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Assessing competition using absolute and relative growth rates and relative density of wood for red pine… LaRocque, G. 1991

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ASSESSING COMPETITION  USING ABSOLUTE AND RELATIVE  GROWTH RATES AND RELATIVE DENSITY OF WOOD FOR RED PINE  (Pinus  resinosa  Ait.)  By GUY LAROCQUE Laval Laval  B . Sc M.SC  A THESIS SUBMITTED  University, University, IN PARTIAL  THE REQUIREMENTS  1979 1982  FULFILLMENT OF  FOR THE DEGREE OF  DOCTOR OF  PHILOSOPHY  In THE FACULTY OF GRADUATE  STUDIES  DEPARTMENT OF FORESTRY  We  accept to  this the  thesis  required  as  conforming  standard  THE UNIVERSITY OF BRITISH May  COLUMBIA  1991  © Guy L a r o c q u e ,  1991  In  presenting  degree  this  at the  thesis  in  University of  partial  fulfilment  of  of  department  this thesis for or  by  his  or  scholarly purposes may be her  representatives.  permission.  Department The University of British Columbia Vancouver, Canada  DE-6 (2/88)  / ?  vLrAn  / <t<T I  for  an advanced  Library shall make  it  agree that permission for extensive  It  publication of this thesis for financial gain shall not  Date  requirements  British Columbia, I agree that the  freely available for reference and study. I further copying  the  is  granted  by the  understood  that  head of copying  my or  be allowed without my written  ABSTRACT Effects resinosa were  of  Ait.)  competition on t r e e  examined.  spacings were  among t r e e s  g r o w t h and on t h e  D a t a came  for  DBH, h e i g h t ,  red pine  relative  from a s p a c i n g  r a n g i n g from 1 . 2 x 1 . 2 m t o  measured  of  trial  6.0x6.0  (Pinus  density  with  of  wood  initial  m; i n d i v i d u a l  and crown d i m e n s i o n s  at  trees  several  ages. The (RGR)  first  objective  expressed  the  was  growth  rate  (AGR),  Relative  growth  rate  was  always  tree  size  severe,  This  trees  tion.  at  trees  onset  res  of  of  the  competitive  objective  status  and o f  foliage  with  tree  size  after.  competition,  reduce  with not  too  competitive  the  whether  in forestry The r a t i o s  of  than competi-  efficiency  to  DBH, t h e and t h e  onset  Crown r a t i o  different were  of  of  to  crown w i d t h  to  ratio  i i  tree  size  of  of to  AGR i n DBH  AGR i n RGR:  competition, showed  a p a r t i c u l a r spacing u n t i l  and i n c r e a s e d w i t h  measu-  related  ratio  of  increase  W h i l e AGR  was  onset  the  before  for  the  similar  size  than  more e f f i c i e n t  a pattern  tree  size  severe  rate  forestry.  t o AGR.  showed  with  in  o r when i t  before  examine  stands.  decrease  tree  to  crown l e n g t h ,  biomass  better  RGR d e c r e a s e d  under  to  growth  ones.  r a r e l y used of  size,  t r e e s were  crown l e n g t h  crown w i d t h and t o  tion with  size  small  was  stands  competition  tree  large  of  relative  superior  tree  c o m p e t i t i o n was  crown e f f i c i e n c y  to  of  to  if  n o r m a l l y used  be  p r o d u c i n g new b i o m a s s  The s e c o n d  area  that  compared to  crown l e n g t h ,  which i s  related  implies  The e f f e c t  small  to  the  status  found to  and i n c r e a s e d w i t h  stress. large  positively before  evaluate  competitive  absolute  was  to  little the  afterwards.  basal  a and an varia-  onset  of  The  third  tive  density  tial  spacings.  30  objective  o f wood i n r e d Increment  trees within  every  X-ray densitometer Ring width,  consisted  the  cores  spacing  relative  the  and  Their  scanned  the  density  of  of  the  status  of  and  latewood  the  status use  management  of  ring,  The  for evaluating still  remains  with  the  the  than  response  t o be  of  earlywood  and  late-  iii  proportions density  proportions the  the  of  change  changes  the  stands under  of early-  in  ratio.  competi-  measures of  of  i n wood  i n crown  describe  investigated.  reading wood.  changes  classical  on  the  with  Furthermore,  ini-  of  relative  the  crown e f f i c i e n c y  stands b e t t e r  density  rela-  height  a direct  relative  z o n e s and  stands.  measures of  at breast  on  the  different  maximum d e n s i t i e s , and  were c l o s e l y a s s o c i a t e d  RGR tive  and  l a t e w o o d were c l o s e l y a s s o c i a t e d  competitive density  a f f e c t e d by  l a t e w o o d were a n a l y s e d .  r i n g s and  wood and  was  examining whether  were s a m p l e d  to determine  wood d e n s i t i e s , minimum and earlywood  pine  of  growth.  intensive  TABLE OF CONTENTS Page ABSTRACT  ii  TABLE OF CONTENTS  iv  L I S T OF TABLES  ix  L I S T OF FIGURES  xxii  ACKNOWLEDGEMENTS  xxx  Chapter 1.  GENERAL INTRODUCTION  1  2.  LITERATURE REVIEW  5  2.1-  Definition  and N a t u r e  2.2-  Even-aged  2.3-  Single-tree  2.4-  Characteristics  of  Competition  Stand Development Distance-dependent of  5 7  Growth M o d e l s  Red P i n e  10 13  3.  DESCRIPTION OF DATA  17  4.  STAND DEVELOPMENT STUDY  19  4.1-  Introduction  19  4.2-  L i t e r a t u r e Review  4.3-  Hypotheses  23  4.4-  M a t e r i a l and Methods  26  on R e l a t i v e  iv  Growth R a t e  20  4.4.1-  C l a s s i c a l Approach  27  4.4.2-  F u n c t i o n a l Approach  31  4.4.3-  E s t i m a t i n g the of  4.5-  Results 4.5.1-  Stand-grown  Potential Trees  32  and D i s c u s s i o n  34  C l a s s i c a l Approach 4.5.1.1-  34  DBH and B a s a l A r e a 4.5.1.1.1-  4.5.1.2-  4.5.1.3-  Development  Cumulative in  4.5.2-  Growth R a t e  34  Increment  DBH. . . .  34  4.5.1.1.2-  Absolute  G r o w t h Rate  37  4.5.1.1.3-  Relative  Growth Rate  54  Development  i n Height  77  4.5.1.2.1-  C u m u l a t i v e Increment  77  4.5.1.2.2-  Absolute  Growth Rate  80  4.5.1.2.3-  Relative  Growth Rate  87  Development  i n Volume  93  4.5.1.3.1-  Cumulative Increment  93  4.5.1.3.2-  Absolute  Growth R a t e  93  4.5.1.3.3-  Relative  Growth R a t e  98  F u n c t i o n a l Approach v  98  4.5.3-  4.5.2.1-  C u m u l a t i v e Increment  101  4.5.2.2-  Absolute  Growth R a t e  101  4.5.2.3-  Relative  Growth R a t e  102  E s t i m a t i o n of of  4.6-  the  Stand-grown  Potential  Trees  Growth Rate  from Open-grown  Trees...103  Summary and C o n c l u s i o n s  127  CROWN DEVELOPMENT STUDY  130  5.1-  Introduction  130  5.2-  L i t e r a t u r e Review  131  5.3-  Hypotheses  138  5.4-  Material  and Methods  140  5.5-  Results  and D i s c u s s i o n  143  5.5.1-  Relationships and  5.6STUDY  Bole  between Crown  Dimensions  Sizes  143  5.5.2- Absolute  Measures  145  5.5.3-  Relative  Measures  157  5.5.4-  Relative  Growth M e a s u r e s  183  Summary and C o n c l u s i o n s OF WOOD FORMATION  193  IN RELATION TO STAND  DEVELOPMENT  198 vi  6.1-  Introduction  198  6.2-  L i t e r a t u r e Review  199  6.2.1-  Physiological  6.2.2-  Factors  Influencing  6.2.2.1-  Genetic  6.2.2.2-  Effect  o f Wood F o r m a t i o n  Relative  Density  Inheritance of  Stand D e n s i t y  199 207 209 210  6.3-  Hypotheses  214  6.4-  Material  and Methods  216  6.5-  Results  and D i s c u s s i o n  220  6.5.1-  Effects  6.5.2-  Relationships  6.5.3-  Showing at  6.67.  Aspects  the  of D i f f e r e n t  the  with  Effect  Spacings  Crown V a r i a b l e s of  Individual-tree  Level  7.2-  Proposal  7.3-  301  Findings  ...301  f o r the Development  Distance-dependent  ...293 299  GENERAL CONCLUSIONS Summary o f  280  Spacing  Summary and C o n c l u s i o n s  7.1-  220  of  Growth Models  A d d i t i o n a l R e s e a r c h Needs  LITERATURE CITED  Single-tree 302 306 308  vii  APPENDIX  1:  BASIC  STATISTICS  OF THE PERMANENT SAMPLE  PLOTS STUDIED  332 349  APPENDIX  2:  SUPPLEMENTARY RESULTS OF CHAPTER 4  APPENDIX  3:  RESULTS OF THE APPLICATION OF THE FUNCTIONAL APPROACH  354 379  APPENDIX  4:  ADDITIONAL RESULTS OF CHAPTER 5  APPENDIX  5:  ADDITIONAL REGRESSION EQUATIONS RELATING CROWN VARIABLES TO THE RELATIVE OF WOOD  DENSITY 393  viii  L I S T OF TABLES Table 4.1  P r o p o r t i o n s of overlapping by t h e  trees  their  (%)  that  growing  crown  area  as  defined  spacings  over  age.  spacing.  Mean DBHs  4.3  Mean AGRs i n DBH ( c m / y e a r )  4.4  Mean AGRs i n b a s a l  4.5  their  space  4.2  over  have  (cm)  for  all  area  for  every  (cm /year) 2  spacing  for  over  every  age  spacing  age.  Summary o f  the  principal  component  taken with  the  climatic  variables.  analysis  under-  4.6  Two-level  nested  anova  tests  f o r AGR i n DBH ( c m / y e a r )  4.7  Two-level  n e s t e d anova  tests  f o r AGR i n b a s a l  area  (cm /year). 2  4.8  Mean RGRs i n DBH ( c m / y e a r / c m )  for  every  spacing  over  age. 4.9  Mean RGRs i n b a s a l spacing  4.10  over  Two-level  area  (cm /year/cm ) 2  2  for  every  age.  n e s t e d anova  tests  for  RGR i n DBH  tests  for  RGR i n b a s a l  (cm/year/cm). 4.11  Two-level  nested  anova  area  (cm /year/cm ). 2  4.12  2  Correlation coefficients  between DBH ( i n i t i a l  and RGR f o r  at  all  spacings  ix  different  ages.  size)  4.13  Two-level  nested  anova  tests  f o r mean h e i g h t  4.14  Two-level  nested  anova  tests  f o r AGR  (m).  i n height  (m/year). 4.15  83  Two-level  nested  anova  tests  f o r RGR  i n height  (m/year/m).  90  4.16  Mean v o l u m e s  4.17  Two-level  4.18  Mean AGRs i n volume over  4.19  per t r e e  nested  (m ) 3  anova  f o r a l l spacings  tests  for total  over  volume  age.  (m ). 3  nested  anova  tests  f o r AGR  i n volume 96  3  Mean RGRs over  4.21  i n volume  (m /year/m ) f o r a l l spacings 3  3  99  age.  Two-level  nested  anova  tests  f o r RGR  i n volume  (m / y e a r / m ) . 3  99  3  4.22  B a s i c g r o w t h i n f o r m a t i o n on t h e open-grown  trees.  4.23  C o m p a r i s o n o f v a l u e s between  from Ek's  equation 4.24  DBHs o b t a i n e d  AGRs and RGRs  s t a n d - g r o w n t r e e s f r o m t h e 4.3 of competition with  tree values  105  107  and t h e d e r i v e d e q u a t i o n .  Comparison o f observed  onset  94  96  age.  Two-level  94  f o r a l l spacings  (m 3/yeat)  (m /year). 4.20  81  i n DBH o f t h e  m spacing before the  calculated  open-grown  a s d e f i n e d by t h e s e c o n d h y p o t h e s i s .  Increment p e r i o d : 1 y e a r .  112  x  4.25  Comparison  of observed  stand-grown onset tree  t r e e s from  of competition values  AGRs and RGRs i n DBH o f t h e t h e 6.0  with  m spacing  calculated  a s d e f i n e d by t h e s e c o n d  before the  open-grown hypothesis.  Increment p e r i o d : 1 y e a r . 4.26  Comparison  of observed  stand-grown the  onset  tree  4.27  tree  4.28  tree  t r e e s from  t h e 4.3 with  4.29  hypothesis. 117  with  m spacing calculated  a s d e f i n e d by t h e t h i r d  of observed t r e e s from  of competition  before open-grown  hypothesis. 118  AGRs and RGRs i n DBH o f t h e t h e 6.0  with  m spacing  calculated  a s d e f i n e d by t h e t h i r d  Increment  open-grown  period: 1 year.  stand-grown  values  calculated  before  AGRs and RGRs i n DBH o f t h e  of competition  Comparison  onset  m spacing  a s d e f i n e d by t h e t h i r d  o f observed  values  Increment  hypothesis. 115  s t a n d - g r o w n t r e e s f r o m t h e 6.0 onset  open-grown  period: 1 year.  Comparison  the  calculated  before  AGRs and RGRs i n DBH o f t h e  of competition  values  Increment  with  m spacing  a s d e f i n e d by t h e s e c o n d  of observed  stand-grown onset  t h e 6.0  period: 5 years.  Comparison  the  AGRs and RGRs i n DBH o f t h e  of competition  values  Increment  t r e e s from  113  period: 5 years.  xi  before the  open-grown  tree  hypothesis. 119  4.30  Comparison  of observed  stand-grown onset  Comparison  Comparison  calculated  before the  open-grown  period:  Increment  AGRs and RGRs i n DBH o f t h e  t r e e s f r o m t h e 4.3 with  m spacing  calculated  before the  open-grown  hypothesis.  tree  Increment 124  of observed  AGRs and RGRs i n DBH o f t h e  t r e e s f r o m t h e 6.0  of competition  values  tree  1 year.  stand-grown  5.1  m spacing  123  of observed  Comparison  onset  with  a s d e f i n e d by t h e f i f t h  period:  Increment  AGRs and RGRs i n DBH o f t h e  t r e e s f r o m t h e 6.0  of competition  values  tree  5 years.  stand-grown  4.34  open-grown  a s d e f i n e d by t h e f o u r t h h y p o t h e s i s .  period:  onset  calculated  before the  122  o f observed  of competition  values  Increment  1 year.  stand-grown  4.33  with  m spacing  a s d e f i n e d by t h e f o u r t h h y p o t h e s i s .  period:  tree  AGRs and RGRs i n DBH o f t h e  t r e e s f r o m t h e 6.0  of competition  values  onset  open-grown  121  of observed  stand-grown  4.32  calculated  before the  1 year.  Comparison  onset  with  m spacing  a s d e f i n e d by t h e f o u r t h h y p o t h e s i s .  period: 4.31  t r e e s f r o m t h e 4.3  of competition  values  AGRs and RGRs i n DBH o f t h e  with  m spacing  calculated  a s d e f i n e d by t h e f i f t h  before the  open-grown  hypothesis.  tree  Increment  1 year.  Equations  125  f o r crown w i d t h  (m) a s a f u n c t i o n o f DBH  (cm) f o r a l l a g e s and e v e r y xii  spacing.  144  5.2  Equations  f o r crown l e n g t h  (m) as a f u n c t i o n o f  DBH 144  (cm) f o r a l l a g e s and e v e r y s p a c i n g . 5.3  Two-level  n e s t e d anova t e s t s  f o r crown w i d t h  5.4  Two-level  n e s t e d anova t e s t s  f o r crown l e n g t h  5.5  Two-level  n e s t e d anova t e s t s  f o r crown  149  (m). (m).  projection  (m ).  151  2  5.6  Two-level  n e s t e d anova t e s t s  f o r crown s u r f a c e  5.7  Two-level  n e s t e d anova t e s t s  f o r crown volume  5.8  Two-level  n e s t e d anova t e s t s  f o r f o l i a g e biomass ( k g ) .  5.9  Two-level (kg).  n e s t e d anova t e s t s  f o r branches biomass  Two-level  n e s t e d anova t e s t s  5.10  length 5.11  5.12  5.13  (m/m)  2  (m ). 3  f o r crown  164  3  n e s t e d anova t e s t s  f o r f o l i a g e biomass/ 165  (kg/m ) r a t i o . 3  Two-level  n e s t e d anova t e s t s  f o r biomass of f o l i a g e / 169  n e s t e d anova t e s t s  f o r crown  width/DBH 173  (m/cm) r a t i o . 5.15  Two-level (m/m)  154  surface/crown  biomass of branches (kg/kg) r a t i o . 5.14  153  160  ratio.  n e s t e d anova t e s t s 2  Two-level  152  f o r crown w i d t h / c r o w n  (m /m ) r a t i o .  Two-level volume  (m ).  155  Two-level volume  150  n e s t e d anova t e s t s  f o r crown w i d t h / h e i g h t 175  ratio. xiii  5.16  Two-level (m/cm)  nested  anova  tests  f o r crown  length/DBH  ratio.  177  5.17  Two-level  n e s t e d anova  tests  f o r crown r a t i o  5.18  Two-level  nested  tests  f o r DBH AGR p e r u n i t  of  crown w i d t h  5.19 T w o - l e v e l of 5.20  unit  n e s t e d anova  nested  One-way a n o v a  6.2  Two-level  6.3  One-way a n o v a  6.4  Two-level  6.5  6.6  6.7  tests  tests  tests  185 for height  AGR p e r 196  for ring width tests  tests  (mm).  222  for r i n g width  for relative  n e s t e d anova  density  for r e l a t i v e  of  (mm).  223  rings.  228  density 229  tests  earlywood  zones.  Two-level  nested  earlywood  Two-level  for relative  density  of 235  anova  tests  for relative  density  zones.  One-way a n o v a  of  DBH AGR p e r u n i t  rings.  latewood 6.8  tests_for  (m/year/m).  n e s t e d anova  One-way a n o v a  of  anova  180  185  (cm/year/m).  o f crown w i d t h  6.1  of  (cm/year/m).  crown l e n g t h  Two-level  anova  (m/m)  tests  237 for relative  density  of  zones. nested  latewood  242 anova  tests  zones.  for relative  density 244  xiv  X V  6.20  Multiple (mm)  as  length 6.21  (m)  as  for  6.22  Multiple (mm)  as  ratio 6.23  base  density  for  Multiple density  rings  height 6.25  (m)  Multiple density  6.26  (m)  of  for  equations  crown volume  as  distance height  (m)  for  as  (m)  of  different  equations  a function base  of of  the  (m)  for  285 relative  crown and  (m) breast  ages. equations  a function for  286  of  different  of  different  xvi  for  relative  crown volume  a function for  relative  crown w i d t h  equations  (m)  for  ages.  regression  as  width  and crown  crown w i d t h  Multiple  linear  ring  283  equations  regression as  for 3  (m/m)  crown l e n g t h  width  ages.  a function  different  rings  earlywood  ring  and  (m )  and crown r a t i o  of  for  282  between t h e  linear of  and crown  crown and b r e a s t  regression  rings  and d i s t a n c e  equations  regression  linear of  the  width  281  crown w i d t h  different  and crown l e n g t h 6.24  (m)  ring  ages.  regression  linear of  of  of  a function  Multiple  crown w i d t h  for  ages.  linear  (m/m)  equations  regression  a function  different  of  different  linear  between the for  regression  a function  Multiple (mm)  linear  3  ages. for  crown w i d t h ages.  (m ) 287  proportion (m)  and 289  6.27 M u l t i p l e earlywood distance height  regression  as a f u n c t i o n  earlywood  equations  for p r o p o r t i o n of  o f crown w i d t h  (m) and  between t h e b a s e o f t h e crown and b r e a s t  (m) f o r d i f f e r e n t  6.28 M u l t i p l e  crown  linear  linear  regression  as a f u n c t i o n  ratio  ages.  290  equations  f o r p r o p o r t i o n of  o f crown volume  (m/m) f o r d i f f e r e n t  ( m ) and 3  ages.  291  APPENDIX 1 1-A  AECL  SPACING T R I A L .  sample  plot  #364.  Spacing:  1-B AECL SPACING T R I A L . sample 1-C  AECL  plot  #373.  plot  #374.  sample  plot  #371.  sample 1-G AECL  #372.  plot  #368.  AECL SPACING T R I A L . sample  plot  #375.  335 Permanent 336 Permanent 337 Permanent  1 . 8 x 1 . 8 m.  338 Permanent  2 . 1 x 2 . 1 m.  BASIC S T A T I S T I C S .  Spacing:  Permanent  1 . 8 x 1 . 8 m.  BASIC S T A T I S T I C S .  Spacing:  334  1 . 5 x 1 . 5 m.  BASIC S T A T I S T I C S .  Spacing:  SPACING T R I A L .  sample 1-H  plot  Permanent  1 . 5 x 1 . 5 m.  BASIC S T A T I S T I C S .  Spacing:  333  m.  BASIC S T A T I S T I C S .  Spacing:  1 - F AECL SPACING T R I A L .  1.2x1.2  Permanent  m.  BASIC S T A T I S T I C S .  Spacing:  AECL SPACING T R I A L .  1.2x1.2  BASIC S T A T I S T I C S .  Spacing:  SPACING T R I A L .  sample 1-E  #365.  SPACING T R I A L .  sample 1-D AECL  plot  BASIC S T A T I S T I C S .  2 . 1 x 2 . 1 m.  xvi i  339 Permanent 340  1-1 AECL SPACING T R I A L . sample 1-J  Spacing:  plot  #377.  plot  #378.  sample  plot  #366.  sample  plot  #367.  sample 1-0 AECL  #369.  plot  #385.  4.3x4.3  data  6.0x6.0  343 Permanent 344 Permanent 345 Permanent  m.  346 Permanent  m.  347  f r o m May t o S e p t e m b e r , a n d  b e t w e e n 1961 a n d 1982 a t t h e Petawawa Forestry  Permanent  m.  BASIC S T A T I S T I C S .  Spacing:  Summary o f c l i m a t i c  4.3x4.3  342  m.  BASIC S T A T I S T I C S .  Spacing:  SPACING T R I A L .  sample 2  plot  3.0x3.0  Permanent  m.  BASIC S T A T I S T I C S .  Spacing:  1-N AECL SPACING T R I A L .  3.0x3.0  341  m.  BASIC S T A T I S T I C S .  Spacing:  1-M AECL SPACING T R I A L .  2.4x2.4  Permanent  m.  BASIC S T A T I S T I C S .  Spacing:  AECL SPACING T R I A L .  2.4x2.4  BASIC S T A T I S T I C S .  Spacing:  AECL SPACING T R I A L . sample  1-L  #376.  AECL SPACING T R I A L . sample  1-K  plot  BASIC S T A T I S T I C S .  National  Institute  348  APPENDIX 2 1  Mean h e i g h t s  (m) f o r a l l s p a c i n g s  over  age.  350  APPENDIX 3 1.1 A p p l i c a t i o n o f t h e f u n c t i o n a l the  1.2  m spacing.  a p p r o a c h t o DBH f o r 355  xvi i i  1.2  A p p l i c a t i o n of the  1.3  3.0  6.0  the  the  the  m spacing.  A p p l i c a t i o n of the  the  m spacing.  A p p l i c a t i o n of the  3.4  1.8  the  m spacing.  A p p l i c a t i o n of the  3.3  1.2  the  m spacing.  A p p l i c a t i o n of the  3.2  6.0  the  m spacing.  A p p l i c a t i o n of the  3.1  3.0  the  m spacing.  A p p l i c a t i o n of the  2.4  1.8  the  m spacing.  A p p l i c a t i o n of the  2.3  1.2  to  DBH f o r  functional  approach  to  DBH f o r  functional  approach  to  DBH f o r  functional  approach  to  DBH f o r  to  DBH f o r  to  DBH f o r  to  DBH f o r  to  DBH f o r  to  DBH f o r  to  DBH f o r  to  DBH f o r  m spacing.  A p p l i c a t i o n of the  2.2  6.0  approach  m spacing.  A p p l i c a t i o n of the  2.1  3.0  functional  m spacing.  A p p l i c a t i o n of the  1.4  1.8  the  the  m spacing.  Equations functional Equations functional Equations functional Equations functional Equations functional Equations functional Equations functional Equations  xix  f o r AGR. approach f o r AGR. approach f o r AGR. approach f o r AGR. approach f o r RGR. approach f o r RGR. approach f o r RGR. approach f o r RGR.  APPENDIX 4 1  Two-level of  2  Two-level  4  of 5  foliage  Two-level unit  6  8  9  Two-level unit  10  of  anova  381 f o r DBH AGR p e r u n i t  tests  381  for basal  a r e a AGR p e r  (cm /year/m).  386  2  tests  for basal  a r e a AGR p e r  (cm /year/m).  386  2  surface  foliage  ).  tests  tests  n e s t e d anova  nested  3  f o r DBH AGR p e r u n i t  (cm/year/kg).  for basal  a r e a AGR p e r  (cm /year/m ). 2  tests  387  2  for basal  a r e a AGR p e r  (cm /year/m )• 2  anova  o f crown volume  Two-level unit  anova  n e s t e d anova  nested  380  tests  n e s t e d anova  o f crown  f o r DBH AGR p e r u n i t  ).  (cm/year/m  biomass nested  2  o f crown p r o j e c t i o n  Two-level unit  tests  anova  o f crown l e n g t h  Two-level unit  nested  380  2  o f crown w i d t h  Two-level unit  7  nested  f o r DBH AGR p e r u n i t  (cm/year/m ) .  (cm/year/m  crown volume  Two-level  tests  n e s t e d anova  surface  Two-level of  anova  crown p r o j e c t i o n  crown 3  nested  tests  for basal  2  (cm / y e a r / m  anova biomass  tests  3  for basal 2  a r e a AGR p e r  ).  (cm /year/kg).  xx  387  2  388 a r e a AGR p e r 388  APPENDIX  1  Multiple density  linear of  e a r l y w o o d as  and d i s t a n c e height 2  (m)  Multiple density  3  of  (m)  linear  relative  density  height  Multiple  linear  relative  density  and d i s t a n c e breast  height  base  of  of the  crown and  (m)  breast  for  relative  crown w i d t h crown and  equations  base o f  breast  for d i f f e r e n t  x x i  f o r minimum  crown w i d t h the  (m)  crown and  ages.  equations  base o f  (m)  395  a f u n c t i o n of  between t h e  crown w i d t h  ages.  regression  (m)  equations  for d i f f e r e n t  as  relative  394  a f u n c t i o n of  between t h e (m)  the  for  ages.  regression as  of  a function  different  Multiple  breast  as  between t h e  for  base  regression  latewood  and d i s t a n c e  4  different  linear  equations  a f u n c t i o n of  between t h e  for  and d i s t a n c e height  regression  5  396 f o r maximum  crown w i d t h the  ages.  (m)  crown and 397  L I S T OF  FIGURES  FIGURE  Page  4.1  MEAN DBHs FOR A L L SPACINGS OVER A G E .  36  4.2  DBH AGR DATA SUPERIMPOSED ON CLIMATIC V A R I A B L E S .  40  4.3  PNFI WEATHER DATA FROM 1961  TO 1982.  GRAPH OF  THE FIRST TWO PRINCIPAL COMPONENTS.  45  4.4  DBH AGRS AS A FUNCTION  47  4.5  BASAL AREA AGRs AS A FUNCTION  4.6  MEAN DBH RGRS FOR A L L SPACINGS OVER A G E .  57  4.7  MEAN BASAL AREA RGRs FOR A L L SPACINGS OVER A G E .  58  4.8  DBH RGR DATA SUPERIMPOSED ON CLIMATIC V A R I A B L E S .  60  4.9  DBH RGRS AS A FUNCTION  65  4.10  BASAL AREA RGRs AS A FUNCTION  4.11  MEAN HEIGHTS  FOR A L L SPACINGS OVER A G E .  78  4.12  MEAN HEIGHTS  AS A FUNCTION  79  4.13  HEIGHT AGRS AS A FUNCTION  4.14  HEIGHT AGR DATA SUPERIMPOSED ON CLIMATIC V A R I A B L E S .  85  4.15  MEAN HEIGHT RGRs FOR A L L SPACINGS OVER A G E .  88  4.16  HEIGHT RGRS AS A FUNCTION  89  4.17  HEIGHT RGR DATA SUPERIMPOSED ON CLIMATIC V A R I A B L E S .  91  4.18  MEAN VOLUMES AS A FUNCTION OF DBH S I Z E C L A S S . xxii  95  OF DBH S I Z E C L A S S . OF DBH S I Z E C L A S S .  OF DBH S I Z E C L A S S . OF DBH S I Z E C L A S S .  OF DBH S I Z E C L A S S . OF DBH S I Z E C L A S S .  OF DBH S I Z E C L A S S .  48  66  82  4.19  VOLUME AGRs AS A FUNCTION OF DBH S I Z E  CLASS.  97  4.20  VOLUME RGRs AS A FUNCTION OF DBH S I Z E  CLASS.  100  4.21  DBH = F(AGE)  FOR OPEN-GROWN T R E E S .  106  4.22  DBH = F(AGE)  FOR OPEN-GROWN T R E E S .  108  4.23  RGR(DBH)  = F(AGE)  FOR OPEN-GROWN TREES AND  STAND-GROWN TREES BEFORE THE ONSET OF COMPETITION. 4.24  RGR(DBH)  (SPACING:  = F(AGE)  STAND-GROWN COMPETITION.  4.3  M).  110  FOR OPEN-GROWN TREES AND  TREES BEFORE THE ONSET OF (SPACING:  6.0  M).  F(AGE AT BREAST HEIGHT)  Ill  4.25  DBH -  5.1  CROWN LENGTH -  5.2  MEAN ABSOLUTE CROWN DIMENSIONS  (1).  147  5.3  MEAN ABSOLUTE CROWN DIMENSIONS  (2).  148  5.4  CROWN WIDTHS PER 1 CM DBH CLASS FOR A L L SPACINGS AND  F(DBH)  FOR OPEN-GROWN T R E E S .  FOR DIFFERENT SPACINGS.  DIFFERENT A G E S . 5.5  MEAN R E L A T I V E CROWN MEASURES BASED ON CROWN 159  CROWN WIDTH/CROWN LENGTH RATIOS  PER 1 CM DBH CLASS  FOR A L L SPACINGS AND DIFFERENT A G E S . 5.7  146  158  DIMENSIONS. 5.6  116  CROWN SURFACE/CROWN VOLUME RATIOS  PER 1 CM DBH CLASS  FOR A L L SPACINGS AND DIFFERENT A G E S .  xxiii  162  166  5.8  FOLIAGE BIOMASS/CROWN CLASS  5.9  5.10  PER 1 CM DBH  FOR A L L SPACINGS AND DIFFERENT A G E S .  BIOMASS 1  VOLUME RATIOS  OF FOLIAGE/BIOMASS  167  OF BRANCHES RATIOS  PER  CM DBH CLASS FOR A L L SPACINGS AND DIFFERENT A G E S .  R E L A T I V E CROWN WIDTH AND LENGTH MEASURES BASED ON TREE S I Z E .  5.11  172  CROWN WIDTH/DBH  RATIOS  PER 1 CM DBH CLASS  FOR A L L  SPACINGS AND DIFFERENT A G E S . 5.12  CROWN WIDTH/HEIGHT  RATIOS  17 4  PER 1 CM DBH CLASS  FOR ALL  SPACINGS AND DIFFERENT A G E S . 5.13  CROWN LENGTH/DBH RATIOS  176  PER 1 CM DBH CLASS FOR A L L  SPACINGS AND DIFFERENT A G E S . 5.14  CROWN RATIOS  178  PER 1 CM DBH CLASS FOR A L L SPACINGS  AND DIFFERENT A G E S . 5.15  RATIOS  181  OF MEAN DBH AGR TO DIFFERENT CROWN  MEASUREMENTS. 5.16  184  DBH AGR/CROWN WIDTH RATIOS  PER 1 CM DBH CLASS FOR  A L L SPACINGS AND DIFFERENT A G E S . 5.17  DBH AGR/CROWN LENGTH RATIOS  187  PER 1 CM DBH CLASS FOR  A L L SPACINGS AND DIFFERENT A G E S . 5.18  RATIOS  188  OF MEAN BASAL AREA AGR TO DIFFERENT CROWN  MEASUREMENTS. 5.19  170  190  BASAL AREA AGR/CROWN VOLUME RATIOS  PER 1 CM DBH  CLASS FOR A L L SPACINGS AND DIFFERENT A G E S .  X X I V  191  5.20  BASAL AREA A G R / F O L I A G E BIOMASS RATIOS PER 1 CM DBH CLASS  5.21  FOR A L L SPACINGS AND DIFFERENT  AGES.  RATIOS OF MEAN HEIGHT AGR TO DIFFERENT  192  CROWN  MEASUREMENTS. 5.22  194  HEIGHT AGR/CROWN WIDTH RATIOS PER 1 CM DBH FOR A L L SPACINGS AND DIFFERENT  6.1  CLASS  AGES.  195  MEAN RING WIDTHS AT BREAST HEIGHT FOR A L L SPACINGS OVER TOTAL AGE OF PLANTATION.  6.2  RING WIDTHS PER 1 CM DBH CLASS DIFFERENT  6.3  221 FOR A L L SPACINGS AND  TOTAL AGES OF PLANTATION.  226  MEAN R E L A T I V E DENSITIES OF RINGS AT BREAST  HEIGHT  FOR A L L SPACINGS OVER TOTAL AGE OF PLANTATION. 6.4  R E L A T I V E DENSITIES OF RINGS PER 1 CM DBH CLASS ALL  6.5  227  SPACINGS AND DIFFERENT  FOR  TOTAL AGES OF PLANTATION.  MEAN RELATIVE DENSITIES OF EARLYWOOD ZONES AT  BREAST  HEIGHT FOR A L L SPACINGS OVER TOTAL AGE OF PLANTATION 6.6  R E L A T I V E DENSITIES OF EARLYWOOD ZONES CLASS  FOR A L L SPACINGS AND DIFFERENT  TOTAL AGES 240  MEAN R E L A T I V E DENSITIES OF LATEWOOD ZONES AT  BREAST  HEIGHT FOR A L L SPACINGS OVER TOTAL AGE OF PLANTATION. 6.8  234  PER 1 CM DBH  OF PLANTATION. 6.7  232  RELATIVE DENSITIES OF LATEWOOD ZONES  PER 1 CM DBH  CLASS  TOTAL AGES  FOR A L L SPACINGS AND DIFFERENT  OF PLANTATION.  241  248  X X V  6.9  MEAN MINIMUM  RELATIVE DENSITY VALUES AT  BREAST  HEIGHT FOR A L L SPACINGS OVER TOTAL AGE OF PLANTATION. 6.10  MINIMUM  RELATIVE DENSITY VALUES OF RINGS PER 1 CM  DBH CLASS  FOR A L L SPACINGS AND DIFFERENT  TOTAL  AGES OF PLANTATION. 6.11  254  MEAN MAXIMUM RELATIVE DENSITY VALUES AT  BREAST  HEIGHT FOR A L L SPACINGS OVER TOTAL AGE OF PLANTATION. 6.12  FOR A L L SPACINGS AND DIFFERENT  TOTAL  AGES OF PLANTATION.  261  MEAN PROPORTIONS OF EARLYWOOD AT BREAST  HEIGHT  FOR A L L SPACINGS OVER TOTAL AGE OF PLANTATION. 6.14  PROPORTIONS OF EARLYWOOD PER 1 CM DBH CLASS A L L SPACINGS AND DIFFERENT  6.15  TOTAL AGES OF PLANTATION.  MEAN PROPORTIONS OF LATEWOOD AT BREAST  6.17  FOR A L L  TOTAL AGES OF PLANTATION.  273  M SPACING.  294  R E L A T I V E DENSITIES AND PROPORTIONS OF EARLYWOOD FOR TREES OF THE 2.1  6.19  ' 268  R E L A T I V E DENSITIES AND PROPORTIONS OF EARLYWOOD FOR TREES OF THE 1.2  6.18  267  HEIGHT  PROPORTIONS OF LATEWOOD PER 1 CM DBH CLASS SPACINGS AND DIFFERENT  262  FOR  FOR A L L SPACINGS OVER TOTAL AGE OF PLANTATION. 6.16  255  MAXIMUM R E L A T I V E DENSITY VALUES OF RINGS PER 1 CM DBH CLASS  6.13  249  M SPACING.  295  R E L A T I V E DENSITIES AND PROPORTIONS OF EARLYWOOD FOR TREES OF THE 3.0  M SPACING.  xxvi  296  6.20  R E L A T I V E DENSITIES AND PROPORTIONS OF EARLYWOOD FOR TREES OF THE 6.0  M SPACING.  297  APPENDIX 2 1 PERCENTAGES OF TREES IN DIFFERENT CROWN RATIO CLASSES.  351 APPENDIX 3  1  DBH AS A FUNCTION OF AGE FOR THE 1.2 (PLOTS #  2  359  371  378  M SPACING.  AND 3 7 2 ) .  360  DBH AS A FUNCTION OF AGE FOR THE 3.0 (PLOTS #  4  AND 3 6 5 ) .  DBH AS A FUNCTION OF AGE FOR THE 1.8 (PLOTS #  3  364  M SPACING.  M SPACING.  AND 3 6 6 ) .  361  DBH AS A FUNCTION OF AGE FOR THE 6.0  M SPACING.  (PLOT # 3 8 5 ) . 5  DBH AGR AS A FUNCTION OF AGE FOR THE 1.2 (PLOTS # 364  6  8  367 M SPACING.  AND 3 7 2 ) .  368  DBH AGR AS A FUNCTION OF AGE FOR THE 3.0 (PLOTS # 378  M SPACING.  AND 3 6 5 ) .  DBH AGR AS A FUNCTION OF AGE FOR THE 1.8 (PLOTS # 371  7  362  M SPACING.  AND 3 6 6 ) .  369  DBH AGR AS A FUNCTION OF AGE FOR THE 6.0 (PLOTS # 3 8 5 ) .  H SPACING. 370  xxvi i  9  DBH RGR AS A FUNCTION OF AGE FOR THE 1.2 (PLOTS  10  375  # 371  #  367  376  # 385)  377 M SPACING.  .  378  APPENDIX 1  M SPACING.  AND 3 6 6 ) .  DBH RGR AS A FUNCTION OF AGE FOR THE 6.0 (PLOTS  M SPACING.  AND 3 7 2 ) .  DBH RGR AS A FUNCTION OF AGE FOR THE 3.0 (PLOTS  12  AND 3 6 5 ) .  DBH RGR AS A FUNCTION OF AGE FOR THE 1.8 (PLOTS  11  # 364  M SPACING.  4  DBH AGR/CROWN PROJECTION RATIOS  PER 1 CM DBH CLASS  FOR A L L SPACINGS AND DIFFERENT A G E S . 2  DBH AGR/CROWN SURFACE RATIOS ALL  3  382  PER 1 CM DBH CLASS FOR  SPACINGS AND DIFFERENT A G E S .  DBH AGR/CROWN VOLUME RATIOS  383  PER 1 CM DBH CLASS FOR {  A L L SPACINGS AND DIFFERENT A G E S . 4  DBH A G R / F O L I A G E BIOMASS  RATIOS  384  PER 1 CM DBH CLASS  FOR A L L SPACINGS AND DIFFERENT A G E S . 5  BASAL AREA AGR/CROWN WIDTH RATIOS  385  PER 1 CM DBH CLASS  FOR A L L SPACINGS AND DIFFERENT A G E S . 6  BASAL AREA AGR/CROWN LENGTH RATIOS CLASS  7  389  PER 1 CM DBH  FOR A L L SPACINGS AND DIFFERENT A G E S .  BASAL AREA AGR/CROWN PROJECTION RATIOS  PER 1 CM DBH  CLASS FOR A L L SPACINGS AND DIFFERENT A G E S .  xxvi i i  390  391  8  BASAL AREA AGR/CROWN SURFACE RATIOS PER 1 CM DBH CLASS  FOR A L L SPACINGS AND DIFFERENT  xxix  AGES.  392  ACKNOWLEDGEMENTS I wish help, also  to  t h a n k my s u p e r v i s o r ,  guidance, grateful  first  two  encouragement,  to  years  Dr. at  were D r s .  of  U n i v e r s i t y of  Canada C o r p . , of I  Forests. am a l s o  Their  Johnson of  the  X-ray  years sample  his  looking plots  Forestry  Smith,  Mitchell  to  Mr.  advice after  used  Canada,  in  D.D.  of  this  R.M.  Jozsa,  and r e m e a s u r i n g study.  gave me t h e  XXX  me d u r i n g my  my g r a d u a t e  com-  Jolliffe  K e l l o g g of  Forintek  J.  to  R i c h a r d s and Ms. assistance  He s p e n t trees  to  appreciated.  with  thank M r . W . M .  of  I am g r a t e f u l  opportunity  I am  and P . A .  their  like  the  his  thesis.  were much  Ms.  for  and e n c o u r a g e m e n t .  for  B r i t i s h Columbia M i n i s t r y  and c r i t i c i s m s L.A.  of  Munro,  the  I would a l s o  this  Marshall,  for  members  F o r i n t e k Canada C o r p .  densitometer.  for  The o t h e r  guidance  grateful  and s u p p o r t  B r i t i s h Columbia,  and K . J .  S.  Stiell  J.H.G.  P.L.  Weetman who s u p e r v i s e d  U.B.C.  mittee the  G.F.  Dr.  nearly  the that  30  permanent my e m p l o y e r ,  go on s t u d y  leave.  CHAPTER 1 GENERAL Studies increment time  o f g r o w t h and y i e l d  measures based  (absolute  stands  grow.  predict  growth  rate  p r o d u c e new m a t e r i a l measure,  relative  per  of material  was c o n s i d e r e d among t r e e s extended  This  type  of competitors  tition  i s modelled  i s because  been  fully  from other tance  in  that  of plants to  (e.g.,  The c o n c e p t  One  gr/year/gr).  o f RGR  c a n a l s o be  of single-tree  requires  i m p r o v e d by  q u a n t i f y i n g the  on t h e g r o w t h o f i n d i v i d u a l t r e e s .  trees  and t h e d i s t a n c e s  i t h a s been d i f f i c u l t  Also,  factors that  affect  competition tree  conditions).  growth This  1  b a s e d on t h e  relative that  i s not easy (i.e., type  c l a s s o f model, the growth o f the stand area,  Compe-  t o each competition.  s t r e s s has n o t y e t  single-tree distance-independent  t e r m s o f mean DBH, b a s a l  index  t o model  t h e mechanism o f c o m p e t i t i v e  Ford  to f o l i a g e weight.  be g r e a t l y  a competition  It  competition  For instance,  increment  such  as the increment  f o r assessing  area  t r e e s or  Other  the development  understood.  than  fast  i n t e r m s o f AGR.  i s defined  o f g r o w t h model  and m i c r o c l i m a t i c  complex this  of basal  how  mostly  of the p l a n t .  by c o m p u t i n g  o f the competing  This  1984).  a period of  in agriculture.  (RGR),  used  growth models  accumulated  parts  over  the c a p a c i t y  growth models c o u l d  effect  To d a t e ,  express  promising  (1979,  (1979) s t a t e d  RGR.  or stands  rate  t o be v e r y  distance-dependent  other.  or whole-stand  already  the r a t i o  i n size  to evaluate  have been u s e d  to productive  Ford  size  o r AGR)  that  growth  by F o r d  (1982) used  using  rate  Single-tree  measures o f growth  i n f o r e s t r y have g e n e r a l l y  on t h e change  the growth o f t r e e s  unit  INTRODUCTION  or volume.  to separate  genetic  o f model  inherii s more  growth models. is first  In  predicted  Then, g r o w t h i s  allocated based  to i n d i v i d u a l  on i n d i v i d u a l  (e.g., 1975;  basal  area)  (e.g.,  Loucks e t a l . 1981;  stem o r crown g r o w t h little  DBH)  classes  as w e l l  1983;  S m i t h and W i l l i a m s  studies  have g e n e r a l l y  to evaluate  more  intimately  the e f f e c t  on d e t e r m i n i n g  competitive  stress  stress. density  o f wood  Ek and M o n s e r u d 1980). focused  on m e a s u r i n g  of competition.  other  anatomical  to physiological  m e a s u r e s o f stem g r o w t h .  the usual  characteristics  thesis,  i twill  constitutes  cha-  to the The  w o u l d be v e r y u s e f u l f o r  o r new m e a s u r e s o f c o m p e t i t i o n adequately  Very  processes  than  trees  In t h i s  characteristics  r e s p o n d more s e n s i t i v e l y  i f existing  individual  rules  i f these would  measurement o f s u c h determining  related  by a p p l y i n g  as s t a n d  e m p h a s i s has been p u t on e x a m i n i n g  racteristics  among  or s i z e  ( A v e r y and B u r k h a r t  Growth and y i e l d  and  trees  represent  the competitive  be e x a m i n e d  a sensitive  intensity  i f the r e l a t i v e  measure o f t h e e f f e c t o f  competi t i o n . There  i s no i n t e n t  distance-dependent related  (i.e.,  competition  among  this  will  thesis  improving  how  of t h i s  to better  trees). provide  single-tree  improvement  ability  utility.  from a f o r e s t r y  stand  point  strategies,  butions,  and (4)  stands, (3)  that  (2)  analyses  delimitation  (1)  problem  o f g r o w t h model i s the i n t e n s i t y of that  the r e s u l t s of  contribute  towards  growth models.  important  prediction  comparison  The will  advantages  o f g r o w t h and  of s i l v i c u l t u r a l  of d i f f e r e n t  diameter  o f maximum r e s p o n s e s  2  single-tree  o f growth models  The most  are:  a  the major  will  distance-dependent  their  ment  type  quantify  insight  o f the p r e d i c t i v e  o f managed  to derive  I t i s expected  increase  yield  thesis  g r o w t h m o d e l ; however,  t o the development  considered  indeed  in this  treat-  distrito s p e c i f i c  treatments  and o f g r o w t h  Furthermore, stand  a g r o w t h model  dynamics  fundamental  (Titus  changes  development  Three (1)  major  objectives  of (3)  are addressed  The  the value  thesis: b a s e d on  of red pine  AGR;  there i s a  of these  (Pinus  efficiency,  relationship  m e a s u r e s and t h e o n s e t  competition i n red pine; the e f f e c t  the r e l a t i v e  of different  initial  spacings  d e n s i t y o f wood i n r e d p i n e . stands  trees w i l l  d u r i n g the t r a n s i t i o n be e m p h a s i z e d  from  f o r each o f  objectives. Remeasurement d a t a  from  a red pine  Petawawa N a t i o n a l F o r e s t r y I n s t i t u t e  study.  The d a t a  s e t was p a r t i c u l a r l y  because  the data  cover  a wide  remeasurements accumulated onset  i n this  m e a s u r e s o f crown  t o examine w h e t h e r  open-grown t o s t a n d - g r o w n  the  than  changes o c c u r r i n g i n young  these  d i o x i d e on  o f c o m p e t i t i o n on t h e  characteristics  different  to analyse on  on  but the e f f e c t of  as t h e i n c r e a s e i n carbon  resinosa Ait.) better  between  f o r studying  Not o n l y hypotheses  c a n be t e s t e d ,  the e f f e c t  growth o f b o l e  and  1980a).  tool  i f a measure o f e f f i c i e n c y  RGR e x p r e s s e s  to study  1979,  and s u c c e s s i o n c a n be e v a l u a t e d .  t o determine  (2)  1985).  and Morton  such  1972,  (Smith  i s a very powerful  growth p r o c e s s e s  environmental forest  trends  range  several  spacing t r i a l were u s e d  useful  years before  o f c o m p e t i t i o n , and c o n t a i n d e t a i l e d  Because e v e r y associate  t r e e was i n i t i a l l y  for this  forthis  of i n i t i a l  located at  study  spacings,  and a f t e r t h e  measurements.  identified,  i t was p o s s i b l e t o  stem a n d crown g r o w t h d a t a w i t h wood r e l a t i v e  3  involve  density  at  the ring  level.  Major c o n t r i b u t i o n s of t h i s study  thesis  of the development of i n d i v i d u a l  several years  before  and a f t e r  evaluation of p o t e n t i a l a n d (3)  forestry, tition  a detailed  tree characteristics for  the onset  of c o m p e t i t i o n ,  measures o f e f f i c i e n c y  a simultaneous  (1)  include:  (2)  an  r a r e l y used i n  study of the e f f e c t  on s t e m g r o w t h , c r o w n d e v e l o p m e n t , and wood  o f compe-  anatomy.  E v e n t h o u g h r e d p i n e h a s b e e n t h e s u b j e c t o f many s t u d i e s , i t was s e l e c t e d f o r t h i s importance  particular  study because o f i t s economic  i n northeastern North America,  v e r y good d a t a  set available.  and b e c a u s e o f t h e  The u n d e r s t a n d i n g  development of red pine p l a n t a t i o n s gained efficiency natural  c a n be e x t e n d e d t o a s s i s t  stands  of the  u s i n g measures o f  i n t h e management o f  o f r e d p i n e and p l a n t a t i o n s o f o t h e r  coniferous  species. A general nature  literature  c o v e r i n g t h e d e f i n i t i o n and  o f c o m p e t i t i o n , even-aged stand growth,  distance-dependent pine  review  i s provided  Chapter  3.  Chapters  literature  growth models, and c h a r a c t e r i s t i c s o f r e d i n Chapter  2.  The d a t a  set i s described i n  The t h r e e m a i n o b j e c t i v e s f o r m t h e themes f o r  4,  organized  single-tree  5,  a n d 6,  i n a similar review,  respectively.  Each o f these  chapters i s  f a s h i o n c o n t a i n i n g an i n t r o d u c t i o n , a  hypotheses statements,  d e s c r i p t i o n of the  m e t h o d o l o g y , p r e s e n t a t i o n and d i s c u s s i o n o f t h e r e s u l t s , summary a n d c o n c l u s i o n s . of the major  results,  distance-dependent results of this  The f i n a l  chapter  and a  c o n t a i n s a summary  a d i s c u s s i o n s u g g e s t i n g how  single-tree  g r o w t h m o d e l s c o u l d be i m p r o v e d u s i n g t h e  r e s e a r c h , and s u g g e s t i o n s  4  for future  research.  CHAPTER 2 LITERATURE REVIEW 2.1-  D e f i n i t i o n and N a t u r e o f C o m p e t i t i o n Competition  considered 1984).  among t r e e s  a fundamental process  Several definitions  refer  to  the  vital  resources  plants.  same  Grime  neighbouring a mineral  necessary (1979)  plants  element,  o c c u r s when t h e  1979;  Harper  to  the  of  that  "the  same quantum o f  water,  light,  o r volume o f  and Tourney and K o r s t i a n resources  the  have  Krebs of  1978;  the  site  may a f f e c t  the  Shepherd 1986). the  not  following  for  For  competition every  1979;  plant  Grime  m o r p h o l o g i c a l and  competitive  status  The c o m p e t i t i v e  features:  i n the  necessarily  same  grow a t  s u r r o u n d e d by c o m p e t i t o r s  differences  i o n of  i n d i v i d u a l s , and p h y s i c a l and c h e m i c a l  and/or l i v i n g  will  Leme'e 1 9 7 8 ) ,  of  space".  (1962),  available  of  tendency  community ( F o r d  (Perry 1985),  production ment  and d e v e l o p m e n t  R e n n o l l s and B l a c k w e l l 1 9 8 8 ) ;  accentuates size  survival  the  same d i m e n s i o n s  1979;  the  all  several  of  (Lemee 1978;  may be  of  characteristics  of  they  shortage  c o m p e t i t i o n as  or  they  the  many i n d i v i d u a l s .  conditions  availability  but  one  is  (Shugart  too  1977;  to  stand dynamics  competition exist,  utilize  molecule  of  community  of  aspects  considered  defined  comprise a f o r e s t  aggregation  biological  plant  for  r e d u c t i o n of  from the  Spatial  of  situation:  Long and S m i t h (1984)  results  that  of  (2)  (1)  process  plants  conditions the  same  different the  of  of  rate  a s t a n d may a c h i e v e  depends  5  (3)  the  sizes  the  (Ford stress  1982),  potential  is  because  among i n d i v i d u a l s f o r p a r a m e t e r s  ( W e i n e r and Thomas 1 9 8 6 ) ;  every  resource  competitive  p o p u l a t i o n d i s t r i b u t i o n (Gates  of  like or  seed  develop-  on c o m p e t i t i o n among  individuals  (Hamilton  1969);  (4)  the smallest i n d i v i d u a l s  a p o p u l a t i o n a r e t h e most a f f e c t e d 1977;  Harper (5)  and  (Begon and M o r t i m e r  Tourney and K o r s t i a n 1 9 6 2 ;  the occurrence  Weiner  within  1986; 1986);  and Thomas  of m o r t a l i t y i s density-dependent  (Harper  1977) . The  m a j o r i t y o f growth models  competition other  among t r e e s i m p l i c i t l y  proportionally to their  re-evaluated  1990),  Weiner  competition because effect low.  and D i g g l e  a n d Thomas  f o rsolar  of small  radiation  and W e i n e r would  hand,  competition  competition exceptions  growth models i s different  have  by T i l m a n  (1990).  sizes.  specific  resources  Competition in  growth  r a t e between  competition size,  c a n be q u a n t i f i e d  (Curtis  location,  neighbouring  Perry  (Mithen  above-ground Notable  a  deve-  mechanistic  the competition f o r (Tilman  1976,  1977).  by e v a l u a t i n g t h e d i f f e r e n c e t r e e and a t r e e f r e e o f  1985),  e t a l . 1984;  6  affect  o r t h e model  a n d by d e t e r m i n i n g t h e  age, and genotype c h a r a c t e r i s t i c s  trees  would be  the majority of  competition.  1984)  studied  a stand-grown  1970;  ones, b u t the  that  has l o n g promoted  was i n t e n s i v e l y  (asymmetric)  resources  Thus,  not considered  a p p r o a c h b a s e d upon e x p e r i m e n t s i n w h i c h  (1986,  be d i s p r o p o r t i o n n a l l y  forsoil  (Shugart  Tilman  Weiner  et a l . (1990),  the small  from below-ground  a r e t h e F o r e t model  (1986),  and l a r g e t r e e s w o u l d  proportionnally to their  existing  According to  be o n e - s i d e d  greatly affect  (symmetric) because small  each other  Huston  each  l i t e r a t u r e has  of competition.  t r e e s on l a r g e ones w o u l d  On t h e o t h e r  loped  Some r e c e n t  (1981),  (1986),  l a r g e t r e e s would  two-sided  the  Ford  assume t h a t p l a n t s a f f e c t  size.  the symmetric nature  (1984),  Ford  b a s e d on t h e q u a n t i f i c a t i o n o f  Weiner  o f the  1984).  2.2-  Even-aged Three  (1)  Stand  classes  intrinsic  allow tion  of  as  biotic  environment  changes  factors  that  of competi-  The a b i o t i c e n v i r o n m e n t  physical  or s p a t i a l  envi-  Intrinsic  i n the absence  constraints.  such as c l i m a t e ,  of trees:  a b i o t i c and b i o t i c  o f t h e p h y s i o l o g i c a l and g e n e t i c  topography,  competition.  the development  (Husch e t a l . 1 9 8 2 ) .  environmental  factors  the s o i l ,  The  (2)  t o grow a t a maximum r a t e  or other  includes  influence  of trees;  disturbance  consist  trees  of factors  properties  ronment; and ( 3 ) properties  Development  or chemical  arrangement  conditions  of the trees.  r e l a t e s t o i n t e r a c t i o n s among p l a n t s  Disturbance  i n the s t r u c t u r e  r e f e r s t o any n a t u r a l  of the population  that  such  or a r t i f i c i a l  affect its  development. The major  development  steps  small,  there  individual  with  stand (1)  proceeds  through  When t h e t r e e s  are not f u l l y among t r e e s ,  d e p e n d s on t h e s p e c i e s ,  three  are very  exploited.  the growth o f every  a g e , a b i o t i c f a c t o r s , and  herbaceous  species.  The v a r i a t i o n i n  s i z e a p p r o x i m a t e s a n o r m a l d i s t r i b u t i o n ( L o n g and S m i t h  1984).  (2)  largely  determine  The  of the s i t e  i s no c o m p e t i t i o n  perhaps competition tree  1984).  ( L o n g and S m i t h  the resources  Because  o f an e v e n - a g e d  onset  The i n i t i a l  stand  density  the i n i t i a t i o n  of competition  t o be t h e b e g i n n i n g  correspond  to the occurrence  (Ford  1984;  Long a n d S m i t h  t o be s t r a t i f i e d 1975;  Hamilton  Spurr  and B a r n e s  o f development  of i n t r a - s p e c i f i c  among t r e e s  considered  and r a t e  i n even-aged  o f stand  Long and S m i t h  1980).  (3)  At this  1984;  Competition  7  c a n be  or a l i t t l e a f t e r  time,  i n t o d i f f e r e n t crown d o m i n a n c e  1969;  stands  g r o w t h , and w o u l d  o f crown c l o s u r e  1984).  competition.  the stand classes  begins  (Ford  Mithen e t a l . 1984; becomes more  intense  with  age, and t h e s t r a t i f i c a t i o n  distribution  becomes i r r e g u l a r a n d a p p r o a c h e s b i m o d a l i t y  1975).  However,  tition  for solar  resources  is  r a d i a t i o n (one-sided)  that  a function  1986).  s i z e d i f f e r e n c e s would  (two-sided)  probability  a given  o f both  ages as s i t e  t r e e wins  i t s genetic  terized  al.  height,  basal  by a s i g m o i d a l  The  a n d becomes d o m i n a n t  p o t e n t i a l and chance  (Daniel  for soil  i sattained e t a l . 1979).  (Shepherd a t younger The  o r s t a n d s , whether e x p r e s s e d i n  area,  volume, o r biomass,  f o r m when p l o t t e d o v e r  i s charac-  time  (Zedaker e t  1987). The  effect of i n i t i a l  even-aged trials.  s t a n d s h a s been Bibliographies  (1971,  Evert  initial costs  spacing  (Evert  density  of this  studies  Also,  As s p a c i n g i n diameter  the production  o f the stand  production  substantially  (Evert  Stem d i a m e t e r height  area  (Evert  1971;  Ford  1981).  total  individual  Ford  occurs  earlier  However,  i n the  total  v o l u m e ) may d e c r e a s e  1984).  (Clutter e t a l . 1983; Daniel  Shepherd  1 9 8 6 ; Tourney a n d K o r s t i a n  affected  only  dense o r v e r y  8  trees  1984) u n t i l a  i s much more s e n s i t i v e t o s t a n d  i n very  that  (Tourney a n d K o r s t i a n  o f sawtimber  (e.g.,  1971;  demonstrated  i s increased,  (Harms a n d L l o y d  per unit  spacing  r a t e , management p r a c t i c e s , a n d  maximum i s r e a c h e d b y open-grown t r e e s 1962).  through  t y p e o f s t u d y were p r e p a r e d by  These  a f f e c t s growth  1971).  on t h e d e v e l o p m e n t o f  intensively studied  1973, 1984).  grow f a s t e r m o s t l y  life  competition  compe-  a n d Thomas 1 9 8 6 ) .  the race  o f development  q u a l i t y i s improved  growth o f i n d i v i d u a l t r e e s  than  Size  (Ford  r e s u l t more f r o m  1 9 9 0 ; Weiner  (Weiner  A p a r t i c u l a r stage  diameter,  o f the f o r e s t accentuates.  density  than  e t a l . 1 9 7 9 ; Lanner 1 9 8 5 ; 1962).  The l a t t e r  open s t a n d s  w o u l d be  (Clutter et  al.  1983;  that  D a n i e l et  physiologists  cambial  cells (1985)  is  affected  draws to  all  has  the  function  1979).  have  failed  respond to  Lanner not  al.  suggested  by s t a n d  its  full  Stem f o r m ( t a p e r ) boles  of  open-grown 1986;  take  the  growth of  because  its  needs e a r l y  greatly tend  influenced to  be  Basal  area development  per u n i t  three  forms  al.  basal  basal  area per  has  total  (Daniel  tree  by a g e ,  also  response species,  Normally,  of  optimal  (1962),  to  effect  with  to  densities If  trees  because a tree  shoot  meristem  growing  season  always  al.  there  stand  trees  has  its  9  the  to  area)  is  competi-  no  stems,  al.  and  begins,  stems,  number o f  but  stems.  is  affected  1983).  r e s p o n d more  ( O l i v e r 1982).  to  thinning  However,  on d o m i n a n t  and Tourney and  trees.  Korstian  than dominants  a r e v e r y much a f f e c t e d  growth  may  overcrowded,  thinning  concentrated  trees  (Shepherd  volume.  may r e s p o n d b e t t e r such  is  of  basal  number o f  ( C l u t t e r et  (1983)  form  number o f  the  stand  trees  The those  When c o m p e t i t i o n  total  quality  suppressed not  the  When the  an e v e n - a g e d  C l u t t e r et  suppressed  competition.  is  leading  (total  If  rate.  d o m i n a n t and c o d o m i n a n t or  the  by s t o c k i n g .  area decrease with  applies  and s i t e  intermediate  According  basal  area  with  increases  decreases.  and t r e e  space.  c y l i n d r i c a l while  1979).  increases  still  same p a t t e r n The  et  a maximum g r o w t h  area  growing  potential.  trees  area  of  i n the  1987).  basal  mentioned  lateral  apical  al.  total  stand  availability  Zedaker et  tree  the  e x p l a i n why o n l y  c h a r a c t e r i z e d by a c o n i c a l  every  than  (1974)  are  total  The  it  and Dosen  trees  tion,  both  that  density  is  forest-grown  to  increased  carbohydrate  at  Iyer  at  low  by  r e d u c e d by c o m p e t i t o r s  for  a long in  p e r i o d of  available  time,  it  might  growing  space,  (Tourney and K o r s t i a n  1962).  following of  solar  t h i n n i n g may be  and t h e  residual  trees  2.3-  for  et  delay  of  to  canopy,  the  the  availability al.  of  Single-tree  distance-dependent  growth models  options  g r o w t h and e v a l u a t i n g  ( A r n e y 1974;  Avery  the  Ek and Dudek 1980;  Garcia  Hegyi  1975;  Loucks et  and W i l l i a m s 1980; (1984)  and S m i t h and B e l l  flexibility full  because  they  are  the  different  al.  al.  1981;  1987).  (1983), not  discussion  about  al.  pointed  (1988)  population they  symmetrical  ecological out  of  the  tree  must  following be  computed as  known;  whole-stand  volume)  of  and t o  to  between  (1)  10  lack  adequately In a  et for  biological  specific  location,  a bias  genetic and t o  the  individuals.  the  growth  location  of  a p a r t i c u l a r tree  potential  et  integrate  Huston  distance-dependent  growth of  its  or  1975;  Mithen  situations.  introduce  conditions,  various  Smith  models  enough  i n d i v i d u a l s with  characteristics:  a function  to  predicting variables  single-tree  the  to  Daniels  Munro 1974;  competitive  interactions  (2)  1983;  According  sensitive  of  models  environmental  aspect  of  effects  in general,  to  new  flexible  models  total  refer  The m a j o r i t y o f have  that  (e.g.,  do n o t  constitutions,  types  of  Ek and M o n s e r u d  v a r i a b i l i t y among i n d i v i d u a l t r e e s  represent  because  Zedaker et  penetration  are  and B u r k h a r t  1988;  1988;  growth  and n u t r i e n t s  Growth M o d e l s  stand  long  1979).  1975,  whole  greater  water  increase  may be  tree  Distance-dependent  predicting  an  development  and B u r k h a r t  the  of  Single-tree  management  al.  to  response  The a c c e l e r a t i o n  the  increased  (Daniel  the  respond w e l l  attributed  radiation within  foliage,  or  not  growth  models  every is  r e d u c e d by a  competition depend of  index;  and ( 3 )  on t h e s u b j e c t ' s t r e e  the competitors  regression equations.  have been u s e d  The i n d e p e n d e n t  of the subject tree  period, such  as b a s a l a r e a  over  which p r e d i c t i o n s  Smith  and W i l l i a m s  (5) a v a i l a b l e  overlap. being on  Although  1988;  the  t h e space  studies of B e l l a  their  tested  own d a t a :  (1983),  most o f t h e s e concept  crown  (1971),  (1969),  first  potential.  (1971),  (1971),  the performance Alemdag  tree  draws  (1974a,  Keister  and O p i e  This  (1968).  Chen and Rose  G a n z l i n and L o r i m e r  M a r t i n and Ek ( 1 9 8 4 ) ,  11  zone resources  The f o l l o w i n g indexes  (1978),  (1983),  Mugasha  1974b,  and T i d w e l l  o f some c o m p e t i t i o n  (1978),  used i n  Good e x a m p l e s a r e  Ek and M o n s e r u d  Keister  models a r e  1972; D a n i e l s and B u r k h a r t  i n w h i c h an i n d i v i d u a l  (1976) , E r i k s o n ( 1 9 7 8 ) , Lorimer  area  of the competitors  1975; L o u c k s e t a l . 1 9 8 1 ) .  ( 1 9 7 5 ) , Newnham a n d Mucha authors  (Arney  t o grow a t i t s f u l l  1979), G e r r a r d  (4) b a s a l  and (6)  of the s i z e  zone o f i n f l u e n c e  by Newnham ( 1 9 6 4 )  the s i t e  s i x g r o u p s by o v e r l a p ; (2)  area;  space;  (Daniels 1976)),  Ek a n d M o n s e r u d  from  growing  of the e f f e c t  on t h e c i r c u l a r  represents  into  m o d i f i c a t i o n s have been made ( t h e m a j o r one  the i n c l u s i o n  simulation  The t i m e - s t e p  5 years.  number o f t r e e s p e r u n i t  the subject tree  based  quality.  (1) zone o f i n f l u e n c e  per  of the  and sometimes a measure o f d e n s i t y  have been c l a s s i f i e d  (1980):  consist  of the p r e d i c t i o n  a r e made i s u s u a l l y  (3)  area;  normally  and a measure o f s i t e  size-distance; unit  Multiple  t o d e r i v e most o f t h e  a t the beginning  indexes  and d i m e n s i o n s  Ek and M o n s e r u d 1975;  variables  a competition index,  Competition  and t h e l o c a t i o n  and W i l l i a m s 1 9 8 0 ) .  Smith  techniques  size  e t a l . 1984;  (Alig  Loucks e t a l . 1981;  size  the competition indexes g e n e r a l l y  with  Daniels  Ker ( 1 9 8 0 ) ,  (1989),  Pukkala  (1989),  Rudolph e t a l . ( 1 9 8 2 ) ,  (1975),  and W e i n e r  The  major  rate  (1983),  Tennent  (1984). o f Newnham ( 1 9 6 4 )  assumptions  growing without  S m i t h and B e l l  competition  (1)  were:  i s c h a r a c t e r i z e d by a d i a m e t e r  increment  proportional related growth  rate that  of every  crown w i d t h cases,  of competition  i s less  than  t r e e i s reduced  by an amount  i t r e c e i v e s ; and ( 3 )  to the competition  to a level  influence  of a p a r t i c u l a r  corresponding  to a  a threshold value.  tree i s f i r s t  computed  mortality i s diameter  The zone o f  as a f u n c t i o n o f the  o f an open-grown t r e e o f t h e same d i a m e t e r .  adjustments  a r e made f o r f a c t o r s  the  size  of the competitors.  lar  tree  (i.e.,  its  growth) i s q u a n t i f i e d  like  The c o m p e t i t i o n  the computation  of the e f f e c t  by m e a s u r i n g  growth  (2) the  o f an open-grown t r e e t h a t h a s t h e same d i a m e t e r ;  diameter  a tree  shade  I n some  tolerance or  index  of a particu-  of competitors  on  t h e o v e r l a p between i t s  zone o f i n f l u e n c e a n d t h e zone o f i n f l u e n c e o f i t s c o m p e t i t o r s . An  implicit  affect  assumption  each other  Competition and  competitors,  have b e e n l e s s Mitchell  (1969,  of this  approach  i s t h a t two  proportionally to their indexes  based  popular. 1971,  simulated,  and  Hatch e t a l . (1975)  of the subject  and a v a i l a b l e  tree  growing  space  Crown o v e r l a p h a s b e e n e m p l o y e d by  1975)  was  size.  on t h e s i z e  density, basal area,  competitors  where t h e g r o w t h o f s i n g l e  and by B e a u r e g a r d  (1975),  Ford  branches  and D i g g l e  where t h e crown was r e p r e s e n t e d  (1981), by a cone  of i n f l u e n c e . According The  t o Ford  (1979),  Perry  m a j o r i t y o f t h e models d e v e l o p e d  simulated  (1985),  (1989),  s o f a r have n o t s u c c e s s f u l l y  t h e g r o w t h o f t r e e s and s t a n d s .  12  and Pukkala  Indeed,  the studies  comparing v a r i o u s differ  v e r y much i n t h e i r  studies  of  (1983),  Gerrard  initial  diameter  (1969), of  point,  integrate for  it  a given  various  ronments,  the  symmetrical  tition  a one-sided are  The d e v e l o p m e n t infancy 2.4-  (Ford  continent Lakes  the  of  Canada,  it  this  grows the  St.  found  of  only  identified northern Rudolf  is  two-sided  type  that of  make s t a n d  g r o w t h model  to  allow the  competitive microenvi-  (whether  and  models  modelling  past  competition  At  actual  different  process),  better  compe-  other  growth v e r y  complex.  is  its  still  in  Red P i n e  i n the  northern p o r t i o n of  boreal  forest  Resources  by R o b e r t s  p a r t of  the  (1985)  of  1986).  i n three  province.  or a e o l i a n !  sides  forest  the  This  to  regions  soils  deposits.  is  It  areas  less  (Ontario it  is  in  the  (1985),  environment  that  in  were  Bassett  a good e d a p h i c  that,  Newfoundland  twenty stands geographic  Great means  In Newfoundland,  d r a i n e d sandy  13  North American  of  Manitoba to  According  (1978),  well  the  (Rudolf 1981).  Fewer t h a n  and S t i e l l  consists  on b o t h  L a w r e n c e and A c a d i a n  on some s i t e s .  glacio-fluvial  of  to  competition  easy because  found from s o u t h e a s t  Natural  (1981),  red pine  nature  the  increment.  (1985),  potentials,  Lawrence R i v e r  Great Lakes-St.  Ministry  not  Perry  that  the  The  Lorimer  from e q u a l  ask w h e t h e r  to  and  showed  of  not  1979).  below  and t h e  is  factors  C h a r a c t e r i s t i c s of Red p i n e  in  all  to  understanding  genetic  or  (1983)  t h e s e do  (Mugasha 1 9 8 9 ) .  Ganzlin  may r a n g e  According  interactions,  ability  that  p r e d i c t i n g diameter  biological  individual trees  interactions  tree  at  suggest  (1971),  becomes e s s e n t i a l  good p r e d i c t i o n s .  is  Bella  and L o r i m e r  indexes  enough  growth of  indexes  predictive  Alemdag (1978),  than c o m p e t i t i o n this  competition  originate  frequently  for from  found  on  lacustrine  Red p i n e  1978).  6 . 0 , bulk  to  centimeter, per with  matter  to achieve  of Natural  northeastern pine  part  (Pinus  Although  1978).  will  this  species  1986).  Resources  found  Red  pine  from brush  on s i t e s  white  a serial  northern  species  and n o r t h e r n on l e s s  New E n g l a n d ,  i n the course  1965;  stands  1978).  pine  Ontario  (Fowells i n Ontario,  In the  (Pinus  stands  with  strobus  (Stiell  or other  Resources  species.  succession  hardwoods. sites.  1986). to  i n t h e Lake o f Jack  However, In e a s t e r n  i t may be r e p l a c e d by s p r u c e ,  of succession.  major  According  establishement  fertile  14  after  i t may be a s s o c i a t e d  to f i r e s  the normal e c o l o g i c a l  pine,  light  i n plantations, natural  subject  c o n s i s t s of the successive  sub-climax  (Stiell  i n hardwood  found  of solar  i s important  Lamb.) and w h i t e  i t i s mostly  i s basically  at a level  (Fowells  cold  1981).  (Rudolf  i n even-aged pure  (Ontario Ministry of Natural  (1965),  pine,  hemlock  Its climatic  1965).  However, t h e s e e d l i n g s do  Lake S t a t e s  banksiana  4 . 5  1 0 t o 4 0 % , and  from  requires f u l l  of i t s d i s t r i b u t i o n ,  persist  disturbances  and  (Fowells  c a n grow w e l l  a n d may o c c a s i o n n a l l y be f o u n d  States  from  1 t o 1 1 m.s.  from  varying  i t s maximum g r o w t h  Quebec, a n d t h e n o r t h e r n  a  content  the s e e d l i n g s  I t i s normally  1965).  Fowells  Stiell  1 . 1 0 t o 1 . 4 0 grams p e r c u b i c  content  grow w e l l when c o m p e t i t i o n  stands  a ph v a r y i n g  capacity varying  silt-plus-clay  as low as 3 5 % ,  stage  Ministry  red  from  with  1981;  (Rudolf  and l o w t o m o d e r a t e p r e c i p i t a t i o n  radiation  L.)  soils  on s o i l s  c a t i o n exchange  Although  Jack  till  i s c h a r a c t e r i z e d by m o d e r a t e l y warm t o warm summers,  winters,  not  grows w e l l  of organic  1.7%  and f i n e  density varying  1 0 0 grams,  regime  this  deposits  pine, i t may be Canada f i r ,  or  The y i e l d stocking. United The  of  red pine  Because  States,  report  of  it  has  several  varies  been w i d e l y  studies  Bassett  with  (1985)  have  various  conditions  stocking.  Several  spacing  trials  1965,  1969,  (e.g.,  1970,  Buckman 1 9 6 2 a , al.  1959;  1962b;  Stiell  1953,  Althen  and S t i e l l  These  1957,  1964,  1970,  1978;  demonstrated  that  resulting  from l a r g e r  spacing  closely  related  to  spacing  (Rudolf  1981;  1977).  Crown w i d t h and l e n g t h  and a c o n i c a l  1978;  Stiell  class  with  a conical  one  crown d e v e l o p m e n t . the  when crown d e v e l o p m e n t found has  to  been  1951). total  be  insensitive  subject  to  While wider s t a n d volume  is to  heavy  1966,  1978; vary  stands  Stiell Full  Height  15  and  the  stem i s  result  from  associated  closer  is  on Berry  very closed  Stiell form  results  are  in  developped  g r o w t h has  ( B e r r y 1969; of  space  considerably  been  e x c e p t when t h e  trees  Von  Diameter  Stiell  c y l i n d r i c a l forms  produce with  growing  ( B e r r y 1970;  (1978)  stand d e n s i t y ,  increases  1977;  crown d e v e l o p m e n t  inhibited.  spacings  1956;  growth  thinning.  The f o r m o f  thinning  et  1978).  diameter  or  can a l s o  stem w h i l e  Heiberg  al.  have  1949;  which i n t u r n depend  f r o m open  1977).  and  Berry  al.  and B e r r y  a c y l i n d r i c a l form w i l l  and B e r r y  form o f  1962,  (Berry 1965).  density;  1980;  a v a i l a b i l i t y of  crown d i m e n s i o n s , Stiell  quality,  Schantz-Hansen  Von A l t h e n e t  the  stands,  site  Bramble et  Stiell  p r o p o r t i o n a l l y with  to  age,  1946;  increases  sensitive  of  R a l s t o n 1954;  initial  productivity.  much i n f o r m a t i o n i n a  1981;  experiments  thinning  its  and t h i n n i n g e x p e r i m e n t s  Bickerstaff  1982;  and  i n b o t h Canada and  B y r n e s and B r a m b l e 1955;  1965,  following  quality,  B e l l a and D e F r a n c e s c h i 1974,  1977;  Lundgren  planted  contains  form f o r  reported  site  addressed  condensed  been  age,  stand  E n g l e and S m i t h  greater  spacings  volume,  (Stiell  and  Berry in  1977).  Bertrand  Ontario  Detailed (1976),  Ministry  This  Bolghari  of  species  g r o w t h and y i e l d  Natural  has  reforestation century  projects  resulted  Because  ability  resist  was  to  considered  as  of  its  had t h e  fifth  1988  (Ontario Ministry in the  sixth  and s e v e n t h  numbers o f  (Ministere products  are  boltwood, Natural  de  of  Natural  plantations  Raile  (1984),  85% o f  the  and i n s e c t for planting  Natural  Resources  seedlings 4.4%  of  in  Resources  planted,  in  large  des  1988) .  Ressources  normally obtained logs,  from  poles,  1986).  16  and p i l i n g  this  soils  were  and it  southern Red p i n e Ontario  number)  In Quebec,  it  respectively 3.2%  1987).  red p i n e :  in  1986).  total  representing  both  plantations  produced i n  the  (1977).  infestations,  i n 1984-1985 and 1985-1986  l ' E n e r g i e et  Resources  to  to  diseases  number o f  seedlings  loghouse  for  found  (1984),  and B e r r y  good p r o d u c t i v i t y on s a n d y  (representing of  used  35  a prime s p e c i e s  (Ontario Ministry  to  where  several  largest  (1986),  Marty  i n M i c h i g a n and W i s c o n s i n e a r l y  Ontario  f r o m 1984  Resources  According  i n areas  red p i n e .  and B e r t a n d ( 1 9 8 4 ) ,  been w i d e l y  Canada and U n i t e d S t a t e s .  i n f o r m a t i o n may be  and  The  came for  4.2%  following  pulpwood,  sawlogs,  (Ontario Ministry  of  CHAPTER 3 DESCRIPTION OF DATA The  data  established  set  used  i n 1953  in this  with  2+2  study  came  transplants  Petawawa  National Forestry Institute.  composed  of  predicted Berry  fine  to  be  24.4  to  1973,  4 . 3 x 4 . 3 m. of  0.101  and  located  was  t h i n n e d to  3.0x3.0  m at  first  Also,  m s p a c i n g was  Every  t h i n n e d to  a subset  to  These this and  data.  T h e s e were  measured e v e r y  are  study.  r e f e r r e d to  Basic  number o f 1 for  as  statistics  trees)  of  each  each v a r i a b l e  the  to  the  30,  measured.  17  are  height  crown from  age  ages  33.  measured d a t a  given  of  detailed  year  and a t  23,  every  crown w i d t h ,  intensively  plot  18,  range  (minimum, maximum, mean, sample  with  total  on w h i c h  and t a p e r  f r o m a g e s 24  plots  identified  Within  height,  trees  Appendix  tree,  DBH, t o t a l  two y e a r s  sample  ages 13,  made:  every  m, and  1965.  spacing.  selected  and  2.1x2.1 m spacing  were  24,  (Stiell  plantation  at  t r e e s were  is  1 . 2 x 1 . 2 m,  representing  sample  13  tree  index  clearly  6.0x6.0 m in  i n diameter w i t h i n every  length,  was  DBH was m e a s u r e d on e v e r y  of  is  deep and  3.0x3.0  and a n o t h e r  trees  is  circular  tree  distribution  measurements  two  t a k e n on e v e r y  the  from s e e d were:  trial  v i c i n i t y of  The s i t e  a plantation with  was m e a s u r e d o n l y on s u b s a m p l e  plot,  age  spacings  4 . 3 x 4 . 3 m i n 1962  While  of  5 spacings,  established.  on a map.  and 3 3 .  The s o i l  m, 2 . 1 x 2 . 1 m, 2 . 4 x 2 . 4 m,  M e a s u r e m e n t s were 28,  50 y e a r s  The i n i t i a l  For the  ha were  i n the  medium w i n d b l o w n s a n d .  1977).  1 . 5 x 1 . 5 m, 1 . 8 x 1 . 8  from a s p a c i n g  in  variance,  in Table  1 of  Several Petawawa  climatic  National  information  the  25 d e g . climatic  different climatic  snowfall,  C ,  months  The f o l l o w i n g  minimum t e m p e r a t u r e , rainfall,  have  Forestry Institute  covering  were e x t r a c t e d .  parameters  for  total  variables  is  given  growth parameters  of  frost.  on T a b l e 2 o f studied  variables.  18  Climatic  September  were  the  inclusive  retained:  mean  mean maximum t e m p e r a t u r e ,  precipitation, days  many y e a r s .  f r o m May t o  mean t e m p e r a t u r e ,  and number o f  variables  been m o n i t o r e d d a i l y a t  will  degree-days  above  10 and  A summary o f  these  A p p e n d i x 1.  The  be  c o r r e l a t e d with  the  CHAPTER 4 STAND DEVELOPMENT STUDY 4.1- I n t r o d u c t i o n Even  though  growth model,  this  new a n a l y t i c a l single-tree are  based  this  (2)  techniques  This  i s not to develop a  c o u l d improve models.  hypotheses  the development o f  The t e c h n i q u e s The s p e c i f i c  proposed  o b j e c t i v e s of  to study  the development  a wide  range  before  and a f t e r  t o examine  to test  to test  of trees  originating  from  o f s p a c i n g s i n t e r m s o f AGR and RGR the onset  i f RGR  reflects  better  than  of competition; the occurrence of  AGR;  t h e major assumption  o f t h e zone o f  concept;  alternative  hypotheses  on p o t e n t i a l  growth.  chapter begins with a l i t e r a t u r e  review  statement  of hypotheses,  o f m a t e r i a l and  methods.  T h i s i s f o l l o w e d by t h e r e s u l t s  which  and  of the study a r e :  influence (4)  that  on m e a s u r e s o f e f f i c i e n c y .  competition (3)  thesis  s t u d y does c o n s i d e r a l t e r n a t i v e  distance-dependent  portion (1)  the goal o f t h i s  i s divided  into  and a d e s c r i p t i o n  t h r e e main p a r t s .  on RGR, a  and d i s c u s s i o n The f i r s t  part  section compares  AGR a n d RGR.in t e r m s o f DBH, b a s a l a r e a , h e i g h t , a n d volume u s i n g the  classical  using  the f u n c t i o n a l  potential  growth  competition. and  approach.  rate  The s e c o n d  approach.  part  compares AGR and RGR  The t h i r d  o f stand-grown  S e v e r a l hypotheses  RGR.  19  part  trees  are tested  addresses the  before the onset of based  upon b o t h  AGR  4.2-  L i t e r a t u r e R e v i e w on R e l a t i v e  Growth  A major c r i t i c i s m of  single-tree  growth models terms  of  is  process  resources  1979).  model  is  1984;  Zedaker et  of to  (Erikson  In o t h e r  stress  to  words,  as  the  suitable  and D i g g l e by a g i v e n that  for  1976;  share  of  Ford Ford  or groups  inheritance,  that  of  age,  plants  that It  differ  or e n v i r o n m e n t a l  Kramer and K o z l o w s k i 1979;  Osteryoung  Cannell  that  its  the  1984; it  measures  may a l s o the  Ledig  1974;  for  the  a  growth measure Hunt  "relative  considered  increment  in i n i t i a l  to  with  1977;  be  (Ford  et  such a  Harper  conditions  of  response  capacity  comparison of  that  type  s h o u l d be e v a l u a t e d  1982,  size".  place)  competition  RGR c o n s t i t u t e s  stated  allows  takes  1984),  felt  in  available  AGR i n t h i s  assessing  characterizes  per u n i t  tool  of  (1981)  1979,  (1975)  resources  an a n a l y t i c a l  1975,  p a r t i t i o n of  (1979,  tree  competition  competition  use  Ford  distance-dependent  represent  conditional  p r o d u c e new m a t e r i a l ) .  1982).  1988;  the  1987),  efficiency  1978,  plants  al.  and F o r d  competitive  (i.e.,  (i.e.,  a p p a r e n t l y not  (1984)  measure  inability  among i n d i v i d u a l t r e e s  (Ford  al.  their  existing  Rate  size,  as  of  genetic  (Buchman and  Benzie  R a d o s e v i c h and  1987).  When e x p r e s s e d  as  a differential  equation,  RGR i s  defined  as: RGR where  W represents  may be d e s c r i b e d  as  the  (Erikson (1987),  1976; it  Hunt  measures  quantity  the  accumulated m a t e r i a l ,  (1/W)(dW/dT)  increase  or  1982).  productive 20  material  at  in material  increase  1978, the  of  per u n i t According capacity  time  T.  adjusted  size to  It by  per u n i t  also  the time  F i t t e r and Hay  independently  of  secondary  processes  s u c h as  RGR may i n d i c a t e even-aged  stand  measurement (Bong.) the  conclude  of  where  1982,  stand,  all  they  competition,  before  substantially  the  trees  decreased  hypothesis the  45 p l a n t s  d i d not  among t h e  their  o r i g i n a l plants  authors  rienced  for  plants  m i g h t have  competition,  were  the  per u n i t g r o w t h as  time.  the  collected  resulting  This  plants  in different RGR m e a s u r e s  r a t i o may a l s o  a percentage.  b a s e d upon compound i n t e r e s t  stress stress. in  In f o r e s t r y , have  is:  21  testing  repens  been  on t h e  L.  Even  is  They though  field,  10  no  compe-  different: a  o n l y when i t  that  of  c o n c l u d e d t h a t RGR  c o u l d have  experiment  be  the  occurrence  a s p e c i e s when t h e r e  collected  to  to  up t o  pots.  w i t h i n a radius of  As p r e v i o u s l y m e n t i o n e d , size  interested  they  sitchensis  them  under h i g h  Trifolium  The  considered  allowed  i n separate  conclusion  selected  s u r r o u n d e d by o t h e r  they  t h o s e u n d e r low also  1981).  (Picea  F o l l o w i n g the  differ,  i n d i v i d u a l s of  i n a young  efficiency  trees  to  were  statistically  when t h e  the  the  48 p l a n t s  However,  p l a n t was  of  (1980)  tition.  cular  competing.  relative  growth of  what  same  w i t h i n a p o p u l a t i o n of  monitored  varies  and a f t e r  had t h e  efficiency  B u r d o n and H a r p e r this  place  and F o r d and D i g g l e  (crown i n t e r l o c k ) ,  started  the  1984  takes  or r e p r o d u c t i o n .  a r e a RGR i n a S i t k a s p r u c e  competition  that  support,  when c o m p e t i t i o n  (Ford basal  Carr.)  onset  point  of  defence,  cm.  partiwas  Therefore,  had a l r e a d y  expe-  RGRs. the  increment  be v i e w e d  as  unit  measuring  growth p e r c e n t  been d e r i v e d .  per  formulas  The g e n e r a l  form  p where or  p is  growth p e r c e n t ,  biomass)  the  end o f  at  beginning  the  formulas based  loped  i n order al.  of  to  that  tree  (Belyea  1959);  material  that  1949;  or  Spurr  is  Husch et  individual  stand  the  some e f f o r t  has  been  easy-to-use  formulas  stands  1959;  Chapman and Meyer  these  studies,  (1980)  forest  approach,  stands  Gottfried  mated g r o w t h p e r c e n t DBH s i z e  in  class  been  to  class.  also  deve-  percent  lies  a geometric adjusted  of  time  rare in  was been  inversely  the  progression  by t h e  amount  growth p e r c e n t  forestry;  of  for  however,  based  Rudolf  related  computed f o r  ratio  of  basal  area per  longer  that  periods  to  tree  of  for  interest  (1971)  periods  esti-  for  acre.  every  basal  Their  w i t h an  time.  size.  interest  a compound  In  Kohmo  p e r i o d i c annual  i n growth p e r c e n t  They p o i n t e d o u t  1930).  a simple  5-year  (Belyea  stands.  on s i m p l e  Also using  area over  22  in  (Chapman and Meyer  G e v o r k i a n t z 1927;  initial  for  growth  and Embry and G o t t f r i e d  in basal  s h o u l d be u s e d  been  time.  d e r i v i n g and/or comparing  in Finland.  to  also  at  of  a p p r o x i m a t e compound i n t e r e s t  i n d i c a t e d a decrease  DBH s i z e  formula  has  1949;  (1978)  size  units  formulas  The c o m p u t a t i o n o f  by c o m p u t i n g t h e  growth per a c r e  results  has  as is  each u n i t  computed g r o w t h p e r c e n t a g e  various  area  percent  growth p e r c e n t  Growth p e r c e n t  have  DBH, h e i g h t , tree  number o f  compound i n t e r e s t  devoted that  (e.g.,  computation of  growth o c c u r s  1982).  or  size  and n t h e  the  increment  trees  tree  100  1952).  added o v e r  al.  x  g r o w t h p e r i o d , Wn t h e  facilitate  1982;  1  on compound i n t e r e s t  The a p p l i c a b i l i t y o f fact  Wo t h e  growth p e r i o d ,  Other  (Husch et  \/(Wn/Wo) -  increase  interest  Avery  (1971)  Gottfried predict stand good  growth  five  growth p e r c e n t  growth p e r c e n t  or stands  stand  RGR a l s o interest.  age.  t o compare  plants  Husch e t  extrapolating a  t o Chapman and Meyer  as a b a s i s  the s o c i a l  relatively  (1949),  i tinvolves  rate.  the actual  p r o c e d u r e was c o n s i -  for determining i f  However, status  t h e growth o f d i f f e r e n t  growth o c c u r s  be u s e d t o  p r e d i c t i o n s may be  remains  According  may be u s e d  presumes t h a t  that  This  because  However, i t d i f f e r s  postulating  could  by Chapman and Meyer  grow a t a d e s i r e d  o r t o compare  Resulting  considered.  known t o d e c r e a s e w i t h  and Embry and  a h e a d by m u l t i p l y i n g  growth p e r c e n t  (1952)  and S p u r r  u s e d much a s a t o o l a  that  t o be i n a p p r o p r i a t e  (1949), trees  that  or t e n years  f o rthe period  (1982),  ratio  Gottfried (1978),  volume by i t s g r o w t h p e r c e n t .  constant  al.  mentioned  i f i t i s assumed  dered  (1983),  and B u r k h a r t  i t h a s n o t been of trees  within  stands.  accumulate  b i o m a s s a t compound  from growth p e r c e n t a t a continuous  f o r m u l a s by  rate.  The b a s i c  equation i s : RGR x ( T n - To) Wn = Wo x e The  first  derivative of this  previously 4.3-  Hypotheses  appropriate stands.  mentioned  t h a n AGR f o r a s s e s s i n g  Even  (e.g.  forestry trees  r e s u l t s i n t h e RGR e q u a t i o n  stated.  Many o f t h e s t u d i e s  time  formula  though  Blackman  t o study  the concept 1919),  stand  above  suggest  competition  that  i n even-aged  o f RGR h a s e x i s t e d  i t has been used  only  for a long  recently i n  d y n a m i c s and draw c o n c l u s i o n s  i n t e r a c t (Buchman a n d B e n z i e  23  1988).  RGR i s more  Besides  on how  the studies  mentioned  above,  o f C a n n e l l e t a l . (1984)  those  are worth mentioning. al.  (1987)  not  been performed  Except  f o r the s t u d i e s o f Brand e t (1988),  a n d B r a n d a n d Magnussen u s i n g a wide  Some h y p o t h e s e s  be  both  tition. and  time,  Furthermore,  stand  same d a t a The  first  hypothesis  same RGR b e f o r e data  this  start  following tition,  (1982,  If major  varying.  one w i l l  need t o  o f compe-  h a s been made t o compare  tree  t h a t o f AGR u s i n g t h e  i ti s .  the f i r s t  estimate  simplified.  be t e s t e d i s b a s e d  of competition. 3,  Before  to tree size:  (1981) have t h e  the spacing  be p o s s i b l e t o o b s e r v e  i s true several years  hypothesis  a stand  Using  i t will  on t h e  and D i g g l e  a l l trees comprising  be c o n s i d e r e d .  t r e e growth  impact  before  the onset o f  the l a t e r  t h a t RGR  i s rejected,  then the  the onset  thebigger  T h i s i m p l i e s t h a t both  o f compe-  the tree, the  AGR a n d RGR  similarly.  hypothesis  i s not rejected,  on t h e d e v e l o p m e n t As t h i s  type  of single-tree  i t c o u l d have a distance-dependent  o f model u s e s open-grown t r e e  the p o t e n t i a l  growth  of individual  t r e e g r o w t h w o u l d be c o n s i d e r a b l y  r a t e o f stand-grown  However, i f i t i s f o u n d  same RGR b e f o r e  relative  and long-term  the onset  1984) and F o r d  I f this  RGR i s r e l a t e d  computation  the  o f study has  t o RGR s t i l l  Also, the greater the spacing,  growth models. to  the onset  hypothesis  more e f f i c i e n t describe  and a f t e r  that w i l l  d e s c r i b e d i n Chapter  competition. should  type  set.  t h a t was d i s c u s s e d a b o v e :  whether  related  i n t e r m s o f RGR w i t h  main c o n c l u s i o n o f F o r d  trial  before  no a t t e m p t  development  this  range o f s p a c i n g s  remeasurement d a t a . t e s t e d over  (1985)  and P e r r y  the onset  trees, the  t h a t a l l t r e e s do n o t have  of competition,  to the estimation of thep o t e n t i a l  24  data  other  growth  hypotheses rate of  stand-grown  trees  be c o n s i d e r e d .  from t h e growth r a t e o f open-grown t r e e s  First  will  o f a l l , i t becomes i m p o r t a n t t o t e s t t h e  m a j o r a s s u m p t i o n i n many s i n g l e - t r e e d i s t a n c e - d e p e n d e n t g r o w t h models:  the p o t e n t i a l increment of a stand-grown t r e e  i n terms  o f AGR i s e q u a l t o t h a t o f a n o p e n - g r o w n t r e e o f t h e same diameter  (Ek a n d M o n s e r u d  hypothesis w i l l  1975;  L o u c k s e t a l . 1981).  a l s o be t e s t e d u s i n g RGR:  increment o f a stand-grown t r e e  This  the p o t e n t i a l diameter  i n t e r m s o f RGR i s e q u a l t o t h a t  o f a n o p e n - g r o w n t r e e o f t h e same d i a m e t e r . A f u r t h e r s e t o f h y p o t h e s e s e m p h a s i z e s age w i t h  some  adjustment f o r s i z e : - The p o t e n t i a l d i a m e t e r i n c r e m e n t o f a s t a n d - g r o w n tree  i n t e r m s o f AGR i s e q u a l t o t h a t o f a n  o p e n - g r o w n t r e e o f t h e same a g e , b u t a d j u s t e d by the  respective  diameters of both types of trees:  AGRn = AGRo X (DBHn/DBHo) w h e r e AGRn a n d AGRo a r e t h e AGRs o f t h e s t a n d - g r o w n and o p e n - g r o w n t r e e s a n d DBHn a n d DBHo respective  diameters at breast  their  height;  - The p o t e n t i a l d i a m e t e r i n c r e m e n t o f a s t a n d - g r o w n tree  i n t e r m s o f RGR i s e q u a l t o t h a t o f a n  o p e n - g r o w n t r e e o f t h e same a g e , b u t a d j u s t e d b y the  respective  diameters of both types of trees:  RGRn =• RGRo X (DBHn/DBHo) w h e r e RGRn a n d RGRo a r e t h e RGRs o f t h e s t a n d - g r o w n and o p e n - g r o w n t r e e s  respectively;  - The p o t e n t i a l d i a m e t e r i n c r e m e n t o f a s t a n d - g r o w n tree  i n t e r m s o f AGR i s e q u a l t o t h a t o f a n  o p e n - g r o w n t r e e o f t h e same a g e , b u t a d j u s t e d by 25  its  efficiency: AGRn - ( R G R n / R G R o ) [ t - 1 ]  This  e q u a t i o n i s based  stand-grown last  The  last  assumption  period.  o f the future  s e t o f hypotheses  - The p o t e n t i a l  diameter  i n terms  ratio  of both  i s based  increment  tree  o f RGR i s e q u a l t o t h a t  i n terms  increment  d a t a used  f o rthis  and  tree  DBH and b a s a l  volume.  of the d i f f e r e n t  and J a r v i s  basal  (1963)  predicting Smalian's  o f an and a g e .  DBH, b a s a l  increment  a r e a were b o t h  relationships  that  For instance,  Lorimer  diameter formula.  measured e v e r y  of basal  results with  from  initial  increment. D a t a were  4 feet  area, height, analysed  they d e s c r i b e ( 1 9 8 3 ) and  obtained higher correlations  i n terms  obtained better area  stand-grown  i n d e x e s and AGRs when c o m p e t i t i o n f r o m  t r e e s was e x p r e s s e d (1983)  size  populations of trees.  competition  and a g e ;  s t u d y were d e s c r i b e d i n t h e p r e v i o u s  a n a l y s e d were:,  Steneker  o f an  a n d Methods  The v a r i a b l e s  within  stand-grown  of a  o f t h e same d i a m e t e r  chapter.  because  RGRs.  of a  diameter  total  t o be a good  on t h e o r i g i n a l  The p o t e n t i a l  Material The  I t i s assumed  o f t h e same d i a m e t e r  open-grown t r e e 4.4-  obtained a t the  o f AGR i s e q u a l t o t h a t  open-grown t r e e -  o f RGR o f  (1964):  o f Newnham  tree  on t h e r a t i o  a n d open-grown t r e e s  increment  estimate  X R G R o [ t ] X DBH.  (1.23  area  rather  relationships  diameter  between  surrounding t h a n DBH.  West  predicting  than with  those  T r e e v o l u m e s were computed u s i n g from  m).  26  trees  that  had t h e i r  stem  Two methods were u s e d t o  describe  t r e e growth:  approach  (Hunt 1 9 7 8 ,  4.4.1  Classical The  the c l a s s i c a l  approach and t h e f u n c t i o n a l  1982).  Approach  classical  approach c o n s i s t s o f computing  f r o m t h e mean o f two s u c c e s s i v e measurements involves  the a n a l y s i s of data  put  on t h e c o m p a r i s o n  the  ratios  period  i n a discrete  o f growth v a l u e s  derived describe  growth  (Hunt 1 9 8 2 ) . manner.  at fixed  t h e mean g r o w t h  rates It  Emphasis i s  points  r a t e over  i n time; t h e time  considered.  If W(i) represents  a given dimension,  f o r i n s t a n c e DBH, a t  t i m e T ( i ) , t h e n AGR i s computed a s : AGR - (W(2) Relative  growth  plots  a t every  analyses  t o compare  -  compared w i t h A nested  -  Single  classification  a n d volume were  means o f i n d i v i d u a l  DBH c l a s s e s o b t a i n e d  spacings  into  analysed,  i t s DBH.  This procedure  s i z e s w i t h i n any s p a c i n g .  27  These  1 cm DBH c l a s s e s .  c o n s t i t u t e d t h e DBH n e s t i n g f a c t o r  mine w h e t h e r o r n o t RGR was s i g n i f i c a n t l y  were  t o compare AGR and  A t each growth p e r i o d  subdivided  analysis of variance.  different  performed.  1981).  ( S o k a l and R o h l f  spacings.  v a l u e s were t h e n  T(l)}.  f r o m t h e two sample  t r e e h a d i t s AGR and RGR a s s o c i a t e d w i t h  increment  nested  data  a n a l y s i s o f v a r i a n c e was u s e d  RGR f o r t h e d i f f e r e n t every  f o r DBH, h e i g h t ,  Tukey's t e s t  T(l)}.  from:  the spacings,  were s i g n i f i c a n t ,  -  In W(l)} /{T(2)  s p a c i n g were merged.  of variance  When t h e s e  W(l)} /{T(2)  rate i s obtained  RGR - { I n W(2) In o r d e r  -  was u s e d  different  The  o fthe  to deter-  f o rtrees of  I f t h e DBH n e s t i n g  factor  was  not  significant  significantly the of  " a l l the  competition" were  performed  the  onset  important following  hypothesis  spacings  before  trees  c o u l d not  be  of  the  have  competition,  onset  the  same  rejected.  the  statistical  package  became  competition,  RGR b e f o r e  Means f o r  compared w i t h T u k e y ' s t e s t .  using  of  but  These  "BIOME"  the  the  then onset  individual  analyses  were  ( S o k a l and R o h l f  1981) . In o r d e r to closure  have  i n d e x was  computed f o r  crown d e v e l o p m e n t (Stiell the  1970;  following  occupies (i.e.  at  an a p r i o r i  of  red pine  Stiell  least  78% o f  [[crown w i d t h ]  p r o p o r t i o n of  This  is  degree  the  However,  progression  of  4.1).  spacings These  closure  but  it  later  at  the  and age  by s t a n d  the  by t h e  space]  rather  was  it  trees  with  that  index  age,  expected  and (2)  spacings.  28  this  indicate  and  crown c l o s u r e  will  square. the  crowns  that show  age.  determined  trends:  it  reflected  had o v e r l a p p i n g crowns  c o m b i n a t i o n s were the  then  a p r a c t i c a l way t o spacing  tree  spacing  p r o p o r t i o n of  considered  b a s e d upon  x 100),  does not  the  density  crown b a s e on a  The crown c l o s u r e  because  data displayed  wider  area of  a  because  The i n d e x was  square d e f i n e d  crown c l o s u r e  increasing with  and age  o c c u p y i n g more t h a n 78% o f  The p r o p o r t i o n s o f various  the  the  index  overlapping,  may do s o .  if  crown c l o s u r e ,  much a f f e c t e d  1977).  crowns.  trees  an i m p e r f e c t of  is  of  spacing  x n /4]/growing  2  overlap with adjacent the  every  and B e r r y  principle:  idea  (1)  for  (Table crown  occurring  the  Table  4.1:  Proportions  of  trees  their  as  spacing.  defined  by t h e  growing  their  space  area  13  14  15  16  17  18  19  20  21  22  23  24  26  28  30  1 .2x1 .2  65  67  76  87  98  98  98  100  93  86  89  94  90  96  93  1 . 5x1 .5  75  79  74  75  84  92  93  95  93  93  93  93  93  89  87  1 .8x1 .8  62  62  66  65  83  86  89  93  93  91  84  81  79  81  76  2 .1x2 .1  43  56  50  58  69  75  80  87  85  87  80  86  88  82  88  2 .4x2 .4  31  53  52  62  62  72  76  78  91  95  91  89  96  88  88  3 .0x3 .0  5 25  27  46  56 68  83  86  95  90  93  91  97  97  97  4 . 3x4 .3  0  0  2  2 12  16  21  47  58  66  86  88  93  93  0  0  0  0  0  1  6 20  73  84  97  The e f f e c t examined height)  0  tivity  of  over  age.  (1987),  of  crown  tree  vigor  that  closure  takes  place  occurs,  trees  have  canopy  closes,  smaller  the  their  ratio  live  to  is  start  the  (crown (1984)  the  also  to  1986).  Before  dying  along  crown  the  from below.  be  produca  measure  crown  closure  stem.  When  The h i g h e r  takes p l a c e .  r a p i d l y crown r a t i o  29  and  photosynthetic  considered  crown r e c e s s i o n more  and S p r i n z  o c c u r r i n g when  all  also  length/tree  changes  branches  faster  tree,  Farrar  reflects  (Holdaway  branches the  to  Crown r a t i o relates  on i n d i v i d u a l t r e e s was  crown r a t i o  According  a tree.  density,  0  crown c l o s u r e  by c o m p u t i n g  Burkhart  the  have  Age  6 . 0x6 .0  stand  that  crown o v e r l a p p i n g  Spacing  of  (%)  would  the the  Normally,  decrease.  It  is  a p p r o p r i a t e to  competitive  status  because  the  to  (1)  crown d i m e n s i o n s and  growth of  (3)  (2)  different  there  and t r e e  the  study  red pine  above-ground  the  crown d e v e l o p m e n t  stand d e n s i t y ,  1977),  of  is  of  on t h e  competition  seven groups w i t h 39%,  40  to  percent  of  trees  ages a r e  the  59%,  shown  Stiell  studied  unaffected  by t h e  logical crown pine are  because  ratio trees  of is  generally  not  70  for  crown t r e e The f i r s t  every  necessarily  at  d i r e c t e d upward ( S t i e l l  around  River.  soil  of  these  i n Chapter  3,  several  been m o n i t o r e d d a i l y a t many y e a r s .  relation using the  the  10  to  was  to  This  and  several  assumed  trees  of  that  trees  limit  This  25  The  is imply a  young  and t h e  red pine  24%,  100%.  necessarily  level  into  red  branches  l i m i t was trees  also  located  had a crown r a t i o  of  85%.  As m e n t i o n e d  for  between and B e r r y  that  open-grown  1962).  Several  9%,  branches  d e t e r m i n e d by s u r v e y i n g y o u n g o p e n - g r o w n around Chalk  It  does not  the  Stiell  spacing  crowns.  whorl of  sensitive  classified  and 85  g r o w i n g as  other  very  competition.  1 o f A p p e n d i x 2.  of  ratio  l i m i t e d more by  0 to  84%,  the  relationship  t r e e s were  to  is  suggests  is  limits:  >85% were  a full  site  all  classes  presence  100%.  of  69%,  i n these  crown r a t i o  (1970)  in  crown  1970;  than below-ground  55 t o  trees with  (Stiell  changes to  red pine  a very close  following  in Figure  the  spacings  of  diameter  The crown r a t i o v a l u e s  to  associate  the  to  the  Petawawa  The f l u c t u a t i o n s  c l i m a t i c parameters  National Forestry  i n g r o w t h d a t a were  these v a r i a b l e s .  A principal  c o v a r i a n c e m a t r i x as  i n p u t was  importance of  every  component  variability. 30  institute examined  analysis  performed to  c l i m a t i c v a r i a b l e on  have  determine  year-to-year  in  4.4.2-  F u n c t i o n a l Approach  The  f u n c t i o n a l approach i n v o l v e s f i t t i n g (Hunt 1 9 8 2 ) .  observations  over  time  nuous n a t u r e  o f growth.  loping mechanistic interact matical  the o b s e r v a t i o n s  The  lations,  sets of mathematical  values  equation)  of  may be e x p r e s s e d  compare d i f f e r e n t  time,  matheequation)  t o represent  1982):  (1)  large  as c o n c i s e mathematical  and (3)  the value  sets  formu-  o f a growth  i t becomes r e l a t i v e l y  easy t o  sets of observations.  Because t h e data used f o r t h i s  context,  equations)  that  increment.  i t i spossible to evaluate  r a t e a t any p o i n t i n time,  over  but for forming  main a d v a n t a g e s a r e (Hunt 1978,  (2)  models  o f t h e phenomenon u n d e r i n v e s t i g a t i o n , a n d  instantaneous  of o b s e r v a t i o n s  i s n o t f o r deve-  (e.g., Chapman-Richards  or e m p i r i c a l (e.g., p o l y n o m i a l  deriving  utility  t o simulate a n a t u r a l system), functions (mechanistic  to a set of  E m p h a s i s i s on t h e c o n t i -  i t s primary  models ( i . e . ,  a curve  study  consist of observations  the f u n c t i o n a l approach appears a p p r o p r i a t e .  i t s use i m p l i e s t h a t a curve  under i n v e s t i g a t i o n ,  i sfitted  In this  f o r every  tree  that i s : W - f(T).  where W r e p r e s e n t s is  a growth v a r i a b l e l i k e  d e r i v e d by f i n d i n g  the f i r s t  D e r i v i n g a RGR e q u a t i o n the  that i s :  ln(W)  31  The AGR  d e r i v a t i v e o f a growth  involves f i r s t  s e l e c t e d growth v a r i a b l e ,  DBH.  - f(T).  fitting  equation equation.  the logarithm of  The RGR e q u a t i o n i s t h e f i r s t The 1.8  f u n c t i o n a l approach  m, 3 . 0  derivative of this  o f DBH a t a g e s 13  t o DBH f o r t h e 1 . 2  was a p p l i e d  m, a n d 6 . 0 m s p a c i n g s . a n d 33 were  equation.  Ten t r e e s c o v e r i n g t h e r a n g e  s e l e c t e d w i t h i n e v e r y sample  B e c a u s e o f t h e s h a p e o f t h e c u r v e s w i t h i n t h e age r a n g e , to reduce used.  t h e amount o f c o m p u t a t i o n ,  T h i s approach  comparison  of competition, a l l the curves  onset  of competition.  s h o u l d be s i m i l a r up t o t h e  the study of the e v o l u t i o n of the s o c i a l  p o s i t i o n of the trees,  c u m u l a t i v e i n c r e m e n t s , AGRs a n d RGRs o f  s a m p l e t r e e w i t h i n a p l o t were  t h e l o w e s t v a l u e s a t a g e s 13  and 3 0 .  ranked  from  For each  the highest to  plot,  r e n c e b e t w e e n t h e r a n k s a t b o t h a g e s was c o m p u t e d T h e n , t h e mean f o r a p l o t was c a l c u l a t e d . trees, rank  inverted, from  The c l o s e r  t h e same r a n k . different 4.4.3-  t o 0,  The c l o s e r  tree.  o f 10  i s 5.  rank  Thus, t h i s  totally index  varies  t h e more t h e t r e e s t e n d t o k e e p  t o 5,  t h e more t h e t r e e s t e n d t o have  ranks.  Estimating the Potential  T h i r t e e n open-grown the s p a c i n g t r i a l . Krajicek  f o r every  For a t o t a l  I f a l l t h e t r e e s have t h e i r  t h e mean c h a n g e i n r a n k  0 to 5.  the d i f f e -  i s 0 i f t h e y a l l k e e p t h e same  t h e mean c h a n g e i n r a n k  a t both ages.  o f b o t h AGR  I f t h e t r e e s have t h e same RGR b e f o r e t h e  onset  every  and a l s o  d i s p l a y of the evolution of the s o c i a l  p o s i t i o n of the trees.  To f a c i l i t a t e  plot.  p o l y n o m i a l f u n c t i o n s were  allowed a temporal  and RGR, a n d i m p r o v e d  m,  (2)  t r e e s were m e a s u r e d  o f Stand-grown  Trees  i n the v i c i n i t y of  The s e l e c t e d t r e e s met t h e s p e c i f i c a t i o n s o f  e t a l . (1961):  competition,  Growth Rate  (1)  c r o w n d e v e l o p m e n t was u n a f f e c t e d by  c r o w n r a t i o was e q u a l o r n e a r l y e q u a l t o o n e , 32  (3)  the  crown,  location and (4)  factors  breast  Increment  This  in  cores  following  growth  were  the  the  methods  of  the  4.3  m and 6 . 0  not  subject  rent  to  hypotheses,  open-grown upon t h e  tree  every that  hypothesis  C o m p a r i s o n s were and s t a n d - g r o w n one-  spacings test.  It  increment  was  at  of  tested)  those  same  for  ages. tree  and t h e i r  periods.  periods  possible because  to the  data  years.  33  the  evaluation  to  of  the  growth  were  selected  17 and 16  to  22  very  likely  the  diffe-  with  an  o r RGR ( d e p e n d i n g  increments of  trees  compared.  open-grown  m and 6 . 0  same  their  associated  The o n e - y e a r  use  and  estimating  For t e s t i n g  was  cm)  as  recons-  t r e e s were  increment 4.3  (15  such  (1963).  trees  13  the  natural  ones  was  before  These  compared w i t h o p e n - g r o w n not  the  trees  by  and by  Von A l t h e n  DBH, a g e ,  both the  caused  tree  rings,  from a g e s  made between t h e trees  every  l i m i t e d to  stand-grown  base of  stump h e i g h t  The s t a n d - g r o w n  had t h e  and f i v e - y e a r were  of  crown c l o s u r e .  competition  the  o r by a r t i f i c i a l  stand-grown  m spacings  before  at  defects  taken at  s t u d y was  rate  of  annual growth  r e d u c e d by c o m p e t i t i o n .  respectively,  for  an a b s e n c e  The g r o w t h h i s t o r y  p a r t of  potential  b r a n c h e s was  infestations  by m e a s u r i n g t h e  bark widths  was  longest  was  insect  height.  tructed  the  there  s u c h as  pruning.  of  m spacings  increments using  test  covered only  trees  for  a  for  and both  Student the  five-year  1 p e r i o d of  five  4.5-  Results  4 . 5 . 1 -  and D i s c u s s i o n  Classical  Approach  DBH a n d B a s a l A r e a  4 . 5 . 1 . 1 -  C u m u l a t i v e I n c r e m e n t i n DBH  4 . 5 . 1 . 1 . 1 -  No s i g n i f i c a n t and  Development  d i f f e r e n c e i n mean DBH was f o u n d a t a g e s 1 3  1 4 among a l l s p a c i n g s  a t age 1 5 .  f i c a n t differences occurred be  an anomaly.  4 . 2 ; Figure  (Table  The 1 . 2 m s p a c i n g  ficantly  from i t .  trends  existing  This  before  as s p a c i n g  not d i f f e r  significantly  Some r e s u l t s o f t h i s reported  by S t i e l l  update t h i s  and B e r r y  information  to particular  Also,  t r i a l have a l r e a d y Table  4.2  been  and F i g u r e Stiell  concluded  t h a t t h e d i a m e t e r g r o w t h r a t e was d e c r e a s i n g  reduction  i n the area  f o r each t r e e .  These  correspond  t o what has been g e n e r a l l y o b s e r v e d :  increased,  t h e mean d i a m e t e r  Clutter Korstian  increases  (Avery  et a l . 1 9 8 3 ; Daniel et a l . 1 9 7 9 ;Evert 1962).  that  i n s i z e w i t h age.  f r o m age 2 3 t o age 3 3 .  available  diffe-  groups of spacings  became s m a l l e r  (1977).  signi-  From age 1 6  was e n l a r g e d .  w i t h age:  spacing  were  d i d not d i f f e r  a n o m a l y may be a t t r i b u t e d  r e n c e s became more a c c e n t u a t e d did  two s p a c i n g s  the onset of competition.  o n w a r d s , DBH i n c r e a s e d  different  from t h e 2 . 1 m and 3 . 0 m  than t h e 4 . 3 m one, they  larger  signi-  However, t h i s a p p e a r s t o  E v e n t h o u g h t h e means o f t h e l a t t e r  slightly  Some  was n o t s i g n i f i c a n t l y  f r o m t h e 4 . 3 m o n e , b u t was d i f f e r e n t ones.  4 . 1 ) .  4.1  and B e r r y with a results  as s p a c i n g i s  and B u r k h a r t  1983;  1 9 7 1 ; Tourney a n d  These f i n d i n g s a r e a l s o c o n s i s t e n t w i t h t h e  r e s u l t s of red pine  spacing  DeFranceschi  1 9 8 0 ) ,  (1974,  trials  r e p o r t e d by B e l l a and  Bramble e t a l . 34  (1949),  B y r n e s and  TABLE  4.2:  Mean DBHs  Spacing (m) 1.2x1.2  Mean  Mean N  1.8x1.8  Mean N  2.1x2.1  Mean N  2.4x2.4 U) Ul  Mean N  3.0x3.0  Mean N  4.3x4.3  Mean H  6.0x6.0  Mean H  *: **:  for a l l spacings  over  age. Ages  13  N 1.5x1.5  (cm)  14  15  16  17  19  20  21  22  7.915 a 61  8.352 a 61  8.821 a 61  9.292 a 59  9.514 a 59  23  24  26  28  33  12.073 a 45  13.454  5.428 * 65  4.802 a 64  5.858 a 66  6.651 ab 66  7.498 ab 65  8.318 ab 62  8.940 ab 62  9.593 ab 61  10.238 ab 61  10.690 ab 60  11.005 ab 59  11.322 ab 58  11.684 a 57  11.937 a 57  12.287 a 56  12.687 a 55  13.211 a 54  4.825 a 59  6.122 a 60  7.103 ab 60  8.119 abc 59  8.978 abc 58  9.591 abc 58  10.507 be 58  11.223 be 57  11.763 be 57  12.063 be 57  12.321 be 57  12.612 ab 57  12.954 ab 57  13.739 ab 54  14.119 ab 54  14.506 a 54  4.967 a 58  6.329 a 61  7.377 b 62  8.576 be 62  9.544 bed 61  10.339 be 61  11.261 be 61  12.064 cd 61  12.702 cd 61  13.353 cd 60  13.824 cd 59  14.414 be 58  14.862 b 58  15.495 b 57  16.161 be 56  17.111 b 54  4.654 a 55  6.159 a 56  7.328 ab 58  8.810 be 58  9.965 cd 58  10.852 cd 58  12.078 cd 58  13.198 de 58  14.124 d 58  14.876 d 58  15.428 d 58  16.209 c 57  16.951  17.653  57  57  18.304 c 57  19.216 b 56  5.004 a 54  6.729 a 55  9.575 10.934 d d 59 59  12.053 d 59  13.655 d 58  15.071 f 58  16.264 17.214 e e e 58 58  18.110 d 58  19.041  20.271  21.348  22.233  23.359  58  58  58  58  58  4.743 a 54  6.137 a 57  8.742 be 57  9.959 cd 58  11.303 cd 58  13.133 d 58  14.979 ef 58  16.471 e 58  17.837 e 57  19.143 e 56  20.636 d 56  22.680  24.446  25.875  27.521  56  56  56  56  10.786 d 96  12.612  14.122  16.198  18.371  20.196  21.803  23.416  25.267  28.310  30.631  32.390  34.724  96  95  95  95  94  94  94  94  94  94  94  94  -  -  7.995 b  e 58 7.052 ab 59  T h e s p a c i n g s f o r a g i v e n age f o l l o w e d by t h e N u a b e r o f t r e e s t h a t were l e i s u r e d . A t ages  s a a e l e t t e r do n o t d i f f e r 13 and 1 4 , t h e t r e e s t h a t  9.927 10.440 11.121 11.615 a a a a a 55 52 48 46  30  4.434 a 64**  -  5.927 6.787 7.495 a a a a 66 63 61  18  s i g n i f i c a n t l y at the l e v e l of had not r e a c h e d b r e a s t h e i g h t  37  p r o b a b i l i t y of 0 . 0 5 . were n o t m e a s u r e d .  F I G U R E 4.1: M E A N D B H s F O R A L L S P A C I N G S O V E R A G E  TOTAL  36  AGE  Bramble  (1955),  4.5.1.1.2-  Lundgren  Absolute  Mean AGR f o r spacing  (Tables  occurred very 4.3 to  at  close  slight  onset the  of  3.0  until  than  that  these  tables.  closures there  was  cings  at  1.2  a g e s 13  competition  thus  appears  13  to  start  had n o t  by Newnham (1964) (Pseudotsuga for  for  Menziesii  Sitka  denser  situation  took  small are the  difference  yet  This  can o v e r l a p  (Mirb.)  4.3 m  m spacing to  they  were  indicated the  at  on b o t h  high  among t h e  two  i n any o f  ages the  spa-  suggests  spacings. before  a l r e a d y been of  noted,  difference  some d e g r e e  dense p l a n t a t i o n  crown  crown  previously  these  to  not  earlier  showed  reported  Douglas-fir  F r a n c o ) , and by C o c h r a n e and  spruce.  37  was  30.  significant  phenomenon has  a young,  mean AGR o f  1.5  i n diameter  taken place  the  the  as was  spacings  the  the  also  of  before  for  that  the  attributed  that  stands  The a b s e n c e  AGRs t h a n  stands  stand,  However,  trend  a g e s and  may be  place,  with  this  older  f r o m a g e s 26  densest  15.  crowns  competing.  so  to  had g r e a t e r  among t h e  classes  and l a r g e s t  that  and a t  mean AGR o f  were  The t h r e e  and 14.  closest  This  m spacing  the  no s i g n i f i c a n t  among t h e  (1978)  the  case,  Crown c l o s u r e  from ages  m spacing  existed  differences  occurred.  spacings  16.  increased  Exceptions  reduced w e l l , below  second of  generally  As c o m p e t i t i o n  T h e y show t h a t  closure  trees  age  that  m s p a c i n g was In the  area  Figure 4.2).  The 3 . 0 the  (1956).  Rate  a g e s and wide  spacings.  significant.  It  4.4;  competition.  However,  that  4.3,  differences  spacing. lower  Growth  and S c h a n t z - H a n s e n  DBH and b a s a l  early  m spacing  (1981)  Ford  Table 4.3: Mean AGRs i n DBH (cm/year) f o r every spacing over age. Spacing  13  1.2x1.2  1.05 $*  1.5x1.5  16  17  18  19  20  21  22  23  24  26  28  30  0.67 0.66 $ $  0.57 #  0.42 #  0.44 #  0.47 #  0.29 #  0.22 #  0.21 #  0.21 #  0.13 #  0.17 #  0.17 #  0.15 «  1.20 $  0.79 0.79 $ $  0.63 $  0.62 $  0.56 #  0.64 #  0.33 #  0.19 #  0.20 #  0.24 #  0.13 #  0.13 #  0.15 #  0.14 #  1.8x1.8  1.38 $  0.98 0.95 0.77 0.61 $ $ $ $  0.79 #  0.71 #  0.54 #  0.30 #  0.26 #  0.29 $  0.17 $  0.19 $  0.19 $  0.13 $  2.1x2.1  1.59 &  1.14 &  1.19 &  0.88 &  0.79 $  0.92 $  0.80 $  0.64 «  0.51 $  0.32 #  0.40 $  0.22 #  0.24 #  0.25 $  0.21 #  2.4x2.4  1.58 +  1.36 &  1.48 &  1.15 $  0.87 $  1.22 $  1.12 $  0.93 $  0.75 #  0.55 #  0.59 #  0.37 #  0.35 #  0.32 #  0.24 #  3.0x3.0  1.87  1.58 +  1.72 +  1.36 1.12 & . &  1.46 $  1.41 $  1.19 *  0.95 «  0.87 #  0.93 #  0.61 #  0.54 #  0.44 #  0.37 «  1.64 <  1.25 <  1.55 <  1.36  1.34  1.83  1.85  1.49 +  1.35 &  1.32 &  1.49 $  1.02 #  0.88 #  0.71 «  0.55 #  -  -  -  1.82 <  2.17 1.81 < <  1.61 <  1.61  1.85  1.52  1.16 $  0.88 $  0.78 «  >  4.3x4.3 6.0x6.0  14  15  >  >  1.55 <  >  2.07 <  >  >  >  >  *: Crown closure classes: (Proportion of trees whose crowns occupy more than 78% of the square spacing). (%)  0 1 21 41 61 86  : < - 20: > - 40: + - 60: & - 85: $ - 100: #  2 Table 4.4: Mean AGRs in basal area (cm /year) for every spacing over age. Spacing  13  14  15  16  17  18  19  20  21  22  23  24  26  28  30  1.2x1.2  8.53 $*  6.24 $  7.17 $  7.18 #  5.54  t  6.53 #  7.48 #  5.05 #  4.13 #  4.02 #  4.22 #  2.79 #  3.65 #  3.81 #  3.51 #  1.5x1.5  10.52 $  8.10 $  9.58 $  8.53 $  9.08 $  8.95 #  11.17 #  6.18 #  3.82 #  4.06 #  4.86 #  2.75 #  2.89 #  3.34 #  3.16 *  1.8x1.8  12.30 10.48 12.05 11.09 $ $ $ $  9.55 $  13.40 13.14 10.68 * # #  6.49 #  5.77 #  6.57 $  4.11 $  4.59 $  4.76 $  3.47 $  2.1x2.1  15.04 &  12.79 15.88 13.39 13.12 16.83 16.02 13.96 11.79 & & & # $ $ $ $  7.69 #  10.04 $  5.90 #  6.51 #  6.78 $  6.34 #  2.4x2.4  14.57 +  15.17 19.64 17.58 14.99 22.63 23.13 20.71 17.98 13.86 & & # # $ $ $ $ $  15.55 #  10.29 10.27 # #  9.93 #  7.44 #  3.0x3.0  18.09  19.17 24.67 22.59 20.50 29.96  27.57  19.24  >  4.3x4.3  +  +  &  &  32.64 29.51 25.47 24.87 $  $  #  #  #  15.27 14.17 20.99 21.11 23.42 36.11 40.57 37.26 36.11 37.97 < < < > > > > + & &  6.0x6.0  -  34.33 33.03 49.61 59.14 54.55 52.86 <  <  <  <  <  <  56.96 >  >  #  46.42  #  17.89 15.47 13.77 #  #  34.81 32.91 28.49 23.25 $ # # # #  70.36  63.89  >  $  53.72 $  43.59 41.12 #  *: Crown closure classes: (Proportion of trees whose crowns occupy more than 78% of the square spacing). (%) 0 1 21 41 61 86  -  : 20: 40: 60: 85: 100:  < > + & $ #  #  4.2:  FIGURE  DBH AGR DATA SUPERIMPOSED CLIMATIC VARIABLES  0  AVERAGE AOB (DBH) FOR ALL SPACINOS OVER A G E  o a o  •  — — — —  LEOCNP 1-2 X 1 2 1 .5 X 1.9 •* 1 . 8 X i a a.i X 2. 1 a.* X 2 . 4 3 . 0 X 3.0 *.3 X + .3 e.o X e.o  M M M M M M M M  JO  33  30  33  24.0 22.4 JO  cd  LS  UJ  SEP  .O,  o1— 3  8  1 9.2  A O o  LEGEND — MEAN MAXIMUM TEMPERATURE — MEAN MINIMUM T E M P E R A T U R E — MEAN TEMPERATURE  1 7.S 1 S.O 1 4.4 1 2.8 11.2 9.6 8.0  1 2  1 S  1 8  21  21  24  TOTAL  40  AGE  27  F I GURE 4 . 2 :  (CONT I NUED)  33  o  TOTAL A G E  41  LEGEND — MAY JUNE — S I P T t M iem  The  absence  of competitive stress  a t a g e s 13 and 14  ponded  t o a s t a g e where t h e m a j o r i t y o f t r e e s  had crown  values  g r e a t e r than  2).  of  85% (Figure  83 i n t h e 1.2 m s p a c i n g had a crown  age  13.  later  However, e i g h t  and two had crown  ratios  1 4 , 13 t r e e s  had crown  one  o r two y e a r s  later,  ratio  ratios  had crown  F i v e were  s i x o f the remaining  trees  had crown  o n l y some t r e e s  ratios  were a f f e c t e d Despite  by  lower  lower  than  that  80%.  ratios  The f a c t  irregularities,  mean DBH AGR  (Figure  4.2).  probably  not caused  that  than  o n l y some the e f f e c t i n f e r i o r or  Also,  tended  to decrease  These  fluctuations  amplitudes  suggest  factors  that  can s u b s t a n t i a l l y  to year.  Climatic  factors  such  as t e m p e r a t u r e  fluctuate  yearly  c o u l d be a s s o c i a t e d near  with  1980).  certain  the study  Figure 4.2).  42  site  were  t h e same p a t t e r n s were  the i r r e g u l a r  ( S p u r r and B a r n e s  over  I n c r e a s e s c a n , however, be  by c o m p e t i t i o n b e c a u s e  common t o a l l s p a c i n g s .  yearly  lower  t h e y were g e n e t i c a l l y  a t a g e s 1 5 , 1 8 , 19 and 2 3 .  monitored  spacings  85% does n o t suggest  observed  tions  dead  two had crown  For a l l the other had crown  At  injuries.  f o r a l l spacings  variations  years  85%.  competition, but rather  time  two o r t h r e e  85% a t  than  and t h e y were a l l g r e a t e r t h a n  trees of  two a g e s ,  than  o f 8 4 % and 8 1 % r e s p e c t i v e l y .  o f 7 8 % and 7 9 % r e s p e c t i v e l y .  these  ratio  Ten t r e e s out  lower  r a n g i n g b e t w e e n 8 1 % and 8 5 % , and t h e o t h e r  ratios  85%  ratio  o f t h e s e were d e a d  age  at  1 o f Appendix  corres-  vary  from  year  a r e known t o  The g r o w t h  climatic  o f the  fluctua-  variables  (Table 2 o f Appendix  1;  A principal years  into  overall  component  relatively  fluctuations  analysis  indicated  in  the  first  (Table  4.5).  two  pitation  above  pitation total  associated  with  99 p e r c e n t  the  most  C and 25 d e g .  Increases increase  slight  (Figure small  4.2).  ratures, 10 d e g . total in  C.  precipitation.  decreased  first  10 d e g .  is  group,  above  the  one  two  on t o t a l C for the  shown  preci-  both number o f  in Figure  mean v a l u e s  10 and 25 d e g . increased  4.3,  the  C are  i n the  number o f  a g e s 18 and 23  4.3.  for  for  preci-  given.  While  d i r e c t i o n of degree-days  the  above  corresponded with a  i n degree-days increase  above at  age  the  this  increase  year  Even i f  was there  T h i s was  remeasurements  year,  15 c o r r e s p o n d e d t o and mean  i n degree-days  were  substantial after  made e v e r y  age  AGRs  two y e a r s ,  a  tempeabove  c h a r a c t e r i z e d by a d e c l i n e  p r o b a b l y because  43  previous  large  10 and 25 d e g . C  p r e c i p i t a t i o n and d e g r e e - d a y s  regularly.  computed from  on t h e  The  included  first  groups having s i m i l a r v a l u e s  a substantial  However,  both t o t a l  above  growth.  i n the  i n mean maximum, mean minimum,  and t o  of  C decreased.  The s l i g h t  increase  the  v a r i a t i o n was  p r e c i p i t a t i o n compared t o  decreases  determine  high loadings  components  For each  i n AGR a t  in total  the  i m p o r t a n t v a r i a b l e was  precipitation generally  10 d e g .  focused  the  given  those  75 p e r c e n t  showed  two  into  and d e g r e e - d a y s  the  to  group  C.  first  1 and 2.  of  degree-days  two a r r o w s drawn on F i g u r e  but  with  analyses  25 d e g .  aggregated  components  most  components,  The t h i r d  A graph of A g e s were  helped  The e i g e n v a l u e s  components. degree-days  technique  that  and number o f  conditions,  This  Therefore,  components.  was u n d e r t a k e n t o  similar climatic  variability.  climatic  analysis  in  fluctuations 24, AGR were  averaging  out  Table 4 . 5 :  Summary o f t h e p r i n c i p a l component a n a l y s i s taken with the c l i m a t i c v a r i a b l e s . Eigenvalue  Principal Principal Principal Principal Principal Principal Principal Principal  component component component component component component component component  1 2 3 4 5 6 7 8  Proportion  8427.11 2859.52 10.26 6 31 3 76 0 09 0.03 0.00  0.74529 0.25289 0.00091 0.00056 0.00033 0.00000 0.00000 0.00000  under-  Cumulative 0 74529 0 99819 0 99910 0 99966 0.99999 1 00000 1 00000 1 00000  Eigenvectors Principal Variables  I  Number o f d a y s o f f r o s t i n J u n e Number o f d a y s o f f r o s t i n S e p t e m b e r Mean maximum t e m p e r a t u r e ( D e g . C.) Mean minimum t e m p e r a t u r e ( D e g . C.) Mean t e m p e r a t u r e ( D e g . C.) Total precipitation (mm) Number o f d e g r e e - d a y s a b o v e 10 Deg. C, Number o f d e g r e e - d a y s a b o v e 25 Deg. C,  44  0.008281 0.002471 •0 006115 -0 001522 -0.003681 0.904307 -0.426204 -0.021259  component II -0.009532 -0.017230 0.004309 0.008304 0.006405 0.426652 0 903793 0 024705  FIGURE 4.3: PNFI WEATHER DATA FROM 1961 TO 1982 GRAPH OF THE FIRST TWO PRINCIPAL COMPONENTS  -250  -192  -133  -75  -16  43  101  160  FIRST C O M P O N E N T  *: Rainfall precipitations Means of each group.  (mm), and degree-days above 10°C and 25 °C.  45  the  annual  results in  effect  suggest  of  comparable to the  long  a certain  degree-days  Even  18  spacing of  23,  and  minimum  decreased  climatic  intensity Few and  become a l i m i t i n g  of  (1974,  with  magnitude  of 1976,  the  on  (1978).  red  pine  factors.  AGR  and  climatic  the  s u b j e c t may  1982).  data  found  with  as  of  though  the  spacing  diminished  at  as  t h a t the i n f l u e n c e increase i n  and the  that precipitation  between  of the  above  Kozlowski daily  the  radial  results  may  growth of growing  variables.  more c l o s e l y  Complete and  and  related  growth  correlate  (1982)  (1975)  f o r a complete  was  stand  studies that  i n Bednarz  1 9 environmental  Fritts be  Braekke  made et  38-year-old season, They to  and  also  stem  temperature.  3 0 are  and  basal area  two  level-nested analyses  was  fluctuation  well  of  Even  independently  relationships  Wisconsin  and  normally  number  as  that,  have been more p o p u l a r .  be  They measured  f o r DBH  Tables  i n degree-days  factor.  decreases  Comparisons  24,  in  the  Dendrochronological  simultaneously monitored  than  fluctuations  competition.  i n Northern  concluded  by  these  t h e y were n o t  This suggests  mean AGR  s t u d i e s of Braekke  al.  growth  of  s t u d i e s have e x a m i n e d  width  reviews  occurred  case,  This suggests  i s maintained,  (Figure 4 . 2 ) .  factors  climatic  ring  the  mostly  fluctuations  i n mean AGR.  same p a t t e r n s o f v a r i a t i o n ages  the  In any  in precipitation,  variation  does not  i s affected  though  to those  related as  conditions.  t h a t mean AGR  precipitation.  were  climatic  1  cm  DBH  d i s p l a y e d i n F i g u r e s 4 . 4 and  4 . 6 and  4.7.  i n c l u d e d i n the  impossible  by  of v a r i a n c e  For  to e l i m i n a t e with 46  However, data  a t ages 1 3 ,  18,  4.5.  The  of  ( a n o v a ) on AGR  a g i v e n age,  anova.  class  a l l the  results are  spacings  listed were  i f heteroscedasticity  transformation,  the  FIGURE  4.4:  DBH  A G R s AS A F U N C T I O N SIZE CLASS  FIGURE 4 . 4 . 1 : AGE 13  DBH  FIGURE 4 . 4 . 2 : AGE 18  2.20i  2. 30  2.03  2.07  1 .86  1.84  — y  <  OF  K LSI* \1.J8 1 O 1.15  •^1.522 O —^1.35-  /  w  «  /  >  I CD  Q 0.92  LEGEND SPACING: 1.2X1.2 SPACING: 1.5X1.5 SPACING: 1.8X1.8 SPACING: 2.1X2.1 SPACING: 2 . 4 X 2 . 4 SPACING: 3 . 0 X 3 . 0 SPACING: 4 . 3 X 4 . 3  0.50  —•—i—1—i—•—i—•  4  3  6  i  ^0.69 0.46  M M M M M M M  0.23  o . o o  —r~  7  10  8  i .62 i . 44 1 . 26  A = * = 0 7 * * o  a  >- I .08 \ 1 o  = = = =  A  /  LEGEND SPACING" 1.2X1.2 SPACING 1.5X1.5 SPACING 1.8X1.8 SPACING 2.1X2.1 SPACING 2 . 4 X 2 . 4 SPACING 3 . 0 X 3 . 0 SPACING 4 . 3 X 4 . 3 SPACING 6 . 0 X 6 . 0  = = = = = =  M M M M M M M M  - I — i — i — • — i — ' — r  6  8  10  12  14  18  18  20  DBH SIZE CLASS (CM) FIGURE 4 . 4 . 4 : AGE 3 0  FIGURE 4 . 4 . 3 : AGE 2 4  LEGEND SPACING: 1 . 2 X 1 . 2 SPACING: 1 . 5 X 1 . 5 SPACING: 1 . 8 X 1 . 8 SPACING: 2.1X2.1 SPACING: 2 . 4 X 2 . 4 SPACING: 3 . 0 X 3 . 0 SPACING: 4 . 3 X 4 . 3 SPACING: 6 . 0 X 6 . 0  / J / <rV  a * « 0 7 . * o  1  DBH SIZE CLASS (CM) 1.80  .*/ k / '' y T * ' / /  0.870 M M M M M M M M  0. 783  i  ;\/  /V *  t  A  /<  V /^  v A  /  ^0.90  I CO  Q0.72 \X ^0.54  i'M  , f\  0.36 0. 18  0.000^  0.00^;  7  V V  A= • = «= 0= 7= • * = o=  LEGEND SPACING: 1.2X1.2 M SPACING: 1.5X1.5 M SPACING: 1.8X1.8 M SPACING: 2.1X2.1 M SPACING: 2 4 X 2 . 4 M SPACING: 3 . 0 X 3 . 0 M SPACING: 4 . 3 X 4 . 3 M SPACING: 6 . 0 X 6 . 0 M  J4  DBH SIZE CLASS (CM)  DBH SIZE CLASS (CM)  47  38  FIGURE 4 . 5 : BASAL AREA AGRs AS A FUNCTION OF DBH SIZE CLASS FIGURE 4.5.1: AGE 13  FIGURE 4.5.2: AGE 18  36.0 32.5  29.0 tr  25.5  71.0  LEGEND = SPACING: 1.2X1.2 M = SPACING: 1.5X1.5 M = SPACING: 1.8X1.8 M = SPACING: 2.1X2.) M = SPACING: 2.4X2.4 M = SPACING: 3.0X3.0 M = SPACING: 4.3X4.3 M  A 0 0 0 7 . *  63.9  56. 8  tr  3  49.7  >-  \ CN  \  22.0  CN  * *  18.5  LEGEND A = SPACING: 1.2X1.2 M * « SPACING: 1.5X1.5 M G = SPACING: 1.8X1.8 M 0 = SPACING: 2.1X2.1 M 7 = SPACING: 2.4X2.4 M • = SPACING: 3.0X3.0 M ft = SPACING: 4.3X4.3 M o - SPACING: 6.0X6.0 M  42.  /  O 35.  / /  /  M*  r  / ,r  f  <28.  m  1.0  -1— —r1  2  3  -1—•—i—•—r-  4  5  8  7  8  9  10  DBH SIZE CLASS (CM)  DBH SIZE CLASS (CM  FIGURE 4.5.3: AGE 24  FIGURE 4.5.4: AGE 30  87.0 78.3 69.8  tr  y  50  LEGEND A = SPACING: 1.2X1.2 M * = SPACING: 1.5X1.5 M *= SPACING: 1.8X1.8 M 0 = SPACING: 2.1X2.1 M 7 = SPACING: 2.4X2.4 M . = SPACING: 3.0X3.0 M * = SPACING: 4.3X4.3 M o = SPACING: 6.0X6.0 M  45 40  l\J  339  v  LEGEND 4-SPACING: 1.2X1.2 M * = SPACING: 1.5X1.5 M $= SPACING: 1.8X1.8 M 0 = SPACING: 2-1X2.1 M V = SPACING: 2.4X2.4 M * = SPACING: 3.0X3.0 M * - SPACING: 4.3X4.3 M o = SPACING: 6.0X6.0 M  i  \  /8 /  \ •  »  2 o 43.3  /i  25  K  < 34.8 CD  *  *  /  i  /1 ' I  /;  < 20 GO  tr 26. 1  / |  /  / V i. / 1 1  < 10  17.4 8.7  0.0 10  13  20  10  25  14  18  22  26  30  DBH SIZE CLASS (CM)  DBH SIZE CLASS (CM) 48  34  38  Table Age  4 . 6 : T w o - l e v e l n e s t e d anova Spacings  included  (m)  tests  DBH c l a s s D.F.  13 13 14 14  15 16  16 17  18  19 20  20  21 21  22 22  23  23  24 24  26  26 28  30 30  f o r AGR i n DBH ( c m / y e a r ) .  1. 2 ; 1 . 5 ; 1 . 8 ; 3 . 0 2 . 1 ; 2 .4,-4 .3 1. 2 ; 1 . 5;1 . 8 ; 2 . 1 ; 2 . 4 ; 3 . 0 2 . 1 ; 2 • 4;3 . 0 ; 4 .3 1. 2 ; 1 . 5 ; 1 . 8 ; 2 . 1 ; 2 • 4;3 . 0 1. 2 ; 1 . 5 ; 2 • l ; 3 . 0 ; 4 . 3 ; 6 . 0 1. 2 ; 1 . 5;1 . 8 ; 2 . 1 ; 2 . 4 ; 3 .0 All 1 . 2 ; 1 . 5 ; 1 . 8 ; 2 . 1 ; 2 • 4;3 . 0 ; 6.0 all 1. 2 ; 1 . 5 ; 1 . 8 ; 2 . 4 ; 6 . 0 1 . 8 ; 2. 1 ; 3 • 0 ; 4 . 3 1. 2 ; 1 . 5 ; 1 . 8 2 . 1 ; 2 • 4;3 . 0 ; 4 . 3 ; 6 . 0 1. 2 ; 1• 5 ; 1 . 8 ; 2 . 1 ; 2 . 4 ; 3 .0 4 . 3 ; 6 .0 1. 2 ; 1 . 5;1 . 8 ; 2 .1 2 . 4 ; 3. 0 ; 4 . 3 ; 6 . 0 1. 2 ; 1 . 5 ; 1 . 8 ; 2 . 1 ; 2 . 4 ; 3 .0 2 . 4 ; 4 . 3; 6 . 0 1. 2 ; 1 . 5 ; 1 . 8 ; 2 . 1 ; 2 . 4;3 . 0 2 . 1 ; 2 . 4;4 . 3;6 .0 all 1. 2 ; 1 . 5 ; 1 .8 2 . 1 ; 2 • 4;3 . 0;4 . 3 ; 6 . 0  F  29/205 4 .49* 22/142 4 .77* 5 5 / 3 0 1 2 .76* 37/187 4 .25* 60/299 4 .61* 65/325 5 .03* 64/289 5 . 0 0 * 92/412 4 .21* 81/363 100/401 61/262 53/177 37/135 70/252 84/255 27/121 51/169 55/206 83/246 38/166 85/237 56/204 110/357 41/101 73/240  * : S i g n i f i c a n t d i f f e r e n c e s at the n . s . : no s i g n i f i c a n t difference.  49  level  4 .28* 5 .01* 3 .72* 1 .81* 5 .96* 2 .60* 4 .12* 2 .08* 4 .89* 1 .39* 4 .61* 1 .25* 5 .02* 2 .49* 2 .88* 5 .68* 1 .73*  Spacing D.F.  F  3/26 2/20 5/44 3/32 5/52 5/58 5/57 7/79  33 .72* 0 . 08n 53 .02* 7 .74* 35 .38* 55 . 0 1 * 27 .04* 68 .86*  6/70 7/89 4/51 3/40 2/34 4/53 5/71 1/19 3/46 3/30 5/72 2/19 5/7 4 3/40 7/110 2/36 4/44  164 .52* 90 .84* 163 . 7 1 * 63 .07* 1 .08* 91 . 0 0 * 40 . 3 9 * 16 . 6 7 * 2 .89* 171 . 0 9 * 32 . 9 7 * 399 .92* 20 .08* 146 . 9 0 * 75 . 9 3 * 0.lln 139 . 5 5 *  of p r o b a b i l i t y of 0 . 0 5 .  Table 4.6:  (Continued). Comparison of mean AGRs among the spacings. Tukey's multiple range tests Spacing (m)  Age  13 13 14 14 15 16 16 17 18 19 20 20 21 21 22 23 23 24 24 26 26 28 30 30  1.2  1.5  1.8  1 .052a* 0 .670a 0 .663a 0 .575a 0 .575a 0 .420a 0 .438a 0 .469a 0 .295a 0 .220a 0 .209a 0 .211a 0 .132a 0 .166a  1 .201ab 0 .794ab 0 .795ab 0 .632ab 0 .632a 0 . 622ab 0 .557ab 0 .644ab 0 •335ab 0 .198a  1 .378b 0 .982bc 0 .954bc 0 .772ab 0 .614ab 0 .791bc 0 .716ab 0 .540b 0 . 540a 0 .300a 0 .258a 0 •291ab 0 .171a 0 .187a 0 .189a 0 .129a  —  0 .170a 0 .148a —  —  0 .203a 0 .246a 0 .126a —  0 .132a 0 .152a 0 .136a —  —  2.1 —  1 . 589a 1 .138c 1 .138a 1 .198cd 0 .882b 0 .882b 0 .795bc 0 .921c 0 .803b 0 .638a —  0 .512 0 .317a 0 .403b 0 .224a  2.4  1 .872 — 1 . 584a 1 . 357 1 .584 1 . 357ab 1 .584b 1 .483de 1 .721e — 1 • 359c 1 .155c 1 • 359c 0 .886cd 1 .119de 1 .226 1 .466 1 .121 1 .416 — 0 .926 — 1 .193 —  0 .752a 0 .552 —  0 .591 0 .371 — 0 . 371 0 .238ab 0 . 351b 0 .238 0 . 351 0 .247ab 0 .325bc —  0 .212a  3.0  —  0 .241a  —  0 .950a 0 .897 —  0 .931 0 .615 —  0 .539 —  0 .442c —  0 .375  4.3 1 .641a —  1 .250a —  1 .359c —  6.0 — — — —  1 .824 —  1 . 345ef 1 • 555f — 2 .076 1 .846 2 .173 — 1 .809 — 1 .809 —  1 .351 — —  1 .493 —  1 .022 —  0 .883 0 .714 —  0 .549  —  1 .607 —  1 .851 —  1 .521 1 .161 0 .879  0 .778  *: the spacings for a given age followed by the same l e t t e r do not d i f f e r s i g n i f i c a n t l y at the l e v e l of p r o b a l i l i t y of 0.05.  50  Table  4.7:  T w o - l e v e l n e s t e d anova t e s t s ( cm  Age  Spacings  /year).  included  (m)  DBH c l a s s D.F.  13 14 15 16 17 18 19 20 20 21 21 22 23 24 26 28 30  all all all all all all all 1. 2; 1 2 .1; 2 1. 2 ; 1 2 .1; 2 all all all all all all  f o r AGR i n b a s a l  area  2  . 5 ; 1 .8 .4;3 .0;4 . 3; 6 .0 . 5 ; 1 .8 • 4;3 • 0;4 . 3; 6 . 0  51/347 64/347 71/344 86/418 92/412 93/408 100/401 35/138 67/257 37/135 70/252 111/376 106/375 107/370 110/360 110/357 114/341  F 49 32 31 28 25 32 19 9 5 9 5 6 5 6 5 5 4  .39* .24* .48* .99* .98* .43* .63* .18* .71* .81* .86* .64* .18* .33* .95* .35* .19*  Spacing D.F. 6/51 6/6 3 6/7 0 7/84 7/90 7/91 7/97 2/33 4/60 2/35 4/62 7/111 7/106 7/107 7/110 7/110 7/114  *: S i g n i f i c a n t d i f f e r e n c e s a t t h e l e v e l o f p r o b a b i l i t y n . s . : no s i g n i f i c a n t d i f f e r e n c e  51  F 1 3 4 12 17 27 37 3 44 0 60 152 164 215 157 79 142  . 26n .61* .17* .10* .05* .18* .39* .25* .75* .89n .89* .15* .04* .13* .25* .51* .53*  of0.05.  Table 4.7: (Cont'd). Comparison of mean AGRs between the spacings. Tukey's multiple range tests Spacing (m)  Age 1.2 14 15 16 17 18 19 20 20 21 22 23 24 26 28 30  1.5  6.240a* 8.105a 7.186a 9.577ab 7.182a 8.529ab 5.545a 9.085ab 6.531a 8.948ab 7.485a 11.170ab 5.050a 6.181a 4.074a 4.063a 4.216a 4.861ab 2.795a 2.746a 3.801ab 2.968a 3.809a 3.344a 3.658a 3.192a  1.8  2.1  2.4  3.0  4.3  10.477ab 12.055abc 11.092abc 9.554ab 13.401abc 13.142abc 10.683a 5.773a 6.568ab 4.109a 4.592ab 4.761ab 3.552a  12.794ab 15.882abc 13.391abc 13.122abc 16.831bcd 16.025abc 13.961a 11.788a 7.758a 10.045b 5.906ab 6.512ab 6.779ab 6.356a  15.166ab 19.642bc 17.585bc 14.993bc 22.627cde 23.128cd 20.715ab 17.976ab 13.859 15.547 10.288b 10.275b 9.935bc 7.442a  19.168b 24.669c 22.599cd 20.503c 29.961de 32.643de 29.506bc 25.475b 24.872 27.569 19.237 17.893 15.470c 13.768  14 .165ab 20 .999bc 21.112cd 23 .419cd 36. l l l e f 40.571e 37.259c 36.111 37.979 46.418 34 .812 32 .907 28 .491 23 .304  6.0 34 .327d 33 .035d 49.612f 59.137 54 .554 52.865 56.961 70.362 63 .899 53.716 43.597 41.124  *: the spacings for a same age followed by the same letter do not differ significantly at the level of probalility of 0.05.  a n a l y s e s were p e r f o r m e d between the variances. test  for  nesting  Bartlett's  cates  that  trees  of  (DBH) was  different  spacings  2.1  spacings. 13  for  for  DBH AGR i s  (Table these  4.2). two  down i n t o ficant  because  the  spacing may be  analysis  seemed t o  differences  of  A t age  spacings, These  the the  14,  basal  differed  the  2.1  among  age  13  between three all  ages  not  differences  spacings  and the  four  m, and 3 . 0 m with with  first  the the  results  c a s e were to  4.3 m  30,  just  the  accentuated. among s p a c i n g s  a r e a AGR ( T a b l e  4.7).  A t age  two  narrowest  an a n o m a l y b e c a u s e  the  4.3  were o b t a i n e d 14,  spacings.  m spacing  two n a r r o w e s t 53  signi-  three  incompatible  i n the  at  were b r o k e n  the  spacings  f o r DBH  tests  However,  From a g e s 16  spacings  differences  from the  range  when a n a l y s e d  necessarily  13 and 14  obtained  when a n a l y s e d  from the  significantly  the  i n DBH AGR  ages  multiple  m, 2.4  different  significance.  between the  at  results  group of  b u t were n o t  are  calculated of  to  indi-  found at  occur mainly w i t h i n  and between t h i s  No s i g n i f i c a n t for  for  significantly  level  differences  13  significant  4.6).  only.  area, This  at  were  (Table  spacing  age  differences  2 groups  closest  used  30 between t h e  the  were  the  age  because  spacings.  age.  ages e x c e p t  a g e s may be d i f f i c u l t  largest  above  every  differences  m and a t  The i n t e r p r e t a t i o n  spacings  three  all  i n c o n t r a d i c t i o n with  closest  was  a r e a AGR.  of  differences  spacings  at  Significant  The p r e s e n c e  at  Significant  m and 4.3  basal  1981)  a r e a AGRs v a r i e d s i g n i f i c a n t l y  sizes.  2.4  homogeneous  F o r b o t h DBH and b a s a l  were o b t a i n e d  m,  with  and R o h l f  significant  DBH and b a s a l  among s p a c i n g s  except  (Sokal  heteroscedasticity. factor  closest  test  spacings  d i d not  spacings.  The  the  at  3.0 m  However,  this  differ relatively  high  f o r the 3.0 m spacing  value  probably than  r e s u l t e d from a p a r t i c u l a r  the e f f e c t  between not  differ  the  groupings  accentuated.  significantly  that  instead  o f diameter  as  reported  (1963) ,  bigger  was p o s i t i v e l y  increases  as c o m p e t i t i o n  and  1984;  variation size  and  In g e n e r a l ,  These and  Mithen  i n AGR w i t h  the l a t e r results  Cannell  based  i n basal  (1983),  results  area among t r e e s ,  Steneker  and J a r v i s  e t a l . 1984; DBH s i z e  into  Spurr  class  t o those even  into  and B a r n e s  a l l DBH i n AGR w i t h t h e AGR,  dominance c l a s s e s by F o r d  their  two r e m e a s u r e m e n t s and o n l y  occurred.  (1979,  observations  a single  Long  1980), the  Also,  the greater  reported  though  classes  1975;  (Ford  to substantial reductions  the s t r a t i f i c a t i o n  the  and 4 . 5 ) .  dominance  increased.  the l a r g e r the spacing,  correspond  of the t r e e s :  t h e AGR ( F i g u r e s 4 . 4  becomes more i n t e n s e  e t a l . (1984)  on o n l y  rates  o f the f o r e s t  c l a s s e s became s u b j e c t  age.  that did  contradictory  c o r r e l a t e d t o the s i z e  the s t r a t i f i c a t i o n  Smith  of spacings  (1983) .  the t r e e , the greater  Because  the d i f f e r e n c e s  the p a t t e r n o f v a r i a t i o n  by t h e s t u d i e s o f Lorimer  a n d West  AGR  changes  o f growth  rather  a g e s were n o t t h e same as  These a p p a r e n t  the computation  spacing  a t young a g e s  The g r o u p i n g s  a t the various  f o r DBH AGR.  suggest  trend  From age 1 5 ,  of competition.  spacings  to the 4 . 3 m  compared  stand  1984) were density  level. 4.5.1.1.3-  R e l a t i v e Growth  Although increase AGR  with  (Tables  spacings  Rate  t h e r e were some e x c e p t i o n s , spacing,  4.8  mean RGR t e n d e d t o  b u t n o t as markedly as t h e c o r r e s p o n d i n g  and 4 . 9 ;  had n e a r l y equal  Figures values  54  4 . 6 and 4 . 7 ) . a t ages 1 3 ,  The f i r s t two 15,  16,  20,  24,  26,  Table 4.8: Mean RGRs i n DBH (cm/year/cm) for every spacing over age. 13  Spacing  14  15  16  17  18  19  20  21  22  23  24  26  28  30  1.2x1.2  .2509 .1349 .1123 .0809 .0551 .0499 .0502 .0293 .0200 .0180 .0178 .0103 .0132 .0124 .0100 # # # # # # # # # # # # $ $* $  1.5x1.5  .2513 .1444 .1166 .0807 .0723 .0579 .0616 .0299 .0173 .0168 .0205 .0096 .0105 .0113 .0099 # # # # # # # # # # $ $ $ $ $  1.8x1.8  .2965 .1701 .1337 .0922 .0679 .0789 .0652 .0457 .0228 .0189 .0213 .0117 .0125 .0125 .0085 # # * # $ $ $ $ # $ $ $ $ $ $  2.1x2.1  .3215 .1893 .1643 .1022 .0834 .0862 .0677 .0490 .0377 .0214 .0264 .0141 .0143 .0147 .0117 & & & & # # # # * $ $ $ $ $ $  2.4x2.4  .3322 .2247 .2056 .1350 .0907 .1142 .0913 .0692 .0523 .0364 .0369 .0219 .0196 .0185 .0128 + & & # # # # * # $ $ $ $ $ *  3.0x3.0  .3565 .2370 .2191 .1496 .1086 .1229 .1028 .0811 .0587 .0534 .0515 .0320 .0264 .0205 .0166 + + & & > # # # # # # # # $ $  4.3x4.3  .3313 .2063 .2109 .1598 .1426 .1662 .1484 .1010 .0854 .0763 .0793 .0492 .0386 .0290 .0208 + & & < > > > > < < # # # # $  -  6.0x6.0  -  -  .1613 .1213 .1428 .1299 .0969 .0985 .0731 .0776 .0575 .0397 .0280 .0233 < < < < < < > > > * $ $  *: Crown closure classes: (Proportion of trees whose crowns occupy more than 78% of the square spacing). (%) 0 1 21 41 61 86  : - 20: - 40: - 60: - 85: - 100:  < > + & $ #  2 2 Table 4.9: Mean RGRs i n basal area (cm /year/cm )for every spacing over age. Spacing  13  14  15  16  17  18  19  20  21  22  23  24  26  28  1.2x1.2  .5018 $*  .2698 $  .2245 $  .1618 *  .1102 «  .0998 ft  .1005 #  .0577 #  .0483 #  .0390 ft  .0349 #  .0205 #  .0283 ft  .0248 ft  .0226 ft  1.5x1.5  .5027 $  .2887 $  .2333 $  .1614 $  .1446 $  .1157 #  .1231 #  .0597 #  .0340 #  .0337 ft  .0411 ft  .0191 ft  .0211 ft  .0228 ft  .0200 ft  1.8x1.8  .5929 $  .3402 $  .2673 $  .1845 $  .1359 $  .1576 #  .1304 ft  .0913 ft  .0458 ft  .0379 ft  .0427 $  .0233 $  .0251 $  .0252 $  .0157  2.1x2.1  .6429 &  .3787 &  .3284 &  .2043 &  .1669 $  .1724 $  .1354 $  .0765 #  .0741 $  .0449 ft  .0529 $  .0278 ft  .0286 ft  .0295 $  .0234 ft  2.4x2.4  .6644 +  .4494 &  .4112 &  .2699 $  .1817 $  .2285 $  .1826 $  .1383 $  .1046 #  .0726 ft  .0737 #  .0439 ft  .0391 ft  .0348 ft  .0258 ft  3.0x3.0  .7131 >  .4741 +  .4381 +  .2994 &  .2171 &  .2457 $  .2055 $  .1621 #  .1174 #  .1068 ft  .1030 ft  .0641 ft  .0528 ft  .0411 ft  .0331 ft  4.3x4.3  .6626 <  .4126 <  .4219 <  .3196 >  .2850 >  .3324 >  .2969 >  .2019 +  .1707 &  .1527 &  .1586 $  .0984 ft  .0770 #  .0578 ft  .0418 ft  6.0x6.0  -  -  -  .3226 <  .2426 <  .2856 <  .2599 <  .1939 <  .1569 <  .1461 >  .1553 >  .1151 >  .0795 $  .0562 $  .0466 ft  *: Crown closure classes: (Proportion of trees whose crowns occupy more than 78% of the square spacing).  (%)  0 1 21 41 61 86  : < - 20: > - 40: + - 60: & - 85: $ - 100: ft  30  S  FIGURE 4.6: MEAN DBH RGRs FOR ALL SPACINGS OVER AGE 0.3701  13  16  19  22 TOTAL AGE  57  25  28  31  FIGURE 4.7: MEAN BASAL AREA RGRs FOR ALL SPACINGS OVER AGE LEGEND SPACING: 1.2X1.2 SPACING: 1.5X1.5 SPACING: 1.8X1.8 SPACING: 2.1X2.1 SPACING: 2.4X2.4 SPACING: 3.0X3.0 SPACING: 4.3X4.3 SPACING: 6.0X6.0  T  13  1  1  I  I  M M M M M M M  |—I—I—1—I—1—|—i—i—I—1—I—|—1—I—I—I  16  22  19  TOTAL AGE  58  1  |—I—I—I—I  25  1  1—I—I  28  1  1—I—|-  31  28,  and 3 0 .  The 3 . 0 m s p a c i n g had g r e a t e r  spacing u n t i l than  trends the  4.3  the  were  stands  18  before  and 2 3 .  closely  in  have  (Table  4.5  at  age  decrease  amplitudes  The  of  these  These  RGR.  results  that  growth  18  of  the  trends  diminished with  nested  anovas  and no s u i t a b l e  broken i n t o  class each  factor  for  was  differences  significant;  factor  the  4.9.1  at  age  and 4 . 1 0 . 1 ) .  14.  range  listed  test  failed  In b o t h c a s e s ,  59  in  the  4.10  a  found,  the  variances.  with  tree  Even though  to  spacing.  in Tables  However,  significant  and  reduction  statistically  RGR d e c r e a s e d  above  f o r AGR, t h e  homogeneous vary  by  10,  above  a decrease  and 4 . 1 1 ) .  s p a c i n g was  multiple  of  most  followed  problems o c c u r r e d at  RGR d i d n o t 4.10  was  slightly  t r a n s f o r m a t i o n was  groups  (Tables  (Figures  the  limit),  13  age  spacing  value the  at  area,  are  in  degree-days  degree-days  observed  (Figure  and 2 3 .  rainfall  While  for ages  increases  corresponded with a  also  age,  b o t h DBH and b a s a l  o c c u r r e d at  fluctuations,  4.2).  particular  were  among  w i t h age  a g e s 18  total  and 2 3 ,  As was  fluctuations  existed  climatic variables  i n mean RGR a t  When h e t e r o s c e d a s t i c i t y  spacings  Increases  and mean maximum t e m p e r a t u r e s  15. of  that  between s u b s t a n t i a l  and 4 . 1 1 .  spacings  differences  and 4 . 7 ) .  ages  As w i t h AGR, t h e s e  mean RGR d e c r e a s e d  and F i g u r e  at  mean minimum,  the  19.  to  value  competition.  indicated  with  C decreased  increased  4.6  and i n c r e a s e s  analyses  degree-days  mean,  of  a correspondance  associated  25 d e g .  slight  some f l u c t u a t i o n s ,  rainfall  Previous  to  onset  (Figures  17  from a g e s  P l o t t i n g DBH RGR d a t a w i t h  showed  total  the  6 . 0 m s p a c i n g had a l o w e r  and t h e  p r o b a b l y due  spacings  4.8)  15,  age  m spacing  Despite all  the  4.3 m  RGRs t h a n t h e  (but  among  t h e DBH size  for  the "F"  very close  detect  absence  For  of  to  significant significant  FIGURE  4.8:  DBH RGR DATA SUPERIMPOSED ON CLIMATIC VARIABLES  A V E R A G E  R O R  S P A C I N O S  ( D B H ) O V E R  F O R  A L L  A O E  A O  —  2  M  X 1  5  1 .0  X 1  M M  2.1 2 . 4  X 2 X 2  S 1  — —  3 . 0  —  c  —  o  —  -  L E G E * I D i a x 1 1 . 5  —  —  M  4  M  o  M  4 . 3  X 3 X 4  3  M  8 . 0  X S  O  M  SO  33  2 4 . 0  2 2 . 4  2 0 . 8  O O =>  1 9 . 2  O O  _  ^  i«.o  ^  ^  1 4 . 4  3  1  — M E A N — M E A N — M E A N  L E G E N D M A X I M U M T E M P E R A T U R E M I N I M U M T E M P E R A T U R E T E M P E R A T U R E  1 7 . 6  &  ^  i i  A O o  2  -  8  1 1 . 2 9 . 6 S O  1  5  1  s  1  33  8  2 1  2  TOTAL  60  4  AGE  2 7  33  FIGURE  12  I S  I S  4.8:  21  (CONTINUED)  2 4  2 7  • o  TOTAL A G E  61  3 0  UEOENO — MAY JUNE — SEPTEMBER  Table Age  4.10:  Two-level nested (cm/year/cm).  Spacings included  anova t e s t s  (m)  f o r RGR i n DBH  DBH c l a s s D.F.  13 14 15 16 17 17 18 18 19 20 20 21 21 22 23 24 26 28 30  all all 1.2; 1.2; 1.2; 3.0; 1.2; 3.0; 1.2; 1.2; 3.0; 1.2; 1.5; 1.2; all all all all 1.2;  1 .8;2 .1;2 1 .5;2 .1;2 1 . 5;1 . 8 ; 2 4 .3 1 .5;2 .1;2 4 . 3 ; 6 .0 1 .5;1 .8;2 1 . 5;1 . 8 ; 2 4. 3 2 • 1;3 . 0 ; 6 1 .8;2 . 4 1 . 5;1 . 8 ; 2  • 4;3 . 0 ; 4 .3 . 4 ; 3 . 0;4 . 3 ; 6 . 0 . 1;2 . 4;6 .0 .4 . 1 ; 2 . 4;3 . 0 ; 6 . 0 . 1 ; 2 . 4 ; 6 .0 .0 . 1 ; 2 • 4;3 . 0 ; 6 . 0  1 . 5;1 . 8 ; 2 . 1 ; 2 . 4;3 . 0 ; 4 . 3  * : S i g n i f i c a n t d i f f e r e n c e s at the n . s . : no s i g n i f i c a n t d i f f e r e n c e . Comparison of  *:  level  of  1.2  1.5  1.8  2.1  2.4  0 .135a* 0 .112a 0 .081a 0 .055a 0 .050a  0 .144a  0 .170a 0 .134ab  0 .189a 0 .164bc 0 .102ab 0 .083b 0 .086bc  0 .225a 0 .206c 0 .135bc 0 .091b 0 .114c  —  0 .050a 0 .029a 0 .020 —  0 .018a 0 .017a 0 .010a 0 .014ab 0 .012a 0 .010a  —  -  0 .081a 0 .072ab 0 .058ab  0 .066ab  —  —  0 .061a 0 .030ab  0 .065ab 0 .046ab  —  0 .017a 0 .017a 0 .021a 0 .009a 0 .010a 0 .011a 0 .010a  -  -  F 21 . 9 3 * 22 . 1 6 * 6 .18* 5 .04* 5 .96* 17 . 0 5 * 9 .94* 20 . 5 5 * 7 .12* 3 .87* 5 .09* 4 .63* 2 .08* 3 .82* 4 .11* 4 . 44* 3 .12* 2 .67* 3 .53*  0 .023a 0 .019a 0 .021a 0 .012a 0 .012a 0 .012a 0 .008a  -  0 .068ab 0 .048b 0 .037 . —  0 .021ab 0 .026ab 0 .014ab 0 .014ab 0 .015ab 0 .012a  -  0 .091bc 0 .069  -  0 .052 0 .036b 0 .037bc 0 .022b 0 .019b 0 .017ab 0 .013a  D.F.  F  6/50 6/62 4/40 6/67 5/60 1/2 5 3/43 2/36 6/79 5/6 4 1/24 3/47 2/29 6/80 7/91 7/91 7/86 7/8 5 6/84  1 . 2 0 n . s. 2 .46* 11 . 1 1 * 15 . 9 7 * 16 .34* 2 . 35n. s. 7 .19* 2 . 9 6 n . s. 23 .04* 35 . 6 7 * 2 . 5 1 n . s. 35 .74* 78 . 0 1 * 46 . 3 9 * 55 . 1 2 * 95 .42* 68 . 0 3 * 28 . 3 5 * 7 .44*  probability  mean RGRs i n DBH among t h e  T u k e y ' s m u l t i p l e range S p a c i n g (m)  Age  14 15 16 17 18 18 19 20 21 21 22 23 24 26 28 30  51/347 64/347 45/219 76/371 66/323 26/89 46/191 37/171 86/358 75/308 27/87 54/213 39/132 97/335 106/375 107/370 110/360 110/357 103/259  Spacing  of  0.05.  spacings  tests 3.0  4.3  0 .237a 0 .219c 0 .149c  0 .206a 0 .211c 0 .160c  0 .123a 0 .103cd  0 .166a  -  0 .057  -  0 .053 0 .051c 0 .032 0 .026 0 .020b 0 .016a  -  -  0 .079d 0 .049c 0 .038c 0 .029c 0 .021b  6.0  -  0 .161c 0 .121  -  0 .143a 0 .130d 0 .097 0 .078  -  0 .073 0 .077d 0 . 056c 0 .040c 0 . 028c 0 . 023b  t h e s p a c i n g s f o r a g i v e n age f o l l o w e d by t h e same l e t t e r do n o t d i f f e r s i g n i f i c a n t l y at the l e v e l of p r o b a l i l i t y of 0 . 0 5 .  62  Table 4.11: Two-level nested anova tests for RGR i n basal area ( cm /year/cm ) . 2  Age  2  Spacings included (m)  DBH class D.F.  13 14 15 16 16 17 17 18 18 19 20 20 21 21 22 23 24 26 28 30  all all all 1. 2 ; 1. 5;2 .1;6 .0 2 . 4 ; 4. 3;6 .0 1. 2 ; 1. 5;1 .8;2 .1; 2 .4;6 .0 4 .3 ; 6 .0 1. 2 ; 1.5;2 ,1;2 • 4; 3 .0;6 .0 3 .0 ; 4 .3;6 .0 1. 2 ; 1.5;1 • 8;2 .1; 2 . 4;3 .0 6.0 1. 2 ; 1.5;1 .8;2 .1; 2 .4;6 .0 4 .3 ; 6 .0 1. 2 ; 2• i;3 . 0;6 .0 1. 5 ; 1.8;2 .4 1. 2 ; 1.5;1 .8,-2 .1; 2 • 4;3 • 0; 6.0 all all all all 1. 2 ; 1. 5;1 • 8;2 .1; 2 . 4;3 • 0; 4.3  Spacing F  D.F.  F  51/347 64/347 71/344 41/235 35/136 66/323 26/89 71/317 37/171  21 .91* 22 .16* 5 .94* 3 .24* 10 .03* 5 .26* 17 .03* 11 .93* 20 .69*  6/50 6/62 6/64 3/34 2/33 5/59 1/2 5 5/67 2/36  0 . 95n. s. 2 .46* 10 .59* 41 .93* 0 .63n. s. 17 .55* 2 .34n. s. 24 .34* 2 .98n. s.  86/358 75/308 27/87 54/213 39/132  7 .17* 3 .89* 5 .13* 4 .62* 2 .11*  6/79 5/64 1/25 3/47 2/29  22 .94* 35 .43* 2 . 51n. s. 35 .85* 76 .77*  97/335 106/375 107/370 110/360 110/357  4 .44* 3 .54* 4 .10* 3 .83* 2 .69*  6/82 44 .17* 7/106 65 .29* 7/90 108 .42* 7/110 53 .73* 7/110 21 .73*  103/259  2 .32*  6/103  12 .26*  *: S i g n i f i c a n t differences at the l e v e l of p r o b a b i l i t y of 0.05. n . s . : no s i g n i f i c a n t difference.  63  Table 4.11:  (Continued). Comparison of mean RGRs among the spacings. Tukey's multiple range tests Spacing (m)  Age 1.2 14 15 16 16 17 18 18 19 20 21 21 22 23 24 26 28 30  1.5  0 .270a* 0 .289a 0 .225a 0 .162a 0 .161a 0 .110a 0 .145ab 0 .099a 0 .116ab 0 .100a 0 .123a 0 .058a 0 .059a 0 .039a 0 .034a 0 .036a 0 .034a 0 .035a 0 .041a 0 .021a 0 .019a 0 . 025a 0 . 020a 0 .025a 0 .023a 0 .020ab 0 .019ab  1.8 0. 340a 0. 267ab 0. 133ab -  -  2.1  2.4  0 .379a 0 .449a 0 .328ab 0 .411b — 0 .204a 0 .270a 0 .167b 0 .182b 0 .172bc 0 .228cd  0. 130ab 0 .135ab 0. 091ab 0 .096b 0 .074a 0. 046a 0. 038a 0 . 043a 0. 043a 0 .053ab 0. 023a 0 . 028a 0. 025ab 0 .028ab 0. 025a 0 .029ab 0. 016a 0 .023ab  3.0  4.3  0 .474a 0 . 438b  0. 413a 0. 422b  —  —  0 .299a 0. 320a — — 0 .246cd — 0 .246a 0. 332a — 0 .182bc 0 .205cd — — 0 .138 — — 0 .117 — — 0 .105 — 0 .073 0 .107 0 .074b 0 .103 0. 159c 0 .044 0 .064 0. 098b 0 .039bc 0 .053c 0. 077d 0 . 035ab 0 .041b 0. 058c 0 .026bc 0 .033c 0. 042d  6.0 —  0. 323 —  0. 242 0. 286d 0. 286a 0. 260d 0. 194 0. 157 —  0. 146 0. 155c 0. 115b 0. 079d 0. 056c 0. 047d  *: the spacings for a given age followed by the same l e t t e r do not d i f f e r s i g n i f i c a n t l y at the l e v e l of p r o b a l i l i t y of 0.05.  64  FIGURE 4 . 9 : DBH RGRs AS A FUNCTION OF DBH SIZE CLASS FIGURE 4.9.1: AGE 13  FIGURE 4.9.2: AGE 18 0.530 4  o « * 0 V • * o  0.477  LEGEND = SPACING: 1.2X1.2 M = SPACING: 1.5X1.5 M = SPACING: 1.8X1.8 M = SPACING: 2.1X2.1 M = SPACING: 2.4X2.4 M = SPACING: 3.0X3.0 M = SPACING: 4.3X4.3 M  0.424  5 O o . 371  LEGEND - SPACING: 1.2X1.2 M - SPACING: 1.5X1.5 M = SPACING: 1.8X1.8 M = SPACING: 2.1X2.1 M = SPACING: 2.4X2.4 M = SPACING: 3.0X3.0 M = SPACING: 4.3X4.3 M = SPACING: 6.0X6.0 M  OC ui o. 318  \  5o.  265  0.212  7  CC 0.159 O 0. 106 0.053 0.000  o. 10 2  3  *  5  6  18  7  DBH SIZE CLASS (CM)  DBH SIZE CLASS (CM)  FIGURE 4.9.3: AGE 24  FIGURE 4.9.4: AGE 30  LEGEND 0. 0420 6 = SPACING: 1.2X1.2 M 0 = SPACING: 1.5X1.5 M «= SPACING: 1.8X1.8 M 0. 0 = SPACING: 2.1X2.1 M 7 = SPACING: 2.4X2.4 M • = SPACING: 3.0X3.0 M , „ * = SPACING: 4.3X4.3 M^, \>*\p = SPACING: 6.0X6.0 M ^  0.09  LEGEND o= SPACING: 1.2X1.2 M 0-SPACING: 1.5X1.5 M SPACING: 1.8X1.8 M 0= SPACING: 2.1X2.1 M 7= SPACING: 2.4X2.4 M o • = SPACING: 3.0X3.0 M \ * - SPACING: 4.3X4.3 M o = SPACING: 6.0X6.0 M  0  *  20  \  i  1  i • i • i • i • i  1  i • i *i  6 8 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 0 2 4 6 8 0 2 4 6 8 0 2 4 6 8  DBH SIZE CLASS (CM)  DBH SIZE CLASS (CM) 65  FIGURE 4 . 1 0 : BASAL AREA RGRs AS A FUNCTION OF DBH SIZE CLASS FIGURE 4.10.2: AGE 18  FIGURE 4.10.1: AGE 13 i . 10  1 .40  0.99  A « * 0 7 • *  LEGEND = SPACING: 1.2X1.2 M = SPACING: 1.5X1.5 M = SPACING: 1.8X1.8 M = SPACING: 2.1X2.1 M = SPACING: 2.4X2.4 M = SPACING: 3.0X3.0 M = SPACING: 4.3X4.3 M  A 0 « 0 7 • * o  (N 0. 88 t * 2  oo.  \  ct  LEGEND = SPACING: 1.2X1.2 M = SPACING: 1.5X1.5 M = SPACING: 1.8X1.8 M = SPACING: 2.1X2.1 M - SPACING: 2.4X2.4 M - SPACING: 3.0X30 M - SPACING: 4.3X4.3 M - SPACING: 6.0X6.0 M  66 >-  \  *  55  I  2  o 0. 44 CD  0.33 0.22 0.11 0.00  0.24 9  10  DBH SIZE CLASS (CM)  DBH SIZE CLASS (CM)  FIGURE 4.10.4: AGE 30  FIGURE 4.10.3: AGE 24 0.190 H  0.090  0.171  0.081  CN 0 . 152  CM 0.072  * *  1  # #  2 O 0.133-  2 O 0.083  UjO.114-  L) 0. 054  \  M P  \ *  A  ^ 0.095^ * 2  I  I \  >  >\  045  2  \  1  *  P,o. 036  P.0.07H  J; 0.027 00  : 0.057  0.038-  LEGEND A = SPACING: 1.2X1.2 M «= SPACING: 1.5X1.5 M «= SPACING: 1.8X1.8 M 0-SPACING: 2.1X2.1 M 7= SPACING: 2.4X2.4 M . = SPACING: 3.0X3.0 M * = SPACING: 4.3X4.3 M „o = SPACING: 6.0X6.0 M  A / WX\  tt O 0.018  0.019  0.009 0.000  0.000^;  i • i ' i ' i  6 10  13  20  25  8  1  i '  i • i  DBH SIZE CLASS (CM)  DBH SIZE CLASS (CM) 66  1  i  1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 0 2 4 6 8 0 2 4 6 8 0 2 4 8 8  differences these  only  suggests  differences  appeared  the c l o s e s t  and l a r g e s t  spacings d i f f e r e d  among t h e g r o u p s o f s p a c i n g s  was l e s s  The s i z e  For  both  significantly identical  years  decreased  a t every  that  o c c u r r e d w i t h AGR.  later,  tree  tree  The  largest  size,  and t h o s e  increased with  the 2.4  tree  m spacing  spacings  still  t h e RGR o f  and 4 . 1 0 . 1 ) .  spacings  m and 2 . 1  A t age 2 4 ,  clearly  m remained  spacings the four  ( F i g u r e s 1 4 . 9 . 3 and  size  remained  relatively  decreased  with  spacings  invariant.  increase i n tree still  decreased  ( F i g u r e s 4 . 9 . 4 and 4 . 1 0 . 4 ) .  change i n t h e r e l a t i o n s h i p  of individual  t r e e s were  (Table 4 . 1 2 ) . with  tree  size,  cate  RGR d i d n o t v a r y  b e t w e e n RGR a n d t r e e  coefficients  s i z e was  b e t w e e n DBH and  computed f o r a l l s p a c i n g s a t d i f f e -  Negative  decreased that  factor  were n o t  A t age 1 3 ,  of the four l a r g e s t  e v i d e n t when t h e c o r r e l a t i o n  ages  the v a r i a t i o n s  of the 1.8  those  A t age 3 0 , o n l y t h e two l a r g e s t  The  f o r both  RGR v a r i e d  (Figure 4 . 9 . 1  size  ( F i g u r e s 4 . 9 . 2 and 4 . 1 0 . 2 ) .  Only  rent  with  However,  t h e RGRs o f t h e two c l o s e s t  constant,  size  age and t h e r e  nesting  This implies that  t o those  4.10.3).  RGR  age.  t h e DBH c l a s s  size.  spacings  tree  with  The same p a t t e r n o c c u r r e d  tree  closest  three  were n o t s t a t i s t i c a l l y  with  with  relatively  that  Initially,  a n d t h e r e was  groups decreased  DBH and b a s a l a r e a ,  spacings decreased  increased  also  place at  area.  was s i g n i f i c a n t  with  o f these  o v e r l a p among them.  DBH and b a s a l  size.  f r o m age 15 o n .  Significant  different.  Five  c o m p e t i t i o n had n o t y e t taken  two a g e s .  overlap  all  that  coefficients  not s i g n i f i c a n t significantly 67  indicate  t h a t RGR  low c o e f f i c i e n t s with  tree  size,  indi-  and h i g h  Table 4.12:  C o r r e l a t i o n c o e f f i c i e n t s b e t w e e n DBH ( i n i t i a l and RGR f o r a l l s p a c i n g s a t d i f f e r e n t a g e s .  Age  s p a c i n g (m) 1 .2  13 14 15 16 17 18 19 20 21 22 23 24 26 28 30  size)  -0 .83* -0 .80* -0 .48* - 0 .16 -0 .10* 0 .55* 0.60* 0.50* 0 . 55* 0.58* 0 .59* 0 .67* 0.60* 0 .63* 0 . 54*  1 .5  1 .8  -0 .88* -0 .80* -0 .56* - 0 .24 -0 .05* 0.34* 0 .51* 0 .31* 0 .42* 0 .46* 0 .17 0 .61* 0 .49* 0 .42* 0 .53*  -0 .92* -0 .81* -0 .76* -0 .47* -0 .10* - 0 .19 0 .09 0 .23 0 .65* 0.68* 0 .59* 0 .70* 0.66* 0 .57* 0.66*  *: S i g n i f i c a n t  at the l e v e l  2 .1 -0 .86* -0 .86* -0 .79* -0 .54* -0 .50* - 0 .15 0 .18 0.39* 0 . 32* 0 .49* 0 .48* 0 .65* 0 .59* 0 .30* 0 .62*  2 .4 -0 .91* -0 .92* -0 .84* -0 .86* -0 .84* -0 .90* -0 .45* -0 .34* - 0 .17 0 .02 0 .05 0 .19 0 . 41* 0 .32* - 0 .11  of probability  68  3 .0 -0 -0 -0 -0 -0 -0 -0 -0 -0 -0 -0 -0 -0 -0 -0  .91* .85* .87* .80* .83* .84* .66* .67* . 54* .77* .49* . 58* .49* .23* .13  of 0.05.  4 .3 -0 -0 -0 -0 -0 -0 -0 -0 -0 -0 -0 -0 -0 -0 -0  .68* .69* . 51* .80* .81* .77* .85* .66* .91* .82* .83* .77* .63* .44* .33*  6.0 — —  -0.73* -0.83* -0.91* -0.86* -0.89* -0.80* -0.78* -0.76* -0.70* -0.51* -0.38* -0.33*  positive  coefficients  4.12  Table  completes  included, ficients  and  from  increased remained largest  well  spacings  were  still  and  with  At  these  tree size.  hypothesis a l l the must be  of  competition  absence of  14  high values  of  was  1984)  took  of  then  spacing, Table  Ford  and  Diggle  before  the  onset  As  previously  d i f f e r e n c e s a t ages 13  crown  suggested  ratio  Even though  that individual  i t was  arid 14  69  be  were n o t  argued  t h a t no  and  spacing  concluded  i n any  crowns were n o t  i t may  of  varied considerably  place.  o c c u r r i n g a t a g e s 13  competitors,  and  the  size. and  4.10;  and  same RGR  b e c a u s e most g r o w t h p a r a m e t e r s a n a l y s e d and  tree  and  significant  s u b j e c t to competition.  four same  f o r DBH  with  wider  (Figures 4.9  (1982,  Ford  the The  tree sizes  The  r e j e c t e d b e c a u s e RGR  the  competition  across  to tree s i z e .  t r e e s have t h e  mentioned, the  decreased  became c o n s t a n t  changes o c c u r r e d  spacings  30.  young ages they  related  of  negative.  RGRs o f  p a t t e r n s of v a r i a t i o n  RGRs.  those  spacings m  show t h r e e  (i.e.,  presence  2.1  m and  the  different  closest  tree size,  decreasing  18,  were  results  The  different  two  1.8  the  with  spacings  coef-  well  age  and  among t r e e s b e f o r e  was  of  At  significantly  the  the  4.9.1  Figure  size.  are  were p o s i t i v e ,  four  of  tree  13,  age  a t a g e s 24  competition)  and  spacings  largest  RGR  At  tree size.  were n o t  constant  i n c r e a s e d , RGR  4.12).  the  and  ages  occurred  area  later  (1981)  of  tree size,  became p o s i t i v e l y the  were n e g a t i v e  closest  a l l the  indicated.  shows t h a t RGR  relatively  These  age  are  m spacings  those  with  situation  As  two  increased with  because  decreasing with  the  2.1  and  4.9.2  Figure  basal  of  m and  zero,  was  t h a t RGR  4.9  trends  of a l l spacings  coefficients 1.8  Figure  similar  shows t h a t RGR  the  indicate  that  spacing  significantly  affected  by  that competition  the for  no  nutrient  e l e m e n t s was maybe  analysed  in this  importance  of  competition  study  soil  young ages because Furthermore, that  do n o t  below-ground  for  the  the  of  ces  important at  w o u l d have Finally,  individual  the  was  not if  very  rich  grafts  Horton  According  Graham and Bormann  1969).  grafting because  decreases  reported Cannell  al.  (Pinus to  sities.  for  basal  height  Dougl.) the  The d a t a  of  Cannell  periods  at  the  in populations Perry  i n RGR w i t h  inversely  tree  or not  corresponds  share  size  to  related  a phase to  its  was  (1987)  would  i n which the  70  and  limited  were  inten-  to  three  pattern  thinning  Meerb.  al. that  (1984),  efficiency the  the  competition  mortality.  smaller  and  lodgepole  thinning  following  et  that  stands  A similar  capensis  induce  the  to  P e r r y ' s data  were  indicate  to  trees  similar  stage.  1959;  resources.  spruce  and C a n n e l l  size:  are  root  among  soil  (1984)  al.  enough  (1966),  However,  Impatiens  (1985)  growth.  a stand  but d i f f e r e n t  al.  et  spacings  in Douglas-fir  in Sitka  seedling  of  severe  time  area  same a g e , et  resour-  soil  diameter  competition  stands.  r e p o r t e d by S c h m i t t  non-existent  is  (1984)  to  of  better  for  of  According  period  (1985)  stands  treatments  decline  trees  for  (Armson and D r i e s s c h e  RGR c h a n g e s o v e r  contorta  remeasurement also  of  by P e r r y et  limited  was  intensity  interconnected  The p a t t e r n  pine  the  to  suggests to  composing  by many r o o t  pine.  compared  different  interconnected  at  red  same s i t e  i n term of  trees  for  the  this,  important  competition  differences  of  Despite  on t h e  the  variables  analysis  important  young a g e s ,  red pine  direct  stress.  (1970)  was  the  p r o b a b l y not  site  Also,  shown g r e a t e r  the  was  Stiell  competition  competition.  However,  competitive  studied  above-ground had been  permit  resources  study  below-ground  important.  is  This of  the  tree  tree,  the  more  capable  it  dominant  is  of  trees with large  productivity, greater roots, size,  maintenance  it  and b r a n c h e s .  would i n d i c a t e  to  severe  between  under  stress  heavy  less  Perry  (1985)  large  range o f  when t r e e s  between  declines  determine  is  of  from  just  their larger  size.  with  Finally,  a  of  the  to  stand  positive  The e f f i c i e n c y that  tree  beginning  c h a r a c t e r i z e d by a  initial  if  the  al.  (1984)  spacings,  because  way c o n s i s t s  of  trees  trees  subject  the  of  it  1985;  onset  If  stands  young a g e s ,  yet  differences  there  is  not  a n a l y s i n g the  begin  to it  such t h a t  takes  and a t r e e  difference free  of  the  various  i n a stand  is  One  i n growth  rate  (Curtis  The same p r i n c i p l e may be stands  with others  to  possible  When  possible  to  of  among  conclude  appear p r o g r e s s i v e l y  71  (i.e.,  competition  competition  it  begins.  for  place  difference  becomes  and t o a  competition  no s i g n i f i c a n t is  red pine  of  a measurable q u a n t i t y .  had an i m p a c t on g r o w t h .  spacings,  competition  is  of  must be e s t i m a t e d  Pienaar 1965).  density.  and c o n c l u s i o n s  a p p l y to  reach a s i z e  by c o m p a r i n g v e r y d e n s e  at  findings  D e t e r m i n i n g when c o m p e t i t i o n  Perry  not  is  mortality.  compared t o  et  a stand-grown tree  applied  widest  cause  a r e d u c t i o n i n growth)  possible  has  because  resulting  competition  RGR and t r e e  and C a n n e l l  an e a s y t a s k  1970;  that  composing a stand  spacings. not  efficient  photosynthetic  competition.  In o r d e r t o  causes  highest  Although  When RGR r e m a i n s c o n s t a n t  competition  correlation  ( P e r r y 1985);  the  r e s p i r a t i o n needs  i m p o r t a n t enough t o  subject  to  crowns have  t h e y w o u l d be l e s s  stems,  become  p r o d u c i n g new m a t e r i a l  that  low these competition  significant from t h e  determine  closest when  to  the  Determining particular  exact  s p a c i n g was  given  stand  Also,  because  density,  the  become  the  the  age  difficult  subject five  onsets  to  of  at  of  a g e s 13 and 14  yet  tition  had n o t  spacings  is  based  spacings).  Even though  at  age  13,  basal  a r e a RGRs  differences  began  tition  was  to  in  all  crown that  spacings. the  spacings  trees  two  with  lation the  4.10.1; showed  Table  spacings  age  for  4.12).  started  lower  than  tree  every  competition  18,  They showed  tree  at  the  tree  compe-  closest when  initial  i n DBH AGR were  Because the  at the  signi-  onset  least  of  the  compe-  two  m a j o r i t y of  trees  c h a r a c t e r i z e d by h i g h It  and t h e at  is  at  age  age  negative  13  15 of  size  (Figures  (Figures  constant  4.9.1  and  spacings 4.9.2  relationship  because  corre-  corresponded  two n a r r o w e s t  respectively 72  not  having high proportions  size  a relatively  16 and 17  had  a r e a AGR, DBH and  15,  for  i n any s p a c i n g  A t age  the  spacings  85%.  spacing  i n RGR w i t h  4.10.2).  ages  this  age  much i n  differences  4.11).  two a g e s were  i n RGR w i t h  an i n c r e a s e  size  basal  (Figure 1 of Appendix 2).  coefficients of  competition  differences  4.10,  a  time.  concluding that  for  of  a  probably  i n DBH among  that  for  time.  differ  spacings  ages w i t h i n  appear at  these  crown r a t i o s  absence  d i d not  trees  c h a r a c t e r i z e d by l a r g e  4.7,  occur at  at  closest  The d e c l i n e  same  As p r e v i o u s l y m e n t i o n e d ,  ratio values the  to  the  significant  obtained  4.6,  ficant  closest  of  significant  (Tables  assumed  these  stands  none were  at  differences  absence  a r e made w i t h  the  p e r i o d of  above,  competition  all  these  suggests  o c c u r r e d at  comparisons  found  short  significant  on t h e  in  of  not  spacings  competition  (As m e n t i o n e d  yet  onset  competition  (Table 4.2)  taken p l a c e .  the  because  narrowest  occurred within a r e l a t i v e l y The a b s e n c e  of  their  and with  with  correlation zero.  The 1.8  basal than  coefficients m spacing  a r e a RGRs w i t h the  two  relatively spacings,  constant  tree  mean DBH, b a s a l  at  16  (Tables  2).  4.2,  As t h e  4.7,  and 2 . 1  m spacings,  were  close  Finally, with  to  the  DBH a t  limit  age  m spacings  former  effective the to  4.3 age  largest  age  at  spacing  16  two  a r e a RGRs  However,  trees with  (6.0  17  for  the  values 1.8 m  16 and t h a t  many o t h e r  affected still  by  some  ( F i g u r e 1 of  crown r a t i o  age  m)  only  age  that  none  of  3.0  was trees  competition.  showed  a decline  the  i n RGR  the  lower  values  these  a r e a RGRs  2.4  m spacing  differ  (Tables  73  the  3.0  differed 4.10  6.0  4.3 m  the  the  a trend  of  remained  competition.  than  spacings  f r o m the  that  m,  (Table  between  competition  of  the  imply that but  is  2.4  m ones d i d n o t  necessarily  of  the  significantly,  differences  onset  spacings  mean DBHs o f  differ  onset  b o t h DBH and b a s a l to  16,  by c o m p e t i t i o n ,  for  began  four widest  m and 6 . 0  d i d not  after  showed  the  significant  before  a few y e a r s  Also,  d i d not  affected  existing  of  A t age  the  m spacings  m spacing 20.  but  suggests  s p a c i n g was  low v a l u e s  For these  stress  being  evaluate.  m ones d i d ,  m and 6 . 0  remained  competitive  at  condition  3.0  4.3  18.  Other  that  spacings  to  This  m spacing  and 4 . 1 1 ) .  drastically  of  more d i f f i c u l t  4.2).  4.12).  18.  The c o m p e t i t i v e  and 6 . 0  age  t h a n 85% a t  appears  four widest  m, and 4 . 3  4.10,  on some t r e e s the  (Table  2.1  from the  p r o p o r t i o n of  it  17  at  from  v a r i a b i l i t y i n DBH and  the  size  lower  t h a n 85% d e c r e a s e d  only  age  different  a r e a AGR, and DBH and b a s a l  greater  occurring  little at  different  had a crown r a t i o  Appendix  size  significantly  DBH c l a s s e s ,  with  significantly  trees  showed  tree  smallest  became age  were n o t  In  fact,  m spacing  up  significantly  and 4 . 1 1 ) .  m spacing  at  The age  16  for  basal  all  the  at  trees  ages  Despite that  a r e a AGR and 17  differences  i n the age  age  (Table  then  stress  spacing when  Appendix size  at  at  2).  two w i d e s t  of  for  widest  30  to  m spacings,  the  the  19  of  competition,  growth  rate  4.9.4  by  competitive tree  began  wide  size  appear  m spacing lower  well  or not  a r e a RGRs o f  became  at  to  the  as very  be  under  3.0 m  a r o u n d age  20  t h a n 85% ( F i g u r e  i n v a r i a n t with Table  4.12).  i n RGR w i t h 4.12).  to  as  non-existent  and 4 . 1 0 . 4 ;  Table  for  d i d not  6.0  a decline  onset  of  m and 1.5 for  the of  closest  in tree  is  crown r a t i o s  spacings  the  4.3  tree  However,  show v a l u e s  et  competition m spacings,  2.4  1 of  tree Only  size the  lower  related  al.  (1984)  spacings.  size  appeared 1.6  m spacing,  m spacing,  change  s u g g e s t e d by C a n n e l l  increase  appears  it  19.  the  at  age  crown t h a n 85%  respectively.  1.2  for  from t h e  showed  two  The p a t t e r n  five  17 and 18,  invariant with  spacings  and 4 . 1 0 . 4 ;  and 30  2.1  the  t h a n 85%  age  affected  DBH and b a s a l  have  (Figures  4.9.4  15  to  RGR became  three  24.  Relative  age  26  became  competition  differing  I n summary,  spacing,  that  age  these  a g e s 26  m spacing  ages  greater  a r o u n d 35% a t  i n RGR w i t h DBH i n d i c a t e s  spacings  (Figures  ratios  the  began  age  at  However,  4.12).  started  trees  p r o p o r t i o n was  and t h a t  narrow spacings  heavy  at  19,  a decline  severe,  30  2.4  a r e a RGR.  had a crown r a t i o  significant  at  for  spacing  This  stress  If  that  DBH and b a s a l  17 and 1 8 .  trees  21  of  for  20 for  to  onset  the  and P e r r y the  exclusively  and c o m p e t i t i o n 74  does not  the  for  and 30  However,  does not  for  to  1.8  the  the of  m and  m spacing.  competition  decrease indicate  at  3.0 m  6.0  (1985)  begin  occur  is  as  applicable  i n RGR w i t h the  absence  o n l y when RGR  shows l i t t l e occurrence 1 year 1.8  v a r i a b i l i t y with  of  after  little the  m spacings,  years  for  spacings size. were 1.8  the were  of  2 years  for  52%,  m, 2 . 1  60%,  m, 2 . 4  became  invariant.  age  the  of  onset  51%,  trees 95%,  m, and 3 . 0 However, of  the  crown r a t i o v a l u e s  onset  increase  of  with  between  1.2  the  transition occurred the  density the  is  85%)  of  to  the  and t h e  other time  for  for  the  occurring  began  stress  stress  proceeds  little  still  relatively  2).  the to  to  This  3.0  age  of  show to  (all the  to  between  have  all  This  longer the  little  two  trees  closest  as  75  related  stand However,  p e r i o d might of  be  competition lower  be a f f e c t e d  lower  spacings  the  s u r p r i s i n g l y high  onset  appeared to  years  that  c o u l d be  crown r a t i o v a l u e s  crown r a t i o v a l u e s five  is  the  increase  more s l o w l y  m spacing  the  important  suggests  size  m,  between  from one y e a r  tree  tree  when RGR  occurrence of  increased.  spacings.  t i m e where  years  i n RGR w i t h  and 10  m, 1.5  respectively  This  and  competition  1.2  t r e e s were  m spacings.  place  1.5m,  ( R a d o s e v i c h and O s t e r y o u n g 1 9 8 7 ) .  10 y e a r s the  to  when RGR began  increased  self-thinning  when t r e e s  three  size  age  took  m and 6.0 m  was p r o b a b l y n o t the  the  i n RGR w i t h  o b s e r v e d between  s p a c i n g was  decreased  competitive was  as  that  compared t o  (i.e.,  tree  of  delay  from d e c r e a s e  fact  delay  related  i n the  m and 2.4  slower  4.3  (Figure 1 of Appendix  c o m p e t i t i o n and t h e  variability  to  transition  size  size  of  m spacings,  the  competitive  c o m p e t i t i o n and t h e  because  The  the  age  1.2m,  already subject  m spacings  RGR w i t h t r e e  this  30,  and 100% f o r  of  high during  the  m and 2.4  A t age  variability the  2.1  for  tree  c h a r a c t e r i z e d by a d e c r e a s e  The p r o p o r t i o n s o f 75%,  the  The f i r s t  RGR w i t h  competition  m spacing.  still  size.  v a r i a b i l i t y of  onset  3.0  tree  than by  t h a n 85%).  and t h e  4.3 m  This  spacing  and 5 y e a r s  Examining tree has  size  to  showing  curves  stockings  at  separating  a  over  correlated  where  of  in  the  the  competition  derived curves  densities  the at  an e s t i m a t e  several of  the  maximum i n c r e a s e  growth apply  the  (Pienaar the  range  with  part of  this  does n o t  to  volume  the  for  remeasurement  of  initial the  that  data  stands.  with  competition  began  (1935),  i n the  by more t h a n 1.25  However,  he d i d n o t  limit.  76  curve  of  the  provides obtain a authors  difficult  need  to  stand to  analyse  data.  (1965)  high density  stands  inches)  a  Working  Pienaar  mm ( 0 . 0 5  give  then  DBH o r mean  found i t the  is  stand  Other  remeasurement  O'Connor  section  r e q u i r e d to  mean s t a n d  spacings  mean  points  any a g e .  of  derived.  g r a p h where  the  This  (1965)  is  the  periods.  because  of  is  inflection  at  S-curve  on t h e  initial  O'Connor  set  zone  different  volume  Pienaar  a  The M-V c u r v e  trees  (1935)  initial  affect  zone  occur.  joining  O'Connor  Then,  section  suppression  stands  d e r i v i n g a graph  different  the  trees  i n mean t r e e  mean DBH d i f f e r e d  density  as  considered  1965).  of  periods.  maximum number o f  approach of  considered  for  same a p p r o a c h , b u t u s e d  wide  the  defined  and t h e  mean t r e e  i n even-aged  zone and a s u p p r e s s i o n  by d r a w i n g a c u r v e of  applied  is  consists  remeasurement  is  begins  between RGR and  The method o f  volume  number o f  trees,  relationship  methods.  mean t r e e  zone  m spacing.  i n the  trend)  a free-growth  reduction  volume  other  several  free-growth  3.0  when c o m p e t i t i o n  curve  of  the  changes  estimate  advantages  (i.e.,  The  the  for  when  f r o m low  any j u s t i f i c a t i o n  for  Similar developed.  approaches based One o f t h e b e s t  on t h e s e l f - t h i n n i n g  examples  i s the stand  gement d i a g r a m d e v e l o p e d  by Drew a n d F l e w e l l i n g  Douglas-fir.  o f mean t r e e volume  densities,  they  competitive effect  On" a g r a p h  stress.  The  several  application  of stands  that  the occurrence closely  range o f s p a c i n g s .  that this  4.5.1.2-  spacings  the onset  stands  which  d e n s i t y and a t f o r a l l commerMy r e s u l t s  o f RGR w i t h  of competition  on d i f f e r e n t  size  f o r a wide  sites with  without  variability  of competition  The r e s u l t s i s true  making  different  of l i t t l e  probably  of Perry  (1985)  for Douglas-fir.  i n Height Increment  t o DBH, mean h e i g h t d i d n o t d i f f e r  the graph  tree  show  f o r a s s e s s i n g the onset of  The o c c u r r e n c e  correspondance  Table  of S t i e l l  shows t h e same l i n e a r 4.12  variability  s p e c i e s as w e l l .  (Figure 4.11;  completes  by S m i t h and  requires the  qualities.  a t the beginning  Cumulative  Compared  site  open-grown t r e e s o r s t a n d s  Development  4.5.1.2.1-  methods  do n o t e x i s t  T h i s c a n be u s e d  tree size  f o rother  suggest  with  on t h e same s i t e .  RGR w i t h  occurs  of l i t t l e  f o r red pine  comparisons with  of  to p r e d i c t the  a p p r o a c h was a d o p t e d  Such d a t a  s p e c i e s and f o r d i f f e r e n t  spacings  stand  i n t e n s i t i e s of  used  range o f i n i t i a l  cial  competition  showing d i f f e r e n t  o f these  f o r a wide  remeasurements.  corresponds  (1979) f o r  f o r red pine.  correct  analyses  A similar  also  d e n s i t y mana-  for different  These diagrams a r e a l s o  of thinning. (1988)  Brand  d e l i m i t e d zones  r u l e were  illustrates  trend.  1 o f Appendix and B e r r y  (1977)  More d e t a i l s  how t o t a l  77  height  2).  much among Figure  4.11  up t o age 3 3 , and  c a n be f o u n d  increased with  i n Figure DBH  size  FIGURE 4.11: MEAN HEIGHTS FOR ALL SPACINGS OVER AGE 16.001  13  16  19  22  25  TOTAL AGE  78  28  31  34  FIGURE 4 . 1 2 : MEAN HEIGHTS AS A FUNCTION OF DBH SIZE CLASS FIGURE 4 . 1 2 . 1 : A G E 1 3  FIGURE 4 . 1 2 . 2 : A G E 1 8  Vr /  / / // /4 '  a « * 0 V  = = = =  LEGEND SPACING: 1.2X1.2 M SPACING: 1 . 5 X 1 . 5 M SPACING: 1 . 8 X 1 . 8 M SPACING: 2.1X2.1 M SPACING: 2 . 4 X 2 . 4 M  * = SPACING: 3 . 0 X 3 . 0 M * - SPACING: 4 . 3 X 4 . 3 M o = SPACING: 6 . 0 X 6 . 0 M  1 .30  i  6  DBH SIZE CLASS (CM)  •  10  8  i  1  12  i  14  •  i  •  It  i  18  •  i  20  DBH SIZE CLASS (CM)  FIGURE 4 . 1 2 . 3 : A G E 2 4  FIGURE 4 . 1 2 . 4 : A G E 30  12.70 1 1 .98  1  »  ^* *  1  j LEGEND / a = SPACING: 1.2X1.2 M / 0 = SPACING: 1.5X1.5 M o 0= SPACING: 1.8X1.8 M 0 = SPACING: 2.1X2.1 M V = SPACING: 2.4X2.4 M • = SPACING: 3.0X3.0 M * = SPACING: 4.3X4.3 M o = SPACING: 6.0X6.0 M 10  15  20  25  30  J  LEGEND 6 = SPACING: 1.2X1.2 / 0 = SPACING: 1 . 5 X 1 . 5 < / SPACING: 1 . 8 X 1 . 8 'i / 0 = SPACING: 2.1X2.1 / \ / V = SPACING: 2 . 4 X 2 . 4 ' i / • = SPACING: 3 . 0 X 3 . 0 / * • * = SPACING: 4 . 3 X 4 . 3 ,1 o = SPACING: 6 . 0 X 6 . 0 • fl i i /  10  14  18  22  26  30  DBH SIZE CLASS (CM)  DBH SIZE CLASS (CM) 79  r  M M M M M M M M i"  34  38  class.  The DBH n e s t i n g  anova  (Table While  spacings and 33 to  tests  a g e s 13  (Table  situation  may be  m spacing  3.0  m, and 2 . 1  As  the  appeared.. spacing 1954), been  the  effect  closest  which  corresponds  least  is  1969;  al. of  not 15  of  has  test  statistical  from the  The  2.4  m,  differences because  significantly  differ.  been  generally  al.  affected  (Bella  1949;  Stiell  trend with found to  observed by  1964).  spacing  increase  stand d e n s i t y  and De F r a n c e s c h i 1980;  the  and De  B y r n e s and B r a m b l e 1949;  c o r r e l a t i o n with  failed  This  these  20 y e a r s  been  30,  competition  has  no c o n s i s t e n t  24,  significance.  differ  of  Bramble et  1949;  the  significantly to  ages  with  Ralston  has  also  Lemmien 1950;  Stiell  AGR i n c r e a s e d  with  1959).  there  the  what  among  and 30.  However,  d i d not  to  first  older,  (Bella  Absolute  This the  the  Berry  absence  size:  4.13).  spacings  mean h e i g h t  that  limit  to  and B i c k e r s t a f f  tree  nested  comparisons  significantly  A l t h o u g h mean h e i g h t  Although  the  attributed  became  reported  4.5.1.2.2-  at  fact  33.  (Bramble et the  the  age  1974;  v a r i e d at  a g e s 24  at  at  stand  for  m spacing  red p i n e :  Franceschi  to  just  found to  pattern  for  differences  in values  and t h e  spacing  mean h e i g h t  attributed  was  c a n h a r d l y be  for  i n the  were o b t a i n e d  The T u k e y m u l t i p l e  significant  6.0  This  significant  differences  and 18,  4.13).  resulted  widest  was  4.13).  no s i g n i f i c a n t  at  detect  factor  Growth  were l a r g e  larger  trend  Rate  is  DBH n e s t i n g  the  oscillations,  tree,  the  faster  c o n f i r m e d by t h e factor  was  80  it  results  significant  grew of  (Figure  the  (Table  anova  4.14).  in  Table Age  4.13:  T w o - l e v e l - n e s t e d anova  Spacings  included  (m)  tests  f o r mean h e i g h t  DBH c l a s s D.F.  13 18 24 30 33  all all all all all  * : S i g n i f i c a n t d i f f e r e n c e s at the n . s . : no s i g n i f i c a n t d i f f e r e n c e . Comparison  1.2  1.5  1.8  2.1  24 9.64a* 10.19a 10.05a 10.47a 30 1 3 . 1 5 a 13.36a 13.29a 14.16a 33 1 5 . 0 7 a b 1 4 . 5 8 a b 1 4 . 3 7 a b 1 5 . 6 6 a *:  of  F  6/54 7/95 7/108 7/118 7/113  0.33n.s. 0.99n.s. 2.18* 2.71* 5.34*  probability  of  0.05.  among t h e s p a c i n g s  Tukey's m u l t i p l e range s p a c i n g (m)  Age  D.F.  8.13* 58.84* 23.10* 13.67* 10.78*  level  o f mean h e i g h t s  Spacing F  54/395 95/409 108/373 118/349 113/342  (m).  2.4 10.32a 13.92a 15.36a  tests 3.0 10.47a 14.02a 15.59a  4.3 9.36a 12.92a 14.32ab  6.0 9.51a 13.02a 13.89b  t h e s p a c i n g s f o r a g i v e n age f o l l o w e d by t h e same l e t t e r do n o t d i f f e r s i g n i f i c a n t l y at the l e v e l of p r o b a b i l i t y of 0 . 0 5 .  81  FIGURE 4 . 1 3 : HEIGHT AGRs AS A FUNCTION OF DBH SIZE CLASS FIGURE 4.13.1: AGE 13  FIGURE 4.13.2: AGE 18  0.950  0.885  0.820  c t o <  755  bJ  >-  690  \ 0  2  (—0.625 I  o U I  0 . 560  oo. <  495  0.4  JO  0.365  0.300  DBH SIZE CLASS (CM)  DBH SIZE CLASS (CM)  FIGURE 4.13.3: AGE 24  FIGURE 4.13.4: AGE 30  H  0 . 900  0.800  0.827i  0. 726  0.754  tC  0.681 •  >\ 0 .  608  J  2 h O . 535-^  I  ill  o  U o 462-  i  Mi  I  i vw  QC OO. 389 <  i  LEGEND A = SPACING: 1.2X1.2 M 4 = SPACING: 1.5X1.5 M «= SPACING: 1.8X1.8 M 0 = SPACING: 2.1X2.1 M 7 = SPACING: 2.4X2.4 M • = SPACING: 3.0X3.0 M * = SPACING: 4.3X4.3 M o = SPACING: 6.0X6.0 M  0.316  0.243-  L'i  LEGEND I A = SPACING: 1.2X1.2 M i *= SPACING: 1.5X1.5 M «= SPACING: 1.8X1.8 M i o= SPACING: 2.1X2.1 M 7-SPACING: 2.4X2.4 M ; • = SPACING: 3.0X3.0 M * = SPACING: 4.3X4.3 M o = SPACING: 6.0X6.0 M  0.060  0. 170 10  15  20  23  30  10  I  18  22  26  30  DBH SIZE CLASS (CM)  DBH SIZE CLASS (CM) 82  34  38  Table  4.14:  Age  Two-level (m/year).  n e s t e d anova  Spacings included  (m)  tests DBH  f o r AGR i n h e i g h t  D.F. 13 18 24 30  a a a a  l l l l  F  54/392 93/408 107/370 114/341  l l l l  * : s i g n i f i c a n t d i f f e r e n c e s at the n . s . : no s i g n i f i c a n t d i f f e r e n c e .  level  C o m p a r i s o n o f mean h e i g h t s Tukey's multiple Spacing  Age 1.2 13 0 . 6 2 a * 18 0 . 4 4 a 30 0 . 4 5 a b c *:  1.5 0.74a 0.55bc 0.38abc  1.8 0.75a 0.50b 0.36c  Spacing  class  D.F.  5.55* 1.82* 2.16* 1.70* of  6/54 7/93 7/107 7/114  3.10* 12.54* 1.14n.s 11.58*  probability  among t h e range (m)  F  of  0.05,  spacings  tests  2.1  2.4  3.0  4.3  0.76a 0.54bc 0.45abc  0.73a 0.62cd 0.45abc  0.76a 0.65d 0.51ab  0.59a 0.56bcd 0.57ab  6.0 0.45a 0.29  t h e s p a c i n g s f o r a g i v e n age f o l l o w e d by t h e same l e t t e r do n o t d i f f e r s i g n i f i c a n t l y a t the l e v e l o f p r o b a l i l i t y o f 0 . 0 5 .  83  Even though  there  not  show any t r e n d o f  the  main f a c t o r  multiple  of  and 30.  was  vary  is  over  differences generally  a wide  1979).  age  it  13,  the  spacings.  A t age  intermediate The  differences for  T h e r e was  17,  be  20,  24,  a delayed  and i n c r e a s e s years,  the  elongation as  is  red pine  Daniel  et  at  age  the  tended  other  age  30.  ages  growing  et  compared t o 4.14).  no  not  Shepherd (Daniel  this.  Even  differences  from t h e  and n a r r o w e s t  closer  at  intermediate  f o u n d among  the  However,  between i n c r e a s e s 17,  20,  effect  process,  al.  to  there  closed  of  the ones.  signi-  values  between i n c r e a s e s  and 24.  s e a s o n was  delayed  a two-year  1983;  The a b s e n c e  corresponded  (Figure  i n AGR a t  al.  were  widest  ages  in  years.  relationship  (1979),  the  that  growth does  support  differ  differed  Finally,  significant  differences  correspondance  and 26  This  to  the  24.  mean h e i g h t  demonstrate  24  showed  age  While  found at  v e r y open o r v e r y  i n degree-days  (Daniel  al.  to  13,  age  spacing.  r e p o r t e d above  o c c u r r e d at  previous  precipitation.  is  at  ( C l u t t e r et  compared t o  a good  AGR and i n c r e a s e s ages  stand  slight  spacings  mean AGR t h a n  to  18,  that  4.14).  w h i c h means  test  at  mean AGR d i d  (Table  were a l s o  range  spacing  spacing  same t r e n d a l s o  ficant  of  difficult  widest  detect  i n AGR w i t h  The r e s u l t s  was  to  differences  accepted  et  spacing  were d e t e c t e d  range  differences,  significant  multiple  variation  e x c e p t when t h e  though  failed  the  1986), al.  a n o v a was  Significant  no t r e n d o f  It  the  However,  significant  significant  v a r i a t i o n with  comparison t e s t  significantly. 18  were  1979).  and L a n n e r 84  in  in  previous there  For each  of  fact  that  especially  for  a species  t o Assmann  these  high  the  the  at  precipitation  reflects  (1985),  year  appeared  c h a r a c t e r i z e d by  According  height  shoot such  (1970),  f o r m a t i o n of  the  FIGURE  4 . 14  HEIGHT AGR DATA SUPERIMPOSED CLIMATIC VARIABLES  o.soo A V E R A G E AOR (HEIGHT) ' O R ALL SPACINGS OVER A C E  0.748 0.69S O.S44 \  0.592  h^"  0.540  g  0.488  ^  0.436 0.384 — — —  0.332  —  —  0.280 1 2  1 »  -2 X .5 X .9 X 2.1 X 2.4 X 3.0 X 4-.3 X e.o X 1 1 1  1 8  .2 M I S M .8 M 2-1 M 2.4 M 3.0 M 4.3 M 6.0 M 1 1  21  24  27  24.0 22.4 .—. CO  ^  20.S  g  ~ 25 FU J UJ <  19.2  >  OO  1 7  *  A O ©  LEGEND — MEAN MAXIMUM TEMPERATURE — M E A N MINIMUM T E M P E R A T U R E — MEAN TEMPERATURE  ce co O  1 eo  2 a|  1 4.4  ^  =S  11.2  e.e 8.0 1 2  27  1 5  21  TOTAL  85  24  AGE  33  FIGURE  4.14:  (CONTINUED)  A V E R A G E AOR (HEIGHT) F O R ALL SPACINGS OVER A G E  2.4 3.0 4.3 S.O  1S  1 5  1 8  X X X X  2.4 3.0 4.3 C O  M M M M  21  24  21 2 4 T O T A L A G E  86  27  3 0  3 3  30  3 3  meristematic moisture  bud i n t h e  conditions,  meristematic gation  is  4.5.1.2.3-  Despite (Figure within  was  reduced.  the  stand  closest  and t r e e  was  is  size  at  all  still  (Figures  change  When elon-  conditions.  later,  age  tree  spacings 24.  size  widest  relationship  S i t k a spruce  differences  and l o d g e p o l e  range  spacing,  tests  and t h a t  different,  most  ones. were  tree factor  experiment In  this  found o n l y  that  of  the  between RGR  pine.  were  showed  in  v a r i a t i o n was  in a competition  among s p a c i n g s  When  there  DBH n e s t i n g  The same p a t t e r n o f  size  the  narrowest at  age  tree  and 4 . 1 0 ) ,  i n which the  (1984)  The m u l t i p l e  with  i n the  4.9  with  The v a r i a t i o n i n RGR w i t h  4.15  ages.  i n the  of  significantly  the  decreased  seedlings  v a r y much w i t h  for  years  RGR i n c r e a s e d w i t h  al.  did  decreased  Five  size  et  and 2 4 .  soil  shoot  RGR d e c r e a s e d  more n o t i c e a b l e  occurred slowly.  a g e s 18  not  tree  area  and t h e  significant  not  generally  by C a n n e l l  involving  were  it  by  and t e m p e r a t u r e .  prevailing climatic  height  trend is  confirmed i n Table  observed  it  RGR w i t h  DBH and b a s a l  significant  study,  13,  while  influenced  Rate  30 y e a r s ,  fluctuations  is  current season,  (Figure 4.16.1).  The same  spacings,  Compared t o  size  of  reached  by t h e  Growth  A t age  rate  i n the  fluctuations,  spacings  decreasing  more  large  4.15). all  begins  influenced  Relative  season  nutritional status,  activity  also  previous  the  at  h e i g h t RGR spacings  being p a r t i t i o n e d into  only  two  groups.  Even though than  those  increases 24  fluctuations  o f AGR, t h e r e  climate  appeared to  i n RGR and i n c r e a s e s  (Figure 4.17).  with  Except for  were  87  20,  pronounced  be a c o r r e s p o n d a n c e  i n degree-days age  less  at  an i n c r e a s e  ages 17,  between 20,  i n RGR was  and  FIGURE 4.15: MEAN HEIGHT RGRs FOR ALL SPACINGS OVER AGE 0.240  0.218 LEGEND SPACING: 1.2X1.2 M SPACING: 1.5X1.5 M SPACING: 1.8X1.8 M SPACING: 2.1X2.1 M SPACING: 2.4X2.4 M SPACING: 3.0X3.0 M SPACING: 4.3X4.3 M SPACING: 6.0X6.0 M  0.196  0.174  < 0.152-  Id >-  .0.130I o u I 0.108 O cr 0.086  0.064  0.042  0.020  ^ — i — i — i — i — i — j — i — i — i — i — i — | — i — i — i — i — i — j — i — i — i — < — i — i — i — i — i  13  16  19  22 TOTAL AGE  88  25  i  i  i—i—i—'—i—>  28  i  31  FIGURE 4 . 1 6 : HEIGHT RGRs AS A FUNCTION OF DBH SIZE CLASS FIGURE 4.16.1: AGE 13  FIGURE 4.16.2: AGE 18 0. 20  0.340  LEGEND SPACING: 1.2X1.2 M SPACING: 1.5X1.5 M SPACING: 1.8X1.8 M SPACING: 2.1X2.1 M SPACING: 2.4X2.4 M SPACING: 3.0X3.0 M SPACING: 4.3X4.3 M  0.316 0.292<  2  268  \ 0  4 0 0 0  0. 18  LEGEND = SPACING: 1.2X1.2 M = SPACING: 1.5X1.5 M = SPACING: 1.8X1.8 M - SPACING: 2.1X2.1 M - SPACING: 2.4X2.4 M = SPACING: 3.0X3.0 M = SPACING: 4.3X4.3 M = SPACING: 6.0X6.0 M  244  2 0.220 H I  S2o. LI  196  i  cc  o.  172  o  0. 148  0. 124 0 . 100 6  LEGEND A = SPACING: 1.2X1.2 M « = SPACING: 1.5X1.5 M 0= SPACING: 1.8X1.8 M 0 = SPACING: 2.1X2.1 M V = SPACING: 2.4X2.4 M • = SPACING: 3.0X3.0 M * = SPACING: 4.3X4.3 M o = SPACING: 6.0X6.0 M  14  LEGEND A-SPACING: 1.2X1.2 M 0= SPACING: 1.5X1.5 M *= SPACING: 1.8X1.8 M 0= SPACING: 2.1X2.1 M 7= SPACING: 2.4X24 M • = SPACING: 3.0X3.0 M * = SPACING: 4.3X4.3 M o - SPACING: 6.0X6.0 M  v  £ 0  .0000 o . o o o  20  12  FIGURE 4.16.4: AGE 30  0.130  15  10  DBH SIZE CLASS (CM)  DBH SIZE CLASS (CM) FIGURE 4.16.3: AGE 24  10  8  'i  i i i i • i ' i • i • i ' i ' i ' i ' i ' i ' i  1  i  1  i  1  i  6 8 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 0 2 4 6 8 0 2 4 6 8 0 2 4 6 8  25  DBH SIZE CLASS (CM)  DBH SIZE CLASS (CM) 89  Table  4.15:  Age  13 18 24 30  Two-level nested (m/year/m).  Spacings  a a a a  l l l l  included  anova  (m)  DBH  l l l l  1.2  *:  0.07a* 0.03ab  1.5  54/392 93/408 107/370 114/341  8.88* 4.58* 2.88* 1.52*  level  of  0.08b 0.03b  0.07a 0.02b  2.1  2.4  0.08b 0.03ab  0.09b 0.03ab  The s p a c i n g s f o r a g i v e n not d i f f e r s i g n i f i c a n t l y  age f o l l o w e d a t the l e v e l  90  height Spacing  F  mean RGRs i n h e i g h t  1.8  RGR i n  class  D.F. 6/54 7/93 7/107 7/114  F 0.81n.s 5.36* 1.07n.s 10.16*  p r o b a b i l i t y of  among t h e  T u k e y ' s m u l t i p l e range S p a c i n g (m)  Age  18 24  for  D.F.  * : S i g n i f i c a n t d i f f e r e n c e s at the n . s . : no s i g n i f i c a n t difference. Comparison of  tests  0.05  spacings  tests 3.0  4.3  0.10b 0.03a  0.10b 0.03a  6.0 0.07a 0.02b  by t h e same l e t t e r do of p r o b a l i l i t y of 0.05.  FIGURE  4 . 1 7 : HEIGHT RGR DATA SUPERIMPOSED CLIMATIC VARIABLES  0.2 40 A V E R A G E ROR (HEIGHT) FOR ALL SPACINGS OVER AGE  0.218 O. 1 9 6 O. 1 7 4  A O  O. 1 5 2  V •  o  — — — — — — — —  O. 1 3 0  LEGEND 1 .2 X 1 . 2 1 . 3 X 1 .S 1 .8 X 1.8 2.1 X 2.1 2.4 X 2.4 3.0 X 3.0 4.3 X 4.3 «.0 X 6.0  M M M M M M M M  O. 1 O S O.OSS 0.084 0.042 0.020 12  21  24  .2 7  30  24.0 22.4 20.S 19.2  A O o  LEGEND  — MEAN MAXIMUM TEMPERATURE — M E A N MINIMUM T E M P E R A T U R E — MEAN TEMPERATURE  6  £2  o  1 6.o  3—  1 4.4  LP  1  2  8  1 1 .2 9.6 8.0  3b  1 2  21 TOTAL  91  24 AGE  33  p r e f a c e d by an i n c r e a s e i n t o t a l p r e v i o u s growing  season.  The same r e a s o n s  may e x p l a i n t h i s d e l a y e d 4.5.1.3-  p r e c i p i t a t i o n during the  effect.  D e v e l o p m e n t i n Volume  4.5.1.3.1The  Cumulative  general  with spacing  Increment  t r e n d was a n i n c r e a s e i n t h e mean t r e e v o l u m e  (Table  4.16).  Except  f i c a n t d i f f e r e n c e s among s p a c i n g s factor  t r e e v o l u m e a n d DBH ( T a b l e  (Table  4.17).  signi-  The DBH n e s t i n g  relationship  between  T h e r e a p p e a r s t o be a n e x p o (Figure 4.18).  This  t h a t t h e e f f e c t o f s p a c i n g on t r e e volume i s m o s t l y  caused by t h e s e n s i t i v i t y was n o t f o u n d  Contrary  o f DBH t o d e n s i t y b e c a u s e h e i g h t  Growth Rate  t o DBH a n d b a s a l a r e a , t h e t r e n d i n v o l u m e AGR was  i n c r e a s e f r o m a g e 13 t o a g e 2 3 , a n d t h e n a s t a b i l i z a t i o n  slight  r e d u c t i o n (Table  4.18).  nesting  a t a l l ages ( T a b l e  t h e g r e a t e r AGR.  a t every  or a  significant  t r e n d was a n i n c r e a s e i n AGR w i t h s p a c i n g .  f a c t o r was s i g n i f i c a n t  age; t h e l a r g e r  4.19). The DBH the tree,  A t a g e 1 3 , t h e r e l a t i o n s h i p b e t w e e n DBH a n d  v o l u m e AGR was l i n e a r spacings,  a t age 1 3 ,  Except  d i f f e r e n c e s among s p a c i n g s w e r e f o u n d general  growth  t o be much a f f e c t e d b y s p a c i n g .  4 . 5 . 1 . 3 . 2 - Absolute  The  t h e r e were  4.17).  r e l a t i o n s h i p b e t w e e n DBH a n d v o l u m e  suggests  an  a t age 1 3 ,  i n t h e anova i n d i c a t e d a s i g n i f i c a n t  nential  a s m e n t i o n e d f o r AGR  f o r the widest  i t was e x p o n e n t i a l  spacings;  (Figure 4.19).  r e l a t i o n s h i p s were a l l l i n e a r .  93  f o r t h e narrow  Above age 1 3 , t h e  TABLE  4.16:  Mean v o l u m e s age.  Spacing (m)  per  13  tree  (m ) 3  for  all  Age 23  18  spacings  over  28  33  1 .2x1 .2  Mean N-  0 .004841 0 .021800 0 .047590 0 .085120 0 .134100 83 61 55 46 37  1 .5x1 .5  Mean N  0 .006861 0 .027996 66 62  1 .8x1 .8  Mean N  0 .006919 0 .032480 0 .070682 0 .113120 0 .147410 63 58 57 54 54  2 .1x2 .1  Mean N  0 .007388 0 .037179 0 .090677 0 .146110 0 .211770 63 61 54 59 57  2 .4x2 .4  Mean N  0 .007273 0 .039879 0 .106000 0 .177510 0 .249300 58 58 58 57 56  3 . 0x3 .0  Mean N  0 .007683 0 .047819 0 .141000 0 .251160 0 .353940 60 59 58 58 58  4 .3x4 .3  Mean N  0 .006982 0 .041389 0 .140250 0 .285650 0 .432260 62 58 56 56 53  6 . 0x6 .0  Mean N  0 .059785 0 .194800 0 .413490 0 .634690 95 94 94 92  -  Table  4.17: T w o - l e v e l  Age  Spacings  nested  included  anova  tests  DBH  (m)  D.F. 13 18 23 28 33  0 .060310 0 .092080 0 .124120 58 56 54  f o r t o t a l volume ( m ) . 3  F  54/394 199.88* 95/409 175.73* 110/377 113.67* 80.72* 111/359 113/339 59.47*  all all all all all  Spacing  class D.F.  6/54 7/95 7/110 7/111 7/113  *: S i g n i f i c a n t d i f f e r e n c e s a t t h e l e v e l o f p r o b a b i l i t y n . s . : no s i g n i f i c a n t d i f f e r e n c e .  94  F 0.29n.s. 4.30* 16.93* 35.20* 48.17* o f 0.05.  FIGURE 4 . 1 8 :  MEAN VOLUMES AS A FUNCTION OF DBH SIZE CLASS  FIGURE 4.18.1: AGE 13  FIGURE 4.18.2: AGE 18  0.0230 0.0207 0.0184  0.0181  0. I 10  LEGEND -SPACING: 1.2X1.2 M -SPACING: 1.5X1.5 M -SPACING: 1.8X1.8 M -SPACING: 2.1X2.1 M = SPACING: 2.4X2.4 M = SPACING: 3.0X3.0 M = SPACING: 4.3X4.3 M  0.099 0.088  0.077 10 » 0 066  10  * 0.0138 * 2  LEGEND -SPACING: 1.2X1.2 M -SPACING: 1.5X1.5 M -SPACING: 1.8X1.8 M -SPACING: 2.1X2.1 M - SPACING: 2.4X2.4 M - SPACING: 3.0X3.0 M - SPACING: 4.3X4.3 M = SPACING: 6.0X6.0 M  * 2 ^—'  UJ 0.01 15 2 D 0.0092  LI 0 055 2  D  O  044  >  0.0069  0 033  0.0046  0.022  0.0023  0.011  0.0000  0.000 3  4  5  6  7  10  DBH SIZE CLASS (CM)  0. 196  12  14  16  18  20  FIGURE 4.18.4: AGE 28 0.550  0.280  0.224  10  DBH SIZE CLASS (CM)  FIGURE 4.18.3: AGE 23  0.252  8  6  LEGEND A-SPACING: 1.2X1.2 M 0 = SPACING: 1.5X1.5 M «= SPACING: 1.8X1.8 M 0 = SPACING: 2.1X2.1 M 7 = SPACING: 2.4X2.4 M • = SPACING: 3.0X3.0 M * = SPACING: 4.3X4.3 M o = SPACING: 6.0X6.0 M  0. 495 0. 440 0.383  10  LEGEND A-SPACING: 1.2X1.2 M * = SPACING: 1.5X1.5 M SPACING: 1.8X1.8 M 0= SPACING: 2.1X2.1 M 7= SPACING: 2.4X2.4 M * = SPACING: 3.0X3.0 M * = SPACING: 4.3X4.3 M o = SPACING: 6.0X6.0 M  4 7  11 f/f  » 0. 168  UJ 0. 140 2 D 0.112 0.084 0.056 0.055  0.028  0.000  0.000 6  8  10  12  14  16  18 20 22 24 26 28  12  15  18  21  24  27  DBH SIZE CLASS (CM)  DBH SIZE CLASS (CM) 95  30  33  36  TABLE 4 . 1 8 :  Mean AGRs i n volume spacings over age.  Spacing (m)  (m /year)  for a l l  3  Ages 13  18  23  28  1 . 2 x 1 .2  Mean N  0 .003090 61  0 .004900 55  0 .006030 46  0 .006880 37  1 .5x1 .5  Mean N  0 .004150 62  0 .006120 58  0 .005990 56  0 .005850 54  1 . 8 x 1 .8  Mean N  0 .005003 58  0 .007530 57  0 .007810 54  0 .006860 54  2 .1x2 .1  Mean N  0 .005913 61  0 .010472 59  0 .010497 57  0 .011716 54  2 .4x2 . 4  Mean N  0 .006521 0 .013220 58 58  0 .013950 57  0 .013804 56  3 . 0 x 3 .0  Mean N  0 .008010 59  0 .018493 58  0 .022030 58  0 .020557 58  4 .3x4 .3  Mean N  0 .006842 58  0 .019747 56  0 .029080 56  0 .029934 55  6 . 0x6 .0  Mean N  0 .026962 94  0 .043738 94  0 .044532 92  Table  4.19:  -  Two-level-nested (m /year).  anova t e s t s  f o r AGR i n volume  3  Age  Spacings  included  (m)  DBH c l a s s D.F.  13 18 23 28  a a a a  l l l l  54/356 89/398 103/367 106/346  l l l l  * : S i g n i f i c a n t d i f f e r e n c e s at the n . s . : no s i g n i f i c a n t d i f f e r e n c e .  96  F 62.44* 39.59* 17.65* 6.66*  level  Spacing D.F. 6/54 7/89 7/103 7/106  F 2.22n.s. 26.13* 72.55* 103.21*  of p r o b a b i l i t y of  0.05  VOLUME AGRs AS A FUNCTION OF DBH SIZE CLASS  FIGURE 4. 19  FIGURE 4.19.1: AGE 13  FIGURE 4.19.2: AGE 18  0 .016B 0.0151 0.0135  : 0.0115  2  0.040  LEGEND : SPACING: 1.2X1.2 M SPACING: 1.5X1.5 M ^SPACING: 1.8X1.8 M ^SPACING: 2.1X2.1 M •• SPACING: 2.4X2.4 M • SPACING: 3.0X3.0 M • SPACING: 4.3X4.3 M  0.036 0.032 028  LEGEND A =SPACING: 1.2X1.2 M 0 - SPACING: 1.5X1.5 M « = SPACING: 1.8X1.8 M 0 = SPACING: 2.1X2.1 M V = SPACING: 2.4X2.4 M • = SPACING: 3.0X3.0 M * = SPACING: 4.3X4.3 M o = SPACING: 6.0X6.0 M  >-  ">0 .0102  024 #  *  ,0.0085  2 0.020 O O . 016  :>  go. <  012  0.008  o. oo 1 9  0.004  0.0002  0.000 3  4  5  B  7  8  9  10  10  DBH SIZE CLASS (CM)  % 0.0378^  16  18  20  33  36  FIGURE 4.19.4: AGE 28  0.0540  0.04321  14  DBH SIZE CLASS (CM)  FIGURE 4.19.3: AGE 23  0.0486-  12  0.060  LEGEND A = SPACING: 1.2X1.2 M * = SPACING: 1.5X1.5 M « = SPACING: 1.8X1.8 M 0 = SPACING: 2.1X2.1 M V = SPACING: 2.4X2.4 M * = SPACING: 3.0X3.0 M - / * - SPACING: 4.3X4.3 M „ 4 o = SPACING: 6.0X6.0 M ,*"*\ }  / 0.054 0.048 042  \o.036  ^>0.0324J  I  LEGEND A-SPACING: 1.2X1.2 M 0= SPACING: 1.5X1.5 M «= SPACING: 1.8X1.8 M 0 = SPACING: 2.1X2.1 M 7= SPACING: 2.4X2.4 M • = SPACING: 3.0X3.0 M * = SPACING: 4.3X4.3 M o = SPACING: 6.0X6.0 M  Pi y •  ,0.030 _l  O  0  J  024  >  et  oo  018  <  0.012 0.0054  0.006  0.0000  0.000* 9  DBH SIZE CLASS (CM)  12  15  18  21  24  27  DBH SIZE CLASS (CM) 97  30  4.5.1.3.3-  Relative  Mean volume ficant  Growth  RGR d e c r e a s e d  differences  were  general  trend consisted  results  of  tree  the  diameter  13  (Figure  at  the  anova (Table  4.20.1).  narrowest  spacings  of  1.5  Rate with  found at of  all  4.21).  that  It  When t h e  decreased  with  4.20.2).  The same t r e n d c o n t i n u e d  4.20.3  increasing  and 4 . 2 0 . 4 ) .  patterns  as  those  interpretation 4.5.2-  i n terms  of  spacing.  The  as  with  18 y e a r s  lowest  widest  and b a s a l is  age  the RGR  classes),  spacings  RGR showed area. the  at  and  (Figure  a g e s 23 and 28  volume  efficiency  old,  at  DBH, r e m a i n e d c o n s t a n t  from the  at  DBH i n c r e a s e d  with  (Figures the  same  Therefore,  the  same.  F u n c t i o n a l Approach  complement  development observe  tions  have  chers  (e.g.,  1978).  mentioned, classical  how t h e  before  been  the  to  the  better  of  individual  of  possible  to  individual Equa-  individual trees  by d i f f e r e n t  resear-  1973,  were  Sweda 1984,  found i n which  s u c h as AGR o r RGR were d e r i v e d and u s e d  development  is  the  competition.  no s t u d i e s  onset  visualize  it  efficiency)  used  of  P i e n a a r and T u r n b u l l However,  a p p r o a c h may be  For i n s t a n c e ,  RGR ( i . e . ,  and a f t e r  fitted  functional  a p p r o a c h and t o  individual trees.  precisely  varies  indices,  the  of  trees  al.  diameter  The  RGR v a r i e d s i g n i f i c a n t l y  the  Essentially,  of  As p r e v i o u s l y to  DBH a t  Signi-  4.21).  i n RGR w i t h  s t a n d s were  m (apart  4.20).  (Table  decreased  increased  m and 1.8  (Table  ages  an i n c r e a s e  indicated  spacing  age  trees.  98  to  and Yang  et  growth compare  the  TABLE 4 . 2 0 :  Mean RGRs i n volume ( m / y e a r / m ) a l l spacings over age. 3  Spacing (m)  3  f r 0  Ages 13  18  23  28  1 . 2 x 1 .2  Mean N  0. 255830 0 .128140 61 55  0 .075880 46  0 .053640 37  1 .5x1 .5  Mean N  0. 281900 0 .137070 62 58  0 .073086 56  0 .048586 54  1 . 8 x 1 .8  Mean N  0. 311860 0 .147990 58 57  0 .078509 54  0 .047720 54  2 .1x2 .1  Mean N  0. 342040 0 .171400 61 59  0 .083402 57  0 .061938 54  2 .4x2 .4  Mean N  0. 366340 0 .204300 58 58  0 .100070 57  0 .065037 56  3 . 0x3 .0  Mean N  0. 406490 0 .229120 59 58  0 .120700 58  0 .070599 58  4 .3x4 .3  Mean N  0. 369140 0 .268200 58 56  0 .151270 56  0 .088417 55  6 . 0x6 .0  Mean N  0 .153690 94  0 .087128 92  Table  4.21:  -  T w o - l e v e l n e s t e d anova t e s t s (m / y e a r / m ) . 3  Age  13 18 23 28  Spacings  a a a a  l l l l  0 .245860 94  f o r RGR i n volume  3  DBH  i n c l u d e d (m)  l l l l  Spacing  D.F.  F  D.F.  F  54/356 89/398 103/367 106/346  8.05* 12.05* 6.52* 4.49*  6/54 7/89 7/103 7/106  16.91* 30.89* 45.80* 24.93*  * : S i g n i f i c a n t d i f f e r e n c e s at the l e v e l n . s . : no s i g n i f i c a n t d i f f e r e n c e .  99  class  of p r o b a b i l i t y of  0.05,  FIGURE 4 . 2 0 :  VOLUME RGRs AS A FUNCTION OF DBH SIZE CLASS  FIGURE 4.20.1: AGE 13  FIGURE 4.20.2: AGE 18  0.500  0.440  0.563  A 0 0 0 7 • *  N0.526  10  2 0.489  LEGEND = SPACING: 1.2X1.2 M = SPACING: 1.5X1.5 M -SPACING: 1.8X1.8 M = SPACING: 2.1X2.1 M = SPACING: 2.4X2.4 M = SPACING: 3.0X3.0 M = SPACING: 4.3X4.3 M  0.399  w  LEGEND A - SPACING: 1.2X1.2 M « - SPACING: 1.5X1.5 M 0 = SPACING: 1.8X1.8 M 0 -SPACING: 2.1X2.1 M A 7 = SPACING: 2.4X2.4 M • = SPACING: 3.0X3.0 M V\ * = SPACING: 4.3X4.3 M " -^,o = SPACING: 6.0X6.0 M  \  0.358  ^0.317  x  C£  \\\  fi 0.276 \ 10  0.071 0.030 7  8  9  DBH SIZE CLASS (CM)  DBH SIZE CLASS (CM)  FIGURE 4.20.3: AGE 23  FIGURE 4.20.4: AGE 28 0.150  LEGEND A-SPACING: 1.2X1.2 M 0 = SPACING: 1.5X1.5 M 0 = SPACING: 1.8X1.8 M v-SPACING: 2.1X2.1 M 7 = SPACING: 24X24 M V • = SPACING: 3.0X3.0 M ^ * = SPACING: 4.3X4.3 M o = SPACING: 6.0X6.0 M cure  LEGEND A-SPACING: 1.2X1 2 M «-SPACING: 1.5X1.5 M 0= SPACING: 1.8X1.8 M 0 = SPACING: 21X21 M 7= SPACING: 2.4X2.4 M • = SPACING: 3.0X3.0 M * - SPACING: 4.3X4.3 M o = SPACING: 6.0X6.0 M  0.015 0.000 0.010 12  13  18  21  24  27  30  6  8  0  1 1 1 1 2 2 2 2 2 3 2 4 6 8 0 2 4 6 8 0  3 2  DBH SIZE CLASS (CM)  DBH SIZE CLASS (CM) 100  3 4  3 6  3 8  4.5.2.1-  Cumulative  All  the  functions  determination DBH were  (Table  close  O n l y a few  function results still  of  the  (Payandeh  the  increased.  This  increased the  a young age,  33  the  This for  DBH a t  with  are  0 or  1.  trees  3,  difference  as  large  4.5.2.2- Absolute  tive  values  because  the  trees  13 and 3 3 .  of  growth  it  1 of  it  better was  33 as  the  The l a r g e r  ages.  their  the  However,  rank  differences  and o n l y  was  age  tree  by  age  slightly.  by c o m p a r i n g the  4,  same  spacing  In  ranks  between of  2,  ranks  7 had a  1 had a  Rate as  the  first  ( T a b l e 2 and F i g u r e 2 o f for  model u s e d  produced  80 had a d i f f e r e n c e  f o r AGR were o b t a i n e d  appeared  repre-  a nonlinear  Appendix 3).  older  of  of  5.  Growth  functions  that  for  was  of  not  parameters  status.  4 had a d i f f e r e n c e as  age  i n the  had c h a n g e d  out  functions.  approximately at  the  3).  trees.  social  Most o f  is  shortcomings,  values  of  a r o u n d 33 y e a r s  m i g h t have  DBHs was  at  derived  possible  among  (Table  Appendix  situation  i n T a b l e 1 ( A p p e n d i x 3)  difference  the  is  these  apparent  their  larger the  Seven  Equations  It  greater  spacing  by t h e  this  function)  initial  kept  the  ages  of  t r e n d was  seen  age.  Despite  reached  m a j o r i t y of  may be  this  1 of  a decline  good,  make c o m p a r i s o n s  trees  at  was  Weibull  range  trees  general,  fit  1983).  to  13,  which  the  (Figure  showed  of  The p r e d i c t e d v a l u e s  represented  some t r e e s  growth at  possible  age  observations  were b a d l y  for  (i.e.,  While  d e r i v e d had v e r y h i g h c o e f f i c i e n t s  1 of Appendix 3).  the  Even though  sentative  at  to  trees  The e q u a t i o n s age.  Increment  some t r e e s  d i d not  a r o u n d age  represent  101  derivative  Appendix 3). 33.  adequately  This the  of Nega-  occurred rate  of  decline major  i n growth at  trends  risons each  age.  i n s u c h a way  because  a l l the  3).  spacing  The  that  trees  increased,  parameters  functions, 3).  occurred  a little  This  examination  o f AGR trees  AGR  suggests  the  showed  the  t o make compa-  same p o s i t i o n s  relative  to  a  a g e s 13  AGRs were g e n e r a l l y  AGRs w i t h  large  f o r AGR  have  show t h a t 2  increment,  i n AGR  with  Relative  the  the  For  Growth  first  natural  stated,  close  the  observations,  was  density. order  with  small 3).  of Appendix ages,  AGRs.  large  The  ranks  r e l a t i o n s h i p with the  i s higher  d i d not  age  mean d i f f e r e n c e than  that  for  d i f f e r e n c e s were g r e a t e r  trees  the  logarithm  Even though  this  the  RGR  keep t h e  same  in  cumuthan  social  e q u a t i o n s were d e r i v e d  d e r i v a t i v e of  3).  were o b t a i n e d  33  AGR  decreasing  both  of  Rate  Appendix to  consistent  and  2  high  every p l o t ,  most o f the  at  trees  in  i n stand  by  the 2  (Table  associated  (Figure  of  age.  previously  computing fitting  and  indicates that  4.5.2.3-  no  between a g e s 13  f o r AGR  As  3).  of Appendix  This  was  small  33  and  exceptions:  AGRs, and there  ones  slopes  spacing  reduction  low  high  the  Appendix  of decrease  showed t h a t  low  status  rate  DBHs a t  may  lative  the  the  trees  rank  that  with  of  and  (Table  value  2 of  (Figure  which c o n s t i t u t e  more r a p i d l y w i t h  were n o t a b l e  AGR,  equations  possible  increased  i n absolute  However, t h e r e  33  i t was  kept  f o r age,  increased  Appendix  3.  However, t h e  other. As  The  this  (Figure  a problem  the  of  the DBH  equations over  predicted  negative  r e l a t e d to  102  values  values  3 of Appendix the  time  3).  obtained (Table f o r RGR  around As  was  regression  the the  3  by by  of were  ages case  model.  very 30  and  for  Similar with  trends  spacing,  same p a t t e r n the  and  between the the  1.8  6.0  m  by  age  m  RGRs had  RGR. very  spacings,  and  27  and  one  set of  (Figure  3.4  t r e e , the  greater  Some s m a l l  13,  and  vice versa•  was  c h a r a c t e r i z e d by A l l the  the  and  trees  lower  T h i s was  less  less  and  by  both  (Table  ages  differences o f AGR).  the  f o r the  33  3).  the  m  very  was  values  rate  (Alig  S m i t h and  e t a l . 1984; Williams  smaller reached  and  this  a  place 26  for  For  the  in  RGR  period,  the  close values  the  larger  age  3).  than  pattern  13  For 2  were g r e a t e r  Ek  of  the  became  change  age RGR  than of  comparatively  These o b s e r v a t i o n s  the  ranks  three  (i.e., than  Monserud  1975;  The  majority  of (Ek  f o r RGR  were at  v a r i a b l e s , mean  smaller  than  those  3.  model  and  103  f o r AGR;  same t y p e  estimating  b a s e d upon Newnham's ( 1 9 6 4 ) a s s u m p t i o n s  described  l a r g e r trees at  pronounced  c o n s i s t s of  1980).  25  pattern  RGRs t h a n  When a s i n g l e - t r e e d i s t a n c e - d e p e n d e n t step  took  reversed;  the  vice versa.  3 of Appendix  a major  the  The  spacing.  4 . 5 . 3 - E s t i m a t i o n o f t h e P o t e n t i a l Growth R a t e o f T r e e s f r o m Open-Grown T r e e s  simulation,  increased  trees  This  mean d i f f e r e n c e s between t h e  a few  13,  Following  RGR  were m o s t l y between 1 and  Only  age  3.0  age  increased.  spacing,  shown were a f f e c t e d by  a t age  age  At  m  a more s y s t e m a t i c  trees at  supported  1.2  followed  change; h i g h l y e f f i c i e n t efficient  plot.  any  RGR.  t r e e s had  trees  over  t r e e s had  size  a l l the  above.  28  of Appendix  between t r e e  at  close values.  f o r the  only  RGR  Subsequently,  23  However, n o t  AGR.  the  every  and  spacing, 31  within  a g e s 22  relationship the  greater  where t h e  were e v i d e n t ;  i t s rate of decrease  occurred  t r e e , the  point  t o AGR  Stand-Grown  i s used  p o t e n t i a l growth  Loucks et  these and  in  al.  m o d e l s have Monserud  1982; been  1975;  Loucks et  a l . 1981).  One  potential  growth  of  simulation, objective but  also  rate  this  of  section  for  the  of  Ek  first  is also  the  of  middle were  departed  group  The  this  the  main  assumption,  This  from  (Figure  4 . 2 2 ) .  estimated  this  asymptotic  to  values  values  the  as  used  least  equation  trees  in  It i s located  of  the  close  to  The  trees  by  of  of  the  to d e r i v e age  at  the the  near  first  and  four they  from  fact  that  spacing  group  equation  trial  the  substantial differences were a t t a i n e d  first  i t was  are  differ  because For  the  to perform  tests using (They w i l l  gnated  equation  and  104  so.  Ek's  equation,  13  years.  graph.  greatly within  t o do  derived  30  first  the  also  equation  occurred  shown on  from  5 to  trees  at d i f f e r e n t ages.  3 5 years  decided  height  derived  l e a s t the  growth  e q u a t i o n was  f o r m e d by  and  c l o s e l y for at  a local  breast This  4 . 2 3 ) .  possible  the  4.21.  supported  e q u a t i o n s when i t was as  pine  at  The  4 . 2 1 ) .  red  majority  located  e q u a t i o n s d i d not  considered,  trend,  study because  (Table  13  B o t h Ek's  the  Figure  4.22,  a function  middle  point,  only the  5  the  DBH  same g e n e r a l  trees  trees.  trees  near  open-grown  this  as  located  the  purposes of  f o r DBH  open-grown  the  d e c i s i o n was  t r e e s were n o t  remaining  trees,  13.  equation  age  only  of  in  5 to  f u n c t i o n was  though  estimation  trees  Weibull  reason,  t e s t not  f o r m e d by  The  Beyond  the  been t e s t e d .  i n Figure  f o r the  considerably  four  the  never  f r o m open-grown  included  rejected  equation.  these as  the  four  (Table  developed  Minnesota,  Ek's  has  t o have  years  35  (1971),  trees  concerns  Although w i d e l y used  i s to  first  measured a l l appeared the  trees.  assumption  this  these  a l t e r n a t i v e ones.  Except  for  of  this Even range  of  both be  desi-  respectively).  TABLE 4 . 2 2 : B a s i c g r o w t h i n f o r m a t i o n on t h e o p e n - g r o w n t r e e s . Tree numbe r 1 2 3 4 5 6 7 8 9 10 11 12 13  DBH ( cm) 56 .7 53.9 54 .9 50.0 50.5 51.3  49.8 39.7 65.7 43.5 38.7 46.5 59.2  Total height (in) 17 .9 17.2 15.2 16.6 12.1 15.1 14.1  11.0 16.0 13.5 15.0 13.9 16.2  Crown w i d t h (m) 8.8 9.3 9.8 9.2 9.7 11.0 9.2 9.3 9.7 8.5 10.0 9.0 10.3  105  Crown l e n g t h (m) 12.2 13.4 12.4 12.8 11.4 14.2 1 1 1 1 1 1 1  3.3 0.0 3.9 2.5 3.8 2.3 2.7  Breast height age 84 77 79 70 37 35 36 27 78 30 25 35 55  FIGURE 4.21: DBH = F(AGE) FOR OPEN-GROWN TREES 55.0  49 . 5  44 . 0  LEGEND A = TREE| 1 0= TREEf 2 0= TREEf 3 0 = TREEf 4 V= TREE* 5  38 . 5  33.0  CJ 27.5I  00  Q  22.0-  16.5  11.0-  5.5-  0.0  1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1  10  15  • 1 1 1 1 1 1 1 1 1 1  20  AGE AT BREAST HEIGHT  106  25  • i  • 1 1 1 •  30  111  35  Table  4.23:  Comparison of Ek's equation  values and t h e  between DBHs o b t a i n e d derived equation.  Ek's  DBH (cm)  equation: - 0 . 0 4 5 9 1 3 x A G E ) 1.469047 = 59.721242(1-E ) Equation  derived: 1.238790  -(0.034162xAGE) DBH (cm)  -  63.014384(1-E  ) DBH  Age 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35  Ek's equation 0.6 1.6 2.9 4.3 5.7 7.3 8.8 10.4 11.9 13.6 15.1 16.7 18.2 19.7 21.2 22.6 24.0 25.4 26.7 27.9 29.2 30.4 31.6 32.7 33.8 34.8 35.8 36.8 37.8 38.7 39.5 40.4 41.2 41.9 42.7  107  (cm) Derived  equation  0.9 2.2 3.6 5.1 6.7 8.2 9.8 11.4 13.0 14.6 16.2 17.8 19.3 20.8 22.3 23.7 25.2 26.6 27.9 29.2 30.5 31.8 33.0 34.2 35.3 36.4 37.5 38.5 39.6 40.5 41.5 42.4 43.3 44.1 44.9  from  FIGURE 4.22: DBH = F(AGE) FOR OPEN-GROWN TREES  O  5  10  15  20  AGE AT BREAST HEIGHT  108  25  30  35  The (1979,  first  1984)  step  consisted  f o r open-grown t r e e s  same RGR b e f o r e  (solid  with  hypothesis  In effect,  (dotted  stand-grown data before  are  for the6.0 m spacing.  theonset of competition  The h y p o t h e s i s  rejected. trees  open-grown t r e e s . potential The  (1979,  o f Ford  w i t h i n the Therefore,  by the  f o l l o w i n g two h y p o t h e s e s w e r e t e s t e d :  increment o f a stand-grown t r e e  o p e n - g r o w n t r e e s was c o m p u t e d f r o m t h e  and  derived  (1971)  equation  and Ek's  e q u a t i o n s f o r DBHs e q u a l t o t h a t o f t h e  compared.  In general,  the potential  The i n c r e m e n t o f  Results  arelisted  4 . 2 5 f o r t h e 4 . 3 m and 6 . 0 m spacing  period.  the potential  i n t e r m s o f RGR i s e q u a l t o t h a t  o f a n o p e n - g r o w n t r e e o f t h e same DBH.  stand-grown t r e e s  (1)  considered.  i n t e r m s o f AGR i s e q u a l t o t h a t  o f a n o p e n - g r o w n t r e e o f t h e same DBH, a n d ( 2 )  by s o l v i n g the  RGRs o f  hypotheses estimating the  g r o w t h r a t e o f s t a n d - g r o w n t r e e s c a n be  increment o f a stand-grown t r e e  equation  open-grown  t h e RGRs o f s t a n d - g r o w n  l i m i t s defined other  diffe-  1984) must a g a i n be  T h e s e f i g u r e s a l s o show t h a t  arecontained  and on F i g u r e  B o t h f i g u r e s show s u b s t a n t i a l  r e n c e s a t e v e r y age among t h e RGRs o f i n d i v i d u a l trees.  open-grown  l i n e s ) a r e shown  4.23 for the 4.3 m spacing  l i n e s ) on F i g u r e  o f Ford  a l l t h e t r e e s have t h e  theonset of competition  DBH RGR o f o p e n - g r o w n t r e e s  together  4.24  (i.e.,  theonset o f competition).  stand-grown t r e e s before trees.  o f t e s t i n g the  the  resulted i nnearly  derived  i nTables 4.24  f o r a 1-year  equation  equal values.  growth  and t h e e q u a t i o n With respect  o f Ek  t o AGR, 4  and  14 s i g n i f i c a n t d i f f e r e n c e s w e r e f o u n d b e t w e e n t h e c a l c u l a t e d  AGR  o f stand-grown t r e e s and the  values  computed from t h e  e q u a t i o n s f o r t h e 4 . 3 m and 6 . 0 m spacing 4.24  and 4 . 2 5 ) .  F o r RGR, o n l y 109  respectively  (Tables  one s i g n i f i c a n t d i f f e r e n c e was  FIGURE 4 . 2 3 : RGR(DBH) = F(AGE) FOR O P E N - G R O W N T R E E S AND S T A N D - G R O W N TREES B E F O R E THE ONSET O F COMPETITION (SPACING: 4 . 3 M)  « $  o  LEGEND = STAND-GROWN TREE = STAND-GROWN TREE = STAND-GROWN TREE = STAND-GROWN TREE = STAND-GROWN TREE= OPEN-GROWN TREE! 5 = OPEN-GROWN TREES 6 = OPEN-GROWN TREE 7 = OPEN-GROWN TREE 8 = OPEN-GROWN TREE 9 = OPEN-GROWN TREE 10 = OPEN-GROWN TREE 11 = OPEN-GROWN TREE! 12 = OPEN-GROWN TREEf 13 = STAND-GROWN TREES = OPEN-GROWN TREES  3  4  LEGEND = STAND-GROWN TREE;33 : STAND-GROWN TREE) 35 = STAND-GROWN TREE 38 = STAND-GROWN TREE)82 • STAND-GROWN TREEJ 99 • OPEN-GROWN TREE) 5 = OPEN-GROWN TREE)6 • OPEN-GROWN TREEj7 : OPEN-GROWN TREE 8 OPEN-GROWN TREEj 9 OPEN-GROWN TREE 10 OPEN-GROWN TREE 11 OPEN-GROWN TREE 12 OPEN-GROWN TREE 13 = STAND-GROWN TREES = OPEN-GROWN TREES  5  AGE AT BREAST HEIGHT  AGE AT BREAST HEIGHT  TIT  RGR(DBH) ( C M / Y E A R / C M )  r-o to  OJ ro O  3)  O L71C  >'73 m  z o  O J)  CO  « > ll II II II II II o o o o o o "O ~T3 "O "O T3 *T3 1 < i m m m m rn 2 2 2 2 2 2 I I I I I I O O O O O O S3 S 3 S 3 S3 S3 S 3 O O O O O O  o rr:  O  -O-O  O 3D  Ca-  II II II II II O COCO CO co co  m  i222  I I o o O O oI oI S3 S3 o o O O  o  I I I oO O S3 S3 S3 OO O  -—GO „ -ODD  >m~n  O © O Cn -T  O O  cn  CO  Q3>  RGR(DBH) ( C M / Y E A R / C M ) o O 00 OO  p ^  —' -J  1  p '—•  p '-^  CT)  cn  -c'—W  1  o ro o  p ro CD  o ro 0-1 OJ ,W " S i —  w  p CD  O  ro  ^ 3  is  CT)  00  00  ro  5-«  CO —H  m m  II  O  II  II 11 11 11 CO CO CO CO  dm dm  co m  2  ro  2 2 2 2 2 Z 0 0 I I I I I I OO I I 1 1 O O O O O O . _ S 3 S 3 S 3 S 3 S 3 S 3O O 0 0 o Q O Q Q O O Q S 3 S 3 S3 S 3 O O O O S3 * * * * * * * ; * * o Z 2 2 2 Z 2 Z  ^ —H — l - j —I —I —I —I —I S3S3S3S3S3S3S3S3S3 rnrnrrir^rHrnrnrn rn S 3  : z z*z S3 S3  —I m m S3  £~!rororo — —  0 0 0  z> z o  TABLE 4 . 2 4 :  Comparison of observed AGRs and RGRs i n DBH o f the stand-grown trees from t h e 4 . 3 m s p a c i n g b e f o r e the onset of competition with calculated open-grown t r e e v a l u e s as d e f i n e d by t h e s e c o n d h y p o t h e s i s . Increment p e r i o d : 1 y e a r . A b s o l u t e growth r a t e (cm/year)  Tree  1 2 3 4 5 7 8 9 12 16 17 27 30 31 32 33 35 36 37 38 42 46 53 54 64 65 74 82 98 99 *:  #  R e l a t i v e growth r a t e (cm/year/cm)  De r i v e d Ek's Observed equation equation  1.80 1.87 1.75 1.85 1.65 1.62 1.65 1.80 1.65 1.75 1.85 0.57 1.67 1.65 1.92 1.82 1.50 1.67 1.25 1 . 58 1.57 1.73 1.92 1.83 1.53 1.47 1.63 1.60 1.20 1.22  significant  1.57 1.60 1.60 1.60* 1.60 1.57 1.60 1.60 1.55 1.57 1.60 1.33* 1.57 1.52 1.60* 1.60 1.52 1.57 1.50* 1.57 1.60 1.60 1.60 1.55 1.47 1.50 1 . 50 1.52 1.43 1.47  difference  1.57 1.60 1.57 1.57* 1.57 1.57 1.60 1.60 1.52 1.57 1.60 1.20* 1.55 1.50 1.60* 1.57 1.50 1.52 1.42* 1.55 1.60 1.60 1.60 1.53 1.40 1.47 1.40 1.47 1.40 1.42 at  the  112  level  Derived Observed equation  0.2230 0.1669 0.2078 0.2056 0.1947 0.2082 0.1518 0.1625 0.2649 0.2569 0.1637 0.3310 0.2584 0.3159 0.1836 0.2037 0.2990 0.2628 0.3323 0.2256 0.1438 0.1540 0.1855 0.3415 0.4057 0.3178 0.3804 0.3408 0.3662 0.3286 of  0.1959 0.1413 0.1890 0.1786 0.1859 0.2035 0.1463 0.1438 0.2485 0.2258 0.1419 0.6684* 0.2373 0.2910 0.1528 0.1776 0.3016 0.2445 0.3813 0.2249 0.1439 0.1429 0.1534 0.2653 0.3920 0.3627 0.3622 0.3162 0.4291 0.3893  p r o b a b i l i t y of  Ek's equation  0.1950 0.1414 0.1884 0.1782 0.1855 0.2024 0.1464 0.1439 0.2453 0.2237 0.1419 0.6259* 0.2347 0.2851 0.1528 0.1773 0.2952 0.2416 0.3685 0.2231 0.1441 0.1430 0.1534 0.2602 0.3776 0.3166 0.3514 0.3083 0.4125 0.3759 0.05  TABLE 4 . 2 5 : C o m p a r i s o n o f o b s e r v e d AGRs a n d RGRs i n DBH o f t h e stand-grown t r e e s from t h e 6 . 0 m s p a c i n g before t h e onset of competition w i t h c a l c u l a t e d open-grown t r e e v a l u e s as d e f i n e d by t h e second h y p o t h e s i s . Increment p e r i o d : 1 year. A b s o l u t e growth rate (cm/year) Tree # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30  Observed 1.85 1.93 1.75 1.65 1.65 1.53 1.87 1.85 1.95 1.85 1.95 1.88 2.03 1.82 2.07 1.73 1.92 1.63 1.85 1.83 1.53 1.82 1.83 1.80 1.82 1.67 1.77 2.07 1.85 2.03  Derived equation  Ek's equation  1.55 1.55* 1.60 1.55 1.58 1.58 1.53* 1.48 1.57* 1.57* 1.55* 1.57 1.57* 1.52 1.53* 1.55 1.55* 1.57 1.55 1.52* 1.55 1.55* 1.57* 1.52 1.57 1.55 1.53 1.50* 1.55 1.57*  1.53* 1.55* 1.60 1.52 1.57 1.58 1.52* 1.47 1.55* 1.57* 1.53* 1.57 1.57* 1.50 1.50* 1.53 1.53* 1.57 1.53 1.48* 1.55 1.55* 1.57* 1.50 1.55 1.53 1.52 1.47* 1.52 1.57*  *: s i g n i f i c a n t d i f f e r e n c e a t t h e l e v e l  113  R e l a t i v e growth rate (cm/year/cm) Observed  Derived equation  Ek' s equation  0.1072 0.1200 0.1542 0.0933 0.1164 0.1095 0.1048 0.0918 0.1248 0.1227 0.1169 0.1297 0.1311 0.0998 0.1135 0.1027 0.1155 0.1084 0.1065 0.0951 0.0919 0.1111 0.1219 0.0953 0.1133 0.0986 0.0977 0.1035 0.1065 0.1329  0.0891 0.0971 0.1423 0.0871 0.1112 0.1127 0.0866 0.0739 0.1000 0.1049 0.0931 0.1095 0.1027 0.0837 0.0846 0.0917 0.0932 0.1041 0.0889 0.0785 0.0932 0.0964 0.1060 0.0804 0.0978 0.0909 0.0848 0.0756 0.0882 0.1047  0.0884 0.0967 0.1422 0.0865 0.1111 0.1126 0.0859 0.0728 0.0996 0.1046 0.0926 0.1093 0.1024 0.0829 0.0838 0.0912 0.0926 0.1038 0.0882 0.0774 0.0927 0.0959 0.1058 0.0795 0.0974 0.0903 0.0840 0.0745 0.0876 0.1044  of probability of 0.05  found. not  The c o m p u t a t i o n  result  period  in  (Table  in  of  of  hypothesis  also  tree  various  open-grown  because  of  trees  distinct  equation  A set  curves  of  4.25).  by v a r i o u s  However,  cially  consisted  tree  the  than  1-year  same s i z e set  of  the  i n terms  This  for  the  growth  assumption  potential  of  AGR i s  and a g e .  of  sizes  at  first  diameter  equal  This  hypotheses  reach d i f f e r e n t  genetic  it of  at  of  to  that  hypothesis  implies  that  a given  age  characteristics,  site,  the  potential  f u n c t i o n was  derived with  was  obtained  trees  all  have  was  believed  the  the  potential  young a g e s .  the  data d i s p l a y e d  the at  different  the  and/or micro-  that  the  growth  growth  as  the  error  rate  resulting  rates  reached  similar  in Figure  in Figure from the  w o u l d be v e r y  approach i s  4.22.  parameter  The t r e e s  curves  based  in Figure  asymptotic  same a g e .  same shape  This  growth  by v a r y i n g t h e  They r e f l e c t  open-grown  do n o t  utation  period did  conditions.  upon t h e  4.22  of  RGR.  The d e v e l o p m e n t  (Figure  errors  by Newnham ( 1 9 6 4 ) :  tested with  climatic  tested  a stand-grown  an o p e n - g r o w n  was  greater  a 5-year  4.26).  simulation  increment  AGR and RGR f o r  significantly  The n e x t used  of  small,  to  that  4.25. comp-  espe-  used  by  Newnham ( 1964 ) . F o r AGR, 17 and 8 s i g n i f i c a n t observations 4.3  m and 6 . 0  (Tables rences for  and t h e  the  4.27 were  derived values  m spacings and 4 . 2 8 ) .  found f o r  5-year  differences  were  found  between  from open-grown  trees  for  respectively  and f o r  On the  hand,  RGR.  other  Relatively  g r o w t h p e r i o d on t h e  114  6.0  close  a 1-year  period  no s i g n i f i c a n t values  m spacing  the  were  (Table  diffeobtained 4.29).  TABLE 4 . 2 6 :  C o m p a r i s o n o f o b s e r v e d AGRs and RGRs i n DBH o f the stand-grown t r e e s f r o m t h e 6 . 0 m s p a c i n g b e f o r e the onset of competition w i t h c a l c u l a t e d open-grown t r e e v a l u e s as d e f i n e d by t h e s e c o n d h y p o t h e s i s . Increment p e r i o d : 5 y e a r s . A b s o l u t e growth r a t e (cm/5 y e a r s )  Tree #  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30  Derived Observed equation  8.9 9.5 8.8 8.3 8.2 7.6 9.4 9.1 9.5 9.1 9.6 9.2 10.3 8.9 10.2 8.6 9.4 8.2 8.9 8.8 7.6 9.2 9.2 8.9 9.0 8.1 8.6 10.1 9.1 10.2  Ek's equation  7.7 7.8 8.0 7.7 7.9 7.9 7.7 7.5 7.8 7.8 7.7 7.8 7.8 7.6 7.6 7.7 7.7 7.8 7.7 7.5 7.7 7.8 7.8 7.6 7.8 7.7 7.6 7.5 7.7 7.8  7.6 7.7 8.0 7.6 7.8 7.8 7.6 7.3 7.8 7.8 7.7 7.8 7.8 7.5 7.6 7.7 7.7 7.8 7.6 7.4 7.6 7.7 7.8 7.5 7.7 7.6 7.5 7.4 7.6 7.8  115  Relative (cm/5  growth r a t e years/cm)  Derived Observed equation  0.47859 0.54534 0.70471 0.44521 0.53827 0.50734 0.49703 0.42668 0.55849 0.55727 0.53408 0.58016 0.61586 0.45850 0.52151 0.47889 0.52542 0.51083 0.47598 0.42744 0.43114 0.52884 0.56909 0.44452 0.52297 0.44880 0.44603 0.47299 0.48977 0.61519  0.42477 0.46560 0.65492 0.41676 0.52069 0.52069 0.42207 0.36228 0.47844 0.49532 0.45033 0.51322 0.49882 0.40391 0.41414 0.43868 0.45033 0.49187 0.42207 0.37542 0.43584 0.46248 0.50235 0.38928 0.46560 0.43025 0.40391 0.37096 0.42750 0.50235  Ek's equation  0.42171 0.46353 0.65524 0.41348 0.51968 0.51968 0.41894 0.35738 0.47664 0.49386 0.44790 0.51209 0.49742 0.40028 0.41079 0.43597 0.44790 0.49034 0.41894 0.37094 0.43306 0.46034 0.50102 0.38522 0.46353 0.42733 0.40028 0.36634 0.42451 0.50102  FIGURE 4.25: DBH = F(AGE AT BREAST HEIGHT) FOR OPEN-GROWN TREES  AGE AT BREAST HEIGHT  116  TABLE 4 . 2 7 :  Comparison o f o b s e r v e d AGRs a n d RGRs i n DBH o f t h e stand-grown t r e e s from t h e 4 . 3 m s p a c i n g before t h e onset of competition with calculated open-grown tree values as d e f i n e d by t h e t h i r d hypothesis. Increment p e r i o d : 1 year. A b s o l u t e growth r a t e (cm/yea r )  Tree # 1 2 3 4 5 7 8 9 12 16 17 27 30 31 32 33 35 36 37 38 42 46 53 54 64 65 74 82 98 99  Observed 1.80 1.87 1.75 1.85 1.65 1.62 1.65 1.80 1.65 1.75 1.85 0.57 1.67 1.65 1.92 1.82 1.50 1.67 1.25 1.57 1.57 1.72 1.92 1.82 1.52 1.47 1.63 1.60 1.20 1.22  Derived equation 2.07 2.32* 2.15* 1.80 1.70 1.97* 2.25* 2.27* 1.55 3.75* 2.30 1.03* 2.20* 1.75 2.70* 5.00* 2.62* 2.12* 0.72* 2.35* 2.87 2.27* 2.72* 3.12 1.90 1.52 2.50 1.60 2.00* 1.17  *: s i g n i f i c a n t d i f f e r e n c e a t t h e l e v e l o f  117 /  R e l a t i v e growth r a t e (cm/year/cm) Observed  Derived equation  0.22300 0.16688 0.20782 0.20559 0.19467 0.20823 0.15182 0.16047 0.26494 0.25695 0.16373 0.33108 0.25837 0.31592 0.18363 0.20369 0.29906 0.26280 0.33228 0.22556 0.14384 0.15405 0.18548 0.34152 0.40567 0.31781 0.38039 0.34083 0.36620 0.32858  0.24887 0.20057 0.24887 0.20057 0.20057 0.24887 0.20057 0.20057 0.24887 0.48647 0.20057 0.56092 0.32738 0.32738 0.24887 0.48647 0.48647 0.32738 0.20057 0.32738 0.24887 0.20057 0.24887 0.48647 0.48647 0.32738 0.56092 0.32738 0.56092 0.32738  p r o b a b i l i t y of 0.05  TABLE 4 . 2 8 :  Comparison of observed AGRs and RGRs i n DBH o f t h e s t a n d - g r o w n t r e e s from t h e 6 . 0 m s p a c i n g b e f o r e t h e the o n s e t o f c o m p e t i t i o n w i t h c a l c u l a t e d open-grown tree values as defined by the t h i r d hypothesis. Increment p e r i o d : 1 y e a r . A b s o l u t e growth (cm/year)  Tree #  Observed  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 *:  1.85 1.93 1.75 1.65 1.65 1.53 1.87 1.85 1.95 1.85 1.95 1.88 2.03 1.82 2.07 1.73 1.92 1.63 1.85 1.83 1.53 1.82 1.83 1.80 1.82 1.67 1.77 2.07 1.85 2.03 significant  difference  rate  Derived equation 1.97 2.07 1.67 2.00 1.82* 1.58 2.67* 2.32 2.35 1.93 1.90 1.87 1.98 2.08 2.07 2.18* 1.90 1.93* 1.95 2.18 2.15 2.08* 1.93 1.90 2.05 1.92 2.35* 2.25 2.25* 1.70* at  the l e v e l  118  R e l a t i v e growth r a t e (cm/year/cm)  Observed  Derived equation  0.10719 0.12001 0.15416 0.09327 0.11637 0.10953 0.10477 0.09185 0.12479 0.12272 0.11697 0.12967 0.13111 0.09977 0.11354 0.10275 0.11552 0.10836 0.10655 0.09509 0.09193 0.11112 0.12194 0.09530 0.11328 0.09856 0.09769 0.10353 0.10655 0.13292  0.11221 0.12783 0.14786 0.11221 0.12783 0.11221 0.14786 0.11221 0.14786 0.12783 0.11221 0.12783 0.12783 0.11221 0.11221 0.12783 0.11221 0.12783 0.11221 0.11221 0.12783 0.12783 0.12783 0.09967 0.12783 0.11221 0.12783 0.11221 0.12783 0.11221  of p r o b a b i l i t y of  0.05  TABLE 4 . 2 9 : C o m p a r i s o n o f o b s e r v e d AGRs a n d RGRs i n DBH o f t h e stand-grown t r e e s from t h e 6 . 0 m s p a c i n g before the onset of competition with c a l c u l a t e d open-grown tree values as d e f i n e d by t h e t h i r d hypothesis. Increment p e r i o d : 5 y e a r s . A b s o l u t e growth r a t e (cm/5 y e a r s ) Tree #  Observed  Derived equation  8.9 9.5 8.8 8.3 8.2 7.6 9.4 9.1 9.5 9.1 9.6 9.2 10.3 8.9 10.2 8.6 9.4 8.2 8.9 8.8 7.6 9.2 9.2 8.9 9.0 8.1 8.6 10.1 9.1 10.2  10.0 10.5 8.6 10.2 9.3 7.9 14.1 11.7 12.2 9.8 9.3 9.4 9.7 10.5 10.2 11.3 9.3 9.9 10.0 11.3 11.3 10.6 9.7 9.5 10.5 9.8 12.3 11.5 11.6 8.2  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 *: s i g n i f i c a n t  difference at the level  119  R e l a t i v e growth r a t e (cm/5 y e a r s / c m ) Observed  Derived equation  0.47859 0.54534 0.70471 0.44521 0.53827 0.50734 0.49703 0.42668 0.55849 0.55727 0.53408 0.58016 0.61586 0.45850 0.52151 0.47889 0.52542 0.51083 0.47598 0.42744 0.43114 0.52884 0.56909 0.44452 0.52297 0.44880 0.44603 0.47299 0.48977 0.61519  0.52266 0.59037 0.67520 0.52266 0.59037 0.52266 0.67520 0.52266 0.67520 0.59037 0.52266 0.59037 0.59037 0.52266 0.52266 0.59037 0.52266 0.59037 0.52266 0.52266 0.59037 0.59037 0.59037 0.46727 0.59037 0.52266 0.59037 0.52266 0.59037 0.52266  of p r o b a b i l i t y of 0.05  The  f o u r t h set  tial  increment of  that  of  of  hypotheses  a stand-grown tree  an o p e n - g r o w n t r e e  respective performed  diameters for  differences  RGR.  were  (1971)  equation.  4.32.  For the  of  stand-grown  trees  number o f  to  of  the  same a g e ,  the  tests  calculated  the  values  from t h e  4.30).  were  computed  derived  For the  6.0  11 and 18  and  (Tables  4.30  and  values  were  AGRs and t h e  equation,  while  obtained values  other  for  some  from t h e  trees  5-year  trees  equation  respectively  growth  between  from  m spacing,  The c o r r e s p o n d i n g numbers f o r RGR w e r e : For the  and  significant  4.31).  close  also  4.31,  18 and 26  f o u n d between  and 4 . 3 1 ) .  the  slight  (Table 23  to  d e r i v e d e q u a t i o n and E k ' s  m spacing,  differences  equal  were  hypothesis,  4.3  (Tables  poten-  b u t a d j u s t e d by  shown i n T a b l e s 4 . 3 0 ,  and t h o s e  significant  the  the  o f AGR i s  The same first  as:  are  30 were  equation  stated  i n terms  both t r e e s .  Results  out  the  the  o b s e r v e d between  differences  E k ' s (1971)  of  Contrary  AGR o f  and  may be  8,  8,  14,  period,  observed  RGRs  d e r i v e d e q u a t i o n and E k ' s  showed  substantial  differences  (Table  4.32) . The  last  set  of  hypotheses  of  a stand-grown tree  i n terms  an  open-grown t r e e  the  ciency. the  F o r AGR, t h e  4.3  rence  m spacing  (Tables  better  4.33  for  the that  differed  sets the  (except  The t h i r d  of  RGR.  T h i s was  120  to  that  the  computed from  fifth  set  of  effi-  f o u n d was  equation d i f f e r e d only  neither  and f o u r t h s e t s  equal  increment  No s i g n i f i c a n t  The v a l u e s  examined,  because  in 1 case).  potential  difference  and 4 . 3 4 ) .  hypotheses  others  the  b u t a d j u s t e d by i t s  significant  e q u a t i o n and E k ' s (1971)  Of  that  o f AGR o r RGR i s  same a g e ,  only  c o u l d be d e t e c t e d  derived  set.  of  was  for  diffethe  slightly. performed  AGR n o r RGR s i g n i f i c a n t l y followed  by t h e  second  had many more s i g n i f i c a n t  diffe-  TABLE  4.30:  Comparison of observed AGRs and RGRs i n DBH o f t h e stand-grown t r e e s from t h e 4 . 3 m s p a c i n g b e f o r e t h e onset of competition w i t h c a l c u l a t e d open-grown t r e e v a l u e s as d e f i n e d by t h e f o u r t h h y p o t h e s i s . Increment p e r i o d : 1 y e a r . A b s o l u t e growth (cm/year)  Tree 1 2 3 4 5 7 8 9 12 16 17 27 30 31 32 33 35 36 37 38 42 46 53 54 64 65 74 82 98 99 *:  #  Derived Observed equation 1 .80 1 .87 1 .75 1 .85 1 .65 1 .62 1 .65 1 .80 1 .65 1 .75 1 .85 0 .57 1 .67 1 .65 1 .92 1 .82 1 . 50 1 .67 1 .25 1 .58 1 .58 1 .72 1 .92 1 .82 1 .52 1 .47 1 .63 1 .60 1 .20 1 .22  significant  rate Ek's equation  2 .07 2 .32* 2 .15* 1 .80 1 .70 1 .97* 2 .25* 2 .27* 1 .55 3 .75* 2 .30 1 .03* 2 .20* 1 .75 2 .70* 5 .00* 2 .62* 2 .12* 0 .73* 2 . 35* 2 .88* 2 .27* 2 .72* 3 .12 1 .90 1 .52 2 .50 1 .60 2 .00* 1 .18  difference  2 .35 2 .62* 2 .42* 2 .00* 1 .92* 2 .22* 2 .50* 2 .52* 1 .77 4 .47* 2 .60* 1 .27* 2 .55* 2 .02* 3 .07* 6 .00* 3 .12* 2 . 47* 0 .83* 2 .72* 3 .27* 2 . 57* 3 .07* 3 .75* 2 .25 1 .75* 3 .03* 1 .85* 2 .37* 1 . 37 at  the l e v e l  121  R e l a t i v e growth r a t e (cm/year/cm) Derived Ek's Observed equation equation 0 .22300 0 .16688 0 .20782 0 .20559 0 .19467 0 .20823 0 .15182 0 .16047 0 .26494 0 .25695 0 .16373 0 .33108 0 .25837 0 .31592 0 .18363 0 .20369 0 .29906 0 .26280 0 .33228 0 .22556 0 .14384 0 .15405 0 .18548 0 .34152 0 .40567 0 .31786 0 .38039 0 .34083 0 .36620 0 .32858  0 .33249 0 .29782* .0 .34742 0 .22931 0 .21901 0 .31912 0 .28785* 0 .29290* 0 .24923 1 .50161 0 .29696* 0 .46534 0 .49915 0 .38220 0 .44371* 2 .09149 1 .02340 0 .48113 0 .08999* 0 .53977 0 .47894 0 .29513* 0 .44087* 1 .14550 0 .68773 0 . 33126 1 .10878 0 .34242 0 .87454 0 .25934  of p r o b a b i l i t y of  0 .44143 0 .37825* 0 .46180* 0 .29077 0 .27783 0 .42430 0 .36572* 0 .37224* 0 .33004 2 .45965 0 .37931* 0 .77510 0 .70983 0 . 54069 0 .59067 3 .45335 1 .67056 0 .68435 0 .11340* 0 .77062 0 .63914 0 .37516* 0 .58661* 1 .84105 1 .10509 0 .46885 1 .83932 0 .48296 1 .44956 0 .36682 0.05  TABLE  4.31:  Comparison of observed AGRs and RGRs i n DBH o f t h e stand-grown trees from t h e 6 . 0 m s p a c i n g b e f o r e the o n s e t o f c o m p e t i t i o n w i t h c a l c u l a t e d open-grown tree v a l u e s as d e f i n e d by the f o u r t h hypothesis. Increment p e r i o d : 1 y e a r . A b s o l u t e growth r a t e (cm/year)  Tree # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 *:  Derived Observed equation 1.85 1.93 1.75 1.65 1.65 1.53 1.87 1.85 1.95 1.85 1.95 1.88 2.03 1.82 2.07 1.73 1.92 1.63 1.85 1.83 1.53 1.82 1.83 1.80 1.82 1.67 1.77 2.07 1.85 2.03  significant  Ek's equation  1.97 2.07 1.67 2.00 1.82* 1.58 2.67* 2.32 2.35* 1.93 1.90 1.87 1.98 2.08 2.07 2.18* 1.90 1.93* 1.95 2.18* 2.15* 2.08* 1.93 1.90 2.05 1.92 2.35* 2.25 2.25* 1.70*  difference  R e l a t i v e growthi r a t e (cm/year/cm)  2.10 2.25* 1.80 2.15* 1.98* 1.70* 2.92* 2.48* 2.58 2.12* 2.03 2.03 2.15 2.23* 2.22 2.38* 2.03 2.10* 2.10 2.38* 2.33* 2.28* 2.08* 2.02 2.23* 2.07* 2.57* 2.43 2.48* 1.83 at  the  122  level  Derived Observed equation  Ek' s equation  0 .10719 0 .12001 0 .15416 0 .09327 0 .11637 0 .10953 0 .10477 0 .09185 0 .12479 0 .12272 0 .11697 0 .12967 0 .13111 0 .09977 0 .11354 0 .10275 0 .11552 0 .10836 0 .10655 0 .09509 0 .09193 0 .11112 0 .12194 0 .09530 0 .11328 0 .09856 0 .09769 0 .10353 0 .10655 0 .13292  0.16140* 0.19765* 0.18565 0.16511* 0.17364* 0.12896 0.30732* 0.19052* 0.26698* 0.18360* 0.15456 0.17584 0.18691 0.17076* 0.16876* 0.20941* 0.15452 0.18557* 0.16175* 0.18140* 0.20740* 0.19956* 0.18176* 0.13751* 0.19662* 0.15870* 0.22545* 0.18658* 0.21654* 0.13813  0.13990 0.16787 0.15398 0.14301* 0.14743 0.11178 0.25401* 0.16503* 0.22101* 0.15594 0.13405 0.14942 0.15886 0.14796* 0.14634 0.17767* 0.13401 0.15749* 0.14019 0.15712* 0.17581* 0.16937* 0.15436 0.12125 0.16692* 0.13750 0.19120* 0.16170* 0.18379* 0.11988  of p r o b a b i l i t y of  0.05  TABLE 4 . 3 2 :  Comparison of observed AGRs and RGRs i n DBH o f t h e stand-grown trees from t h e 6 . 0 m s p a c i n g b e f o r e t h e onset of competition w i t h c a l c u l a t e d open-grown t r e e v a l u e s as d e f i n e d by t h e f o u r t h h y p o t h e s i s . Increment p e r i o d : 5 y e a r s . A b s o l u t e growth r a t e (cm/5 y e a r s )  Tree #  Observed  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30  8.9 9.5 8.8 8.3 8.2 7.6 9.4 9.1 9.5 9.1 9.6 9.2 10.3 8.9 10.2 8.6 9.4 8.2 8.9 8.8 7.6 9.2 9.2 8.9 9.0 8.1 8.6 10.1 9.1 10.2  Derived Ek's equation equation 10.0 10.5 8.3 10.2 9.3 7.9 14.1 11.7 12.2 9.8 9.3 9.4 9.7 10.5 10.2 11.3 9.3 9.9 10.0 11.3 11.3 10.6 9.7 9.5 10.5 9.8 12.3 11.5 11.6 8.2  10.8 11.6 9.3 11.1 10.2 8.6 15.8 12.8 13.7 10.8 10.2 10.4 10.7 11.4 11.1 12.4 10.2 10.9 10.9 12.3 12.5 11.7 10.7 10.2 11.6 10.7 13.6 12.5 12.8 9.0  123  Relative (cm/5  growth r a t e years/cm)  Derived Observed equation  Ek' s equation  0.47859 0.54534 0.70471 0.44521 0.53827 0.50734 0.49703 0.42668 0.55849 0.55727 0.53408 0.58016 0.61586 0.45850 0.52151 0.47889 0.52542 0.51083 0.47598 0.42744 0.43114 0.52884 0.56909 0.44452 0.52297 0.44880 0.44603 0.47299 0.48977 0.61519  0.76655 0.92932 0.85454 0.78241 0.81582 0.60795 1.45072 0.90400 1.26193 0.86547 0.71897 0.83000 0.85838 0.80884 0.78770 0.99317 0.71897 0.87257 0.77187 0.87228 1.00026 0.93641 0.85129 0.64744 0.92932 0.75598 1.08539 0.88286 1.02154 0.63439  0.66199 0.78536 0.70354 0.67568 0.68944 0.52502 1.19438 0.78069 1.03894 0.73141 0.62090 0.70143 0.72541 0.69851 0.68025 0.83932 0.62090 0.73740 0.66655 0.75330 0.84531 0.79136 0.71942 0.56945 0.78536 0.65286 0.91725 0.76243 0.86330 0.54785  TABLE 4 . 3 3 :  C o m p a r i s o n o f o b s e r v e d AGRs and RGRs i n DBH o f t h e stand-grown t r e e s from t h e 4 . 3 m s p a c i n g b e f o r e t h e onset of competition with calculated open-grown t r e e v a l u e s as d e f i n e d by t h e f i f t h hypothesis. Increment p e r i o d : 1 y e a r . A b s o l u t e growth r a t e (cm/year)  Tree # 1 2 3 4 5 7 8 9 12 16 17 27 30 31 32 33 35 36 37 38 42 46 53 54 64 65 74 82 98 99 *:  Derived Observed equation 1.73 1.77 1.73 1.83 1.60 1.63 1.60 1.80 1.60 1.60 1.77 0.65 1.57 1.60 1.83 1.73 1.50 1.63 1.27 1. 57 1.47 1.70 1.83 1.43 1.40 1.50 1.85 1.53 1.30 1.30  significant  Ek's equation  1.73 1.77 1.60 1.77 1.60 1.47 1. 53 1.63 1.57 1.40 1.73 0.45 1.47 1.43 1.73 1.47 1.17* 1.43 1.20 1.33 1.37 1.57 1.87 1.90 1.50 1.33 1.20 1.50 1.10 1.10  difference  1.70 1.77 1.60 1.70 1.57 1.43 1. 50 1.63 1.57 1.40 1.73 0.45 1.47 1.43 1.73 1.43 1.17* 1.43 1.17 1.33 1.37 1.57 1.87 1.90 1.50 1.30 1.20 1.47 1.00 1.10 at  the l e v e l  124  R e l a t i v e growth r a t e (cm/year/cm) Derived Observed equation  Ek' s equation  0.18518 0.14061 0.18120 0.17966 0.16665 0.18509 0.13401 0.14631 0.21494 0.19349 0.14061 0.32837 0.20045 0.24587 0.15487 0.16858 0.24692 0.21525 0.27277 0.19530 0.12155 0.13851 0.15621 0.19255 0.26812 0.26527 0.36066 0.25516 0.32839 0.29083  0.19991 0.15220 0.18234 0.18460 0.17681 0.17988 0.13615 0.14323 0.23256 0.18691 0.14908 0.23657 0.21234 0.25938 0.15875 0.15013 0.21545 0.21430 0.29924 0.18268 0.12206 0.13767 0.16884 0.27724 0.31427 0.26366 0.27014 0.28638 0.27481 0.27190  0.20189 0.15363 0.18414 0.18633 0.17846 0.18165 0.13742 0.14456 0.23488 0.18909 0.15047 0.23936 0.21460 0.26215 0.16033 0.15185 0.21794 0.21658 0.30205 0.18461 0.12326 0.13896 0.17051 0.28050 0.31789 0.26645 0.27334 0.28945 0.27807 0.27378  of p r o b a b i l i t y  0.05  TABLE 4 . 3 4 :  Comparison of observed AGRs and RGRs i n DBH o f t h e s t a n d - g r o w n t r e e s from the 6.0 m s p a c i n g b e f o r e the onset of competition with calculated open-grown tree values as d e f i n e d by t h e f i f t h hypothesis. Increment p e r i o d : 1 y e a r . A b s o l u t e growth r a t e (cm/year)  Tree # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 *:  Derived Observed equation 1.78 1.70 1.76 1.66 1.64 1.52 1.88 1.82 1.90 1.82 1.92 1.84 2.06 1.78 2.04 1.72 1.88 1.64 1.78 1.76 1.52 1.84 1.84 1.78 1.80 1.62 1.72 2.02 1.82 2.04  significant  Ek's equation  1.82 1.90 1.68 1.64 1. 58 1.44 1.80 1.82 1.88 1.78 1.94 1.90 2.02 1.80 2.08 1.68 1.94 1.58 1.82 1.76 1.46 1.74 1.74 1.78 1.80 1.66 1.72 2.04 1.84 1.98  difference  1.82 1.88 1.68 1.64 1.58 1.44 1.76 1.80 1.86 1.76 1.94 1.90 2.00 1.78 2.06 1.68 1.94 1.56 1.82 1.76 1.46 1.72 1.72 1.78 1.78 1.66 1.70 2.02 1.80 1.98 at  the l e v e l  125  R e l a t i v e growth r a t e (cm/year/cm) Derived Observed equation  Ek' s equation  0.09572 0.10907 0.14094 0.08904 0.10766 0.10147 0.09941 0.08534 0.11170 0.11145 0.10682 0.11603 0.12317 0.09170 0.10430 0.09578 0.10508 0.10217 0.09520 0.08549 0.08623 0.10577 0.11382 0.08891 0.10459 0.08976 0.08920 0.09460 0.09796 0.12304  0.10130 0.11218 0.14155 0.08908 0.10742 0.10111 0.09720 0.08716 0.11583 0.11333 0.11155 0.12399 0.12378 0.09470 0.10890 0.09593 0.11155 0.10061 0.10073 0.08873 0.08513 0.10210 0.11163 0.09118 0.10668 0.09425 0.09128 0.09833 0.10104 0.12535  0.10209 0.11310 0.14276 0.08977 0.10829 0.10190 0.09803 0.08783 0.11682 0.11425 0.11241 0.12499 0.12478 0.09544 0.10974 0.09670 0.11241 0.10142 0.10151 0.08942 0.08582 0.10292 0.11254 0.09186 0.10755 0.09498 0.09202 0.09909 0.10186 0.12632  of p r o b a b i l i t y  0.05  rences. for  H o w e v e r , t h e number o f s i g n i f i c a n t d i f f e r e n c e s was l e s s  these three  h y p o t h e s e s when RGR was u s e d i n s t e a d  poorer performance of these three u s e d may be e x p l a i n e d and  free  conditions.  results useful  s e t s when AGR was  may n o t h a v e t h e same i n c r e m e n t  characteristics, site,  because  or m i c r o c l i m a t i c  The d i f f e r e n c e s among s t a n d - g r o w n a n d o p e n - g r o w n  trees diminished for genetic,  The  by t h e f a c t t h a t two t r e e s o f t h e same s i z e  from c o m p e t i t i o n  of d i f f e r e n t g e n e t i c  hypothesis  o f AGR.  when RGR was u s e d p e r h a p s b e c a u s e i t a d j u s t e d  site,  or other  environmental d i f f e r e n c e s .  These  s u g g e s t t h a t a m e a s u r e o f e f f i c i e n c y b a s e d on RGR may be for estimating  the p o t e n t i a l growth rate o f stand-grown  trees. However, t h i s p a r t  o f t h e s t u d y was n o t d e f i n i t i v e .  As  p r e v i o u s l y m e n t i o n e d , c o m p a r i s o n s w e r e made b e t w e e n o p e n - g r o w n t r e e s and stand-grown t r e e s b e f o r e  the onset of  competition.  When a g r o w t h s i m u l a t o r  i s developed, the growth of every  must be e s t i m a t e d  competition  spacing, real  until  the longer  increment.  The l a r g e r t h e  the p o t e n t i a l growth rate c o n s t i t u t e s the  The n e x t l o g i c a l  hypotheses i n s i m u l a t i o n  i n order  t h a t was t h e m o s t s u c c e s s f u l w i t h onset of competition  occurs.  s t e p w o u l d be t o t e s t to determine i f the  w o u l d a l s o be t h e most s u c c e s s f u l  p o t e n t i a l growth rate of stand-grown t r e e s  by  competition.  trees  f o r e s t growth s i m u l a t o r s  t h a t were n e v e r s u b j e c t e d  were g r o w i n g under c o m p e t i t i v e c e r t a i n age.  In other  these hypothesis  stand-grown t r e e s before the  the  Existing  tree  to predict  t h a t were  affected  do n o t d i s t i n g u i s h b e t w e e n  to competition  and t h o s e  that  s t r e s s , and t h e n r e l e a s e d  at a  w o r d s , i t i s assumed t h a t  same s i z e b u t o r i g i n a t i n g f r o m t h e two c o n d i t i o n s 126  two t r e e s o f t h e just  described  w o u l d have (1964),  this  possible  4.6-  effect  first  red pine  the  w o u l d be  objective  into  tree  errors  t o Newnham  consideration  was u n d e r g o i n g  resulting  the  before  from n o t  consi-  negligible.  these  two  types  always  showed d i f f e r e n t competition. RGR was  onset  of  Finally,  t h a n AGR, was  that  same  fact  all  specific  stand better  to  onset  fully  tree  and a f t e r  size.  One t o  the  not  Small  related  trees  the  tree  were  after tree  size.  same RGR b e f o r e  of  severe,  trees  four years  to  s i z e , RGR onset  too  no v a r i a t i o n w i t h  positively  w h i c h was  i n the  onset  to  determine  competitive  of  status  competition better  RGR had a g r e a t e r  status  the size.  The  the  onset  i f RGR of  stands  better  from a g e s  g r o w t h t h a n AGR.  13 t o  with  My r e s u l t s the  33  suggests change  status  of  that  i n the  clearly indicate  competitive 127  t h a n AGR.  a b i l i t y t h a n AGR t o  and p r e d i c t a b l e p a t t e r n o f  associated  The p e r f o r -  met:  the  that  competition  spacings.  correlated with  tree  have  of  deve-  differed.  before  was  compare t h e  rejected.  changes  social  to  there  objective,  RGR r e f l e c t e d The  growth r a t e  than b i g t r e e s .  RGR became  the  of  the  range o f  positively  competition,  second  represents  and a f t e r  related  c o m p e t i t i o n was The  c h a p t e r was  relationships  negatively  hypothesis  more  this  When c o m p e t i t i o n began o r was  more e f f i c i e n t  of  of  growing under a wide  W h i l e AGR was  the  that  the  i n AGR and RGR b e f o r e  mance o f  2-  stress  take  According  Summary and C o n c l u s i o n s  lopment  1-  growth r a t e .  a s s u m p t i o n does not  He assumed  this  The  for  same p o t e n t i a l  physiological  release. dering  the  retain it  course  that  trees  has  of  a of  RGR i s diffe-  rent  sizes  every  age  that  different be  the  also  and  this  physiological  of  water)  to  to  the  changes  in  The  than  indicated  small  different  i n the  ones.  ages  might  status,  biological  causes,  be d i f f i c u l t  in of  accumulated  the  field,  trees  (e.g.,  in order  The  competitive  of  to  More  only  but i.e.,  speci-  photosynthesis  to  study  other  these  approaches  such  p r o d u c e new m a t e r i a l  chlorophyll, to  at  c o u l d not  e q u i l i b r i u m between  processes  c o u l d be u n d e r t a k e n  AGR o n l y  p r o d u c e new b i o m a s s .  efficiency  resources  faster  i n terms  While i t  the  grow  change  trees  relates  estimating  unit  the  of  respiration.  basic  the  interpreted  efficiency  fically,  trees  t h a n AGR.  shown by RGR a t  with  be  a stand  large  patterns  associated  could  as  composing  better  per  nutrients,  understand  the  efficiency.  third  potential  and f o u r t h o b j e c t i v e s growth  rate  of  concerned  stand-grown  trees  the  estimation  from  of  open-grown  trees. 3-  Hypotheses  based  on AGR f o r  every  These  results  single-tree measures  than hypotheses  This  efficiency  that is  of  also  trees  s u p p o r t e d by the at  using  A m a j o r p r o b l e m o c c u r r i n g when t h e  seperate  the  teristics particular matic  effect  (i.e., tree  effect  of  is  estimated  of  competition  genetic depends  conditions, all  predict  on i t s  from the  genetic  amount o f  factors.  128  relative  If  and  with t h a t RGR that  partition  competitive  in single-tree  inheritance).  and t h e these  the  use  fact  resources  resources.  individual trees  to  promising for  models  the  attempt  RGR i s  single-tree  of  based  set. suggest  models.  the  on RGR p e r f o r m e d b e t t e r  models  is  physiological  The i n c r e a s e potential,  competition. RGR e x p r e s s e s  in  the  of  stress to charac-  size  of  microcli-  AGR e x p r e s s e s the  increment  a  of  trees  independently  conditions Kozlowski (1987)), in  (as  will  single-tree The n e x t  be  to  study  genetic  Ledig  (1974),  (1988),  Kramer and  the  effect  of  competition  models. logical  the  step before  development  of  the  by S m i t h  which examined  good  or m i c r o c l i m a t i c  and R a d o s e v i c h and O s t e r y o u n g  very probably r e f l e c t  A combination of  meters  inheritance  s u g g e s t e d by Buchman and B e n z i e  (1974), it  of  (1966),  growth models  individual trees  functional  and s t a n d v a r i a b l e s  developing  a p p r o a c h and t h e the  effect  of  129  detail.  methodology  several  on i n d i v i d u a l t r e e s ,  results.  i n more  would  might  crown  used para-  produce  CHAPTER 5 CROWN DEVELOPMENT 5.1-  Introduction The  been  dependence  recognized  Curtin 1988,  1970,  of  at  Ford  the  1985,  researchers 1977,  1987).  canopy l e v e l  different  stand density  development  has  crown w i d t h ) . ciency. based  stem  provides  positions  dominance  The  first  various  of  range  better  correlated with  before small  spacings  In the  and a f t e r trees  that  were  the  efficiency  of  last the  that  (measure  over  the  to of  resources  under  measures  measures  a measure the  time  the  F u r t h e r m o r e , crown  a measure  measure  of  this  of of  of  the  site  of  the  study  effi-  efficiency growing  how t r e e s  of  (e.g.,  of  h o r i z o n t a l area of  space  occupied different  than comparing  the  onset  chapter, of  trees  of it  determine  competition was  than b i g  greatly  130  stress  affected  It  trees was  if  than  observed  competition.  competitive  is  to  examine  on crown c h a r a c t e r i s t i c s  and a g e s and t o  onset  of  phase  based  more e f f i c i e n t  effect the  small.  competitors  However,  been made o f  increment  efficiency  a wide  measures.  of  is  of  classes.  objective  measures  influence  (Perry 1985).  has  a better  utilize  the  competition  considered  crown p r o j e c t i o n crown)  social  of  The m a j o r i m p a c t o f  studied with absolute use  1970, Kuuluvainen  crown d e v e l o p m e n t  been  Assmann  has  K o z l o w s k i 1971,  conditions  little  (1988)  on a r a t i o  the  only  Very  O'Hara  s u c h as  following  mostly  (e.g.,  t h r o u g h the  crown d i m e n s i o n and s t r u c t u r e studies  and  g r o w t h upon crown d e v e l o p m e n t  Harper  al.  number o f  by  stem  by s e v e r a l  and Z e d a k e r e t  occurs on  STUDY  that was  are  absolute RGR changed  concluded  before to  they  for  that  competition  decrease  by c o m p e t i t i o n .  the If  the  various  f o r m s o f r e l a t i o n s h i p s b e t w e e n RGR a n d t r e e s i z e  indicate  a change  i n the e f f i c i e n c y  s h o u l d a l s o o c c u r w i t h measures characteristics.  of trees,  t h e same  o f e f f i c i e n c y b a s e d on c r o w n  i sa similarity  c h a n g e s i n RGR a n d t h e c h a n g e s i n r e l a t i v e on c r o w n d i m e n s i o n s .  and methods,  basic  examined s u c c e s s i v e l y . interesting after Literature  R e s u l t s t h a t were  analysis are included  relationships  growth measures a r e c o n s i d e r e d as l e s s 4.  i n Appendix  Review  d e n s i t y and t h e r e i s a c l o s e stem d i a m e t e r ( S t i e l l  1970;  r i m e n t s u n d e r t a k e n by S t i e l l crown l e v e l  between  Then, t h e a b s o l u t e  Crown d e v e l o p m e n t o f r e d p i n e i s v e r y s e n s i t i v e  the  based  r e v i e w and a  crown d i m e n s i o n s and b o l e s i z e s a r e examined. r e l a t i v e measures, and r e l a t i v e  between t h e  growth measures  Following a literature  description of material  5.2-  trends  Thus, t h e second o b j e c t i v e o f t h i s phase o f t h e  study i s t o determine i f there  measures,  really  t o stand  r e l a t i o n s h i p between crown w i d t h and and B e r r y 1 9 7 7 ) .  Stiell (1970)  i s more l i m i t i n g  The e x p e -  suggest that competition a t  than below-ground s t r e s s  f o r red  p i n e a t Petawawa. Three methods teristics  have been u s e d t o a n a l y s e t h e s p a t i a l  o f crowns.  The f i r s t  one i n v o l v e s m e a s u r i n g d e t a i l e d  c h a r a c t e r i s t i c s on i n d i v i d u a l b r a n c h e s s u c h a s l e n g t h , location,  or foliage  Ford 1978; 1980,  1986;  Ford 1982;  (Beadle e t a l .  Gary 1978;  1982;  Ilonen et a l .  K i n e r s o n and F r i t s c h e n 1971;  s e c o n d method in  content  charac-  Stiell  diameter,  Cochrane and  1979; 1962,  Kellomaki 1966).  The  c o n s i s t s of measuring the d i s t r i b u t i o n of f o l i a g e  t e r m s o f mass o r l e a f a r e a a l o n g t h e s t e m ( H a l l  Stephens 1969).  The t h i r d method 131  1965,  1966;  c o n s i s t s o f m e a s u r i n g crown  ( C u r t i n 1970;  d i m e n s i o n s , u s u a l l y w i d t h and l e n g t h Reukema 1 9 7 0 ; defined  Stiell  as a b s o l u t e  Although very practical  1977).  and B e r r y  C u r t i s and  A l l these parameters a r e  measures. rich  f o rstudies  i nd e t a i l ,  the f i r s t  two m e t h o d s a r e n o t  o f stand growth i n v o l v i n g  d a t a f r o m many t r e e s .  Because c o l l e c t i n g  remeasurement  thenecessary  mation i s very laborious  and c o n s i s t s o f d e s t r u c t i v e  v e r y few t r e e s  are analysed.  to obtain  generally  reliable  information  measurement,  I t i stherefore  applicable  t h i r d method i s n o t as b i o l o g i c a l l y  infor-  difficult  t o other trees.  informative,  The  b u t crown  dimensions a r e e a s i l y measureable i n a non-destructive  manner.  Also,  often can  be  reliable  relationships applicable  derived. Two m a j o r t y p e s o f s t u d i e s  The  first  the  DBH o f o p e n - g r o w n t r e e s .  type addressed  relationship al.  to other trees  1979).  (Pinus  crown  dimensions.  r e l a t i o n s h i p s between crown w i d t h and This  usually highly  significant  i s i n d e p e n d e n t o f s i t e q u a l i t y a n d age ( D a n i e l e t I t was u s e d b y K r a j i c e k  e t a l . (1961)  f a c t o r , a n d b y McMinn ( 1 9 8 6 )  crown c o m p e t i t i v e factors  have u s e d b a s i c  f o rquantifying  crown c o m p e t i t i o n  t a e d a L.) s t a n d .  This  t o derive the  to derive  i na loblolly  prism pine  r e l a t i o n s h i p h a s a l s o been used i n  s i n g l e - t r e e d i s t a n c e - d e p e n d e n t g r o w t h m o d e l s t o e s t i m a t e t h e zone of  influence  o f each t r e e  (Alemdag 1978;  E q u a t i o n s have been d e v e l o p e d by Alemdag Alexander (1974) for  (1971)  Douglas-fir, White  (1988)  (1978)  f o r white  f o r E n g e l m a n n s p r u c e , Ek ( 1 9 7 1 )  f o r several  loblolly  Loucks e t a l . 1981).  pine,  s o f t w o o d and hardwood s p e c i e s , Arney  (1972)  Newnham ( 1 9 6 6 ) forsitka  f o r r e d p i n e , Ek Leech  (1984)  a n d Newnham ( 1 9 6 4 ) f o r  f o r r e d and w h i t e p i n e s ,  spruce, Vezina 132  spruce,  (1962,  Tabbush and  1963) f o r b a l s a m  fir,  white  spruce,  and J a c k  and l o b l o l l y p i n e .  pine,  (1986)  and Z e i d e  A substantial  r e v i e w was  for  r e d oak  p r e p a r e d by Honer  ( 1972) . The s e c o n d dimensions  type  and DBH o f  relating  crown w i d t h  tive  to  was  addressed  While  not  this  affect  stand-grown to  determine  tionship.  relationships  DBH a r e most  the  effect  Bonnor ( 1 9 6 4 ) relationship  for  found a s i g n i f i c a n t  impact  pine.  In t h e i r  slope  to  spacing  age  and t h e  and s i z e  significant for  of  the  intercept  the  trees.  difference  Douglas-fir.  o n l y between  intercepts  ficantly area one  age.  the  Jensen  DBH.  Other  be u s e d  height are  differed  versus  could  other  to  the  studies (1982),  Kellomaki  of  and B u r k h a r t  was  These  however,  of  the  the  (1964,  (1965), 1970),  R i t c h i e and Hann  (1987),  Wile  versus  (1964),  133  with  to  the  found a  coefficients to  other were  crown found  and i n t e r c e p t s  were  and  signi-  surface  performed only  derive  equations  (width,  surface).  Bonnor ( 1 9 6 8 ) ,  Seitz  and Z a r n o v i c a n  for that  length,  Good Cole  D y e r and B u r k h a r t (1987),  related  DBH r e l a t i o n -  crown d i m e n s i o n s  crown, volume,  Beekhuis  associated  crown volume  made s o l e l y  lodgepole  closely  study  slopes  for  studies,  was  and  among s p a c i n g s  crown l e n g t h  did  S m i t h and B a i l e y  intercept  their  rela-  stand d e n s i t y  and Reukema ( 1 9 7 0 )  among s p a c i n g s  Curtin  (1986),  coefficient  objec-  on t h i s  Douglas-fir  coefficient  hand, b o t h the  determine  base  for  differences  s t u d i e s were  to  stand d e n s i t y  extended  for  equations  A frequent  l o b l o l l y pine,  Curtis  They a l s o  Significant  On t h e  common.  o n l y between t h e  dimensions.  ships.  of  Linear  concluded that  (1964)  study,  trees.  between crown  examples and  (1987),  (1986), (1982).  Sprinz  Crown d e v e l o p m e n t c a n a l s o be s t u d i e d ciency. of  i n terms o f e f f i (1)  Two t y p e s o f c r o w n e f f i c i e n c y m e a s u r e s a r e :  crown s i z e t o crown d i m e n s i o n o r s t e m s i z e a n d (2)  length)  (e.g.,  ratio  crown w i d t h t o crown  r a t i o o f i n c r e m e n t t o crown  size.  T h e s e a r e m e a s u r e s o f e f f i c i e n c y b e c a u s e t h e y a r e b a s e d on r a t i o s t h a t e x p r e s s t h e growth o f stems o r crowns r e l a t i v e dimensions s e n s i t i v e t o s i t e ciency  measure  length  to tree height).  of a t r e e parts  (or a b i l i t y  of the tree)  1987),  I t estimates  t o provide  ( F a r r a r 1984;  According  competition  inversely  size.  grow a t i t s maximum c a p a c i t y t h a n 50% ( F a r r a r  greater  ( r a t i o o f crown  the photosynthetic  Smith 1986;  Sprinz  capacity  of i t svigor (1986),  and B u r k h a r t  (Chapman 1 9 5 3 ;  crown r a t i o  i n t e n s i f i e s w i t h i n a stand,  related to tree  effi-  photosynthate t o the d i f f e r e n t  t o Holdaway  for light  The most common  type i s crown r a t i o  and c o n s t i t u t e s a measure  Smith 1986). as  of the f i r s t  conditions.  t o other  However,  as long  decreases  and i s  a p a r t i c u l a r tree can  as i t s crown r a t i o i s  1984).  The e f f e c t o f v a r i o u s  initial  s p a c i n g s arid/or  thinning  t r e a t m e n t s o n t h e c r o w n r a t i o o f Norway s p r u c e , S i t k a s p r u c e , a n d Douglas-fir  a t a g e 15 was p e r f o r m e d b y Kramer  showed  i t increased  that  thinning.  with  spacing  The e f f e c t o f v a r i o u s  (1966).  Results  and t h e i n t e n s i t y o f  initial  s p a c i n g s was a l s o  by Smith  (1977,  1987),  W a l t e r s and Smith  (1973)  f o r D o u g l a s - f i r , w e s t e r n hemlock  reported  heterophylla Donn). ages 16,  (Ref.) Sarg.),  and w e s t e r n redcedar  The c r o w n r a t i o was f o u n d t o i n c r e a s e 20,  2 5 , and 5 5 .  computed by K u u l u v a i n e n  This (1988)  (1987) and  Reukema a n d S m i t h  measure  134  with  plicata  spacing a t  o f e f f i c i e n c y was a l s o  and Z a r n o v i c a n  studies.  (Thuja  (Tsuga  (1982)  i n their  Other  studies  developed  ratio  of  pine,  D y e r and B u r k h a r t  for  individual  various  r e d oak)  softwood  or  Following  trees  its  increment  crown v o l u m e , of  the  last  Crown r a t i o bility of  of  pendent 1984  -  For  shape  a l s o used of  used (i.e.,  fullness  Kuuluvainen  (1988)  Smith  DBH and h e i g h t  to  lodgepole  stands,  open  and 0.8  crown w i d t h  dense  crown w i d t h  to  per  length.  unit  ranging  of  ratios.  they would  conditions. c a n be  9.4  m, S m i t h  135  al.  1982). developed. crown  to  the  (1977)  called  computed  of  by  needle  crown w i d t h  Douglas-fir be  to  and  a r o u n d 2 and 3  normal c o n d i t i o n s ,  related  proba-  Holdaway  on mean  use  to  two.  height  was  In y o u n g  According  use  measure  DBH ( a l s o  Smith  and  0.7  (1963),  the  number o f  In a p a r t i c u l a r D o u g l a s - f i r  m to  the  called  effect the  first  1983;  et  stem  respectively  1 and 5 u n d e r  DBH r a t i o  f r o m 1.21  recommended  The  have b e e n  ratio  its  width,  This  1981,  to  to  the  distance-inde-  (also  crown w i d t h  examine  the  predict  Wykoff  crown l e n g t h  to  (1969)  conditions,  under  1975;  1982).  crown  stands.  Belcher  The crown f u l l n e s s  mass d e n s i t y .  pine  pine  and crown w i d t h  mainly  than  crown d i m e n s i o n s  to  with  to  for  predicting  single-tree  1973,  ratio),  ratio),  1982).  two  STEMS -  Stage  crown w i d t h  (1980)  (1986)  (1964)  variables.  results  i n white in  involving  (Zarnivocan  under  trees  also  models  crown p r o j e c t i o n  independent  by Graham  slash  plantations,  equations  as  ratios  crown  pine  ratio  provided better  for  crown  Holdaway  and Ward  and crown  and PROGNOSIS -  or  pine,  the  C o l e and J e n s e n  loblolly  developed  (1979)  DBH, and volume  was  instance,  loblolly  (e.g.,  in  al.  area,  mortality  Other  et  predicting  species,  value  (1983)  for  in basal  was  growth  for  treatments  variable  efficiency  (1987)  Dell  and hardwood  B u r t o n and S h o u l d e r s mean  (e.g.,  mean s t a n d  thinning  equations  spacing  reported  that  rings trial the  crown w i d t h  to  DBH r a t i o  the  height  to  the  latter  r a t i o was  and  then  same  hemlock  crown w i d t h  decrease.  ratios at  for  evident,  for  Douglas-fir  for  western  the  crown w i d t h  to  a 2.7  ciency and  for  Reukema 1 9 7 0 ) .  Ford  The  has  a direct  other  type  ratio  of  bole  ratio  of  volume  released  associated with  the  were more e f f i c i e n t  cient  trees  of  thinning concluded  used  it  size  of  the  a small  by O ' H a r a  of  for  that  the  is  other  measure However,  at  redcedar,  of  age it  only  up  effi(Curtis  control  based  of  of  found to  the  stand,  the  used to  the  compare acting  efficiency  released  in every  analysing  on  trees  was  trees  DBH c l a s s , be more  DBH c l a s s e s .  an u n t h i n n e d  136  crown  species,  crown volume  in a 64-year-old Douglas-fir  compared t o  to  ratio  crown p r o j e c t i o n  trees  larger  (1988)  height  Hamilton (1969)  this  tree.  decreased  productivity.  DBH c l a s s were  trees  the  spacing  and i n c r e a s e d  trees with  categories,  with  slightly  efficiency  of  spacing  same t h r e e  to  the  and w e s t e r n  A n o t h e r measure  on s t a n d  spruce  computed  for western  mentioned  per u n i t  also  while  3 . 6 6 m,  up t o  crown f u l l n e s s  crown s u r f a c e  than u n r e l e a s e d  treatments that,  the  crown s i z e .  Sitka  than unreleased  r a t i o was  to  increment  For both  spacing  For the  crown measure  increment  23 y e a r - o l d  controls.  released  of  however,  species,  noticeable  effect  55,  increased  while  these  (1985)  A t age  much v a r i a t i o n w i t h  spacing.  of  20,  (1973)  DBH r a t i o  computed  age  redcedar,  Douglas-fir.  ratio  ratio  with  for western hemlock,  the  this  as  with  spacing  is  not  to  For a l l  (1987)  m spacing  used  western  and w e s t e r n h e m l o c k ,  decreased  with  increase  at  spacing  decreased.  Even though  W h i l e no v a r i a t i o n was  decreased  with  and S m i t h  Douglas-fir,  Reukema and S m i t h 25.  found to  redcedar.  ratio  ratio  Walters  16.  age  was  width  increased  and  effi-  The same effect  stand. tall  of He  trees  from  thinned  stands with  efficiently Badoux  small  crowns  than those with  (1945),  ground cover  used  larger  Assmann (1970)  i n a 88 y e a r - o l d S c o t s p i n e  social  status,  within  each  efficient  class.  crowns.  with  These  stand tree  three  space the  volume  increment  area,  increased  size  more  Citing  crown s u r f a c e  volume  tree  growing  reported that  (crown p r o j e c t i o n ) ,  but d e c r e a s e d  the  (thus  studies  study  with  the  concluded  size) that  trees  are  c h a r a c t e r i z e d by deep n a r r o w c r o w n s .  same c o n c l u s i o n  was  r e a c h e d by K u u l u v a i n e n  spruce  (Picea  abies  Absolute tion with  growth  foliage  competitive  (L.)  stress  used  the  ratio  studying measure  of  value,  vigor, up t o  the  stress.  Waring  et  a similar  ratio,  different  studies  stem b i o m a s s area.  increment  to  S i t k a spruce  concluded  al.  to  that  The  Norway  the  a tree (1980)  is  foliage  leaf  two m e a s u r e s  137  (1982)  weight  while  have  the  Then,  this  ratio  the  of  under  severe  of  very  this  competition;  a low c a p a c i t y  low  produce  (1981)  leaf  area.  used  volume  similar  to  a  same  new  competitive  al.  they  a r e a and o f  RGR.  Ford  the  1983;  trees  stands,  are  (Waring  all  per u n i t  on D o u g l a s - f i r  evaluate  B a s e d upon  and W a r i n g e t  stem i n c r e m e n t  to  trees  conjunc-  stand.  effect has  in  to  1980).  competition.  foliage  that  increment These  by i n d i v i d u a l  area  onset of  be u s e d  efficiency  al.  that  indicates  of  Waring et  related  w h i c h means  material,  leaf  he  inversely  a measure  can a l s o  1985;  basal  a 15-year-old  efficiency becomes  of  as  measures  experienced  W a r i n g and S c h l e s i n g e r  for  very  Korst.).  rate  data  per  and crown  crown  (1988)  of  the  proposed In  two  ratios  increment  i n concept  to to  of  Very  significant  confidence or  leaf  limits)  sapwood  1982;  al.  area  (Grier  1978).  foliage  weight  estimation to  (1964a,  of  g r o w t h model pipe-model  area of  area or  More  Some m e a s u r e s  foliage  recently, the  and t h e of  applied  indexes  them t o  redcedar. ciency 5.3-  have  not  ships  fullness,  based  best  been  1982).  The area  by S h i n o z a k i e t (1988)  western  also  developed  red  a  the  based  been d e v e l o p e d . i n hardwood  and c o l o r . of  hemlock,  my k n o w l e d g e ,  al.  rule.  (1986)  depth,  a p p l i e d to  estimate  f r o m sapwood  on c o l o u r and v i g o r  of  1981;  Smith  the and  on The  stands (1980a)  crown and western  such measures  of  effi-  pine.  Hypotheses Although  have  have  u s e d by F a i r w e a t h e r  Douglas-fir,  To t h e  weight  (Ford  to  p a r t i a l l y or e n t i r e l y  index  developed  trees  self-thinning  crown v i g o r  or  1982;  al.  carbon-balance budget,  crown c h a r a c t e r i s t i c s  crown s i z e ,  1982;  Ford  c a n be u s e d  Valentine  efficiency  weight  W h i t e h e a d 1978)  Waring et  other  qualitative  involved  narrow  Kaufmann and T r o e n d l e  theory developed  integrating  theory,  1974;  relationships  pipe-model  1964b).  1978;  al.  Marchand 1 9 8 4 ;  leaf  leaf  the  Waring et  These  or  relatively  (Cable 1958;  area  and W a r i n g  Long and S m i t h 1 9 8 4 ; Whitehead  (with  c a n n o r m a l l y be d e r i v e d between f o l i a g e  a r e a and DBH o r b a s a l  Kaufmann e t  relate  relationships  been to  some o f  the  measures  of  computed on many o c c a s i o n s , s t a n d d y n a m i c s have  not  been  efficiency their  mentioned  potential  above  relation-  determined because  they  i  have  been used  situations. vary  before  in a relatively  More  narrow range  specifically,  and a f t e r  the  onset  138  never  of  it  has  of  competition  analytical  been for  shown how a wide  they  range  of  spacings  crown r a t i o  and ages and f o r  trees  and t h e  crown w i d t h  ratio  of  computed by S m i t h  (1977,  1987),  Walters  and S m i t h  (1973)  with data  trials,  it  did  show how t h e s e  not  mentioned The  was  only  a few  Before  the  onset  of  red p i n e ,  in  terms  are of  of  These  of  all  been  (1987),  from  the  and  spacing studies  conditions  hypotheses  are  characteristics  are  similar  the  of  last  rejected.  chapter Thus,  trees  the  same  chapter: stands  efficiency  low e f f i c i e n c y  experiencing  high e f f i c i e n c y  of  to  that  following  the  values  tested  efficiency  1982,  high  values levels are  stress.  those  i n concept  (1979,  suggest  the  have  place,  similar  measures  Ford  in this  i n even-aged  low c o m p e t i t i v e  the  conclusions  trees  while  with  tested  competition  takes  with  competition,  be  development.  because  the  Although  Furthermore, these  varied with  the  crown  associated  associated  in  DBH have  originating  hypotheses w i l l  H 5 . 2 - When c o m p e t i t i o n  chapter  to  sizes.  Reukema and S m i t h  ages.  ratios  different  above. following  H5.1-  for  of  to  based RGR.  1984). first  hypothesis  i n the on crown  They a l s o  The r e s u l t s hypothesis  will  last  be  reflect obtained  will  be  considered  as  well: H5.3-  Before stands,  the  onset  small  of  trees  competition are  in  even-aged  more e f f i c i e n t  than  large  ones. Three measures, will  types  of  relative  be d e f i n e d  crown m e a s u r e s measures,  i n the  next  will  be d e r i v e d :  and r e l a t i v e section.  139  absolute  growth measures.  Absolute  and  relative  These  measures  will  be  c o m p a r e d , and i t  relative  measures  show t h e  same  will  trends  be d e t e r m i n e d as  the  if  relative  the growth  measures. 5.4-  Material  and Methods  The d a t a  e m p l o y e d were  above, three and as  the  crown c h a r a c t e r i s t i c s  different  relative measures  classes:  of  measures  Sprinz  studies to  in  the  measure of  of  Stiell  the  measures,  area,  field.  Crown s u r f a c e  following  the  measures,  c a n be  considered  two  crown  crown v o l u m e ,  length, foliage  Crown p r o j e c t i o n was  d e l i m i t e d by crown w i d t h .  photosynthetic 1966),  area.  the  as  According  to  the  As s u g g e s t e d by  form o f  the  crown s u r f a c e  were  computed  crown p r o j e c t i o n c o n s t i t u t e s  Therefore,  following  R is  into  relative  crown w i d t h ,  crown was a r e a was  an the assumed computed  formula: 2  where  mentioned  Crown w i d t h and crown l e n g t h  (1987),  (1962,  be p a r a b o l o i d .  with  the  circle  and B u r k h a r t  indirect  of  crown s u r f a c e  measured d i r e c t l y of  As  c a n be g r o u p e d  The l a t t e r  consist  and b r a n c h w e i g h t .  surface  3.  efficiency.  crown p r o j e c t i o n ,  the  i n Chapter  studied  absolute  growth measures.  Absolute  weight,  described  4  4  1.5  1.5  area  radius of  the  f o r m u l a was u s e d  to  crown and L i t s compute  length.  crown v o l u m e : 2  Crown volume  0 . 5 x I I x R  140  x L .  The  The  foliage  weight  of  formula  d e r i v e d by S t i e l l  Foliage  weight  every  the  develop  this  derived  from the  This  data  rized  was  the  of  width  first  to  relative  crown l e n g t h .  When t h i s  r a t i o of the  measure u s e d was This  ratio  unit  of  biomass  represents  -  the  (1988)  as  and a g e .  every  characte-  T h e r e was  tree  was  no  predicted (1983)  s t u d y o f Alemdag  the  0.91  c a l l e d the  ratio  ratio  the  efficiency  of  to  the  derived. needle  crown  to  The  was u s e d  density.  It  tissue,  ratio the  calcu-  The  closer  third  branch  The r a t i o o f It  of  measure  1970).  photosynthetic  141  shape  photosynthetic  (Perry 1985).  of  the  crown v o l u m e .  biomass  p r o p o r t i o n of  r a t i o of  crown f u l l n e s s  relative  (Curtis  foliage  a measure  the  increases,  The s e c o n d  r a t i o of  x Crown w i d t h (m) x Crown l e n g t h (m)  computed was  crown volume was a l s o  Kuuluvainen reflects  larger the  (1982).  equations.  crown s u r f a c e  respiratory tissue to  2  T h i s was  l a t e d was  spacing,  size  0.66314  •  measure  more r o u n d e d .  the  the  (kg)  crown becomes the  tree  to  (1982):  branches  by Assmann ( 1 9 7 0 ) .  (m)  equation  same a r e a and was  branches of  R The  data used  by A l e m d a g and S t i e l l  d e r i v e d from the  and A l e m d a g and S t i e l l Biomass of  of  between  biomass  f r o m an e q u a t i o n a l s o  x crown w i d t h  l i m i t e d range o f  i n the  range  difference  Finally,  (m)  a c o m p a r i s o n was made w i t h an  collected  the  - 0.99  data c o l l e c t e d  by a much w i d e r  significant  2  relatively  equation,  set  computed w i t h  = 0 . 4 9 8 8 x crown l e n g t h  (kg)  of  was  (1977):  and B e r r y  R Because  tree  biomass. tissue  per  foliage by also given  the  space  allocated. The o t h e r  relative  crown and b o l e called  dimensions.  crown p r o j e c t i o n  width exceeds width  measures  to  Crown r a t i o ,  The r a t i o o f  ratio)  is  a measure  w h i c h was d i s c u s s e d  also  calculated.  area  ratio  These  (leaf  ratios  area/stem  photosynthetic  tissue  it  was d e c i d e d  apply this  following  to  ratios  crown p r o j e c t i o n t o crown volume  DBH and  height.  to  The RGR m e a s u r e s area,  b a s e d upon t h e  unit  rate:  on f o l i a g e material between  biomass  crown  and f o l i a g e  on t h e  t o DBH,  DBH and biomass  increment  i n DBH,  crown s u r f a c e  -  to  retained  The c o m p u t a t i o n o f  Ln[CR(2)]  As  dimensions,  to  were: area,  every  (1982)  e q u a t i o n p r o v i d e d by Hunt  -  CR(2) -  T(l)  area,  or h e i g h t ,  mentioned above,  (sapwood the  biomass.  leaf  the p r o p o r t i o n  crown l e n g t h  crown p r o j e c t i o n ,  the  (Hunt 1 9 8 2 ) .  crown s u r f a c e  based  to  was  for  Ln[CR(l)]  x  DBH, b a s a l  characteristics  other  computed:  W(2) - W ( l )  T(2) where W i s  to  5.1,  in Section  which r e f l e c t s  crown  1970).  (Assmann  The crown c h a r a c t e r i s t i c s  and f o l i a g e  _ RATIO •»  t o w h i c h crown  s i m i l a r i n concept  concept  s t u d i e d were  r a t i o was leaf  are  DBH ( a l s o  The r a t i o o f  respiratory tissue  were  crown l e n g t h ,  crown v o l u m e ,  degree  spread  DBH and h e i g h t ,  and h e i g h t .  crown w i d t h ,  the  extensively  DBH and h e i g h t ,  height,  basal  to  also  of  biomass)  of  the  measures  b a s e d upon b o t h  crown w i d t h t o  (Assmann 1 9 7 0 ) .  stem d i a m e t e r  stem h e i g h t  c a l c u l a t e d were  reflect area)  the  and CR one  and T t h e  RGR a d j u s t e d  because  of  sapwood a r e a and l e a f  142  the  CR(1)  age. for  of  the  crown  The r a t i o s  based  productive  relationship  area or biomass  that  (Waring  exists et  al.  1981). As  the  the  two  each  emphasis  sample  spacing  diameter  classes This  whether  the  various  sizes.  parameters onset  5.5-  for  a given into  constituted  design  was  used  crown p a r a m e t e r s It  based of  a l s o was  analysed  of  and  regression  equations  stem d e v e l o p m e n t .  the  slopes  of  the  relationship  for  the  first  six  spacings  The s l o p e s than  increased  of  those  with  the  of  Douglas-fir,  (1964, found  of  with  1970)  for  trees  some o f  for  and  test of  the  crown  variability  and B o l e  before  for  to  the  Sizes  relate 1.5  differ  m and 6 . 0  first  six  crown  m spacing,  between crown w i d t h and  diameter  significantly  m spacings  spacings.  for  been  on t h e  studied  (Table  were much  The  intercepts  among s l o p e s ,  but  relationship  for  and Reukema (1970)  spacing.  affect  and l o d g e p o l e  Except  stand d e n s i t y  Curtis  difference  to  testing  were d e r i v e d  d i d not  4.3  the  crown w i d t h and DBH has  increase  nested  spacing.  The e f f e c t  ficant  differed  efficiency  in a  from  These  spacings,  between Crown D i m e n s i o n s  to  greater  for  the  Trees  classes.  factor  from  Discussion  dimensions  5.1).  nesting compare  used  on m e a s u r e s  Relationships  Linear  to  data  s p a c i n g were m e r g e d .  1 cm d i a m e t e r  the  effects,  competition.  Results  5.5.1-  on c o m p a r i n g s p a c i n g  were d i v i d e d  anova.  the  plots  was  the  other  pine  slope  of  the  also  was  For  any  signi-  found  noticed  by  Stand d e n s i t y  relationships  ( S m i t h and B a i l e y 1 9 6 4 ) .  143  obtain  intercept  Eucalyptus obliqua L ' H e r i t . the  species.  d i d not  The same t r e n d was  between  for  to Curtin was  Douglas-fir  The r a t e  of  change  Table  5.1:  E q u a t i o n s f o r crown w i d t h (m) as a f u n c t i o n (cm) f o r a l l a g e s and e v e r y s p a c i n g .  Form o f Spacing  crown w i d t h - a + bxDBH  equation:  (m)  a  2  b  0.8551.017 1.026 1.060 1.288 1.536 1.410 1.003  1.2 1.5 1.8 2.1 2.4 3.0 4.3 6.0  o f DBH  n  0.125ab* 0.119b 0.129ab 0.132a 0.133a 0.132a 0.162 0.182  r  901 963 915 950 916 924 893 1127  SEE  0.69 0.61 0.66 0.77 0.81 0.86 0.93 0.96  0.316 0.359 0.398 0.362 0.357 0.348 0.357 0.297  *: s p a c i n g s w i t h t h e same l e t t e r do n o t s i g n i f i c a n t l y d i f f e r at the l e v e l of p r o b a b i l i t y o f 0 . 0 5 . SEE: s t a n d a r d e r r o r o f e s t i m a t e . N o t e : B o t h c o e f f i c i e n t s were s i g n i f i c a n t f o r e v e r y s p a c i n g a t the l e v e l o f p r o b a b i l i t y o f 0 . 0 5 .  Table  5.2:  E q u a t i o n s f o r crown l e n g t h (m) as a f u n c t i o n (cm) f o r a l l a g e s and e v e r y s p a c i n g .  o f DBH  2 Form o f e q u a t i o n : Spacing 1.2 1.5 1.8 2.1 2.4 3.0 4.3 6.0  (m)  crown l e n g t h  a  b  c  1.151 1.556 1.4 56 0.982 0.911 0.333 0.479 0.278  0.461 0.438 0.453 0.570 0.604 0.662 0.553 0.482  -0.011 -0.012 -0.011 -0.015 -0.016 -0.015 -0.009 -0.005  = a + bxDBH + cxDBH n 896 961 915 948 917 924 910 1229  SEE: s t a n d a r d e r r o r o f e s t i m a t e . N o t e : t h e t h r e e c o e f f i c i e n t s were s i g n i f i c a n t a t t h e l e v e l o f p r o b a b i l i t y o f 0.05.  144  r  2  0.72 0.64 0.72 0.81 0.82 0.86 0.93 0.90 f o r every  SEE 0.591 0.585 0.556 0.538 0.560 0.623 0.607 0.649 spacing  o f crown w i d t h w i t h d i a m e t e r until  a maximum was r e a c h e d  concluded  i n c r e a s e d as s t a n d d e n s i t y w i t h open-grown  trees.  decreased  They  t h a t t h e i n t e r c e p t was d e p e n d e n t u p o n t h e age a n d s i t e  of the t r e e s sampled. Q u a d r a t i c p o l y n o m i a l s were u s e d t o r e l a t e DBH  (Table 5 . 2 ) .  Little  f r o m DBH = 0 t o DBH = 15 smaller off,  difference existed cm ( F i g u r e 5 . 1 ) .  the s p a c i n g , the lower  except  f o r the f i r s t  crown l e n g t h t o  among t h e s p a c i n g s Beyond t h i s  l i m i t , the  the corresponding, curve  two s p a c i n g s .  leveled  This suggests  t h a t when  c o m p e t i t i o n i s n o n - e x i s t a n t o r n o t v e r y s e v e r e , crown l e n g t h does n o t v a r y much among s t a n d s tion  intensifies,  tality  of d i f f e r e n t  the reduction i n l i g h t  of the lowest branches,  density  i s increased.  competi-  f a s t e r as s t a n d  T h i s i s why c r o w n l e n g t h d e c r e a s e s  crown l e n g t h w i l l  5.5.2-Absolute  When  p e n e t r a t i o n i n d u c e s mor-  and t h u s o c c u r s  s p a c i n g i s i n c r e a s e d f o r t h e same DBH. for  spacings.  More e x t e n s i v e  as  results  be e x a m i n e d b e l o w .  Measures  The mean v a l u e s o f c r o w n w i d t h , c r o w n l e n g t h , c r o w n p r o j e c tion,  crown s u r f a c e , crown volume, f o l i a g e biomass and biomass o f  branches and 5 . 3 .  f o r every  s p a c i n g a n d age a r e i l l u s t r a t e d  A t age 1 3 ,  significantly  none o f t h e s e  among s p a c i n g s  i n Figures  crown parameters  (Tables 5.3  to 5.9).  differed Only  crown  w i d t h and crown p r o j e c t i o n had s i g n i f i c a n t d i f f e r e n c e s a t ages and 1 5 .  However,  v a r i a n c e were (Tables 5.3  the c a l c u l a t e d values of the nested  j u s t above t h e l e v e l  and 5 . 5 ) .  Indeed,  of significance  m and 3 . 0  14  a n a l y s i s of  i n both  cases  the m u l t i p l e range t e s t c o u l d n o t  d e t e c t s i g n i f i c a n t d i f f e r e n c e s a t age 14 o n l y the 1.2  5.2  f o r crown w i d t h , and  m spacings d i f f e r e d 145  f o r crown  projection.  FIGURE 5.1: CROWN LENGTH = F(DBH) FOR DIFFERENT SPACINGS 12.0  LEGEND A= 1.2X1.2 M 0 = 1.5X1.5 M $ = 1.8X1.8 M 0 = 2.1X2.1 M V= 2.4X2.4 M - = 3.0X3.0 M * = 4.3X4.3 M • = 6.0X6.0 M  10.9-  9.8-  8.7  I  Io z  A"  s  7.61  LU  6.51  o  5.4  U  4.3-  3.2-  2.1  1.0 < 0  8  12  16  20  DBH (CM)  146  24  28  32  36  40  FIGURE  5.2:  MEAN  ABSOLUTE  CROWN  FIGURE 5.2.1: MEAN CROWN WIDTH VALUES FOR ALL SPACINGS OVER AGE 1 1 .00  LEGEND 4 = SPACING: 1.2X1.2 M * = SPACING: 1.5X1.5 M « = SPACING: 1.8X1.8 M 0 = SPACING: 2.1X2.1 M f V = SPACING: 2.4X2.4 M / . = SPACING: 3.0X3.0 M / * = SPACING: 4.3X4.3 M / o = SPACING: 6.0X6.0 M /  6.28  5.67  2 j  (1)  FIGURE 5.2.2: MEAN CROWN LENGTH VALUES FOR ALL SPACINGS OVER AGE  7. 50  6.89  DIMENSIONS  LEGEND 4 = SPACING: 1.2XI.2M 0 = SPACING: 1.5X1.5 M * = SPACING: 1.8X1.8 M 0 - SPACING: 2.1X2.1 M 7 = SPACING: 2.4X2.4 M * = SPACING: 3.0X3.0 M * - SPACING: 4.3X4.3 M o = SPACING: 6.0X6.0 M  1 0 . 16  9.32  8.48  5.06  9 J  4 . 45  z §3.84  IX  o 3.23  2.62  21.. 040 1  1 13  15  1  1 ' 17  1 ' 19  I ' 1 • I '-I 21  23  25  27  '  I 29  1  1  l—  31  2.60  T 33  J  1  13  I 15  1  I 17  1  I ' I 19  21  AGE  35.4  * 31.1  1 •—I  23  25  27  1 • I —T  1  29  31  33  FIGURE 5.2.4: MEAN CROWN SURFACE VALUES FOR ALL SPACINGS OVER AGE LEGEND 4 - SPACING: 1.2X1.2 M 0 = SPACING: 1.5X1.5 M * = SPACING: 1.8X1.8 M 0 = SPACING: 2.1X2.1 M 7 = SPACING: 2.4X2.4 M * - SPACING: 3.0X3.0 M * = SPACING: 4.3X4.3 M o - SPACING: 6.0X6.0 M  172  LEGEND 4 - SPACING: 1.2X1.2 M 0 = SPACING: 1.5X1.5 M * = SPACING: 1.8X1.8 M 0 = SPACING: 2.1X2.1 M 7 = SPACING: 2.4X2.4 M . = SPACING: 3.0X3.0 M * = SPACING: 4.3X4.3 M o = SPACING: 6.0X6.0 M  39.7  I  AGE  FIGURE 5.2.3: MEAN CROWN PROJECTION VALUES FOR ALL SPACINGS OVER AGE 44.0  1  156  139 M * »  123  2  Ul 107  o  if Q:  3  (/) Z  5  O oc o  58  A.  13  15  19  21  23  25  27  29  31  33  13  15  21  23  AGE  AGE  147  25  27  29  -0  31  33  FIGURE  ? •  DIMENSIONS  (2)  FOR ALL SPACINGS OVER AGE  LEGEND - SPACING: 1.2X1.2 - SPACING: 1.5X1.5 S P A C I N G : 1.8X1.8 - SPACING: 2 . 1 X 2 . 1 = SPACING: 2 . 4 X 2 . 4 = SPACING: 3 . 0 X 3 . 0 = SPACING: 4 . 3 X 4 . 3 = SPACING: 6 . 0 X 6 . 0  /  M M M M M M M M  \  A * « 0 7 • » o  /  '801  2  = = =  LEGEND SPACING: 1.2X1.2 SPACING: 1 . 5 X 1 . 5 SPACING: 1 . 8 X 1 . 8 SPACING: 2 . 1 X 2 . 1 SPACING: 2 . 4 X 2 . 4 SPACING: 3 . 0 X 3 . 0 SPACING: 4 . 3 X 4 . 3 SPACING: 6 . 0 X 6 . 0  M M M M M M M M  /  2  a: o  CROWN  FIGURE 5 . 3 . 2 : MEAN FOLIAGE BIOMASS VALUES  U  O > Z ? O  ABSOLUTE  FOR ALL SPACINGS OVER AGE  A 4 «0 7 • ft o  182-  MEAN  FIGURE 5 . 3 . 1 : MEAN CROWN VOLUME VALUES  227 -  205  5.3:  /  » i  70 ]  1/1  «8i  -7^--7\^  —7  25  13  -i—•—i—'  13  17  19  i '—r~  21  23  25  27  29  31  33  FOR ALL SPACINGS O V E R A G E  47.98  42.96  A 0 0 0 7 • ft o  = = = = =  LEGEND SPACING: 1.2X1.2 SPACING: 1 . 5 X 1 . 5 SPACING: 1 . 8 X 1 . 8 SPACING: 2 . 1 X 2 . 1 SPACING: 2 . 4 X 2 . 4 SPACING: 3 . 0 X 3 . 0 SPACING: 4 . 3 X 4 . 3 SPACING: 6 . 0 X 6 . 0  M M M M M M M M  23  AGE  AGE FIGURE 5 . 3 . 3 : MEAN BRANCHES BIOMASS VALUES  53.00  21  /  \  2.80  AGE 148  23  27  29  31  33  Table  5.3:  T w o - l e v e l - n e s t e d anova  tests  f o r crown w i d t h  (m).  Factor DBH Age 13 14 15 16 18 24 30  Spacings 1.2 1.2 1.2 All All All All  to to to  included(m)  4.3 4.3 4.3  class  Spacing  D.F.  F  54/395 67/379 73/360 90/424 95/409 108/373 118/349  43.00* 32.55* 44.01* 28.12* 30.82* 17.12* 8.87*  * : s i g n i f i c a n t d i f f e r e n c e s at the n . s . : no s i g n i f i c a n t d i f f e r e n c e .  level  of  D.F. 6/54 6/66 6/72 7/88 7/93 7/108 7/118  T u k e y ' s m u l t i p l e range S p a c i n g (m) 1.2  1.51n.s. 2.33* 2.72* 6 .88* 8.40* 64.25* 158.50*  probability  C o m p a r i s o n o f mean crown w i d t h s among t h e Age  F  of  0.05.  spacings.  test  1. 5  1.8  2.1  2.4  3.0  4.3  6.0  -  14  1.52a*  1.90a  2 .02a  2.13a  2.30a  2.40a  2 . 31a  15  1.57a  1.86ab  2 .Olab  2.14ab  2.31ab  2.53b  2 .49b  16  1.73a  1.95ab  2 . 02ab  2.20ab  2.52abc  2.79bc  2 .76bc  3.14c  18  1.93a  2.27a  2 .44ab  2.52ab  2.76abc  3.22bc  3 . 28bc  3.66c  24  2.09a  2.28a  2 .43ab  2.83bc  3.29c  4.00  4 .91  5.46  30  1.93a  2.03a  2 .40ab  2.86bc  3.32c  4.10  5 .35  7.18  * : t h e s p a c i n g s f o r a g i v e n age f o l l o w e d by t h e same l e t t e r do n o t differ  significantly  at  the  level  149  of p r o b a l i l i t y  of  0.05.  Table  5.4:  Two-level  n e s t e d anova  tests  for  crown l e n g t h  (m).  Factor DBH c l a s s Age 13 14 15 16 18 24 24 30  Spacings  included(m)  1.2 t o 4.3 1.2 t o 4 . 3 1.2 t o 4 . 3 All All 1. 2 ; 1. 8 ; 2 . 1 ; 4 . 3 1. 5 ; 2 . 4 ; 3 . 0 ; 6 . 0 All  D.F.  Spacing  F  D.F.  54/395 146.77* 67/379 121.38* 73/360 62.20* 90/424 59.79* 95/409 59.27* 56/163 16.82* 9.44* 52/210 118/349 5.33*  * : s i g n i f i c a n t d i f f e r e n c e s at the n . s . : no s i g n i f i c a n t difference.  150  level  of  6/54 6/67 6/7 2 7/89 7/94 3/54 3/48 7/118  F 0 . 32n. s. 0 . 6 0 n . s. 1 . 0 8 n . s. 1 . 4 8 n . s. 2 .85* 38 .16* 78 .48* 204 .86*  p r o b a b i l i t y of  0.05.  Table  5.5:  Two-level  n e s t e d anova  tests  f o r crown  projection  Factor  DBH class Age 13 14 15 16 18 24 30  Spacings included(m)  D.F.  1.2 to 4.3 1.2 to 4.3 1.2 to 4.3 All All All All  Spacing D.F.  F  54/395 67/379 73/360 90/424 95/409 108/373 118/349  F  6/54 1.35n.s. 6/66 2.32* 6/72 2.74* 7/88 6.78* 7/9 3 8.86* 7/108 46.51* 7/118 110.64*  36.95* 32.39* 42.42* 29.03* 28.56* 15.37* 8.29*  *: s i g n i f i c a n t differences at the l e v e l of p r o b a b i l i t y of 0.05. n . s . : no s i g n i f i c a n t difference.  C o m p a r i s o n o f mean crown p r o j e c t i o n s among t h e Tukey's multiple Spacing  Age  range (m)  spacings  test  1.2  1.5  1.8  2.1  2.4  3.0  4.3  6.0  14  2. 13a*  3.02ab  3 . 50ab  3.87ab  4.43ab  4 .87b  4.51ab  -  15  2. 26a  2.96ab  3 . 50ab  3.93ab  4.97ab  5. 32b  5.19b  -  16  2. 53a  3.20ab  3 . 47ab  4.13ab  5.24abc 6.48bc  18  3. 07a  4.27a  4 .94ab  5.33abc 6.27abc 8.56bcd 8.98bcd 10 .85d  24  3. 71a  4.31a  5 .02a  6.65ab  30  3. 20a  3.40ab  4 .90abc 6.83cd  6.36bc  7 .99c  8.41bc  12.90c  19.45d  26 .63d  9.10d  13.52  23.00  40 .90  the spacings for a given age followed by the same• l e t t e r do not d i f f e r s i g n i f i c a n t l y at the l e v e l of p r o b a l i l i t y of 0.05.  151  Table  5.6: T w o - l e v e l  nested  anova  tests  f o r crown s u r f a c e  (m ). 2  Factor DBH Age 13 14 15 16 18 24 30  Spacings 1.2 1.2 1.2 All All All All  class  D.F.  included(m)  t o 4.3 t o 4.3 t o 4.3  54/395 67/379 73/360 90/424 94/409 108/373 118/349  F 97 69 84 65 66 22 10  .96* .79* .91* .87* .06* .61* .27*  Spacing D.F. 6/54 6/67 6/7 3 7/89 7/94 7/108 7/118  *: s i g n i f i c a n t d i f f e r e n c e s a t t h e l e v e l o f p r o b a b i l i t y n . s . : no s i g n i f i c a n t d i f f e r e n c e .  152  F 0.51n.s. 0.92n.s. 1.41n.s. 3.27* 5.27* 77.49* 200.5* o f 0.05.  Table  5.7:  Two-level  n e s t e d anova t e s t s  f o r crown volume (m  3  Factor DBH c l a s s Age 13 14 15 16 18 24 30  Spacings included(m) 1.2 1.2 1.2 All All All All  to to to  D.F.  4 .3 4 .3 4 .3  Spacing  F  D.F.  54/395 8 2 . 7 8 * 67/379 6 0 . 1 9 * 73/360 7 1 . 1 9 * 90/424 5 2 . 1 1 * 95/409 4 8 . 7 6 * 108/373 2 0 . 9 7 * 118/349 1 0 . 3 3 *  * : s i g n i f i c a n t d i f f e r e n c e s a t the n . s . : no s i g n i f i c a n t d i f f e r e n c e .  level  6/54 6/66 6/72 7/89 7/93 7/108 7/118  T u k e y ' s m u l t i p l e range S p a c i n g (m) 1.2  1.5  1.8  16  5.40a*  7.745ab  8.91ab  18  7.42a  11.32ab 13.76ab  24  9.12a  10.84a  13.61ab 19.65ab 29.07bc  30  8.63a  8.15a  11.98ab 20.25bc  *:  2.1  0.78n.s. 1.29n.s. 1.72n.s. 4.16* 6.46* 75.01* 123.79*  of p r o b a b i l i t y  C o m p a r i s o n o f mean crown v o l u m e s among t h e Age  F  2.4  of  0.05.  spacings  test 3.0  4.3  6.0  1 1 . 5 2 a b c l 3 . 9 8 a b c l 7 . 2 4 b c 14.76abc  20.66c  15.86ab  33.48c  20.12bc  28.17bc  26.17bc  49.99c  87.76d  109.87d  28.59cd 47.39d  100.15  226.40  t h e s p a c i n g s f o r a g i v e n age f o l l o w e d by t h e same l e t t e r do n o t d i f f e r s i g n i f i c a n t l y a t the l e v e l o f p r o b a b i l i t y of 0 . 0 5 .  153  Table  5.8:  Two-level  nested  anova t e s t s  for  foliage  biomass  (kg).  Factor Spacing  DBH c l a s s Spacings  Age 13 14 15 16 18 24 30  1.2 1.2 1.2 All All All All  to to to  included(m)  4.3 4.3 4.3  D.F.  F  54/394 67/379 73/359 90/424 95/409 108/373 118/385  102.36* 73.11* 77.44* 68.55* 62.48* 22.65* 10.23*  * : s i g n i f i c a n t d i f f e r e n c e s a t the n . s . : no s i g n i f i c a n t d i f f e r e n c e .  Comparison of  level  mean f o l i a g e  Tukey's Age  of  1.2  1.5  1.8  2.1  2.4  16  3 .52a*  4 . 55ab  4 .99ab  5 . 86ab  6. 46ab  18  4 . 45a  5 .84ab  6 .59ab  7 .23ab  24  4 .90a  5 .55ab  6 . 37ab  30  4 .95a  4 • 77a  5 . 66ab  *:  6/54 6/66 6/72 7/89 7/94 7/108 7/118  probability  b i o m a s s among t h e  m u l t i p l e range S p a c i n g (m)  F  D.F.  0.45n.s. 0.88n.s. 1.38n.s. 3.14* 5.40* 77.99* 133.96* of  0.05.  spacings  test 4.3  6.0  7.15ab  6. 12ab  7.93b  8. 57ab  10.25b  9 . 21b  11.11  8 .13bc  10 . 56c  15.32  21 . 7 9 d  25.18d  8 . 28bc  10 . 2 4 c  14.22  23 .10  39.49  3.0  t h e s p a c i n g s f o r a g i v e n age f o l l o w e d by t h e same l e t t e r do n o t d i f f e r s i g n i f i c a n t l y at the l e v e l of p r o b a l i l i t y of 0 . 0 5 .  154  Table  5.9: T w o - l e v e l - n e s t e d  anova t e s t s  f o r branches  biomass  (kg)  Factor DBH c l a s s Spacings  Age 13 14  15  16 18 24 30  1.2 1.2 1.2 All All All All  D.F.  included(m)  t o 4.3 t o 4.3 t o 4.3  F  54/395 103.43* 67/379 73.76* 73/360 85.48* 90/424 68.33* 62.72* 95/409 22.70* 108/373 118/349 10.91*  Spacing D.F. 6/54 6/67 6/7 3 7/89 7/94 7/108 7/118  *: s i g n i f i c a n t d i f f e r e n c e s a t t h e l e v e l o f p r o b a b i l i t y n . s . : no s i g n i f i c a n t d i f f e r e n c e .  155  F 0.47n.s. 0.88n.s. 1.39n.s. 3.14* 5.39* 78.02* 126.24* of  0.05.  However, the  this  onset  because 4.3  of  particular competition  3.0  the  A t age 1.2  between the  suggested a trend e x i s t i n g  rather  m spacing  m spacing.  appear  case  t h a n an e f f e c t  had a h i g h e r  15,  mean t h a n  significant  m spacing  of  before  competition that  differences  of  the  began  to  3 . 0 m and 4 . 3 m  and t h e  spacings. Except  for  significant closer lower  crown l e n g t h ,  differences  the  spacing,  the  at  all  smaller  increment  rate.  virtually  no c h a n g e  in values,  5.2  and 5 . 3 ) .  parameter of  The l a r g e r  value,  16.  age  the  and t h u s  of  Stiell  For the  projection, 5.7  differences  largest spacings largest spacings age  15,  spacings ages  showed  16,  except  the  greater  and t h e  and crown w i d t h o f  spacings  as  began  differ  5.2.1  pattern.  crown The g r a p h s  and 5 . 2 . 2 )  update  different 1.8  different  the  onset  i n Chapter  between the  close  156  4.  smallest  differences  m,  4.3  2.4  6.0  5.3).  competition  and l a r g e  and among and  m and 1 . 5 m m spacing  at  m, and 3 . 0 m  from the  The o t h e r  signi-  smallest  1.2  the  from the  (Table of  5.5,  A t young a g e s ,  between t h e  2.1  m,  crown  5.3,  (Tables  intensified,  and 20 r e s p e c t i v e l y  determined  was  (Figures  crown w i d t h ,  Crown w i d t h o f  the  significantly  ages of  the  the  the  there  increment.  biomass  differences  significantly  the  greater  performed for  following  became  to  and  crown l e n g t h  the  and f o l i a g e  accentuated.  19,  33,  (1977).  spacings  16,  spacings,  the  (Figures  As c o m p e t i t i o n  increased,  became  for  showed  up t o  g r a d u a l l y a p p e a r e d between t h e  spacings.  correspond  to  the  closest  spacing,  tests  crown v o l u m e ,  and 5 . 8 )  ficant  range  age  crown p a r a m e t e r s ,  the  and B e r r y  The m u l t i p l e  crown p a r a m e t e r s  From t h i s  the  crown w i d t h and crown l e n g t h  those  the  m spacing  These for  crown  spacings  at  ages  these parameters  one  or  two  years  after  crown w i d t h .  Crowns s t a r t e d cially  for  occurred  the  at  it  appears  is  a little  o v e r l a p p i n g at  closest  ages that  spacings  13,  14,  even  if  the  a maximum r a t e .  sustain  some r e d u c t i o n  The DBH n e s t i n g  of  Indeed, in light  on crown d i m e n s i o n s  (Table  4.1).  i n the  first  growing  o c c u p i e d by t h o s e  grow a t  effect  and 15  relatively  or  factor  space  other this  was  of  5.3  o c c u r r e d among t r e e s  Crown w i d t h  increased  DBH c l a s s  occurred  increased with  for  the  5.5.3-Relative  other  5.5.1).  ratio  1.5  for  the  m spacings).  ratio  d i d not The  up t o  up t o  ages  afterwards. same t r e n d ,  (Table  closest  Contrary  necessarily  ratios  decreased  crowns  still can  period.  for  implies  different  that  and t h e  not  all  sizes.  The same  and a r e  tree  any m a j o r  a short  This  5.4).  measures  30,  computed ages 28,  15  24,  The 2 . 4 but  generally  Significant  ages between s p a c i n g s competition  absolute  for  and s p a c i n g ,  (Figure  a  crown c a n  that  of  Thus,  range  patterns  shown  here.  Measures  Crown f u l l n e s s (Figure  age  the  significant  5.9).  variations  in  crown o f  without  be  significant  size  the  biomass  (Tables  tree  spacings.  suggests  s e v e n crown p a r a m e t e r s  with  to  six  trees,  found to  espe-  Overlapping  intensities  foliage  young a g e s ,  they  m,  increased  with  differences  were  5.10),  before  even  spacings  15  (age  obtained  for  the  or 16, and 24  with  four  157  the  1.2  of m and  fullness  spacings age  and  3 . 0 m and 4 . 3 m s p a c i n g s less  all  onset  crown  up t o  respectively,  fluctuated  at  age.  narrowest  increased  the  for  t o Assmann ( 1 9 7 0 ) , increase  spacing  after  they  22,  decreased  fluctuated followed stop  the  decreasing.  FIGURE 5 . 4 : FOR A L L  CROWN WIDTHS PER 1 CM DBH C L A S S S P A C I N G S AND D I F F E R E N T A G E S  7  3  30  3  O 3  2  7 7  2  SO  LOWNMO  2  4  •  7  3  /  3  / * £  i  4  i  1 7  o  9  o  O 4  i  4  40  3  O S  CROWN WIDTH 1  .2  SS  2  3  1  7 7  1  SO  S  DBH  CLASS  DBH  CLASS  O  as  o  es  7  7 4  3  . ,2 a  SS  2 2  1  S  3  1 3  2  04  7 O  <->  40  7  2  3a  o s 7 1 3  7  1  03  O  e 9  o  3  A  7 O  O  A-  2e  3  s s 4  7  o e  5 2  a s 2  i -  e,  4  S 3  1  4  2  i  O  1  o  eo  s  so  7  7  a  7  O  2  _.e  2 a  §°  S 4  DBH  CLASS  AOC—30  LEGEND A  = SPACING:  1.2X1.2 M  <C = S P A C I N G :  1 .5X1 .5 M  = SPACING:  1 .8X1 .8 M  SO  O  ^  4  o a  O  = SPACING:  2.1X2.1  O  3  3  2  V  = SPACING:  2.4X2.4 M  -  = SPACING: 3.0X3.0 M  *  = SPACING:  4.3X4.3 M  o  = SPACING:  6.0X6.0 M  m*  2  SS  1  S 4  1  1 O DBH  CLASS  158  M  FIGURE  5.5:  MEAN R E L A T I V E CROWN M E A S U R E S ON CROWN D I M E N S I O N S  BASED  FIGURE 5.5.2: MEAN CROWN SURFACE/CROWN VOLUME RATIOS FOR ALL SPACINGS OVER AGE  FIGURE 5.5.1: MEAN CROWN WIDTH/CROWN LENGTH RATIOS FOR ALL SPACINGS OVER AGE  LEGEND i - SPACING: 1.2X1.2 M 0 - SPACING: 1.5X1.5 M « = SPACING: 1.8X1.8 M 0 = SPACING: 2.1X2.1 M V = SPACING: 2.4X2.4 M • = SPACING: 3.0X3.0 M * = SPACING: 4.3X4.3 M o = SPACING: 6.0X6.0 M  o . * o o  13  15  17  19  21  23  25  27  29  31  33  1 •  * 2  15  17  19  21  23  LEGEND 4 = SPACING: 1.2X1.2 M 0 - SPACING: 1.5X1.5 M 0 = SPACING: 1.8X1.8 M 0 = SPACING: 2.1X2.1 M V = SPACING: 2.4X2.4 M • = SPACING: 3.0X3.0 M * = SPACING: 4.3X4.3 M o = SPACING: 6.0X6.0 M  LEGEND A = SPACING: 1.2X1.2 M » = SPACING: 1.5X1.5 M « = SPACING: 1.8X1.8 M 0 - SPACING: 2.1X2.1 M 7 = SPACING: 2.4X2.4 M . = SPACING: 3.0X3.0 M ft = SPACING: 4.3X4.3 M o = SPACING: 6.0X6.0 M  n  \  (/) 0 (/)  27  29  31  FIGURE 5.5.4: MEAN FOLIAGE BIOMASS/BRANCHES BIOMASS RATIOS FOR ALL SPACINGS OVER AGE  _l O > z°  o o  25  AGE  AGE FIGURE 5.5.3: AVERAGE FOLIAGE BIOMASS/CROWN VOLUME RATIOS FOR ALL SPACINGS OVER AGE  *  13  39  < 0.49 2  o CO  o < 0. 17  AGE  AGE  159  33  Table  5.10: T w o - l e v e l n e s t e d anova l e n g t h (m/m) r a t i o .  tests  f o r crown w i d t h / c r o w n Factor  DBH Age 13 14 15 15 16 16 18 24 30  Spacings  F  D.F.  54/395 67/379 32/160 41/200 66/331 24/9 3 95/409 108/373 118/349  1 .87* 1 . 37n.s. 4 .07* 2 .41* 1 .98* 7 .73* 3 .19* 2 .25* 2 .43*  6/44 6/43 2/28 3/31 5/46 1/23 7/78 7/78 7/85  *: s i g n i f i c a n t d i f f e r e n c e s a t t h e l e v e l n.s.: no s i g n i f i c a n t d i f f e r e n c e .  Comparison  Tukey's 1.2  1.5  of probability  o f mean crown w i d t h / c r o w n the s p a c i n g s  Age 1.8  Spacing  D.F.  included(m)  1.2 t o 4.3 1.2 t o 4.3 1. 2 ; 1. 8 ; 2 . 4 3.0 1. 2 ; 1. 5 ; 2 .1 2 ;. 4 ; 3 . 0 ; 6 . 0 1. 8 ; 4 . 3 All All All  class  multiple Spacing 2.1  range (m) 2.4  length  F 25 .96* 39 .11* 28 .96* 29 .61* 59 .86* 33 .97* 30 .53* 10 .02* 25 .88* o f 0.05.  ratios  among  test 3.0  4.3  6.0  13  0.54a*  0.57ab  0 . 62ab  0.62ab  0.68ab  0.72ab  0.78b  -  14  0.49a  0.48a  0 .54ab  0.56bc  0.63c  0.67c  0.71c  -  15  0.44a  15  0.69  0 .49a 0.44a  0.47a  0.54  0.60  0.43a  0.51bc  0.58cd  0.64d  16  0.44ab  0.43a  18  0.44a  0.46a  0 .47ab  0.46a  0.45a  0.52b  0.62c  0 .62c  24  0.48a  0.48a  0 .48a  0.50a  0.52a  0.53ab  0.56bc  0.59c  30  0.41a  0.45ab  0 .53c  0.50bc  0.55cd  0.59de  0.63ef  0.65f  *:  t h e s p a c i n g s f o r a g i v e n age f o l l o w e d by the same' l e t t e r do n o t d i f f e r s i g n i f i c a n t l y a t t h e l e v e l o f p r o b a l i l i t y o f 0.05.  160  The  crown f u l l n e s s  age 2 3 , the  ratio  and i n c r e a s e d  f o r the 6.0  thereafter.  age w h e r e c r o w n f u l l n e s s  ratio  m spacing  For the four c l o s e s t stopped decreasing  time corresponded t o the onset of competition. not  true f o r the four l a r g e s t The c r o w n f u l l n e s s  changes i n crown w i d t h 1.2  the  m spacing,  age 1 8 .  18  t o 22,  and l e n g t h  H o w e v e r , t h i s was  sensitive to slight  (Figures 5.2.1  and 5 . 2 . 2 ) .  and l e n g t h b o t h i n c r e a s e d  t h e crown f u l l n e s s  ratio  r e m a i n e d more o r l e s s c o n s t a n t  increased.  Thus, t h e crown f u l l n e s s  increased.  i n the 1.5  also occurred different  m, 1 . 8  ratio  dimensions.  and crown  increased.  width  m spacings,  intensity  but at  o f changes i n crown  The same f l u c t u a t i o n s c a n a l s o be o b s e r v e d  f o r the  spacings.  e x c e p t f o r 14  (Table  5.10).  This  spacings, (Figure  i t d e c r e a s e d w i t h an i n c r e a s e  5.6).  From age 14  between crown f u l l n e s s size  occurred.  t o age 3 0 ,  ratio  to increasing.  f o r a given  sizes.  161  a t age 13  t h e p a t t e r n o f change from d e c r e a s i n g  The l a r g e r t h e s p a c i n g ,  spacing  full-  For a l l  i n tree size  a n d DBH s h i f t e d  The age when c r o w n f u l l n e s s  tree size  a t a l l ages,  i n d i c a t e s t h a t t h e crown  n e s s r a t i o v a r i e d among t r e e s o f d i f f e r e n t  with  Finally,  The same p a t t e r n  The n e s t i n g f a c t o r (DBH c l a s s ) was s i g n i f i c a n t  tree  length  r a t i o decreased.  m, a n d 2 . 1  ages and w i t h d e c r e a s i n g  From a g e s  increased.  crown l e n g t h d e c r e a s e d and crown  So, crown f u l l n e s s  up t o  From a g e s 22 t o 3 0 ,  increased.  crown w i d t h  f r o m a g e s 30 t o 3 3 ,  For  faster  r a t i o decreased.  crown l e n g t h d e c r e a s e d , b u t crown w i d t h  Thus, t h e crown f u l l n e s s  other  the f i r s t  B e c a u s e c r o w n l e n g t h was l a r g e r a n d i n c r e a s e d  t h a n crown w i d t h ,  spacings,  spacings.  r a t i o was v e r y  crown w i d t h  d e c r e a s e d up t o  the l a t e r  ratio d i d not vary  with this  much  corresponded w e l l with the  F I G U R E 5 . 6 : CROWN DBH C L A S S FOR  WIDTH/CROWN L E N G T H R A T I O S A L L S P A C I N G S AND D I F F E R E N T  PER 1 CM AGES  DBH C L A S S o . a  3 0  7 8 8  \  7 o e  a** ^  AOE—ia  ^  \ * A  o . 9 8 2  IiI::  S 2  O  4sa 3 9 8 3 3 4 2 7 2 2 1  O  DBH CLASS  * I  DBH CLASS  i> \  A  DBH CLASS  162  LEGEND A  =  SPACING:  1.2X1.2  O  =  SPACING:  1 .5X1 .5 M  =  SPACING:  1.8X1.8  M  O  =  SPACING:  2.1X2.1  M  V  =  SPACING:  2.4X2.4 M  -  =  SPACING:  3.0X3.0 M  •  == S P A C I N G :  4.3X4.3 M  o  =  6.0X6.0 M  SPACING:  M  onset  of  1.2  the 16  competition, m and 1 . 5  for  2.1  the  plus  o r minus  30,  spacings).  A t age  relatively  constant  (i.e.,  age  14  for age  age  15  for  the  1.8  m spacing,  and age  18  for  the  2.4  m and 3 . 0 m  m spacings,  m spacing,  two y e a r s  4.3  the  m and 6 . 0 m s p a c i n g s  r e l a t i o n with  tree  size  showed  in spite  of  a  fluctua-  tions . B o t h the biomass  to  5.5.3). every  age.  also  15  largest  so  became at  contained  measures for  each  that  spacings. of  as  spacing  (Figure  age.  of  in  per u n i t As t h e s e  volume their  of  5.5.1),  occupation  were  an i n v e r s e  n a r r o w crowns  two  occupy  became  that  did  not  factor  with  was  tree  volumes  increased  areas,  and the  less  For t r e e s  ratios  size  the  i n the  larger.  crown,  found i n  growing  trees  the as  the  foliage  became  When mean v a l u e s crown f u l l n e s s found.  space w i t h  they  same DBH  p r o d u c t i v i t y of  by t h e  faster  foliage  may be c o n s i d e r e d  r e l a t i o n s h i p was  163  two  gradually  their  compared w i t h  their  and the  differences  crown volume was  estimating  crowns  and age  of  appeared  5.8).  and  size,  virtually  in a  closest  decreased  and  crown volume  The DBH n e s t i n g  crown v o l u m e .  efficiency  30,  age  Both r a t i o s 5.7  to  at  differences  c o n t a i n i n g means  corresponding surface  a given  efficient  between the  and s m a l l e r .  increased  per u n i t  crown s u r f a c e  foliage  5.5.2  (Figures  and Reukema ( 1 9 7 0 )  to  groups  (Figures  more f o l i a g e  closest  16  and  increased  Significant  and 5 . 1 2 )  the  every  spacing  their  class,  that  crown volume  spacing  the  stand.  to  same t r e n d  as  by C u r t i s  From age  smaller  As crowns than  5.11  spacings.  every  the  decreased  observed  (Tables  significant at  ratios  showed  Douglas-fir  accentuated differ  crown s u r f a c e  The same t r e n d f o r  43-year-old age  of  crown volume  These  r a t i o was  at  ratios  less for  ratio  This  suggests  greater  Table  5.11:  T w o - l e v e l n e s t e d anova t e s t s volume ( m / m ) r a t i o . 2  f o r crown  surface/crown  3  Factor DBH c l a s s Spacings included(m)  Age 13 14 15 16 18 24 30  1.2 1.2 1.2 All All All All  to to to  D.F.  4.3 4.3 4.3  F  54/395 67/379 73/360 90/424 95/409 108/373 118/349  * : s i g n i f i c a n t d i f f e r e n c e s a t the n . s . : no s i g n i f i c a n t d i f f e r e n c e .  Spacing  level  D.F. 6/54 6/66 6/72 7/88 7/93 7/108 7/118  97.96* 69.79* 84.91* 65.87* 66.06* 22.61* 10.27* of  probability  C o m p a r i s o n o f mean crown s u r f a c e / c r o w n among t h e s p a c i n g s Tukey's multiple Spacing  Age  range (m)  F 1. 2. 2. 6. 8. 69. 163.  32n.s. 31n.s. 55* 37* 49* 52* 59  of  0.05.  volume r a t i o s  test  1.2  1.5  1.8  2.1  2.4  15  4.77a*  3.27ab  3 .25ab  2.82ab  2.57ab  2.40b  2 . 44b  16  3.43a  3.05ab  3 . 02ab  2.75ab  2.32abc  2.12bc  2 .17bc  1.83c  18  2.97a  2.61a  2 .38ab  2.38ab  2.10ab  1.83bc  1 .81bc  1.55c  24  2.81a  2.54ab  2 .45ab  2.08bc  1.74cd  1.41d  1 .15e  1.02e  30  3.06a  2 .82a  2 .48ab  2.08bc  1.75c  1.38  1 .06  0.78  3.0  4.3  6.0  -  *: t h e s p a c i n g s f o r a g i v e n age f o l l o w e d by t h e same l e t t e r do n o t differ  s i g n i f i c a n t l y at  the  164  level  of p r o b a b i l i t y  of  0.05.  Table  5.12:  T w o - l e v e l n e s t e d anova t e s t s f o r f o l i a g e crown volume ( k g /m ) r a t i o .  biomass/  3  Factor DBH Age  13 14 15 16 18 24 30  Spacings  included(m)  class  D.F.  1.2 to 4. 3 1.2 to 4. 3 1.2 to 4. 3  54/394 67/379 73/359 90/424 95/409 108/349 118/349  All All All All  Spacing  F  D.F.  F  6/54 1.43n.s. 6/66 2.33n.s. 6/72 2.74* 7/28 6.80* 7/93 8.85* 7/108 48.59* 7/118 158.79*  41.89* 31.58* 41.16* 28.36* 28.59* 14.81* 8.55*  *: s i g n i f i c a n t differences at the l e v e l of p r o b a b i l i t y of 0.05. n . s . : no s i g n i f i c a n t difference.  Comparison of mean foliage biomass/crown volume ratios among the spacings Tukey's m u l t i p l e Spacing  Age  range (m)  1.2  1.5  1.8  2.1  2.4  15  1.17a*  0.77ab  0 .72ab  0.66ab  16  0 .80a  0.72a  0 .71a  18  0.70a  0.61a  24  0.67a  30  0.72a  test  3.0  4.3  6.0  0.60ab  0.55b  0 . 56b  0 .65ab  0.54ab  0.49ab  0 . 50ab  0.42b  0 . 56ab  0.56ab  0.49ab  0.42bc  0 ,42bc  0.36c  0 .60a  0 .57a  0.49ab  0.41bc  0.32c  0 .27d  0.24d  0 .66a  0 . 58ab  0.48bc  0.41c  0.32  0 .24  0.13  -  *: the spacings for a given age followed by the same l e t t e r do not d i f f e r s i g n i f i c a n t l y at the l e v e l of p r o b a l i l i t y of 0.05.  165  FIGURE 5 . 7 : CROWN SURFACE/CROWN VOLUME RATIOS PER 1 CM DBH CLASS FOR ALL SPACINGS AND DIFFERENT AGES  O  1  2  7  9  3  1 1 1 1 1 1 3  S  7  2 1  9  2  2  2  3  S  T  2 9  DBH CLASS  DBH C L A S S  LEGEND A  O V m  • 3 O  3 2  3 4  3  e  3 8  166  O  = =  SPACING:  1 2X1  SPACING:  1 5X 1 5 M  =  SPACING:  1 8X 1 8 M  = = = =  SPACING: 2 4X2  SPACING: 2  2 M  1 X2 1 M 4 M  SPACING: 3 OX3 O M SPACING: 4 3X4  3 M  SPACING: 6 OX6 O M  FIGURE 5 . 8 : FOLIAGE BIOMASS/CROWN VOLUME RATIOS PER 1 CM DBH CLASS FOR ALL SPACINGS AND DIFFERENT AGES  O  1  2  3  4-  5  e  7  s  s  7  s  1 1  1  1 3  1 B  1 7  z 9  3 3  2  »  s 7  a 9  DBH CLASS  DBH CLASS  LEGEND  = •O = = o = A  V m  * o  e s c  DBH  CLASS  167  = =  SPACING:  1 2X 1 2 M  SPACING:  1 5X 1 5 M  SPACING:  1 8X 1 8 M  SPACING: 2  SPACING: 2 4X2  4 M  SPACING: 3 OX3 O M  == S P A C I N G : —  1 X2 1 M  4 3X4  3 M  SPACING: 6 OX6 O M  efficacy (1970),  than  large  crowns.  This  Kuuluvainen (1988),  crowns  are  their  higher  r e s p i r a t i o n needs  and of  of  strictly  thetic  branches  capacity  tration  of  Kuuluvainen crown) in  increases  have  and P e r r y  with  theory  in  the  specified  the  structure crown.  may n o t  would  of  in  with  crown volume were o b t a i n e d  Even though trend  branches found  over  there  for  the  time  was  5.9).  At these  trees,  but  proportion  at  of  ages, was  of  shade  of  of  5.5.4).  only at small  greatly  trees  tissue  168  if  as  rate in  the  red pine)  and l e a v e s  is  minimum. shade  foliage  the  result of  needle theory  appropriate.  This are  is  such  Such  within  the  biomass  to  (1988).  biomass  5.13). ages  to  (Table  This  per u n i t  there  was  biomass  no  of  difference  was  The DBH n e s t i n g  differed  no p a r t i c u l a r t r e n d .  photosynthetic  decreased  No s i g n i f i c a n t  certain  (within  T h i s would  fluctuations,  (Table  to  and r e d u c t i o n  little  foliage  any age  the  According  (such  by K u u l u v a i n e n  ratio  significant  there  pene-  branches  ratio  were a l o t  (Figure  among s p a c i n g s  factor  the  distribution is  the  proportion  c a u s e may be  contribute  relatively  stems,  photosyn-  o v e r l a p between l e a v e s  result  accumu-  the  shade,  of  of  reduces  crown.  trees  great  a large  internal  the  under  intolerant  Similar results  evident  of  The o r g a n i z a t i o n  degree  Also,  with  because  branches,  branch m o r t a l i t y ,  on l e a f  that  (i.e.,  crowns.  (1985),  trees  from the  which  A second  size  leaves  this  1975)  multilayered. that  the  However, (1971,  Horn  leaves,  1985).  proportionally increased  density.  1985).  Perry  radiation within  (1988)  photosynthesis  of  do n o t  (Ford  solar  resulting  by Assmann  Big trees  than s m a l l e r  supporting material  (Assmann 1 9 7 0 ;  roots) these  efficacious  noted  (1985).  and P e r r y  large  lation  less  t r e n d was  of  5.13;  from the suggests  Figure larger that  respiratory  the  Table 5.13: Two-level nested anova tests for biomass of foliage/biomass of branches (kg/kg) r a t i o . Factor DBH class Age 13 13 14 15 16 16 18 18 24 30  Spacings included(m)  D.F.  1. 5 ; 1. 8 ; 2 .1; 2 . 4 ; 4 . 3 38/270 1. 2 ; 3 . 0 16/124 1. 5 ; 2 .1; 2 . 4 ; 3 . 0 ; 4 . 3 48/255 1. 5 ; 2 .1; 2 . 4 ; 3 . 0 ; 4 . 3 52/249 1. 5 ; 1. 8 ; 2 .1; 3 . 0 ; 4 . 3 59/241 2, 4 ; 6 . 0 22/130 1. 8 ; 2 .1; 2 . 4 ; 3 . 0 ; 4 . 3 ; 6 . 0 74/309 1. 2 ; 1. 5 21/100 1. 5 ; 1. 8 ; 2 .1 42/127 1. 2 ; 1. 5 ; 1. 8 43/108  F  1 . 22n. s. 0 • 81n.s. 1 . 06n. s. 4 .11* 2 .52* 1 .86* 1 .77* 1 .69* 0 .77n. s. 1 . 27n. s.  Spacing D.F.  4/30 1/7 4/28 4/45 4/47 1/15 5/50 1/15 2/16 2/24  F  1 . 21n. s. 0 . 12n. s. 0 . 57n. s. 0 .30n. s. 1 . Oln. s. 0 .39n. s. 1 . 22n. s. 2 .09n. s. 1 .73n. s. 0 . 02n. s.  *: s i g n i f i c a n t differences at the l e v e l of p r o b a b i l i t y of 0.05. n . s . : no s i g n i f i c a n t difference.  169  FOLIAGE BIOM./BRANCHES BIOU. (KG/KG) 0  0  0  M  M  M  0 v  0 t  M  0  0  0  M  H  H  0  0  M  ^  M  FOLIAGE BI0U./BRANCHES BIOM. (KG/KG) 0  0  0  0  0  0  0  0  0  0  0  0  FOLIAGE SOIL/BRANCHES BIOM. (KG/KG) o o o o o o o o o o -  I  FOLIAGE BIOM./BRANCHES BIOM. (KG/KG) o o o o o o o o o o o «  o n o u o o o o o w o  W  o cr  o 0  o  co  CD ' '  CO CO CO  o  o FOLIAGE BIOM./BRANCHES BIOM. (KG/KG) o o o o o o o o o o o  FOLIAGE BIOM./BRANCHES BIOM. (KG/KG) o o o o o o o o o o o  FOLIAGE BIOM./BRANCHES BIOM. (KG/KG) o o o o o o o o o o o  o O  0  *  '  0 fl> «  <3  o  >  CO OO  II II II II II II H II  oo  U)U)U)U)U)U)U)U)  " O D D D D D D T )  >>>>>>>>r o o o o o o o o m z z z z z z z z £ o o o o o o o o C J  CD TO O  0>4>C N)N)- - -' ' J  O  0(  i  b V ^  Co  i  C  In  x x x x x x x x  N  OO  ( J i ^ O i W M - ' - ' - ' b b i b ^ £  £  £  £  -'bouifo £  £  £  £  rn oo  O oo  tissue  was n o t a f f e c t e d  tended  t o remain c o n s t a n t  the  by c o m p e t i t i o n . over  time,  ratio  generally  o f crown w i d t h  increased  with  spacing  and l a r g e s t  spacings  ficant size  at every  ratio  generally  5.14).  always  the  factor  decreased  agrees with  age,  but  Significant  Only  The DBH n e s t i n g  pattern  o f crown w i d t h  increased  differences  the f a s t e r  6.0 m s p a c i n g  smallest was s i g n i -  with  tree  the observations of  the r a t i o  (Table  5.12).  between t h e r a t i o  constant,  and i n c r e a s e .  vary with  tree  well  the onset  with  size  No s i g n i f i c a n t crown l e n g t h Table  only  decreased  at every  with  tree  size:  However,  size  decrease,  Most o f t h e at  either  remain  t h e age when t h e r a t i o d i d n o t  for a p a r t i c u l a r spacing  d i d not correspond  of competition. differences  However,  t h e 6.0 m s p a c i n g  significant  5.15).  factor  15 t o 30, t h e r e was a g r a d u a l  and t r e e  t o DBH r a t i o ,  5.16).  f o r the  The DBH n e s t i n g  tree  but  The n a r r o w e r  The r a t i o  13 a n d 14 ( T a b l e  From a g e s  age,  Significant  5.15).  decreased.  constant.  with  5.10.2).  (Figure  a t a l l ages  a t ages  decreased  d i d n o t show much v a r i a t i o n w i t h  (Figure  5.10.3;  to height  spacing  was r e l a t i v e l y  not s i g n i f i c a n t  spacings  with  were o b t a i n e d  spacing,  shift  This  with  (1969). The  ages  differed.  a g e , and t h e r a t i o  5.11).  (Figure  Smith  that  proportion  of the s i z e of  5.10.1).  (Figure  a p p e a r e d a t age 15 ( T a b l e  the  independent  t o DBH d e c r e a s e d  differences  was  this  trees.' The  the  Also;  age. size  were o b t a i n e d except  a t ages  the m u l t i p l e  differed.  171  5^13).  16 a n d 18 ( F i g u r e  range  test  The DBH n e s t i n g  The crown l e n g t h  (Figure  among s p a c i n g s f o r  showed f a c t o r was  t o DBH r a t i o  always  FIGURE 5 . 1 0 : RELATIVE CROWN WIDTH AND LENGTH MEASURES BASED ON TREE SIZE FIGURE 5.10.2: MEAN CROWN WIDTH/HEIGHT RATIOS FOR ALL SPACINGS OVER AGE  FIGURE 5.10.1: MEAN CROWN WIDTH/DBH RATIOS FOR ALL SPACINGS OVER AGE 0.  0 . 5 5 4  LEGEND A = SPACING: 1.2X1.2 M 0 = SPACING: 1.5X1.5 M $ = SPACING: 1.8X1.8 M 0 = SPACING: 2.1X2.1 M 7 = SPACING: 2.4X2.4 M SPACING: 3.0X3.0 M SPACING: 4.3X4.3 M SPACING: 6.0X6.0 M  LEGEND 6 = SPACING: 1.2X1.2 M SPACING: 1.5X1.5 M $ = SPACING: 1.8X1.8 M 0 = SPACING: 2.1X2.1 M 7 = SPACING: 2.4X2.4 M • = SPACING: 3.0X3.0 M * = SPACING: 4.3X4.3 M o = SPACING: 6.0X6.0 M  750  0.688  ^0.626 2 \ 2  0.564  <V \ V  O  0.502  • I  \ 0 . 4 4 0  I rQ  ^ V  "  0.378  z $  *> >--*  0.316  O O  1^  0.254  0.  192  0.  130 13  15  17  19  21  0.970  LEGEND A = SPACING: 1.2X1.2 M 0 = SPACING: 1.5X1.5 M 0 = SPACING: 1.8X1.8 M 0 = SPACING: 2.1X2.1 M 7 = SPACING: 2.4X2.4 M . = SPACING: 3.0X3.0 M * = SPACING: 4.3X4.3 M o = SPACING: 6.0X6.0 M  0.902  2  (j  0.494  0.426  0.358  0.290  270 13  15  17  19  23  27  29  31  33  FIGURE 5.10.4: MEAN CROWN LENGTH/HEIGHT RATIOS FOR ALL SPACINGS OVER AGE  O  0.  25  AGE  AGE FIGURE 5.10.3: MEAN CROWN LENGTH/DBH RATIOS FOR ALL SPACINGS OVER AGE 0.810  23  25  27  29  31  33  S T  LEGEND A = SPACING: 1.2X1.2 M\ « = SPACING: 1.5X1.5 Mi « = SPACING: 1.8X1.8 M 0 = SPACING: 2.1X2.1 M 7 = SPACING: 2.4X2.4 M • = SPACING: 3.0X3.0 M * = SPACING: 4.3X4.3 M o = SPACING: 6.0X6.0 M —,—I—i—i—i—T—•—I—1—I—•—i—1—I—'—i—1—i—'—r 13  15  17  19  21  23  AGE  AGE 172  25  27  29  31  33  Table  5.14:  Two-level nested (m/cm) r a t i o .  anova  tests  f o r crown  width/DBH  Factor DBH c l a s s Spacings  Age 13 14 15 16 18 24 24 30  1.2 1.2 1.2 All All  D.F.  4.3 4.3 4.3  to to to  1. 5 ; 1. All  included(m)  8  * : s i g n i f i c a n t d i f f e r e n c e s at the n . s . : no s i g n i f i c a n t difference.  Comparison of  1.2  1.5  D.F.  34 . 6 0 * 15 . 1 9 * 8 . 31* 6 .24* 6 .59* 2 .94* 2 .64* 2 .03*  level  of  6/51 6/62 6/67 7/80 7/86 . 3/4 3 3/40 7/118  range (m)  F 0 .6 2 n . s . 1 .34n.s. 3 .12* 4 .73* 2 .27* 11 . 8 4 * 10 .24* 40 .02*  p r o b a b i l i t y of  mean crown width/DBH r a t i o s Tukey's m u l t i p l e Spacing  Age  F  52/349 64/349 72/350 88/423 95/409 55/164 53/209 118/349  4.3 ; 3 . 0 ; 6.0  Spacing  among the  0.05.  spacings  test  1.8  2.1  2.4  3.0  4.3  6.0  -  15  0 .30a*  0 .29a  0 .30ab  0 .31ab  0 • 34ab  0 . 35ab  0 .41b  16  0 .27a  0 .27a  0 .25a  0 • 26a  0 . 30ab  0 . 31ab  0 .36b  0 .30ab  18  0 .26a  0 . 26ab  0 . 26ab  0 . 25a  0 . 26ab  0 . 27ab  0 .31b  0 . 26ab  24  0 .20a  0 .20a  0 .22a  24  -  -  -  30 *:  0 .16a  -  -  0 .20a  0 .19a  0 .17a  0 .17ab  0 .18ab  0 .18b  0 .21b 0 .19b  0 .24  0 .21c  0 .22b 0 .22c  t h e s p a c i n g s f o r a g i v e n age f o l l o w e d by t h e same l e t t e r do d i f f e r s i g n i f i c a n t l y at the l e v e l of p r o b a l i l i t y of 0 . 0 5 .  173  not  FIGURE 5 . 1 1 : CROWN WIDTH/DBH RATIOS PER 1 CM DBH CLASS FOR ALL SPACINGS AND DIFFERENT AGES  LEGEND  DBH CLASS  174  SPACING:  1. 2 X 1 . 2  M  SPACING:  1 .5 X 1 . 5 M  SPACING:  1 .8 X 1 . 8 M  SPACING:  2. 1 X 2 . 1  M  SPACING:  2. 4 X 2 . 4  M  SPACING:  3. 0 X 3 . 0  M  SPACING:  4, 3 X 4 . 3  M  SPACING:  6, 0 X 6 . 0  M  Table  5.15:  Two-level nested (m/m) r a t i o .  anova t e s t s  f o r crown  width/height  Factor DBH c l a s s Spacings  Age 13 14 14 15 16 18 24 30  included(m)  D.F.  F  54/395 39/207 28/172 73/360 90/124 95/409 108/373 118/349  1.2 t o 4.3 1. 5 ; 1. 8 ; 2 .1 2.4 ; 1. 2 ; 3 . 0 ; 4 . 3 1.2 t o 4.3 All All All All  Tukey's  Multiple Spacing  13  0.50a*  1.5  1.8  2.1  2.4  0.54ab  0 . 59bc  0 .60c  0.65cd  0 . 50a  0.53a  0.60  14  -  0.45  14  0.43  -  15  0.36a  0.38ab  0 .43bc  0.45cd  16  0.34a  0.36ab  0 . 39ab  18  0.32a  0.35ab  24  0.21a  30  0.15a  -  -  ratios  42.28* 39.27* 136.56* 46.88* 69.59* 109.24* 306.86* 230.77* o f 0.05.  among t h e  test 3.0 0.68de  -  4.3 0.74e  -  6.0  -  0 .63a  0.67a  -  0.51de  0.57e  0.65  -  0.41b  0.49c  0.55cd  0.65  0.61d  0 . 37bc  0.38c  0.43  0.50  0.60d  0.60d  0 .22a  0 .24ab  0.27bc  0.32c  0.38  0.53  0.58  0.15a  0 .18ab  0.20bc  0.24c  0.29  0.42  0.55  -  *: t h e s p a c i n g s f o r a g i v e n age differ  range (m)  F  6/41 3/2 5 2/16 6/62 7/74 7/7 5 7/108 7/118  of probability  o f mean crown w i d t h / h e i g h t the s p a c i n g s  Age 1.2  D.F.  1 .52n.s. 1 .39n.s. 0 .97n.s. 3 .72* 3 .20* 2 .78* 3 .16* 3 .60*  *: s i g n i f i c a n t d i f f e r e n c e s a t t h e l e v e l n . s . : no s i g n i f i c a n t d i f f e r e n c e .  Comparison  Spacing  significantly  f o l l o w e d by t h e same' l e t t e r do n o t a t t h e l e v e l o f p r o b a l i l i t y o f 0.05.  175  FIGURE 5 . 1 2 : CROWN WIDTH/HEIGHT RATIOS PER 1 CM DBH CLASS FOR ALL SPACINGS AND DIFFERENT AGES BIO  a i 2  / \ / \  7 8 4 7 1 8 e e a  u3  s1° s ° o  a  ao  S72 5 2 +  • 7 8 * 2 a  380  o  7SO  o  898  o ,  \  / *  a * a s o *  a.  S * 2 t o o 4 3 9  s e e  33* 2 a 2 2 3O  1  2  3  DBH C L A S S .  770  1  DBH C L A S S e a o  AOE-18  .71* e s s  . a o 2 . s * a  .  \ ,A A  0 7 o  V \ /'  s  8° s  *oo  1 s  * a o  V  * o s  3SO 295  378  2*0  322 ,  ^  a 2 s  , *3* ,  ACE-2*  1 a s  288  1 30  . 2 1 O  DBH CLASS  LEGEND  DBH C L A S S  176  A  =  SPACING:  1.2X1.2  M  «•  =  SPACING:  1 .5X1 .5 M  O  =  SPACING:  1.8X1.8  M  O  =  SPACING:  2.1X2.1  M  V  =  SPACING:  2.4X2.4  M  -  =  SPACING:  3.0X3.0  M  •  =  SPACING:  4.3X4.3  M  o  =  SPACING:  6.0X6.0  M  Table  5.16: T w o - l e v e l n e s t e d a n o v a t e s t s (m/cm) r a t i o .  f o r crown  length/DBH  Factor  DBH class Age 13 14 15 16 18 24 24 30 30  Spacings  included(m)  1.2 to 4.3 1.2 to 4.3 1.2 to 4.3 All All 1. 2 ; 1. 5 ; 2 .1; 2 . 4 1. 8 ; 3 . 0 ; 4 . 3 1. 2 ; 1. 5 ; 1. 8 ; 2 .1 2 .4 ;3 .0 ;4 . 3  Spacing  D.F.  F  52/349 64/349 72/350 88/423 95/409 54/166 43/125 59/147 48/120  72 . 56* 86 .86* 49 .42* 22 .61* 21 .92* 7 .20* 14 . 34* 4 .50* 12 .62*  F  D.F.  6/52 6/64 6/71 7/86 7/92 3/49 2/42 3/52 2/4 5  0. 22n. s. 0. 59n. s. 0. 49n. s. 5. 36* 9. 41* 0. 33n. s. 0. 40n. s. 2. 57n. s. 0. 75n. s.  *: s i g n i f i c a n t differences at the l e v e l of p r o b a b i l i t y of 0.05. n . s . : no s i g n i f i c a n t difference.  C o m p a r i s o n o f mean crown l e n g t h / D B H the s p a c i n g s T u k e y ' s m u l t i p l e range S p a c i n g (m)  Age  1.2  ratios  among  test  1.5  1.8  2.1  2.4  16  0.61a* 0.64a  0.63a  0.63a  0.59a  0.54ab 0.53ab 0.47b  18  0.58a  0.57a  0.56a  0.58a  0.53a  0.57a  3.0  4.3  0.50a  6.0  0.43  *: the spacings for a given age followed by the same l e t t e r do not d i f f e r s i g n i f i c a n t l y at the l e v e l of p r o b a l i l i t y of 0.05.  177  FIGURE 5 . 1 3 : CROWN LENGTH/DBH RATIOS PER 1 CM DBH CLASS FOR ALL SPACINGS AND DIFFERENT.AGES  LEGEND SPACING:  1.2X1.2 M  SPACING:  1 .5X1 .5 M  SPACING:  1 , 8 X 1 .8 M  S P A C I N G : 2. 1 X 2 . 1 M SPACING: 2.4X2.4 M SPACING: 3.0X3.0  M  SPACING: 4.3X4.3 M SPACING: 6.0X6.0 DBH C L A S S  178  M  Crown r a t i o d e c r e a s e d  (Figure 5.10.4).  was e n l a r g e d it  over  decreased.  The c l o s e r  the spacing, the faster  S i g n i f i c a n t d i f f e r e n c e s among s p a c i n g s  o b t a i n e d a t a l l a g e s , b u t 18 only the 1.2  time, b u t i n c r e a s e d as spacing  (Table 5 . 1 7 ) .  were  A t a g e s 13 a n d 1 4 ,  m s p a c i n g was s i g n i f i c a n t l y d i f f e r e n t .  However,  t h e s e d i f f e r e n c e s w e r e s o s m a l l t h a t t h e y do n o t s u g g e s t t h e A t age 1 5 ,  e f f e c t o f heavy c o m p e t i t i v e s t r e s s . spacings d i f f e r e d was d i f f e r e n t t h e 3 . 0 m.  from  from  t h e l a r g e s t ones, and t h e 1.8  the 2.1  A t age 1 6 ,  c r o w n r a t i o on t h e f i v e The 2 . 1  s h o w i n g much l o w e r v a l u e s a t a g e s 17  t h a t c r o w n r a t i o s on t h e s e  t h a n on t h e w i d e r  spacings.  s h o w i n g a much l o w e r  crown r a t i o  s p a c i n g s a t age 2 1 .  A t age 2 4 ,  from  the 4.3 m spacing.  largest  spacings  m and 2 . 4 m s p a c i n g s  a n d 19 r e s p e c t i v e l y .  t h o u g h a n a n o v a was n o t c o m p u t e d f o r t h e s e  lower  m spacing  m, 2 . 4 m, a n d 4 . 3 m s p a c i n g s , b u t n o t  did not s i g n i f i c a n t l y d i f f e r .  probable  t h e two c l o s e s t  Even  two a g e s , i t i s  s p a c i n g s were  significantly  The 3 . 0 m s p a c i n g than  began  started  t h e 4 . 3 m and 6 . 0 m  i t was s i g n i f i c a n t l y  For the s i xnarrowest  different  spacings,  there  was a g o o d c o r r e s p o n d a n c e  b e t w e e n t h e age when t h e y became d i f f e -  r e n t from  s p a c i n g s and t h e i r  t h e two l a r g e s t  competition The  (as determined  i n chapter  r e s p e c t i v e onsets of  4).  DBH n e s t i n g f a c t o r was s i g n i f i c a n t a t a l l a g e s ,  a t age 3 0 .  Most o f these  s p a c i n g s d i d n o t v a r y much w i t h t r e e  s i z e a t t h i s age ( F i g u r e 5 . 1 4 ) . with tree size  The r e l a t i o n s h i p o f c r o w n  changed w i t h age.  remained  constant with tree size or increased a l i t t l e .  the  the f i r s t  three spacings  ratio  When c o m p e t i t i o n was  n o n - e x i s t a n t o r n o t v e r y s e v e r e , crown r a t i o  that  except  relatively  Despite the fact  seemed t o f l u c t u a t e c o n s i d e r a b l y ,  r a n g e o f v a r i a t i o n was r e l a t i v e l y 179  l o w a n d the,re was no  Table  5.17:  Two-level  n e s t e d anova  tests  f o r crown  ratio  (m/m).  Factor DBH c l a s s Spacings  Age 13 14 15 16 18 24 30 30  included(m)  1.2 t o 4 . 3 1.2 t o 4 . 3 1.2 t o 4 . 3 All 2. 4;3. 0;4 . 3; 6.0 1. 5 ; 1. 8 ; 2 . 1 ; 2 . 4 ; 3 . 0 ; 4 . 3 1. 8 ; 2 . 1 ; 2 . 4 ; 3 . 0 ; 6 . 0 1. 2 ; 1. 5 ; 4 . 3  D.F. 2. 2. 1. 1. 3. 2. 1. 2.  level  C o m p a r i s o n o f mean crown  D.F.  F  54/395 67/379 73/360 90/424 50/216 108/373 75/239 43/110  * : s i g n i f i c a n t d i f f e r e n c e s at the n . s . : no s i g n i f i c a n t d i f f e r e n c e .  Spacing  ratios  1.2  1.5  1.8  6/55  6/34 7/65 3/40 5/79 4/39 2/32  probability  among t h e  Tukey's m u l t i p l e range S p a c i n g (m)  Age  4.64* 6.59* 36.06* 62.78* 2.12n. 675.86* 1361.58* 231.27*  6/44  00* 90* 96* 99* 05* 37* 38n.s. 42* of  F  of  0.05.  spacings  test  2.1  2.4  3.0  4.3  6.0  13  0.91a  0.94ab  0 .95b  0.96b  0.96b  0.95b  0.95b  -  14  0.89  0.94a  0 .94a  0 .95a  0.95a  0.95a  0.95a  -  15  0.81  0.88  0 .91a  0.95b  0.95b  0.94ab  0.95b  -  16  0.78a  0 .85a  0 .91  0.95b  0.96b  0.95b  0.95b  0.46a  0 . 50ab  0 . 53b  0.61  0.73  0.94  0 .34  0.40a  0.43a  0.49  24  -  30  -  33  0.36a  0.34a  -  -  * : the  -  -  -  0.96b  0.85  0.67  s p a c i n g s f o r a g i v e n age f o l l o w e d by the same l e t t e r do d i f f e r s i g n i f i c a n t l y at the l e v e l of p r o b a l i l i t y of 0 . 0 5 .  180  not  FIGURE 5 . 1 4 : CROWN RATIOS PER 1 CM DBH CLASS FOR ALL SPACINGS AND DIFFERENT AGES  o  O  97  o  94  o  9 1  o  88  o  8S  o  8 2  z *  o  7 9  g  o  7 8  o  7 3  o  7 O  o  e 7  o o o  o  9 9  9 s e  o  9 2  9 1 2  o  88  sea  78  780 7 38  8 4 8 « O  o  84  I  o  S 7  o  SO  §  0 9 2  4  s e o 5  8  7  8  9  1 1 0 1  1 2  1 3  1 4  1 5  1 B  1 7  1 B  7 1  RATIO  a. o  8 2 4  o  4 3  o  38  o  29 7  1 B  9  1 1  1 3  1  S  1  1 7  2 1  9  2 3  2 5  2 7  2 9  DBH CLASS  DBH C L A S S  L E G E N D A o>  o V  -  o  DBH C L A S S  181  = = = = = = = =  S P A C I N G :  1  2X1  2  M  S P A C I N G :  1  5X1  5  M  S P A C I N G :  1  8X  8  M  S P A C I N G :  2  1 X 2 1  M  S P A C I N G :  2  4 X 2  4  M  S P A C I N G :  3  O X 3  O  M  S P A C I N G :  4  3 X 4  3  M  S P A C I N G :  6  O X 6  O  M  1  noticeable two  increasing  closest  tree  size  showed  This  ratio  began  18.  age  spacings  30.  crown  at  an i n c r e a s e  largest age  spacings  or d e c r e a s i n g to  pattern  is  increases  with  tree  after  competition,  it  took.  longer 1.5  m spacings  5.14).  second  first  case, 17  initial  effect  increment  18  case,  of  with as  increase  with  size;  spacings  all  only  three  with  the  3.0  larger  m spacing  crown r a t i o  values.  competition  changed the  This  (i.e.,  trees)  size  literature  the  when  increases  at  at  (i.e.,  accentuates years  spacing, 1.2  s e e n by c o m p a r i n g t h e  close  the  tree  competition  30  age  (Figure  from 0 . 5 6  and 0 . 5 4  suggests  the  m and  same v a l u e .  v a r i e d between 0 . 4 7  stand-grown  The  c h a n g e s o c c u r r e d a few  had a p p r o x i m a t e l y  had v e r y of  tree  and the  and t h e  crown r a t i o  of  these  may be  age  DBH c l a s s e s  classes  is  This at  In the  and f i v e  of  size  size.  closest  constant  i n agreement  However,  onset  four  relatively  (Holdaway 1 9 8 6 ) ) . the  the  i n crown r a t i o w i t h  remained  tree  show a s u b s t a n t i a l 24,  A t age  trend with  0.78  to In  the  and 16 DBH  that  it  begins  to  in  intensity  the  reduce as  the  spacing  decreased. According  potential suggests the  six  well  growth that  5.10.4). of  if  this  their  (1984),  Farrar  narrowest  after  onset  to  its  crown r a t i o  limit  is  spacings age  of  a tree  too  is  low  88%  for  the  1.5  age  16,  90% f o r age  the  onset  were 81%  19,  spacing  at  (Figure  5.10.4).  2.1  at  for  of  age  15,  and 90% f o r  the  a close  182  at  red p i n e .  age  at  16,  the  examination  of  study when  (Figure the  1.8  83% f o r  m spacing  This  50% o c c u r r e d  of  m spacing  86% f o r  full  The age  competition  1.2  3.0  of  50%.  least  attained  the  m spacing  However,  capable  r e a c h e d a crown r a t i o  their  m spacing  at  for  The mean crown r a t i o v a l u e s competition  is  at  age  at  of  age  the  15,  m spacing the age  at  2.4 m 20  crown r a t i o  for  different  tree  sizes  trees with values onset the  of  Among a l l  the  onset  of  for  5.5.4-  ratio  trees  with  of  by t h e  length,  Relative  different  all  the  ratios.  age  nesting  5.19). factor  it  is  age  all to  their  very close  4 as  to  indicating  only  efficiency  are  those  at  stand  crown the  any a g e .  that  are  that  latter  rela-  spacing,  that  available  and t h o s e These  The  Except for  size  to  the  with  showed  the  related  size.  increased  ratios  their  examined:  in  DBH.  these  of  of  implied that  increased  size  with  studies  were  The f l u c t u a t i o n s  Significant  13  fluctuations  Thus,  when  the  not  are  (crown  ratios  are  dynamics.  i n the  crown m e a s u r e m e n t s ,  DBH AGR p e r u n i t  for  as  ratios  competition  for  value  the  and crown r a t i o were  and crown r a t i o ) .  (Table  (AGR(DBH)/crown l e n g t h ) (Table  is  of  there  (Figure 5 . 1 5 ) .  except  size  of  at  several  competition.  crown l e n g t h  decreased  lower  had  Growth M e a s u r e s  age  for  by  crown r a t i o ,  onset  interesting  DBH AGR t o  of  spacings  on crown d i m e n s i o n s ,  on t r e e  measures  tree  Even though  ages  based  the  i n Chapter  The o t h e r  declined  and t h e  of  width/crown most  based  of  This  considered  ratios  a tree  categories  variation  the  the  the  efficiency  affected  was  becoming a f f e c t e d  ratios  width/length  two  82% o r even  competition.  of  growth  except  most  crown w i d t h / c r o w n l e n g t h  efficiency tive  low as  85% t h a t  of  when t r e e s were  of  that  (Figure 5.14).  competition  limit  ratio  as  showed  For both  of  one  occurred at  of  the  same  were  crown w i d t h  (AGR(DBH)/crown  significantly  ratios,  the  different  tree  at  on crown at  high significance  indicated v a r i a t i o n with  183  obtained  The r a t i o b a s e d  mean  decreased  differences  5.18). was  each  ratios  size.  age  for  all width), length  every of  with  age  t h e DBH  However,  FIGURE 5 . 1 5 : RATIOS OF MEAN DBH AGR TO DIFFERENT CROWN MEASUREMENTS FIGURE 5.15.2: MEAN D8H AOR PER UNIT OF CROWN LENGTH FOR ALL SPACINGS OVER AGE  FIGURE 5.15.1: MEAN DBH AGR PER UNIT OF CROWN WIDTH FOR ALL SPACINGS OVER AGE  • . • • • • • .  LEGEND SPACING: 1.2X1.2 SPACING: 1.5X1.5 SPACING: 1.8X1.8 SPACING: 2.1X2.1 SPACING: 2.4X2.4 SPACING: 3.0X3.0 SPACING: 4.3X4.3 SPACING: 6.0X6.0  M M M M M M M M  A • t» O  13  13  19  r  IS  21  LEGEND SPACING: 1, 2X1.2 SPACING: 1. 5X1.S SPACING: 1. 8X1.8 SPACING: 2. 1X2.1 SPACING: 2, 4X2.4 SPACING: 3. 0X3.0 SPACING: 4. 3X4.3 SPACING: 6. 0X6.0  = -  23  17  10  21  23  2S  27  2  AGE FIGURE 5.15.4: MEAN DBH ACR PER UNIT OF CROWN SURFACE FOR ALL SPACINOS OVER ACE  FIGURE 5.15.3: MEAN DBH AGR PER UNIT OF CROWN PROJECTION FOR ALL SPACINGS OVER AGE  A * * © V . * o  IS  LEGEND SPACING: 1.2X1.2 M SPACING: 1.5X1.5 M SPACING: 1.8X1.8 M SPACING: 2.1X2.1 M SPACING: 2.4X2.4 M SPACING: 3.0X3.0 M SPACING: 4.3X4.3 M SPACING: 6.0X8.0 M  -  LEGEND SPACING: 1. 2X1.2 M SPACING: 1, 5X1.5 M SPACING: 1. 8X1.8 M SPACING: 2, 1X2.1 M SPACING: 2 4X2.4 M SPACING: 3 0X3.0 M SPACING: 4. 3X4.3 M SPACING: 6 0X6.0 M  -  M M M M M M M M  13  25  1S  17  1»  21  23  25  27  29  AGE  AGE  FIGURE 5.15.6: MEAN OBH AOR PER UNIT OF FOLIAGE BIOMASS FOR ALL SPACINGS OVER AGE  FIGURE 5.15.5: MEAN DBH AGR PER UNIT OF CROWN VOLUME FOR ALL SPACINGS OVER AGE LEGENO i SPACINC: 1.2X1.2 M i SPACING: 1.5X1.5 M i SPACING: 1.8X1.8 M • SPACING: 2.1X2.1 M i SPACING: 2.4X2.4 M • SPACING: 3.0X3.0 M • SPACING: 4.3X4.3 M i SPACING: 6.0X6.0 M  A o t> O  -  AGE  184  LEGEND SPACING: 1. 2X1.2 M SPACING: 1. 5X1.5 M SPACING: 1 8X1.8 M SPACING: 2 1X2.1 M SPACING: 2 4X2.4 M SPACING: 3 0X3.0 M SPACING: 4. 3X4.3 M SPACING: 6 0X6.0 M  31  Table  5.18:  T w o - l e v e l n e s t e d anova t e s t s crown w i d t h (cm/year/m).  f o r DBH AGR p e r u n i t o f Factor  DBH Age  13 14 15 15 16 18 18 24 30  Spacings  included(m)  1.2 t o 4.3 1.2 t o 4.3 1. 2 ; 2 .1; 3 . 0 ; 4 . 3 1. 5 ; 1. 8 ; 2 . 4 All 1. 5 ; 1. 8 ; 2 .1; 2 . 4 1. 2 ; 3 . 0 ; 4 . 3 ; 6 . 0 All All  class  D.F.  F  51/347 64/347 42/194 29/150 86/418 46/187 47/221 107/341 114/341  4 .22* 5 .15* 2 .23* 2 .64* 2 .12* 4 .57* 8 .88* 3 .26* 2 .51*  Spacing D.F.  F  6/46 1 . 85n 6/57 5 .24* 3/31 11 .70* 2/23 24 .28* 7/64 29 .02* 20 .94* 3/40 3/44 27 .53* 7/107 103 .18* 7/114 13 .82*  *: s i g n i f i c a n t d i f f e r e n c e s a t t h e l e v e l o f p r o b a b i l i t y o f 0.05. n . s . : no s i g n i f i c a n t d i f f e r e n c e .  Table  5.19:  T w o - l e v e l n e s t e d anova t e s t s of crown l e n g t h (cm/year/m)  f o r DBH AGR p e r u n i t Factor  Age 13 13 14  15 15 16 18 24 30  Spacings  included(m)  1. 2 ; 1. 8 ; 2 . 4 1. 5 ; 2 . 1 ; 3 . 0 all 1. 2 ; 2 . 4 ; 3 . 0 1. 5 ; 1. 8 ; 2 .1 All All All All  DBH  class  D.F.  F  24/150 21/150 64/347 31/145 29/154 86/418 93/408 107/370 114/341  8.27* 7.73* 3.61* 4.21* 1.14n.s. 2.35* 8.11* 3.94* 3.02*  * : s i g n i f i c a n t d i f f e r e n c e s at the l e v e l n . s . : no s i g n i f i c a n t d i f f e r e n c e .  185  Spacing D.F. 2/23 2/2 0 6/54 2/27 2/17 7/66 7/86 7/107 7/114  of p r o b a b i l i t y  F 9 .68* 11 . 2 5 * 26 . 53* 36 .96* 39 .20* 78 .04* 51 .46* 124 .92* 32 . 4 9 * of  0.05.  there  were d i f f e r e n t  (Figures both  5.16  ratios  and 5 . 1 7 ) .  remained  ponded c l o s e l y 15,  15,  2.4  m spacings  the  ratios  with  16,  tree  with  16,  for  cings  were  still  Before  the  than  became  The  correlated of  Appendix  with  decreasing of  of  ratios  small  DBH AGR t o  increased, the  onset  the of  large  a g e s were 2.1  m, and  showed  that  constant  largest  began,  trees.  were n o t  most  The DBH n e s t i n g ratios  18  corres-  spa-  the  This  smaller is  in  f o r RGR.  length at  m,  two  crown p r o j e c t i o n ,  biomass or  the  when  t r e e s were more  When c o m p e t i t i o n  concluded  these  the  competition,  than  age  probably occurred  size.  significant  age  time  size  These 1.8  over  the  remaining r e l a t i v e l y  with  trees.  as  (Figure ages  factor  crown  meaningful  5.15).  (Tables was  with  1,  occurrences  of  tree the  2,  size  shifts  (Figures  as  those  The e f f e c t  significant  decreased  competition  surface,  1,  2,  3,  of  and 4  at  every  at  early  were 3,  not  and 4  4). of  (AGR(BA)/crown w i d t h ) ,  basal  a r e a AGR p e r u n i t  crown l e n g t h  biomass  surface),  crown volume  (AGR(BA)/foliage 186  of  (AGR(BA)/crown  (AGR(BA)/crown p r o j e c t i o n ) ,  (AGR(BA)/crown foliage  The g r a p h f o r  tree  efficient  The mean v a l u e s  projection  m,  for  Even though  a g e s and l a t e r  1.5  the  Appendix 4).  age.  m,  30,  and f o l i a g e  not  1.2  A t age  of  size  tree  competition.  this  onset  tree  with  m spacing;  w i t h what was  was  of  the  point  i n c l u d e d crown w i d t h  spacing of  for  constant  3.0  large  ratios  with  the  less  crown v o l u m e , that  onset  were on t h e  20.  agreement  the  change  For a p a r t i c u l a r s p a c i n g ,  relatively  and 18  a r o u n d age  trees  of  respectively.  size  efficient  patterns  crown  crown w i d t h length),  crown  surface  (AGR(BA)/crown volume),  biomass)  all  showed  similar  and  FIGURE  5 . 1 6 : DBH AGR/CROWN WIDTH RATIOS PER 1 CM DBH CLASS FOR ALL SPACINGS AND DIFFERENT AGES  L E G E N D S P A C I N G :  DBH  CLASS  187  1 . 2 X 1 . 2  M  S P A C I N G :  1 .5X1 . 5  M  S P A C I N G :  1 ,8X 1 .8  M  S P A C I N G :  2 . 1 X 2 . 1  M  S P A C I N G :  2 . 4 X 2 . 4  M  S P A C I N G :  3 . 0 X 3 . 0  M  S P A C I N G :  4 . 3 X 4 . 3  M  S P A C I N G :  6 . 0 X 6 . 0  M  A G R ( 0 6 H ) / C R 0 W N LENGTH ( C M / Y E A R / M )  o o o o o o o o o o o o o o o o o o o o o a o  AGR(D8H)/CR0WN LENGTH (CM/YEAR/M)  o o o o o o o o o o o 0  -  >  -  M  U  u  »  a  AGR(OBH)/CROWN LENGTH (CM/YEAR/M)  o o o o o o o o o o o  AGR(08H)/CR0WN LENGTH (CM/YEAR/M)  o o o o o o o o o o o  w  o c:  o o w o o o m o w o  0 0 - - > M M M t i l ( i l  r n  I—  c n  3> •  OO — OO —-J  O CT CD  =c  l— >• r— O  oo\  ~D O  o  <r> 00 00 AGR(OBH)/CROWN LENGTH (CM/YEAR/M)  o o o o o o o o o o o O O  O M  O O O M O  ' H  O  ' ^  ACR(DBH)/CROWN LENGTH (CM/YEAR/M)  o o o o o o o o o o o  AGR(DBH)/CROWN LENGTH (CM/YEAR/M)  o o o o o o o o o o o  oo  I  H O  o w o w o o o a o 0 1!  *  •  <]  0  fl>  Q  0  II II II II II II II  CT —  U)U)U)U)U)U)U)U)  D T J D D T J - O T J T )  > o> o> o>o>o>o>o>mr o z z z z z z z z £  O  m  oo  —I  TD  3>  rn  JO  <T5  O O J O V  ^  CO in N  x x x x x x x x  OO  O l ^ U W M - ' - ' - '  2  2  ^  2  1  1  2  CT CD  (Figure 5.18).  trends  fluctuations. sed w i t h  A l l t h e r a t i o s d e c r e a s e d w i t h age d e s p i t e  For nearly every  spacing.  cings d i f f e r e d  age, t h e r a t i o s  However, t h e s t a t i s t i c a l  Appendix 4 ) .  No s i g n i f i c a n t  15 w i t h b a s a l  area  comparison o f spaa n d 10 o f  d i f f e r e n c e s were o b t a i n e d  u n t i l age  (Tables  Basal  6,  7,  8,  a g e 14 w i t h  basal  a r e a AGR/crown l e n g t h ,  basal  AGR/crown w i d t h  a r e a AGR/crown p r o j e c t i o n .  increa-  9,  among t h e r a t i o s  5,  normally  and u n t i l  a r e a AGR/crown s u r f a c e , and b a s a l a r e a A G R / f o l i a g e  b i o m a s s were  significant  AGR/crown  a t every  age.  v o l u m e was s i g n i f i c a n t  only  b a s a l a r e a AGR/crown w i d t h competition The  The r a t i o  a t ages 16,  for  a l l the ratios  The  ratios  5,  and crown s u r f a c e  (Figures 5,  6,  4.3  7,  much a t c e r t a i n a g e s .  After  after  all  Before  these  biomass remained r e l a t i v e l y  15,  22,  spacings  24,  f o r the  or d i d not vary  (Figure  5.19).  gradually started  shifts  t h e changes i n c o m p e t i t i v e  occurred  status  Basal  constant  well  AGR/foliage (Figure  fora particular  tree size.  size  AGR/crown volume  Only b a s a l area  the onset of competition  4).  crown  tree  Only t h e r a t i o s  However, t h e s e  r a t i o s decreased with  16,  crown l e n g t h ,  of basal area  AGR/foliage 16,  a n d 10 o f A p p e n d i x  of the c l o s e s t spacings  tree size.  biomass approximated  9,  s i z e up t o a g e 18  the onset of competition.  5.20).  8,  a t a l m o s t e v e r y age  decreased with, tree s i z e  The v a l u e s  that, thevalues  only  t h e onset o f  generally increased with  decreased with  to increase w i t h  7,  and 8 o f Appendix 4 ) .  m and 6 . 0 m spacings  at a l l spacings  6,  a r e a AGR t o c r o w n w i d t h ,  projection,  Thus,  spacings.  f a c t o r was s i g n i f i c a n t  (Tables  of basal  24 a n d 3 0 .  corresponded with  f o r t h e two c l o s e s t  DBH n e s t i n g  of basal area  spacing,  area a t ages 14,  14,  a n d 30 f r o m t h e c l o s e s t t o t h e l a r g e s t  respectively.  Except f o r the 6.0 m spacing, 189  a l l these  FIGURE 5 . 1 8 : RATIOS OF MEAN BASAL AREA AGR TO DIFFERENT CROWN MEASUREMENTS FIGURE 3 . 1 8 . 2 : MEAN BASAL AREA AGR PER UNIT OF CROWN LENGTH FOR ALL SPACINGS OVER AGE  FIGURE 5 . 1 8 . 1 : MEAN BASAL AREA AGR PER UNIT OF CROWN WIDTH FOR ALL SPACINGS OVER AGE  LEGEND A « SPACING: 1 . 2 X 1 . J SPACING: 1 5X1 SPACING: 1.8X1 PACING: 2 . 1 X 2 PACING: 2.4X2 4 PACING: 3 . 0 X 3 " .PACING: 4.3X4 SPACING: e.oxe  0.00150 0.00136  ac  >^ 0 . 0 0 1 2 2 j>  0.00108  O ^  0.00094  i  0.00080 |  0.000...  ^0.00052  j  ^  \  f « : ^  V f  , ^  V  A  ^  *.  \  \ .  o  -  Oj 0.000305  ^  O.OOOSg  0.000220  ^  0.00024  0.00013S 0.000050  0.00010 21  23  AGE FIGURE 5 . 1 8 . 4 : MEAN BASAL AREA PER UNIT OF CROWN SURFACE FOR ALL SPACINGS OVER AGE  AGE FICURE 5.18.3: MEAN BASAL AREA AGR PER UNIT OF CROWN PROJECTION FOR ALL SPACINGS OVER AGE  A 9 » £  A - SPAcfffc^P.gXI. -PACING: 1.SXIPAC1NG: 1 8x £ - SPACING: 2.1X  21  SPACINCT: SPACING: SPACING: SPACING:  ?2X12 M 1.5X1.S M 1.8X1.8 M 2.1X2.1 M  23 AGE FIGURE 5.18.8: MEAN BASAL AREA PER UNIT OF FOLIAGE BIOMASS FOR ALL SPACINGS OVER AGE  AGE FIGURE 5 . 1 8 . 5 : MEAN BASAL AREA PER UNIT OF CROWN VOLUME FOR ALL SPACINGS OVER AGE  K  -  0.000O41 0.000019  190  M M M M M M M M  FIGURE 5 . 1 9 : BASAL AREA AGR/CROWN VOLUME RATIOS PER 1 CM DBH CLASS FOR ALL SPACINGS AND DIFFERENT