I I I I I I I  ZONE 11  +H +H +H +H +H +H +H  ZONE 12  Remarks: PURE—pure type;CMIX--conifer mixed type;HMIX—hardwood  mixed type.  - 92 -  V a r i a t i o n s i n the mean annual h e i g h t increment o f dominant and codominant apparent.  t r e e s among t h e i n v e n t o r y zones i s expected and  F o r D o u g l a s - f i r , t h e h e i g h t growth i n Coast zones  (Zones  2 and 3) d i f f e r s d r a s t i c a l l y from t h a t i n the I n t e r i o r zones  (Zones  4 t o 8 ) . Among t h e I n t e r i o r zones, t h e h e i g h t growth i n t h e I n t e r i o r Wet B e l t  (Zone 7) exceeds  t h a t i n o t h e r zones.  F o r spruce and  l o d g e p o l e p i n e i n I n t e r i o r B.C., i t i s apparent t h a t t r e e s i n the Southern and C e n t r a l I n t e r i o r zones grow f a s t e r i n h e i g h t than i n t h e N o r t h e r n I n t e r i o r Zones (Zones 11 and 1 2 ) , because s h o r t e r i n growing  5.5.3  season and severe i n c l i m a t i c  the l a t t e r are  conditions.  Mean Annual B a s a l Area Growth  The mean annual b a s a l a r e a increments f o r D o u g l a s - f i r , spruce, and l o d g e p o l e p i n e stands a r e l i s t e d F i g u r e s 5-4, 5-5, and 5-6.  i n T a b l e 5-5 and diagrammed i n  On the Coast, pure D o u g l a s - f i r stands i n  Zone 2 ( t h e Southern Coast Region) or hardwood mixed type s t a n d s .  grow f a s t e r than c o n i f e r mixed type  However, on medium s i t e zones such as  Zone 3 ( t h e South Coast T r a n s i t i o n B e l t ) the r e v e r s e i s t r u e .  In the  I n t e r i o r , mean annual increment i n D o u g l a s - f i r c o n i f e r mixed type stands i s c o n s i s t e n t l y h i g h e r than i n pure D o u g l a s - f i r and D o u g l a s - f i r hardwood mixed type s t a n d s , because D o u g l a s - f i r c o n i f e r mixed stands a r e c a p a b l e of growing more t r e e s p e r a c r e than t h e l a t t e r  ( T a b l e 5-4).  Z o n a l v a r i a t i o n s i n mean annual b a s a l a r e a growth o f Douglas-f stands a r e a l s o apparent  ( F i g u r e 5-4).  The b e s t zones f o r D o u g l a s - f i r  stands a r e i n descending o r d e r Zone 2, Zone 3, Zone 7, Zone 5, Zone 6,  Figure  5-4. C o m p a r i s o n of t h e mean b a s a l a r e a i n c r e m e n t s o f D o u g l a s - f i r s t a n d s by t y p e s a n d z o n e s  3.0 + I I I I H I H I+H I+H I+H I+H I+H I+H I +H I+H I +H I+H I +H I+H I +H I+H I+H I+H I+H I+H I+H I+H I +H I+H I+H  H H +H +H I+H I +H I+H I+H I +H I+H I+H I +H I +H I+H I+H I +H I+H I+H I+H I +H I+H I +H I+H I+H I+H I +H  I: PURE + : CM IX H: HMIX  + +  + +  1+ I+H I+H I+H I+H I +H I+H I +H  0.0 ZONE ZONE 2 3  ZONE 4  1+ I+H I+H I+H I+H I+H I+H I+H I+H I+H ZONE 5  +  1+ I+H I+H I+H I+H I+H I+H I+H I+H ZONE 6  1+ I +H I+H I+H I +H I+H I+H I+H I+H I+H I +H I +H I+H ZONE 7  1+ 1+ 1+ 1+ 1+ 1+ 1+ ZONE 8  Remarks: PURE--pure t y p e ; C M I X - - c o n i f e r  ZONE 9  mixed  ZONE 10  ZONE 1 1  ZONE 12  t y p e ; H M I X — hardwood  mixed  type.  Figure  5-5.  Comparison stands  I I H I +H I+H I+H I+H I +H I+H I+H I+H I +H I +H I+H I+H ZONE 2  ZONE 3  JONE  4  H H H H H H I H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H ZONE  5  o f t h e mean b a s a l a r e a i n c r e m a n t s o f s p r u c e by t y p e s and f o r e s t i n v e n t o r y z o n e s  I:  H H H +H I+H I+H I+H I+H I +H I+H I+H I+H I+H I+H ZONE  6  H H H +H +H I+H I+H I+H I +H I+H I +H I+H I+H I+H I+H I+H ZONE  7  PORE CMIX H: HMIX  +  1+  I+H I+H I+H I +H I +H I+H I+H I+H I+H I+H I+H I+H ZONE  Remarks: P 0 R S - - p u r e t y p e ; C M I X - - c o n i f e r  8  H H *H I+H I+ H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H ZONE  mixed  9  +•  4I +H I +H I+H I +H I+H I+H I+H I +H I +H ZONE 10  ZONE 1 1  H I H I +H I+H I +H I+H I +H I+H I +H I+H I +H I+H I+H ZONE 12  t y p e ; H M I X — hardwood  mixed  type.  Figure 5-6. Comparison of the mean annual b a s a l area increments of l o d g e p o l e pine stands by types and i n v e n t o r y zones 2.0 + < Pi  +  o  <  + +  H  <  +H  1.0  +H +H I+K I+H I +H I +H I +H I +H I+H I+H  < 00  <  0.0 + • ZONE 2  ZONE 3  ONE 4  1+ I+H I +H I+H I+H I+H I+H I+H I+H I+H I+H I+H  ZONE 5  1+ 1+ 1+ 1+ 1+ 1+ 1+ 1+ 1+ 1+ 1+ 1+  ZONE 6  1+ 1+ I+H I+H I+H I +H I+H I +H I+H I +H I+H I+H I+H  1+ I +H I +H I+H I+H I+H I +H I +H I +H I +H I+H  ZONE 7  ZONE 8  +  Remarks: PURE--pure type;CMIX--conifer  I+H 1+ H I+H I+H I+H 1+ H I+H I+H I+H I+H I+H I+H I+H I+H  ZONE 9  I : PURE CM IX H: HMIX I I I H I H I H I H I H I H I+H I+H I+H I+H I +H I+H I +H  ZONE 10  +H +H +H •H +H I +H I +H I +H I +H I+H I +H I +H  ZONE 11  ZONE 12  mixed type;HMIX—hardwood  mixed type.  - 96  Zone 4, and Zone 8. by K r a j i n a (1969).  -  The sequence c o n f i r m s the f i e l d  observations  In Zone 4 (the I n t e r i o r Dry B e l t ) and Zone 8  (the Nechako-Fraser P l a t e a u Region) the numbers of t r e e s per a c r e a r e s i g n i f i c a n t l y l e s s than those i n o t h e r I n t e r i o r zones (Table 5-4). A comparison of the mean b a s a l a r e a growth of spruce by s p e c i e s c o m p o s i t i o n types and  stands  i n v e n t o r y zones i n d i c a t e s t h a t mixed  type stands y i e l d more than pure spruce type stands i n b a s a l a r e a growth.  I n s p e c t i o n of T a b l e s 5-4  and 5-6  r e v e a l s t h a t the mean b a s a l  a r e a growth i s h i g h l y c o r r e l a t e d w i t h number of t r e e s per a c r e . V a r i a t i o n s i n mean b a s a l a r e a increment  of spruce stands i n the  I n t e r i o r zones a r e much l e s s than those of D o u g l a s - f i r stands, Zone 11  although  (the Northern C e n t r a l P l a t e a u Region) shows more r e d u c t i o n i n  mean b a s a l a r e a growth than do the o t h e r  zones.  The advantages of c o n i f e r mixed stands i n term of b a s a l a r e a growth a r e shown i n l o d g e p o l e p i n e .  Lodgepole  p i n e - c o n i f e r mixed stand  grow c o n s i s t e n t l y f a s t e r i n mean annual b a s a l a r e a increment  per a c r e  than do pure l o d g e p o l e p i n e or l o d g e p o l e pine-hardwood mixed type stand T a b l e 5-6  and F i g u r e 5-6  i n d i c a t e , e x c e p t i n g i n Zone 10 where sample  p l o t s f o r l o d g e p o l e p i n e - c o n i f e r mixed type stands were too few ascertain  ( T a b l e 5-2),  to  l o d g e p o l e p i n e - c o n i f e r mixed stands grow f a s t e r  than pure l o d g e p o l e p i n e stands i n mean annual b a s a l a r e a .  The  conifer  mixed stands a r e not o n l y c a p a b l e of growing more t r e e s per a c r e but a l s o c a p a b l e of p r o d u c i n g t r e e s l a r g e r i n DBH evidenced  i n Table  5-4.  than pure type stands  as  - 97 -  5.5.4''  Mean Annual Volume Growth  Mean annual volume increments  f o r the pure and mixed stands o f  D o u g l a s - f i r show a s i m i l a r p a t t e r n t o t h e mean annual b a s a l area growth ( T a b l e 5-6 and F i g u r e 5-7).  F o r I n t e r i o r stands, t h e t r e n d  i s c o m p l i c a t e d by t h e f a c t t h a t pure stands grow f a s t e r i n some zones and slower i n the o t h e r s ( T a b l e 5-6, F i g u r e 5-8). F i g u r e 5-9 and T a b l e 5-6 show t h a t l o d g e p o l e p i n e - c o n i f e r mixed type stands grow u n i f o r m l y f a s t e r than pure type stands i n t h e mean annual volume growth w i t h an e x c e p t i o n o f Zone 10 where pure  stands  grow e x c e l l e n t l y .  5.6  D i f f e r e n c e i n Growth and Y i e l d Between Coast and I n t e r i o r Douglas-fir  Stands  F o r e s t t r e e s grown on t h e Coast have been observed different  from those grown i n t h e I n t e r i o r  t o be  (B.C. F o r e s t S e r v i c e , 1976);  however, t o what e x t e n t they d i f f e r has n o t y e t been r e p o r t e d .  The  D o u g l a s - f i r i n v e n t o r y d a t a p r o v i d e a sound b a s i s f o r a comparison o f growth and y i e l d between these two g e o g r a p h i c a l r e g i o n s . T a b l e 5-10 p r e s e n t s some stand parameters f o r D o u g l a s - f i r stands on t h e Coast and i n t h e I n t e r i o r . a r e p r i m a r i l y second  growth, t h e r e f o r e , the average  younger than t h a t i n t h e I n t e r i o r . age  The Coast D o u g l a s - f i r stands stand age i s much  Because o f t h e d i f f e r e n c e i n stand  (55 and 89, r e s p e c t i v e l y ) , a d i r e c t  comparison cannot be made;  F i g u r e 5-7. Comparison of the mean a n n u a l volume D o u q l a s - f i r by types and zones  i n c r e m e n t s of  100 +  80.0<  60. 0< w oi o < H  3 U 40. 0< o >  20. Q<  0. 0+-  I+H I +H I+H I+H I+H I +H I + H. I+H I+H I +H I+H I+H I+H I+H I+H I+H I+H I +H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+K I+H I+H ZONE 2  H H H +H +H +H +H I+H I+H I+H I+H I+H I+H I+H I+H I +H I +H I+H I+H I+H I+H I+H I +H I+H I +H I+H I +H I+H I +H I +H I +H I +H I+H I+H I +H I+H I + Ii I+H I+H I+H I +H I+H I +H I+H ZONE 3  I : PU8E +: CMIX H: HMIX  oo  + +  + +  1+ + + +  1+  I+H I +H I +H I +H I +H I+H I+H I+H ZONE U  I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H ZON E 5  + +  1+ 1+  I+H I+H I+H I+H I +H I+H I +H I+H I+H  ZONE 6  +H I+H I+H I+H I+ H I+K I+H I+H I+H I +H I +H I +H I+H I+H I+ H I+H I+H I+K ZONE 7  +  1+ 1+ 1+ 1+ 1+ 1+ 1+ 1+ 1+ ZONE 8  Remarks: PURr>-pure type;CMIX--coni£er  ZONE 9  mixed  ZONE 10  ZONE 11  ZONE 12  type;HMIX—hardwood  mixed  typa.  F i g u r e 5-8. Comparison of the mean annual volume i n c r e m e n t s o f s p r u c e by t y p e s and zones 50. 0 +  40.  H H H H H H H I H I H I H I I H I I H I H I H H I+H I H I H I +H I+H I H I+H I+H I H I+H I+H I H I+H I+H I+H I+H I+K I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I +H I+H I+ H I+H I+H I+H I+H I+H I +H I +H I+H I+H I+H I+H I+H I+H I+H I+H I +H I+H I+H I+H I+H I+H I +H I+H I+H I+H I+H I+H I+U I+H I+H I+H I+U I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+U I+H I+H I+H I+H I+H I+H I+ H I+H I+H I+H I+H I+H I+H I+H • I+H I+H I+H I+H I+H I+H I+H I+H ' I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H  O-i  30. 0<  at  <  3  20. 0 +  s  o >  10. O-i  0.0 ZCNE 2  ZCNI 3  ZONE 4  ZONE 5  ZONE 6  + +  I+H 1+ I+H 1+ I+H 1+ I+ H 1+ I+H 1+ I+H 1+ I+H 1+ I+H I+'H I+H I+H I+H I+H I+ H I+H I+H I+H I+H I+H I+H I+H I+H I+ H I+H I+H I+H I+H I+H I+H I+H I+H I+H • I+H I+H I+H I+H I+H I +H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I +H I+H I+H I+H I +H I+H I+H I+H I+H I+H I+H I+H I+H I+H I + il I+H I+H I+H ZON E 7  ZONE 8  Remarks: PURE--pure t y p e ; C M I X - - c o n i f e r  H H H +H •H +H +H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H 1+ H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H 1+H I+H I+H ZONE 9  I : PURE + : CMIX H: H MI X  + + + + •  + +  1+  I+H I +H I+H I+H I+H I +H I +H I +H I+H I+H I+H I+H I +H I +H I +H I+H I +H I+H I+H I+H I+H I +H I +H ZONE 10  ZONE 11  I I I H I H I H I H I+H I +H I+H I+H I+H I+H I+H I +H I +H I +H I+H I+H I+H I+H I+H I+H I +H I+H I+H I +H I+H I +H I +H I+H I+H I+H I+H I+H I+H  vo  ZONE 12  mixed type;HMIX—hardwood  nixed type.  F i g u r e 5-9. Comparison of t h e mean a n n u a l volume i n c r e m e n t s o f l o d g e p o l e p i n e by t y p e s and z o n e s 50. 0 +  + +  I: PORE fii:; CMIX HMIX  40. 0<  + + + +  + +  1+  H H H +H +H +H +H +H +H +H +H +H I+H I +H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H  30.0*  < 1=3  ix W  OA  20. O-i  o >  10. 0<  0.0 ZONE 2  ZONE 3  ONE 4  I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+ H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H ZONE 5  Remarks: P U R E — p u r e  + +  1+ 1+ 1+ 1+ 1+ 1+ 1+ 1+ 1+ 1+ 1+ 1+ 1+ 1+ 1+  I* 1+ 1+ 1+ 1+ 1+ 1+ 1+ 1+ 1+ 1+ 1+ 1+ 1+ • 1+ 1+  ZONE 6  1+ 1+ 1+ 1+ 1+ 1+ 1+ 1+ 1+  I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H 1+H I+H 1 +H I+H I+H I+H I+H I+H I+ H I+H I +H ZONE 7  I+H I+H I+H I+H I+H I+H + I+H + I+H + I+H + I+H 1+ I+H 1+ I+H I+H 1+ H I + H • I+H I+H I+H I+H I+H I+H I+H I+H 1+ H I+H I+H I + H. 1+ H I+H I+H I+H I+H I+H I+H I+H 1+ H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I +H I+H I +H I+H I+H I+H I+H I+H I+H I+H I +H I+H I+H I+H I+H I+H I+H I+H I +H I+H I+H I+H I+H I+H ZONE 8  type;CMIX--conifer  ZONE 9  I I I I I I I I I I I H I H I H I H I H I H I H I H I H I H I H I H I H I H I H I H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H ZONE 10  H +H +H +K +H +H +H +H +H •H •H •H +H I+H I+H I+H I +H I+H I +H I+H I +H I+H I +H I+H I+H I+H I+H I+H I+H I+H I+H I+H ZONE 11  o o  ZONE 12  mixed type;HMIX—hardwood  nixed  type.  - 101  -  however, the s t a t i s t i c s l i s t e d i n T a b l e 5-10  w i l l shed some l i g h t  on the d i f f e r e n c e i n growth and y i e l d between these two  regions.  The d i f f e r e n c e i n growth and y i e l d between Coast and  Interior  can be e x p l a i n e d i n p a r t by the d i f f e r e n c e i n s i t e index which i s 120 f o r the Coast and 78 f o r the I n t e r i o r s t a n d s .  Because of the d i f f e r e n c e  i n s i t e q u a l i t y , the average number of t r e e s p e r a c r e i s 188 f o r the Coast stands and 121 f o r the I n t e r i o r s t a n d s . per a c r e has two i m p l i c a t i o n s f o r : and  The number of t r e e s  (1) the r a t e of b a s a l a r e a  (2) the measurement of t o l e r a n c e t o crowding.  growth,  The h i g h e r number of  t r e e s per a c r e on the Coast seems t o suggest t h a t D o u g l a s - f i r i s f a i r l y plastic  i n response t o growing space.  more space t o grow w h i l e on good s i t e s growing  On poor s i t e s D o u g l a s - f i r  requires  i t reduces the requirements of  space t o some e x t e n t . At  average age 55, the Coast D o u g l a s - f i r stands are c h a r a c t e r i z e d  by stand parameters  as f o l l o w i n g :  h e i g h t o f dominant and codominant square f e e t p e r a c r e , and y i e l d parameters  average DBH  i s 11.38  i n c h e s , average  t r e e s 87 f e e t , average b a s a l a r e a  4584 c u b i c f e e t per a c r e .  f o r the I n t e r i o r stands a t age 89 a r e 11.51  The same  i n c h e s , 73  88 square f e e t , and 2264 c u b i c f e e t per a c r e f o r average DBH, b a s a l a r e a , and volume y i e l d  140  feet,  height,  respectively.  Comparing the mean annual increments of h e i g h t , b a s a l a r e a , and volume between these two more e v i d e n t .  g e o g r a p h i c a r e a s , the d i f f e r e n c e becomes  In mean annual h e i g h t increment, the Coast stands  outgrow the I n t e r i o r by 2 times; the mean annual b a s a l a r e a by times; and by 3.3  2.6  times on the mean annual volume growth (84.00 v s . 25.53  c u b i c f e e t p e r a c r e per y e a r ) .  Table  5-10.  Comparison of D o u g l a s - f i r stands and i n t h e I n t e r i o r COAST  g r o w n on t h e C o a s t INTERIOR  Plf HE  CM IX  HMIX  404  172  51  TOTAL  PURE  CMIX  HMIX  59  635  1450  798  84  2332  • 67  47  55  91  87  67  39  122  113  129  120  77  80  85  78  196  178  161  188  1 04  149  138  121  1. 03  0.93  0. 98  1.00  0.90  1.16  1.15  1 . 00  .1 1 .03  12.19  1 1.43  11.38  11. 77  11.14  .10.35  86  91  86  87  71  75  75  73  Basal Area, 136 (sq.ft./acre) Volume, 4416 (cu. f t / a c r e ) M.A.I.—HT 1.70 (ft/yr.) M. A. I . — BA 2. 68 isq. ft/acre/yr. M. A. I . — V O L 87. 29 (cu.ft/acre/yr.)  156  119  140  79  103  83  88  5240  3823  4584  200 1  2753  2146  2264  1. 36  1. 84  1 .60  0.78  0.87  1.12  0. 82  2. 34  2. 54  2. 56  0. 87  1.19  1.25  0. 99  78.64  81. 88  84.00  21.97  3 1.77  32.25  25. 53  No.  Plots  S t a n d Age (Year) S i t e Index No. T r e e s per acre Relative Stand Density A v e r a g e DBH (inch) Height, f t  R e m a r k s : PURE, CMIX„ a n d HMIX a s d e f i n e d i n T a b l e 5-2. HT-- h e i g h t ; B A — b a s a l a r e a ; VOL-- n e t v o l u m e .  TOTAL  11.51  - 103  -  Among the t h r e e s p e c i e s c o m p o s i t i o n types  investigated,  pure D o u g l a s - f i r type stands seem to be the b e s t type on the Coast w h i l e D o u g l a s - f i r c o n i f e r mixed type grows the b e s t i n the  Interior.  C o a s t a l pure D o u g l a s - f i r type stands have more t r e e s (196 per a c r e ) , h i g h e r r e l a t i v e stand d e n s i t y i n b a s a l a r e a (2.68  (1.03), h i g h e r mean annual  increment  s q . f t . per a c r e / y e a r ) and volume (87.29 c u . f t .  per a c r e / y e a r ) than stands of mixed t y p e s .  Interior Douglas-fir  c o n i f e r mixed type stands have more t r e e s per a c r e and h i g h e r r e l a t i v e stand d e n s i t y than pure, and D o u g l a s - f i r hardwood mixed type s t a n d s .  5.7  Comparison o f Volume Y i e l d by S p e c i e s Composition  Types  and F o r e s t I n v e n t o r y Zones  The main o b j e c t i v e s of t h i s study were t o a s s e s s the d i f f e r e n c e i n y i e l d between s p e c i e s c o m p o s i t i o n types and among f o r e s t i n v e n t o r y zones:  To accomplish these ends, the i n v e n t o r y d a t a were c l a s s i f i e d  by s p e c i e s c o m p o s i t i o n types and i n v e n t o r y zones and a n a l y z e d by fixed effect  Y  where  l i n e a r model:  ijk  y + a. i  + 3. + .1  (ag).. + xi  yX  ijk  + e  Ijk  = g e n e r a l mean;  l  3.  the  = i - t h s p e c i e s c o m p o s i t i o n type; = j - t h F o r e s t I n v e n t o r y Zone;  J  = i n t e r a c t i o n term f o r s p e c i e s type and F o r e s t I n v e n t o r y Zone  (5-1)  - 104  Y  -  = a c o e f f i c i e n t f o r age,  c o v a r i a b l e , age i n  natural logarithmic scale; e .  = unexplained residues.  13k  Because of the unbalanced (Table 5-2),  n a t u r e of the i n v e n t o r y d a t a  a n a l y s e s f o l l o w e d the procedures  by u s i n g the F o r t r a n program developed squares  d e s c r i b e d i n Chapter  by the w r i t e r .  f o r these a n a l y s e s a r e i n Appendix 3.  are l i s t e d  i n T a b l e 5-11,  5-12,  5-16,  respectively.  The  i n T a b l e s 5-13,  The  and 5-19  I n t e r i o r D o u g l a s - f i r , I n t e r i o r spruce, and  used  The  3  least  estimated  constants  f o r Coast D o u g l a s - f i r ,  l o d g e p o l e p i n e volume d a t a ,  c o r r e s p o n d i n g a n a l y s i s of v a r i a n c e t a b l e s a r e p r e s e n t e d  5-14,  5-17,  and  5-20.  To f a c i l i t a t e comparison among s p e c i e s types and i n v e n t o r y zones,  p o t e n t i a l y i e l d s at age 100 were c a l c u l a t e d based  constants l i s t e d i n T a b l e s 5-15, pine,  i n T a b l e s 5-11, 5-18,  5-16,  and  5-19  and were p r e s e n t e d  f o r D o u g l a s - f i r , spruce, and  lodgepole  respectively. In  stand age,  a l l f o u r a n a l y s i s of v a r i a n c e tables,'-.the c o v a r i a t e f a c t o r ,  accounts f o r more v a r i a t i o n than do the s p e c i e s t y p e s ,  i n v e n t o r y zones, and  5.7.1  and 5-21  5-12,  on the e s t i m a t e d  the  interactions.  Douglas-fir  For the Coast D o u g l a s - f i r stand d a t a , the s p e c i e s types  and  i n v e n t o r y zones a r e not s i g n i f i c a n t ; however, the i n t e r a c t i o n s f o r s p e c i e s types and zones a r e s i g n i f i c a n t at the 1% l e v e l  ( T a b l e 5-13).  Table  5-11.  Estimated constants f o rCoast (Unit; cu. f t .per acre)  INVENTORY  volume  yield  ZONE  2 5.50  TYPE  Douqlas-fir  3 -5.50  INTERACTIONS PUEE  -71.20  5.20  -5.20  CMIX  -89. m  -2.93  2.93  HMIX  160.61  -2. 27  2. 27  MEAN = -16176.0  LOG AGE =  121.51  R e m a r k : P U R E , C M I X , a n d HMIX a s d e f i n e d i n T a b l e 5 - 2 .  o  Table  5-12  Estimated constants f o r I n t e r i o r y i e l d (Unit: cu.ft/acre)  TYPE  .4 -389. 62  INVENTORY ZONE 5 6 278. 35  Douqlas-fir  volume  7  -171. 52  931. 35  -648.55  INTERACTIONS PURE  -93.02  2.43  16.13  4. 97  -136. 71  113.18  CM IX  270. 83  -4.89  -61.93  80.00  100.00  -113. 18  H MIX  -177.81  2. 45  45. 80  -84. 97  36. 71  GENERAL MEAN = LOG  -7079.17  AGS = 4794.69  Remark: PURE, CMIX, and HMIX as d e f i n e d  i n Table  5-2.  o  ON  Table  5-13.  A n a l y s i s of v a r i a n c e f o r the Coast net  Source_of Variation  Douqlas-fir  volume y i e l d b y s p e c i e s t y p e s and i n v e n t o r y zones.  D.F.  Mean Squares  F-Value  Tabulated F-Value (5%)  S p e c i e s type  2  976320.0  0.13  3.01  F.I.2.  1  6518.0  0.00  3.86  Type X F . I . Z .  2  31763000.0  4.19**  3.01  300.30**  3.86  5  Log.  Age  Error ** S i g n i f i c a n t  1 628 at 1%  22745X10 7575800 level.  hO  1  Table  5-14.  Analysis of variance net volume y i e l d  Source of Variation  D.F.  f o r the I n t e r i o r D o u q l a s - f i r by s p e c i e s t y p e s and i n v e n t o r y F-Value  Mean S g uares •7  Tabulated F-value {5%)  2  1.45038X10  6. 19**  3. 00  F.I.Z.  4  4.50359X10  19.24**  2.38  Type X F . I . Z .  7  1 . 24560X10  1  1 . 3999 1X10  Species  type  Covariate-Log. age Error  2317  2.34 107X10  * S i g n i f i c a n t a t 5% l e v e l ; ** S i g n i f i c a n t a t 1% l e v e l .  0. 53  6  6  zones.  2. 02  o oo  5  597.98**  3.00  'able  5-15. P o t e n t i a l B.C.  TYPE  y i e l d o f D o u q l a s - f i r a t a q e 100 i n F o r e s t I n v e n t o r y Zones FOREST INVENTORY  COAST 2 PURE MEAN  CMIX  ZONES  INTERIOR 3  ALL  4  5  6  7  8  ALL  8579  7540  8433  2216  2898  2437  3398  2068  2582  MEAN 7 7 4 8  8335  7970  2139  2997  2687  3812  2019  3114  o  fiflIX  MEAN 8 0 6 5  WEIGHTED MEAN  Remarks:  8354  8518  8157  1945  2656  2076  3300  8013  8232  2194  2920  2590  3599  P U R E , C M I X , a n d HMIX a s d e f i n e d i n T a b l e 5 - 2 . Unit: cu. f t .per acre. ALL a r e w e i g h t e d m e a n s f o r s p e c i e s composition.  VO  3097 2064  2793  Table  5-16.  Estimated constants f o r I n t e r i o r yield (Unit.cu. ft./acre)  MAIN  FOREST INVENTORY  EFFECTS  TYPE  4  5  136.08  1330.26  6  .  spruce  ZONE  7  -164.79  n e t volume  8 195.60  -47.91  9  10  12  266.24  -1174.91  -540.56  278.15 -307.11  -179.68  3 14.23  INTERACTIONS PURE  -13.74  CMIX  -51.23  H MIX  64.97  519.70 -1033.73  298.51  109.93  -212.58  -438.58-190.61  74.65  345.51  100.34  638.33  •317.56  -307.12  1472.31  -107.90 -134.58  -623.60  206.27  -458.64  3. 33 I-  1  GENERAL  Remark:  MEAN = -9876. 69  LOG  AGE  =  6873.34  PURE, CMIX, and HMIX a s d e f i n e d  i n Table  o 5-2.  Table  5-17. A n a l y s i s o f v a r i a n c e f o r n e t v o l u m e y i e l d s o f I n t e r i o r S p r u c e s t a n d s by s p e c i e s t y p e s and i n v e n t o r y zones.  Source o f Variation  D, F„  Mean Squares  F-Value  Species type  2  3. 4836X10  5  F.I.Z.  7  4. 1757X10  7  Type x F. I. Z.  14  ,7 1.1101X10'  Covariate— Loq. Age  1  2. 3211X10  2594  3.2018X10  Error  ** S i g n i f i c a n t  a t 155 l e v e l .  1  10  0.11  Tabultaed F - V a l u e (5%)  3.00  13.04**  2.02  3.47**  1.70  724.94**  3.00  T a b l e 5-18. P o t e n t i a l by  y i e l d o f I n t e r i o r s p r u c e s t a n d s a t age f o r e s t i n v e n t o r y z o n e s and t y p e s  TYPE  FOREST  PURE, MEAN  4  5  4513  4154  6 3991  INVENTORY 7 4297  100  ZONE 8  4221  9  11  12  MEAN  3950  2636  3765  3901  CMIX, MEAN  3743  4711  3464  4090  4117  4187  3283  2 96 2  3924  HMIX, MEAN  3765  6739  3663  3947  3264  4408  2302  3399  3722  WEIGHTED MEAN  3944  4364  3581  4119  4076  4131  2751  3561  Remarks: PURE, CMIX, and HMIX a s d e f i n e d i n T a b l e Weighted  mean: w e i g h t e d  by number o f  5-2.  plots.  i  i - 11 i-  I  Table  5-19. E s t i m a t e d c o n s t a n t s f o r l o d q e p o l e by s p e c i e s t y p e s and i n v e n t o r y  TYPE  p i n e n e t volume zones  yield  FOREST INVETOHY ZONE 5 -506.26  104.00  6 99.73  7  8  234.07  -137.85  10 984.27  15.34  12 -593.84 i  INTERACTIONS PORE  9.06  -590.48  -21.30  50.93  CMIX  1.68  148. 63  154.70  -50. 93  H MIX  -10.74  441.85  -133.40  GENERAL MEAN  -8459. 30  LOG AGE =  i—  110.76  -123.20  -133.27  280. 40  369. 56  396.15  -391.15  -237.35  -262.88  5929.69  Remarks: PURE, CMIX, and HMIX a s d e f i n e d i n T a b l e U n i t : cu. f t . per acre.  5-2.  1  H to  1498.15  -782.59 •  1637.15  338.65  138.99  443.95  Table  5-20. A n a l y s i s o f v a r i a n c e f o r l o d q e p o l e p i n e n e t volume y i e l d by s p e c i e s t y p e s and i n v e n t o r y z o n e s  Source of  D. F.  Variation 2  F.I.z.  7  Covariate-Log Age Error ** S i g n i f i c a n t  F-Value  Squares  Species type  Type x F . I . Z .  M e an  7alues  41288.4  0.02  8 1. 1084X10'  13  2.10421xl0 ;  1  2.9628X10  4175 at 1%  7  2.3502X10 level.  Tabulated  10  3.00  47.18**  2.02  8.69**  1.73  1260. 63**  3.00  F  15%)  Table  TYPE  5-21. P o t e n t i a l y i e l d s o f I n t e r i o r l o d q e p o l e p i n e a t aqe , 100 by s p e c i e s t y p e s and f o r e s t i n v e n t o r y zones (Unit: cu. f t . per acre)  4  5  6  FOREST INVENTORY ZONE 7 8 9 10  12  MEAN  PURE, MEAN  3583  3629  3720  3657  3845  3881  4480  3496  3786  CMIX, MEAN  3955  3429 .  3802  3583  4123  4263  2379  4294  3921  HMIX, MEAN  3577  3519  3167  3457  3926  2967  4061  3525  WEIGHTED MEAN  3664  3563  3598  3782  4045  3824  3919  —  3760  F e m a r k s : PURE, CMIX, and HMIX as d e f i n e d i n T a b l e 5-2. W e i g h t e d means a r e w e i g h t e d by number o f p l o t s .  - 116 -  In the I n t e r i o r , s p e c i e s types and i n v e n t o r y zones a r e s i g n i f i c a n t at the 1% l e v e l w h i l e t h e - i n t e r a c t i o n s a r e n o n - s i g n i f i c a n t . Comparing the p o t e n t i a l y i e l d o f D o u g l a s - f i r stands a t age 100 i n T a b l e 5-15 and F i g u r e 5-10,  one observes D o u g l a s - f i r stands i n  Zone 2 ( t h e South Coast Region) y i e l d  251 c u b i c f e e t per a c r e more  than i n Zone 3 (the South Coast T r a n s i t i o n B e l t ) .  T h i s i s i n agreement  w i t h g e n e r a l o b s e r v a t i o n s which f i n d Zone 2 i s more p r o d u c t i v e than Zone 3. Wet  In t h e I n t e r i o r , t h e most p r o d u c t i v e zone i s 7 (the I n t e r i o r  B e l t ) w i t h a p o t e n t i a l y i e l d of 3599 c u b i c f e e t p e r a c r e a t age 100.  The next most p r o d u c t i v e zone i s 5 (the West Kootenay Region) w i t h a p o t e n t i a l y i e l d o f 2920 c u b i c f e e t p e r a c r e .  Zone 5 i s f o l l o w e d i n  p r o d u c t i v i t y by Zone 6 (the E a s t Kootenay Region) w i t h a p o t e n t i a l y i e l d o f 2590 c u b i c f e e t per a c r e and Zone 4 (the I n t e r i o r Dry B e l t ) w i t h 2194 c u b i c f e e t .  The l e a s t p r o d u c t i v e zone i s 8 (the Nechako-  F r a s e r P l a t e a u Region) w i t h 2064 c u b i c f e e t p e r a c r e at age 100.  The  d r y and severe weather c o n d i t i o n s i n the l a t t e r two zones p r o b a b l y inhibit  the growth of D o u g l a s - f i r s t a n d s . The p o t e n t i a l y i e l d  i s 8282 c u b i c f e e t per a c r e f o r Coast  D o u g l a s - f i r and 2793 c u b i c f e e t f o r the I n t e r i o r stands a t age (Table 5-15).  In o t h e r words, the Coast D o u g l a s - f i r stands  100  outyield  the"-Interior ones by as much as 3 times. Among the s p e c i e s c o m p o s i t i o n t y p e s , pure D o u g l a s - f i r type stands y i e l d the b e s t among t h r e e types i n v e s t i g a t e d i n Zone 2 w i t h a p o t e n t i a l y i e l d of 8579 c u b i c f e e t per a c r e which i s 831 c u b i c f e e t more than t h a t o f D o u g l a s - f i r mixed type stands a t age 100.  However,  F i g u r e 5 - 1 0 . P o t e n t i a l y i e l d of D o u q l a s - f i r a t age 1 0 0 by t y p e s and i n v e n t o r y zones  9000  8000 +  5000 +  • 4000 +  2000 +  I H I +H I H +H I H +H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I +H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H 1+H I+H I + H •I + H I+H I+H I+H I +H I+H I+H I+H I +H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I +H I+H I+H I+H I+H I+H I +H I +H I+H ZONE 2  ZONE 3  I:  PORE  +: K:  CMIX H MIX  +  1+  1+  I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H ZONE 4  I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H ZONE 5  +  1+ 1+  I+H I+H I+H I +H I+H I +H I +H I+H I+H I+H ZONE 6  + I+H I+H I+H I+H I+H I +H I+H I +H I+H I+H I+H I+H I+H I+H I+H I+H I+H ZONE  1+ 1+ 1+ 1+ 1+ 1+ 1+ 1+ 1+ 1+  ZONE  7  8  Remarks: PURE--pure type;CMIX - - c o n i f e r HMIx--hardvood mixed t y p e .  mixed  ZONE 9  ZONE 10  ZONE 1 1  ZONE 12  - 118  -  i n Zone 3, the r e v e r s e i s t r u e ; D o u g l a s - f i r hardwood mixed type stands produce  8518  and D o u g l a s - f i r c o n i f e r mixed type 8335 c u b i c f e e t per  a c r e which a r e s u b s t a n t i a l l y h i g h e r than the p o t e n t i a l y i e l d of pure D o u g l a s - f i r type stands  (7540 c u b i c f e e t per a c r e ) a t age  The r e s u l t s suggest t h a t on a v e r y f e r t i l e t h a t i n the South Coast Region,  pure D o u g l a s - f i r  to grow e x c e l l e n t l y ; however, on a medium s o i l ,  100.  soil,  such as  type stands tend  i t i s advantageous  t o e s t a b l i s h D o u g l a s - f i r hardwood mixed type or D o u g l a s - f i r  conifer  mixed type s t a n d s . In the I n t e r i o r , d i f f e r e n c e i n y i e l d among these t h r e e type stands i s not as c o n t r a s t i n g as t h a t on the Coast, because p r o d u c t i v e s i t e e f f e c t i v e l y reduces the d i f f e r e n c e .  the l e s s  The e s t a b l i s h m e n t  of D o u g l a s - f i r hardwood type stands i n the I n t e r i o r i s l e s s d e s i r a b l e than on the Coast, because i n a l l zones  (Table 5-15).  the stands y i e l d the l e a s t among t h r e e types A g a i n Zone 7 shows the advantages  of e s -  t a b l i s h i n g D o u g l a s - f i r c o n i f e r mixed stands on the medium s o i l where D o u g l a s - f i r c o n i f e r mixed stands produce  3812  c u b i c f e e t per a c r e  compared to 3398 f o r pure D o u g l a s - f i r stands at age 100. the p o t e n t i a l y i e l d i s 3114  In  general,  f o r D o u g l a s - f i r c o n i f e r mixed type stands  and 2582 c u b i c f e e t per a c r e f o r pure D o u g l a s - f i r type stands. o t h e r words, the e s t a b l i s h m e n t o f mixed stands e f f e c t i v e l y f o r e s t p r o d u c t i v i t y by  21%.  In  increases  - 119  5.7.2  -  Spruce  The a n a l y s i s of v a r i a n c e f o r volume y i e l d of I n t e r i o r stands  i n d i c a t e s that species composition  type e f f e c t i s not  spruce  significant  w h i l e t h e d i f f e r e n c e i n volume y i e l d among 8 i n v e n t o r y zones i s significant.  I n t e r a c t i o n s f o r s p e c i e s types and  zones a r e a l s o  s i g n i f i c a n t which i n d i c a t e t h a t y i e l d of t h r e e s p e c i e s  composition  types changes from zone to zone. On  z o n a l p r o d u c t i v i t y of spruce  stands  i n the  Interior,  Zone 5 (the WestKootenay Region) w i t h a p o t e n t i a l y i e l d of 4364 c u b i c f e e t per a c r e a t age  100  i s the most p r o d u c t i v e zone.  C e n t r a l I n t e r i o r Region),  Zone 7 (the I n t e r i o r Wet  Zone 9  (the  B e l t ) , and  Zone 8  (the Nechako-Fraser P l a t e a u Region) are e q u a l l y p r o d u c t i v e w i t h 4119,  and  4076 c u b i c f e e t per a c r e a t age  of spruce stands  100.  The p o t e n t i a l  The p r o d u c t i v i t y of spruce and  stands  f e e t per a c r e , r e s p e c t i v e l y . p r o d u c t i v e zone f o r spruce  yield  acre.  i n Interior  (Figure  3561  cubic  least  5-11).  change i n l a t i t u d e does not account f o r the v a r i a t i o n i n  c a p a c i t y of spruce stands  observed  and  Zone 11 i s , t h e r e f o r e , the  stands  inferior  i n Zone 6 (the E a s t Kootenay Region)  Zone 12 ( t h e N o r t h E a s t e r n P l a i n s Region) i s 3581  The  yield  i n Zone 4 (the I n t e r i o r Dry B e l t ) i s s l i g h t l y  to the above t h r e e zones w i t h a y i e l d of 3944 c u b i c f e e t per  4131,  in Interior.  K o i v i s t o (1971) i n F i n l a n d  t h a t the mean wood p r o d u c t i o n c a p a c i t i e s of the growth r e g i o n s  from south to n o r t h f o l l o w the sequence 100 the increment of southernmost r e g i o n as 100.  —  82 —  56 —  36 based  on  I f the y i e l d c a p a c i t y of  Figure  5-11. P o t e n t i a l by  4900 +  I I I I I I I I H I +H I+H I +H I +H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+ H I+H I+H I+H I +H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H  4000-I  3000<  DA  < H  3  2000-i  o >  1000<  0.0 ZONE 2  ONE 4 Remarks:  H +H +H +H +H +H +H +H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H 'I + H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H ZONE 5  y i e l d s o f I n t e r i o r s p r u c e a t aqe 100 s p e c i e s t y p e s and i n v e n t o r y z o n e s I : PURE + : CMIX H : HMIX  I I 1+  I I +H I I +H I I+H I H 1 +H I+H I . H I+H I+H I +H I+H I +H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I +H I+H I+H I+U I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H ' I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I +H I+H I+H I+H I+H I+H I+H I+H I +H ZONE 6  ZONE 7  I 1+ 1+ 1+ 1+ 1+ 1+ 1+ 1+  I+H I+H I +H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+K I +H I+H 1+H I+H I+H I+H I+H I+H I +H I+H I+H ZONE 8  P U R E — p u r e type;CMIX- - c o n i f e r hardwood mixed t y p e .  *H +H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H 1+ H I+H I+H I+H I+H I+H I+H I+H I+H I+H 1+ H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+U ZONE 9 mixed  + + + + + + +  1+ 1+ 1+  I+H I+H I+H I +H I+H I+H I+H I+H I+H I+H I+H I+H I +H I+H I+H I +H I+H I +H I+H I +H I+H I+H I+H ZONE 10  ZONE 11  type,HMIX__  I I I I I H I H I H I H I H I+H I+H I+H I+H I+H I +H I+H I+H I+H I +H I+H I+H I+H I +H I+H I+H I+H I +H I +H I +H I +H I+H I +H I+H I+H I +H I+H I +H I+H ZONE 12  ho  o  - 121  -  spruce stands i n the southernmost  zone which i s Zone 5 i s 100,  p r o d u c t i v i t y o f spruce stands i n the I n t e r i o r i s 92, 100, 95, 63, and 82 r e s p e c t i v e l y f o r Zone 4 t o Zone 12. C e n t r a l I n t e r i o r Region, the I n t e r i o r Wet  the  82, 94,  93,  Zones such as the  B e l t and the  Nechako-Fraser  P l a t e a u a r e h i g h e r i n l a t i t u d e than the I n t e r i o r Dry B e l t , and the East. Kootenay Region; n e v e r t h e l e s s , the former a r e more p r o d u c t i v e than the latter  (Map  1).  There i s no d i f f e r e n c e i n y i e l d among t h r e e spruce s p e c i e s types s t u d i e d as i n d i c a t e d by the n o n - s i g n i f i c a n t F - v a l u e i n T a b l e The p o t e n t i a l y i e l d s f o r pure spruce, s p r u c e - c o n i f e r mixed, and hardwood mixed type s t a n d are 3901, r e s p e c t i v e l y , a t age 100  spruce-  3922, and 3722 c u b i c f e e t per a c r e ,  ( T a b l e 5-18).  The f a c t t h a t i n t e r a c t i o n s between  s p e c i e s types and i n v e n t o r y zones a r e s i g n i f i c a n t a t the 1% l e v e l a f u r t h e r examination of the performance to  5-17.  deserves  of i n d i v i d u a l types from zone  zone. As shown i n T a b l e 5-18,  pure spruce type stands o u t y i e l d  s p r u c e - c o n i f e r mixed type stands by 770 c u b i c f e e t per a c r e i n Zone 4. In o t h e r words, the f o r e s t p r o d u c t i v i t y w i l l  i n c r e a s e by 20.6%  by  e s t a b l i s h i n g pure spruce type stands i n s t e a d of s p r u c e - c o n i f e r mixed type s t a n d s . by 13.2%  S i m i l a r l y , the p r o d u c t i v i t y o f spruce stands w i l l g a i n  i n Zone 6 and 27.1%  i n Zone 12  (the N o r t h - e a s t e r n P l a i n s  Region) by forming pure spruce stands r a t h e r than s p r u c e - c o n i f e r mixed type stands. In Zones 7 and 8 the advantages  of pure spruce type stands  i n y i e l d over s p r u c e - c o n i f e r mixed type a r e n e g l i g i b l e respectively).  (5.1 and  2.5%,  - 122  -  In Zone 5, spruce-hardwood mixed type stands yield  6739 c u b i c f e e t per a c r e at age  based  on 1 sample p l o t  which y i e l d  4711  (Table 5-2).  100;  potentially  however, the e s t i m a t e  S p r u c e - c o n i f e r mixed type  c u b i c f e e t per a c r e a r e about 13.4%  was  stands  more p r o d u c t i v e  than pure spruce type stands i n t h i s zone. The f i g u r e s i n T a b l e 5-8  s t r o n g l y support the f o r m a t i o n of  spruce-hardwood mixed type stands i n Inventory Zone 9 (the C e n t r a l I n t e r i o r Region) where the e s t i m a t e s of p o t e n t i a l y i e l d were based fairly  l a r g e number of samples ( T a b l e 5-2).  on  Spruce-hardwood mixed  type stands i n t h i s zone p o t e n t i a l l y y i e l d 4408 c u b i c f e e t per a c r e which i s 453  c u b i c f e e t more than pure spruce stands.  the stand p r o d u c t i v i t y w i l l i n c r e a s e by 11.5%  In other words,  by forming  spruce-hardwood  mixed type stands i n s t e a d of pure spruce ones.  5.7.3  Lodgepole  Pine  The a n a l y s i s of v a r i a n c e t a b l e i n T a b l e 5-20  suggests t h a t  d i f f e r e n c e i n s p e c i e s composition type has no b e a r i n g on the volume yield  of I n t e r i o r l o d g e p o l e p i n e s t a n d s .  Volume y i e l d d i f f e r s among  i n v e n t o r y zones as shown by the F - v a l u e which i s s i g n i f i c a n t at the 1% l e v e l .  The  i n t e r a c t i o n s f o r s p e c i e s composition types and i n v e n t o r y  zones are a l s o s i g n i f i c a n t a t 1%  level.  To f a c i l i t a t e the i n t e r p r e t a t i o n of the a n a l y s i s of v a r i a n c e t a b l e , p o t e n t i a l y i e l d of l o d g e p o l e p i n e stands a t age based  on the e s t i m a t e d c o n s t a n t s i n T a b l e 5-19  and F i g u r e  5-12.  100 was  and p r e s e n t e d  calculated  i n Table  5-21  F i q u r e .5- 12. P o t e n t i a l y i e l d s a t aqe 100  of I n t e r i o r  lodqepole pine  stands  4900 + I: PURE  +:  cnix  H: HMIX  4000H  + + +  + I +H I +H I +H I+H I +H I +H I +H I+H . I+H I + II I+H I +H I +H I +H I +H I +H I+H I +H I+H I +H I+H I+H I+H I +H I+H I+H I +H I+H I+H I+H I+H I +H I+K I+H I+H I+H  300G<  2000<  S o >  1000^  0.0 ZONE 2  ZONi 3  ONE 4  + I I+H I+H I+H I+H I+H I+ H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+U I+H I+H I+H I+H I+H I+ H I +H I+H I+H I+H I+H I+H I +H I+H ZONE 5  1+ 1+ 1+ 1+ 1+  I+ 1+ 1+ 1+ 1+ 1+ 1+  I* 1+ 1+ 1+ 1+ 1+ 1+ 1+ 1+ 1+ 1+ 1+ 1+ 1+ 1+ 1+ 1+ 1+ 1+ 1+ 1+ 1+ 1+ 1+ 1+  ZONE 6  + + + + + + 1+ I+H 1+ I+H I 1+ I+H 1+ 1+ I+H 1+ I+H I+H 1+ I +H I+H 1+ I + H' I+H I +H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I+H I +H I +H I+H T+H I +H 1+H I +H I+H I+H I+H I + H . I+H I +H I+H I+H I+H 'I+H I+H I+H I+H I+H I+ H I+H 1+ H I +H I+H I+H 1+H I +H 1+ H I+H I+H I+H I+H I +H I+H I +H I+H I+H I+H I+H I+H I+H I +H I+H I+H I+H I+H I+H I +H I+H I+H I+H I+H I +H I+H I+H I+H I+H I+U I +H I+H I+H I+H I+H I+H I+H I+H I+H I+H I +H I+H I +H I +H I+H I+H I+H I+H I+U I+H I+H I+H I+H I+H ZONE 7  ZONE 8  Remarks:PURE--pure t y p e ; C M I X - - c o n i f e r hardwood mixed t y p e .  ZONE 9 mixed  I I I I I I I I I I I I I I I I I H I H I H I H I H I+H I+H I +H I+H I+H I+H I+H I+H I+H I+H I +K I+H I+H I+H I+H I+H I+H I+H 1+H I+H I+H I+H I+H I+H ZONE 10  + + + +H +H +H +H +H I +H I+H I+H I+H I +H I+H I +H I+H I+H I +H I +H I+K I+H I +H I +H I +H I+H I +H I+H I +H I +H I +H I+H I +H I+H I +H I+H I+H I +H I +H I +H I+H I +H I+H I+H ZONE 11  typejHMIX—  ZONE 12  N5  - 124  The  -  z o n a l p r o d u c t i v i t y v a r i e s among I n t e r i o r l o d g e p o l e  pine  stands as i n d i c a t e d by the a n a l y s i s of v a r i a n c e t a b l e (Table 5-20). The p o t e n t i a l p r o d u c t i v i t y of I n t e r i o r l o d g e p o l e p i n e can be i n descending  o r d e r as:  ranked  the C e n t r a l I n t e r i o r Region (Zone 9 ) , the  N o r t h - e a s t e r n P l a i n s Region (Zone 12), the North Western P l a t e a u Region (Zone 10), the Nechako-Fraser P l a t e a u Region (Zone 8 ) , the East Kootenay Region (Zone 6 ) , the I n t e r i o r Dry B e l t I n t e r i o r Wet  Belt  (Zone 7), and  (Zone 4 ) , the  the West Kootenay Region  (Zone 5 ) .  D i f f e r e n c e i n p o t e n t i a l y i e l d between the b e s t zone (Zone 9) and  the l e a s t p r o d u c t i v e zone (Zone 5) i s s m a l l e r i n l o d g e p o l e  than i n spruce.  The h i g h F - v a l u e  (47.18) f o r f o r e s t  pine  i n v e n t o r y zone  seems to be a t t r i b u t e d to the f a i r l y l a r g e number of sample p l o t s used. A c c o r d i n g to K r a j i n a (1969), of l o d g e p o l e p i n e a r e the w i d e s t Columbia.  The  general c l i m a t i c  f o r any  requirements  coniferous tree i n B r i t i s h  i n s e n s i t i v i t y of l o d g e p o l e p i n e toward changes of c l i m a t i c  conditions probably  e x p l a i n s i t s r e l a t i v e l y homogeneous p r o d u c t i o n  c a p a c i t y among i n v e n t o r y zones (Table 5-21  and F i g u r e 5-12) .  Taking the p o t e n t i a l p r o d u c t i o n c a p a c i t y of Zone 5 as the r e l a t i v e p r o d u c t i o n c a p a c i t i e s f o r zones 4 to 12 are 103, 101,  106,  114,  107,  and  110%,  respectively.  t h e r e f o r e c l i m a t i c c o n d i t i o n s , has of l o d g e p o l e p i n e  The  100,  100,  change i n l a t i t u d e ,  and  l i t t l e b e a r i n g on the y i e l d c a p a c i t y  stands.  S p e c i e s composition  types do not s i g n i f i c a n t l y a f f e c t volume  y i e l d of l o d g e p o l e p i n e stands; however, the i n t e r a c t i o n s f o r types i n v e n t o r y zones need f u r t h e r examination at the 1% l e v e l  106,  (Table 5-20).  because they a r e  and  significant  - 125 -  Pure l o d g e p o l e p i n e type stands i n the North Western P l a t e a u Region y i e l d s u b s t a n t i a l l y h i g h e r than l o d g e p o l e p i n e mixed type (Table 5-21, F i g u r e 5-12).  Comparing t h e e s t i m a t e s f o r pure l o d g e p o l e  p i n e type stands w i t h those o f l o d g e p o l e p i n e - c o n i f e r mixed type one  can be m i s l e d by the f i g u r e s because the l a t t e r was based  sample p l o t .  stands  The p o t e n t i a l y i e l d o f pure l o d g e p o l e p i n e  stands,  on o n l y 1  stands  outweighs t h a t o f l o d g e p o l e pine-hardwood mixed type stands by as much as 1513 c u b i c f e e t per a c r e a t age 100; a magnitude o f such h i g h o r d e r should n o t be o v e r l o o k e d by managing f o r e s t e r s .  The p r o d u c t i v i t y  i n c r e a s e s by 51% by e s t a b l i s h i n g pure l o d g e p o l e p i n e stands i n s t e a d of l o d g e p o l e pine-hardwood mixed stands i n Zone 10. The y i e l d s o f pure l o d g e p o l e p i n e stands i n Zones 5 and 7 a r e b e t t e r than t h e c o r r e s p o n d i n g y i e l d s o f l o d g e p o l e p i n e - c o n i f e r mixed type stands; b u t , the i n c r e a s e d magnitudes a r e o f minor order  (6% and 2%, r e s p e c t i v e l y ) . Lodgepole  p i n e - c o n i f e r mixed type stands a r e c o n s i d e r a b l y more  p r o d u c t i v e than pure l o d g e p o l e p i n e type stands i n Zones 4, 8, 9, and 12. The p r o d u c t i v i t y o f l o d g e p o l e p i n e stands i n c r e a s e s by l l v 4 ,  7.2, 9.8,  and.22.8%in Zones 4, 8, 9, and 12, r e s p e c t i v e l y , by e s t a b l i s h m e n t o f l o d g e p o l e p i n e - c o n i f e r mixed type  5.7.4  stands.  Summary o f Volume Y i e l d by S p e c i e s Composition  and Inventory  Zones  From t h e above r e s u l t s and d i s c u s s i o n s , i t i s r e a s o n a b l e t o conclude t h a t  - 126  (1)  -  on the Coast pure D o u g l a s - f i r stand i s more p r o d u c t i v e  on v e r y f e r t i l e s i t e s , w h i l e D o u g l a s - f i r hardwood mixed type  stands  a r e recommended on medium s i t e s i f f o r e s t e r s are a f t e r more wood p r o d u c t i o n per u n i t (2)  area.  In I n t e r i o r B.C.,  D o u g l a s - f i r mixed type  stands  c o n s i s t e n t l y y i e l d more i n volume than do pure D o u g l a s - f i r s t a n d s . (3)  F o r spruce and l o d g e p o l e p i n e stands i n the  Interior,  t h e e f f e c t of s p e c i e s c o m p o s i t i o n types on volume y i e l d i s n o n - s i g n i f i c a n t w h i l e i n t e r a c t i o n s f o r s p e c i e s types and  i n v e n t o r y zones a r e  I n t e r p r e t a t i o n s of t h e s e i n t e r a c t i o n s suggested  significant.  t h a t the advantages of  m o n o c u l t u r a l o r m u l t i c u l t u r a l p r a c t i c e s should not be o v e r - g e n e r a l i z e d . Pure stands a r e more p r o d u c t i v e i n some zones but l e s s i n the o t h e r s . The  same argument a p p l i e s e q u a l l y w e l l t o advocates  practices.  for multicultural  Growth of f o r e s t t r e e s i s e s s e n t i a l l y s i t e - d e p e n d e n t ;  g e n e r a l i z a t i o n of e x p e r i m e n t a l r e s u l t s i s o f t e n hazardous. d e c i s i o n can be reached  Before a  on what s p e c i e s composition type to e s t a b l i s h ,  f o r e s t e r s should c a r e f u l l y i n v e s t i g a t e l o c a l s i t e q u a l i t y and y i e l d h i s t o r y of v a r i o u s f o r e s t (4)  over-  past  stands.  The p r o d u c t i v i t y of f o r e s t l a n d can be a m p l i f i e d  e s t a b l i s h m e n t of a stand a p p r o p r i a t e to the a r e a .  T h i s study  by  identified  theooptimum s p e c i e s c o m p o s i t i o n types f o r D o u g l a s - f i r , spruce,  and  l o d g e p o l e p i n e i n v a r i o u s i n v e n t o r y zones.  edaphic,  Because of l a c k of  c l i m a t i c and b i o t i c i n f o r m a t i o n , i t i s i m p o s s i b l e t o e x p l a i n the  reasons  f o r a s p e c i e s type y i e l d i n g more than o t h e r s i n a p a r t i c u l a r zone. F u r t h e r s t u d i e s a l o n g t h i s l i n e a r e of p r a c t i c a l v a l u e t o f o r e s t e r s i n s e l e c t i o n of an optimum s p e c i e s c o m p o s i t i o n  type.  - 127 -  5.8  I n f l u e n c e o f S p e c i e s Composition  Types on Volume Y i e l d  The above a n a l y s e s compared n e t volume y i e l d s o f t h r e e s p e c i e s c o m p o s i t i o n types i n i n v e n t o r y zones f o r t h r e e major commercial s p e c i e s i n B.C.  The comparison was r e a l i n t h a t i t i n v o l v e d f o r e s t  stands which a r e p r e s e n t l y growing i n B.C., w i t h adjustment  made o n l y  to a common age. D i f f e r e n c e i n y i e l d among these t h r e e c o m p o s i t i o n types might be a t t r i b u t e d t o d i f f e r e n c e i n s i t e q u a l i t y . of  s p e c i e s composition types on volume y i e l d  Consequently,  the i n f l u e n c e  can be b e t t e r p e r c e i v e d by  t a k i n g s i t e index and stand age as c o v a r i a t e s and a d j u s t i n g them t o a common b a s i s .  By a d j u s t i n g d a t a t o a common s i t e index, t h e a n a l y s e s  s e r v e t o answer a h y p o t h e t i c a l question:.  To what e x t e n t do they d i f f e r  i n y i e l d among t h r e e s p e c i e s c o m p o s i t i o n types i f stands o f t h e t h r e e c o m p o s i t i o n types a r e growing on t h e same s i t e ? A n a l y s i s o f v a r i a n c e t a b l e s f o r n e t volume y i e l d f o r t h i s purpose are-shown i n T a b l e s 5-22,  5-24, 5-26 and 5-28 f o r Coast D o u g l a s - f i r ,  I n t e r i o r D o u g l a s - f i r , spruce, and l o d g e p o l e p i n e , r e s p e c t i v e l y .  The  e s t i m a t e d c o n s t a n t s a r e a l s o p r e s e n t e d i n T a b l e s 5-23, 5-25, 5-27, and 5-29,  correspondingly. The a n a l y s i s o f v a r i a n c e t a b l e s show t h a t s i t e and age  r e s p e c t i v e l y account yield  f o r a l a r g e p o r t i o n o f t h e v a r i a t i o n i n volume  f o r a l l three species.  stands, s i t e accounts  With t h e e x c e p t i o n o f Coast D o u g l a s - f i r  f o r more v a r i a t i o n than does stand age.  Table  Source  5-22. A n a l y s i s o f v a r i a n c e f o r n e t volume y i e l d o f the Coast D o u q l a s - f i r stands a d j u s t e d f o r s i t e i n d e x and s t a n d age.  of  D.F.  Variation  Mean  F-Value  Squares  Tabulated F-Value  S p e c i e s type  2  2.3710X10  6  0. 63  3.01  F.I.Z.  1  1.0323X10  6  0.27  3.86  Type X F. I. Z.  2  6. 5791X 1 0  1.76  3.01  6  Covariates— Site Log  1 Age  Error  ••Significant  1 627  a t 1%  2.4070X10  9  642. 40**  3.86  3.4257X10  9  91 4.26**  3.86  3.7470X10  6  level.  (5%)  Table  5-23. E s t i m a t e d c o n s t a n t s from volume y i e l d D o u q l a s - f i r stands (Unit: Cubic f e e t per acre)  TYPE MAIN EFFECTS  INVENTOBY 2  data  3 70.0  INTERACTIONS  S3 VO  PURE  145.0  248.0  -248.0  CMIX  98.0  -114.0  114.0  HMIX -296.0  -134.0  134.0  LOG AGE =  -29642.0  Coast  ZONE  -70.0  GENERAL MEAN  of  S I T E = 66.0  15411.0  Remarks: PURE, CMIX, and HMIX as d e f i n e d  i n Table  5-2.  Table 5-24. A n a l y s i s of v a r i a n c e f o r net volume y i e l d o f the I n t e r i o r D o u g l a s - f i r stands a d j u s t e d f o r s i t e index and stand age. Source of  D.F.  Variation  Mean  F-Value  Squares  Tabulated F-Value (5%)  Species type  2  1.48306X10  10.06**  3. 00  F.I.Z.  4  1.14227X 10  7.75**  2. 38  Type x F.I.Z.  7  2.31154X10  1.57  2.02  Covariates-Site  1  2.01114X10  1364.67**  3. 85  1  1.09590X10  734.63**  3. 85  2316  1. 47371X 10  Loq Age Error  **Siqnificant  at 1% l e v e l .  T a b l e 5-25. E s t i m a t e d c o n s t a n t s f o r n e t volume y i e l d s I n t e r i o r D o u q l a s - f i r stands  TYPE  FOREST INVENTORY ZONE  MAIN  4  EFFECTS  •480. 70  5  6  -2. 98  7  339.69  8  338. 94  -194. 95  INTERACTIONS PURE  16.92  334.42  -154.13  -16.91  -134.82  -38.56  CMIX  350.78  253.95  -145.19  -185.62  38.30  38.56  HMIX -367.70  •598.36  299.32  202.52  96.52  GENERAL MEAN = -12329.0  SITE = 80.59  LOG AGE = 4260.53  Remarks: PURE, CMIX, and HMIX as d e f i n e d i n T a b l e Unit: Cubic f e e t per a c r e .  5-2.  o f the  Table 5-26. A n a l y s i s of v a r i a n c e f o r net volume y i e l d s of the I n t e r i o r spruce stands a d j u s t e d f o r s i t e index and stand age. Source of Variation  D.F,  Mean Sguares  Species type  2  1.5483X10  0.74  3.00  F.I.Z.  7  2. 5496X10*  1.21  2.02  14  5. 5028X10*  2.62*  1.70  Type x F. I. z .  F-Value  Tabulated F-Value (5X)  Covariates— Site Log Age Error  1 1 2589  * S i g n i f i c a n t at 1% l e v e l . ** S i g n i f i c a n t a t 5% l e v e l .  2. 8543X10'  1 358.88**  3. 8  2. 2287X10  9  1061.02**  3.85  2. 1005X10  6  Table  5-27.  Estimated Interior  TYPE  c o n s t a n t s from spruce stands  FOREST  HAlN EFFECTS  4 -9.53  5 646.66  volume d a t a  INVENTORY 6  of t h e  ZONE 7  -371.47 -114.81  8 -113.57  9 -42.57  11  12  193.32  -188.03  -228.08  -90.04  94.68  -56.80  449.91  62.59  284.87  •359.86  -157. 27  INTERACTIONS PURE  26.85  568.94  -768.04  481.62  -77.71  18.64  CMIX  107.55  •205.28  -436. 63  -11.86  -91 .08  289. 15  HMIX - 134.40  •363.66  1204.68. -469.76  168.79  GENERAL MEAN  •15278.77  SITE = 70.93  LOG  -307.79  AGE = 6736.73  R e m a r k s : PURE, CMIX, and HMIX a s d e f i n e d i n T a b l e U n i t : Cubic f e e t per a c r e .  5-2.  UJ  Table 5-28. A n a l y s i s of v a r i a n c e f o r net volume y i e l d s o f I n t e r i o r lodqepole pine stands a d j u s t e d f o r s i t e index and stand age. Source of Variation  D.F  Mean Squares  Species type  2  7.53593X10  F.I.Z.  7  Type x F.I.Z. Covariates-Site Loq Age Error  F-Value  Tabulated F-Value (555)  5. 18**  3. 00  1.01808X10  7. 00**  2.02  13  6.14726X10  4.23**  1.73  1  3.74457X10  2575. 94**  3.86  1  3.72277X10^  2560.94**  3. 86  4174  * * S i g n i f i c a n t at 1% l e v e l .  1.45367X10  1  Table  5-29. E s t i m a t e d Interior  constants lodgepole  f o r n e t volume y i e l d s o f pine stands  TYPE  FOREST INVENTORY ZONE  MAIN EFFECTS  4 4.41  5 -151.08  6 3.66  7  8  9  10  -207.56  131.64  346.69  -401.40  273.65  12  INTERACTIONS PORE  109.66  -207. 39  -5.81  -70.26  78.30  -73.43  -252.30  1094.62  -563. 74  CMIX  51.89  221.93  -148.84  70.26  62.32  263.00  187.97  -948.11  291.48  H MIX  -161.55  -14. 54  154. 64  -140.61  -189.57  64.32  GENERAL MEAN = -15477.60  S I T E = 72.18 LOG AGE = 6689.94  Remarks: PURE, CMIX, and HMIX a s d e f i n e d i n T a b l e 5-2. Unit:  Cubic  feet  per acre.  -146.51  272.26  - 136  5.8.1  -  Douglas-fir  The  e f f e c t s of s p e c i e s c o m p o s i t i o n types on volume y i e l d  a r e n o n s i g n i f i c a n t f o r Coast D o u g l a s - f i r stands a f t e r the has been made f o r s i t e i n d e x  (Tables 5-22  and 5-23).  adjustment  Therefore,  d i f f e r e n c e s i n y i e l d among t h r e e stand types f o r Coast D o u g l a s - f i r stands can be a t t r i b u t e d c o m p l e t e l y to the d i f f e r e n c e i n s i t e  quality.  In I n t e r i o r D o u g l a s - f i r stands, however, the s p e c i e s composition e f f e c t i s s i g n i f i c a n t a t the 1% l e v e l (Table 5-24). a c t i o n s f o r s p e c i e s types and  Because the  inter-  i n v e n t o r y zone a r e n o n s i g n i f i c a n t ,  one  can d i r e c t l y i n t e r p r e t the s p e c i e s type e f f e c t s shown i n T a b l e  5-25.  The  per  e s t i m a t e d e f f e c t s a r e 16.92, 350.78, and -367.70 c u b i c f e e t  a c r e f o r pure D o u g l a s - f i r , D o u g l a s - f i r - c o n i f e r mixed type, and fir-hardwood mixed type s t a n d s , r e s p e c t i v e l y . these e f f e c t s a r e :  I n t e r p r e t a t i o n s of  w i t h the same s i t e q u a l i t y and  stands can be expected  to produce 16.92  type stands 350.78 c u b i c f e e t per a c r e more; D o u g l a s - f i r hardwood mixed type w i l l reduce  5.8.2  age, pure D o u g l a s - f i r  c u b i c f e e t per a c r e more than  g e n e r a l average y i e l d o f a l l D o u g l a s - f i r stands and  yield  Douglas-  the  D o u g l a s - f i r mixed  on the o t h e r hand general  the  average  by 367.70 c u b i c f e e t per a c r e .  Spruce  The  a n a l y s i s of v a r i a n c e f o r volume y i e l d of I n t e r i o r  stands shows t h a t a t the 5% l e v e l e f f e c t s of s p e c i e s c o m p o s i t i o n  spruce types  a r e not s i g n i f i c a n t l y d i f f e r e n t , a l t h o u g h i n t e r a c t i o n s between s p e c i e s c o m p o s i t i o n types and  i n v e n t o r y zones a r e s i g n i f i c a n t l y  different.  - 137  -  The e s t i m a t e d e f f e c t s a r e 26.85, 107.35, and -134.40 c u b i c f e e t p e r a c r e f o r pure spruce type, spruce c o n i f e r mixed type, and hardwood mixed type, r e s p e c t i v e l y  5.8.3  spruce  ( T a b l e 5-27).  Lodgepole P i n e  In I n t e r i o r l o d g e p o l e p i n e stands, T a b l e 5-28  shows t h a t  e f f e c t s of s p e c i e s c o m p o s i t i o n t y p e s , i n v e n t o r y zones, and between these two  factors differ  are 109.66, 51.89, and  significantly.  The  interactions  estimated  effects  -161.55 c u b i c f e e t per a c r e f o r pure l o d g e p o l e  p i n e type, l o d g e p o l e p i n e c o n i f e r mixed type, and hardwood mixed type stands, r e s p e c t i v e l y .  lodgepole pine  The d i f f e r e n c e i n e s t i m a t e d  e f f e c t s between pure l o d g e p o l e p i n e type and l o d g e p o l e p i n e - c o n i f e r mixed type i s n e g l i g i b l e from the p r a c t i c a l p o i n t of view. pure l o d g e p o l e p i n e stands o u t y i e l d  However,  l o d g e p o l e p i n e hardwood type  by 271 c u b i c f e e t per a c r e on average.  stands  The d i f f e r e n c e s i n e f f e c t s among  these t h r e e c o m p o s i t i o n types a r e not v e r y s i g n i f i c a n t i n a p r a c t i c a l sense;  the h i g h F v a l u e shown i n T a b l e 5-28  p r o b a b l y i s due  f o r t h i s source of v a r i a t i o n  t o the l a r g e number of sample p l o t s used which e f f e c t i v e l y  reduces the v a r i a n c e .  In a d d i t i o n , the i n t e r a c t i o n term i s s i g n i f i c a n t ,  t h e r e f o r e , i t i s r i s k y to over-emphasize the s p e c i e s c o m p o s i t i o n  type  effect. The  e f f e c t of hardwood mixed type shows a n e g a t i v e v a l u e  c o n s i s t e n t l y i n the above f o u r a n a l y s e s ; f o r t h i s reason, i t i s l o g i c a l t o conclude t h a t hardwood mixed stands i s the l e a s t d e s i r a b l e s t r u c t u r e f o r D o u g l a s - f i r , spruce, and  lodgepole pine i n  B.C.  composition  - 138  T a b l e s 5-24  and  5-28  -  show t h a t the e f f e c t of f o r e s t  inventory  zone i s s i g n i f i c a n t at the 1% l e v e l f o r volume y i e l d of I n t e r i o r D o u g l a s - f i r , and  lodgepole  p i n e stands a f t e r d a t a have been  adjusted  f o r s i t e index.  I n t e r p r e t a t i o n s f o r the r e s u l t s are as f o l l o w :  zonal  v a r i a t i o n i n volume y i e l d cannot be c o m p l e t e l y a t t r i b u t e d to d i f f e r e n c e i n s i t e q u a l i t y alone;  f a c t o r s such as decay, form, t a p e r , and  thickness  c o n t r i b u t e s i g n i f i c a n t l y to volume y i e l d as w e l l .  5.9  Y i e l d s of D o u g l a s - f i r and  bark  C o n i f e r Mixed Type Stands i n  the Interior  The  previous  s e c t i o n s have demonstrated t h a t  Douglas-fir  c o n i f e r mixed type stands produce more than pure D o u g l a s - f i r ones i n the I n t e r i o r .  The  reasons why  further investigations.  The  mixed c o n i f e r stands grow more m e r i t  average h e i g h t , number of t r e e s ,  area,and volume, per a c r e f o r I n t e r i o r pure and stand at v a r i o u s age  5-30, height  5-31, and :5-32  5-31,  and  5-32  III, respectively.  of dominant and f o r three  codominant t r e e h e i g h t  i n Tables  s i t e c l a s s e s suggests no d i f f e r e n c e i n  growth between pure and  mixed c o n i f e r types.  a l s o can be r e a d i l y drawn from F i g u r e at v a r i o u s age  Douglas-fir  c l a s s a r e i l l u s t r a t e d i n T a b l e s 5-30,  f o r s i t e c l a s s I, I I , and Inspection  mixed  basal  5-13,  5-14,  The  5-15  same c o n c l u s i o n  where the means  c l a s s e s have been smoothed w i t h a W e i b u l l - t y p e growth  f u n c t i o n (Yang e t a l . , 1978)  by weighted l e a s t squares methods.  Table  5 - 3 0 . C o m p a r i s o n o f h e i q h t , number o f t r e e s , b a s a l a r e a , a n d v o l u m e f o r p u r e D o u q l a s - f i r and D o u q l a s - f i r - c o n i f e r m i x t u r e stands qrown o n I n t e r i o r s i t e c l a s s I .  TYPE  AGE  NO.  PLOT  NO.  TREE  CLASS  15  25  35  45  55  65  75  85  95  105  115  -  3  6  9  27  17  20  31  36  23  11  50  58  69  81  88  95  94  104  109  HEIGHT PURE  per a c r a  -.  BA VOLUME  125  135  145  9  19  13  107  1 12  114  115  55  151  13 3  161  220  190  176  174  143  122  135  96  131  29  76  74  105  144  143  136  158  142  145  137  149  169  536  1650  1845  2845  4089  4162  3990  4945  4762  4417  4218  4877  5545 LO  NO.  PLOT  HEIGHT CHIX  NO.  2 30  TREE 5 0  BA VOLUME  18 220  Remarks: J J " " unit.  -  VO  1  5  15  14  32  43  16  22  14  15  60  80  82  93  93  97  102  107  107  107  112  118  38  124  199  240  200  218  202  196  224  181  145  153  14  84  128  161  139  164  177  180  201  179  138  198  265  2236  3398  4 581  4187  4834  5676  5616  6119  5414  3753  6609  J J " D « > « « l l » - J « t y p e ; C M I X - - D o u q l a s - f i r - c o n i f e r mixed t y p e . H e i q h t , f e e t ; B a s a l Area, s q u a r e d f e e t ; Volume, c u b i c f e e t .  BA-  Basal  6  Area,  8  Table  5-31. C o m p a r i s o n o f h e i g h t , number o f t r e e s , b a s a l a r e a , a n d v o l u m e f o r p u r e D o u g l a s - f i r and D o u g l a s - f i r - c o n i f e r m i x t u r e s t a n d s grown o n I n t e r i o r s i t e c l a s s I I .  TYPE  AGE  NO.  PLOT  HEIGHT PUKE NO.  TREE  BA  15  25  35  45  55  65  75  85  95  105  115  125  135  -  145  1  32  53  34  61  72  62  39  4 1  26  76  55  46  30  43  53  64  70  74  75  84  84  84  86  91  94  70  49  85  123  126  124  126  122  126  131  96  103  98  43  71  74  79  94  1327  397  897  1689  1792  198 8  2233  1  6  35  29  42  55  54  30  47  56  66  75  , 76  -  12  74  112  1 18  179  BA  -  4  35  56  66  VOLUME  -  138  666  1252  1656  PLOT  HEIGHT NO.  TREE  —  -  I Ip I  1  23  NO.  CMIX  CLASS  53  VOLUME  p-r a - r -  86  101  100  100  105  115  2613  2510  2545  2824  3232  37  36  13  14  23  13  77  84  83  88  89  87  95  163  174  176  159  166  186  149  136  103  102  106  1 12  123  124  146  128  141  2603  275 1  2675  2951  3458  3613  3456  4152  2189  3021  R e m a r k s : P U R E - p u r e D o u g l a s - f i r t y p e ; CMIX-- D o u g l a s - f i r - c o n i f e r m i x e d t y p e . U n i t ; H e i g h t , f e e t ; B a s a l A r e a , s q u a r e d f e e t ; Volume, c u b i c f e e t .  BA-  Basal  Area  T a b l e 5-32. C o m p a r i s o n o f h e i q h t , number o f t r e e s , b a s a l a r e a , a n d v o l u m e f o r p u r e D o u q l a s - f i r and D o u q l a s - f i r - c o n i f e r m i x t u r e s t a n d s qrown on I n t e r i o r s i t e c l a s s I I I .  TYPE  AGE 15  CLASS  35  45  55  65  75  85  95  105  115  125  135  145  -  10  10  41  53  94  85  41  65  35  19  41  61  73  HEIGHT  -•  27  30  37  46  50  53  55  62  63  64  65  70  71  NO. T R E E  -  38  42  43  61  79  80  79  105  82  91  85  BA  -  16  22  21  32  39  44  47  73  74  84  90  PLOT  VOLUME  -  NO.  1  1  20  NO. TREE BA  PLOT  HEIGHT CMIX  aara  25  NO.  PURE  per  214  105  90  I h-  1  378  871  62  66  295  579  1  16  25  47  39  20  20  30  36  46  53  56  56  5  12  10  41  70  99  112  92  137  116  91  2  7  3  17  35  54  59  50  79  63  91  38  42  670  1 184  1300  1 041  729  956  1449  1332  24 64  19 64  VOLUME  15  Remarks:  P U R E — pure D o u q l a s - f i r t y p e ; C M I X — D o u q l a s - f i r - c o n i f e r mixed t y p e . U n i t : Heiqht, f e e t ; B a s a l Aara, squared f e e t ; Volume, c u b i c f e e t .  279  1724  1399  1383  152 3  7 61  2143  1832  1945  13  17  20  64  69  68  153  126  90  103  99  80  2305  2194  BA-- B a s a l  Area.  1780  K 1  1  - 142 -  -  143  -  140  120 • PURE O CMIX I00r-  -  80h-  X  x  60  40  20 h  50  75 AGE  Figure  5-14.  Height  growth o f  50  100  (years)  Interior Douglas-fir  on  site  class II  - 144 -  • PURE O CMIX  60 h  40  K  50  F i g u r e 5-15.  75 AGE (years)  H e i g h t growth of I n t e r i o r D o u g l a s - f i r  150  on s i t e c l a s s I I I  - 145  -  Average b a s a l a r e a per a c r e of pure and mixed stands of v a r i o u s age c l a s s e s i n the I n t e r i o r s i t e c l a s s I , I I , and listed  i n T a b l e s 5-30,  5-31,  5-32.  The averages were f i t t e d t o the  W e i b u l l - t y p e growth f u n c t i o n w i t h a weighted The  fitted  and 5-18  l e a s t squares method.  curves and the means a r e i l l u s t r a t e d  f o r s i t e c l a s s I, I I , and F i g u r e 5-16  I I I are  i n F i g u r e s 5-16,  5-17,  III respectively.  i n d i c a t e s t h a t the d i f f e r e n c e i n b a s a l a r e a per  a c r e between pure and mixed D o u g l a s - f i r stands on good s i t e i s not s i g n i f i c a n t u n t i l stand age 85 y e a r s .  Examining the number of t r e e s  per a c r e i n T a b l e 5-30,  r e v e a l s t h a t the d i f f e r e n c e i n  5-31,  and  5-32  t r e e s p e r a c r e between pure and mixed stands i s i n c r e a s e d a t t h i s Evidence  i n the above T a b l e s i n d i c a t e s t h a t D o u g l a s - f i r mixed  stage.  stands  a r e capable of growing more t r e e s per a c r e than pure stands a r e . These r e s u l t s p r o v i d e support  f o r the mixed stand advocates who  t h a t mixed stands can b e t t e r u t i l i z e s o i l On medium s i t e s , the  fertility.  s u p e r i o r i t y of D o u g l a s - f i r mixed  overrpure ones remains ( F i g u r e 5-17).  argue  T a b l e 5-31  stands  d i s c l o s e s t h a t numbers  of t r e e s per a c r e remain r e l a t i v e l y c o n s t a n t i n b o t h pure and mixed stands a f t e r stand age  65 and  t h a t t h e r e a r e c o n s i s t e n t l y more stems  i n mixed stands than i n pure s t a n d s . On the poor s i t e  ( s i t e c l a s s I I I ) , the d i f f e r e n c e i n b a s a l  a r e a per a c r e between pure stands and mixed stands becomes i n d i s t i n c t ( F i g u r e 5-18).  While t h e r e a r e more t r e e s per a c r e i n the mixed  stands,  the b a s a l a r e a i n pure stands i s not s i g n i f i c a n t l y d i f f e r e n t from t h a t i n mixed s t a n d s .  T h i s c o u l d be a t t r i b u t e d to the f a c t t h a t under a poor  - 146  AGE F i g u r e 5-16.  Basal area  -  (years)  growth of I n t e r i o r D o u g l a s - f i r on  site class I  - 147  Figure  5-17.  -  B a s a l a r e a growth of I n t e r i o r D o u g l a s - f i r on  site class II  - 148 -  210  180  ~ 150 OJ  o o  • PURE O CMIX  « 120  < cr < _J  <  0 90  CO  <  CQ  50 AGE  75 (years)  100  150  Figure 5-18. Basal area growth of I n t e r i o r Douglas-fir on s i t e class III  - 149 -  7000  6000  • PURE O CMIX  5000  50  75 AGE ( y e a r s )  100  F i g u r e 5-19. Volume growth of I n t e r i o r D o u g l a s - f i r  on s i t e c l a s s I  -  150 -  70001  6000  •  PURE  O CMIX 5000  03  ? 4000! 3  3000 O >  2000  1000  75 AGE ( y e a r s )  100  F i g u r e 5-20. Volume growth of I n t e r i o r D o u g l a s - f i r on s i t e c l a s s I I  150  - 151 -  7000  6000  5000 •  O CMIX  0>  o o  PURE  4000  3  o  3000 o >  2000  1000  50 AGE  75 (years)  F i g u r e 5-21. Volume growth of I n t e r i o r D o u g l a s - f i r on s i t e c l a s s I I I  150  - 152  ~  s o i l c o n d i t i o n , the l a c k o f f e r t i l i t y or m o i s t u r e c o n s t r a i n s the growth o f t r e e s to such an extent  t h a t i n c r e a s e i n number o f t r e e s  per a c r e does not i n c r e a s e the b a s a l a r e a p e r a c r e . The d i f f e r e n c e i n volume y i e l d between pure and mixed stands  i s e s s e n t i a l l y i d e n t i c a l to that i n b a s a l area  5-20, and 5-21).  (Figures  The t r e n d i s expected, s i n c e b a s a l a r e a  and h e i g h t a r e two components  o f the volume f u n c t i o n .  (or DBH)  I t has been  found t h a t no d i f f e r e n c e i n dominant and codominant h e i g h t e x i s t s between these two f o r e s t t y p e s . p r i m a r i l y according  5.10  t o the b a s a l a r e a  Y i e l d Table  The volume y i e l d ( F i g u r e s 5-16,  growth  changes  5-17, and 5-18).  Construction  One o f the main purposes i n y i e l d  studies i s to  estimate  f o r e s t y i e l d p r e c i s e l y a t v a r i o u s s t a g e s o f stand development. y i e l d f u n c t i o n s and t a b l e s ( f o r example, McArdle and Meyer,  recognized  In y i e l d  f u n c t i o n s the t h r e e components  a r e age, s i t e , and b a s a l a r e a expressed  However, i f the y i e l d  t a b l e s are going  most  f o r stand  i n v e n t o r y zones should be c o n s i d e r e d becomes important. (1944', 1947) and T u r n b u l l  different i n yield that the d i f f e r e n c e  have  often density.  t o apply t o a l a r g e geographic  a r e a , t h e q u e s t i o n of whether o r not the s p e c i e s c o m p o s i t i o n  Mulloy  Many  1930;  V u o k i l a , 1966; C u r t i s , 1967; Smith, 1973, 1977; Johnstone, 1976) been prepared.  5-19,  types  and  S t u d i e s by  (1963) showed t h a t mixed s p e c i e s a r e  from pure stands.  P r e v i o u s d i s c u s s i o n s have shown  i s m a i n l y r e f l e c t e d by b a s a l a r e a growth.  If  - 153 -  v a r i a t i o n i n b a s a l a r e a i s b e i n g p r o p e r l y taken c a r e of by a y i e l d f u n c t i o n , i s i t n e c e s s a r y t o c o n s i d e r the s p e c i e s composition and i n v e n t o r y zone e f f e c t ? The l e a s t squares a n a l y s i s developed  i n t h i s study o f f e r s a  unique f e a t u r e t o c o n s i d e r s i m u l t a n e o u s l y q u a l i t a t i v e and q u a n t i t a t i v e variables i n yield analysis.  T a b l e s 5-33, 5-34, 5-35, and 5-36 show  t h a t the r e l a t i v e importance,  as i n d i c a t e d by F - v a l u e s , of s p e c i e s  composition type, f o r e s t i n v e n t o r y zones, i n t e r a c t i o n s f o r type and zone, s i t e , age, age i n l o g a r i t h m i c s c a l e , h e i g h t , number o f t r e e s per a c r e , average DBH, b a s a l a r e a p e r a c r e , r e l a t i v e stand d e n s i t y , and h e i g h t x b a s a l area  (HT x BA) t o volume y i e l d f u n c t i o n s f o r Coast D o u g l a s - f i r ,  I n t e r i o r D o u g l a s - f i r , I n t e r i o r spruce, and I n t e r i o r l o d g e p o l e p i n e , respectively. In a l l f o u r s e t s of i n v e n t o r y d a t a a n a l y z e d , the f a c t o r s HT x BA and b a s a l a r e a a r e the most important v a r i a b l e s among a l l i n v e s t i g a t e d . The r e s u l t s a r e i n c l o s e agreement w i t h the study of Smith (1973) who i n v e s t i g a t e d the f e a s i b i l i t y o f p r e p a r i n g v a r i a b l e d e n s i t y y i e l d  tables.  A stepwise e l i m i n a t i o n of t h e s e q u a l i t a t i v e and q u a n t i t a t i v e v a r i a b l e s p r o v i d e s an e x c e l l e n t method t o a s c e r t a i n the importance of a v a r i a b l e i n r e l a t i o n t o volume y i e l d .  T a b l e s 5-37, 5-38, 5-39, and  5-40 i l l u s t r a t e the stepwise e l i m i n a t i o n procedures  and F - v a l u e s of  v a r i a b l e s a t v a r i o u s s t a g e s f o r Coast D o u g l a s - f i r , I n t e r i o r D o u g l a s - f i r , spruce, and l o d g e p o l e p i n e volume y i e l d d a t a  respectively.  Table 5-33. A n a l y s i s o f v a r i a n c e f o r Coast D o u q l a s - f i r stands Source of Variation  D.F.  Mean Squares  net volume y i e l d o f  F-Value 5  Tabulated F-Value (555)  S p e c i e s type  2  5.78580X10  1.40  3.01  F.I.Z.  1  2.22209X10  5.47**  3.86  Type x F.I.Z.  2  4.86580X10  1. 20  3. 01  Covariates— Site  1  4.21824X10 6 4.99141 X10  10.38**  3.86  12. 28**  3. 86  5.51*  3. 86  1.51  3. 86  1.67  3. 86  0.67  3.86  88.48**  3. 86  11.81**  3.86  98.21**  3. 86  5  6  Aqe  1  Log Age  1  Height  1  No. Trees  1  2.22381X10 5 6.15142X10 5 6.78487X10  Avg.  1  2.73457X10  DBH  Basal Area  1  R e l a t i v e Stand Density Height X Basal A Error  1 1  620  6  3.59477X10  7 6  4.79853X10 7 3.98991X10 4.06263X10  • S i g n i f i c a n t a t 1% l e v e l . * * S i g n i f i c a n t at 5% l e v e l . B a s a l A: B a s a l area.  5  Table  5-34. A n a l y s i s of variance f o r net volume y i e l d s of I n t e r i o r D o u q l a s - f i r stands •  Source of Variation Species  type  D. F.  Mean Squares  F-Value  Tabulated F-Value (5%)  2  2. 04948X 10  5  1.24  3.00  F.I.Z.  4  1. 44 153X10  5  0.87  2. 38  Type x F. I. Z.  7  2. 64390X10  5  1.6 1  2.02  Covariates— Site  1  . 0.04  3. 85  24.4 1**  3. 85  1. 83111X 10  11.13**  3.85  1. 01642X 10  6  6.18*  3.85  Aqe  6. 06500X 10  3  4. 01504X10  Log Age  v  Height  6  6  No. Trees  1  4. 46446X 10  6  28.23**  3.85  Avg.  1  3. 70467X10  6  22.52**  3. 85  1  8. 96057X 10  54.47**  3.85  1 R e l a t i v e Stand Density Height X Basal A 1  3. 19160X 10  19.40**  3.85  6.66622X10  404. 98**  3.85  Basal  Error  DBH Area  2309  • S i g n i f i c a n t at 5% l e v e l ; * * S i g n i f i c a n t a t 1% l e v e l . Basal A: Basal Area.  6  6  164597.0  7  Table 5-35. A n a l y s i s of v a r i a n c e f o r net volume y i e l d I n t e r i o r spruce stands Source of Variation  Mean Squares  F-Value  Species type  2  4. 4777X1 0  F.I.Z.  7  4. 1875X10  Type x F.I.Z.  14  6  14. 40**  5  data of  Tabula ted F-Value (555) 3.00  1.35  2.02  3. 63**  1.70  0. 14  3. 85  4. 36*  3.85  1.6891X10  5  0.54  3. 85  1.3306X10  6  4. 28*  3. 85  2.91  3. 85  0. 22  3. 85  69. 92**  3. 85  7.67**  3.85  247. 63**  3. 85  1 . 1289X10  6  Covariates— Site  1  Aqe  1  Loq Age Heiqht  1 1  No. Trees  1  Avq.  1  DBH  Basal Area 1 R e l a t i v e Stand 1 Density Heiqht x Basal A 1 Error  2582  * S i q n i f i c a n t at 5% l e v e l ; * * S i q n i f i c a n t at 15? l e v e l . B a s a l A = Basal Area.  44401.0 1 .3566X10  9.0562X10  5  69011.0 2.1745X10  7  2.3866X 10 7.7008X10 3.1098X10  6  7  5  6  Table  5-36. A n a l y s i s o f v a r i a n c e f o r net volume y i e l d of I n t e r i o r l o d q e p c l e pine stands  Source of Variation  D. F.  Species type  2  F.I.Z.  F- Value  Tabulated F-Value  2.08  3.00  8.26**  2.02  1.39  1.73  362497.0  2. 21  3.85  350023.0  2. 14  3. 85  592440.0  3.62  3.35  175710.0  1.07  3. 85  341511.0 6  7  Type x F.I.Z.  13  1.35337X10 227514. 0  Covariates— Site Aqe Loq  Mean Squares  Aqe  Heiqht No.  Trees  18426.3  0.1 1  3.85  Avq.  DBH  15104.3  0.09  3. 85  Basal  Area  5. 96779X10  R e l a t i v e Stand Density Height Error  6  809279.0  x Basal A 4167  • S i g n i f i c a n t at 5% l e v e l ; * * S i g n i f i c a n t a t 1% l e v e l . Basal A = Basal Area.  1.31858X10  8  163838. 0  36.42**  3.85  4. 94*  3.85  804.81**  3.85  Table 5-37. Comparison of F-values i n Coast D o u q l a s - f i r y i e l d QUALITATIVE SP . TYPE F.I.Z. D. F.  QUANTITATIVE TYPE X F. I.Z  AGE  LOG AGE  1  1  1  1  1  1  1  1.67  0. 67  88. 48  11.81  93.21  HE IGUT NO. OF TREES  1  STEP 1  1. 40  5. 47  1.20  10.38 12.28  5.51  1.51  2  1. 53  5. 22  1.26  10. 37 12.33  5. 93  1 .12  3  1. 08  3. 94  1.44  10. 64  8.75  4.2 3  --  4  --  6. 70  --  9. 90 10.45  4. 82  5  —  6. 35  —  9. 83  9.21  3.60  6  --  8. 63  —  7.63  8. 1 8  7*  --  10.06  --  16.18  8  --  1 1. 93  --  4.50  9  —  27. 69  --  14. 79  10  VARIABLES  SIT S  2  2  analysis  --  --  AVG. DBH  BASAL AREA  R. S.D. 1  HT X 3 1  10.17  —  129.21  11.18  9 9.88  1. 74  —  139. 64  11.79  180.82  1 .42  --  137.70  10.74  135.57  —  186.51  14. 24  301.54  260. 85  21. 35  301.96  277. 19  14.01  572.54  335.68  • --  636.40  —  —  —  329. 64  Remarks: R.S.D.-- R e l a t i v e Stand Density; HT X BA — Heiqht X B a s a l D.F.—Deqree o f Freedom. •Estimated c o e f f i c i e n t s qiven i n Table 5-41.  Area.  —  631.67  Table  5-33. C o m p a r i s o n  of F-values  in Interior  QUALITATIVE SP.TYPE F . I . Z . D.F.  2  4  Douqlas-fir yield  QUANTITATIVE TYPE X F.I.Z 7  SITE 1  AGE 1  LOG AGE 1  HEIGHT 1  NO. OF TREES 1  analysis  VARIABLES AVG. D3H 1  BASAL AREA 1  R. S. D. 1  HT X BA 1  STEP 1  1.24 0.87  1. 61  0.04  14.41  11.13  6.18  28.23  22.52  54.47  19. 40  404.98  2  1.25 0.88  1. 60  --  24.59  12.08  9.03  28.27 22.53  55.04  19.41  407.41  3  3. 90  --  25.21  12.87  8.10  26.10  22.57  53.56  19.51  412. 92  4  --  26.30  15.44  4.14  26,17 21.38  52.11  18. 40  423.37  5  --  35.85  27.56  22.04  17. 34  60. 02  26.45  1234.57  6  --  25. 59  16.28  0.38  37.83  15.06  1552.64  7*  --  29.19  16.93  38.95  14.76  1568.88  8  19.87  6.45  9  70. 00  10  74.07  —  U l VO  --  — —  222.22 233.15  11  Remarks: R . S . D — R e l a t i v e S t a n d D e n s i t y ; HT X BA -- H e i q h t D . F . — D e q r e e o f Freedom. • E s t i m a t e d c o e f f i c i e n t s q i v e n i n T a b l e 5- 41.  1703.11  x Basal  Area;  1692.70 —  33404. 25  —  36945. 74  Table 5-39. Comparison of F-values i n I n t e r i o r QUALITATIVE  QUANTITATIVE  SP. TYPE F. I.Z. TYPE X FIZ D.  F.  2  7  spruce  SITE  AGE  LOG AGE  1  1  1  14  yield  analysis  VARIABLES  HEIGHT NO. OF AVG. TREES DBH 1  1  B A SAL R.S.D AREA  1  1  HT X 3A  1  1  STEP 1  14.39  1. 35  3. 63  0.14  4. 36  0.54  4 .38  2. 91  0.2 6  69. 92  7. 67  247.63  2  14.44  1.34  3.62  --  4. 23  0.41  10.71  3. 06  0.26  77. 88  9. 26  256.30  3  14.45'  1. 37  3. 63  —  4. 38  0.43  13.07  7. 55  140.63  9. 94  357.27  4  14.36  1. 36  3.61  --  16. 76  7. 28  —  156.61  11 .12 385.57  ---  --  —  224. 19  10.74 519. 90  5* 29.47 6  29. 13  7  24. 57  —  8  25.57  —  9  24. 37  —  —  —  33.99  —  26. 96  --  21. 85  —  16.79 22.67 9.80  --  --  —  —  194.95 245.97  —  —  —  —  —  —  —  —  —  --  Remarks: R. S. D . — R e l a t i v e Stand D e n s i t y ; HT X BA --Heiqht D.F.--Deqree o f Freedom. •Estimated c o e f f i c i e n t s qiven i n Table 5-41.  216. 88  x Basal Area;  —  ---— —  527.84 596.31 2250. 64 28359. 78  Table 5.40. Comparison of F-values i n I n t e r i o r lodqepole pine y i e l d QUALITATIVE  QUANTITATIVE  SP. TYPE F. I. Z. TYPE X FIZ  VARIABLES  SITE  AGE  LOG AGE  1  1  1  1  1  1  0.09  IIGHT NO. OF AVG. TREES DBH  D. F.  2  7  14  1  1  2. 08  8.26  1.39  2.2 1  2. 14  3.62  1 .07  0.11  2  1. 92  8. 03  1.31  3.76  2. 06  2.23  0.65  0. 05  3  1.94  8. 02  1.33  3.77  2. 16  1.29  0.63  4  1. 99  8.13  1.33  4. 13  1. 57  1.68  --  —  5  26. 77  9. 96  3.96  2. 02  2. 10  —  —  6  29. 19  10.02  2.66  1.84  1.45  —  7  29. 60  10. 24  2.28  0. 47  8  29. 76  10.20  4. 75  9  32. 48  9. 95  10* 40.92 11  _ _  —  '  —  —  36. 42  4.94  804.81  94. 91  2.00  927.82  141.13  2.00  1040.04  229. 14  1. 56  1860.23  --  241.63  1. 54  1945. 19  --  386.46  —  389.46  —  —  — —  —  2054.06 —  2057.06  411.11  2427.70  420.94  3056.58  485.61  31.62  Remarks: 3 . S . D . - - R e l a t i v e Stand D e n s i t y ; HT X BA --Height D.F.—Degree o f Freedom. •Estimated c o e f f i c i e n t s given i n Table 5-4 1.  HT X B.A 1  mm  • •  BASAL R. S. D AREA 1  --  —  —  analysis  --  3185.28 72989.68  x Basal  Area;  - 162  5.10.1  -  Douglas-fir  The  F-value i n Table  5-37  i n d i c a t e s the average DBH  and  h e i g h t are the l e a s t s i g n i f i c a n t v a r i a b l e t o Coast D o u g l a s - f i r volume yield; Species  c o n s e q u e n t l y they were e l i m i n a t e d i n the f i r s t composition  discarded  types and  i n the t h i r d s t e p .  eliminated  simultaneously  age  ( l o g age)  i n t e r a c t i o n s f o r types and These two  steps. zones were  q u a l i t a t i v e v a r i a b l e s were  because i n t e r a c t i o n s do not  s p e c i e s type i s e l i m i n a t e d .  two  exist  Number of t r e e s per a c r e and  once  logarithmic  c o n t r i b u t e n o n s i g n i f i c a n t l y t o the volume y i e l d  Steps 6 and  7 of T a b l e  5-37  function.  demonstrated c l e a r l y the  importance  of r e l a t i v e stand d e n s i t y i n c o n s t r u c t i n g a y i e l d t a b l e f o r D o u g l a s - f i r . The  r e l a t i v e stand  d e n s i t y i s next t o HT x BA,  b a s a l a r e a , and  age  c o n t r i b u t i n g to the v a r i a t i o n of Coast D o u g l a s - f i r volume y i e l d . F - v a l u e of i n v e n t o r y F - v a l u e 10.06 of freedom.  zone i s next to the r e l a t i v e stand  which i s s i g n i f i c a n t a t 0.1% The  analysis provides  l e v e l with  shown i n T a b l e  5-40  d i s p l a y that with  per a c r e , r e l a t i v e stand d e n s i t y , and HT x BA, Region) w i l l y i e l d  248  Coast T r a n s i t i o n B e l t ) . these two decay.  inventory  2 and  626  The with degrees  d e f i n i t e evidence t h a t s u b d i v i s i o n  of the Coast r e g i o n f o r D o u g l a s - f i r i s j u s t i f i e d . constants  density  in  The  estimated  the same age,  basal  area  Zone 2 (the South Coast  c u b i c f e e t per a c r e more than Zone 3 (the South Some of the d i f f e r e n c e i n net volume between  zones can be  e x p l a i n e d by b i o t i c f a c t o r s such as  - 163  -  Among a l l v a r i a b l e s c o n s i d e r e d ,  s i t e c o n t r i b u t e s the  least  to the v a r i a t i o n of net volume y i e l d of I n t e r i o r D o u g l a s - f i r stands as i l l u s t r a t e d i n T a b l e  5-34  and  thus was  first  Two  q u a l i t a t i v e f a c t o r s , i n v e n t o r y zones and  and  types,  are n o n - s i g n i f i c a n t and  e l i m i n a t i o n of these two  eliminated  (Table 5-38).  i n t e r a c t i o n s f o r zones  consequently d i s c a r d e d .  A f t e r the  q u a l i t a t i v e v a r i a b l e s , the f a c t o r s p e c i e s -  c o m p o s i t i o n - t y p e s becomes s i g n i f i c a n t ; however, i t s F - v a l u e i s the l e a s t among a l l v a r i a b l e s i n Step 3 of T a b l e 5-38 i n Step 4.  and hence was  eliminated  A f t e r e l i m i n a t i o n of a l l q u a l i t a t i v e v a r i a b l e s , the a n a l y s i s  i n Step 4 i s reduced p r a c t i c a l l y to o r d i n a r y m u l t i p l e r e g r e s s i o n a n a l y s i s . Variables eliminated average DBH, stand  age.  i n sequence were h e i g h t , number of t r e e s per  r e l a t i v e stand d e n s i t y , l o g age,  b a s a l a r e a , and  acre,  finally  R e l a t i v e stand d e n s i t y i s a v a r i a b l e which c o n t r i b u t e s t o  v a r i a t i o n i n volume y i e l d of I n t e r i o r D o u g l a s - f i r next to HT x BA, area,  and  n o n s i g n i f i c a n c e of s p e c i e s composition  zone shown i n T a b l e analyses  found s i g n i f i c a n t . two  5-38  The  type and  i s i n no c o n t r a d i c t i o n w i t h  (Tables 4-14,  4-24)  the r e s u l t s of  where these two  r e s u l t s i n Table  5-38  simply  inventory  v a r i a b l e s were imply  that  these  v a r i a b l e s have been w e l l taken c a r e of by o t h e r v a r i a b l e s such as  b a s a l a r e a , or HT x BA. composition differ; and  basal  age. The  previous  the  As d i s c u s s e d  section, species  types cause the volume y i e l d of I n t e r i o r D o u g l a s - f i r to  the r e s u l t s i n T a b l e 5-38  HT x BA are e q u a l ,  or i n v e n t o r y  i n a previous  suggest t h a t i f b a s a l a r e a per  then no d i f f e r e n c e i n y i e l d among s p e c i e s  zones i s expected.  acre types  - 164  5.10.2  -  Spruce  T a b l e 5-39  p r e s e n t s the stepwise e l i m i n a t i o n procedure f o r  a l l v a r i a b l e s c o n s i d e r e d i n an I n t e r i o r spruce y i e l d S i t e , average DBH,  table  and stand age i n l o g a r i t h m i c s c a l e  analysis.  ( l o g age)  are  v a r i a b l e s which . c o n t r i b u t e i n s i g n i f i c a n t l y to the volume y i e l d were e l i m i n a t e d f i r s t l y , w h i l e the q u a l i t a t i v e v a r i a b l e s p e c i e s c o m p o s i t i o n types i s next t o b a s a l a r e a , and HT x BA i n importance construction.  in yield  In a d d i t i o n , v a r i a b l e s such as stand age, h e i g h t , and  r e l a t i v e stand d e n s i t y a r e o f s i g n i f i c a n t importance.  The e s t i m a t e d  c o e f f i c i e n t s f o r v a r i a b l e s i n Step 7 a r e l i s t e d i n T a b l e 5-41 it  table  shows a l l q u a n t i t a t i v e v a r i a b l e s  where  (age, b a s a l a r e a , r e l a t i v e stand  d e n s i t y , HT x BA) b e i n g e q u a l , pure spruce type stands o u t y i e l d  spruce  hardwood mixed type stands by 286 c u b i c f e e t per a c r e and spruce c o n i f e r mixed type ones by 23 c u b i c f e e t .  The r e s u l t s p r o v i d e , f o r the  first  time, good e v i d e n c e t h a t e s t a b l i s h m e n t of pure spruce type stands i s more d e s i r a b l e than spruce hardwood mixed type stands i n the  Interior.  Because the same volume e q u a t i o n has been used i n computation for  o f volume  a l l sampled p l o t s , the g a i n o f 286 c u b i c f e e t per a c r e of pure  type stands over spruce hardwood mixed type stands c o u l d be  spruce  interpreted  as pure spruce stands produce b e t t e r q u a l i t y or l e s s decay i n l o g s than do spruce hardwood mixed type s t a n d s .  The  i n t e r p r e t a t i o n i s well-grounded  i n view o f r e c e n t r e p o r t s which i n d i c a t e deciduous  s p e c i e s such as  p o p l a r , r e d a l d e r a r e of l i t t l e u t i l i z a t i o n v a l u e i n mature stands because  of poor q u a l i t y  (Young,  1974).  aspen,  Table  5-41.  Yield  f u n c t i o n s f o r D o u q l a s - f i r , spruce  SPECIES  DF,COAST  DF,INTEEIOB  LODGEPOLE  lodqepole pine  VARIABLE INT.  SPRUCE  and  SP.  TYPE  F.I.Z.  AGE  LOG  AGE  HEIGHT  BASAL  R. S. D.  HT  X BA  S.E. E.  21.34  2.  123.91  -8.053  21.109  -378.931  166.936  646  21.34  3. -123.91  -8.053  21.109  -378.931  166.939  646  5. 613  167. 958  229.523  409  1548.15  -6.965  1111.65  103.34  -2.525  --  55.037  11.621  -152.769  193.349  563  -66.55  P  -66.55  P+C  79.74  -2.525  --  55.037  11.621  -152.759  193.349  563  -66.55  .P + H  -183.08  -2.525  --  55.037  11.621  -152.769  193.349  563  9.446  253.400  408  9.446  253.400  408  9.446  253.400  408  -15.39  P  26.46  -15.39  P+C  -93.80  -15.39  P+H  -67.34  Remarks: R . S . D . - - R e l a t i v e S t a n d D e n s i t y ; HT P — P U R E ; P+C--CHIX, C o n f i e r s M i x e d U n i t : c u b i c f e e t per a c r e .  X BA--Heiqht x B a s a l Area;INT.--Interceptt y p e ; P+H--HMIX, H a r d w o o d M i x e d t y p e .  ON  - 166 -  S i m i l a r l y , pure spruce type stands produce 24 c u b i c f e e t per a c r e more than spruce c o n i f e r mixed type stands  ( T a b l e 5-41).  The amount may be o f no p r a c t i c a l meaning; n e v e r t h e l e s s , i t i n d i c a t e s c l e a r l y t h a t pure spruce type stands produce b e t t e r q u a l i t y wood do spruce c o n i f e r mixed type stands i n t h e i n t e r i o r . to e l u c i d a t e i n f u l l  than  Further studies  the reasons why pure spruce type stands  yield  more than mixed types i n stands w i t h e q u a l h e i g h t , b a s a l a r e a ,  relative  stand d e n s i t y , and HT x BA a r e needed.  5.10.3  Lodgepole  Pine  T a b l e 5-40 p r e s e n t s an e l i m i n a t i o n procedure  for Interior  lodgepole pine f o r a l l v a r i a b l e s considered i n y i e l d t a b l e c o n s t r u c t i o n . Average DBH, number o f t r e e s p e r a c r e , h e i g h t , r e l a t i v e stand d e n s i t y , l o g age, and stand age a r e o f no s i g n i f i c a n c e i n c o n t r i b u t i n g v a r i a t i o n s to n e t volume y i e l d .  In o t h e r words, the e f f e c t s o f these v a r i a b l e s  have been w e l l r e p r e s e n t e d by t h e o t h e r s . i s s i g n i f i c a n t a t t h e 5% l e v e l qualitative variables —  S i t e w i t h an F v a l u e 4.75  (1 and 4186 degree o f freedom).  The two  s p e c i e s c o m p o s i t i o n type and i n v e n t o r y zone  a r e o n l y next t o b a s a l a r e a and HT x BA i n importance t a b l e c o n s t r u c t i o n of I n t e r i o r lodgepole pine. of i n v e n t o r y zone suggests  i n the y i e l d  The h i g h  significance  that a separate y i e l d t a b l e f o r lodgepole  p i n e i n each zone i s warranted. The e s t i m a t e d c o e f f i c i e n t s i n T a b l e 5-41 d i s p l a y the f a c t t h a t pure l o d g e p o l e p i n e outweigh l o d g e p o l e p i n e c o n i f e r mixed  type  stands by 120 c u b i c f e e t p e r a c r e and l o d g e p o l e p i n e hardwood mixed stands by 94 c u b i c f e e t p e r a c r e on stands w i t h t h e same b a s a l a r e a  - 167  per a c r e and HT x BA. is,  -  The e s t a b l i s h m e n t of l o d g e p o l e p i n e  stands  t h e r e f o r e , more d e s i r a b l e than of l o d g e p o l e p i n e mixed  i n the I n t e r i o r .  types  As d i s c u s s e d p r e v i o u s l y , the r e s u l t s might  suggest  t h a t pure l o d g e p o l e p i n e type stands produce l o g s w i t h b e t t e r q u a l i t y ( l e s s decay) than do mixed t y p e s .  5.11  T e s t of Homogeneity of V a r i a n c e  The  s t a n d a r d d e v i a t i o n s of net volume y i e l d by s p e c i e s  c o m p o s i t i o n types and and  5-44  i n v e n t o r y zones a r e shown i n T a b l e s 5-42,  f o r D o u g l a s - f i r , s p r u c e , and  lodgepole pine.  t a b l e s , v a r i a n c e s d i f f e r from zone t o zone and type.  In f a c t the assumption  r e j e c t e d by B a r t l e t t ' s  5-43,  As shown i n these  from stand type t o stand  of homogeneous v a r i a n c e s of the d a t a  was  test.  A c l o s e r examination  of the d a t a w i l l  f i n d t h a t the sample p l o t s  i n the i n v e n t o r y zone and s p e c i e s c o m p o s i t i o n types were measured a t v a r i o u s stand ages. Coast Region  In some i n v e n t o r y zones,  f o r i n s t a n c e , the  (Zone 2) where most p l o t s observed were second  the v a r i a t i o n i n net volume y i e l d T r a n s i t i o n B e l t where a wider  age range of sample p l o t s was  5-43,  5-44  i n each s p e c i e s c o m p o s i t i o n type and T h e r e f o r e , the assumption this  ground.  growth stands,  i s much l e s s than the South Coast  S i n c e stand y i e l d s were measured at d i f f e r i n g age ranges, e r r o r s shown i n T a b l e s 5-42,  Southern  do not r e f l e c t  i n v e n t o r y zone  surveyed.  the standard  true v a r i a t i o n  combination.  of homogeneous v a r i a n c e i s not r e j e c t e d  on  5-42.  Standard d e v i a t i o n s of D o u q l a s - f i r volume y i e l d s p e c i e s types and f o r e s t i n v e n t o r y zones (Unit: c u b i c f e e t per acre) FOREST  TYPE  INVENTORY  data by  ZONE  COAST  INTERIOR  2  3  ALL  4  5  6  7  8  PURE  301 5  4379  3298  1590  1673  1638  1786  1344  1745  CMIX  354 1  4169  4178  1848  1801  2235  191 5  1487  1979  HMIX  2297  3389  2572  430  1458  1186  1545  --  1497  ALL  3078  4273  3523  16 62  1707  2035  1869  1354  1798  ALL  : PURE—pure D o u q l a s - f i r t y p e ; C M I X — D o u q l a s - f i r - c o n i f e r mixed HMIX—Douglas-fir-hardwood mixed type.  type;  Table 5-43. Standard d e v i a t i o n s o f spruce volume y i e l d data by s p e c i e s composition types and i n v e n t o r y zone (Unit: c u b i c f e e t per acre) TYPE  FOREST  INVENTORY  ZONE  4  5  6  7  8  9  11  12  ALL  PURE  2171  2006  1569  2607  1893  2102  1929  2121  2135  CMIX  2236  2136  2188  2040  1681  1 911  1398  1835  2007  HMIX  2502  --  2399  2214  1571  2096  1340  1876  1979  ALL  22 83  2045  2139  2168  1812  2005  1693  2062  2067  Remarks: PURE—pure spruce t y p e ; C M I X — s p r u c e - c o n i f e r HMIX—spruce-hardwood mixed type.  mixed type;  Table  5-44. S t a n d a r d d e v i a t i o n s o f l o d q e p o l e p i n e volume y i e l d by s p e c i e s c o m p o s i t i o n t y p e s and i n v e n t o r y z o n e s ( U n i t : c u b i c f e e t per a c r e )  TYPE  FOREST 4  5  6  7  INVENTORY 8  ZONE  9  10  12  ALL  1992  1573  1892  1 54 3  1868  i  PURE  1585  20 18  2054  1417  1868  19 87  CMIX  1737  1511  1950  1456  1639  1775  HMIX  1631  1960  718  1616  18 56  1598  1 480  1700  ALL  1665  1925  1431  1817  19 56  2166  1658  1874  —  2007  data  —  Remarks: P U R E — p u r e l o d q e p o l e pine t y p e ; C M I X — l o d q e p o l e p i n e - c o n i f e r s mixed t y p e ; H M I X — l o d q e p o l e p i n e - h a r d w o o d mixed t y p e .  i—  1  o i  - 171  5.12  -  L e a s t Squares A n a l y s i s  In d i s c u s s i n g the l e a s t  squares a n a l y s i s , S e a r l e (1971)  p o i n t e d out t h a t  "The c a l c u l a t i o n s i n v o l v e d i n t h i s method of a n a l y s i s a r e , f o r unbalanced d a t a , u s u a l l y more c o m p l i c a t e d than those of t r a d i t i o n a l a n a l y s i s of v a r i a n c e f o r b a l a n c e d d a t a , so t h a t p r i o r t o the p r e s e n t e r a of computers t h e r e has been l i m i t e d demand f o r a n a l y z i n g unbalanced d a t a . Nowadays, however, i n view of the a v a i l a b i l i t y of v a s t computer s t o r a g e and e d i t i n g of d a t a we a r e w i t n e s s i n g a g r e a t i n c r e a s e i n the demand f o r a n a l y s i s o f unbalanced d a t a , a n a l y s i s which cannot be made merely by means of minor adjustments to t r a d i t i o n a l a n a l y s e s of v a r i a n c e of b a l a n c e d d a t a . "  Indeed, S e a r l e c o n t i n u e d :  "The s i t u a t i o n i s j u s t the o p p o s i t e : unbalanced d a t a have t h e i r own a n a l y s i s of v a r i a n c e t e c h n i q u e , and those f o r b a l a n c e d d a t a a r e merely s p e c i a l cases of the t e c h n i q u e s f o r unbalanced d a t a . The p o s i t i o n i s t h a t unbalanced d a t a can be couched i n m a t r i x e x p r e s s i o n s , many of which s i m p l i f y v e r y l i t t l e i n terms of summation f o r m u l a s . In c o n t r a s t , when the numbers, o f o b s e r v a t i o n - . i n the s u b c l a s s e s a r e a l l the same, these m a t r i x e x p r e s s i o n s s i m p l i f y c o n s i d e r a b l y . They reduce, i n f a c t , t o the well-known summation formulae of t r a d i t i o n a l a n a l y s i s of v a r i a n c e of designed experiments, such as randomized complete b l o c k s , f a c t o r i a l experiments d e s i g n s and o t h e r s . "  T h e r e f o r e , one can t h i n k of such a n a l y s e s simply as cases of the more b a s i c a n a l y s e s of v a r i a n c e f o r unbalanced  special  data.  - 172 -  Although the l e a s t squares a n a l y s i s handles unbalanced  data  w i t h h i g h v a r i a t i o n i n numbers o f o b s e r v a t i o n i n s u b c l a s s e s , a few o b s e r v a t i o n s w i t h u n u s u a l l y h i g h o r low v a l u e may i n f l u e n c e t h e r e s u l t s . T h i s i s e x e m p l i f i e d by t h e spruce d a t a i n p r e v i o u s s e c t i o n s where one sample p l o t w i t h extremely h i g h volume and b a s a l a r e a was observed. For t h i s r e a s o n , i t i s e s s e n t i a l t o s c r e e n the s u b c l a s s d a t a w i t h few o b s e r v a t i o n s and d e c i d e whether o r n o t these o b s e r v a t i o n s should be i n c l u d e d i n the a n a l y s i s .  A f u r t h e r study on t h e e f f e c t o f t h e  v a r i a t i o n i n c e l l f r e q u e n c i e s on t h e power o f h y p o t h e s i s t e s t should be undertaken. The  i m p o s i t i o n o f c o n s t r a i n t s on parameters  t o be e s t i m a t e d  i n o r d e r t o o b t a i n unique s o l u t i o n s f o r the normal e q u a t i o n s d e r i v e d by the l e a s t squares p r i n c i p l e i s n o t accepted by s t a t i s t i c i a n s objections.  Kempthorne (1952), F e d e r e r  without  (1955), S t e e l and T o r r i e  (1960),  and Harvey (1960) c o n s i d e r e d t h a t t h e r e s t r i c t i o n s  E a. i i  = I 6. . j 3  =  £ (aB).. • i Jl i  = I (a$).. = 0 13 3  (5-2)  a r e s a t i s f a c t o r y w h i l e S c h e f f e (1959) c o n s i d e r e d t h e systems o f weights f o r l t h e s e e q u a t i o n s do n o t matter t o o much. However, S e a r l e (1971) argued  that  (1) t h e c o n s t r a i n t s a r e  g e n e r a l l y n o t t h e s i m p l e s t , (2) such c o n s t r a i n t s a r e n o t n e c e s s a r y f o r s o l v i n g normal e q u a t i o n s ; they a r e o n l y s u f f i c i e n t ;  and (3) they can  be used whether o r n o t a s i m i l a r r e l a t i o n s h i p h o l d s f o r t h e elements  - 173 -  of  t h e model; and o n l y i f i t does w i t h enough such r e l a t i o n s h i p s  in  the model t o make i t a f u l l  normal e q u a t i o n s  rank model, w i l l t h e s o l u t i o n s o f t h e  then be e s t i m a t e s  According  o f the parameters o f t h e model.  t o S e a r l e (1971), t h e c o n s t r a i n t s e a s i e s t t o use  w i t h unbalanced d a t a a r e the s i m p l e s t ones o f p u t t i n g p - r elements of  b vector equation  of  course,  t o zero.  They cannot be j u s t any p - r elements ' x ' x  c "  I  0  f o r they must be j u d i c i o u s l y chosen so as t o make  non-singular.  However, Harvey  (1960) found  C  t h i s c o n s t r a i n t un-  satisfactory i n practice. The to  l e a s t squares a n a l y s i s o f f e r s a unique s t a t i s t i c a l method  analyze f o r e s t inventory data.  the technique  i s powerful  i n e x t r a c t i n g i n f o r m a t i o n out o f i r r e g u l a r -  structured f o r e s t inventory data. to  As demonstrated i n p r e v i o u s s e c t i o n s ,  I t a l s o p r o v i d e s a v a l u a b l e method  i n c o r p o r a t e q u a l i t a t i v e and q u a n t i t a t i v e v a r i a b l e s i n volume y i e l d  a n a l y s i s , a method, t o t h e b e s t knowledge o f t h e w r i t e r , which has n o t been attempted i n f o r e s t y i e l d for  a technique  study.  F o r e s t e r s have l o n g been s e a r c h i n g  t o q u a n t i f y q u a l i t a t i v e v a r i a b l e s such as s p e c i e s  type  group and i n v e n t o r y zones which a r e f r e q u e n t l y encountered i n p r a c t i c e s and r e s e a r c h e s . need  The l e a s t squares technique  as used here f u l f i l l s the  satisfactorily. Methodology i s e s s e n t i a l t o t h e e x p l o r a t i o n o f new t e r r i t o r y  of  knowledge; p r o g r e s s  of  appropriate techniques  (data).  i n s c i e n c e r e l i e s p r i m a r i l y on t h e a v a i l a b i l i t y e i t h e r i n c o l l e c t i n g or analyzing information  I n f o r e s t s c i e n c e , and i n the study o f growth and y i e l d i n  p a r t i c u l a r , a huge amount o f d a t a has been c o l l e c t e d a n n u a l l y by means  - 174 -  of f o r e s t i n v e n t o r y surveys o r o t h e r methods. p r o v i d e a sound b a s i s f o r v a r i o u s s p e c i f i e d procedures  Those d a t a can  studies i f a n a l y t i c a l  a p p r o p r i a t e t o t h e d a t a become a v a i l a b l e .  Therefore,  to make f u l l use o f those d a t a , t h e r e i s a p r e s s i n g need t o develop a sound s t a t i s t i c a l procedure.  As demonstrated i n p r e v i o u s s e c t i o n s ,  the l e a s t squares a n a l y s i s i s v e r y p o w e r f u l and s u i t a b l e f o r a n a l y s e s of f o r e s t i n v e n t o r y d a t a .  5.13  Chapter  Summary  In t h i s c h a p t e r r e s u l t s from a n a l y s e s o f Coast D o u g l a s - f i r , I n t e r i o r D o u g l a s - f i r , I n t e r i o r spruce, and l o d g e p o l e p i n e i n v e n t o r y d a t a by t h e l e a s t  squares  t e c h n i q u e developed  i n Chapter  3 were  p r e s e n t e d and d i s c u s s e d . Because sampled p l o t s were randomly s e l e c t e d , i t was p o s s i b l e to i n f e r the r e l a t i v e f r e q u e n c i e s o f s p e c i e s types i s a u s e f u l of t h e frequency w i t h which t h e v a r i o u s types occur n a t u r a l l y . found  indicator I t was  t h a t more than 50% o f D o u g l a s - f i r , spruce, and l o d g e p o l e p i n e  stands c u r r e n t l y e x i s t as pure type  forests.  S i t e d e t e r i o r a t i o n r e l a t e d t o pure type stands was d i s c u s s e d . Although  s i t e i n d i c e s f o r stands o f mixed types were shown t o be h i g h e r  than those o f pure type stands, t h e d a t a were inadequate - t o demonstrate c o n c l u s i v e l y whether or not the h i g h e r index has r e s u l t e d from  beneficial  e f f e c t s o f mixed stands on s o i l o r simply from t h e b e t t e r s i t e c o n d i t i o n s when stands were o r i g i n a l l y e s t a b l i s h e d .  - 175  -  A n a l y s e s o f the numbers of t r e e s per a c r e , show t h a t  conifer  mixed type stands a r e c a p a b l e of growing more t r e e s p e r a c r e than or hardwood mixed type s t a n d s . r e q u i r e s more growing  pure  Among t h r e e s p e c i e s , D o u g l a s - f i r  space thus r e d u c i n g the number of t r e e s per a c r e .  The r e l a t i v e stand d e n s i t y c a l c u l a t e d from b a s a l a r e a has a s i m i l a r p a t t e r n t o number o f t r e e s per a c r e . Stand age, mean annual increments of h e i g h t , b a s a l a r e a , and volume were d i s c u s s e d .  In g e n e r a l , stand age i s younger i n hardwood  mixed stands than i n pure or c o n i f e r mixed stands because of the dynamic n a t u r e of hardwood mixed type s t a n d s . increment  The mean annual h e i g h t  of t h r e e s p e c i e s c o m p o s i t i o n types i n v e s t i g a t e d  indicates  t h a t hardwood"mixed type stands grow f a s t e r than pure, or c o n i f e r mixed type s t a n d s .  The  f a s t e r growth i n h e i g h t can p r o b a b l y be e x p l a i n e d  i n p a r t by younger age of hardwood mixed type s t a n d s . increments  The mean annual  f o r b a s a l area a r e g e n e r a l l y h i g h e r i n c o n i f e r mixed  type  stands than i n pure o r hardwood mixed type stands w h i l e the mean annual increments  f o r volume show a s i m i l a r p a t t e r n t o t h a t of b a s a l a r e a . D i f f e r e n c e s i n growth and y i e l d between Coast and  D o u g l a s - f i r stands were a l s o  Interior  illustrated.  Net volume y i e l d s o f D o u g l a s - f i r , spruce, and l o d g e p o l e p i n e i n v e n t o r y d a t a were f u r t h e r a n a l y z e d and p o t e n t i a l p r o d u c t i o n c a p a c i t y of v a r i o u s s p e c i e s types on B.C. identified.  i n v e n t o r y zones was  compared  and  The volume y i e l d d a t a were i n t u r n a d j u s t e d f o r age  and  s i t e index to t e s t the h y p o t h e s i s t h a t t h e r e .was no d i f f e r e n c e i n y i e l d among s p e c i e s c o m p o s i t i o n types f o r stands o f same s i t e q u a l i t y .  The  - 176 -  disparity  i n y i e l d between pure D o u g l a s - f i r type and D o u g l a s - f i r  c o n i f e r mixed type i n the I n t e r i o r stand  parameters were used i n y i e l d  was e l u c i d a t e d .  Finally, a l l  t a b l e a n a l y s i s , and a stepwise  e l i m i n a t i o n procedure was used t o r a t i f y the r e l a t i v e a stand  parameter i n the c o n s t r u c t i o n o f a stand Standard d e v i a t i o n i n y i e l d  f o r species  zone combinations was i l l u s t r a t e d and d i s c u s s e d . using  the r e v i s e d l e a s t  d a t a were  discussed.  yield  importance of table.  types and  inventory  The advantages of  squares method i n the a n a l y s i s of i n v e n t o r y  - 177  6.0  SUMMARY AND  -  CONCLUSIONS  Methodology i s e s s e n t i a l t o the e x p l o r a t i o n of new of knowledge; p r o g r e s s i n s c i e n c e depends p r i m a r i l y on the of  In f o r e s t  s c i e n c e , i n the study of growth and y i e l d i n  p a r t i c u l a r , a huge amount of d a t a has  been c o l l e c t e d a n n u a l l y by means  f o r e s t i n v e n t o r y surveys o r o t h e r methods.  a sound b a s i s f o r v a r i o u s s p e c i f i e d  has been accumulated  Those d a t a can p r o v i d e  studies i f analytical  a p p r o p r i a t e t o the d a t a become a v a i l a b l e .  of  availability  a p p r o p r i a t e t e c h n i q u e s e i t h e r i n c o l l e c t i n g or a n a l y z i n g i n f o r m a t i o n  (data).  of  territory  procedures  A tremendous amount of d a t a  from p a s t f o r e s t i n v e n t o r y s u r v e y s , but the  use  s t a t i s t i c a l methods o t h e r than o r d i n a r y r e g r e s s i o n a n a l y s i s t o a n a l y z e  those d a t a has  seldom been attempted.  To make f u l l use of those  data  p r o v i d e d by i n v e n t o r y s u r v e y s , t h e r e i s a p r e s s i n g need t o develop statistical  procedures  f o r the a n a l y s i s of those  sound  data.  C o n t r i b u t i o n s of the study t o the spectrum can, t h e r e f o r e , be summarized i n m e t h o d o l o g i c a l and  of f o r e s t s c i e n c e substantial  connotations. M e t h o d o l o g i c a l l y , the study developed to  a n a l y z e i r r e g u l a r , unbalanced  Admittedly, to  i n v e n t o r y d a t a by l e a s t  the l e a s t squares a n a l y s i s was  a n a l y z e unbalanced  a statistical  d a t a f o r t y y e a r s ago;  employed by  procedure  squares  principle.  statisticians  however, i n f o r e s t  d i s c i p l i n e s , where d a t a c o l l e c t e d a r e o f t e n unbalanced  i n nature  because :the e x p e r i m e n t a l p l o t s a r e u s u a l l y s u b j e c t e d t o u n c o n t r o l l a b l e environmental  f a c t o r s and experiments  are o f t e n long i n duration,  the methods have u n f o r t u n a t e l y been n e g l e c t e d .  - 178 -  Furthermore,  the study developed  which e f f e c t i v e l y a n a l y z e s unbalanced  a computing a l g o r i t h m  d a t a w i t h some s u b c l a s s e s  without  o b s e r v a t i o n s , when i n t e r a c t i o n s a r e t o be i n c l u d e d i n t h e  model.  Computer programs a d a p t i n g the l e a s t squares p r i n c i p l e f o r  the a n a l y s i s o f unbalanced  d a t a do e x i s t ; but they f a i l when t h e r e  a r e empty s u b c l a s s e s and i n t e r a c t i o n s a r e t o be c o n s i d e r e d . program which c o n s i d e r s more g e n e r a l i z e d unbalanced one  step f a r t h e r i n s t a t i s t i c a l computation In a d d i t i o n , the developed  The  data has p r o g r e s s e d  technique.  method p r o v i d e s a unique means  t o i n c o r p o r a t e q u a l i t a t i v e as w e l l as q u a n t i t a t i v e v a r i a b l e s i n f o r e s t yield analysis attempted  ( y i e l d t a b l e c o n s t r u c t i o n ) . Such a n a l y s e s have never been  i n yield  s t u d i e s because o f l a c k o f s u i t a b l e methods.  The  method as demonstrated i n the study, o f f e r s s a t i s f a c t o r y a l t e r n a t i v e s t o q u a n t i f y i n g q u a l i t a t i v e v a r i a b l e s which a r e o f t e n encountered  by  f o r e s t e r s i n r e s e a r c h as w e l l as i n p r a c t i c e . Some v a l u a b l e i n f o r m a t i o n has been induced by a p p l y i n g t h e d e v e l o p i n g l e a s t squares a n a l y s i s t o D o u g l a s - f i r , spruce, and l o d g e p o l e p i n e i n v e n t o r y d a t a p r o v i d e d by the B.C. F o r e s t S e r v i c e Inventory D i v i s i o n , i n c o n n e c t i o n w i t h t h e study o f growth and y i e l d o f pure and mixed stands i n B.C. f o r e s t  i n v e n t o r y zones.  From t h e r e s u l t s and  d i s c u s s i o n s p r e s e n t e d i n the p r e v i o u s c h a p t e r s , t h e f o l l o w i n g summaries a n d ^ c o n c l u s i o n s can be drawn. The r e l a t i v e frequency o f the v a r i o u s k i n d s o f i n v e n t o r y ' p l o t s i s a u s e f u l i n d i c a t o r o f the r e l a t i v e frequency w i t h which the v a r i o u s types occur i n n a t u r e .  More than 50% o f D o u g l a s - f i r , spruce, and  l o d g e p o l e p i n e stands occur n a t u r a l l y as pure t y p e s ; i f t h e r e a r e any  - 179  -  adverse e f f e c t s on e s t a b l i s h m e n t of pure type stands, these should have been w e l l r e f l e c t e d q u a n t i t a t i v e l y i n those  effects  stands.  A main c r i t i c i s m of the e s t a b l i s h m e n t of pure stands has been t h a t pure type stands u s u a l l y d e t e r i o r a t e s o i l c o n d i t i o n s .  Estimates  of s i t e index from the i n v e n t o r y d a t a a n a l y z e d seem t o support argument; however, i t was i n mixed type stands may  p o i n t e d out t h a t the h i g h e r s i t e  the  indices  be a t t r i b u t e d t o the b e t t e r s i t e c o n d i t i o n s  when the stands were o r i g i n a l l y e s t a b l i s h e d . Comparing the number of t r e e s per a c r e among t h r e e s p e c i e s c o m p o s i t i o n t y p e s , one  sees c l e a r l y t h a t c o n i f e r mixed  stands  a r e capable of growing more t r e e s per a c r e than pure or hardwood mixed type stands.  Among t h r e e s p e c i e s i n v e s t i g a t e d , D o u g l a s - f i r  r e q u i r e s more growing space thus r e d u c i n g the number of t r e e s per a c r e . A l t e r n a t i v e l y , s t o c k i n g may  be l e s s complete because of m o r t a l i t y and/or  incomplete r e g e n e r a t i o n . The r e l a t i v e stand d e n s i t y based  on b a s a l a r e a per a c r e a l s o  i n d i c a t e s t h a t stand d e n s i t y i s h i g h e r i n c o n i f e r mixed type  stands  than i n pure type o r hardwood mixed type stands f o r a l l t h r e e s p e c i e s . The  average  stand age  i n hardwood mixed type stands i s much  younger than i n pure o r c o n i f e r mixed type s t a n d s .  The r e s u l t s  suggest  that hardwoods a r e " p i o n e e r " s p e c i e s i n B r i t i s h Columbia f o r e s t s t h a t the c o m p o s i t i o n of hardwood stands i s g r a d u a l l y changing hardwood mixed type t o c o n i f e r mixed type o r t o pure type w i t h i n c r e a s e of stand  age.  and  from the  - 180  The  -  f i g u r e s show t h a t the mean annual h e i g h t increment  i s h i g h e r i n hardwood mixed type stands than i n pure or c o n i f e r mixed type ones.  The r e s u l t s can be i n t e r p r e t e d by the f a c t t h a t stand age  i n hardwood mixed type stands i s much younger than i n pure o r c o n i f e r mixed type s t a n d s .  V a r i a t i o n s i n mean annual h e i g h t increments among  f o r e s t i n v e n t o r y zones a r e noted. The annual b a s a l increment of c o n i f e r mixed type stands i s c o n s i s t e n t l y h i g h e r t h a n those o f o t h e r two  species composition types.  Z o n a l v a r i a t i o n s i n the mean annual b a s a l a r e a growth are a l s o  apparent.  The mean annual volume increment f o l l o w s a t r e n d s i m i l a r t o t h a t of the mean annual b a s a l a r e a increment. D i f f e r e n c e s i n growth and y i e l d between Coast and D o u g l a s - f i r stands were compared.  I t was  can grow more t r e e s per a c r e on the Coast i n the I n t e r i o r  (121 t r e e s ) .  c u b i c f e e t per a c r e  Interior  found t h a t D o u g l a s - f i r  stands  (188 t r e e s per a c r e ) than  The mean annual volume growth i s 84.00  f o r the Coast stands and 25.53 c u b i c f e e t f o r the  I n t e r i o r stands; the former outgrow the l a t t e r by 3.3 i n growth between these two by d i f f e r e n c e s i n s i t e index  times.  Difference  geographic areas can be accounted f o r i n p a r t (120 and 78 f o r the Coast and the  Interior,  respectively). On the Coast f e r t i l e s i t e s  (the Southern Coast R e g i o n ) ,  pure  D o u g l a s - f i r type stands y i e l d more than D o u g l a s - f i r c o n i f e r or hardwood mixed stands.  However, on medium  sites  (the South Coast  Transition  B e l t ) , D o u g l a s - f i r hardwood mixed type stands o u t y i e l d pure type s t a n d s . In the I n t e r i o r D o u g l a s - f i r c o n i f e r mixed type stands c o n s i s t e n t l y more wood than the o t h e r two  composition types.  produce  - 181  -  A n a l y s e s of the net volume y i e l d d a t a of Coast D o u g l a s - f i r , I n t e r i o r D o u g l a s - f i r , spruce, and l o d g e p o l e p i n e w i t h stand age as a c o v a r i a b l e p r o v i d e comparisons i n volume y i e l d f o r v a r i o u s s p e c i e s c o m p o s i t i o n types i n B.C.  inventory  zones.  E f f e c t s of s p e c i e s c o m p o s i t i o n types and f o r e s t i n v e n t o r y zones a r e not s i g n i f i c a n t i n Coast D o u g l a s - f i r stands, but for  types and zones a r e .  yield at  Based on the e s t i m a t e d c o n s t a n t s , the p o t e n t i a l  f o r t h r e e s p e c i e s composition types i n two  stand age 100.  Region,  interactions  On v e r y f e r t i l e  Coast  zones were t a b u l a t e d  s o i l such as t h a t i n the Southern  Coast  pure D o u g l a s - f i r type tends t o grow e x c e l l e n t l y ; however, on  medium s o i l ,  i t i s advantageous t o e s t a b l i s h D o u g l a s - f i r mixed  type  stands. In and  types  i n v e n t o r y zones e f f e c t s a r e s i g n i f i c a n t w h i l e i n t e r a c t i o n s t h e r e o f  are not. fir  I n t e r i o r D o u g l a s - f i r stands, the s p e c i e s composition  In g e n e r a l , the p o t e n t i a l y i e l d i s 3114  c o n i f e r mixed type stands and  type at age 100.  The  c u b i c f e e t f o r Douglas-  2582 c u b i c f e e t f o r pure D o u g l a s - f i r  e s t a b l i s h m e n t of D o u g l a s - f i r c o n i f e r mixed  stands e f f e c t i v e l y i n c r e a s e s f o r e s t p r o d u c t i v i t y by 21%.  type  The most  p r o d u c t i v e D o u g l a s - f i r stands are found i n Zone 7 w h i l e the p o o r e s t a r e i n Zone 8.  The p o t e n t i a l y i e l d s of D o u g l a s - f i r c o n i f e r mixed  stands are i n v a r i a b l y h i g h e r than the o t h e r two all  c o m p o s i t i o n types i n  zones. F o r the I n t e r i o r spruce d a t a , the e f f e c t s of s p e c i e s  composition  type on net volume y i e l d a r e not s i g n i f i c a n t w h i l e z o n a l e f f e c t s i n t e r a c t i o n s f o r zones and  types a r e .  and  The most p r o d u c t i v e spruce  stands a r e i n Zone 5 w i t h a p o t e n t i a l y i e l d  of 4264 c u b i c f e e t per a c r e  - 182 -  at age 100; Zones 7, 8 and 9 a r e e q u a l l y p r o d u c t i v e w h i l e Zone 11 i s the l e a s t p r o d u c t i v e zone f o r spruce i n t h e I n t e r i o r . z o n a l p r o d u c t i o n c a p a c i t y , i t was observed do not account  From the  t h a t changes i n l a t i t u d e  f o r t h e v a r i a t i o n i n volume y i e l d f o r spruce i n t h e  Interior. I n s p e c t i o n o f the i n t e r a c t i o n s  suggests t h a t pure  spruce  stands o u t y i e l d mixed type stands i n Zones 4, 6, and 12 w h i l e  spruce-  c o n i f e r mixed type stands i n Zone 5 and spruce-hardwood mixed  type  stands i n Zone 9 produce more volume than do pure spruce  stands.  F o r t h e I n t e r i o r l o d g e p o l e p i n e d a t a , t h e e f f e c t s of s p e c i e s c o m p o s i t i o n types a r e n o t s i g n i f i c a n t w h i l e z o n a l e f f e c t s and i n t e r a c t i o n s are.  The b e s t zone f o r l o d g e p o l e p i n e y i e l d i s Zone 9 and  the p o o r e s t Zone 5.  Zonal v a r i a t i o n s  i n volumes a r e s m a l l e r i n  l o d g e p o l e p i n e than i n D o u g l a s - f i r and spruce because the g e n e r a l c l i m a t i c requirements Consequently,  o f l o d g e p o l e p i n e a r e wider  than t h e l a t t e r .  t h e changes i n l a t i t u d e have l i t t l e b e a r i n g on the  p r o d u c t i v e c a p a c i t y o f l o d g e p o l e p i n e i n the I n t e r i o r . Pure l o d g e p o l e p i n e type stands i n Zone 10 outweigh of mixed types by 51% i n volume.  stands  On t h e o t h e r hand l o d g e p o l e p i n e  c o n i f e r mixed type stands a r e more p r o d u c t i v e than pure l o d g e p o l e p i n e type stands by more than 10% i n Zones 4 and 12. advantages o f m o n o c u l t u r a l o r m u l t i c u l t u r a l over-generalized.  practices  can not be  Pure type stands a r e more p r o d u c t i v e i n some zones  but l e s s i n t h e o t h e r s . disadvantages  Therefore, the  The same i s t r u e as t o the advantages and  of m u l t i c u l t u r a l  practices  with regard to f o r e s t  crops.  - 183  -  Growth of f o r e s t t r e e s i s e s s e n t i a l l y s i t e - d e p e n d e n t . d e c i s i o n i s reached  Before a  on what s p e c i e s composition type t o e s t a b l i s h ,  f o r e s t e r s s h o u l d c a r e f u l l y i n v e s t i g a t e the l o c a l s i t e q u a l i t y  and  past y i e l d h i s t o r y of v a r i o u s f o r e s t types t o ensure the maximum p o t e n t i a l p r o d u c t i v i t y of a p a r t i c u l a r s i t e can be I t goes without  realized..,  s a y i n g t h a t the p r o d u c t i v i t y of f o r e s t l a n d  can be a m p l i f i e d by e s t a b l i s h i n g a f o r e s t type a p p r o p r i a t e t o the a r e a . The fir,  study i d e n t i f i e d the optimum s p e c i e s c o m p o s i t i o n types f o r Douglasspruce, and  l o d g e p o l e p i n e i n B.C.  s t u d i e s to e l u c i d a t e the reasons  f o r e s t i n v e n t o r y zones.  Further  f o r a s p e c i e s type t o y i e l d more than  o t h e r s i n a p a r t i c u l a r zone a r e needed i n order t o h e l p f o r e s t e r s i n t h e i r s e l e c t i o n of an optimum s p e c i e s composition  type.  The volume y i e l d d a t a were f u r t h e r a n a l y z e d f o r the s p e c i e s c o m p o s i t i o n e f f e c t s by t a k i n g s i t e index and stand age as c o v a r i a b l e s t o t e s t the h y p o t h e s i s t h a t no d i f f e r e n c e s i n volume y i e l d e x i s t among t h r e e s p e c i e s c o m p o s i t i o n types f o r stands growing on same s i t e conditions.  The r e s u l t s i n d i c a t e t h a t f o r Coast D o u g l a s - f i r the  effects  f o r s p e c i e s types and  i n v e n t o r y zones as w e l l as i n t e r a c t i o n s t h e r e o f  a r e not s i g n i f i c a n t .  T h e r e f o r e , the d i f f e r e n c e i n y i e l d among s p e c i e s  c o m p o s i t i o n types can be i n t e r p r e t e d i n f u l l by d i f f e r e n c e i n s i t e index f o r the Coast D o u g l a s - f i r stands. In I n t e r i o r D o u g l a s - f i r stands, however, the s p e c i e s types a r e s i g n i f i c a n t a t the 1% l e v e l ,  composition  the e s t i m a t e d e f f e c t i s 16.92,  350.78, and -367.70 c u b i c f e e t per a c r e f o r pure D o u g l a s - f i r , D o u g l a s - f i r c o n i f e r mixed, and D o u g l a s - f i r hardwood mixed types  respectively.  - 184 -  In o t h e r words, on same s i t e c o n d i t i o n s , D o u g l a s - f i r c o n i f e r mixed type stands y i e l d 334 c u b i c f e e t more than pure type and  stands  718 c u b i c f e e t p e r a c r e than D o u g l a s - f i r hardwood mixed  type  stands i n t h e I n t e r i o r . On equal s i t e c o n d i t i o n s , t h e r e i s no d i f f e r e n c e i n volume y i e l d among t h r e e s p e c i e s c o m p o s i t i o n types i n I n t e r i o r spruce  stands  w h i l e z o n a l e f f e c t s and i n t e r a c t i o n s f o r types and zones a r e significant.  I n I n t e r i o r l o d g e p o l e p i n e stands, e f f e c t s o f s p e c i e s  c o m p o s i t i o n t y p e s , zones, and i n t e r a c t i o n s t h e r e o f d i f f e r  significantly.  On same s i t e c o n d i t i o n s , pure l o d g e p o l e p i n e type stands y i e l d 48 c u b i c f e e t p e r a c r e more than l o d g e p o l e p i n e c o n i f e r mixed type stands and 272 c u b i c f e e t more than l o d g e p o l e p i n e hardwood mixed type In a l l t h r e e s p e c i e s —  stands.  D o u g l a s - f i r , spruce, and l o d g e p o l e p i n e  i n v e s t i g a t e d , t h e e f f e c t s o f hardwood mixed type show c o n s i s t e n t l y a negative value.  Consequently,  hardwood mixed type stands a r e t h e l e a s t  d e s i r a b l e stand composition s t r u c t u r e f o r these s p e c i e s i n t h e I n t e r i o r . Because t h e I n t e r i o r D o u g l a s - f i r stands show d i f f e r e n c e s i n volume y i e l d between pure and c o n i f e r mixed type stands a f t e r  site  index and stand age have been a d j u s t e d , the d a t a were f u r t h e r a n a l y z e d by f i t t i n g t h e average h e i g h t , b a s a l a r e a , and volume i n v a r i o u s age c l a s s e s on t h r e e s i t e c l a s s e s u s i n g W e i b u l l - t y p e growth f u n c t i o n s . I t was found t h a t t h e r e was no d i f f e r e n c e i n h e i g h t growth between pure and c o n i f e r mixed t y p e s .  The d i s p a r i t y i n volume between pure and  mixed type stands has r e s u l t e d from the i n e q u a l i t y i n b a s a l a r e a p e r acre.  D o u g l a s - f i r c o n i f e r mixed type stands a r e c a p a b l e o f growing  - 185  -  more t r e e s per a c r e , thus more b a s a l a r e a per a c r e , and more volume than do pure D o u g l a s - f i r type stands Analyses  consequently  i n the  were f i n a l l y c a r r i e d out f o r y i e l d  Interior.  table construction  by i n c o r p o r a t i n g a l l stand parameters, q u a l i t a t i v e and q u a n t i t a t i v e v a r i a b l e s , e.g.  s p e c i e s composition  i n t e r a c t i o n s f o r types and  height x b a s a l area.  forest inventory  zones, s i t e , age,  t r e e s per a c r e , average DBH, and  type,  l o g age,  zones,  h e i g h t , number of  b a s a l a r e a per a c r e , r e l a t i v e stand  A stepwise  e l i m i n a t i o n procedure was  density,  used to  a s c e r t a i n the importance of these v a r i a b l e s i n y i e l d t a b l e c o n s t r u c t i o n . In a l l f o u r s e t s of i n v e n t o r y data analyzed,  the v a r i a b l e s ,  h e i g h t x b a s a l a r e a and b a s a l a r e a are most important. stand age,  r e l a t i v e b a s a l a r e a , and  In a d d i t i o n ,  f o r e s t i n v e n t o r y zone are a l l h i g h l y  s i g n i f i c a n t i n c o n t r i b u t i n g to the v a r i a t i o n s i n volume y i e l d of Coast D o u g l a s - f i r stands.  The  h i g h F-value  for forest  suggests t h a t the s u b d i v i s i o n of the Coast-area justified. same age,  Estimated  constants  i n v e n t o r y zone  for Douglas-fir i s  f o r i n v e n t o r y zones i n d i c a t e t h a t on  b a s a l a r e a , r e l a t i v e stand d e n s i t y , and h e i g h t x b a s a l  Zone 2 w i l l y i e l d  248  i n y i e l d between these  c u b i c f e e t per acre more than Zone 3. two  the  The  i n v e n t o r y zones can be e x p l a i n e d by  the  area, disparity  biotic  f a c t o r s such as decay. For I n t e r i o r D o u g l a s - f i r , the most s i g n i f i c a n t v a r i a b l e s are h e i g h t x b a s a l area, b a s a l a r e a , stand age, density.  E f f e c t s of s p e c i e s c o m p o s i t i o n  l o g age,  type and  and  forest  relative  stand  inventory  zones a r e n o n - s i g n i f i c a n t i n comparison w i t h the above 5 v a r i a b l e s . Accordingly,  i f h e i g h t x b a s a l a r e a , b a s a l a r e a , stand age,  relative  - 186 -  stand d e n s i t y a r e e q u a l , no v a r i a t i o n i n volume y i e l d among s p e c i e s composition types and f o r e s t i n v e n t o r y zones i n t h e I n t e r i o r i s expected. F o r I n t e r i o r spruce, the prominant v a r i a b l e s i n y i e l d  table  a n a l y s i s a r e height x b a s a l area, b a s a l area, species composition stand age, h e i g h t , and r e l a t i v e stand d e n s i t y .  types,  I n s p e c t i o n of the  e s t i m a t e d e f f e c t s f o r t h r e e s p e c i e s c o m p o s i t i o n types suggests t h a t a l l v a r i a b l e s , b a s a l a r e a , h e i g h t , stand age, and r e l a t i v e  stand  d e n s i t y b e i n g e q u a l , pure spruce type stands o u t y i e l d stands o f spruce-hardwood mixed type by 286 c u b i c f e e t p e r a c r e and s p r u c e c o n i f e r mixed type by 23 c u b i c f e e t .  The r e s u l t s p r o v i d e good  evidence  t h a t e s t a b l i s h m e n t o f pure spruce type stands i s more d e s i r a b l e than of spruce hardwood mixed type s t a n d s . better quality  Pure spruce stands produce  ( l e s s decay) l o g s than do spruce-hardwood mixed  type  stands. For l o d g e p o l e p i n e , t h e most s i g n i f i c a n t v a r i a b l e s i n y i e l d t a b l e a n a l y s i s a r e height x b a s a l area, species composition and f o r e s t i n v e n t o r y zones. i n v e n t o r y zones suggests  The h i g h s i g n i f i c a n c e of t h e f o r e s t  that a separate y i e l d  i n each zone i s warranted.  types,  t a b l e f o r lodgepole pine  The e s t i m a t e d e f f e c t s f o r t h r e e s p e c i e s  c o m p o s i t i o n types i n d i c a t e t h a t pure l o d g e p o l e p i n e type  stands  outweigh l o d g e p o l e p i n e c o n i f e r mixed type by 120 c u b i c f e e t p e r a c r e and  l o d g e p o l e p i n e hardwood mixed type by 94 c u b i c f e e t p e r a c r e .  In o t h e r words, t h e e s t a b l i s h m e n t o f pure l o d g e p o l e p i n e type  stands  i s p r e f e r r e d t o t h e mixed types s i n c e on t h e same b a s a l area and h e i g h t x b a s a l a r e a bases, pure type stands tend t o produce, more n e t volume p e r a c r e than do mixed type  stands.  - 187  -  A p p l i c a t i o n of these methods t o the temporary sample plot  data p r o v i d e d  by  the B.C.  Forest  S e r v i c e has  the widespread d i s t r i b u t i o n of pure stands and effects  o f monocultures on y i e l d .  y i e l d s may  result  and  Nevertheless,  the f a c t  clarified  from a n a l y s e s  trials  d a t a by  applied i n this  higher  establishment Only time  can r e s o l v e the i s s u e s  of i n v e n t o r y  methods such as those developed and  that  encourage  and m i x t u r e s of s p e c i e s .  c a r e f u l ' o b s e r v a t i o n iof f i e l d  cannot be  l a c k of s u b s t a n t i a l  from some m u l t i c u l t u r e s should  of l o n g term s t u d i e s of s p a c i n g  c l e a r l y demonstrated  least  thesis.  that  squares  - 188  7.0  -  LITERATURE CITED  Andody, E. 1968. G r a p h i c a l methods f o r determining y i e l d MAI, and age of MAI c u l m i n a t i o n f o r f o r e s t stands w i t h s p e c i a l r e f e r e n c e t o the C e n t r a l I n t e r i o r Region of B r i t i s h Columbia. Assn. P r o f . 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Stand development and s o i l f e r t i l i t y i n a Douglas-fir - red alder plantation. F o r e s t S c i . 7: 238-245. Tourney, J.W. and C F . K o r s t i a n . 1947. Foundations o f S i l v i c u l t u r e . John W i l e y and Sons. New York. 414p. T u r n b u l l , K.J. 1963. P o p u l a t i o n dynamics i n mixed f o r e s t s t a n d s . A system of mathematical models o f mixed stand growth and structure. Ph.D. T h e s i s . Univ. o f Washington, S e a t t l e , Wash. 186p. Urquhart, N.S., D.L. Week and C R . Henderson. 1973. E s t i m a t i o n a s s o c i a t i o n e d w i t h l i n e a r models: a revisitation. Communications i n S t a t . 1. 303-330. V a c o v s k i , H. 1967. Growth s t r u c t u r e and p r o d u c t i v i t y o f pure and mixed stands o f Ouercus s e s s i l i f l o r a and Fagus o r i e n t a l i s i n t h e Strandzda P l a n i n a . Govskostop nauka s o f i a 4: 29-50. ( o r i g i n a l n o t seen, c i t e d from F o r e s t r y A b s t r a c t . 29: 400).  - 195  -  V u o k i l a , V. 1966. Functions for v a r i a b l e density y i e l d tables of p i n e based on temporary sample p l o t s . F o r . Fenn. 60: 1-86. W a l t e r s , J . and J.H.G. Smith. 1973. Review o f methods used i n e s t a b l i s h m e n t and summary of e a r l y r e s u l t s from s p a c i n g t r i a l s on the U.B.C. Research F o r e s t . F a c u l t y of F o r e s t r y , U.B.C., Vancouver, B.C. 40p. Week, J .  1955. F o r s t l i c h e Zuwochs-und E r t r a g s k u n d e . V e r l a g , Raaebenl und B e r l i n . 92p.  Neumann  . 1957. Neuer Versuch zum Problem der K o r r e l a t i o n Klima und F o r s t l i c h e s Produktions p o t e n t i a l . F o r s t a r c h i v . 28: 223-227. W h i t f o r d , H.N. and R.D. Craig. 1918. F o r e s t s o f B r i t i s h Columbia. Commission of C o n s e r v a t i o n Canada. Ottawa. 409p. Whyte, A.G.D. 1973. P r o d u c t i v i t y of f i r s t and second crops of Pinus r a d i a t a of the Moutere G r a v e l S o i l o f Nelson. New Zealand J o u r . F o r e s t r y . 18: 84-103. W i l k s , S.S. 1938. A n a l y s i s of v a r i a n c e and c o v a r i a n c e i n nono r t h o g o n a l d a t a . Metron. 13: 141-154. Yang, R.C., A. Kozak and J.H.G. Smith. 1978. The p o t e n t i a l o f W e i b u l l - t y p e f u n c t i o n s as f l e x i b l e growth c u r v e s . Accepted. Can. J o u r . F o r . Res. Y a t e s , F.  1934. The a n a l y s i s of m u l t i p l e c l a s s i f i c a t i o n s w i t h unequal numbers i n the d i f f e r e n t c l a s s e s . J o u r . Amer. S t a t . Assn. 29: 51-66.  Young, W.E.L. 1966. Modern f o r e s t i n v e n t o r y , i t s purpose, g o a l and message. WFCA. P o r t l a n d . P r o c e e d i n g s 1965 meeting 16-20. "  . 1974. The r e s o u r c e and f o r e s t management p o l i c y — B r i t i s h Columbia. Proceedings P o p l a r U t i l i z a t i o n Symposium. P17-23. Western F o r e s t P r o d u c t s Lab., Canadian F o r . Serv. VPX-127.  Zakopal, V. and V. Mares. 1968. The importance o f Norway spruce admixtures f o r volume and v a l u e p r o d u c t i o n of oak stands on the r i c h e r types of the beech/oak c l a s s . Lesn Cas 14: 923-942. ( o r i g i n a l not seen, c i t e d from F o r e s t r y A b s t r a c t 32: 6181).  - 196 -  APPENDICES  - 197  -  APPENDIX B.  C.  Forest  1 .  I n v e n t o r y Zones  L i s t i n g o f a l l P.S.Y.U. 's and T.F.L. *s t o show a r e a s i n c l u d e d i n e a c h o f t h e 12 B r o a d G r o u p s u s e d as a b a s i s f o r p l a n n i n g Growth and Y i e l d and L o s s F a c t o r S t u d i e s . 1.  N o r t h e r n and  Central  C o a s t R e q i o n - C e d a r , Hemlock  P.S.Y.U.«s:  T.F.L  2.  «s: No.  1,  2,  12,  17,  Dean Hecate Queen C h a r l o t t Rivers Inlet Lower P a r t Of Skeena (Terrace Block of Skeena) 24, 25,  S o u t h e r n C o a s t R e g i o n - F i r , Hemlock P. S. Y. U. ' s : :  T.F.L ' s : No. 2, 6, 7, ( b l o c k 1, 2, 3, 4 ) , 27,  3.  South C o a s t T r a n s i t i o n  P.S.Y.U.'s: -  T.F.L  4.  «s: No.  South Western Spruce Types  (block Kitimat  5 ) , 39, 41 T.F.L r e s e r v e  Types Nootka Quadra Kingcome  10, 12, 17, 36, 38, 39, Belt -  Types  19, 20, 21, 22, 25, ( b l o c k 1, 2, 3, 4, 5)  Hemlock, F i r , B a l s a m  Types  Dewdney Soo Vancouver  26  Interior  Dry B e l t - F i r , Lodgepole  P.S.Y.U.' s : -  Pine,  Ashnola Barton H i l l B i g Bar Botanie Kamloops fieqion L a c L a Hache Nicola Okanagan Similkameen W i l l i a m s Lake Yalakom  - 198 -  South part S a l e Area T.F.L  «s: No.  West Kootenay  5, 9, 15, 16, 32, 35 Reqion - Spruce, Balsam Cedar, F i r Types P.S.Y.U.'s: -  T.F.L  ' s : No.  East Kootenay  «s: No.  Creston Edqewood Granby Kettle Salmo  8 Reqion - Spruce, Lodqepole Pine, F i r Types P.S.Y.U.'s:  T.F.L  of S p e c i a l  Cranbrook Fernie Upper Kootenay Windermere Crows Nest Pass C o a l Co.  13  C e n t r a l Columbia Reqion - I n t e r i o r Wet B e l t - Spruce, Cedar, Hemlock, F i r Types P.S.Y.U.'s:  T.F.L  «s: No.  3,14,18,23  Adams Arrowhead Barriere Canoe Eaqle Kinbasket Nakusp Nehalliston North Thompson Quesnel Lake Raft Robson Salmon Arm Shuswap Spallumcheen  (blok 1, 2, 3, 4 ) , 32, 33  Nechako - Fraser Plateau Reqion - Lodqepole P i n e , F i r , Spruce Types P.S.Y.U.'s:  Burns Lake Nareosli Necha ko  - 199 -  Stum  Westlake Chilko 9.  Central Types  Interior  Reqion  - Spruce,  P.S.Y.U.•s:  T.F.L  10.  » s : No.  » s : No.  and Skeena  Drainaqes  Bell Irvinq Skeena Kitwanqa; Hazelton B l k s . o f Skeena Proposed: S t i k i n e , A l s e k , B o u n d a r y , Taku  1  N o r t h - C e n t r a l P l a t e a u Reqion - C a s s i a r and Omineca P l a t e a u s - S p r u c e , Balsam Deciduous Types P.S. Y. D. »s;  12.  Pine  Babine Bowron Carp Cottonwood Crooked R i v e r Lonqworth Honkman Morice Naver Parsnip P u r den Smithers S p e c i a l S a l e A r e a (N) S t u a r t Lake Takla Willow R i v e r P o r t S t . James S. S. A,  North-Western P l a t e a u Reqion - S t i k i n e Hemlock, B a l s a m , S p r u c e T y p e s  T.F.L  Lodqepole  30  P.S. Y. U. «s:  11.  Balsam,  North-Eastern Plains  Reqion  P.S.Y.U. «s:  Finlay P r o p o s e d ; Dease, Kechika, Klappan  - Spruce,  Decidous  Blueberr y Moberly Peace Wapita  Types  Proposed:  Kotcho F o r t Nelson Fontas Sikanni Liard  - 201 Appendix 2. Computer Program.  MICHIGAN TFRMINAL SYSTEM FORTRAN G141336) 0001 0002  MAI N  02-10-78  1 3 : 39:47  DOUBLE PRECISION P R 1 0 , A A , 3 , A V , S S C , C O E F DIMENSION P R O O ( 1 2 0 , 1 2 0 ) , A A ( 1 2 0 , 1 2 0 ) , R ( 8 0 , 0 0 ) , A V ( 3 0 , 1 2 0 ) , S S C ( 1 2 0 ) . 1 COEFf 8 0 ) , N A M E ! 1 2 0 ) , N I T ( 8 0 ) , F M T { 2 0 ) , N F L ( 1 0 ) 0003 COMMON NF.NI ,NI NT,NX,NCOV,NY,NAM,ILS, IRL 0004 EXTERNAL MATINV 0005 CALL T ITLEIFMT.NFL.NAME) 0006 CALL OATAIPRnO.AV,SSC, NFL.FMTI 0007 CALL INF0P.M(PP.0D,AV.SSC,NAME ,NFL) 0308 I F ( I L S . E 0 . 1 ) C A L L LSMAT(PROD,NAME ) 0009 6 F0RMAT(26I3) 0010 CALL REOUCEtPROO.NX) 0011 00 I 1=1,NX 0012 00 1 J = l , N X 0013 1 AA(J,I) = PRODU,J) 0014 CALL REDUCE!AA,NX 1 0015 99 READ(5,6)NEX,(NIT(I),1=1,NEX) 0016 DO 7 1=1,MEX 0017 COEF(II=0.0 0018 DO 7 J=l,MEX 0019 7 R ( I , J ) = A A f N IT( I ) , N I T ( J )) 0020 I F U R L . E Q . l t CALL RLSMATIR, NAME, NEX, NCOV. NY. NIT) 0021 N0C=NEX-1 00?? CALL GSPACE(C,N0C*N0C*8) 0023 CALL CALLERfMATINV,C.IPTR(R).IPTR(NDC)) 0024 CALL FSPACE(C) 0025 DO 25 I=1,NDC 0026 00 25 J=l,NDC 0027' 25 COEF! I>=C0EF! I ) + R( I, J )*R(NJEX, J ) 0028 WRITEI6.90) 0029 90 FORM AT! ' 1 ' , 2 0 X , ' M A T R I X INVERSE TO THE COMPLETE V ARI ANCE-COVAR I ANCF 1 MATRIX'//) 0030 DO 2 6 I=1,N0C 0031 K=MIT(1> 0032 WRITE16,8)K,NAME(K) 0033 8 FORMAT ( ' ' . ' R O W , 2 X . I 4 . 1 X . A 4 ) 0034 26 W R I T E ( 6 , 2 7 M R ( I , J ) , J = 1,I) 0035 27 FORMAT(* ' , 9 0 1 4 . 6 1 0036 28 FORMAT!'1«,///,3X,'ESTIMATED COEFFICIENTS',///) 0037 WRITE(6,28) 0038 DO 31 I=1,NEX 0039 NA=N IT( I ) 004 0 WRIT E(6,32INAME(NA),CO EFIII 0041 31 CONTINUE 0042 32 FORMAT!'0',A4,2X,G13.6) 0043 N0FT=PR0D(1,1) 0044 SSOR=0.0 0045 DO 33 1=1,NEX 0046 33 SSOP. = SSDR*COEF(I l * R ( NEX, I 1 0047 ERR=R!NEX,NEX)-SSDR 0048 CALL ANOVA(R,COEF,ERR,NOFT) 0049 IRL=IRL-l 0050 REA0(5,6)NREP,NC0V 0051 I F ( N R E P . G E . l )G0T0 99 0052 STOP 0053 END "OPTIONS TN EFFECT* ID,EBC D I C , S O U R C E « N O L 1 S T , NODECK,LOAD, NOMAP •OPTIONS IN E F F r C T * NAME = MAIN , LI NECNT = 60 •STATISTICS* SOURCE STATEMENTS = 53,PROGRAM S I Z E = 315032  1.000 1.500 2.00 J 3. 000 4.000 5.000 6.000 7.000 8.000 10.000 11.000 12.000 13.000 14.000 15.000 15.500 16.000 1 7.000 18.000 19.000 20.000 21.000 22.000 23.000 24.000 25.000 26.000 27.000 28.000 29.000 30.000 31.000 32.000 33. 000 34.000 35.000 36.000 37.000 38.000 39.000 40.000 41.000 42.000 43.000 44.000 45.000 46.000 47.000 48.000 49.000 49.200 49.500 49.700 50.000 51.000  - 202 -  MICHIGAN TERMINAL SYSTEM FORTRAN GI41336)  TITLE  02-10-78  0001 SUBROUTINE T IT LE f FMT, N FL , N A*l E ) 0002 DIMENSION NAME(120). T I T L E ( 2 0 ) , F M T ( 2 0 1 . N F L ( 1 0 » 0003 COMMON NF.NI ,N INT,NX,NCOV,NY ,N AM , I LS, I Rl. 0004 NI=0 0005 NINT=0 0006 READ(5 » 1 )T ITL E 0007 1 FORMAT(20A4) 0008 READ(5,l)FMT 0009 READ!5,2 IMF,(NFL ( I ) . I = 1 , N F ) , N C O V , N Y , N A M , I L S , I R L 0010 2 FORMAT(20141 0011 NK=NF-1 0012 DO 3 1=1,NK 0013 IJ=I+1 0014 DO 3 J=IJ,NF 0015 3 NINT=MINT+NFL(I) *N F L ( I J ) 0016 DO 4 I = 1 , NF 0017 4 NI=NI+NFL(I) 001R NX=NI+NINT+NCOV*NY-l 0019 READ!5, I)( N4MEU ) ,1 = 1, NX) 0020 WRITE(6,5)TITLE 0021 5 FORMAT (• 1' , / / ,2 0*4 / / ,1 OOC * • M 0022 WRITE(6,6 INF 0023 6 FORMyr(i • , 5 X . ' * ' , IX, 'NUMBERS OF F A C T O R ' » 1 2 ( ' . ' ) , I 4) 0024 WRI T E ( 6 , 7 ) ( N F L ( I ) , 1 = 1,NFI 0025 7 FORM A T ( • ' , 5 X , ' * ' , l X , ' L E V E L S OF F A C T O R S ' , 1 2 ( ' . ' ) ,1 014) 0026 WRITE<5 ,81NC0V 0027 8 F ORM A T ( • < , 5 X , , I X , ' NUMBERS OF COVARIATES ' , 3 ( .' ' ), 14) 0028 WRITE<6. 10)NY 0029 10 FORMAT ( ' ' ,5X , * * ' , IX ,'NUMBERS OF YIELD VARIABLES ' , 3( ' . « ),I 4) 0030 WRITE(6,9)FMT 0031 9 FORMAT(• • , 5 X , ' * ' , I X , ' FORMAT', 1 0 ( ' . ' ) , 20A4) 0032 RETURN 0033 END *PPTIONS IN EFFECT* ID,EBCDIC,SOURCE,NOLIST,NODEC<,LOAD,NOMAP "OPTIONS IN E F F E C T * NAME = TITLE , LINECNT = 60 *STATISTICS* SOURCE STATEMENTS = 33,PROGRAM SIZE = 1428 ^STATISTICS* NO DIAGNOSTICS GENERATED NO ERRORS IN TITLE  10:08:48 52.000 53.000 54.000 55.000 56.000 57.000 58.000 59.000 60.000 61. 000 62.000 63.000 64.000 65.000 66.000 6 7 . 000 68.000 69. 000 70.000 71.000 72.000 73.000 74.000 75.000 76.000 77. 000 78.000 79.000 80.000 31.000 82.000 83.000 84.000  - 203 -  MICHIGAN TERMINAL SYSTEM FORTRAN G(41336)  DATA  02-10-78  SURROUT INE OAT A (PROD, A V, S S C N F L . F M T ) 0001 DOUBLE PRECISION PROD,AV,SSC,X 0002 DIMENSION PRODI 120, 120),AVI 30, 120) ,SSC(120) ,X( 120) 000? DIME MS I ON NFL(10 ).NS (10 I,FMT(20 ),A( 30 1 0004 COMMON NF ,NI ,NI NT,NX, NCOV,NY,N AM , ILS , I RL 0005 00 I 1=1, NX 0006 0007 SSC( I 1=0.0 OOOR DO 1 J=1,NX 1 PPOD(I,J)=0.0 0009 NRFA 0 = NCOV+NY 0010 READ(4,FMT,EN0 = 99)(NS( I ) , 1 = 1 , N F ) , ( A ( I ) , 1=1 .NREAD) 10 0011 DO 15 1=1,NX 0012 001 3 15 X(II=0.0 0014 K=l 001 5 KK=1 0016 X(l)=1.0 0017 00 2 T=1,NF 0018 K=K+NS(I) 0019 X(KI=1.0 00 20 KK=KK+NFL(I) 0021 K = KK 002? 2 CONTINUE 0023 NK=NF-1 0024 DO 8 1=1,NK 0025 I J=T +1 0026 00 8 J=IJ,NF 0027 K = K-(NS(II-11*NFL(J)-NS(J ) X(K) = 1.0 0028 0029 KK=KK+NFL(J) 0030 K=KK 0031 8 CONTINUE 0032 K=1+NI+NINT 0033 DO 6 1=1,NREAD 0034 K=K+1 0035 6 X(K)=A(I) 0036 DO 4 1=1,NX 0037 SSC<I) = SSC(I)+X( I )*X(NX)*X(MX) 0038 00 4 .1 = 1 ,NX 0039 PROD(I,J)=PR00(I,J ) + X ( I ) * X ( J ) 4 PRODI.), II=PROD(I,J ) 0040 0041 GOTO 10 0042 99 RETURN 0043 ENO •OPTIONS TN E F F E C T * 10,ESC01C,SOURCE,NOLIST,NODE CK.LOAD,NOMAP • OPTIONS TN EFFECT* NAME = 0 AT A , LINECNT = 60 2582 •STATISTICS* SOURCE STATEMENTS = 43,PROGRAM SIZE = •STATISTICS* NO DIAGNOSTICS GENERATED NO ERRORS IN DATA  10:08:48 85.000 85.500 86.000 87.000 88.000 89.000 90.000 91.000 9 2 .000 93.000 94.000 95.000 96.000 97.000 98.000 99.000 100.000 101.000 102.000 103.000 104.000 105.000 106.000 107.000 108.000 109.000 110.000 111.000 112.000 113.000 114.000 115.000 116.000 117.000 118.000 119.000 120.000 121.000 122.000 123.000 124.000 125.000 126. 000  - 204 -  MICHIGAN TERMINAL SYSTEM FORTRAM G!41336) 0001 0002 0003 0004 0005 0006 0007 0008 0009 0010 0011 0012 0013 0014 0015 0016 0017 0018 0019 0020 0021 0022  LSMAT  02-10-78  SUBROUTINE LSMAT(PROD,NAMF) DOUBLE PRECISION PROD 01 MENS ION PRODI 1 20, 120 >, NA ME ( 1 20) COMMON NF.NI , NI NT , NX , N COv , Nr1, N AM, ILS. IPL CALL FTNCMDt 'SET ZEROSUPPRESS=ON' ,19) 1 FORMAT ( • l ' , / / / 1 0 X , ' L E A S T SQUARES E Q U A T I O N S ' , / / / ) NTB=1 NLAST=NX-NY-NCOV 10 NTE=NLAST IF((NTE-NTBI.GT.251NTE=NTB*25 WRITE!6, I ) WRITE(6.2 1 (NAME( I ), I = NTB,NTE > 2 FORMAT(•0',26{A4,1X1> DO 3 I=1,NLAST 3 WRIT E(6 ,6 ){ PROD ( I, J 1 , J =\lT B , NT E ) 1F(NLAST-NTE)4,4,5 5 NTE=NLAST NTB = NT B-26 GOTn 10 6 FORMAT(• « , 2 6 F 5 . 0 ) 4 WRITE(6,11I 11 FORMAT( • I' , / / / , 1 0 X , ' L E A S T SQUARES EQUATIONS - - COVARIATF.S AND RHS« 1/// ) 0023 NC=NLAST*1 0024 WRITE!6,12) I NAME ( I ),I = NC,NX) 0025 12 FORMAT('0' , 1 0 ( 5 X , A 4 , 4 X )) 002600 7 1=1,NX 0027 7 WRITE(6,8)IPROO(I,J),J=NC,NX) 002R CALL FTNCMDI'SET ZEROS U P P P ES S= OFF • , 20 I 0029 8 FORMAT! > « , 10G 13.6) 003 0 RETURN 0031 END *DPTIONS IN EFFECT* ID,EBCDIC,SOURCE,NOLIST,NODECK,LOAD, NOMAP *OPTIONS IN EFFECT* NAME = LSMAT , LINECNT = 60 • STATISTICS* SOURCE STATEMENTS = 31.PROGRAM SIZE = 1182 •STATISTICS* NO DIAGNOSTICS GENERATED v|0 ERRORS IN LSMAT  v  1008:48 127.000 127.500 128.000 129.000 130.000 131.000 132.000 133.000 134.000 135.000 136.000 137.000 138.000 139.000 14 0. 000 141.000 142.000 143.000 144. 000 145.000 146.000 147.000 148.000 149.000 150.000 151.000 152.000 153.000 154.000 155.000 156.000 157.000  - 205 -  MICHIGAN TERMINAL SYSTEM FORTRAN GI41336)  REDUCE  SUBROUTINE REDUCE(D,NX) 0001 DOUBLE PRECISION D 0002 DIMENSION D U 2 0 , 120 1 , I RV( 15) , I AV (1 5t, NTRD( 101 0003 REWIND 1 0004 0005 READ (1 , U N , (NTRDI I ) , 1= l . N ) 0006 1 F0RMATI20I4) 0007 NAA=NTR D(1 I 0008 00 2 1 = 1 , NA A REAO{ 1, I ) 1A , IF , IL 0009 00 3 I J = I F , I L 0010 0011 IF(IJ.EO.IAIGOTO 3 DO 4 J=1,NX 0012 0013 4 O t I J , J ) = -D( I A , J ) + 0 ( I J , J) 0014 3 CONTINUE 0015 2 CONTINUE 0016 I F l N . E Q . l JRFT'JRN 1 0017 00 5 IJK=2,N REA0(1, 1 )NVA,( IAV( I ) , I = 1 » NV4) 0018 0019 NAA=NTRDIIJK) 0020 00 6 11=1,NAA READ!1,1 ) N V R , ( I R V ( I ) , I = 1.NVR) 0021 002? DO 7 1=1 ,MVR 0023 DO 8 J=l,NX 8 0024 o(iRvm,j) = - o ( i A v m , j ) + D U R v m . j i 7 CONTINUE 0025 0026 6 CONTINUE 0027 5 CONTINUE 0028 RETURN 0029 END •OPTIONS IN EFFECT* ID,EBCDIC,SOURCE,NOLIST,NOOECK,LOA 0, NOMAP NAME = REDUCE , LINFCNT = 60 "OPTIONS IN F F F E C T * 29,PROGRAM SIZE = •STATISTICS* SOURCE STATEMENTS = •STATISTICS* NO DIAGNOSTICS GENERATED MO ERRORS IN REDUCE  02-10-78  10:08:49 158. 000 158. 500 159. 000 160. 000 161. 000 162. 000 163. 000 164. 000 165. 000 166 . 000 167. 000 168. 000 169. 000 170. 000 171. 000 172. 000 173. 000 174. 000 175. 000 176. 000 177 000 178. 000 179. 000 180. 000 181. 000 182. 000 183. 000 184. 000 135. 000  1278  -  MICHIGAN TERMINAL SYSTEM FORTRAN G!41336) 0001 0002 0003 0004 0005 0006 0007 OOOR 0009 0010 0011  206 -  RLSMAT  02-10-78  SU8R0UT INE RLSMAT (P., NAME, N EX , NCO V, NY.NIT) DOUBLE PRECISION R DIMENSION R ( 80,80 ),NAM E( 12 0) , N I K 8 0) NL=NEX-MCOV -NY 4 WRITE(6,51 5 FORMAT!<1',20X,'REDUCED SET OF LEAST SQUARES E Q U A T I O N S ' , / / / ) DO 1 1=1,NL 1 W R I T E ! 6 , 3 ) t R ( I , J ) , J = I,I) 3 FORMAT(' ' . 2 0 F 6 . 0 ) 7 WRITE(b,8) 8 FORMAT! ' 1',20X,'REDUCED SET OF LEAST SQUARES E OUAT IONS — COVARIAT 1 ES AND YIELD V A R I A T E S ' / / / 1 0012 NLl=NL*l 0013 DO 12 1=1,NEX 0014 12 WRITE!6,10)(R(I,J),J=NL1,NEX) 0015 10 FORMAT! ' • , 10G12.6) 0016 RETURN 0017 END •OPTIONS IN EFFECT* ID,EBCDIC,SOURCE,NOLIST,NODECK ,LOAD,NOMAP •OPTIONS IN E FFECT* NAME = RLSMAT , LINECNT = 60 • STATISTIC S* SOURCE STATEMENTS = 17,PROGRAM SIZE = 868 •STATISTICS*  MO  ERRORS  NO DIAGNOSTICS  IN RLSMAT  GENERATED  10:08:49 186.000 186.500 137.000 188.000 189.000 190.000 191.000 192.000 193.000 194.000 195.000 196.000 197.000 198.000 199.000 200.000 201.000 2 02.000  - 207 -  MICHIGAN TERMINAL SYSTEM FORTRAN GC41336)  MATINV  0001 SUBROUTINE MATINV<C,R,NDCI 0002 DOUBLE PRECISION R,C,DDET,DCOND 0003 DIMENSION R(80,801,C(NOC,NDC) 0004 00 1 1=1,NOC 0005 DO 1 J=l,NOC 0006 1 C (I , .11 =R (T . JI 0007 CALL D1NVRT(C,NDC,NDC,DDET,DCOND) 0008 00 2 1=1,NDC 0009 DO 2 J=1,NDC 00 10 2 R(I,J)=C(1,J) 0011 RETURN END 0012 •OPTIONS IN EFFECT* ID,EBCDIC,SOURCE,NOL1ST,NODECK,LOAD,NOMAP •OPTIONS IN E F F E C T * NA ME = MATINV , LI NECNT = 60 *STATISTICS* = 12,PROGRAM SIZE = SOURCE STATEMENTS = •STATI ST ICS* MO DIAGNOSTICS GENERATED FRPOPS IN MATINV  O.  02- 10-78  10:08:49 203. 000 2 03. 500 204. 000 205. 000 2 06. 000 207. 000 208 . 000 2 09. 000 210. 000 211. 000 212. 000 213. 000  666  - 208 -  MICHIGAN TERMINAL SYSTEM FORTRAN GI41336)  ANOVA  02-10-78  10:08:49  SUBRDUTINE A NOVA IC,COEF,ERR, NDFT) DOUBLE PRECISION C.COEF EXTERNAL SUMSO DIMENSION C 1 8 0 , 8 0 ) , C O E F ( 8 0 ), IOF( 30 I, SS( 30) , SMI 30) DOUBLE PRECISION NC AT ( 30 I READ(5, 1 I N , ( I D F ( I ) , 1 = 1,N) FORMAT (2014) 1 REA0(5,9I(NCATU),I=l,N) FORMAT(10A8 ) 9 Nl = l N2 = l NOF=0 ST=0.0 DO 2 1=1,N Nl=N2+l N2 = N2*-I DF (I I N3=IDF(I) CALL GSPACEIZ,N3*N3*8) CALL CALLER! SUMSO,Z,IPTR(C),IPTR(COEF) , IPTRfNl ), IPTR(N3), IPTR(SO) ) CALL FSPACE(Z) SSI I )=S0 SM|I)=SO/IDF(I) NDF=N DF + 1DFI I) 2 CF=COEF(1)*(1.0/C(1.1Il*COEF(lI NERR-NDFT-NDF-1 RES= ERR/NERR WRITE(6,10) 10 FORM A T ( « I S / / , 1 5 X , • A N A L Y S I S OF VARIANCE TABLE ' / / ) WRITE(6,11) 11 F O R M A T ! ' 0 ' , 6 X , « SOURCES',3X,' SUM SOUARES' , 5 X . ' D . F . • , 5 X , 'MEAN SQUARE l',4X,'F-VALUE',//) 0031 DO 12 1=1,N 0032 F=SM(I)/RES 0033 12 WRITE!6,131NCAT!I ) , S S ( I ) , I D F ! I ) , S M I I ) , F 0034 13 F O R M A T ( ' 0 ' , 6 X , A 8 , 3 X , G 1 3 . 6 , 3 X , 14, 3X , G I 2 . 6 , F 1 2 . 4 > 0035 14 FORMAT! • 0 « , 6 X , ' E R R O R • , 5 X , G 1 3 . 6 , 3 X , I 4 , 3 X , G 1 2 . 6 J 0036 WRITE!6,14)ERR,NERR,RES 0037 WRITEI6.15) 0038 15 FORMATJ * 0 ' » / / / » 1 2 0 ! * * * ) , / ' • , • * • • END OF ANALYSIS • * * • ) 0039 RETURN 0040 END • OPTIONS IN EFFECT* I'D. EBCDIC . SOURCE, NOL I ST, NODECK .LOAD, NO MAP •OPTIONS IN EFFECTS NAME = ANOVA , LINECNT = 60 •STATISTICS* SOURCE STATEMENTS = 4 0, PROGRAM SIZE = 2120 •STATISTICS* NO DIAGNOSTICS GENERATED MO ERRORS IN ANOVA 0001 0002 0003 0004 0005 0006 0007 0008 0009 0010 001 1 0012 0013 0014 0015 0016 0017 0018 0019 0020 0021 0022 0023 0024 0025 0026 0027 0028 0029 0030  214 000 214 500 215 000 216. 000 217. 000 213. 000 219. 000 220. 000 221. 000 222. 000 223. 000 224. 000 225. 000 226. 000 227. 000 228. 000 229. 000 23 0. 000 231. 000 232. 000 233. 000 234. 000 000 235. 000 236. ,000 237. ,000 238. ,000 239. ,000 240. 000 241. 000 242. 000 243. 000 244. 000 245. 000 246, 000 247. ,000 248, 000 249, 000 250. ,000 251, 000 252, ,000 253  - 209 -  MICHIGAN TERMINAL SYSTEM FORTRAN 0(41336)  SUM SO  0001 SUBROUTINE SUMSOIZ.C,COEF,NB,NE.SO I 0002 DOUBLE PRECISION C Z . C O E F 0003 DIMENSION C (80 ,8 01 , COE F( 80 t, SM (30 ) 0004 01 MENS I ON Z(NE ,NE) 0005 S0=0.0 0006 00 3 1=1,NE 0007 3 SM( 1 )=0.0 0008 00 5 1=1,NE 0009 K1=I-1*NB 0010 DO 5 .1=1, NE 0011 K2=J-1+NB 0012 5 Z(I»JI=C(K1,K2) 0013 CALL DINVRT(Z,NE,NE,DDET, DCDND) 0014 DO 1 1=1,NE 0015 DO I J=l,NF 0016 K=J-1+NB 0017 1 SMII l=SM(I)*COEF(K(*Z( I, J) 0018 00 2 1=1,NE 0019 K=!-1+NB 0020 2 SO=SO*SM(II*COEF(K) 0021 RETURN 002? END •OPTIONS IN E F F E C T * IO.EBCDIC,SOURCF,N0L1ST,NO DECK,LOAD, NC M A P •OPTIONS IN EFFECT* N&ME = SUMSO , L1NE"NT = 60 •STATISTICS* SOURCE STATEMENTS = 22,PROGRAM SIZE = •STATISTICS* NO DIAGNOSTICS GENERATED ERRORS IN SUMSO  02-10-78  10:08:50 254. 000 254. 5 00 255. 000 256. 000 257. 000 258. 000 259. 000 260. 000 261. 000 262. 000 263. 00 0 264. 000 265. 00 0 266. 000 267. 000 268. 000 269. 000 270. 000 271 . 000 272. 000 273. 000 274. 000  1098  - 210 -  TERMINAL SYSTEM FORTRAN G(41336) 0001 0002 0003 0004 0005 0006 0007 0008 0009 0010 001 1 0012 0013 0014 0015 0016 001 7 0018 0019 0020 0021 0022 0023  21 20  26 25 8  INFORM  02-10-78  10:08 :50  SUBROUTINE INFORM I PROD,AV,SSC, NAME,NFL > DOUBLE PRECISION PROD,AV,S D,SS C COMMON N F , N I , N I N T , N X , N C O V . N Y , N A M , I L S , I R L DI MENS ION PROD(120, 120 I,A V(30,120),SD(1201•NAME(120) ,SSC(120) 1 ,NFL(10) NDUM=1+NI+MINT NREAD=NCOV+NY DO 20 1=1,NREAD IK=I+NDUM DO 20 J = l , N X I F ( P R O D ( I , J » . L E . O . O ) G O TO 21 AV( I ,JI = P R O D ( I K , J l / P R O D ( 1 , J I GOTO 20 A V U . J ) =0.0 CONTINUE DO 25 I=1,NDUM IFCPRODd ,1 ) . L E . l .01G0TO 26 SD( I )=SSC( I) —PROD(NX,I ) * * 2 / P R 0 D ( 1,1) SD(I ) = DSORT(SD( I )/(PRODI 1 , I l - l . D O ) ) GOTO 25 SD(I)=0.0 CONT INJFWRITE(6,8) FORM AT{ • ' , / / / , 1 0 X , • M E A N , NUMBERS OF OBSERVATIONS, STANDARD DEVI AT HONS AND COVARIATE MEANS IN CLASSES AND S U B C L A S S E S ' / / / )  IF = 1 0024 NL= 1 0025 CALL STAT(PR0D,4V,SSC,SD,NAME, IF,ML I 002 6 DO 1 I = 1 , NF 0027 IF=NL+1 0028 NL=NL+NFL(II 0029 CALL STAT(PROD,AV,SSC,SO,NAME,IF , NL) 0030 1 'NE=NF-1 0031 DO 2 1=1,NE 0032 K=NFL(I ) 0033 K1 = NFL(1+1 I 0034 DO 3 IJ=1,K 0035 IF=NL + 1 0036 NL=NL+K1 0037 CALL STAT(PR00,4V,SSC,SD,NAME,IF,NL) 0038 3 CONTINUE 0039 2 RETURN 0040 END 0041 •OPTICNS 1M E F F E C T * 10,EBCD!C,SOURCE,NOLI ST, NO DECK,L0AD,NO MAP •OPTIONS TN E F F E C T * NAME = INFORM , LINFCNT = 60 •STATISTICS* SOURCE STATEMENTS = 41,PROGRAM SIZE = •STATISTirs" NO DIAGNOSTICS GENERATED ERRORS IN INFORM  2382  275. 000 275.500 2 76.000 277.000 278.000 279.000 280.000 281 .000 282.000 283.000 284.000 235.000 286.000 287.000 288.000 289.000 290.000 291.000 292.000 293.000 294.000 295.000 296.000 297.000 298.000 299.000 300 .000 301.000 302.000 303.000 304.000 305.000 3 06.000 307.000 308.000 309.000 310.000 311.000 312.000 313.000 314.000 315.000 316.000  - 211 -  MICHIGAN  TERMINAL  SYSTEM  FORTRAN  0001  SIJBROUT I N E  0002  DOUBLE  0(41336)  STAT  STAT(PROD,A  PRECISION  02-10-78  V,SSC,SD,NAME,IF,NL)  PROD,AV,A  10:08:50 •  AX,SD  317.000 317.500  0003  DIMENSION  0004  COMMON  0005  N0UM=1+NI+NINT  0006  NREAD=NCOV~NY  321.000  0007  WRITE!6,  32 2 . 0 0 0  1  0008 0009  P R O D ( 1 2 0 , 1 2 0 I , AV ( 3 0 , 1 2 0 1, S S C ( 1 2 0 1, S D ( 120 1, NA ME ( 1 2 0 > NF,NI,NINT,NX,NCOV,NY.NAM,ILS,IRL  318.000 319.000 320.003  1)(NAME( I ) , I = I F , N L )  FORMAT('0',//,6X,10(5X,A4,3X))  323.OOJ  WRITE(6,2I(AV(NREA0,II,I=IF,NL)  324.000  0010  W R I T E I 6 , 7 ) ( P R O D I 1, I ) , ! = I F , N L )  325.000  001 1  WRITE16,3 1( S D ( I 1,I = I F , N L 1  326.000  0012 001 3  IF(NCOV.EO.O)GOTO  327.000  10  00 5 1=1,NCOV K=NDUM-1  0014  328.003 32 9 . 0 0 0  0015  5  W R I T E ! 6 , 4 ) N A M E ( K ) , ( AV( I , J ) , J = 1 F , N L )  33 0.003  001 6 0017  2  FORMAT('0'.' EAN'»  331.000  7  FORMAT (' 0'  0018 0019  3 4  FORMAT!'  0020  10  RETURN  33 5.000  END  336 .00 3  ii  OB • , 2 X , 1 0( F l 0 . 0 . 2 X ) 1  332.000  FORMAL!<0','S.D.',2X,10(F12.4))  0021  ',A4,2X,10(  3 3 3.003 3 3 4.00 3  2X,F8.2,2X))  •OPTIONS  TN E F F E C T *  I D , E B C D I C , S O U R C E . N O L 1 S T , NO.DEC'< , L 0 A D , N DM AP  •OPTIONS  TN E F F E C T *  NAME  • STATISTICS*'•STATISTICS* NO  ERRORS  NO  STATEMENTS  N AM F  IN  SOURCE  STAT  ,  L I NECNT  =  C  LAGGE0  NUMBER  IN  GENERATED  T H E ABOVE  OF ERRORS/WARNINGS  0 0 0 0 0 0 0 0 0 0 0  L S MA T 9 EDUCF RLSMAT MA T I N V ANOVA SUMSO T NF ORM STAT TERMINATED  =  2 1 , PROGRAM  STAT  MAIM  EXECUTION  =  STATEMENTS  NO D I A G N O S T I C S  TITLE OAT A  $SIG  2X,10IF10.0,2X11  U  COMPILATIONS.  SEVERITY  0 0 0 0 0 0 0 0 0 0 0  60 SIZE  =  10R3  APPENDIX  Mf VI 635 404 172 59 5C1 134 347 57 1C7 65 47 12  V\  P  4C4 404 347 57 347 57  y\  SS  P*H PZ2 P<C 1 2 Z 3 172 501 134 347 59 34 7 57 347 1C7 65 172 47 59 12 47 107 501 347 134 ts 12 347 347 57 107 IC7 65 65 47 47 12 • 12  /v. PZ3 57 57  SS  y\  3.1  /*  PC22 PC 23 PH22 PH23 107 65 47 12 107  65 47 47  107 57  65  12 12  57 107 65 47 12  Least squares equations f o r Coast D o u g l a s - f i r i n v e n t o r y data-  SITE 76.J60.0 49J10.0 19450.0 76JO.O0 . 62.20.0 14J60.0 4 3-, 4 0 . 0 5870.00 12460.0 6970.00 6C30.00 1520.00 0.9ol48CF-07 0.402540E«C7 12o236. 68". 170. 0.144496E*08 8824?7. 0. 1 1C651E*08 81624. 1 ' 0.115507E-C7 0.3725426*09  AGE L AGE HT 34655.0 1076.38 5540.00 20440.0 674.488 3469.00 305.422 1564.00 11460.0 2755.00 96.9688 507.030 824.084 23545.0 / 4178.00 11110.0 252.794 1362.00 567.740 29 0 6 . 0 0 15855.0 45E5.0C 1C6.748 563.000 179.719 5575.00 379.J00 5835.00 125.702 685.000 76.6253 393.000 2115.00 640.000 20.3435 114.000 0.402540E-07 128236. 639170. 328510. 0.228623E*07 61633.7 1848.59 9599.36 61633.7 9599.36 53C56.0 328510. 205333. O . 109727E*07 0.681219E*07 12456.1 66 364 . 8 422841. 156664. 894136. C.565701E*07 1076.87 • 59 3 3 . 3 0 34654.6 16075.5 97164.1 610394. 0.192616E*09 0.519648E*07 0 . 3 0 7 8 4 7 E * 0 8  SO B4 OBH NT 634.999 88591.0 7225.88 1 19107. 416.565 54776.0 4455.53 79032.0 160.461 26807.0 2095.98 30565.0 57.9730 7008.00 674.366 9510.00 5 01.200 62769.0 5403 .58 93169.0 133.799 25822.0 1*22.30 25938.0 3 6 2.653 44818.0 3702.64 68462.0 53.9070 9958.00 752.B91 I 0570.0 9 3 . 3360 12629.0 1183.84 17017.0 67.0750 14178.0 912.142 13548.0 4 5 . 1560 5 32 2.00 517.097 7690.00 12.8170 1666.00 157.269 1820.00 61624.1 0. U 0 6 5 1 E * 0 8 882427. 0.144496E*C8 34654.6 0.565701E*07 422341. 0.681219E»C7 1076.37 156664. 12456.1 205383. 5933.SO 894136. 6 6 8 6 4 . 8 0 . 109727E*07 134231. 0.271085E*03 0.1361125*07 0 . 1 9 5 6 1 B E » 0 8 7513.67 0. 11 1616E-07 87191.9 0.136112E-C7 104136. 0.195618E*C8 O . U 1 6 1 6 E * 0 7 0 . 1 6 7 0 3 0 E » 0 8 771.074 104135. 7518.67 134201. 10854.7 0.184973E*07 119368. 0.196880E-07 0.353960; 1*07 0. 646765E*09 0.380133E*08 0.5844S4E*O9  Remarks: P - Pure; P + C - D o u g l a s - f i r c o n i f e r mixed; P + f l — D o u g l a s - f i r hardwood mixed; A — F o r e s t  Inventory Zone 2; z V - F o r e s t  Inventory Zone 3; PZ&, PZ3, PCZ2, PCZ3, PHZ2, and PHZ3 a r e i n t e r a c t i o n s f o r types and zones, L A G E — l o g a r i t h m i c age; HT—height;  NT—number of t r e e s per a c r e ; B A — b a s a l  a r e a j S D — r e l a t i v e stand d e n s i t y ; HTBA-—HTxBA; VOL—volume.  HT Ba 8941.36 5363.56 2393.20 679.600 5933.74 2957.62 4243.23 1125.23 1249.12 1644.03 491.340 1S8.260 C.llS507E*O7 610394. 16075.5 9 7164.1 0.196330E*37 119363. 0 . 13<-973E*07 10854.7 213792. 0.672933E*03  0.291393E*D7 0.176400E*07 901337. 225535. 0.2-.2344EO7 ' 0 . i " ? 9 = E-37 , 34 1017. ; 412521. 433316. 167729. 57655.3 0.372543=*09 0 . 1 = 261SE* 09 C-.5V9r»3 = -:7 0.307547;.03 0.646765E-39 C.3e:i53=-0? I 0.524454 »39 0.35:963E'07 0 . 6 7 2 9 3 3 E * ~ 3 |_i 0-212151E.ili^j c  APPENDIX /\  MFAN  /S  P P + C P+H  2332 1450 145C 1450 793 34  931 230 130 759 252 691 164  44  320 231 232 62 S3 430 21  8  691 164  44  320 231 691 164 44 320 231  793  64  793 232 62 ' 83400  21  232 62 83 400 21  4  3 69  Remarks:  84 8 4 , 3  3.2  Z4 931 691 232 8  931  >V  Z5 230 164 62 4  230  69  691  232  8 4 3  69  8  164  62  4  Least squares equations for Interior Douglas-fir inventory data—qualitative variables Z6 130 44 83  3  130  44  83  3  y\ P, P-i-C, p+H, Z4,  /*  /V  A  ^  #*\  / V - A  A  A>  >V  /V  /\  Z7 Z8 PZ4 PZ6 PZ7 PZ8 PCZ4 PCZ5 PCZ6 PCZ7 PCZ8 PHZ4 PHZ5 PHZ6 PHZ7 PHZ8 719 252 6 91 PZ5 164 44 320- 231 232 62 83 400 21 8 4 3 69 320 231 691 164 44 320 231 4 CO 21 232 62 83 400 21  69  789  320  691 252  691  231 *  400  164  164  8 8  232  4  .3  69  6 2  44  44  32 0  320  83 231  231  232  62  83  21  400  400  21  ro  21  69  s\ y\ ^ Z5, EZ4, PCZ4, PIIZ4 e t c . , a r e d e f i n e d  69  69  i n Appendix 3.1.  APPENDIX 3.2 L e a s t — SITE  13^110. i 10593.  63553.0 7170.00 53*10.0 18j70 . 0 94s3. 66P3  00 0.G  ISJSO.O  •  SGJOO.O 13450.0  3105.03 26/00.0 16*55.0 I7 0 5 . 0 50=0.00 61 j 5 . 00  33055.0 1 4 j 5 . 00  70j.or,o  3 2./ • 3 0 0 210.300 55J5.G0 0 . 145573F*C3 0. lol313E+33 3 A,21 A . 0.1j62e7f*07 0.22S483E+C3 0.2ill66E-:7 0.1 uS6 34S*C3 192393. 0.14176SE+C7 0.4-.4357E + C9  4GE 2C6770. 132030. 69150.0 5590.00 86345.0 21690.0 11900.0 612E5.0 25050.0 64455.0 155O.0 4C6C.00 24763.0 23215.0 21350.0 5840.00 7605.00 32020.0 1835. 00 540.000 310.000 235.000 4505.00  squares e q u a t i o n s f o r I n t e r i o r D o u g l a s - f i r i n v e n t o r y  quantitative variables  LAGS 4472.00 2794. 10 1526.55 . , 151.342 1806.58 446.643 251.232 1470.93 496.516 1338.96 218. 356 6 5. 32 53 594.987 456.474 453. 093 120.956 160.342 752.120 40.0'<21 14.5238 7.33130 5.614C0 123.8 73  0.161318E+08 349214. 40S524. 0.206559E+08 664 1.05 438524. 32364.6 C.157359E+07 543302. 0.253076E+0S 52015.0 C.245165E-07 0. 156617E+08 4CC719. 4466.18 2C6438. 33019.1 0.U5517E+07 0.513444E+09 0 . IO3825E+08  HT 16900.0 10260.0 6012.00 623.000 6370.00 1842. 00 072.000 6119.00 1697.00 4671.00 1304.00 233.000 2433.00 1569.00 1640.00 508.000 569. 000 3167.00 123. COO 59.0000 30 .0000 20.0000 51 9. 000 ,0. 1362875 + 07 0.157899E+07 32 864.6 132004. 0.220146E+07 200576. 0. 167125E + 07 18319.1 143900. 0.447164E+08  data  ,  NT 281783. 151174. 119055. 11554.0 91542.0 28066.0 15883.0 123784. 22503.0 62928.0 10932.0 4757. 00 43991 .0 20566.0 2 7544.0 3711.00 10827.0 69631.0 I 942 .00 670. 000 4 23.000 299.000 10162.0  26829.7 17067.2 8892.33 869.653 10873.2 2701.96 1423.81 8770.63 3055 .1 1 8153.60 • 1949 .85 507.755 3626 .7 1 2829.26 2643.22 711.047 • 884.476 4428.24 225.844 81.3400 41 .0600 31 .5780 715.675  84 204380. 115236. 82170.0 6974.00 63337.0 21550.0 11061.0 84750.0 18182.0 49170.0 14788.0 3551.00 30380.0 16047.0 19300.0 6486.00 7320.30 47729.0 1335.00. 367.000 276.000 190.000 614 1. 00  0.229483E+08 0.253076E+C8 543802. 0. 22C146E+G7 0.471926E+08 0.319500E+07 0.326559E+C8 368638. 0. 275397E + C7 0.864974E+C9  0.21U66E+07 0.249 165E+07 52015.0 2006 76. 0.319500E+07 323261 . 0.249127E+07 27615.9 208263. 0.651238E+08  192390. 0 . 168634E + 08 206433. 0. 196617E + 08 4463.13 400719. 13319 .1 0.1A7125E+07 0.326559E + 08 363638. 27615.9 0.249127E+07 274790. 0.254053E+08 3227.84 274790. 23465.9 0.2224566+07 0.736113E+07 0.689218E+09  Remarks: LAGE, HT, NT, 3A, SD, HTBA, and VOL a r e d e f i n e d  J  SO  2333 .35 1309.05 92*..321 96.9330 739. 205 242.026 117.377 1039.60 191.646 531.423 172.119 33.7930 389.148 177.562 202.215 66.5720 76.9400 564.502 14.0340 5.56700 3.33500 • 2.13600 85.9500  HTHA  16712.5 9231.71 6 503.43 572.360 5371.95 1910.71 863.300 7 199.51 1306.53 3815. e9 1299.70 2 54.400 2587.39 1274.33 1523.46 586.770 595.280 4.105.72 92.2000 27.6000 24.2400 14.1200 5 36.4 C O 0.141763E+07 0.165517E+07 33319.1 143900. 0.275397E-07 203263. 0.222456E+07 23465.9 202912. 0.621015E+03  i n Appendix 3.1.  VOL  0.527S53=+07 0.2°0122r-07 0.219713E + 07 1S0277. 0.173624E+07 5771 40. 2S6!)5S. 0.276735S + 07 441223. 0 . 1 19638E-07 3554 75. E6706.0 811962 . 4032 05. 501377. 171245. 1961 33. 0.125539E-07 33Ci S.O 8434 .03 7420.03 4377.30 159996. ,444857H«09 ,5l3444=+09 . 103?.25F»"3 ,447164=»03 .364974F-05 • 651 23S3 + 0S ,6&5?16F+35 .736S13E-07 .621015= + 03 .194312E + U  Appendix 3.3  Least squares equations for the Interior spruce inventory data — q u a l i t a t i v e variables  XX SS ^ S*. S\ ^ f> •»> ^ f\ / \ f \ C211 « i N PURE P»C P*H 87 4 8Z_5 EZ 6 B7 7 81 8 B Z 9 BZ11 BZIZ PZ 4 P Z 5 PZ 6 PZ 7 PZ 8 P 9 PZ1 P » . « * CZ * CI | « 7 CZ . CZ * 2 . 4 4 . 90. % B 1 . 0 0 / l 2 ; / V , / z 7 ; . " 3 3 . . 3 ^ . ' ' 80. 7 « . » . 84. " l 6 . 45. 9 6 . 292. 3 7 . 522. ! 4 4 . 44. 59. 220. ,1*. 439 1U<..!1«. 52. 34. .16. 45. 9 6 . 292. 37. 522. 52. 84. 16. 45. 96. 292. 37. 522. 144. 44. 5 9 . 2 2 0 . 114. 4 3 9 . 2 4 . 146. **• " ° " * ' 1 190. 1150. I, 1. 4. 9. 2 3 . 103. 19. 113. 281. 231. 144. 4 . 200 2C C . . 52. 144. 129. 44. 1. 12C. 84. 59. 79. 59. 4. 16. 79. 220. 274. 9. 45. 22C. 274. 96. 9 6 . 114. 23. 233. 2 9 2 . B34 . 2 9 2 . 4 3 9 . 1C3. 19. 24. 37. ac. 7c t . 5 2 2 . 146. l i e . 52. 52. £4. 84. 16. 16. 45. 45. 96. 96. 292. 292. 37. 37. 52 2. 5 2 2 . 144. 144. 44. 44. 59. 59. 220. 22C. 114. 114. 439. 439. 24. 24. 146. 146. 4. 4. 1. 1. 4. 4 . 9. 9. 23. 23. 1C3. 103. 19. 19. 11$. HE.  CZ12  B  3  -  H z " \ H p S HZ^6 HZ^7 ^ ^ ^  *'  + .  Remarks: 'pDRE-pure spruce type; P^-spruce-conifer mixed type; Prt-.pruce-h.rdw.od mixed type; other symbols are similarly defined in Appendix 3.1.  \  \  HZ^e HZ*9 K i l l HZ 12 „ . . . L S  L  U  t Appendix 3.3  L e a s t squares e q u a t i o n s f o r t h e I n t e r i o r s p r u c e i n v e n t o r y d a t a —  SITE  AGE  2 1J34?.  2S2C55.  9 U 5 7 . 0  127530-  95 ,42  16C35.0  127633. 26E75.0 21940.0  1Ji17  .0  14345-0  CO  9215.CC  .0  22s03.C  62/0.  23*26.0  29930.0  19J20.0  24355.C  7CC53.0  £ - 4 6 0 . 0 9C30.00  4 3 34.CO 55-.36.G 4207. CO 71  J5.CC  CAGE  63730.0 6010.00  •  9963.00 2262.00  4C5.065 261.532  1686.00  2 14753. 53819.0 37352.C  1180.00  23124.0  161.393 551.045  677.000 2469.00  12636.0 42533.0  1616.22 955.148 3582.00  '65.917 1672.59  1936.00 72 3 3 . 0 0  46333.0 142038.  16 3 . 2 9 0  53 5 . C O O 61 6 4 . 0 0  15CS3 . 0 151 0 4 4 .  C57.  1 533. 25 1C6.590  455.00C  327C0.0 4395.00  55C.77C 74.9460  56950.C 15590.0  1C57.03  11-37.0  25C.351  33-6.  CO  4730.00  46<;4.0C  67C5.00  83.3350 119.688  13395.C  24020.0  24;58.C 21ol.  00  4Ci93 .C  9 C •» 2 .  C  0  3 7.^1  .0  1 4 ; ; . cc 57at.CC 34>.C0C  «*.:oco  36j.:cc  443.142 226.727 381.979 .  11540.C 47225.C 275C.C3 14 9 4 0 . 0 3--0.0C0 75.COCO  •  SO 30843.4  2391.76  51.59C0 194.990  C C  NT  ' 5 5 3 . 533  5 29 5 • C O 1C790.0 "  3 1 v.C.  .  21834.0 9659.00  171-222 34.I960  3 5 . 5 . C O  HT  5264.13 2321.83  9543.CO 22CC.C0  12=3.CO  quantitative variables  '  47C693. 202126.  774.000  1C696.0 . 1 4 4 3 5 .0  157.000 42C.000  2454.00 6749.00  845.000 2536.00  18209.0 44830.0  235.000 4237.00  6533.00 93170.0  1199.00  25555.0  396.000  8351.CO  DBH  8AHT  3152.62  352736.  13603.5 14154.2  1390.99 1447-44  154232. 162784.  3085.69  280.996  2342.98  200.032 129.002  31'-. 134 246.921 136.846  37935.0  233.031  275.313  31663.0  10216.8  833.936  1066.73 68.3120  115239.  0.343355E+07  9501.00  237770. 0-279362E+07  157  8656.79  ..  80.0020 735.992  353. U 9 72.4140  8159.00  2231.00  84.C020  593.  16.0010  119.045 22.4260  45.0020 96.0000  59.0220 123.S98  6033.30 13471.0 33890.0 3935.00  0.116122E+07 99110.0  6e973.0  C.I97991E+07  992  1127.15 3680.3 8 334.129  292.002  363.035  37.C013  5915.92  522.000  23.3110 603.039  1675.32  144.002  '  5537C3.  65.8010  7 043.00  205972.  58.9970  67.9920 294-313  7530.00 30396.0  216660. 92 1 6 2 0 . 4607C7.  4S3.000  9576.CO  1939.00  34999.0  2888.59  220.042  921.000 3313.00  23934.0 77536.0  163.00C  1255.87 5351.67 264. 357 1471.03  569.778 24.5740  6 1336-0 3397.33  122.075 4.022C0  16337.0 433.000  2.03000  200.COO  697.300  40.7300  1.37503  10.0000  238.000  11.2840  1.00033  132-  427  310.000  7.5C500  32.000C  656.3C0  4 3.2600  4.0C000  3.77800  15.9130  60.0000  99.4170  9-00300  7.35200  13.i7.C0  2 325.00  44.2300  170.000  1 135.00 4240.00  £334.CC  229.237  .23.0010  553 5 . C C  159.333  879.000  19722.0  1184.80  102.993  1 lo3.  C O  2195.00  136.000  34C2.00  C C  11S40.0  39.1C70 234.472  206.171 1263.80  19.0910 117.996 210044.  0.  1;2047E+C7 C.2443C3E+07 C . 3 c C 5 < : 6 f + C8 O . 5 1 7 5 8 3 E + 0 8 C . 2 5 2 3 2 6 E + C7 C - 3 4 2 2 0 4 E + 0 7 2lvC44. 26*246.  232055.  364063. C.2T3542E +C S 0.359454E+08 C I 1 7 6 9 3 S + 10  C.2/1527E+C9  1C643.3 44492.6 951742. 6253 3.1 5 2 6 4 . 19 6 466.94 715955. C 2 1 0 3 2 3 S + 08  0.393994E+07 267575. 22C02.9 29 3 3 9 . 3  0-252 376E+07 0-3422O4E+O7 62533.1 267575.  0 . 101 3 7 9 E - C9  0.542 697E-07 0- 5 4 2 3 5 7 E + C 7 378998. 5C4938. 630919.  0 . 3 1 5 2 6 2 " + 07 C . 7 1 5 7 1 1 E + C 8 0-9443125+06 0.205855E+10  282059. 5264.19 22002.9 504933.  .  19.4330 133.862 ' 1 5 . 72 7 0 127.  555  269243. 3640 63. 6466.94 29339.3 630919.  3U4J.1  39832.3  31143.1  2 3 9 6 . 38  39882.3  3395.16 3S1363.  3395.16 4 9 7 7 . 73 5219 3 6 .  0.434607E+C7 0.128938E + 09  7913S.0 201066. 413032.  44.COOO  32.000C  570179.  2525 51. 371317.  19309.0  984.000  422862.  12435.0  170.435  7.624C0  C-3261 36E«-03 576175.  14 3 S 3 F + 0 7  936447-  1061.20 211.294  5153-00 29745.0  0.226522E+C8  0.1  52.0000  555.000  42*362.  1C0570.  3071 1 4.  626.432  49.2370 251.753  0.2i6532S+CS  53 7 6 6 9 .  2512.25  10299.0  545. 730 700.594  943.OOC 23629.0 0. 1 3 2 C 4 7 E + 0 7 . C . 3 S C 5 5 6 E + C 8 0 . 2 ' . 4 3 0 8 E * 0 7 0 . 5 1 2 5 3 3 E * C8 44452.6 951742. 194344. 0.353994E+C7  966125823741.  94.I960 360.587  73u.0OO  9*^2.  35720.0 27936.0 19678.0  VOL 0. 1 0 2 7 3 5 E - 0 3 0.4557S4E+07 0 . 4 7 4 9 9 7 E + 07  78.9980 274.044  114.000 438.936 2 4 . 0 3 00 145.956 4.00030  C . 1 752&1E+CS  BA  2615.03 1144.01 119C.02  0.110393E+08  0.153571S-08  15796-C  433.000 .  876.000  0.1S6  570E + 07  373C0.0 4 25293. 124.52.0 5333.00 11216.0 21134.0  2401.00  67703.0  14463-0  41 1 7 7 3 .  2119.30 14735.0  5135 0 . 0 .3.-.54 1 7 .  0 - 2 9 3 5 4 2 E+ 0 8 0 . 3 7 1 5 7 7 F + C 9 0 . 3 9 9 4 5 4 E - 0 3 • 3 . 1 17 4 0 3 F - I Q 719955. 0.315262E •07 0 . 7 1 5 7 U E -OS 0.434807E+C7 381J63 . 521906. 0.566227H+03 0.15dJ?:Sc -10  C-210272E+CS 0 . 544 3 ! 2 F + 0? 0.2C5-55E-1C 0.12353PE+C9 C. 1 1 0 3 9 3 = 0 3 C.l53S71E+06 0.1633??E+1C O . S l i ^ i t - i l  Appendix  3.4  Least  squares  equations  —qualitative  for  the  Interior  lodgepole  pine  inventory  data  variables  S*\ /*>  * = AN PCSE 4199 2356 2356 2356 1010 833 1130 642 273 153 274 142 306 137 1434 964 533 213 47 27 197 78 642 642 153 153 142 142 137 137 964 964 213 213 27 27 73 78 250 49 132 154 133 217 1 69 23 8 76 15 332 103 19 5C  HMIX P.Z 4 833 1130 1C10 642 250 1C1C 233 333 238 1130 250 76 49 132 154 1 5 133 3 3 2 217 1 C 3 1 1 9 69 5 C 6 4 2  /X  BZ 8 ez 5 ei 6 6Z3067 1434 278 274 137 964 152 142 154 138 49 132 15 332 76 278  / X / X /"•/>» /v /s PZ 8 PZ 9 PZ10 PZ 6 PZ 7 BZ 9 BZ10 BZ12 PZ 4 PZ 5 9 6 4 2 1 3 2 137 1 4 2 1 5 3 6 4 2 47 197 533 , 6 4 2 1 3 2 137 1 4 2 1 5 3 64 2 73 27 213 69 1 217 19 50 103 6 4 2 1 5 3  1 3 7  3 0 6  1434  PZ12 7 7 7 7  CZ 4 CZ 8 2 5 0 4 8 2  5  (  )  5 9 ^  CZ  CZ10 6 CZ 7 C Z 8 C Z 1 3 8 2 1 7 1 3 2 1 5 4 1  1 3 2  1 5 4  1 3 8  2 1 7  1 5 4  s** S*< S\ s** s*\ H Z 4 HZ 5 HZ 6 K Z 7 H Z 8 H Z 9 H Z 1 0 1 5 3 3 2 1 0 3 1 2 3 8 2 3 8 2 3 8  2 5 0  9 6 4  1 5  6 9  1 3 7  9 6 4  I  r-  2 5 0  1  1 5 4 1 5 4  1 3 8  I  1 3 8 6 9  238  1 5  15 33 2 103 19 50  Remarks  1 0 3  1 5  2 5 0  238 76  3  6 4 2  1 3 7  250 49 132 154 133 217 1 69  3 3 2  HZ 12 9 5  1 3 8  7 8  197  /S  CZ12 6 9  3 3 2 5 0  PuK-pure Inventory  lodgepole Z o n e 4;  pine  other  type;  symbols  CMK-lodgepole ara defined  pine-conifer  i n Appendix  3,1.  mixed  type;  H M I X - l o d g e p o l e pine^hardwood mixed;  BzV-Forest  Appendix 3.4.  L e a s t squares equations f o r t h e I n t e r i o r l o d g e p o l e p i n e i n v e n t o r y data —  SITE  AGE  3 U 8 1 4. 16u466. 77o33 .0 64 7 1 0 . 0 76<:3S . 0 22240.0 •20;30. 0 25840.0 1 03306.  67455.0 59330.0 234 1 0 . 0  4 5*10 . 0 4110.00  501C5.0 4115.00  12^90 4 0 s SO 12u90 10*00 1 li30 6S2S6 1 S.,50 23^0.00 4 7oC.00 16*53.0 41^O.CC 96o0. 00 I 3.. 6 0 . 0 10120.0 13*30.0 70.0000 4 4 s 0 . OC 16/60.0 6 0 . 00  370035. 209 400. 93 1 8 0 . 0  21740.0 23030.0 1 2 9 6 2 3.  18635.0 57940.0 1 3345.C 10320.0 .10455.C 58210.0 19265.0 2 6 9 5 . 00 7 170.30 22790.0 4165.00 11420.0 11630.0 14020.0 22475.0 145.000 6535.OC 1S650.0 5900.00  LGGA  8070.78 4538. 90 1961.69  1570.19 2175. 4 3 527.380 512.361 565.C67  2774.78 • 1034.58 90.1251 386.665  1243.70 292.549 260.546 256.334 1372.20 407. 526 53.5959 L52.056  485. 518 93.0037 251.815 2e6.152 274.453 432. 068 2.16140  135.476 446.214 141.823  .  e o.  26.5415  1010.00  628.123 193.581  22660.0 7 3 5 0.00  1275.00 4530.CO 0 . 27 1 5 7 8 E + 0 8 0.357212E+03  34.3673 99.1335 596043.  149602. 181736. 47196.3 47635.0 63436.0 263272. 112234. 8 790.00 38913.0 95247.0 25333.0  471.930 162.715 139.903 157.246  24212.0 3 1328.0 180560. 42440.0  2 2 84 . CO  945.000 27393.0 3365.00  1 7 : 0 . 03 34-.0. 0 0 0.2J9935E*03 0. 2 715 7 S E * C 3  197285.  o  917.490 273.620 37.1330  56C9.00 11696.0 43960.0 8796.00 23473.0 29824.0 23481.0 47340.0 226.000 15185.0  .  54231.0 225C4.0  03H  4197.60 2206.95 1169.04 821.608 959.069 2 94.904 278.835 366.201 1363.72 700.695 59.0250 174.153  416425.  42529.0 13067.0  1253.00  SO  763312.  935C.O0 10280.0 66 C O O . 0 17000.0 2430.00 4740.00 16650.0 3 8 9 0 . 00 9050.00 117", 0 . 0 10320.0 19290.0 8 0 . 0 00 0 4500. 00 169C0.0 5450.00  2 4*30.0  S o j O . 00  NT  HT 294850. 160340. 75550.C 58960.0 7241 0. 0 21020.0 13400.0 23060.0 98 93 0 . 0 44180.0 3930.00 12820.0 38360.0 116  quantitative variables  •  46.8650 249.854 60.1430 138.932 191.470 157.169 294.436 0 .753000 76.2860 238.085 72.0460 17.4850 289.062 132.839 21.0890 51.0020 330094. 369923. 8068.15 314017. 921778. 5332.96 42303. 1 40246.0  1470.03 2 955.00 3530.00 12032.0 0. 225743E + 08 0.5S5084E+C8 7276 1 8 . 0.267760E+08 0.707974E-C8 5 So 0 4 3 . 727618. 15603.8 5712/4. 0. 1488C9E+C7 0 . 2 . i 5 7 4 S E + C3 0 . 2 6 7 7 6 0 E + 08 57 1 2 7 4 . . 0.217901E+08 0.563518E+CS 0 . 5-50E4E+C8 0 . 7 C 7 5 7 4 E - 0 8 0 . 148309E*07 0 . 5 6 8 9 1 8 E - 0 8 0 . 1 7 6 6 1 7 E * 0 9 33JC94. 369923. SC6S.15 31 4 C i 7 . 921778. 0.3J7029E+07 0.367395E+07 79113.2 0.253699E+07 0.74S926E+C7 0.2J1133E-C7 0.3052 17E-07 61391.7 0.2501S4E-07 0.723263E+07 0.3:3761E+03 0.389306E+08 0.313929;+08 0.929398E+C3 • 509246. 8C1567. 0 . 9 J 4 7 6 4 E + C 9 0. U 3 6 0 3 E + 10 0.231700E+03 0 . 9 2 7 2 5 2 E + 0 9 0 . 2 7 1 5 4 3 E + 1 0 0 . 1 4 9 6 0 9 E + 0 S  '  BAHT  31392.9  41002.8 22582.8  VOL 0.117747E-08 0.620833E + 07 0.333490E+07 0.213044E-07 0.253544E+C7  •  16326.3 9403.08 5657.99 6507.79  74469 .0 92915.0  2224.21 1374.76  27120.0  79 52  .  24340.0  13358.8  2455.07 10293.9  31136.0 137245.  694553. 91 1 2 5 9 .  5714.13  6164.03  517.946  521.770  70331.0 5867.00  1833.62 5981.66  1351.38 3144.94  1584.97 1290.34 1233.63 9260.69 2244.57 313.764 668.010 2548.87 513.158 1286. 89 1538.41 1454.41 2472.82 9.00300 698.350 2 2 5 4 . 57 699.558  1276.78 882. 810 1070.81 6976.37 2229.13 38 1 . 7 3 0 364.260  10521.9  7898.05 ' 10785.1  2797.69 2577.23 2918.32  .  RA 403650. 216548. 117633.  19096.0 46310.0 15353 .0  1798.41 442.800 991.950 1303.99 1321.30 2930.96 8.00000 555.170 1564.44 504.630  11822.0 13730.0 93301 . 0 26206 . 0 4126.00 5 200.00 25320.0 5334.00 13018.0 16374.0 16942.0 32425.0 100.COO 8120.00 20735 .0 6433.00  146.072  75.2700  1032.00  3143.63  1995.72 9 5 3.940  i  996.742 190.174 467.256 0.307029E+07 0.367395E-07 79118.2 0.253699E+07  2 7002.0 11750.0 132.040 1641.00 43 1 . 9 5 0 5776.CO 0.251133E+07 0.31S761E+08 0. 3 0 5 2 1 7 E * 0 7 0 . 3 3 9 3 0 6 E » 0 8 61891.7 801567.  0.250184E+07 0 . 3 1 3 9 2 9 E + 0 3 0. 7 4 8 9 2 6 E - 0 7 0 . 7 2 8 2 6 3 E * 0 7 0 . 9 2 9 3 9 8 E + C 3 42303.1 410976. 325927.  40246.0 325927. 350375.  0.417546E+07 0.42277IE+07  0.121526E+09 0 . 1 2 8 2 9 4 E * 0 9  509246. 0.417546E-07 0.422771E+C7 0.525128E+03 0.156076E-10  Remarks: LAGE, HT, NT. SD, BA, HTBA,' and VOL a r e d e f i n e d i n Appendix 3.1.  64.  0.397 5 4 1 E - 0 7 0.213433E+07 175044. 494141 . 0.12455RE+07 454492. 333096. 405539. 0 . 2 6 9 5 2 1 £ ^ 0 7 8002 34. 13 051 5 . 1351 6 2 . 6751 54. 149736. 356392. 473784. 497243. 0. I 0 3 2 2 1 E + 0 7 2737.00 202145. 6 1470S. 195036. 27976.0 737955. 3521 3=. 4 5 79 2 . 0 15 6 3 3 4 . 0 . 9 3 4 764E+09 0. 1 13603E-10 0 . 2 31 7 C O E * C o 0 . 9 27 7 5 2 5 * 0 9 0.271 543?*1C 0.149535:*03 0.121576E-09 0.123294E+09 0 . 1 5 6 0 7 6 5 + 10 0.477643E-11  I 00 I  

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