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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 (P inus r e s i n o s a A i t . ) By GUY LAROCQUE B. Sc M.SC L a v a l U n i v e r s i t y , 1979 L a v a l U n i v e r s i t y , 1982 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY In THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF FORESTRY We accept t h i s t h e s i s as conforming to the r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA May 1991 © Guy L a r o c q u e , 1991 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department The University of British Columbia Vancouver, Canada Date / ? v L r A n / <t<T I DE-6 (2/88) ABSTRACT E f f e c t s o f c o m p e t i t i o n among t r e e s o f red p i n e (P inus  r e s i n o s a A i t . ) on t r e e growth and on the r e l a t i v e d e n s i t y of wood were examined. Data came from a s p a c i n g t r i a l w i t h i n i t i a l s p a c i n g s r a n g i n g from 1 .2x1 .2 m to 6 .0x6 .0 m; i n d i v i d u a l t r e e s were measured f o r DBH, h e i g h t , and crown d imens ions at s e v e r a l ages . The f i r s t o b j e c t i v e was to e v a l u a t e i f r e l a t i v e growth ra te (RGR) e x p r e s s e d the c o m p e t i t i v e s t a t u s of s tands b e t t e r than a b s o l u t e growth r a t e (AGR), which i s n o r m a l l y used i n f o r e s t r y . R e l a t i v e growth r a t e was found to be s u p e r i o r to AGR. Whi le AGR was always p o s i t i v e l y r e l a t e d to t r e e s i z e , RGR d e c r e a s e d w i t h t r e e s i z e b e f o r e the onset o f c o m p e t i t i o n or when i t was not too s e v e r e , and i n c r e a s e d w i t h t r e e s i z e under severe c o m p e t i t i v e s t r e s s . T h i s i m p l i e s t h a t s m a l l t r e e s were more e f f i c i e n t than l a r g e t r e e s a t p r o d u c i n g new biomass b e f o r e the onset of c o m p e t i -t i o n . The e f f e c t o f c o m p e t i t i o n was to reduce the e f f i c i e n c y of s m a l l t r e e s compared to l a r g e ones . The second o b j e c t i v e was to examine whether d i f f e r e n t measu-res o f crown e f f i c i e n c y r a r e l y used i n f o r e s t r y were r e l a t e d to the c o m p e t i t i v e s t a t u s o f s t a n d s . The r a t i o s o f crown w i d t h to crown l e n g t h , and of crown l e n g t h to DBH, the r a t i o of AGR i n DBH to crown w i d t h and to crown l e n g t h , and the r a t i o o f AGR i n b a s a l a r e a to f o l i a g e biomass showed a p a t t e r n s i m i l a r to RGR: a d e c r e a s e w i t h t r e e s i z e b e f o r e the onset of c o m p e t i t i o n , and an i n c r e a s e w i t h t r e e s i z e a f t e r . Crown r a t i o showed l i t t l e v a r i a -t i o n w i t h t r e e s i z e f o r a p a r t i c u l a r s p a c i n g u n t i l the onset of c o m p e t i t i o n , and i n c r e a s e d w i t h t r e e s i z e a f t e r w a r d s . i i The t h i r d o b j e c t i v e c o n s i s t e d of examining whether the r e l a -t i v e d e n s i t y of wood i n red pine was a f f e c t e d by d i f f e r e n t i n i -t i a l s p a c i n g s . Increment cores were sampled at b r e a s t h e i g h t on 30 t r e e s w i t h i n every spacing and scanned on a d i r e c t reading X-ray densitometer to determine the r e l a t i v e d e n s i t y of the wood. Ring width, the r e l a t i v e d e n s i t y of the r i n g , earlywood and l a t e -wood d e n s i t i e s , minimum and maximum d e n s i t i e s , and p r o p o r t i o n s of earlywood and latewood were an a l y s e d . The r e l a t i v e d e n s i t y of the r i n g s and of the latewood zones and the p r o p o r t i o n s of e a r l y -wood and latewood were c l o s e l y a s s o c i a t e d with the change i n c o m p e t i t i v e s t a t u s of stands. Furthermore, the changes i n wood d e n s i t y were c l o s e l y a s s o c i a t e d with the changes i n crown r a t i o . RGR and measures of crown e f f i c i e n c y d e s c r i b e the competi-t i v e s t a t u s of stands b e t t e r than c l a s s i c a l measures of growth. T h e i r use f o r e v a l u a t i n g the response of stands under i n t e n s i v e management s t i l l remains to be i n v e s t i g a t e d . i i i TABLE OF CONTENTS Page ABSTRACT i i TABLE OF CONTENTS i v LIST OF TABLES ix LIST OF FIGURES x x i i ACKNOWLEDGEMENTS xxx Chapter 1. GENERAL INTRODUCTION 1 2. LITERATURE REVIEW 5 2 . 1 - D e f i n i t i o n and Nature of C o m p e t i t i o n 5 2 . 2 - Even-aged Stand Development 7 2 . 3 - 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 Growth Models 10 2 . 4 - C h a r a c t e r i s t i c s o f Red Pine 13 3. DESCRIPTION OF DATA 17 4. STAND DEVELOPMENT STUDY 19 4 . 1 - I n t r o d u c t i o n 19 4 . 2 - L i t e r a t u r e Review on R e l a t i v e Growth Rate 20 4 . 3 - Hypotheses 23 4 . 4 - M a t e r i a l and Methods 26 i v 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 P o t e n t i a l Growth Rate o f Stand-grown Trees 32 4 . 5 - R e s u l t s and D i s c u s s i o n 34 4 . 5 . 1 - C l a s s i c a l Approach 34 4 . 5 . 1 . 1 - DBH and B a s a l A r e a Development 34 4 . 5 . 1 . 1 . 1 - C u m u l a t i v e Increment i n DBH. . . . 3 4 4 . 5 . 1 . 1 . 2 - A b s o l u t e Growth Rate 37 4 . 5 . 1 . 1 . 3 - R e l a t i v e Growth Rate 54 4 . 5 . 1 . 2 - Development i n H e i g h t 77 4 . 5 . 1 . 2 . 1 - C u m u l a t i v e Increment 77 4 . 5 . 1 . 2 . 2 - A b s o l u t e Growth Rate 80 4 . 5 . 1 . 2 . 3 - R e l a t i v e Growth Rate 87 4 . 5 . 1 . 3 - Development i n Volume 93 4 . 5 . 1 . 3 . 1 - C u m u l a t i v e Increment 93 4 . 5 . 1 . 3 . 2 - A b s o l u t e Growth Rate 93 4 . 5 . 1 . 3 . 3 - R e l a t i v e Growth Rate 98 4 . 5 . 2 - F u n c t i o n a l Approach 98 v 4 . 5 . 2 . 1 - C u m u l a t i v e Increment 101 4 . 5 . 2 . 2 - A b s o l u t e Growth Rate 101 4 . 5 . 2 . 3 - R e l a t i v e Growth Rate 102 4 . 5 . 3 - E s t i m a t i o n of the P o t e n t i a l Growth Rate of Stand-grown Trees from Open-grown T r e e s . . . 1 0 3 4 . 6 - Summary and C o n c l u s i o n s 127 CROWN DEVELOPMENT STUDY 130 5 . 1 - I n t r o d u c t i o n 130 5 . 2 - L i t e r a t u r e Review 131 5 . 3 - Hypotheses 138 5 . 4 - M a t e r i a l and Methods 140 5 . 5 - R e s u l t s and D i s c u s s i o n 143 5 . 5 . 1 - R e l a t i o n s h i p s between Crown Dimensions and Bo le S i z e s 143 5 . 5 . 2 - A b s o l u t e Measures 145 5 . 5 . 3 - R e l a t i v e Measures 157 5 . 5 . 4 - R e l a t i v e Growth Measures 183 5 . 6 - Summary and C o n c l u s i o n s 193 STUDY OF WOOD FORMATION IN RELATION TO STAND DEVELOPMENT 198 v i 6 . 1 - I n t r o d u c t i o n 198 6 . 2 - L i t e r a t u r e Review 199 6 . 2 . 1 - P h y s i o l o g i c a l A s p e c t s o f Wood F o r m a t i o n 199 6 . 2 . 2 - F a c t o r s I n f l u e n c i n g R e l a t i v e D e n s i t y 207 6 . 2 . 2 . 1 - G e n e t i c I n h e r i t a n c e 209 6 . 2 . 2 . 2 - E f f e c t of Stand D e n s i t y 210 6 . 3 - Hypotheses 214 6 . 4 - M a t e r i a l and Methods 216 6 . 5 - R e s u l t s and D i s c u s s i o n 220 6 . 5 . 1 - E f f e c t s o f D i f f e r e n t Spac ings 220 6 . 5 . 2 - R e l a t i o n s h i p s w i t h Crown V a r i a b l e s 280 6 . 5 . 3 - Showing the E f f e c t o f S p a c i n g a t the I n d i v i d u a l - t r e e L e v e l . . . 2 9 3 6 . 6 - Summary and C o n c l u s i o n s 299 7. GENERAL CONCLUSIONS 301 7 . 1 - Summary o f F i n d i n g s . . . 3 0 1 7 . 2 - P r o p o s a l f o r the Development of 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 Growth Models 302 7 . 3 - A d d i t i o n a l Research Needs 306 LITERATURE CITED 308 v i i APPENDIX 1: BASIC STATISTICS OF THE PERMANENT SAMPLE PLOTS STUDIED 332 APPENDIX 2: SUPPLEMENTARY RESULTS OF CHAPTER 4 349 APPENDIX 3: RESULTS OF THE APPLICATION OF THE FUNCTIONAL APPROACH 354 APPENDIX 4: ADDITIONAL RESULTS OF CHAPTER 5 379 APPENDIX 5: ADDITIONAL REGRESSION EQUATIONS RELATING CROWN VARIABLES TO THE RELATIVE DENSITY OF WOOD 393 v i i i LIST OF TABLES T a b l e 4.1 P r o p o r t i o n s o f t r e e s (%) t h a t have t h e i r crown o v e r l a p p i n g t h e i r growing space area as d e f i n e d by the s p a c i n g . 4.2 Mean DBHs (cm) f o r a l l s p a c i n g s over age . 4.3 Mean AGRs i n DBH (cm/year) f o r e v e r y s p a c i n g over age 4.4 Mean AGRs i n b a s a l area ( c m 2 / y e a r ) f o r e v e r y s p a c i n g over age . 4.5 Summary of the p r i n c i p a l component a n a l y s i s u n d e r -taken w i t h the c l i m a t i c v a r i a b l e s . 4.6 T w o - l e v e l n e s t e d anova t e s t s f o r AGR i n DBH (cm/year) 4.7 T w o - l e v e l n e s t e d anova t e s t s f o r AGR i n b a s a l a r e a ( c m 2 / y e a r ) . 4.8 Mean RGRs i n DBH (cm/year /cm) f o r e v e r y s p a c i n g over age . 4.9 Mean RGRs i n b a s a l a r e a ( c m 2 / y e a r / c m 2 ) f o r e v e r y s p a c i n g over age . 4.10 T w o - l e v e l n e s t e d anova t e s t s f o r RGR i n DBH ( c m / y e a r / c m ) . 4.11 T w o - l e v e l n e s t e d anova t e s t s f o r RGR i n b a s a l a r e a ( c m 2 / y e a r / c m 2 ) . 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 between DBH ( i n i t i a l s i z e ) 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 ages . i x 4.13 Two-level nested anova t e s t s f o r mean h e i g h t (m). 81 4.14 Two-level nested anova t e s t s f o r AGR i n h e i g h t (m/year ) . 8 3 4.15 Two-level nested anova t e s t s f o r RGR i n h e i g h t (m/year/m) . 90 4.16 Mean volumes per t r e e (m 3) f o r a l l spacings over age. 94 4.17 Two-level nested anova t e s t s f o r t o t a l volume (m 3). 94 4.18 Mean AGRs i n volume (m 3/yeat) f o r a l l spacings over age. 96 4.19 Two-level nested anova t e s t s f o r AGR i n volume (m 3 / y e a r ) . 96 4.20 Mean RGRs i n volume (m 3/year/m 3) f o r a l l spacings over age. 99 4.21 Two-level nested anova t e s t s f o r RGR i n volume (m 3/year/m 3 ) . 99 4.22 B a s i c growth i n f o r m a t i o n on the open-grown t r e e s . 105 4.23 Comparison of v a l u e s between DBHs o b t a i n e d from Ek's eq u a t i o n and the d e r i v e d e q u a t i o n . 107 4.24 Comparison of observed AGRs and RGRs i n DBH of the stand-grown t r e e s from the 4.3 m spacing before the onset of c o m p e t i t i o n with 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 the second h y p o t h e s i s . Increment p e r i o d : 1 year. 112 x 4.25 Comparison of observed AGRs and RGRs i n DBH of the stand-grown t r e e s from the 6.0 m spa c i n g before the onset of c o m p e t i t i o n with 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 the second h y p o t h e s i s . Increment p e r i o d : 1 year. 113 4.26 Comparison of observed AGRs and RGRs i n DBH of the stand-grown t r e e s from the 6.0 m spa c i n g before the onset of c o m p e t i t i o n with 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 the second h y p o t h e s i s . Increment p e r i o d : 5 y e a r s . 115 4.27 Comparison of observed AGRs and RGRs i n DBH of the stand-grown t r e e s from the 4.3 m spa c i n g b e f o r e the onset of c o m p e t i t i o n with 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 the t h i r d h y p o t h e s i s . Increment p e r i o d : 1 year. 117 4.28 Comparison of observed AGRs and RGRs i n DBH of the stand-grown t r e e s from the 6.0 m spacing b e f o r e the onset of c o m p e t i t i o n with 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 the t h i r d h y p o t h e s i s . Increment p e r i o d : 1 year. 118 4.29 Comparison of observed AGRs and RGRs i n DBH of the stand-grown t r e e s from the 6.0 m spacing b e f o r e the onset of c o m p e t i t i o n with 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 the t h i r d h y p o t h e s i s . Increment p e r i o d : 5 y e a r s . 119 x i 4.30 Comparison of observed AGRs and RGRs i n DBH of the stand-grown t r e e s from the 4.3 m spacing b e f o r e the onset of 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 t r e e v a l u e s as d e f i n e d by the f o u r t h h y p o t h e s i s . Increment p e r i o d : 1 year. 121 4.31 Comparison of observed AGRs and RGRs i n DBH of the stand-grown t r e e s from the 6.0 m spa c i n g before the onset of 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 t r e e v a l u e s as d e f i n e d by the 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 . 122 4.32 Comparison of observed AGRs and RGRs i n DBH of the stand-grown t r e e s from the 6.0 m spa c i n g b e f o r e the onset of c o m p e t i t i o n with 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 the 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 . 123 4.33 Comparison of observed AGRs and RGRs i n DBH of the stand-grown t r e e s from the 4.3 m spa c i n g before the onset of c o m p e t i t i o n with 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 the f i f t h h y p o t h e s i s . Increment p e r i o d : 1 year. 124 4.34 Comparison of observed AGRs and RGRs i n DBH of the stand-grown t r e e s from the 6.0 m spa c i n g before the onset of c o m p e t i t i o n with 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 the f i f t h h y p o t h e s i s . Increment p e r i o d : 1 y e a r . 125 5.1 Equations f o r crown width (m) as a f u n c t i o n of DBH (cm) f o r a l l ages and every s p a c i n g . 144 x i i 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 of DBH (cm) f o r a l l ages and e v e r y s p a c i n g . 144 5.3 T w o - l e v e l n e s t e d anova t e s t s f o r crown w i d t h (m). 149 5.4 T w o - l e v e l n e s t e d anova t e s t s f o r crown l e n g t h (m). 150 5.5 T w o - l e v e l n e s t e d anova t e s t s f o r crown p r o j e c t i o n ( m 2 ) . 151 5.6 T w o - l e v e l n e s t e d anova t e s t s f o r crown s u r f a c e ( m 2 ) . 152 5.7 T w o - l e v e l n e s t e d anova t e s t s f o r crown volume ( m 3 ) . 153 5.8 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 biomass ( k g ) . 154 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 ( k g ) . 155 5.10 T w o - l e v e l n e s t e d anova t e s t s f o r crown w i d t h / c r o w n l e n g t h (m/m) r a t i o . 160 5.11 T w o - l e v e l n e s t e d anova t e s t s f o r crown s u r f a c e / c r o w n volume (m 2/m 3) r a t i o . 164 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 b i o m a s s / volume (kg/m 3) r a t i o . 165 5.13 T w o - l e v e l n e s t e d anova t e s t s f o r biomass of f o l i a g e / biomass o f branches (kg/kg) r a t i o . 169 5.14 T w o - l e v e l n e s t e d anova t e s t s f o r crown width/DBH (m/cm) r a t i o . 173 5.15 T w o - l e v e l 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 (m/m) r a t i o . 175 x i i i 5.16 T w o - l e v e l nes ted anova t e s t s f o r crown l e n g t h / D B H (m/cm) r a t i o . 177 5.17 T w o - l e v e l n e s t e d anova t e s t s f o r crown r a t i o (m/m) 180 5.18 T w o - l e v e l nes ted anova t e s t s f o r DBH AGR per u n i t o f crown w i d t h ( c m / y e a r / m ) . 185 5.19 T w o - l e v e l n e s t e d anova t e s t s _ f o r DBH AGR per u n i t o f crown l e n g t h ( c m / y e a r / m ) . 185 5.20 T w o - l e v e l n e s t e d anova t e s t s f o r h e i g h t AGR per u n i t o f crown width ( m / y e a r / m ) . 196 6.1 One-way anova t e s t s f o r r i n g w i d t h (mm). 222 6.2 T w o - l e v e l n e s t e d anova t e s t s f o r r i n g w id th (mm). 223 6.3 One-way anova t e s t s f o r r e l a t i v e d e n s i t y o f r i n g s . 228 6.4 T w o - l e v e l n e s t e d anova t e s t s f or r e l a t i v e d e n s i t y o f r i n g s . 229 6.5 One-way anova t e s t s f o r r e l a t i v e d e n s i t y o f ear lywood zones . 235 6.6 T w o - l e v e l n e s t e d anova t e s t s f o r r e l a t i v e d e n s i t y o f ear lywood zones . 237 6.7 One-way anova t e s t s f o r r e l a t i v e d e n s i t y o f latewood zones . 242 6.8 T w o - l e v e l n e s t e d anova t e s t s f o r r e l a t i v e d e n s i t y o f la tewood zones . 244 x i v X V 6.20 M u l t i p l e l i n e a r r e g r e s s i o n e q u a t i o n s f o r r i n g w i d t h (mm) as a f u n c t i o n of crown width (m) and crown l e n g t h (m) f o r d i f f e r e n t ages . 281 6.21 M u l t i p l e l i n e a r r e g r e s s i o n e q u a t i o n s f o r r i n g w i d t h (mm) as a f u n c t i o n o f crown w i d t h (m) and d i s t a n c e between the base o f the crown and b r e a s t h e i g h t (m) f o r d i f f e r e n t ages . 282 6.22 M u l t i p l e l i n e a r r e g r e s s i o n e q u a t i o n s f o r r i n g w i d t h (mm) as a f u n c t i o n o f crown volume (m 3 ) and crown r a t i o (m/m) f o r d i f f e r e n t ages . 283 6.23 M u l t i p l e l i n e a r r e g r e s s i o n e q u a t i o n s f o r r e l a t i v e d e n s i t y o f r i n g s as a f u n c t i o n of crown w i d t h (m) and crown l e n g t h (m) f o r d i f f e r e n t ages . 285 6.24 M u l t i p l e l i n e a r r e g r e s s i o n e q u a t i o n s f o r r e l a t i v e d e n s i t y o f r i n g s as a f u n c t i o n of crown w i d t h (m) and d i s t a n c e between the base o f the crown and b r e a s t h e i g h t (m) f o r d i f f e r e n t ages . 286 6.25 M u l t i p l e l i n e a r r e g r e s s i o n e q u a t i o n s f o r r e l a t i v e d e n s i t y o f r i n g s as a f u n c t i o n o f crown volume (m 3 ) and crown r a t i o (m/m) f o r d i f f e r e n t ages . 287 6.26 M u l t i p l e l i n e a r r e g r e s s i o n e q u a t i o n s f o r p r o p o r t i o n of ear lywood as a f u n c t i o n o f crown w i d t h (m) and crown l e n g t h (m) f o r d i f f e r e n t ages . 289 x v i 6.27 M u l t i p l e l i n e a r r e g r e s s i o n e q u a t i o n s f o r p r o p o r t i o n o f ear lywood as a f u n c t i o n of crown w i d t h (m) and d i s t a n c e between the base o f the crown and b r e a s t h e i g h t (m) f o r d i f f e r e n t ages . 290 6.28 M u l t i p l e l i n e a r r e g r e s s i o n e q u a t i o n s f o r p r o p o r t i o n of ear lywood as a f u n c t i o n o f crown volume (m 3 ) and crown r a t i o (m/m) f o r d i f f e r e n t ages . 291 APPENDIX 1 1-A AECL SPACING T R I A L . BASIC S T A T I S T I C S . Permanent sample p l o t #364. S p a c i n g : 1 .2x1 .2 m. 333 1-B AECL SPACING T R I A L . BASIC S T A T I S T I C S . Permanent sample p l o t #365. S p a c i n g : 1 .2x1 .2 m. 334 1-C AECL SPACING T R I A L . BASIC S T A T I S T I C S . Permanent sample p l o t #373. S p a c i n g : 1 .5x1 .5 m. 335 1-D AECL SPACING T R I A L . BASIC S T A T I S T I C S . Permanent sample p l o t #374. S p a c i n g : 1 .5x1 .5 m. 336 1-E AECL SPACING T R I A L . BASIC S T A T I S T I C S . Permanent sample p l o t #371. S p a c i n g : 1 .8x1 .8 m. 337 1 -F AECL SPACING T R I A L . BASIC STATISTICS . Permanent sample p l o t #372. S p a c i n g : 1 .8x1.8 m. 338 1-G AECL SPACING T R I A L . BASIC STATISTICS . Permanent sample p l o t #368. S p a c i n g : 2 .1x2 .1 m. 339 1-H AECL SPACING T R I A L . BASIC S T A T I S T I C S . Permanent sample p l o t #375. S p a c i n g : 2 .1x2 .1 m. 340 x v i i 1-1 AECL SPACING T R I A L . BASIC STATISTICS . Permanent sample p l o t #376. S p a c i n g : 2 .4x2 .4 m. 341 1 - J AECL SPACING T R I A L . BASIC S T A T I S T I C S . Permanent sample p l o t #377. S p a c i n g : 2 .4x2 .4 m. 342 1-K AECL SPACING T R I A L . BASIC S T A T I S T I C S . Permanent sample p l o t #378. S p a c i n g : 3 .0x3 .0 m. 343 1-L AECL SPACING T R I A L . BASIC S T A T I S T I C S . Permanent sample p l o t #366. S p a c i n g : 3 .0x3 .0 m. 344 1-M AECL SPACING T R I A L . BASIC S T A T I S T I C S . Permanent sample p l o t #367. S p a c i n g : 4 .3x4 .3 m. 345 1-N AECL SPACING T R I A L . BASIC S T A T I S T I C S . Permanent sample p l o t #369. S p a c i n g : 4 .3x4 .3 m. 346 1-0 AECL SPACING T R I A L . BASIC S T A T I S T I C S . Permanent sample p l o t #385. S p a c i n g : 6 .0x6 .0 m. 347 2 Summary o f c l i m a t i c d a t a from May to September, and between 1961 and 1982 a t the 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 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 the f u n c t i o n a l approach to DBH f o r the 1.2 m s p a c i n g . 355 x v i i i 1.2 A p p l i c a t i o n o f the f u n c t i o n a l approach to DBH f o r the 1.8 m s p a c i n g . 1.3 A p p l i c a t i o n o f the f u n c t i o n a l approach to DBH f o r the 3.0 m s p a c i n g . 1.4 A p p l i c a t i o n o f the f u n c t i o n a l approach to DBH f o r the 6.0 m s p a c i n g . 2.1 A p p l i c a t i o n o f the f u n c t i o n a l approach to DBH f o r the 1.2 m s p a c i n g . E q u a t i o n s f o r AGR. 2.2 A p p l i c a t i o n o f the f u n c t i o n a l approach to DBH f o r the 1.8 m s p a c i n g . E q u a t i o n s f o r AGR. 2.3 A p p l i c a t i o n o f the f u n c t i o n a l approach to DBH f o r the 3.0 m s p a c i n g . E q u a t i o n s f o r AGR. 2.4 A p p l i c a t i o n o f the f u n c t i o n a l approach to DBH f o r the 6.0 m s p a c i n g . E q u a t i o n s f o r AGR. 3.1 A p p l i c a t i o n o f the f u n c t i o n a l approach to DBH f o r the 1.2 m s p a c i n g . E q u a t i o n s f o r RGR. 3.2 A p p l i c a t i o n o f the f u n c t i o n a l approach to DBH f o r the 1.8 m s p a c i n g . E q u a t i o n s f o r RGR. 3.3 A p p l i c a t i o n o f the f u n c t i o n a l approach to DBH f o r the 3.0 m s p a c i n g . E q u a t i o n s f o r RGR. 3.4 A p p l i c a t i o n o f the f u n c t i o n a l approach to DBH f o r the 6.0 m s p a c i n g . E q u a t i o n s f o r RGR. x i x APPENDIX 4 1 T w o - l e v e l n e s t e d anova t e s t s f o r DBH AGR per u n i t o f crown p r o j e c t i o n ( c m / y e a r / m 2 ) . 380 2 T w o - l e v e l n e s t e d anova t e s t s f o r DBH AGR per u n i t 2 crown s u r f a c e ( cm/year /m ) . 380 3 T w o - l e v e l n e s t e d anova t e s t s f o r DBH AGR per u n i t o f crown volume ( cm/year /m 3 ) . 381 4 T w o - l e v e l n e s t e d anova t e s t s f o r DBH AGR per u n i t of f o l i a g e biomass ( c m / y e a r / k g ) . 381 5 T w o - l e v e l n e s t e d anova t e s t s f o r b a s a l a r e a AGR per u n i t o f crown w i d t h ( c m 2 / y e a r / m ) . 386 6 T w o - l e v e l n e s t e d anova t e s t s f o r b a s a l a r e a AGR per u n i t o f crown l e n g t h ( c m 2 / y e a r / m ) . 386 7 T w o - l e v e l n e s t e d anova t e s t s f o r b a s a l a r e a AGR per u n i t o f crown p r o j e c t i o n ( c m 2 / y e a r / m 2 ) . 387 8 T w o - l e v e l n e s t e d anova t e s t s f o r b a s a l area AGR per u n i t o f crown s u r f a c e ( c m 2 / y e a r / m 2 ) • 387 9 T w o - l e v e l n e s t e d anova t e s t s f o r b a s a l a r e a AGR per 2 3 u n i t o f crown volume (cm / y e a r / m ) . 388 10 T w o - l e v e l n e s t e d anova t e s t s f o r b a s a l area AGR per u n i t o f f o l i a g e biomass ( c m 2 / y e a r / k g ) . 388 xx A P P E N D I X 5 1 M u l t i p l e l i n e a r r e g r e s s i o n e q u a t i o n s f o r r e l a t i v e d e n s i t y o f ear lywood as a f u n c t i o n o f crown w i d t h (m) and d i s t a n c e between the base of the crown and b r e a s t h e i g h t (m) f o r d i f f e r e n t ages . 394 2 M u l t i p l e l i n e a r r e g r e s s i o n e q u a t i o n s f o r r e l a t i v e d e n s i t y o f la tewood as a f u n c t i o n o f crown w i d t h (m) and d i s t a n c e between the base of the crown and b r e a s t h e i g h t (m) f o r d i f f e r e n t ages . 395 3 M u l t i p l e l i n e a r r e g r e s s i o n e q u a t i o n s f o r minimum r e l a t i v e d e n s i t y as a f u n c t i o n o f crown w i d t h (m) and d i s t a n c e between the base o f the crown and b r e a s t h e i g h t (m) f o r d i f f e r e n t ages . 396 4 M u l t i p l e l i n e a r r e g r e s s i o n e q u a t i o n s f o r maximum r e l a t i v e d e n s i t y as a f u n c t i o n o f crown w i d t h (m) and d i s t a n c e between the base o f the crown and b r e a s t h e i g h t (m) f o r d i f f e r e n t ages . 397 x x i LIST OF FIGURES FIGURE Page 4.1 MEAN DBHs FOR ALL SPACINGS OVER A G E . 36 4.2 DBH AGR DATA SUPERIMPOSED ON CLIMATIC VARIABLES. 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 OF DBH SIZE CLASS. 47 4.5 BASAL AREA AGRs AS A FUNCTION OF DBH SIZE CLASS. 48 4.6 MEAN DBH RGRS FOR ALL SPACINGS OVER A G E . 57 4.7 MEAN BASAL AREA RGRs FOR ALL SPACINGS OVER A G E . 58 4.8 DBH RGR DATA SUPERIMPOSED ON CLIMATIC VARIABLES. 60 4.9 DBH RGRS AS A FUNCTION OF DBH SIZE CLASS. 65 4.10 BASAL AREA RGRs AS A FUNCTION OF DBH SIZE CLASS. 66 4.11 MEAN HEIGHTS FOR ALL SPACINGS OVER A G E . 78 4.12 MEAN HEIGHTS AS A FUNCTION OF DBH SIZE CLASS. 79 4.13 HEIGHT AGRS AS A FUNCTION OF DBH SIZE CLASS. 82 4.14 HEIGHT AGR DATA SUPERIMPOSED ON CLIMATIC VARIABLES. 85 4.15 MEAN HEIGHT RGRs FOR ALL SPACINGS OVER A G E . 88 4.16 HEIGHT RGRS AS A FUNCTION OF DBH SIZE CLASS. 89 4.17 HEIGHT RGR DATA SUPERIMPOSED ON CLIMATIC VARIABLES. 91 4.18 MEAN VOLUMES AS A FUNCTION OF DBH SIZE CLASS. 95 x x i i 4.19 VOLUME AGRs AS A FUNCTION OF DBH SIZE CLASS. 97 4.20 VOLUME RGRs AS A FUNCTION OF DBH SIZE CLASS. 100 4.21 DBH = F(AGE) FOR OPEN-GROWN TREES. 106 4.22 DBH = F(AGE) FOR OPEN-GROWN TREES. 108 4.23 RGR(DBH) = F(AGE) FOR OPEN-GROWN TREES AND STAND-GROWN TREES BEFORE THE ONSET OF COMPETITION. (SPACING: 4.3 M) . 110 4.24 RGR(DBH) = F(AGE) FOR OPEN-GROWN TREES AND STAND-GROWN TREES BEFORE THE ONSET OF COMPETITION. (SPACING: 6.0 M ) . I l l 4.25 DBH - F(AGE AT BREAST HEIGHT) FOR OPEN-GROWN TREES. 116 5.1 CROWN LENGTH - F(DBH) FOR DIFFERENT SPACINGS. 146 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 ALL SPACINGS AND DIFFERENT AGES. 158 5.5 MEAN RELATIVE CROWN MEASURES BASED ON CROWN DIMENSIONS. 159 5.6 CROWN WIDTH/CROWN LENGTH RATIOS PER 1 CM DBH CLASS FOR ALL SPACINGS AND DIFFERENT AGES. 162 5.7 CROWN SURFACE/CROWN VOLUME RATIOS PER 1 CM DBH CLASS FOR ALL SPACINGS AND DIFFERENT AGES. 166 x x i i i 5.8 FOLIAGE BIOMASS/CROWN VOLUME RATIOS PER 1 CM DBH CLASS FOR ALL SPACINGS AND DIFFERENT AGES. 167 5.9 BIOMASS OF FOLIAGE/BIOMASS OF BRANCHES RATIOS PER 1 CM DBH CLASS FOR ALL SPACINGS AND DIFFERENT AGES. 170 5.10 RELATIVE CROWN WIDTH AND LENGTH MEASURES BASED ON TREE S I Z E . 172 5.11 CROWN WIDTH/DBH RATIOS PER 1 CM DBH CLASS FOR ALL SPACINGS AND DIFFERENT AGES. 17 4 5.12 CROWN WIDTH/HEIGHT RATIOS PER 1 CM DBH CLASS FOR ALL SPACINGS AND DIFFERENT AGES. 176 5.13 CROWN LENGTH/DBH RATIOS PER 1 CM DBH CLASS FOR ALL SPACINGS AND DIFFERENT AGES. 178 5.14 CROWN RATIOS PER 1 CM DBH CLASS FOR ALL SPACINGS AND DIFFERENT AGES. 181 5.15 RATIOS OF MEAN DBH AGR TO DIFFERENT CROWN MEASUREMENTS. 184 5.16 DBH AGR/CROWN WIDTH RATIOS PER 1 CM DBH CLASS FOR ALL SPACINGS AND DIFFERENT AGES. 187 5.17 DBH AGR/CROWN LENGTH RATIOS PER 1 CM DBH CLASS FOR ALL SPACINGS AND DIFFERENT AGES. 188 5.18 RATIOS OF MEAN BASAL AREA AGR TO DIFFERENT CROWN MEASUREMENTS. 190 5.19 BASAL AREA AGR/CROWN VOLUME RATIOS PER 1 CM DBH CLASS FOR ALL SPACINGS AND DIFFERENT AGES. 191 X X I V 5.20 BASAL AREA AGR/FOLIAGE BIOMASS RATIOS PER 1 CM DBH CLASS FOR ALL SPACINGS AND DIFFERENT AGES. 192 5.21 RATIOS OF MEAN HEIGHT AGR TO DIFFERENT CROWN MEASUREMENTS. 194 5.22 HEIGHT AGR/CROWN WIDTH RATIOS PER 1 CM DBH CLASS FOR ALL SPACINGS AND DIFFERENT AGES. 195 6.1 MEAN RING WIDTHS AT BREAST HEIGHT FOR ALL SPACINGS OVER TOTAL AGE OF PLANTATION. 221 6.2 RING WIDTHS PER 1 CM DBH CLASS FOR ALL SPACINGS AND DIFFERENT TOTAL AGES OF PLANTATION. 226 6.3 MEAN RELATIVE DENSITIES OF RINGS AT BREAST HEIGHT FOR ALL SPACINGS OVER TOTAL AGE OF PLANTATION. 227 6.4 RELATIVE DENSITIES OF RINGS PER 1 CM DBH CLASS FOR ALL SPACINGS AND DIFFERENT TOTAL AGES OF PLANTATION. 232 6.5 MEAN RELATIVE DENSITIES OF EARLYWOOD ZONES AT BREAST HEIGHT FOR ALL SPACINGS OVER TOTAL AGE OF PLANTATION 234 6.6 RELATIVE DENSITIES OF EARLYWOOD ZONES PER 1 CM DBH CLASS FOR ALL SPACINGS AND DIFFERENT TOTAL AGES OF PLANTATION. 240 6.7 MEAN RELATIVE DENSITIES OF LATEWOOD ZONES AT BREAST HEIGHT FOR ALL SPACINGS OVER TOTAL AGE OF PLANTATION. 241 6.8 RELATIVE DENSITIES OF LATEWOOD ZONES PER 1 CM DBH CLASS FOR ALL SPACINGS AND DIFFERENT TOTAL AGES OF PLANTATION. 248 X X V 6.9 MEAN MINIMUM RELATIVE DENSITY VALUES AT BREAST HEIGHT FOR ALL SPACINGS OVER TOTAL AGE OF PLANTATION. 249 6.10 MINIMUM RELATIVE DENSITY VALUES OF RINGS PER 1 CM DBH CLASS FOR ALL SPACINGS AND DIFFERENT TOTAL AGES OF PLANTATION. 254 6.11 MEAN MAXIMUM RELATIVE DENSITY VALUES AT BREAST HEIGHT FOR ALL SPACINGS OVER TOTAL AGE OF PLANTATION. 255 6.12 MAXIMUM RELATIVE DENSITY VALUES OF RINGS PER 1 CM DBH CLASS FOR ALL SPACINGS AND DIFFERENT TOTAL AGES OF PLANTATION. 261 6.13 MEAN PROPORTIONS OF EARLYWOOD AT BREAST HEIGHT FOR A L L SPACINGS OVER TOTAL AGE OF PLANTATION. 262 6.14 PROPORTIONS OF EARLYWOOD PER 1 CM DBH CLASS FOR ALL SPACINGS AND DIFFERENT TOTAL AGES OF PLANTATION. 267 6.15 MEAN PROPORTIONS OF LATEWOOD AT BREAST HEIGHT FOR ALL SPACINGS OVER TOTAL AGE OF PLANTATION. ' 268 6.16 PROPORTIONS OF LATEWOOD PER 1 CM DBH CLASS FOR ALL SPACINGS AND DIFFERENT TOTAL AGES OF PLANTATION. 273 6.17 RELATIVE DENSITIES AND PROPORTIONS OF EARLYWOOD FOR TREES OF THE 1.2 M SPACING. 294 6.18 RELATIVE DENSITIES AND PROPORTIONS OF EARLYWOOD FOR TREES OF THE 2.1 M SPACING. 295 6.19 RELATIVE DENSITIES AND PROPORTIONS OF EARLYWOOD FOR TREES OF THE 3.0 M SPACING. 296 x x v i 6.20 RELATIVE 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 M SPACING. (PLOTS # 364 AND 365) . 359 2 DBH AS A FUNCTION OF AGE FOR THE 1.8 M SPACING. (PLOTS # 371 AND 372) . 360 3 DBH AS A FUNCTION OF AGE FOR THE 3.0 M SPACING. (PLOTS # 378 AND 366) . 361 4 DBH AS A FUNCTION OF AGE FOR THE 6.0 M SPACING. (PLOT # 385) . 362 5 DBH AGR AS A FUNCTION OF AGE FOR THE 1.2 M SPACING. (PLOTS # 364 AND 365) . 367 6 DBH AGR AS A FUNCTION OF AGE FOR THE 1.8 M SPACING. (PLOTS # 371 AND 372) . 368 7 DBH AGR AS A FUNCTION OF AGE FOR THE 3.0 M SPACING. (PLOTS # 378 AND 366) . 369 8 DBH AGR AS A FUNCTION OF AGE FOR THE 6.0 H SPACING. (PLOTS # 385) . 370 x x v i i 9 DBH RGR AS A FUNCTION OF AGE FOR THE 1.2 M SPACING. (PLOTS # 364 AND 365) . 375 10 DBH RGR AS A FUNCTION OF AGE FOR THE 1.8 M SPACING. (PLOTS # 371 AND 372) . 376 11 DBH RGR AS A FUNCTION OF AGE FOR THE 3.0 M SPACING. (PLOTS # 367 AND 366) . 377 12 DBH RGR AS A FUNCTION OF AGE FOR THE 6.0 M SPACING. (PLOTS # 385) . 378 APPENDIX 4 1 DBH AGR/CROWN PROJECTION RATIOS PER 1 CM DBH CLASS FOR ALL SPACINGS AND DIFFERENT AGES. 382 2 DBH AGR/CROWN SURFACE RATIOS PER 1 CM DBH CLASS FOR ALL SPACINGS AND DIFFERENT AGES. 383 3 DBH AGR/CROWN VOLUME RATIOS PER 1 CM DBH CLASS FOR { ALL SPACINGS AND DIFFERENT AGES. 384 4 DBH AGR/FOLIAGE BIOMASS RATIOS PER 1 CM DBH CLASS FOR ALL SPACINGS AND DIFFERENT AGES. 385 5 BASAL AREA AGR/CROWN WIDTH RATIOS PER 1 CM DBH CLASS FOR A L L SPACINGS AND DIFFERENT AGES. 389 6 BASAL AREA AGR/CROWN LENGTH RATIOS PER 1 CM DBH CLASS FOR ALL SPACINGS AND DIFFERENT AGES. 390 7 BASAL AREA AGR/CROWN PROJECTION RATIOS PER 1 CM DBH CLASS FOR ALL SPACINGS AND DIFFERENT AGES. 391 x x v i i i 8 BASAL AREA AGR/CROWN SURFACE RATIOS PER 1 CM DBH CLASS FOR ALL SPACINGS AND DIFFERENT AGES. 392 x x i x ACKNOWLEDGEMENTS I w i sh to thank my s u p e r v i s o r , D r . P . L . M a r s h a l l , f o r h i s h e l p , g u i d a n c e , encouragement , and suppor t f o r t h i s t h e s i s . I am a l s o g r a t e f u l to D r . G . F . Weetman who s u p e r v i s e d me d u r i n g my f i r s t two y e a r s a t U . B . C . The o t h e r members o f my graduate com-m i t t e e were D r s . J . H . G . S m i t h , D . D . Munro, and P . A . J o l l i f f e of the U n i v e r s i t y o f B r i t i s h C o l u m b i a , R . M . K e l l o g g of F o r i n t e k Canada C o r p . , and K . J . M i t c h e l l o f the B r i t i s h Columbia M i n i s t r y of F o r e s t s . T h e i r gu idance and c r i t i c i s m s were much a p p r e c i a t e d . I am a l s o g r a t e f u l to M r . L . A . J o z s a , Ms. J . R i c h a r d s and Ms. S. Johnson of F o r i n t e k Canada C o r p . f o r t h e i r a s s i s t a n c e w i t h the X - r a y d e n s i t o m e t e r . I would a l s o l i k e to thank M r . W.M. S t i e l l f o r h i s a d v i c e and encouragement . He spent n e a r l y 30 y e a r s l o o k i n g a f t e r and remeasur ing the t r e e s of the permanent sample p l o t s used i n t h i s s t u d y . I am g r a t e f u l t h a t my employer , F o r e s t r y Canada , gave me the o p p o r t u n i t y to go on s tudy l e a v e . X X X CHAPTER 1 GENERAL INTRODUCTION St u d i e s of growth and y i e l d i n f o r e s t r y have g e n e r a l l y used increment measures based on the change i n s i z e over a p e r i o d of time ( a b s o l u t e growth r a t e or AGR) to e v a l u a t e how f a s t t r e e s or stands grow. S i n g l e - t r e e or whole-stand growth models mostly p r e d i c t the growth of t r e e s or stands i n terms of AGR. Other measures of growth rate t h a t express the c a p a c i t y of p l a n t s to produce new m a t e r i a l have been used i n a g r i c u l t u r e . One such measure, r e l a t i v e growth rate (RGR), i s d e f i n e d as the increment per u n i t of m a t e r i a l a l r e a d y accumulated (e.g., g r / y e a r / g r ) . I t was c o n s i d e r e d to be very promising f o r a s s e s s i n g c o m p e t i t i o n among t r e e s by Ford (1979, 1984). The concept of RGR can a l s o be extended to p r o d u c t i v e p a r t s of the p l a n t . For i n s t a n c e , Ford (1982) used the r a t i o of b a s a l area increment to f o l i a g e weight. Ford (1979) s t a t e d that the development of s i n g l e - t r e e distance-dependent growth models c o u l d be g r e a t l y improved by u s i n g RGR. T h i s type of growth model r e q u i r e s q u a n t i f y i n g the e f f e c t of comp e t i t o r s on the growth of i n d i v i d u a l t r e e s . Compe-t i t i o n i s modelled by computing a c o m p e t i t i o n index based on the s i z e of the competing t r e e s and the d i s t a n c e s r e l a t i v e to each o t h e r . To date, i t has been d i f f i c u l t to model t h a t c o m p e t i t i o n . T h i s i s because the mechanism of c o m p e t i t i v e s t r e s s has not yet been f u l l y understood. A l s o , c o m p e t i t i o n i s not easy to separate from other f a c t o r s t h a t a f f e c t t r e e growth ( i . e . , g e n e t i c i n h e r i -tance and m i c r o c l i m a t i c c o n d i t i o n s ) . T h i s type of model i s more complex than s i n g l e - t r e e d i s t a n c e - i n d e p e n d e n t growth models. In t h i s c l a s s of model, the growth of the stand i s f i r s t p r e d i c t e d i n terms of mean DBH, b a s a l area, or volume. Then, growth i s 1 a l l o c a t e d to i n d i v i d u a l t r e e s or s i z e c l a s s e s by a p p l y i n g r u l e s based on i n d i v i d u a l (e.g., DBH) as w e l l as stand c h a r a c t e r i s t i c s (e.g., b a s a l area) (Avery and Burkhart 1 9 8 3 ; Ek and Monserud 1 9 7 5 ; Loucks et a l . 1 9 8 1 ; Smith and W i l l i a m s 1 9 8 0 ) . Growth and y i e l d s t u d i e s have g e n e r a l l y focused on measuring stem or crown growth to e v a l u a t e the e f f e c t of c o m p e t i t i o n . Very l i t t l e emphasis has been put on examining other anatomical cha-r a c t e r i s t i c s more i n t i m a t e l y r e l a t e d to p h y s i o l o g i c a l processes and on d e t e r m i n i n g i f these would respond more s e n s i t i v e l y to the c o m p e t i t i v e s t r e s s than the u s u a l measures of stem growth. The measurement of such c h a r a c t e r i s t i c s would be v e r y u s e f u l f o r de t e r m i n i n g i f e x i s t i n g or new measures of c o m p e t i t i o n i n t e n s i t y among i n d i v i d u a l t r e e s adequately r e p r e s e n t the c o m p e t i t i v e s t r e s s . In t h i s t h e s i s , i t w i l l be examined i f the r e l a t i v e d e n s i t y of wood c o n s t i t u t e s a s e n s i t i v e measure of the e f f e c t of competi t i o n . There i s no i n t e n t i n t h i s t h e s i s to d e r i v e a s i n g l e - t r e e distance-dependent growth model; however, the major problem r e l a t e d to the development of t h i s type of growth model i s c o n s i d e r e d ( i . e . , how to b e t t e r q u a n t i f y the i n t e n s i t y of c o m p e t i t i o n among t r e e s ) . I t i s expected t h a t the r e s u l t s of t h i s t h e s i s w i l l p r o v i d e i n s i g h t t h a t w i l l c o n t r i b u t e towards improving s i n g l e - t r e e distance-dependent growth models. The improvement of the p r e d i c t i v e a b i l i t y of growth models w i l l indeed i n c r e a s e t h e i r u t i l i t y . The most important advantages from a f o r e s t r y stand p o i n t a r e : (1) p r e d i c t i o n of growth and y i e l d of managed stands, ( 2 ) comparison of s i l v i c u l t u r a l t r e a t -ment s t r a t e g i e s , ( 3 ) a n a l y s e s of d i f f e r e n t diameter d i s t r i -b u t i o n s , and (4) d e l i m i t a t i o n of maximum responses to s p e c i f i c 2 treatments and of growth trends (Smith 1 9 7 2 , 1 9 7 9 , 1 9 8 0 a ) . Furthermore, a growth model i s a ve r y powerful t o o l f o r st u d y i n g stand dynamics ( T i t u s and Morton 1 9 8 5 ) . Not o n l y hypotheses on fundamental growth processes can be t e s t e d , but the e f f e c t of environmental changes such as the i n c r e a s e i n carbon d i o x i d e on f o r e s t development and s u c c e s s i o n can be e v a l u a t e d . Three major o b j e c t i v e s are addressed i n t h i s t h e s i s : (1) to determine i f a measure of e f f i c i e n c y based on RGR expresses the e f f e c t of c o m p e t i t i o n on the growth of bole c h a r a c t e r i s t i c s of red pine (Pinus  r e s i n o s a A i t . ) b e t t e r than AGR; ( 2 ) to study d i f f e r e n t measures of crown e f f i c i e n c y , and to examine whether there i s a r e l a t i o n s h i p between the value of these measures and the onset of c o m p e t i t i o n i n red p i n e ; (3) to analyse the e f f e c t of d i f f e r e n t i n i t i a l spacings on the r e l a t i v e d e n s i t y of wood i n red p i n e . The changes o c c u r r i n g i n young stands d u r i n g the t r a n s i t i o n from open-grown to stand-grown t r e e s w i l l be emphasized f o r each of these o b j e c t i v e s . Remeasurement data from a red pine s p a c i n g t r i a l l o c a t e d at the 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 were used f o r t h i s study. The data s e t was p a r t i c u l a r l y u s e f u l f o r t h i s study because the data cover a wide range of i n i t i a l s p a c i n g s , i n v o l v e remeasurements accumulated s e v e r a l years b e f o r e and a f t e r the onset of 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 measurements. Because every t r e e was i n i t i a l l y i d e n t i f i e d , i t was p o s s i b l e to a s s o c i a t e stem and crown growth data with wood r e l a t i v e d e n s i t y 3 a t the r i n g l e v e l . Major c o n t r i b u t i o n s of t h i s t h e s i s i n c l u d e : (1) a d e t a i l e d s t u d y of the development of i n d i v i d u a l t r e e c h a r a c t e r i s t i c s f o r s e v e r a l y e a r s b e f o r e and a f t e r the onset of c o m p e t i t i o n , (2) an e v a l u a t i o n of p o t e n t i a l measures of e f f i c i e n c y r a r e l y used i n f o r e s t r y , and (3) a s i m u l t a n e o u s s t u d y of the e f f e c t of compe-t i t i o n on stem growth, crown development, and wood anatomy. Even though red p i n e has been the s u b j e c t of 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 p a r t i c u l a r s t u d y because o f i t s economic imp o r t a n c e i n n o r t h e a s t e r n N o r t h A m e r i c a , and because of the v e r y good d a t a s e t a v a i l a b l e . The u n d e r s t a n d i n g o f the development of red p i n e p l a n t a t i o n s g a i n e d u s i n g measures of e f f i c i e n c y can be extended t o a s s i s t i n the management of n a t u r a l s t a n d s of red p i n e and p l a n t a t i o n s of o t h e r c o n i f e r o u s s p e c i e s . A g e n e r a l l i t e r a t u r e r e v i e w c o v e r i n g the 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 , even-aged s t a n d growth, 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 growth models, and c h a r a c t e r i s t i c s of red p i n e i s p r o v i d e d i n Chapter 2. The d a t a s e t i s d e s c r i b e d i n Chapter 3. The t h r e e main o b j e c t i v e s form the themes f o r C h a p t e r s 4, 5, and 6, r e s p e c t i v e l y . Each of these c h a p t e r s i s o r g a n i z e d i n a s i m i l a r 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 l i t e r a t u r e r e v i e w , hypotheses s t a t e m e n t s , d e s c r i p t i o n of the methodology, p r e s e n t a t i o n and d i s c u s s i o n of the r e s u l t s , and a summary and c o n c l u s i o n s . The f i n a l c h a p t e r c o n t a i n s a summary of the major r e s u l t s , a d i s c u s s i o n s u g g e s t i n g how 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 growth models c o u l d be improved u s i n g the r e s u l t s o f t h i s r e s e a r c h , and s u g g e s t i o n s f o r f u t u r e r e s e a r c h . 4 CHAPTER 2 LITERATURE REVIEW 2 . 1 - D e f i n i t i o n and Nature o f C o m p e t i t i o n C o m p e t i t i o n among t r e e s t h a t comprise a f o r e s t community i s c o n s i d e r e d a fundamental p r o c e s s o f s tand dynamics (Shugart 1984) . S e v e r a l d e f i n i t i o n s o f c o m p e t i t i o n e x i s t , but they a l l r e f e r to the same s i t u a t i o n : the shor tage o f one or s e v e r a l v i t a l r e s o u r c e s n e c e s s a r y f o r the s u r v i v a l and development of p l a n t s . Grime (1979) d e f i n e d c o m p e t i t i o n as "the tendency of n e i g h b o u r i n g p l a n t s to u t i l i z e the same quantum of l i g h t , i o n of a m i n e r a l e l ement , mo lecu le o f w a t e r , or volume of space". For Long and Smith (1984) and Tourney and K o r s t i a n (1962) , c o m p e t i t i o n o c c u r s when the r e d u c t i o n o f r e s o u r c e s a v a i l a b l e f o r every p l a n t r e s u l t s from the a g g r e g a t i o n of too many i n d i v i d u a l s . S p a t i a l c h a r a c t e r i s t i c s o f the community ( F o r d 1979; Grime 1979; Harper 1977; Krebs 1978; Leme'e 1978) , m o r p h o l o g i c a l and b i o l o g i c a l a s p e c t s o f the 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 c o n d i t i o n s o f the s i t e may a f f e c t the c o m p e t i t i v e s t a t u s o f every p l a n t (Lemee 1978; Shepherd 1986) . The c o m p e t i t i v e p r o c e s s i s c o n s i d e r e d to have the f o l l o w i n g f e a t u r e s : (1) p l a n t s o f the same d i m e n s i o n s a n d / o r l i v i n g i n the same c o n d i t i o n s o f r e source a v a i l a b i l i t y w i l l not n e c e s s a r i l y grow at the same r a t e because they may be surrounded by c o m p e t i t o r s o f d i f f e r e n t s i z e s ( F o r d 1979; R e n n o l l s and B l a c k w e l l 1988); (2) the c o m p e t i t i v e s t r e s s a c c e n t u a t e s d i f f e r e n c e s among i n d i v i d u a l s f o r parameters l i k e s i z e ( P e r r y 1985) , p o p u l a t i o n d i s t r i b u t i o n (Gates 1982) , or seed p r o d u c t i o n (Weiner and Thomas 1986); (3) the p o t e n t i a l d e v e l o p -ment t h a t a s tand may a c h i e v e depends on c o m p e t i t i o n among 5 i n d i v i d u a l s (Hamilton 1 9 6 9 ) ; ( 4 ) the s m a l l e s t i n d i v i d u a l s w i t h i n a p o p u l a t i o n are the most a f f e c t e d (Begon and Mortimer 1 9 8 6 ; Harper 1 9 7 7 ; Tourney and K o r s t i a n 1 9 6 2 ; Weiner and Thomas 1 9 8 6 ) ; and ( 5 ) the occurrence 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 of growth models based on the q u a n t i f i c a t i o n of co m p e t i t i o n among t r e e s i m p l i c i t l y assume t h a t p l a n t s a f f e c t each other p r o p o r t i o n a l l y to t h e i r s i z e . Some recent l i t e r a t u r e has r e - e v a l u a t e d the symmetric nature of c o m p e t i t i o n . A c c o r d i n g to Ford ( 1 9 8 4 ) , Ford and D i g g l e ( 1 9 8 1 ) , Huston ( 1 9 8 6 ) , Weiner ( 1 9 8 6 , 1 9 9 0 ) , Weiner and Thomas ( 1 9 8 6 ) , and Weiner et a l . ( 1 9 9 0 ) , c o m p e t i t i o n f o r s o l a r r a d i a t i o n would be one-sided (asymmetric) because l a r g e t r e e s would g r e a t l y a f f e c t the small ones, but the e f f e c t of smal l t r e e s on l a r g e ones would be d i s p r o p o r t i o n n a l l y low. On the other hand, c o m p e t i t i o n f o r s o i l r e s o u r c e s would be two-sided (symmetric) because small and l a r g e t r e e s would a f f e c t each other p r o p o r t i o n n a l l y to t h e i r s i z e s . Thus, the m a j o r i t y of the e x i s t i n g growth models have not c o n s i d e r e d that above-ground c o m p e t i t i o n i s d i f f e r e n t from below-ground c o m p e t i t i o n . Notable e x c e p t i o n s are the F o r e t model (Shugart 1984) or the model deve-loped by Tilman ( 1 9 9 0 ) . Tilman has long promoted a m e c h a n i s t i c approach based upon experiments i n which the c o m p e t i t i o n f o r s p e c i f i c r esources was i n t e n s i v e l y s t u d i e d (Tilman 1 9 7 6 , 1 9 7 7 ) . Competition can be q u a n t i f i e d by e v a l u a t i n g the d i f f e r e n c e i n growth r a t e between a stand-grown t r e e and a t r e e f r e e of c o m p e t i t i o n ( C u r t i s 1 9 7 0 ; P e r r y 1 9 8 5 ) , and by deter m i n i n g the s i z e , l o c a t i o n , age, and genotype c h a r a c t e r i s t i c s of the nei g h b o u r i n g t r e e s (Mithen et a l . 1 9 8 4 ; Weiner 1 9 8 4 ) . 6 2 . 2 - Even-aged Stand Development Three c l a s s e s of f a c t o r s i n f l u e n c e the development of t r e e s : (1) i n t r i n s i c p r o p e r t i e s of t r e e s ; ( 2 ) a b i o t i c and b i o t i c e n v i -ronment; and ( 3 ) d i s t u r b a n c e (Husch et a l . 1 9 8 2 ) . I n t r i n s i c p r o p e r t i e s c o n s i s t of the p h y s i o l o g i c a l and g e n e t i c f a c t o r s that a l l o w t r e e s to grow a t a maximum rate i n the absence of competi-t i o n or other environmental c o n s t r a i n t s . The a b i o t i c environment i n c l u d e s f a c t o r s such as c l i m a t e , p h y s i c a l or chemical c o n d i t i o n s of the s o i l , topography, or s p a t i a l arrangement of the t r e e s . The b i o t i c environment r e l a t e s to i n t e r a c t i o n s among p l a n t s such as c o m p e t i t i o n . D i s t u r b a n c e r e f e r s to any n a t u r a l or a r t i f i c i a l changes i n the s t r u c t u r e of the p o p u l a t i o n t h a t a f f e c t i t s development. The development of an even-aged stand proceeds through three major steps (Long and Smith 1 9 8 4 ) . (1) When the t r e e s are very s m a l l , the resou r c e s of the s i t e are not f u l l y e x p l o i t e d . Because there i s no c o m p e t i t i o n among t r e e s , the growth of every i n d i v i d u a l depends on the s p e c i e s , age, a b i o t i c f a c t o r s , and perhaps c o m p e t i t i o n w i t h herbaceous s p e c i e s . The v a r i a t i o n i n t r e e s i z e approximates a normal d i s t r i b u t i o n (Long and Smith 1 9 8 4 ) . ( 2 ) The i n i t i a l stand d e n s i t y and ra t e of development l a r g e l y determine the i n i t i a t i o n of i n t r a - s p e c i f i c c o m p e t i t i o n . The onset of c o m p e t i t i o n among t r e e s i n even-aged stands can be co n s i d e r e d to be the beg i n n i n g of stand growth, and would correspond to the occurrence of crown c l o s u r e or a l i t t l e a f t e r (Ford 1 9 8 4 ; Long and Smith 1 9 8 4 ) . At t h i s time, the stand begins to be s t r a t i f i e d i n t o d i f f e r e n t crown dominance c l a s s e s (Ford 1 9 7 5 ; Hamilton 1 9 6 9 ; Long and Smith 1 9 8 4 ; Mithen et a l . 1 9 8 4 ; Spurr and Barnes 1 9 8 0 ) . ( 3 ) Competition becomes more i n t e n s e 7 with age, and the s t r a t i f i c a t i o n of the f o r e s t a c c e n t u a t e s . S i z e d i s t r i b u t i o n becomes i r r e g u l a r and approaches b i m o d a l i t y (Ford 1 9 7 5 ) . However, s i z e d i f f e r e n c e s would r e s u l t more from compe-t i t i o n f o r s o l a r r a d i a t i o n (one-sided) than c o m p e t i t i o n f o r s o i l r e s o u r c e s (two-sided) (Weiner 1 9 9 0 ; Weiner and Thomas 1 9 8 6 ) . The p r o b a b i l i t y t h a t a give n t r e e wins the race and becomes dominant i s a f u n c t i o n of both i t s g e n e t i c p o t e n t i a l and chance (Shepherd 1 9 8 6 ) . A p a r t i c u l a r stage of development i s a t t a i n e d at younger ages as s i t e q u a l i t y i s improved ( D a n i e l et a l . 1 9 7 9 ) . The growth of i n d i v i d u a l t r e e s or stands, whether expressed i n diameter, h e i g h t , b a s a l area, volume, or biomass, i s charac-t e r i z e d by a si g m o i d a l form when p l o t t e d over time (Zedaker et a l . 1 9 8 7 ) . The e f f e c t of i n i t i a l d e n s i t y on the development of even-aged stands has been i n t e n s i v e l y s t u d i e d through spacing t r i a l s . B i b l i o g r a p h i e s of t h i s type of study were prepared by Eve r t ( 1 9 7 1 , 1 9 7 3 , 1 9 8 4 ) . These s t u d i e s demonstrated t h a t i n i t i a l s p a c i n g a f f e c t s growth r a t e , management p r a c t i c e s , and co s t s ( E v e r t 1 9 7 1 ) . As spaci n g i s i n c r e a s e d , i n d i v i d u a l t r e e s grow f a s t e r mostly i n diameter ( E v e r t 1 9 7 1 ; Ford 1 9 8 4 ) u n t i l a maximum i s reached by open-grown t r e e s (Tourney and K o r s t i a n 1 9 6 2 ) . A l s o , the p r o d u c t i o n of sawtimber occurs e a r l i e r i n the l i f e of the stand (Harms and L l o y d 1 9 8 1 ) . However, t o t a l p r o d u c t i o n per u n i t area (e.g., t o t a l volume) may decrease s u b s t a n t i a l l y ( E v e r t 1 9 7 1 ; Ford 1 9 8 4 ) . Stem diameter i s much more s e n s i t i v e to stand d e n s i t y than h e i g h t ( C l u t t e r e t a l . 1 9 8 3 ; D a n i e l et a l . 1 9 7 9 ; Lanner 1 9 8 5 ; Shepherd 1 9 8 6 ; Tourney and K o r s t i a n 1 9 6 2 ) . The l a t t e r would be a f f e c t e d o n l y i n ver y dense or ver y open stands ( C l u t t e r et 8 a l . 1983; D a n i e l e t a l . 1979) . Iyer and Dosen (1974) mentioned t h a t p h y s i o l o g i s t s have f a i l e d to e x p l a i n why o n l y l a t e r a l c a m b i a l c e l l s respond to i n c r e a s e d a v a i l a b i l i t y o f growing space . Lanner (1985) has sugges ted t h a t the growth of the l e a d i n g shoot i s not a f f e c t e d by s tand d e n s i t y because i t s a p i c a l meris tem draws a l l the c a r b o h y d r a t e i t needs e a r l y i n the growing season to f u n c t i o n a t i t s f u l l p o t e n t i a l . Stem form ( t a p e r ) i s g r e a t l y i n f l u e n c e d by s t o c k i n g . The b o l e s of f o r e s t - g r o w n t r e e s tend to be c y l i n d r i c a l w h i l e those of open-grown t r e e s are c h a r a c t e r i z e d by a c o n i c a l form (Shepherd 1986; Zedaker e t a l . 1987) . B a s a l a r e a development per u n i t area ( t o t a l b a s a l area) may take t h r e e forms ( D a n i e l e t a l . 1979) . I f t h e r e i s no c o m p e t i -t i o n , t o t a l b a s a l a r e a i n c r e a s e s w i t h the number o f stems, and e v e r y t r e e has a maximum growth r a t e . When c o m p e t i t i o n b e g i n s , t o t a l b a s a l a r e a s t i l l i n c r e a s e s w i t h the number of stems, but b a s a l a r e a per t r e e d e c r e a s e s . When the s tand i s overcrowded , bo th t o t a l and t r e e b a s a l area decrease w i t h the number o f stems. The same p a t t e r n a l s o a p p l i e s to t o t a l volume. The response o f an even-aged s tand to t h i n n i n g i s a f f e c t e d by age , s p e c i e s , and s i t e q u a l i t y ( C l u t t e r e t a l . 1983) . N o r m a l l y , dominant and codominant t r e e s respond more to t h i n n i n g than i n t e r m e d i a t e or s u p p r e s s e d t r e e s ( O l i v e r 1982) . However, the o p t i m a l e f f e c t i s not always c o n c e n t r a t e d on dominant t r e e s . A c c o r d i n g to C l u t t e r e t a l . (1983) and Tourney and K o r s t i a n (1962) , s u p p r e s s e d t r e e s may respond b e t t e r than dominants a t low s t a n d d e n s i t i e s because such t r e e s are v e r y much a f f e c t e d by c o m p e t i t i o n . I f a t r e e has i t s growth reduced by c o m p e t i t o r s f o r 9 a l o n g p e r i o d of t i m e , i t might not respond w e l l to an i n c r e a s e i n a v a i l a b l e growing space , or the d e l a y of response may be long (Tourney and K o r s t i a n 1962) . The a c c e l e r a t i o n of t r e e growth f o l l o w i n g t h i n n i n g may be a t t r i b u t e d to the g r e a t e r p e n e t r a t i o n of s o l a r r a d i a t i o n w i t h i n the canopy, the development of new f o l i a g e , and the i n c r e a s e d a v a i l a b i l i t y of water and n u t r i e n t s to r e s i d u a l t r e e s ( D a n i e l et a l . 1979) . 2 . 3 - 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 Growth Models 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 growth models are f l e x i b l e f o r p r e d i c t i n g s tand growth and e v a l u a t i n g the e f f e c t s of v a r i o u s management o p t i o n s (Arney 1974; A v e r y and B u r k h a r t 1983; D a n i e l s and B u r k h a r t 1975, 1988; Ek and Dudek 1980; Ek and Monserud 1975; G a r c i a 1988; Hegyi 1975; Loucks e t a l . 1981; Munro 1974; Smith and W i l l i a m s 1980; Zedaker e t a l . 1987) . A c c o r d i n g to Mi then et a l . (1984) and Smith and B e l l (1983) , w h o l e - s t a n d models l a c k f l e x i b i l i t y because they are not s e n s i t i v e enough to i n t e g r a t e the f u l l 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 and to a d e q u a t e l y r e p r e s e n t the d i f f e r e n t types of c o m p e t i t i v e s i t u a t i o n s . In a d i s c u s s i o n about e c o l o g i c a l models i n g e n e r a l , Huston et a l . (1988) p o i n t e d out t h a t models p r e d i c t i n g v a r i a b l e s for a whole p o p u l a t i o n ( e . g . , t o t a l volume) i n t r o d u c e b i o l o g i c a l b i a s because they do not r e f e r to i n d i v i d u a l s w i t h s p e c i f i c g e n e t i c c o n s t i t u t i o n s , e n v i r o n m e n t a l c o n d i t i o n s , or l o c a t i o n , and to the s y m m e t r i c a l a s p e c t of i n t e r a c t i o n s between i n d i v i d u a l s . The m a j o r i t y o f 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 growth models have the f o l l o w i n g c h a r a c t e r i s t i c s : (1) the l o c a t i o n of every t r e e must be known; (2) the growth of a p a r t i c u l a r t r e e i s computed as a f u n c t i o n of i t s p o t e n t i a l growth reduced by a 10 c o m p e t i t i o n index; and ( 3 ) the c o m p e t i t i o n indexes g e n e r a l l y depend on the s u b j e c t ' s t r e e s i z e and the l o c a t i o n and dimensions of the competitors ( A l i g et a l . 1 9 8 4 ; Ek and Monserud 1975; Loucks et a l . 1 9 8 1 ; Smith and W i l l i a m s 1 9 8 0 ) . M u l t i p l e r e g r e s s i o n techniques have been used to d e r i v e most of the eq u a t i o n s . The independent v a r i a b l e s normally c o n s i s t of the s i z e of the s u b j e c t t r e e at the begin n i n g of the p r e d i c t i o n p e r i o d , a c o m p e t i t i o n index, and sometimes a measure of d e n s i t y such as b a s a l area and a measure of s i t e q u a l i t y . The time-step over which p r e d i c t i o n s are made i s u s u a l l y 5 y e a r s . Competition indexes have been c l a s s i f i e d i n t o s i x groups by Smith and W i l l i a m s ( 1 9 8 0 ) : (1) zone of i n f l u e n c e o v e r l a p ; (2) s i z e - d i s t a n c e ; ( 3 ) number of t r e e s per u n i t a r e a ; (4) b a s a l area per u n i t a r e a ; (5) a v a i l a b l e growing space; and ( 6 ) crown o v e r l a p . Although m o d i f i c a t i o n s have been made (the major one being the i n c l u s i o n of the e f f e c t of the s i z e of the competitors on the s u b j e c t t r e e ( D a n i e l s 1 9 7 6 ) ) , most of these models are based on the c i r c u l a r zone of i n f l u e n c e concept f i r s t used i n s i m u l a t i o n by Newnham ( 1 9 6 4 ) (Arney 1972; D a n i e l s and Burkhart 1 9 8 8 ; Ek and Monserud 1975; Loucks et a l . 1 9 8 1 ) . T h i s zone r e p r e s e n t s the space i n which an i n d i v i d u a l t r e e draws resources from the s i t e to grow at i t s f u l l p o t e n t i a l . Good examples are the s t u d i e s of B e l l a (1971), Ek and Monserud (1974a, 1974b, 1979), G e r r a r d ( 1 9 6 9 ) , K e i s t e r (1971), K e i s t e r and T i d w e l l ( 1 9 7 5 ) , Newnham and Mucha (1971), and Opie ( 1 9 6 8 ) . The f o l l o w i n g authors t e s t e d the performance of some c o m p e t i t i o n indexes with t h e i r own da t a : Alemdag ( 1 9 7 8 ) , Chen and Rose ( 1 9 7 8 ) , D a n i e l s ( 1 9 7 6 ) , E r i k s o n ( 1 9 7 8 ) , G a n z l i n and Lorimer ( 1 9 8 3 ) , Ker ( 1 9 8 0 ) , Lorimer ( 1 9 8 3 ) , M a r t i n and Ek ( 1 9 8 4 ) , Mugasha ( 1 9 8 9 ) , Pukkala 11 ( 1 9 8 9 ) , Rudolph et a l . ( 1 9 8 2 ) , Smith and B e l l ( 1 9 8 3 ) , Tennent ( 1 9 7 5 ) , and Weiner ( 1 9 8 4 ) . The major assumptions of Newnham ( 1 9 6 4 ) were: (1) a t r e e growing without c o m p e t i t i o n i s c h a r a c t e r i z e d by a diameter growth ra t e of an open-grown t r e e t h a t has the same diameter; ( 2 ) the diameter increment of a p a r t i c u l a r t r e e i s reduced by an amount p r o p o r t i o n a l to the c o m p e t i t i o n i t r e c e i v e s ; and ( 3 ) m o r t a l i t y i s r e l a t e d to a l e v e l of c o m p e t i t i o n c o r r e s p o n d i n g to a diameter growth r a t e t h a t i s l e s s than a t h r e s h o l d v a l u e . The zone of i n f l u e n c e of every t r e e i s f i r s t computed as a f u n c t i o n of the crown width of an open-grown t r e e of the same diameter. In some cases, adjustments are made f o r f a c t o r s l i k e shade t o l e r a n c e or the s i z e of the co m p e t i t o r s . The c o m p e t i t i o n index of a p a r t i c u -l a r t r e e ( i . e . , the computation of the e f f e c t of competitors on i t s growth) i s q u a n t i f i e d by measuring the o v e r l a p between i t s zone of i n f l u e n c e and the zone of i n f l u e n c e of i t s c o m p e t i t o r s . An i m p l i c i t assumption of t h i s approach i s th a t two competitors a f f e c t each other p r o p o r t i o n a l l y to t h e i r s i z e . C o m p e t i t i o n indexes based on the s i z e of the s u b j e c t t r e e and c o m p e t i t o r s , d e n s i t y , b a s a l area, and a v a i l a b l e growing space have been l e s s p o p u l a r . Crown o v e r l a p has been employed by M i t c h e l l ( 1 9 6 9 , 1 9 7 1 , 1975) where the growth of s i n g l e branches was s i m u l a t e d , and by Beauregard ( 1 9 7 5 ) , Ford and D i g g l e ( 1 9 8 1 ) , and Hatch e t a l . ( 1 9 7 5 ) where the crown was represented by a cone of i n f l u e n c e . A c c o r d i n g to Ford ( 1 9 7 9 ) , P e r r y ( 1 9 8 5 ) , and Pukkala ( 1 9 8 9 ) , The m a j o r i t y of the models developed so f a r have not s u c c e s s f u l l y s i m u l a t e d the growth of t r e e s and stands. Indeed, the s t u d i e s 12 comparing v a r i o u s c o m p e t i t i o n indexes suggest t h a t these do not d i f f e r v e r y much i n t h e i r p r e d i c t i v e a b i l i t y (Mugasha 1989) . The s t u d i e s o f Alemdag (1978) , B e l l a (1971) , G a n z l i n and L o r i m e r (1983) , G e r r a r d (1969) , and L o r i m e r (1983) showed t h a t the i n i t i a l d iameter o f a g i v e n t r e e may range from e q u a l to b e t t e r than c o m p e t i t i o n indexes a t p r e d i c t i n g d iameter i n c r e m e n t . A t t h i s p o i n t , i t becomes e s s e n t i a l to ask whether the a c t u a l models i n t e g r a t e enough b i o l o g i c a l u n d e r s t a n d i n g of c o m p e t i t i o n to a l l o w f o r good p r e d i c t i o n s . A c c o r d i n g to P e r r y (1985) , m o d e l l i n g the growth of i n d i v i d u a l t r e e s i s not easy because p a s t c o m p e t i t i v e i n t e r a c t i o n s , v a r i o u s g e n e t i c p o t e n t i a l s , d i f f e r e n t m i c r o e n v i -ronments , the s y m m e t r i c a l n a t u r e o f c o m p e t i t i o n (whether compe-t i t i o n i s a o n e - s i d e d or t w o - s i d e d p r o c e s s ) , and o t h e r i n t e r a c t i o n s are a l l f a c t o r s t h a t make s tand growth v e r y complex. The development o f t h i s type o f growth model i s s t i l l i n i t s i n f a n c y ( F o r d 1979) . 2 . 4 - C h a r a c t e r i s t i c s o f Red P ine Red p i n e grows i n the n o r t h e r n p o r t i o n o f the N o r t h American c o n t i n e n t below the b o r e a l f o r e s t on both s i d e s o f the G r e a t Lakes and the S t . Lawrence R i v e r ( R u d o l f 1981) . T h i s means t h a t , i n Canada , i t i s found from s o u t h e a s t Mani toba to Newfoundland i n the G r e a t L a k e s - S t . Lawrence and A c a d i a n f o r e s t r e g i o n s ( O n t a r i o M i n i s t r y o f N a t u r a l Resources 1986) . In Newfoundland, i t i s found o n l y on some s i t e s . Fewer than twenty s tands were i d e n t i f i e d by R o b e r t s (1985) i n t h r e e g e o g r a p h i c areas i n the n o r t h e r n p a r t o f the p r o v i n c e . A c c o r d i n g to B a s s e t t (1985) , R u d o l f (1981) , and S t i e l l (1978) , a good edaph ic environment f o r red p i n e c o n s i s t s o f w e l l d r a i n e d sandy s o i l s t h a t o r i g i n a t e from g l a c i o - f l u v i a l or a e o l i a n d e p o s i t s . I t i s l e s s f r e q u e n t l y found ! 13 on l a c u s t r i n e d e p o s i t s and f i n e t i l l s o i l s (Rudolf 1 9 8 1 ; S t i e l l 1 9 7 8 ) . Red pine grows w e l l on s o i l s with a ph v a r y i n g from 4 . 5 to 6 . 0 , bulk d e n s i t y v a r y i n g from 1 . 1 0 to 1 . 4 0 grams per cubi c c e n t i m e t e r , c a t i o n exchange c a p a c i t y v a r y i n g from 1 to 1 1 m.s. per 1 0 0 grams, s i l t - p l u s - c l a y content v a r y i n g from 1 0 to 4 0 % , and with 1 . 7 % of o r g a n i c matter content (Fowells 1 9 6 5 ) . I t s c l i m a t i c regime i s c h a r a c t e r i z e d by moderately warm to warm summers, c o l d w i n t e r s , and low to moderate p r e c i p i t a t i o n (Rudolf 1 9 8 1 ) . Although the s e e d l i n g s can grow w e l l at a l e v e l of s o l a r r a d i a t i o n as low as 3 5 % , t h i s s p e c i e s r e q u i r e s f u l l l i g h t a f t e r t h i s stage to achieve i t s maximum growth (Fowells 1 9 6 5 ; O n t a r i o M i n i s t r y of N a t u r a l Resources 1 9 8 6 ) . However, the s e e d l i n g s do not grow w e l l when c o m p e t i t i o n from brush i s important (Fowells 1 9 6 5 ) . I t i s norm a l l y found i n even-aged pure stands i n O n t a r i o , Quebec, and the no r t h e r n Lake S t a t e s ( S t i e l l 1 9 7 8 ) . In the n o r t h e a s t e r n p a r t of i t s d i s t r i b u t i o n , i t may be a s s o c i a t e d with Jack pine (Pinus banksiana Lamb.) and white pine (Pinus strobus L.) and may o c c a s i o n n a l l y be found i n hardwood stands ( S t i e l l 1 9 7 8 ) . Although i t i s mostly found i n p l a n t a t i o n s , n a t u r a l stands w i l l p e r s i s t on s i t e s s u b j e c t to f i r e s or other major d i s t u r b a n c e s ( O n t a r i o M i n i s t r y of N a t u r a l Resources 1 9 8 6 ) . Red pine i s b a s i c a l l y a s e r i a l s p e c i e s . A c c o r d i n g to Fowell s ( 1 9 6 5 ) , the normal e c o l o g i c a l s u c c e s s i o n i n the Lake S t a t e s c o n s i s t s of the s u c c e s s i v e e s t a b l i s h e m e n t of Jack p i n e , red p i n e , white p i n e , and n o r t h e r n hardwoods. However, i t may be a sub-climax s p e c i e s on l e s s f e r t i l e s i t e s . In e a s t e r n Canada and n o r t h e r n New England, i t may be r e p l a c e d by spruce, f i r , or hemlock i n the course of s u c c e s s i o n . 1 4 The y i e l d o f red p i n e v a r i e s w i t h age, s i t e q u a l i t y , and s t o c k i n g . Because i t has been w i d e l y p l a n t e d i n both Canada and U n i t e d S t a t e s , s e v e r a l s t u d i e s have a d d r e s s e d i t s p r o d u c t i v i t y . The r e p o r t o f B a s s e t t (1985) c o n t a i n s much i n f o r m a t i o n i n a condensed form f o r v a r i o u s c o n d i t i o n s o f age, s i t e q u a l i t y , and s t o c k i n g . S e v e r a l s p a c i n g t r i a l s and t h i n n i n g exper iments have been r e p o r t e d ( e . g . , B e l l a and D e F r a n c e s c h i 1974, 1980; B e r r y 1965, 1969, 1970, 1977; B i c k e r s t a f f 1946; Bramble e t a l . 1949; Buckman 1962a, 1962b; Byrnes and Bramble 1955; H e i b e r g et a l . 1959; Lundgren 1981; R a l s t o n 1954; Schantz -Hansen 1956; S t i e l l 1953, 1957, 1964, 1970, 1978; S t i e l l and B e r r y 1977; Von A l t h e n and S t i e l l 1965, 1982; Von A l t h e n et a l . 1978) . These exper iments demonstrated t h a t d iameter growth i n c r e a s e s p r o p o r t i o n a l l y w i t h the a v a i l a b i l i t y o f growing space r e s u l t i n g from l a r g e r i n i t i a l s p a c i n g or t h i n n i n g . Diameter i s c l o s e l y r e l a t e d to crown d i m e n s i o n s , which i n t u r n depend on s p a c i n g ( R u d o l f 1981; S t i e l l 1962, 1966, 1978; S t i e l l and B e r r y 1977) . Crown w i d t h and l e n g t h can a l s o v a r y c o n s i d e r a b l y f o l l o w i n g t h i n n i n g ( B e r r y 1965) . The form of the stem i s v e r y s e n s i t i v e to d e n s i t y ; a c y l i n d r i c a l form w i l l r e s u l t from c l o s e d s t a n d s , and a c o n i c a l one from open s tands ( B e r r y 1970; S t i e l l 1978; S t i e l l and B e r r y 1977) . S t i e l l (1978) a s s o c i a t e d form c l a s s w i t h crown deve lopment . F u l l crown development r e s u l t s i n a c o n i c a l form o f the stem w h i l e c y l i n d r i c a l forms are deve lopped when crown development i s i n h i b i t e d . H e i g h t growth has been found to be i n s e n s i t i v e to s tand d e n s i t y , except when the s tand has been s u b j e c t to heavy t h i n n i n g ( B e r r y 1969; Engle and Smith 1951) . W h i l e wider s p a c i n g s produce t r e e s o f g r e a t e r volume, t o t a l s tand volume i n c r e a s e s w i t h c l o s e r s p a c i n g s ( S t i e l l and 15 B e r r y 1977) . D e t a i l e d growth and y i e l d i n f o r m a t i o n may be found i n B e r t r a n d (1976) , B o l g h a r i and B e r t a n d (1984) , Marty (1984) , O n t a r i o M i n i s t r y o f N a t u r a l Resources (1986) , and B e r r y (1977) . T h i s s p e c i e s has been w i d e l y used f o r p l a n t a t i o n s i n both Canada and U n i t e d S t a t e s . A c c o r d i n g to R a i l e (1984) , l a r g e r e f o r e s t a t i o n p r o j e c t s 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 i n t h i s c e n t u r y r e s u l t e d i n areas where 35 to 85% of the p l a n t a t i o n s were red p i n e . Because o f i t s good p r o d u c t i v i t y on sandy s o i l s and a b i l i t y to r e s i s t s e v e r a l d i s e a s e s and i n s e c t i n f e s t a t i o n s , i t was c o n s i d e r e d as a prime s p e c i e s f o r p l a n t i n g i n s o u t h e r n O n t a r i o ( O n t a r i o M i n i s t r y o f N a t u r a l Resources 1986) . Red p i n e had the f i f t h l a r g e s t number o f s e e d l i n g s produced i n O n t a r i o from 1984 to 1988 ( r e p r e s e n t i n g 4.4% of the t o t a l number) ( O n t a r i o M i n i s t r y o f N a t u r a l Resources 1988) . In Quebec, i t came i n s i x t h and seventh i n 1984-1985 and 1985-1986 r e s p e c t i v e l y for the numbers o f s e e d l i n g s p l a n t e d , r e p r e s e n t i n g 3.2% and 4.2% ( M i n i s t e r e de l ' E n e r g i e e t des Ressources 1987) . The f o l l o w i n g p r o d u c t s are n o r m a l l y o b t a i n e d from red p i n e : pulpwood, sawlogs , b o l t w o o d , loghouse l o g s , p o l e s , and p i l i n g ( O n t a r i o M i n i s t r y of N a t u r a l Resources 1986) . 16 CHAPTER 3 DESCRIPTION OF DATA The d a t a se t used i n t h i s s tudy came from a s p a c i n g t r i a l e s t a b l i s h e d i n 1953 w i t h 2+2 t r a n s p l a n t s i n the v i c i n i t y of the 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 . The s o i l i s deep and i s composed of f i n e to medium windblown s a n d . The s i t e index i s p r e d i c t e d to be 24.4 m at 50 y e a r s of age from seed ( S t i e l l and B e r r y 1973, 1977) . The i n i t i a l s p a c i n g s were: 1 .2x1 .2 m, 1 .5x1 .5 m, 1 .8x1 .8 m, 2 .1x2 .1 m, 2 .4x2 .4 m, 3 .0x3 .0 m, and 4 .3x4 .3 m. For the f i r s t 5 s p a c i n g s , two c i r c u l a r sample p l o t s o f 0.101 ha were e s t a b l i s h e d . E v e r y t r e e was c l e a r l y i d e n t i f i e d and l o c a t e d on a map. A l s o , a p l a n t a t i o n w i t h 2 .1x2 .1 m s p a c i n g was t h i n n e d to 4 .3x4 .3 m i n 1962 and another p l a n t a t i o n w i t h 3 . 0 x 3 . 0 m s p a c i n g was t h i n n e d to 6 .0x6 .0 m i n 1965. Measurements were taken on e v e r y t r e e a t ages 13, 18, 23, 28, and 33. W h i l e DBH was measured on e v e r y t r e e , t o t a l h e i g h t was measured o n l y on subsample t r e e s r e p r e s e n t i n g the range of d i s t r i b u t i o n i n d iameter w i t h i n e v e r y s p a c i n g . W i t h i n every sample p l o t , a subse t o f t r e e s were s e l e c t e d on which d e t a i l e d measurements were made: DBH, t o t a l h e i g h t , crown w i d t h , crown l e n g t h , and t a p e r d a t a . These were measured e v e r y year from ages 13 to 24, e v e r y two y e a r s from ages 24 to 30, and at age 33. These t r e e s are r e f e r r e d to as the i n t e n s i v e l y measured d a t a i n t h i s s t u d y . B a s i c s t a t i s t i c s (minimum, maximum, mean, v a r i a n c e , and number o f t r e e s ) o f each sample p l o t are g i v e n i n T a b l e 1 o f Appendix 1 f o r each v a r i a b l e measured. 17 S e v e r a l c l i m a t i c parameters have been m o n i t o r e d d a i l y a t the 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 f o r many y e a r s . C l i m a t i c i n f o r m a t i o n c o v e r i n g the months from May to September i n c l u s i v e were e x t r a c t e d . The f o l l o w i n g v a r i a b l e s were r e t a i n e d : mean minimum t e m p e r a t u r e , mean t e m p e r a t u r e , mean maximum t e m p e r a t u r e , r a i n f a l l , s n o w f a l l , t o t a l p r e c i p i t a t i o n , d e g r e e - d a y s above 10 and 25 deg . C , and number of days o f f r o s t . A summary of these c l i m a t i c v a r i a b l e s i s g i v e n on T a b l e 2 o f Appendix 1. The d i f f e r e n t growth parameters s t u d i e d w i l l be c o r r e l a t e d w i t h the c l i m a t i c v a r i a b l e s . 18 CHAPTER 4 STAND DEVELOPMENT STUDY 4.1- I n t r o d u c t i o n Even though the goal of t h i s t h e s i s i s not to develop a growth model, t h i s study does c o n s i d e r a l t e r n a t i v e hypotheses and new a n a l y t i c a l techniques t h a t c o u l d improve the development of s i n g l e - t r e e distance-dependent models. The techniques proposed are based on measures of e f f i c i e n c y . The s p e c i f i c o b j e c t i v e s of t h i s p o r t i o n of the study a r e : (1) to study the development of t r e e s o r i g i n a t i n g from a wide range of spacings i n terms of AGR and RGR befo r e and a f t e r the onset of c o m p e t i t i o n ; (2) to examine i f RGR r e f l e c t s the occurrence of c o m p e t i t i o n b e t t e r than AGR; (3) to t e s t the major assumption of the zone of i n f l u e n c e concept; (4) to t e s t a l t e r n a t i v e hypotheses on p o t e n t i a l growth. T h i s chapter begins with a l i t e r a t u r e review on RGR, a statement of hypotheses, and a d e s c r i p t i o n of 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 the r e s u l t s and d i s c u s s i o n s e c t i o n which i s d i v i d e d i n t o three main p a r t s . The f i r s t p a r t compares AGR and RGR.in terms of DBH, b a s a l area, h e i g h t , and volume u s i n g the c l a s s i c a l approach. The second p a r t compares AGR and RGR u s i n g the f u n c t i o n a l approach. The t h i r d p a r t addresses the p o t e n t i a l growth rate of stand-grown t r e e s b e f o r e the onset of c o m p e t i t i o n . S e v e r a l hypotheses are t e s t e d based upon both AGR and RGR. 19 4 . 2 - L i t e r a t u r e Review on R e l a t i v e Growth Rate A major c r i t i c i s m of e x i s t i n g 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 growth models i s t h e i r i n a b i l i t y to r e p r e s e n t c o m p e t i t i o n i n terms of p r o c e s s ( i . e . , the c o n d i t i o n a l p a r t i t i o n o f a v a i l a b l e r e s o u r c e s among i n d i v i d u a l t r e e s as c o m p e t i t i o n takes p l a c e ) ( F o r d 1979) . In o t h e r words , the use o f AGR i n t h i s type o f model i s a p p a r e n t l y not s u i t a b l e f o r a s s e s s i n g c o m p e t i t i o n ( F o r d 1984; Zedaker e t a l . 1987) , F o r d (1979, 1984) , C a n n e l l e t a l . (1984) and F o r d and D i g g l e (1981) f e l t t h a t the response to c o m p e t i t i v e s t r e s s by a g i v e n t r e e s h o u l d be e v a l u a t e d w i t h a measure o f e f f i c i e n c y t h a t c h a r a c t e r i z e s i t s c a p a c i t y f o r growth ( i . e . , to produce new m a t e r i a l ) . RGR c o n s t i t u t e s such a measure ( E r i k s o n 1976; F o r d 1975, 1979, 1982, 1984; Harper 1977; Hunt 1978, 1982) . F o r d (1975) s t a t e d t h a t i t measures the " r e l a t i v e share o f r e s o u r c e s per u n i t s i z e " . I t may a l s o be c o n s i d e r e d as an a n a l y t i c a l t o o l t h a t a l l o w s compar i son of the increment of p l a n t s or groups o f p l a n t s t h a t d i f f e r i n i n i t i a l s i z e , g e n e t i c i n h e r i t a n c e , age , or e n v i r o n m e n t a l c o n d i t i o n s (Buchman and Benz ie 1988; Kramer and K o z l o w s k i 1979; L e d i g 1974; R a d o s e v i c h and O s t e r y o u n g 1987) . When e x p r e s s e d as a d i f f e r e n t i a l e q u a t i o n , RGR i s d e f i n e d a s : RGR - (1/W)(dW/dT) where W r e p r e s e n t s the q u a n t i t y o f m a t e r i a l a t t ime T . I t a l s o may be d e s c r i b e d as the i n c r e a s e i n m a t e r i a l a d j u s t e d by the accumula ted m a t e r i a l , or i n c r e a s e per u n i t s i z e per u n i t t ime ( E r i k s o n 1976; Hunt 1978, 1982) . A c c o r d i n g to F i t t e r and Hay (1987) , i t measures the p r o d u c t i v e c a p a c i t y i n d e p e n d e n t l y o f 20 secondary p r o c e s s e s such as d e f e n c e , s u p p o r t , or r e p r o d u c t i o n . RGR may i n d i c a t e when c o m p e t i t i o n takes p l a c e i n a young even-aged s t a n d ( F o r d 1982, 1984 and F o r d and D i g g l e 1981) . The measurement o f b a s a l a r e a RGR i n a S i t k a spruce ( P i c e a s i t c h e n s i s (Bong. ) C a r r . ) s t a n d , b e f o r e and a f t e r what they c o n s i d e r e d to be the onset o f c o m p e t i t i o n (crown i n t e r l o c k ) , a l l o w e d them to conc lude t h a t a l l the t r e e s had the same e f f i c i e n c y up to the p o i n t where they s t a r t e d compet ing . F o l l o w i n g the o c c u r r e n c e of c o m p e t i t i o n , the e f f i c i e n c y of the t r e e s under h i g h s t r e s s s u b s t a n t i a l l y d e c r e a s e d r e l a t i v e to those under low s t r e s s . Burdon and Harper (1980) were a l s o i n t e r e s t e d i n t e s t i n g t h i s h y p o t h e s i s w i t h i n a p o p u l a t i o n of T r i f o l i u m repens L . They m o n i t o r e d the growth of 48 p l a n t s i n s e p a r a t e p o t s . Even though 45 p l a n t s d i d not s t a t i s t i c a l l y d i f f e r , they c o n c l u d e d t h a t RGR v a r i e s among the i n d i v i d u a l s o f a s p e c i e s when t h e r e i s no compe-t i t i o n . However, t h e i r c o n c l u s i o n c o u l d have been d i f f e r e n t : when the o r i g i n a l p l a n t s were c o l l e c t e d on the f i e l d , a p a r t i -c u l a r p l a n t was s e l e c t e d f o r the exper iment o n l y when i t was s u r r o u n d e d by o t h e r p l a n t s w i t h i n a r a d i u s o f 10 cm. T h e r e f o r e , the a u t h o r s might have c o l l e c t e d p l a n t s t h a t had a l r e a d y expe-r i e n c e d c o m p e t i t i o n , r e s u l t i n g i n d i f f e r e n t RGRs. As p r e v i o u s l y ment ioned , RGR measures the increment per u n i t s i z e per u n i t t i m e . T h i s r a t i o may a l s o be v iewed as measur ing the growth as a p e r c e n t a g e . In f o r e s t r y , growth p e r c e n t formulas based upon compound i n t e r e s t have been d e r i v e d . The g e n e r a l form i s : 21 p - \/(Wn/Wo) - 1 x 100 where p i s growth p e r c e n t , Wo the t r e e s i z e ( e . g . , DBH, h e i g h t , or biomass) a t b e g i n n i n g o f growth p e r i o d , Wn the t r e e s i z e at the end of the growth p e r i o d , and n the number o f u n i t s o f t i m e . Other formulas based on compound i n t e r e s t have a l s o been deve -l o p e d i n o r d e r to f a c i l i t a t e the computa t ion o f growth p e r c e n t (Husch et a l . 1982; Spurr 1952) . The a p p l i c a b i l i t y of compound i n t e r e s t formulas l i e s i n the f a c t t h a t t r e e or s tand growth o c c u r s as a g e o m e t r i c p r o g r e s s i o n ( B e l y e a 1959); the increment p e r c e n t i s a d j u s t e d by the amount of m a t e r i a l t h a t i s added over each u n i t o f t ime (Chapman and Meyer 1949; Husch et a l . 1982) . The computa t ion o f growth p e r c e n t for i n d i v i d u a l t r e e s or s tands has been r a r e i n f o r e s t r y ; however, some e f f o r t has been devoted to d e r i v i n g a n d / o r comparing e a s y - t o - u s e f o r m u l a s t h a t approximate compound i n t e r e s t (Be lyea 1959; Chapman and Meyer 1949; G e v o r k i a n t z 1927; R u d o l f 1930) . In these s t u d i e s , growth p e r c e n t was i n v e r s e l y r e l a t e d to t r e e s i z e . Growth p e r c e n t has a l s o been computed f o r s t a n d s . Kohmo (1980) computed growth percentage based on s imple i n t e r e s t f o r v a r i o u s f o r e s t s tands i n F i n l a n d . A l s o u s i n g a s imple i n t e r e s t a p p r o a c h , G o t t f r i e d (1978) and Embry and G o t t f r i e d (1971) e s t i -mated growth p e r c e n t i n b a s a l a r e a over 5 -year p e r i o d s f o r every DBH s i z e c l a s s by computing the r a t i o o f p e r i o d i c annua l b a s a l a r e a growth per a c r e to i n i t i a l b a s a l area per a c r e . T h e i r r e s u l t s i n d i c a t e d a decrease i n growth p e r c e n t w i t h an i n c r e a s e i n DBH s i z e c l a s s . They p o i n t e d out t h a t a compound i n t e r e s t f o r m u l a s h o u l d be used f o r l o n g e r p e r i o d s o f t i m e . 22 Avery and Burkhart ( 1 9 8 3 ) , G o t t f r i e d ( 1 9 7 8 ) , and Embry and G o t t f r i e d ( 1 9 7 1 ) mentioned t h a t growth percent c o u l d be used to p r e d i c t growth f i v e or ten years ahead by m u l t i p l y i n g the a c t u a l stand volume by i t s growth p e r c e n t . R e s u l t i n g p r e d i c t i o n s may be good i f i t i s assumed t h a t growth percent remains r e l a t i v e l y c o nstant f o r the p e r i o d c o n s i d e r e d . T h i s procedure was c o n s i -dered to be i n a p p r o p r i a t e by Chapman and Meyer ( 1 9 4 9 ) , Husch et a l . ( 1 9 8 2 ) , and Spurr ( 1 9 5 2 ) because i t i n v o l v e s e x t r a p o l a t i n g a r a t i o known to decrease with age. A c c o r d i n g to Chapman and Meyer ( 1 9 4 9 ) , growth percent may be used as a b a s i s f o r d e t e r m i n i n g i f t r e e s or stands grow at a d e s i r e d r a t e . However, i t has not been used much as a t o o l to compare the s o c i a l s t a t u s of t r e e s w i t h i n a stand or to compare the growth of d i f f e r e n t stands. RGR a l s o presumes t h a t p l a n t s accumulate biomass at compound i n t e r e s t . However, i t d i f f e r s from growth percent formulas by p o s t u l a t i n g t h a t growth occurs at a continuous r a t e . The b a s i c e q u a t i o n i s : RGR x (Tn - To) Wn = Wo x e The f i r s t d e r i v a t i v e of t h i s formula r e s u l t s i n the RGR equation p r e v i o u s l y s t a t e d . 4 . 3 - Hypotheses Many of the s t u d i e s mentioned above suggest t h a t RGR i s more a p p r o p r i a t e than AGR f o r a s s e s s i n g c o m p e t i t i o n i n even-aged stands. Even though the concept of RGR has e x i s t e d f o r a long time (e.g. Blackman 1 9 1 9 ) , i t has been used o n l y r e c e n t l y i n f o r e s t r y to study stand dynamics and draw c o n c l u s i o n s on how t r e e s i n t e r a c t (Buchman and Benzie 1 9 8 8 ) . Besides the s t u d i e s 23 mentioned above, those of C a n n e l l et a l . ( 1 9 8 4 ) and Pe r r y ( 1 9 8 5 ) are worth mentioning. Except f o r the s t u d i e s of Brand et a l . ( 1 9 8 7 ) and Brand and Magnussen ( 1 9 8 8 ) , t h i s type of study has not been performed u s i n g a wide range of spacings and long-term remeasurement d a t a . Some hypotheses r e l a t e d to RGR s t i l l need to be t e s t e d over time, both b e f o r e and a f t e r the onset of compe-t i t i o n . Furthermore, no attempt has been made to compare t r e e and stand development i n terms of RGR with t h a t of AGR u s i n g the same data s e t . The f i r s t h y p o t h e s i s t h a t w i l l be t e s t e d i s based on the main c o n c l u s i o n of Ford ( 1 9 8 2 , 1984) and Ford and D i g g l e ( 1 9 8 1 ) t h a t was d i s c u s s e d above: a l l t r e e s comprising a stand have the same RGR be f o r e the onset of c o m p e t i t i o n . Using the spac i n g t r i a l data d e s c r i b e d i n Chapter 3 , i t w i l l be p o s s i b l e to observe whether t h i s h y p o t h e s i s i s true s e v e r a l years before the onset of co m p e t i t i o n . A l s o , the g r e a t e r the spa c i n g , the l a t e r t h a t RGR should s t a r t v a r y i n g . I f t h i s h y p o t h e s i s i s r e j e c t e d , then the f o l l o w i n g one w i l l be c o n s i d e r e d . Before the onset of compe-t i t i o n , RGR i s r e l a t e d to t r e e s i z e : the bi g g e r the t r e e , the more e f f i c i e n t i t i s . T h i s i m p l i e s t h a t both AGR and RGR d e s c r i b e t r e e growth s i m i l a r l y . I f the f i r s t h y p o t h e s i s i s not r e j e c t e d , i t c o u l d have a major impact on the development of s i n g l e - t r e e distance-dependent growth models. As t h i s type of model uses open-grown t r e e data to e s t imate the p o t e n t i a l growth r a t e of stand-grown t r e e s , the computation of i n d i v i d u a l t r e e growth would be c o n s i d e r a b l y s i m p l i f i e d . However, i f i t i s found t h a t a l l t r e e s do not have the same RGR befo r e the onset of c o m p e t i t i o n , other hypotheses r e l a t i v e to the e s t i m a t i o n of the p o t e n t i a l growth rate of 24 stand-grown t r e e s from the growth r a t e o f open-grown t r e e s w i l l be c o n s i d e r e d . F i r s t o f a l l , i t becomes i m p o r t a n t t o t e s t the major 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 growth models: the p o t e n t i a l i n c r e m e n t 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 an open-grown t r e e o f the same d i a m e t e r (Ek and Monserud 1975; Loucks e t a l . 1981). T h i s h y p o t h e s i s w i l l a l s o be t e s t e d u s i n g RGR: 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 stand-grown t r e e i n terms o f RGR i s e q u a l t o t h a t of an open-grown t r e e o f the same d i a m e t e r . A f u r t h e r s e t o f hypotheses emphasizes age w i t h some ad j u s t m e n t 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 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 an open-grown t r e e of the same age, but a d j u s t e d by the r e s p e c t i v e d i a m e t e r s o f b o t h t y p e s o f t r e e s : AGRn = AGRo X (DBHn/DBHo) where AGRn and AGRo are the AGRs o f the stand-grown and open-grown t r e e s and DBHn and DBHo t h e i r r e s p e c t i v e d i a m e t e r s a t b r e a s t h e i g h t ; - 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 stand-grown t r e e i n terms o f RGR i s e q u a l t o t h a t o f an open-grown t r e e o f the same age, but a d j u s t e d by the r e s p e c t i v e d i a m e t e r s o f b o t h t y p e s o f t r e e s : RGRn =• RGRo X (DBHn/DBHo) where RGRn and RGRo are the RGRs o f the stand-grown and open-grown t r e e s r e s p e c t i v e l y ; - 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 stand-grown t r e e i n terms of AGR i s e q u a l t o t h a t o f an open-grown t r e e o f the same age, but a d j u s t e d by 25 i t s e f f i c i e n c y : AGRn - (RGRn/RGRo)[t - 1 ] X RGRo[t] X DBH. T h i s e q u a t i o n i s based on the r a t i o of RGR of stand-grown and open-grown t r e e s o b t a i n e d at the l a s t increment p e r i o d . I t i s assumed to be a good estimate of the f u t u r e r a t i o of both RGRs. The l a s t s e t of hypotheses i s based on the o r i g i n a l assumption of Newnham ( 1 9 6 4 ) : - The p o t e n t i a l diameter increment of a stand-grown t r e e i n terms of AGR i s equal to t h a t of an open-grown t r e e of the same diameter and age; - The p o t e n t i a l diameter increment of a stand-grown t r e e i n terms of RGR i s equal to th a t of an open-grown t r e e of the same diameter and age. 4 . 4 - M a t e r i a l and Methods The data used f o r t h i s study were d e s c r i b e d i n the pre v i o u s c h a p t e r . The v a r i a b l e s a n a l y s e d were:, DBH, b a s a l area, h e i g h t , and t o t a l t r e e volume. DBH and b a s a l area were both analysed because of the d i f f e r e n t s i z e r e l a t i o n s h i p s t h a t they d e s c r i b e w i t h i n p o p u l a t i o n s of t r e e s . For i n s t a n c e , Lorimer ( 1 9 8 3 ) and Steneker and J a r v i s ( 1 9 6 3 ) o b t a i n e d h i g h e r c o r r e l a t i o n s between c o m p e t i t i o n indexes and AGRs when c o m p e t i t i o n from surrounding t r e e s was expressed i n terms of b a s a l area r a t h e r than DBH. West ( 1 9 8 3 ) o b t a i n e d b e t t e r r e s u l t s w i t h r e l a t i o n s h i p s p r e d i c t i n g b a s a l area increment from i n i t i a l diameter than w i t h those p r e d i c t i n g diameter increment. Tree volumes were computed u s i n g Smalian's formula. Data were from t r e e s t h a t had t h e i r stem measured every 4 f e e t ( 1 . 2 3 m). Two methods were used to 26 d e s c r i b e t r e e growth: the c l a s s i c a l approach and the f u n c t i o n a l approach (Hunt 1 9 7 8 , 1 9 8 2 ) . 4 . 4 . 1 C l a s s i c a l Approach The c l a s s i c a l approach c o n s i s t s of computing growth r a t e s from the mean of two s u c c e s s i v e measurements (Hunt 1 9 8 2 ) . I t i n v o l v e s the a n a l y s i s of data i n a d i s c r e t e manner. Emphasis i s put on the comparison of growth v a l u e s at f i x e d p o i n t s i n time; the r a t i o s d e r i v e d d e s c r i b e the mean growth rate over the time p e r i o d c o n s i d e r e d . I f W(i) r e p r e s e n t s a giv e n dimension, f o r i n s t a n c e DBH, at time T ( i ) , then AGR i s computed as: AGR - (W(2) - W(l)} /{T ( 2 ) - T ( l ) } . R e l a t i v e growth rate i s obt a i n e d from: RGR - {In W(2) - In W(l)} /{T ( 2 ) - T ( l ) } . In order to compare the spa c i n g s , data from the two sample p l o t s at every s p a c i n g were merged. S i n g l e c l a s s i f i c a t i o n a n a l y s e s of v a r i a n c e f o r DBH, h e i g h t , and volume were performed. When these were s i g n i f i c a n t , means of i n d i v i d u a l spacings were compared wi t h Tukey's t e s t (Sokal and Rohlf 1 9 8 1 ) . A nested a n a l y s i s of v a r i a n c e was used to compare AGR and RGR f o r the d i f f e r e n t s p a c i n g s . At each growth p e r i o d analysed, every t r e e had i t s AGR and RGR a s s o c i a t e d with i t s DBH. These increment v a l u e s were then s u b d i v i d e d i n t o 1 cm DBH c l a s s e s . The DBH c l a s s e s o b t a i n e d c o n s t i t u t e d the DBH n e s t i n g f a c t o r of the nested a n a l y s i s of v a r i a n c e . T h i s procedure was used to d e t e r -mine whether or not RGR was s i g n i f i c a n t l y d i f f e r e n t f o r t r e e s of d i f f e r e n t s i z e s w i t h i n any s p a c i n g . I f the DBH n e s t i n g f a c t o r 27 was not s i g n i f i c a n t b e f o r e the onset o f c o m p e t i t i o n , but became s i g n i f i c a n t l y i m p o r t a n t f o l l o w i n g the onset o f c o m p e t i t i o n , then the h y p o t h e s i s " a l l the t r e e s have the same RGR b e f o r e the onset o f c o m p e t i t i o n " c o u l d not be r e j e c t e d . Means f o r the i n d i v i d u a l s p a c i n g s were compared w i t h T u k e y ' s t e s t . These a n a l y s e s were per formed u s i n g the s t a t i s t i c a l package "BIOME" ( S o k a l and R o h l f 1981) . In o r d e r to have an a p r i o r i i d e a o f crown c l o s u r e , a c l o s u r e index was computed f o r e v e r y s p a c i n g and age because crown development o f red p i n e i s much a f f e c t e d by s t a n d d e n s i t y ( S t i e l l 1970; S t i e l l and B e r r y 1977) . The index was based upon the f o l l o w i n g p r i n c i p l e : i f the a r e a o f the crown base on a t r e e o c c u p i e s a t l e a s t 78% of the square d e f i n e d by the s p a c i n g ( i . e . [ [crown w i d t h ] 2 x n / 4 ] / g r o w i n g space] x 100) , then i t w i l l o v e r l a p w i t h a d j a c e n t crowns . The crown c l o s u r e index r e f l e c t e d the p r o p o r t i o n o f t r e e s o c c u p y i n g more than 78% of t h i s s q u a r e . T h i s i s an i m p e r f e c t index because i t does not i n d i c a t e the degree o f o v e r l a p p i n g , but r a t h e r the p r o p o r t i o n o f crowns t h a t may do s o . However, i t was c o n s i d e r e d a p r a c t i c a l way to show the p r o g r e s s i o n o f crown c l o s u r e w i t h s p a c i n g and age . The p r o p o r t i o n s o f t r e e s t h a t had o v e r l a p p i n g crowns f o r the v a r i o u s s p a c i n g s and age c o m b i n a t i o n s were d e t e r m i n e d (Tab le 4 . 1 ) . These d a t a d i s p l a y e d the expec ted t r e n d s : (1) crown c l o s u r e i n c r e a s i n g w i t h age, and (2) crown c l o s u r e o c c u r r i n g l a t e r a t the wider s p a c i n g s . 28 T a b l e 4 . 1 : P r o p o r t i o n s o f t r e e s (%) t h a t have t h e i r crown o v e r l a p p i n g t h e i r growing space area as d e f i n e d by the s p a c i n g . S p a c i n g Age 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 0 2 2 12 16 21 47 58 66 86 88 93 93 6 . 0x6 .0 0 0 0 0 0 0 1 6 20 73 84 97 The e f f e c t o f crown c l o s u r e on i n d i v i d u a l t r e e s was a l s o examined by computing t h e i r crown r a t i o (crown l e n g t h / t r e e h e i g h t ) over age . A c c o r d i n g to F a r r a r (1984) and S p r i n z and B u r k h a r t (1987) , crown r a t i o r e f l e c t s the p h o t o s y n t h e t i c p r o d u c -t i v i t y o f a t r e e . Crown r a t i o i s a l s o c o n s i d e r e d to be a measure o f t r e e v i g o r t h a t r e l a t e s to changes o c c u r r i n g when crown c l o s u r e takes p l a c e (Holdaway 1986) . Be fore crown c l o s u r e o c c u r s , t r e e s have l i v e branches a l l a l o n g the stem. When the canopy c l o s e s , branches s t a r t d y i n g from below. The h i g h e r the s t a n d d e n s i t y , the f a s t e r crown r e c e s s i o n takes p l a c e . N o r m a l l y , the s m a l l e r the t r e e , the more r a p i d l y crown r a t i o would 29 d e c r e a s e . I t i s a p p r o p r i a t e to a s s o c i a t e the changes i n the c o m p e t i t i v e s t a t u s o f the d i f f e r e n t s p a c i n g s to crown r a t i o because (1) the crown development of red p i n e i s v e r y s e n s i t i v e to s tand d e n s i t y , (2) there i s a v e r y c l o s e r e l a t i o n s h i p between crown d imens ions and t r e e d iameter ( S t i e l l 1970; S t i e l l and B e r r y 1977) , and (3) the s tudy of S t i e l l (1970) sugges ts t h a t the growth of red p i n e on the s t u d i e d s i t e i s l i m i t e d more by above -ground c o m p e t i t i o n than be low-ground c o m p e t i t i o n . The crown r a t i o v a l u e s o f a l l t r e e s were c l a s s i f i e d i n t o seven groups w i t h the f o l l o w i n g l i m i t s : 0 to 9%, 10 to 24%, 25 to 39%, 40 to 59%, 55 to 69%, 70 to 84%, and 85 to 100%. The p e r c e n t o f t r e e s i n these c l a s s e s f o r e v e r y s p a c i n g and s e v e r a l ages are shown i n F i g u r e 1 o f Appendix 2. I t was assumed t h a t t r e e s w i t h crown r a t i o >85% were growing as open-grown t r e e s u n a f f e c t e d by the presence of o t h e r crowns. T h i s l i m i t i s l o g i c a l because a f u l l crown t r e e does not n e c e s s a r i l y imply a crown r a t i o o f 100%. The f i r s t whor l o f branches o f young red p i n e t r e e s i s not n e c e s s a r i l y a t the s o i l l e v e l and the branches are g e n e r a l l y d i r e c t e d upward ( S t i e l l 1962) . T h i s l i m i t was a l s o d e t e r m i n e d by s u r v e y i n g young open-grown red p i n e t r e e s l o c a t e d around C h a l k R i v e r . S e v e r a l of these t r e e s had a crown r a t i o of around 85%. As ment ioned i n Chapter 3, s e v e r a l c l i m a t i c parameters have been m o n i t o r e d d a i l y a t the 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 f o r many y e a r s . The f l u c t u a t i o n s i n growth d a t a were examined i n r e l a t i o n to these v a r i a b l e s . A p r i n c i p a l component a n a l y s i s u s i n g the c o v a r i a n c e m a t r i x as i n p u t was per formed to de termine the importance o f e v e r y c l i m a t i c v a r i a b l e on y e a r - t o - y e a r v a r i a b i l i t y . 30 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 a cur v e t o a s e t of o b s e r v a t i o n s over time (Hunt 1 9 8 2 ) . Emphasis i s on the c o n t i -nuous n a t u r e o f growth. i t s p r i m a r y u t i l i t y i s not f o r deve-l o p i n g m e c h a n i s t i c models ( i . e . , s e t s of m a t h e m a t i c a l models t h a t i n t e r a c t t o s i m u l a t e a n a t u r a l s y s t e m ) , but f o r f o r m i n g mathe-m a t i c a l f u n c t i o n s ( m e c h a n i s t i c ( e . g . , Chapman-Richards e q u a t i o n ) or e m p i r i c a l ( e . g . , p o l y n o m i a l e q u a t i o n ) e q u a t i o n s ) t o r e p r e s e n t the o b s e r v a t i o n s o f the phenomenon under i n v e s t i g a t i o n , and d e r i v i n g i n s t a n t a n e o u s v a l u e s o f i n c r e m e n t . The main advantages a re (Hunt 1 9 7 8 , 1 9 8 2 ) : (1) l a r g e s e t s o f o b s e r v a t i o n s may be e x p r e s s e d as c o n c i s e m a t h e m a t i c a l formu-l a t i o n s , ( 2 ) i t i s p o s s i b l e t o e v a l u a t e the v a l u e o f a growth r a t e a t any p o i n t i n t i m e , and ( 3 ) i t becomes r e l a t i v e l y easy t o compare d i f f e r e n t s e t s o f o b s e r v a t i o n s . Because the d a t a used f o r t h i s s t u d y c o n s i s t o f o b s e r v a t i o n s over t i m e , 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 n t h i s c o n t e x t , i t s use i m p l i e s t h a t a cur v e i s f i t t e d f o r e v e r y t r e e under i n v e s t i g a t i o n , t h a t i s : W - f ( T ) . where W r e p r e s e n t s a growth v a r i a b l e l i k e DBH. The AGR e q u a t i o n i s 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 a t i v e o f a growth e q u a t i o n . D e r i v i n g a RGR e q u a t i o n i n v o l v e s f i r s t f i t t i n g the l o g a r i t h m of the s e l e c t e d growth v a r i a b l e , t h a t i s : ln(W) - f ( T ) . 31 The RGR e q u a t i o n i s the f i r s t d e r i v a t i v e o f t h i s e q u a t i o n . The f u n c t i o n a l approach was a p p l i e d t o DBH f o r the 1 . 2 m, 1 . 8 m, 3 . 0 m, and 6 . 0 m s p a c i n g s . Ten t r e e s c o v e r i n g the range of DBH a t ages 13 and 33 were s e l e c t e d w i t h i n e v e r y sample p l o t . Because o f the shape of the c u r v e s w i t h i n the age range, and a l s o t o reduce the amount o f c o m p u t a t i o n , p o l y n o m i a l f u n c t i o n s were used. T h i s approach a l l o w e d a t e m p o r a l comparison o f b o t h AGR and RGR, and improved d i s p l a y o f the e v o l u t i o n o f the s o c i a l p o s i t i o n o f the t r e e s . I f the t r e e s have the same RGR b e f o r e the on s e t o f c o m p e t i t i o n , a l l the c u r v e s s h o u l d be s i m i l a r up t o the ons e t o f c o m p e t i t i o n . To f a c i l i t a t e the s t u d y o f the e v o l u t i o n o f the s o c i a l p o s i t i o n o f the t r e e s , c u m u l a t i v e i n c r e m e n t s , AGRs and RGRs of e v e r y sample t r e e w i t h i n a p l o t were ranked from the h i g h e s t t o the l o w e s t v a l u e s a t ages 13 and 3 0 . For each p l o t , the d i f f e -rence between the ranks a t b o t h ages was computed f o r e v e r y t r e e . Then, the mean f o r a p l o t was c a l c u l a t e d . For a t o t a l o f 10 t r e e s , the mean change i n rank i s 0 i f th e y a l l keep the same rank a t b o t h ages. I f a l l the t r e e s have t h e i r rank t o t a l l y i n v e r t e d , the mean change i n rank i s 5 . Thus, t h i s i n d e x v a r i e s from 0 t o 5 . The c l o s e r t o 0 , the more the t r e e s t e n d t o keep the same rank. The c l o s e r t o 5 , the more the t r e e s t e n d t o have d i f f e r e n t r a n k s . 4 . 4 . 3 - E s t i m a t i n g the P o t e n t i a l Growth Rate o f Stand-grown Trees T h i r t e e n open-grown t r e e s were measured i n the v i c i n i t y o f the s p a c i n g t r i a l . The s e l e c t e d t r e e s met the s p e c i f i c a t i o n s o f K r a j i c e k e t a l . ( 1 9 6 1 ) : (1) crown development was u n a f f e c t e d by c o m p e t i t i o n , ( 2 ) crown r a t i o was e q u a l or n e a r l y e q u a l t o one, 32 (3) the l o c a t i o n of the l o n g e s t branches was a t the base o f the crown, and (4) t h e r e was an absence o f d e f e c t s caused by n a t u r a l f a c t o r s such as i n s e c t i n f e s t a t i o n s or by a r t i f i c i a l ones such as p r u n i n g . Increment cores were taken a t stump h e i g h t (15 cm) and b r e a s t h e i g h t . The growth h i s t o r y o f e v e r y t r e e was r e c o n s -t r u c t e d by measur ing the annua l growth r i n g s , and by e s t i m a t i n g bark w id ths f o l l o w i n g the methods o f Von A l t h e n (1963) . T h i s p a r t o f the s tudy was l i m i t e d to the e v a l u a t i o n of the p o t e n t i a l growth r a t e o f s tand-grown t r e e s b e f o r e t h e i r growth was reduced by c o m p e t i t i o n . The s tand-grown t r e e s were s e l e c t e d i n the 4.3 m and 6.0 m s p a c i n g s from ages 13 to 17 and 16 to 22 r e s p e c t i v e l y , b e f o r e crown c l o s u r e . These t r e e s were v e r y l i k e l y not s u b j e c t to c o m p e t i t i o n a t those ages . For t e s t i n g the d i f f e -r e n t h y p o t h e s e s , e v e r y s tand-grown t r e e was a s s o c i a t e d w i t h an open-grown t r e e t h a t had the same DBH, age, or RGR (depending upon the h y p o t h e s i s t e s t e d ) and t h e i r increments compared. Comparisons were made between the increment o f open-grown t r e e s and s tand-grown t r e e s f o r both the 4.3 m and 6.0 m s p a c i n g s and f o r one- and f i v e - y e a r p e r i o d s . The one -year increments f o r both s p a c i n g s were compared w i t h open-grown t r e e s u s i n g a Student t e s t . I t was not p o s s i b l e to use the same t e s t f o r the f i v e - y e a r increment p e r i o d s because the d a t a c o v e r e d o n l y 1 p e r i o d of f i v e y e a r s . 33 4 . 5 - R e s u l t s and D i s c u s s i o n 4 . 5 . 1 - C l a s s i c a l Approach 4 . 5 . 1 . 1 - DBH and B a s a l A r e a Development 4 . 5 . 1 . 1 . 1 - C u m u l a t i v e Increment i n DBH No s i g n i f i c a n t d i f f e r e n c e i n mean DBH was found a t ages 1 3 and 1 4 among a l l s p a c i n g s ( T a b l e 4 . 2 ; F i g u r e 4 . 1 ) . Some s i g n i -f i c a n t d i f f e r e n c e s o c c u r r e d a t age 1 5 . However, t h i s appears to be an anomaly. The 1 . 2 m s p a c i n g was not s i g n i f i c a n t l y d i f f e r e n t from the 4 . 3 m one, but was d i f f e r e n t from the 2 . 1 m and 3 . 0 m ones. Even though the means o f the l a t t e r two s p a c i n g s were s l i g h t l y l a r g e r t h a n the 4 . 3 m one, th e y d i d not d i f f e r s i g n i -f i c a n t l y from i t . T h i s anomaly may be a t t r i b u t e d t o p a r t i c u l a r t r e n d s e x i s t i n g b e f o r e the on s e t o f c o m p e t i t i o n . From age 1 6 onwards, DBH i n c r e a s e d as s p a c i n g was e n l a r g e d . A l s o , d i f f e -r e n c e s became more a c c e n t u a t e d w i t h age: groups of s p a c i n g s t h a t d i d not d i f f e r s i g n i f i c a n t l y became s m a l l e r i n s i z e w i t h age. Some r e s u l t s o f t h i s s p a c i n g t r i a l have a l r e a d y been r e p o r t e d by S t i e l l and B e r r y ( 1 9 7 7 ) . T a b l e 4 . 2 and F i g u r e 4 . 1 update t h i s i n f o r m a t i o n from age 2 3 t o age 3 3 . S t i e l l and B e r r y c o n c l u d e d t h a t the d i a m e t e r growth r a t e was d e c r e a s i n g w i t h a r e d u c t i o n i n the a r e a a v a i l a b l e f o r each t r e e . These r e s u l t s c o r r e s p o n d t o what has been g e n e r a l l y o b s e r v e d : as s p a c i n g i s i n c r e a s e d , the mean d i a m e t e r i n c r e a s e s ( A v e r y and B u r k h a r t 1 9 8 3 ; C l u t t e r e t a l . 1 9 8 3 ; D a n i e l e t a l . 1 9 7 9 ; E v e r t 1 9 7 1 ; Tourney and K o r s t i a n 1 9 6 2 ) . 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 the r e s u l t s o f r e d p i n e s p a c i n g t r i a l s r e p o r t e d by B e l l a and D e F r a n c e s c h i ( 1 9 7 4 , 1 9 8 0 ) , Bramble e t a l . ( 1 9 4 9 ) , Byrnes and 3 4 TABLE 4 . 2 : Mean DBHs (cm) f o r a l l s p a c i n g s over age . S p a c i n g Ages (m) 13 14 15 16 17 18 19 20 21 22 23 24 26 28 30 33 U) Ul 1 .2x1 .2 Mean 4.434 5.428 5.927 6.787 7.495 7.915 8.352 8.821 9.292 9.514 9 .927 10.440 11.121 11 .615 12.073 13.454 a * a a a a a a a a a a a a a a a N 64** 65 66 63 61 61 61 61 59 59 55 52 48 46 45 37 1 . 5 x 1 . 5 Mean 4.802 5.858 6.651 7.498 8.318 8.940 9.593 10.238 10.690 11 .005 11.322 11.684 11.937 12 .287 12.687 13.211 a a ab ab ab ab ab ab ab ab ab a a a a a N 64 66 66 65 62 62 61 61 60 59 58 57 57 56 55 54 1 .8x1 .8 Mean 4 .825 6.122 7.103 8.119 8.978 9.591 10.507 11.223 11.763 12.063 12 .321 12.612 12.954 13 .739 14.119 14.506 a a ab abc abc abc be be be be be ab ab ab ab a N 59 60 60 59 58 58 58 57 57 57 57 57 57 54 54 54 2 . 1 x 2 . 1 Mean 4 .967 6.329 7.377 8.576 9.544 10.339 11.261 12.064 12.702 13.353 13.824 14.414 14.862 15 .495 16.161 17.111 a a b be bed be be c d cd c d cd be b b be b N 58 61 62 62 61 61 61 61 61 60 59 58 58 57 56 54 2 . 4 x 2 . 4 Mean 4.654 6.159 7.328 8.810 9.965 10.852 12.078 13.198 14.124 14.876 15.428 16 .209 16.951 17.653 18.304 19.216 a a ab be cd cd cd de d d d c c b N 55 56 58 58 58 58 58 58 58 58 58 57 57 57 57 56 3 . 0 x 3 . 0 Mean 5.004 6.729 7.995 9 .575 10.934 12.053 13.655 15.071 16.264 17.214 18.110 19.041 20.271 21.348 22.233 23.359 a a b e d d d d f e e e d N 54 55 58 59 59 59 58 58 58 58 58 58 58 58 58 58 4 . 3 x 4 . 3 Mean 4.743 6.137 7.052 8.742 9.959 11.303 13.133 14.979 16.471 17 .837 19.143 20.636 22.680 24.446 25.875 27.521 a a ab be cd c d d e f e e e d H 54 57 59 57 58 58 58 58 58 57 56 56 56 56 56 56 6 . 0 x 6 . 0 Mean - 10.786 12.612 14.122 16.198 18.371 20.196 21.803 23.416 25 .267 28.310 30 .631 32.390 34.724 d H - - 96 96 95 95 95 94 94 94 94 94 94 94 94 * : The 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 saae 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 o f p r o b a b i l i t y of 0 . 0 5 . * * : Nuaber of t r e e s t h a t were l e i s u r e d . At ages 13 and 14, the t r e e s t h a t had not r e a c h e d b r e a s t h e i g h t were not measured . 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 AGE 36 Bramble (1955) , Lundgren (1981) and Schantz -Hansen (1956) . 4 . 5 . 1 . 1 . 2 - A b s o l u t e Growth Rate Mean AGR f o r DBH and b a s a l area g e n e r a l l y i n c r e a s e d w i t h s p a c i n g ( T a b l e s 4 . 3 , 4 .4 ; F i g u r e 4 . 2 ) . E x c e p t i o n s to t h i s t r e n d o c c u r r e d a t e a r l y ages and wide s p a c i n g s and at o l d e r ages and v e r y c l o s e s p a c i n g s . The 3.0 m s p a c i n g had g r e a t e r AGRs than the 4.3 m s p a c i n g u n t i l the age 16. T h i s s i t u a t i o n may be a t t r i b u t e d to s l i g h t d i f f e r e n c e s t h a t e x i s t e d among the s tands b e f o r e the onset o f c o m p e t i t i o n . As c o m p e t i t i o n took p l a c e , the mean AGR of the 3.0 m s p a c i n g was reduced w e l l , below t h a t f o r the 4.3 m s p a c i n g . In the second c a s e , mean AGR of the 1.5 m s p a c i n g was lower than t h a t of the 1.2 m s p a c i n g from ages 26 to 30. However, these d i f f e r e n c e s were so s m a l l t h a t they were not s i g n i f i c a n t . Crown c l o s u r e c l a s s e s are a l s o i n d i c a t e d on both t a b l e s . They show t h a t the denser the s t a n d , the e a r l i e r crown c l o s u r e o c c u r r e d . The t h r e e denses t s tands showed h i g h crown c l o s u r e s from ages 13 to 15. However, as was p r e v i o u s l y n o t e d , t h e r e was no s i g n i f i c a n t d i f f e r e n c e i n d iameter among the s p a -c i n g s a t ages 13 and 14. The absence o f s i g n i f i c a n t d i f f e r e n c e among the c l o s e s t and l a r g e s t s p a c i n g s a t these two ages suggests t h a t c o m p e t i t i o n had not y e t taken p l a c e i n any o f the s p a c i n g s . I t thus appears t h a t crowns can o v e r l a p to some degree b e f o r e t r e e s s t a r t c o m p e t i n g . T h i s phenomenon has a l r e a d y been r e p o r t e d by Newnham (1964) f o r a young , dense p l a n t a t i o n o f D o u g l a s - f i r (Pseudotsuga M e n z i e s i i ( M i r b . ) F r a n c o ) , and by Cochrane and Ford (1978) f o r S i t k a s p r u c e . 37 Table 4.3: Mean AGRs in DBH (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 1.05 $* 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 « 1.5x1.5 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 « 4.3x4.3 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 # 6.0x6.0 - - - 1.82 < 1.55 < 2.07 < 2.17 < 1.81 < 1.61 < 1.61 > 1.85 > 1.52 > 1.16 $ 0.88 $ 0.78 « *: Crown closure classes: (Proportion of trees whose crowns occupy more than 78% of the square spacing). (%) 0 : < 1 - 20: > 21 - 40: + 41 - 60: & 61 - 85: $ 86 - 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 32.64 29.51 25.47 24.87 27.57 19.24 17.89 15.47 13.77 > + + & & $ $ # # # # # # # # 4.3x4.3 15.27 14.17 20.99 21.11 23.42 36.11 40.57 37.26 36.11 37.97 46.42 34.81 32.91 28.49 23.25 < < < > > > > + & & $ # # # # 6.0x6.0 - 34.33 33.03 49.61 59.14 54.55 52.86 56.96 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 - 20: > 21 - 40: + 41 - 60: & 61 - 85: $ 86 - 100: # FIGURE 4 . 2 : DBH AGR DATA SUPERIMPOSED 0 CLIMATIC VARIABLES A V E R A G E A O B ( D B H ) F O R A L L S P A C I N O S O V E R A G E L E O C N P — 1 - 2 X 1 2 M o  1 . 5 X 1 . 9 M a •* 1 . 8 X i a M o — a . i X 2 . 1 M  a . * X 2 . 4 M • — 3 . 0 X 3.0 M  *.3 X + .3 M — e . o X e . o M J O 33 LS cd . O , UJ SEP o 1— 3 2 4 . 0 2 2 . 4 J O 8 1 9 . 2 1 7 . S 1 S . O 1 4 . 4 1 2 . 8 1 1 . 2 9 . 6 8 . 0 L E G E N D A — M E A N M A X I M U M T E M P E R A T U R E O — M E A N M I N I M U M T E M P E R A T U R E o — M E A N T E M P E R A T U R E 1 2 1 S 1 8 2 1 2 1 2 4 T O T A L A G E 2 7 3 0 33 40 F I GURE 4 . 2 : (CONT I NUED) 33 L E G E N D — M A Y - J U N E o — S I P T t M i em T O T A L A G E 41 The absence of c o m p e t i t i v e s t r e s s at ages 13 and 14 c o r r e s -ponded to a stage where the m a j o r i t y of t r e e s had crown r a t i o v a l u e s g r e a t e r than 85% ( F i g u r e 1 of Appendix 2 ) . Ten t r e e s out of 83 i n the 1.2 m spa c i n g had a crown r a t i o lower than 85% at age 13. However, e i g h t of these were dead two or three years l a t e r and two had crown r a t i o s of 84% and 81% r e s p e c t i v e l y . At age 14, 13 t r e e s had crown r a t i o s lower than 85%. F i v e were dead one or two years l a t e r , s i x of the remaining t r e e s had crown r a t i o ranging between 81% and 85%, and the other two had crown r a t i o s of 78% and 79% r e s p e c t i v e l y . For a l l the other spacings at these two ages, o n l y some t r e e s had crown r a t i o s lower than 85% and they were a l l g r e a t e r than 80%. The f a c t t h a t o n l y some t r e e s had crown r a t i o s lower than 85% does not suggest the e f f e c t of c o m p e t i t i o n , but r a t h e r that they were g e n e t i c a l l y i n f e r i o r or were a f f e c t e d by i n j u r i e s . D e s p i t e i r r e g u l a r i t i e s , mean DBH AGR tended to decrease over time f o r a l l spacings ( F i g u r e 4.2). Increases can, however, be observed a t ages 15, 18, 19 and 23. These f l u c t u a t i o n s were prob a b l y not caused by c o m p e t i t i o n because the same p a t t e r n s were common to a l l s p a c i n g s . A l s o , the i r r e g u l a r amplitudes of the v a r i a t i o n s suggest f a c t o r s t h a t can s u b s t a n t i a l l y v a r y from year to y e a r . C l i m a t i c f a c t o r s such as temperature are known to f l u c t u a t e y e a r l y (Spurr and Barnes 1980). The growth f l u c t u a -t i o n s c o u l d be a s s o c i a t e d with c e r t a i n c l i m a t i c v a r i a b l e s monitored y e a r l y near the study s i t e (Table 2 of Appendix 1; F i g u r e 4.2). 42 A p r i n c i p a l component a n a l y s i s was u n d e r t a k e n to group the y e a r s i n t o r e l a t i v e l y s i m i l a r c l i m a t i c c o n d i t i o n s , g i v e n the o v e r a l l v a r i a b i l i t y . T h i s t e c h n i q u e h e l p e d to de termine the c l i m a t i c f l u c t u a t i o n s most a s s o c i a t e d w i t h those o f growth . The a n a l y s i s i n d i c a t e d t h a t 99 p e r c e n t o f the v a r i a t i o n was i n c l u d e d i n the f i r s t two components , w i t h 75 p e r c e n t i n the f i r s t one ( T a b l e 4 . 5 ) . T h e r e f o r e , a n a l y s e s focused on the f i r s t two components . The e i g e n v a l u e s showed h i g h l o a d i n g s on t o t a l p r e c i -p i t a t i o n and number o f d e g r e e - d a y s above 10 deg . C f o r both components . The t h i r d most i m p o r t a n t v a r i a b l e was the number of d e g r e e - d a y s above 25 deg . C . A graph o f the f i r s t two components i s shown i n F i g u r e 4 . 3 . Ages were aggrega ted i n t o groups h a v i n g s i m i l a r v a l u e s f o r components 1 and 2. For each g r o u p , the mean v a l u e s f o r p r e c i -p i t a t i o n and d e g r e e - d a y s above 10 and 25 deg . C are g i v e n . Whi le t o t a l p r e c i p i t a t i o n g e n e r a l l y i n c r e a s e d i n the d i r e c t i o n o f the two arrows drawn on F i g u r e 4 . 3 , the number o f d e g r e e - d a y s above 10 d e g . C and 25 deg . C d e c r e a s e d . I n c r e a s e s i n AGR at ages 18 and 23 c o r r e s p o n d e d w i t h a l a r g e i n c r e a s e i n t o t a l p r e c i p i t a t i o n compared to the p r e v i o u s y e a r , but s l i g h t d e c r e a s e s i n d e g r e e - d a y s above 10 and 25 deg . C ( F i g u r e 4 . 2 ) . The s l i g h t i n c r e a s e a t age 15 c o r r e s p o n d e d to a s m a l l i n c r e a s e i n mean maximum, mean minimum, and mean tempe-r a t u r e s , and to a s u b s t a n t i a l i n c r e a s e i n d e g r e e - d a y s above 10 deg . C . However, t h i s year was c h a r a c t e r i z e d by a d e c l i n e i n t o t a l p r e c i p i t a t i o n . Even i f t h e r e were s u b s t a n t i a l f l u c t u a t i o n s i n both t o t a l p r e c i p i t a t i o n and d e g r e e - d a y s a f t e r age 24, AGR d e c r e a s e d r e g u l a r l y . T h i s was p r o b a b l y because AGRs were computed from remeasurements made e v e r y two y e a r s , a v e r a g i n g out 43 T a b l e 4 . 5 : Summary of the p r i n c i p a l component a n a l y s i s under-t a k e n w i t h the c l i m a t i c v a r i a b l e s . E i g e n v a l u e P r o p o r t i o n C u m u l a t i v e P r i n c i p a l P r i n c i p a l P r i n c i p a l P r i n c i p a l P r i n c i p a l P r i n c i p a l P r i n c i p a l P r i n c i p a l component 1 component 2 component 3 component 4 component 5 component 6 component 7 component 8 8 4 2 7 . 1 1 2 8 5 9 . 5 2 1 0 . 2 6 6 3 0 31 76 09 0 . 0 3 0 . 0 0 0 . 7 4 5 2 9 0 . 2 5 2 8 9 0 . 0 0 0 9 1 0 . 0 0 0 5 6 0 . 0 0 0 3 3 0 . 0 0 0 0 0 0 . 0 0 0 0 0 0 . 0 0 0 0 0 0 0 0 0 74529 99819 99910 99966 0 . 9 9 9 9 9 1 1 1 00000 00000 00000 V a r i a b l e s E i g e n v e c t o r s P r i n c i p a l component I I I Number o f days o f f r o s t i n June Number o f days o f f r o s t i n September Mean maximum t e m p e r a t u r e (Deg. C.) Mean minimum t e m p e r a t u r e (Deg. C.) Mean t e m p e r a t u r e (Deg. C.) T o t a l p r e c i p i t a t i o n (mm) Number o f degree-days above 10 Deg. C, Number o f degree-days above 25 Deg. C, 0 . 0 0 8 2 8 1 0 . 0 0 2 4 7 1 006115 001522 - 0 . 0 0 3 6 8 1 0 . 9 0 4 3 0 7 - 0 . 4 2 6 2 0 4 - 0 . 0 2 1 2 5 9 •0 -0 - 0 . 0 0 9 5 3 2 - 0 . 0 1 7 2 3 0 0 . 0 0 4 3 0 9 0 . 0 0 8 3 0 4 0 . 0 0 6 4 0 5 0 . 4 2 6 6 5 2 903793 024705 0 0 44 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 COMPONENT *: Rainfall precipitations (mm), and degree-days above 10°C and 25 °C. Means of each group. 4 5 the annual e f f e c t of c l i m a t i c c o n d i t i o n s . In any case, these r e s u l t s suggest t h a t mean AGR i s a f f e c t e d mostly by f l u c t u a t i o n s i n p r e c i p i t a t i o n . Even though the f l u c t u a t i o n s i n degree-days were comparable to those i n p r e c i p i t a t i o n , they were not as w e l l r e l a t e d to the v a r i a t i o n i n mean AGR. T h i s suggests t h a t , as long as a c e r t a i n minimum i s maintained, the number of degree-days does not become a l i m i t i n g f a c t o r . Even though the same p a t t e r n s of v a r i a t i o n o c c u r r e d independently of s p a c i n g at ages 1 8 and 2 3 , the magnitude of f l u c t u a t i o n d i m i n i s h e d as s p a c i n g decreased ( F i g u r e 4 . 2 ) . T h i s suggests t h a t the i n f l u e n c e of c l i m a t i c f a c t o r s on mean AGR decreases with i n c r e a s e i n the i n t e n s i t y of c o m p e t i t i o n . Few s t u d i e s have examined r e l a t i o n s h i p s between stand growth and c l i m a t i c f a c t o r s . D e n d r o c h r o n o l o g i c a l s t u d i e s t h a t c o r r e l a t e r i n g width and c l i m a t i c data have been more popu l a r . Complete reviews of the s u b j e c t may be found i n Bednarz ( 1 9 8 2 ) and F r i t t s ( 1 9 7 4 , 1 9 7 6 , 1 9 8 2 ) . Comparisons of the above r e s u l t s may be made with the s t u d i e s of Braekke and Kozlowski ( 1 9 7 5 ) and Braekke et a l . ( 1 9 7 8 ) . They measured the d a i l y r a d i a l growth of 3 8 - y e a r - o l d red pine i n Northern Wisconsin f o r a complete growing season, and s i m u l t a n e o u s l y monitored 1 9 environmental v a r i a b l e s . They a l s o concluded t h a t p r e c i p i t a t i o n was more c l o s e l y r e l a t e d to stem growth than temperature. AGR f o r DBH and b a s a l area by 1 cm DBH c l a s s at ages 1 3 , 1 8 , 2 4 , and 3 0 are d i s p l a y e d i n F i g u r e s 4 . 4 and 4 . 5 . The r e s u l t s of two l e v e l - n e s t e d a n a l y s e s of v a r i a n c e (anova) on AGR are l i s t e d i n T a b les 4 . 6 and 4 . 7 . For a g i v e n age, a l l the spacings were no r m a l l y i n c l u d e d i n the anova. However, i f h e t e r o s c e d a s t i c i t y was i m p o s s i b l e to e l i m i n a t e with data t r a n s f o r m a t i o n , the 4 6 F I G U R E 4 . 4 : DBH A G R s AS A F U N C T I O N OF DBH S I Z E C L A S S FIGURE 4 . 4 . 1 : AGE 13 FIGURE 4 . 4 . 2 : AGE 18 2 . 2 0 i 2.03 1 .86 < • ^ 1 . 5 2 -2 O —^1.35-— y 0.50 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 2. 30 2.07 1.84 K LSI* \ 1 . J 8 1 O w 1 . 1 5 I CD Q 0.92 ^ 0 . 6 9 0.46 0.23 — • — i — 1 — i — • — i — • i 1—r~ 4 3 6 7 8 DBH SIZE CLASS (CM) FIGURE 4 . 4 . 3 : AGE 2 4 10 o . o o / « / > . * / a - SPACING k * = SPACING / ' ' y T * « - SPACING ' / / 0 = SPACING / 7 = SPACING J / . = SPACING <rV * = SPACING o = SPACING LEGEND " 1.2X1.2 M 1.5X1.5 M 1.8X1.8 M 2.1X2.1 M 2 . 4 X 2 . 4 M 3 . 0 X 3 . 0 M 4 . 3 X 4 . 3 M 6 . 0 X 6 . 0 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 1.80 i .62 i . 44 1 . 26 I .08 a >-\ 1 o ^ 0 . 9 0 I CO Q 0 . 7 2 \X ^ 0 . 5 4 0.36 0. 18 0 . 0 0 ^ ; LEGEND A = SPACING: 1 .2X1.2 M * = SPACING: 1 . 5 X 1 . 5 M SPACING: 1 . 8 X 1 . 8 M 0 = SPACING: 2.1X2.1 M 7 - SPACING: 2 . 4 X 2 . 4 M * = SPACING: 3 . 0 X 3 . 0 M * = SPACING: 4 . 3 X 4 . 3 M t o = SPACING: 6 . 0 X 6 . 0 M A A /< / V / ^ v A / 0.870 0. 783 i ; \ / * / V 0 . 0 0 0 ^ i ' M 7 , V LEGEND f\ V 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 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 J4 38 DBH SIZE CLASS (CM) DBH SIZE CLASS (CM) 47 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 \ CN 25.5 22.0 18.5 1.0 LEGEND A = SPACING: 1.2X1.2 M 0 = SPACING: 1.5X1.5 M 0 = SPACING: 1.8X1.8 M 0 = SPACING: 2.1X2.) M 7 = SPACING: 2.4X2.4 M . = SPACING: 3.0X3.0 M * = SPACING: 4.3X4.3 M - 1 — 1 — r -2 3 - 1 — • — i — • — r -4 5 8 7 8 DBH SIZE CLASS (CM) FIGURE 4.5.3: AGE 24 9 10 71.0 63.9 56. 8 tr 3 49.7 >-\ CN 42. * * O 35. < 2 8 . m 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 / , M / * / f / r / r DBH SIZE CLASS (CM FIGURE 4.5.4: AGE 30 87.0 78.3 69.8 tr y » 2 o 43.3 < 34.8 CD tr 26. 1 17.4 8.7 0.0 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 l\J v K * * / 10 13 20 25 DBH SIZE CLASS (CM) 50 45 40 3 3 9 25 < 20 GO < 10 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 \ / 8 \ / • / /i | i / /1 ' I i / ; / V i . / 1 1 10 14 18 22 26 30 34 38 DBH SIZE CLASS (CM) 48 T a b l e 4 . 6 : T w o - l e v e l n e s t e d anova t e s t s f o r AGR i n DBH ( c m / y e a r ) . Age S p a c i n g s i n c l u d e d (m) DBH c l a s s S p a c i n g D . F . F D . F . F 13 1. 2 ; 1 .5;1 . 8 ; 3 . 0 29/205 4 .49* 3 /26 33 .72* 13 2 . 1 ; 2 .4,-4 .3 2 2 /142 4 .77* 2/20 0 . 08n 14 1. 2 ; 1 . 5;1 . 8 ; 2 . 1 ; 2 . 4 ; 3 . 0 5 5 /301 2 .76* 5 /44 53 .02* 14 2 . 1 ; 2 • 4;3 . 0 ; 4 .3 37/187 4 .25* 3/32 7 .74* 15 1. 2 ; 1 . 5 ; 1 . 8 ; 2 .1;2 • 4;3 . 0 60/299 4 .61* 5 /52 35 .38* 16 1. 2 ; 1 . 5 ; 2 • l ; 3 . 0 ; 4 . 3 ; 6 . 0 65/325 5 .03* 5 /58 55 .01* 16 1. 2 ; 1 . 5;1 . 8 ; 2 .1;2 .4;3 .0 64/289 5 . 0 0 * 5/57 27 .04* 17 A l l 92/412 4 .21* 7/79 68 .86* 18 1 . 2 ; 1 . 5 ; 1 . 8 ; 2 . 1 ;2 • 4;3 . 0 ; 6 . 0 81/363 4 .28* 6 /70 164 .52* 19 a l l 100/401 5 .01* 7/89 90 .84* 20 1. 2 ; 1 .5;1 .8;2 . 4 ; 6 . 0 61/262 3 .72* 4/51 163 .71* 20 1 . 8 ; 2 .1 ;3 • 0 ; 4 . 3 53/177 1 .81* 3 /40 63 .07* 21 1. 2 ; 1 . 5 ; 1 . 8 37/135 5 .96* 2/34 1 .08* 21 2 . 1 ; 2 • 4;3 . 0 ; 4 . 3 ; 6 . 0 70/252 2 .60* 4/53 91 . 0 0 * 22 1 . 2 ; 1 • 5 ; 1 . 8 ; 2 . 1 ; 2 . 4 ; 3 . 0 84/255 4 .12* 5 /71 40 .39* 22 4 . 3 ; 6 . 0 27/121 2 .08* 1 /19 16 .67* 23 1. 2 ; 1 . 5;1 . 8 ; 2 .1 51/169 4 .89* 3/46 2 .89* 23 2 . 4 ; 3 .0;4 . 3 ; 6 . 0 55/206 1 .39* 3 /30 171 .09* 24 1. 2 ; 1 . 5 ; 1 .8;2 .1;2 . 4 ; 3 .0 83/246 4 .61* 5/72 32 .97* 24 2 . 4 ; 4 . 3; 6 . 0 38/166 1 .25* 2/19 399 .92* 26 1. 2 ; 1 . 5 ; 1 .8;2 .1;2 . 4;3 . 0 85/237 5 .02* 5/7 4 20 .08* 26 2 . 1 ; 2 . 4;4 . 3;6 .0 56/204 2 .49* 3/40 146 .90* 28 a l l 110/357 2 .88* 7/110 75 .93* 30 1. 2 ; 1 . 5 ; 1 .8 41/101 5 .68* 2/36 0 . l l n 30 2 . 1 ; 2 • 4;3 . 0;4 . 3 ; 6 . 0 73/240 1 .73* 4/44 139 .55* * : 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 of p r o b a b i l i t y o f 0 . 0 5 . n . s . : no s i g n i f i c a n t d i f f e r e n c e . 49 Table 4.6: (Continued). Comparison of mean AGRs among the spacings. Tukey's multiple range tests Age Spacing (m) 1.2 1.5 1.8 2.1 2.4 3.0 4.3 6.0 13 1 .052a* 1 .201ab 1 .378b — 1 .872 13 - - - 1 . 589a 1 . 584a — 1 .641a — 14 0 .670a 0 .794ab 0 .982bc 1 .138c 1 . 357 1 .584 — — 14 - - - 1 .138a 1 . 357ab 1 .584b 1 .250a — 15 0 .663a 0 .795ab 0 .954bc 1 .198cd 1 .483de 1 .721e — — 16 0 .575a 0 .632ab - 0 .882b — 1 • 359c 1 .359c 1 .824 16 0 .575a 0 .632a 0 .772ab 0 .882b 1 .155c 1 • 359c — — 17 0 .420a 0 . 622ab 0 .614ab 0 .795bc 0 .886cd 1 .119de 1 . 345ef 1 • 555f 18 0 .438a 0 .557ab 0 .791bc 0 .921c 1 .226 1 .466 — 2 .076 19 0 .469a 0 .644ab 0 .716ab 0 .803b 1 .121 1 .416 1 .846 2 .173 20 0 .295a 0 •335ab 0 .540b - 0 .926 — — 1 .809 20 - - 0 . 540a 0 .638a — 1 .193 — 1 .809 21 0 .220a 0 .198a 0 .300a — — — — — 21 - — - 0 .512 0 .752a 0 .950a 1 .351 1 .607 22 0 .209a 0 .203a 0 .258a 0 .317a 0 .552 0 .897 — — 23 0 .211a 0 .246a 0 •291ab 0 .403b — — — -23 - - - - 0 .591 0 .931 1 .493 1 .851 24 0 .132a 0 .126a 0 .171a 0 .224a 0 .371 0 .615 — — 24 - — - — 0 . 371 — 1 .022 1 .521 26 0 .166a 0 .132a 0 .187a 0 .238ab 0 . 351b 0 .539 — -26 — - - 0 .238 0 . 351 — 0 .883 1 .161 28 0 .170a 0 .152a 0 .189a 0 .247ab 0 .325bc 0 .442c 0 .714 0 .879 30 0 .148a 0 .136a 0 .129a — — — — -30 — — — 0 .212a 0 .241a 0 .375 0 .549 0 .778 *: the spacings for a given age followed by the same letter do not di f fer s ignif icant ly at the level of proba l i l i ty of 0.05. 50 T a b l e 4 . 7 : T w o - l e v e l n e s t e d anova t e s t s f o r AGR i n b a s a l a r e a ( cm 2/year). Age S p a c i n g s i n c l u d e d (m) DBH c l a s s S p a c i n g D.F. F D.F. F 13 a l l 51/347 49 . 3 9 * 6 / 5 1 1 . 26n 14 a l l 6 4 / 3 4 7 32 . 2 4 * 6/6 3 3 . 6 1 * 15 a l l 71/344 31 . 4 8 * 6/7 0 4 . 1 7 * 16 a l l 8 6 / 4 1 8 28 . 9 9 * 7/84 12 . 1 0 * 17 a l l 9 2 / 4 1 2 25 . 9 8 * 7 / 9 0 17 . 0 5 * 18 a l l 9 3 / 4 0 8 32 . 4 3 * 7/91 27 . 1 8 * 19 a l l 1 0 0 / 4 0 1 19 . 6 3 * 7/97 37 . 3 9 * 20 1 . 2 ; 1 . 5 ; 1 . 8 3 5 / 1 3 8 9 . 1 8 * 2 / 3 3 3 . 2 5 * 20 2 . 1 ; 2 . 4 ; 3 . 0 ; 4 . 3 ; 6 . 0 6 7 / 2 5 7 5 . 7 1 * 4 / 6 0 44 . 7 5 * 21 1 . 2 ; 1 . 5 ; 1 . 8 3 7 / 1 3 5 9 . 8 1 * 2 / 3 5 0 . 8 9 n 21 2 . 1 ; 2 • 4 ; 3 • 0 ; 4 . 3 ; 6 . 0 7 0 / 2 5 2 5 . 8 6 * 4 / 6 2 60 . 8 9 * 22 a l l 111/376 6 . 6 4 * 7/111 152 . 1 5 * 23 a l l 1 0 6 / 3 7 5 5 . 1 8 * 7/106 164 . 0 4 * 24 a l l 107/370 6 . 3 3 * 7/107 215 . 1 3 * 26 a l l 1 1 0 / 3 6 0 5 . 9 5 * 7/110 157 . 2 5 * 28 a l l 110/357 5 . 3 5 * 7/110 79 . 5 1 * 30 a l l 114/341 4 . 1 9 * 7/114 142 . 5 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 l e v e l o f p r o b a b i l i t y of 0 . 0 5 . 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 Table 4.7: (Cont'd). Comparison of mean AGRs between the spacings. Tukey's multiple range tests Age Spacing (m) 1.2 1.5 1.8 2.1 2.4 3.0 4.3 6.0 14 6.240a* 8 .105a 10.477ab 12.794ab 15.166ab 19.168b 14 .165ab 15 7.186a 9 .577ab 12.055abc 15.882abc 19.642bc 24.669c 20 .999bc -16 7.182a 8 .529ab 11.092abc 13.391abc 17.585bc 22.599cd 21 .112cd 34 .327d 17 5.545a 9 .085ab 9.554ab 13.122abc 14.993bc 20.503c 23 .419cd 33 .035d 18 6.531a 8.948ab 13.401abc 16.831bcd 22.627cde 29.961de 36 . l l lef 49 .612f 19 7.485a 11 .170ab 13.142abc 16.025abc 23.128cd 32.643de 40 .571e 59 .137 20 5.050a 6 .181a 10.683a - - - - -20 - - - 13.961a 20.715ab 29.506bc 37 .259c 54 .554 21 - - - 11.788a 17.976ab 25.475b 36 .111 52 .865 22 4.074a 4 .063a 5.773a 7.758a 13.859 24.872 37 .979 56 .961 23 4.216a 4 .861ab 6.568ab 10.045b 15.547 27.569 46 .418 70.362 24 2.795a 2 .746a 4.109a 5.906ab 10.288b 19.237 34 .812 63 .899 26 3.801ab 2 .968a 4.592ab 6.512ab 10.275b 17.893 32 .907 53 .716 28 3.809a 3 .344a 4.761ab 6.779ab 9.935bc 15.470c 28 .491 43 .597 30 3.658a 3 .192a 3.552a 6.356a 7.442a 13.768 23 .304 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 per formed between the s p a c i n g s w i t h homogeneous v a r i a n c e s . B a r t l e t t ' s t e s t ( S o k a l and R o h l f 1981) was used to t e s t f o r h e t e r o s c e d a s t i c i t y . For both DBH and b a s a l a r e a , the n e s t i n g f a c t o r (DBH) was s i g n i f i c a n t a t e v e r y age . T h i s i n d i -c a t e s t h a t DBH and b a s a l area AGRs v a r i e d s i g n i f i c a n t l y among t r e e s o f d i f f e r e n t s i z e s . S i g n i f i c a n t d i f f e r e n c e s i n DBH AGR among s p a c i n g s were o b t a i n e d a t a l l ages except a t age 13 between s p a c i n g s 2.1 m, 2.4 m and 4.3 m and at age 30 between the three c l o s e s t s p a c i n g s . S i g n i f i c a n t d i f f e r e n c e s were found at a l l ages except 13 f o r b a s a l a r e a AGR. The presence o f 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 13 and 14 f o r DBH AGR i s i n c o n t r a d i c t i o n w i t h the r e s u l t s o b t a i n e d f o r DBH ( T a b l e 4 . 2 ) . The i n t e r p r e t a t i o n o f the m u l t i p l e range t e s t s at these two ages may be d i f f i c u l t because the s p a c i n g s were broken down i n t o 2 groups f o r a n a l y s i s (Tab le 4 . 6 ) . However, s i g n i -f i c a n t d i f f e r e n c e s seemed to occur m a i n l y w i t h i n the three c l o s e s t s p a c i n g s and between t h i s group of s p a c i n g s and the four l a r g e s t s p a c i n g s . A t age 14, the 2.1 m, 2.4 m, and 3.0 m s p a c i n g s were s i g n i f i c a n t l y d i f f e r e n t when a n a l y s e d w i t h the t h r e e c l o s e s t s p a c i n g s , but were not when a n a l y s e d w i t h the 4.3 m s p a c i n g o n l y . These are not n e c e s s a r i l y i n c o m p a t i b l e r e s u l t s because the c a l c u l a t e d d i f f e r e n c e s i n the f i r s t case were j u s t above the l e v e l o f s i g n i f i c a n c e . From ages 16 to 30, the d i f f e r e n c e s between the s p a c i n g s a c c e n t u a t e d . No 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 were o b t a i n e d a t age 13 f o r b a s a l a r e a AGR ( T a b l e 4 . 7 ) . A t age 14, the 3.0 m s p a c i n g d i f f e r e d from the two narrowes t s p a c i n g s . However, t h i s may be an anomaly because the 4.3 m s p a c i n g d i d not d i f f e r s i g n i f i c a n t l y from the two narrowes t s p a c i n g s . The r e l a t i v e l y 53 h i g h value f o r the 3 . 0 m spac i n g compared to the 4 . 3 m spacing p r o b a b l y r e s u l t e d from a p a r t i c u l a r t rend at young ages r a t h e r than the e f f e c t of c o m p e t i t i o n . From age 1 5 , the d i f f e r e n c e s between spacings accentuated. The groupings of spacings that d i d not d i f f e r s i g n i f i c a n t l y at the v a r i o u s ages were not the same as the groupings f o r DBH AGR. These apparent c o n t r a d i c t o r y r e s u l t s suggest t h a t the computation of growth r a t e s i n b a s a l area i n s t e a d of diameter changes the p a t t e r n of v a r i a t i o n among t r e e s , as r e p o r t e d by the s t u d i e s of Lorimer ( 1 9 8 3 ) , Steneker and J a r v i s ( 1 9 6 3 ) , and West ( 1 9 8 3 ) . AGR was p o s i t i v e l y c o r r e l a t e d to the s i z e of the t r e e s : the big g e r the t r e e , the g r e a t e r the AGR ( F i g u r e s 4 . 4 and 4 . 5 ) . Because the s t r a t i f i c a t i o n of the f o r e s t i n t o dominance c l a s s e s i n c r e a s e s as c o m p e t i t i o n becomes more i n t e n s e (Ford 1 9 7 5 ; Long and Smith 1 9 8 4 ; Mithen et a l . 1 9 8 4 ; Spurr and Barnes 1 9 8 0 ) , the v a r i a t i o n i n AGR with DBH s i z e c l a s s i n c r e a s e d . A l s o , a l l DBH s i z e c l a s s e s became s u b j e c t to s u b s t a n t i a l r e d u c t i o n s i n AGR with age. In g e n e r a l , the l a r g e r the spac i n g , the g r e a t e r the AGR, and the l a t e r the s t r a t i f i c a t i o n i n t o dominance c l a s s e s o c c u r r e d . These r e s u l t s correspond to those r e p o r t e d by Ford ( 1 9 7 9 , 1984) and C a n n e l l e t a l . ( 1 9 8 4 ) even though t h e i r o b s e r v a t i o n s were based on o n l y two remeasurements and only a s i n g l e stand d e n s i t y l e v e l . 4 . 5 . 1 . 1 . 3 - R e l a t i v e Growth Rate Although there were some e x c e p t i o n s , mean RGR tended to i n c r e a s e w i t h s p a c i n g , but not as markedly as the cor r e s p o n d i n g AGR ( T a b l e s 4 . 8 and 4 . 9 ; F i g u r e s 4 . 6 and 4 . 7 ) . The f i r s t two spacings had n e a r l y equal v a l u e s at ages 1 3 , 1 5 , 1 6 , 2 0 , 2 4 , 2 6 , 54 Table 4.8: Mean RGRs in DBH (cm/year/cm) for every spacing over age. Spacing 13 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 - 20: > 21 - 40: + 41 - 60: & 61 - 85: $ 86 - 100: # 2 2 Table 4.9: Mean RGRs in 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 30 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 S 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 - 20: > 21 - 40: + 41 - 60: & 61 - 85: $ 86 - 100: ft FIGURE 4.6: MEAN DBH RGRs FOR ALL SPACINGS OVER AGE 0.3701 13 16 19 22 25 28 31 TOTAL AGE 57 FIGURE 4.7: MEAN BASAL AREA RGRs FOR ALL SPACINGS OVER AGE LEGEND SPACING: 1.2X1.2 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 T 1 1 I I | — I — I — 1 — I — 1 — | — i — i — I — 1 — I — | — 1 — I — I — I 1 | — I — I — I — I 1 1—I—I 1 1 — I — | -13 16 19 22 TOTAL AGE 25 28 31 58 2 8 , and 3 0 . The 3 . 0 m s p a c i n g had g r e a t e r RGRs than the 4 . 3 m s p a c i n g u n t i l the age 1 5 , and the 6 . 0 m s p a c i n g had a lower v a l u e than the 4 . 3 m s p a c i n g from ages 17 to 1 9 . As w i t h AGR, these t r e n d s were p r o b a b l y due to s l i g h t d i f f e r e n c e s t h a t e x i s t e d among the s tands b e f o r e the onset of c o m p e t i t i o n . D e s p i t e some f l u c t u a t i o n s , mean RGR d e c r e a s e d w i t h age for a l l s p a c i n g s ( F i g u r e s 4 . 6 and 4 . 7 ) . I n c r e a s e s o c c u r r e d a t ages 18 and 2 3 . P l o t t i n g DBH RGR data w i t h c l i m a t i c v a r i a b l e s ( F i g u r e 4 . 8 ) showed a correspondance between s u b s t a n t i a l i n c r e a s e s i n t o t a l r a i n f a l l and i n c r e a s e s i n mean RGR at ages 18 and 2 3 . P r e v i o u s a n a l y s e s have i n d i c a t e d t h a t t o t a l r a i n f a l l was most c l o s e l y a s s o c i a t e d w i t h these growth f l u c t u a t i o n s , f o l l o w e d by d e g r e e - d a y s ( T a b l e 4 . 5 and F i g u r e 4 . 2 ) . Whi l e d e g r e e - d a y s above 25 deg . C d e c r e a s e d a t ages 18 and 2 3 , d e g r e e - d a y s above 1 0 , and mean, mean minimum, and mean maximum temperatures s l i g h t l y i n c r e a s e d a t age 1 5 . These t r e n d s c o r r e s p o n d e d w i t h a r e d u c t i o n i n the d e c r e a s e o f RGR. As was a l s o observed f o r AGR, the a m p l i t u d e s o f f l u c t u a t i o n s d i m i n i s h e d w i t h a decrease i n s p a c i n g . The r e s u l t s o f the n e s t e d anovas are l i s t e d i n T a b l e s 4 . 1 0 and 4 . 1 1 . When h e t e r o s c e d a s t i c i t y problems o c c u r r e d a t a p a r t i c u l a r age, and no s u i t a b l e t r a n s f o r m a t i o n was f o u n d , the s p a c i n g s were broken i n t o groups o f homogeneous v a r i a n c e s . For both DBH and b a s a l a r e a , RGR d i d not v a r y s t a t i s t i c a l l y among s p a c i n g s a t age 13 ( T a b l e s 4 . 1 0 and 4 . 1 1 ) . However, the DBH c l a s s f a c t o r was s i g n i f i c a n t ; RGR d e c r e a s e d w i t h t r e e s i z e f o r each s p a c i n g ( F i g u r e s 4 . 9 . 1 and 4 . 1 0 . 1 ) . Even though the "F" v a l u e f o r the f a c t o r s p a c i n g was s i g n i f i c a n t (but v e r y c l o s e to the l i m i t ) , the m u l t i p l e range t e s t f a i l e d to 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 1 4 . In both c a s e s , the absence o f s i g n i f i c a n t 59 FIGURE 4 . 8 : DBH RGR DATA SUPERIMPOSED ON CL IMATIC VARIABLES A V E R A G E R O R ( D B H ) F O R A L L S P A C I N O S O V E R A O E L E G E * I D A — i a x 1 2 M O — 1 . 5 X 1 5 M c — 1 . 0 X 1 S M o — 2 . 1 X 2 1 M — 2 . 4 X 2 4 M - — 3 . 0 X 3 o M — 4 . 3 X 4 3 M — 8 . 0 X S O M SO 33 O O = > O O 2 4 . 0 2 2 . 4 2 0 . 8 1 9 . 2 1 7 . 6 _ & ^ ^ i « . o ^ ^ 1 4 . 4 i i 1 2 - 8 3 1 1 . 2 9 . 6 S O L E G E N D A — M E A N M A X I M U M T E M P E R A T U R E O — M E A N M I N I M U M T E M P E R A T U R E o — M E A N T E M P E R A T U R E 1 5 1 8 3 3 1 s 2 1 2 4 T O T A L A G E 2 7 3 3 60 FIGURE 4 . 8 : (CONTINUED) 1 2 I S I S 2 1 2 4 2 7 3 0 U E O E N O — M A Y • - J U N E o — S E P T E M B E R T O T A L A G E 61 T a b l e 4 .10: T w o - l e v e l n e s t e d anova t e s t s f o r RGR i n DBH ( c m / y e a r / c m ) . Age Spac ings i n c l u d e d (m) DBH c l a s s Spac ing D . F . F D . F . F 13 a l l 51/347 21 .93* 6/50 1 . 20n. s. 14 a l l 64/347 22 .16* 6/62 2 .46* 15 1 .2; 1 .8;2 .1;2 • 4;3 .0;4 .3 45/219 6 .18* 4/40 11 .11* 16 1 .2; 1 .5;2 .1;2 . 4 ; 3 . 0;4 . 3 ; 6 . 0 76/371 5 .04* 6/67 15 .97* 17 1 .2; 1 . 5;1 .8;2 . 1;2 . 4;6 .0 66/323 5 .96* 5/60 16 .34* 17 3 . 0 ; 4 .3 26/89 17 .05* 1/2 5 2 . 35n. s. 18 1 .2; 1 .5;2 .1;2 .4 46/191 9 .94* 3/43 7 .19* 18 3 . 0 ; 4 .3;6 .0 37/171 20 .55* 2/36 2 . 96n. s. 19 1 .2; 1 .5;1 .8;2 .1;2 . 4;3 . 0 ; 6 . 0 86/358 7 .12* 6/79 23 .04* 20 1 .2; 1 . 5;1 .8;2 .1;2 .4;6 .0 75/308 3 .87* 5/6 4 35 .67* 20 3 . 0 ; 4 . 3 27/87 5 .09* 1/24 2 . 51n. s. 21 1 .2; 2 • 1;3 .0;6 .0 54/213 4 .63* 3/47 35 .74* 21 1 .5 ; 1 .8;2 . 4 39/132 2 .08* 2/29 78 .01* 22 1 .2 ; 1 . 5;1 .8;2 .1;2 • 4;3 . 0 ; 6 . 0 97/335 3 .82* 6/80 46 .39* 23 a l l 106/375 4 .11* 7/91 55 .12* 24 a l l 107/370 4 . 44* 7/91 95 .42* 26 a l l 110/360 3 .12* 7/86 68 .03* 28 a l l 110/357 2 .67* 7/8 5 28 .35* 30 1 .2; 1 . 5;1 .8;2 .1;2 . 4;3 . 0 ; 4 . 3 103/259 3 .53* 6/84 7 .44* * : 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 o f 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 d i f f e r e n c e . Comparison o f mean RGRs i n DBH among the s p a c i n g s T u k e y ' s m u l t i p l e range t e s t s Age S p a c i n g (m) 1.2 1.5 1.8 2.1 2.4 3.0 4.3 6.0 14 0 .135a* 0 .144a 0 .170a 0 .189a 0 .225a 0 .237a 0 .206a 15 0 .112a — 0 .134ab 0 .164bc 0 .206c 0 .219c 0 .211c -16 0 .081a 0 .081a - 0 .102ab 0 .135bc 0 .149c 0 .160c 0 .161c 17 0 .055a 0 .072ab 0 .066ab 0 .083b 0 .091b - - 0 .121 18 0 .050a 0 .058ab - 0 .086bc 0 .114c - - -18 — — — - - 0 .123a 0 .166a 0 .143a 19 0 .050a 0 .061a 0 .065ab 0 .068ab 0 .091bc 0 .103cd - 0 .130d 20 0 .029a 0 .030ab 0 .046ab 0 .048b 0 .069 - - 0 .097 21 0 .020 — - 0 .037 . - 0 .057 - 0 .078 21 — 0 .017a 0 .023a — 0 .052 - - -22 0 .018a 0 .017a 0 .019a 0 .021ab 0 .036b 0 .053 0 .073 23 0 .017a 0 .021a 0 .021a 0 .026ab 0 .037bc 0 .051c 0 .079d 0 .077d 24 0 .010a 0 .009a 0 .012a 0 .014ab 0 .022b 0 .032 0 .049c 0 . 056c 26 0 .014ab 0 .010a 0 .012a 0 .014ab 0 .019b 0 .026 0 .038c 0 .040c 28 0 .012a 0 .011a 0 .012a 0 .015ab 0 .017ab 0 .020b 0 .029c 0 . 028c 30 0 .010a 0 .010a 0 .008a 0 .012a 0 .013a 0 .016a 0 .021b 0 . 023b * : the 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 not 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 of p r o b a l i l i t y o f 0 .05 . 62 Table 4.11: Two-level nested anova tests for RGR in basal area ( cm 2/year/cm 2 ) . Age Spacings included (m) DBH class Spacing D . F . F D . F . F 13 a l l 51/347 21 .91* 6/50 0 . 95n. s. 14 a l l 64/347 22 .16* 6/62 2 .46* 15 a l l 71/344 5 .94* 6/64 10 .59* 16 1. 2 ; 1 . 5;2 .1;6 .0 41/235 3 .24* 3/34 41 .93* 16 2 . 4 ; 4 . 3;6 .0 35/136 10 .03* 2/33 0 .63n. s. 17 1. 2 ; 1 . 5;1 .8;2 .1; 2 .4;6 .0 66/323 5 .26* 5/59 17 .55* 17 4 . 3 ; 6 .0 26/89 17 .03* 1/2 5 2 .34n. s. 18 1. 2 ; 1 .5;2 ,1;2 • 4; 3 .0;6 .0 71/317 11 .93* 5/67 24 .34* 18 3 . 0 ; 4 .3;6 .0 37/171 20 .69* 2/36 2 .98n. s. 19 1. 2 ; 1 6.0 .5;1 • 8;2 .1; 2 . 4;3 .0 86/358 7 .17* 6/79 22 .94* 20 1. 2 ; 1 .5;1 .8;2 .1; 2 .4;6 .0 75/308 3 .89* 5/64 35 .43* 20 4 . 3 ; 6 .0 27/87 5 .13* 1/25 2 . 51n. s. 21 1. 2 ; 2 • i;3 . 0;6 .0 54/213 4 .62* 3/47 35 .85* 21 1. 5 ; 1 .8;2 .4 39/132 2 .11* 2/29 76 .77* 22 1. 2 ; 1 6.0 .5;1 .8,-2 .1; 2 • 4;3 • 0; 97/335 4 .44* 6/82 44 .17* 23 a l l 106/375 3 .54* 7/106 65 .29* 24 a l l 107/370 4 .10* 7/90 108 .42* 26 a l l 110/360 3 .83* 7/110 53 .73* 28 a l l 110/357 2 .69* 7/110 21 .73* 30 1. 2 ; 1 4.3 . 5;1 • 8;2 .1; 2 . 4;3 • 0; 103/259 2 .32* 6/103 12 .26* *: Significant differences at the level of probabil ity of 0.05. n .s . : no significant difference. 63 Table 4.11: (Continued). Comparison of mean RGRs among the spacings. Tukey's multiple range tests Age Spacing (m) 1.2 1.5 1.8 2.1 2.4 3.0 4.3 6.0 14 0 .270a* 0 .289a 0. 340a 0 .379a 0 .449a 0 .474a 0. 413a 15 0 .225a - 0. 267ab 0 .328ab 0 .411b 0 . 438b 0. 422b — 16 0 .162a 0 .161a - 0 .204a — — — 0. 323 16 - - - - 0 .270a 0 .299a 0. 320a — 17 0 .110a 0 .145ab 0. 133ab 0 .167b 0 .182b - — 0. 242 18 0 .099a 0 .116ab - 0 .172bc 0 .228cd 0 .246cd — 0. 286d 18 - - - - — 0 .246a 0. 332a 0. 286a 19 0 .100a 0 .123a 0. 130ab 0 .135ab 0 .182bc 0 .205cd — 0. 260d 20 0 .058a 0 .059a 0. 091ab 0 .096b 0 .138 — — 0. 194 21 0 .039a - - 0 .074a — 0 .117 — 0. 157 21 - 0 .034a 0. 046a - 0 .105 — — — 22 0 .036a 0 .034a 0. 038a 0 . 043a 0 .073 0 .107 — 0. 146 23 0 .035a 0 .041a 0. 043a 0 .053ab 0 .074b 0 .103 0. 159c 0. 155c 24 0 .021a 0 .019a 0. 023a 0 . 028a 0 .044 0 .064 0. 098b 0. 115b 26 0 . 025a 0 . 020a 0. 025ab 0 .028ab 0 .039bc 0 .053c 0. 077d 0. 079d 28 0 .025a 0 .023a 0. 025a 0 .029ab 0 . 035ab 0 .041b 0. 058c 0. 056c 30 0 .020ab 0 .019ab 0. 016a 0 .023ab 0 .026bc 0 .033c 0. 042d 0. 047d *: the spacings for a given age followed by the same letter do not di f fer s ignif icant ly at the level of proba l i l i ty 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 o. 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 0.530 4 2 3 * 5 6 7 DBH SIZE CLASS (CM) FIGURE 4.9.3: AGE 24 0.477 0.424 5 O o . OC ui o. \ 5o. 371 318 265 0.212 CC 0. O 159 0. 106 0.053 0.000 LEGEND o - 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 7 18 20 DBH SIZE CLASS (CM) FIGURE 4.9.4: AGE 30 0.09 LEGEND 0. 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 0 , „ * = SPACING: 4.3X4.3 M^, \>*\p = SPACING: 6.0X6.0 M ^ * \ 0420 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 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 4.10.1: AGE 13 FIGURE 4.10.2: AGE 18 1 .40 0.24 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 9 10 DBH SIZE CLASS (CM) FIGURE 4.10.3: AGE 24 i . 10 0.99 (N 0. t * 2 oo. \ ct >-\ * 2 o 88 66 55 CD 0. 44 0.33 0.22 0.11 0.00 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: 3.0X30 M * - SPACING: 4.3X4.3 M o - SPACING: 6.0X6.0 M DBH SIZE CLASS (CM) FIGURE 4.10.4: AGE 30 0.190 H 0.171 CN 0 . 152 1 # # 2 O 0 .133-\ UjO.114->-\ ^ 0.095^ * 2 P . 0 . 0 7 H : 0.057 0.038- A / WX\ 0.019 0 . 0 0 0 ^ ; 10 13 20 25 DBH SIZE CLASS (CM) 0.090 0.081 CM 0.072 * * 2 O 0.083 L) 0. > \ * 2 P,o. 054 045 036 J; 0.027 00 tt O 0.018 0.009 0.000 M P I \ A 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 I \ 1 * i • i ' i ' i 1 i ' i • 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 8 8 DBH SIZE CLASS (CM) 66 d i f f e r e n c e s suggests t h a t c o m p e t i t i o n had not y e t taken p l a c e at these two ages. S i g n i f i c a n t d i f f e r e n c e s appeared from age 15 on. I n i t i a l l y , o n l y 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 and there was o v e r l a p among the groups of spacings t h a t were not s t a t i s t i c a l l y d i f f e r e n t . The s i z e of these groups decreased w i t h age and there was l e s s o v e r l a p among them. The same p a t t e r n o c c u r r e d f o r both DBH and b a s a l area. For both DBH and b a s a l area, the DBH c l a s s 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 at every age. T h i s i m p l i e s t h a t RGR v a r i e d s i g n i f i c a n t l y w i t h t r e e s i z e . However, the v a r i a t i o n s were not i d e n t i c a l to those t h a t o c c u r r e d with AGR. At age 1 3 , the RGR of a l l s p acings decreased with t r e e s i z e ( F i g u r e 4 . 9 . 1 and 4 . 1 0 . 1 ) . F i v e y ears l a t e r , the RGRs of the two c l o s e s t spacings c l e a r l y i n c r e a s e d w i t h t r e e s i z e , those of the 1 . 8 m and 2 . 1 m remained r e l a t i v e l y c o n s t a n t , and those of the four l a r g e s t spacings decreased ( F i g u r e s 4 . 9 . 2 and 4 . 1 0 . 2 ) . At age 2 4 , the four c l o s e s t s p a c i n g s i n c r e a s e d w i t h t r e e s i z e ( F i g u r e s 1 4 . 9 . 3 and 4 . 1 0 . 3 ) . Only the 2 . 4 m spac i n g remained r e l a t i v e l y i n v a r i a n t . The three l a r g e s t spacings s t i l l decreased w i t h i n c r e a s e i n tree s i z e . At age 3 0 , o n l y the two l a r g e s t spacings s t i l l decreased w i t h t r e e s i z e ( F i g u r e s 4 . 9 . 4 and 4 . 1 0 . 4 ) . The change i n the r e l a t i o n s h i p between RGR and t r e e s i z e was a l s o e v i d e n t when the c o r r e l a t i o n c o e f f i c i e n t s between DBH and RGR of i n d i v i d u a l t r e e s were computed f o r a l l spacings at d i f f e -r ent ages (Table 4 . 1 2 ) . Negative c o e f f i c i e n t s i n d i c a t e t h a t RGR decreased with t r e e s i z e , not s i g n i f i c a n t low c o e f f i c i e n t s i n d i -cate t h a t RGR d i d not vary s i g n i f i c a n t l y with t r e e s i z e , and high 67 T a b l e 4 . 1 2 : C o r r e l a t i o n c o e f f i c i e n t s between DBH ( i n i t i a l s i z e ) 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 ages. Age s p a c i n g (m) 1 . 2 1 . 5 1 . 8 2 .1 2 . 4 3 . 0 4 . 3 6 . 0 13 - 0 . 8 3 * - 0 . 8 8 * - 0 . 9 2 * - 0 . 8 6 * - 0 . 9 1 * - 0 . 9 1 * - 0 . 6 8 * 14 - 0 . 8 0 * - 0 . 8 0 * - 0 . 8 1 * - 0 . 8 6 * - 0 . 9 2 * - 0 . 8 5 * - 0 . 6 9 * — 15 - 0 . 4 8 * - 0 . 5 6 * - 0 . 7 6 * - 0 . 7 9 * - 0 . 8 4 * - 0 . 8 7 * - 0 . 5 1 * — 16 - 0 . 1 6 - 0 . 2 4 - 0 . 4 7 * - 0 . 5 4 * - 0 . 8 6 * - 0 . 8 0 * - 0 . 8 0 * - 0 . 7 3 * 17 - 0 . 1 0 * - 0 . 0 5 * - 0 . 1 0 * - 0 . 5 0 * - 0 . 8 4 * - 0 . 8 3 * - 0 . 8 1 * - 0 . 8 3 * 18 0 . 5 5 * 0 . 3 4 * - 0 . 1 9 - 0 . 1 5 - 0 . 9 0 * - 0 . 8 4 * - 0 . 7 7 * - 0 . 9 1 * 19 0 . 6 0 * 0 . 5 1 * 0 . 0 9 0 . 1 8 - 0 . 4 5 * - 0 . 6 6 * - 0 . 8 5 * - 0 . 8 6 * 20 0 . 5 0 * 0 . 3 1 * 0 . 2 3 0 . 3 9 * - 0 . 3 4 * - 0 . 6 7 * - 0 . 6 6 * - 0 . 8 9 * 21 0 . 5 5 * 0 . 4 2 * 0 . 6 5 * 0 . 3 2 * - 0 .17 - 0 . 5 4 * - 0 . 9 1 * - 0 . 8 0 * 22 0 . 5 8 * 0 . 4 6 * 0 . 6 8 * 0 . 4 9 * 0 . 0 2 - 0 . 7 7 * - 0 . 8 2 * - 0 . 7 8 * 23 0 . 5 9 * 0 .17 0 . 5 9 * 0 . 4 8 * 0 . 0 5 - 0 . 4 9 * - 0 . 8 3 * - 0 . 7 6 * 24 0 . 6 7 * 0 . 6 1 * 0 . 7 0 * 0 . 6 5 * 0 . 1 9 - 0 . 5 8 * - 0 . 7 7 * - 0 . 7 0 * 26 0 . 6 0 * 0 . 4 9 * 0 . 6 6 * 0 . 5 9 * 0 . 4 1 * - 0 . 4 9 * - 0 . 6 3 * - 0 . 5 1 * 28 0 . 6 3 * 0 . 4 2 * 0 . 5 7 * 0 . 3 0 * 0 . 3 2 * - 0 . 2 3 * - 0 . 4 4 * - 0 . 3 8 * 30 0 . 5 4 * 0 . 5 3 * 0 . 6 6 * 0 . 6 2 * - 0 .11 - 0 . 1 3 - 0 . 3 3 * - 0 . 3 3 * *: S i g n i f i c a n t 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 . 68 p o s i t i v e c o e f f i c i e n t s i n d i c a t e t h a t RGR i n c r e a s e d with t r e e s i z e . Table 4 . 1 2 completes F i g u r e 4 . 9 because a l l the ages are i n c l u d e d , and s i m i l a r trends are i n d i c a t e d . At age 1 3 , the c o e f -f i c i e n t s of a l l spacings were ne g a t i v e and F i g u r e 4 . 9 . 1 w e l l shows t h a t RGR was d e c r e a s i n g with t r e e s i z e . At age 1 8 , the c o e f f i c i e n t s of the two c l o s e s t spacings were p o s i t i v e , those of the 1 . 8 m and 2 . 1 m spacings were not s i g n i f i c a n t l y d i f f e r e n t from zero, and those of the l a r g e s t four spacings were n e g a t i v e . F i g u r e 4 . 9 . 2 w e l l shows t h a t RGR of the two c l o s e s t spacings i n c r e a s e d w i t h t r e e s i z e , RGR of the 1 . 8 m and 2 . 1 m spacings remained r e l a t i v e l y c onstant with t r e e s i z e , and RGRs of the four l a r g e s t spacings were s t i l l d e c r e a s i n g with t r e e s i z e . The same s i t u a t i o n o c c u r r e d at ages 24 and 3 0 . These r e s u l t s show three p a t t e r n s of v a r i a t i o n f o r DBH and b a s a l area RGRs. At young ages they decreased w i t h t r e e s i z e . As age i n c r e a s e d , RGR became constant a c r o s s t r e e s i z e s and then became p o s i t i v e l y r e l a t e d to t r e e s i z e . The wider the spacing, the l a t e r these changes o c c u r r e d ( F i g u r e s 4 . 9 and 4 . 1 0 ; Table 4 . 1 2 ) . The h y p o t h e s i s of Ford ( 1 9 8 2 , 1984) and Ford and D i g g l e ( 1 9 8 1 ) ( i . e . , a l l the t r e e s have the same RGR b e f o r e the onset of c o m p e t i t i o n ) must be r e j e c t e d because RGR v a r i e d c o n s i d e r a b l y among t r e e s b e f o r e c o m p e t i t i o n took p l a c e . As p r e v i o u s l y mentioned, the absence of s i g n i f i c a n t d i f f e r e n c e s at ages 13 and 14 and the h i g h v a l u e s of crown r a t i o suggested t h a t no spacing was s u b j e c t to c o m p e t i t i o n . Even though i t was concluded that no c o m p e t i t i o n was o c c u r r i n g at ages 13 arid 14 i n any s p a c i n g because most growth parameters an a l y s e d were not s i g n i f i c a n t l y d i f f e r e n t and t h a t i n d i v i d u a l crowns were not a f f e c t e d by the presence of c o m p e t i t o r s , i t may be argued t h a t c o m p e t i t i o n f o r 69 n u t r i e n t e lements was maybe i m p o r t a n t . However, the v a r i a b l e s a n a l y s e d i n t h i s s tudy do not p e r m i t the d i r e c t a n a l y s i s of the importance o f be low-ground c o m p e t i t i v e s t r e s s . D e s p i t e t h i s , c o m p e t i t i o n f o r s o i l r e s o u r c e s was p r o b a b l y not i m p o r t a n t at young ages because the s t u d i e d s i t e was v e r y r i c h f o r red p i n e . F u r t h e r m o r e , the s tudy of S t i e l l (1970) on the same s i t e suggests t h a t be low-ground c o m p e t i t i o n was not i m p o r t a n t compared to above -ground c o m p e t i t i o n . A l s o , i f c o m p e t i t i o n f o r s o i l r e s o u r -ces had been i m p o r t a n t at young ages , the d i f f e r e n t s p a c i n g s would have shown g r e a t e r d i f f e r e n c e s i n term of d iameter growth. F i n a l l y , the i n d i v i d u a l red p i n e t r e e s composing a s tand are i n t e r c o n n e c t e d by many roo t g r a f t s (Armson and D r i e s s c h e 1959; H o r t o n 1969) . A c c o r d i n g to Graham and Bormann (1966) , roo t g r a f t i n g d e c r e a s e s the i n t e n s i t y o f c o m p e t i t i o n among t r e e s because i n t e r c o n n e c t e d t r e e s b e t t e r share s o i l r e s o u r c e s . The p a t t e r n o f RGR changes over time was s i m i l a r to t h a t r e p o r t e d by P e r r y (1985) f o r b a s a l a r e a i n D o u g l a s - f i r s tands and C a n n e l l e t a l . (1984) f o r h e i g h t i n S i t k a spruce and l o d g e p o l e p i n e (P inus c o n t o r t a D o u g l . ) s t a n d s . However, P e r r y ' s d a t a were l i m i t e d to s tands o f the same age, but d i f f e r e n t t h i n n i n g i n t e n -s i t i e s . The d a t a o f C a n n e l l e t a l . (1984) were l i m i t e d to three remeasurement p e r i o d s a t the s e e d l i n g s t a g e . A s i m i l a r p a t t e r n was a l s o r e p o r t e d by S c h m i t t e t a l . (1987) f o l l o w i n g t h i n n i n g t r e a t m e n t s i n p o p u l a t i o n s o f Impat iens c a p e n s i s Meerb . A c c o r d i n g to P e r r y (1985) and C a n n e l l e t a l . (1984) , the d e c l i n e i n RGR w i t h t r e e s i z e would i n d i c a t e t h a t c o m p e t i t i o n i s n o n - e x i s t e n t or not severe enough to induce m o r t a l i t y . T h i s p e r i o d c o r r e s p o n d s to a phase i n which the e f f i c i e n c y of the t r e e i s i n v e r s e l y r e l a t e d to i t s s i z e : the s m a l l e r the t r e e , the more 70 capab le i t i s of p r o d u c i n g new m a t e r i a l ( P e r r y 1985); A l t h o u g h dominant t r e e s w i t h l a r g e crowns have the h i g h e s t p h o t o s y n t h e t i c p r o d u c t i v i t y , they would be l e s s e f f i c i e n t because of t h e i r g r e a t e r maintenance r e s p i r a t i o n needs r e s u l t i n g from l a r g e r r o o t s , stems, and b r a n c h e s . When RGR remains c o n s t a n t w i t h t r e e s i z e , i t would i n d i c a t e t h a t c o m p e t i t i o n i s j u s t b e g i n n i n g to become i m p o r t a n t enough to cause m o r t a l i t y . F i n a l l y , a s tand s u b j e c t to severe c o m p e t i t i o n i s c h a r a c t e r i z e d by a p o s i t i v e c o r r e l a t i o n between RGR and t r e e s i z e . The e f f i c i e n c y of t r e e s under heavy s t r e s s d e c l i n e s compared to t h a t o f the t r e e s s u b j e c t to l e s s c o m p e t i t i o n . In o r d e r to determine i f the f i n d i n g s and c o n c l u s i o n s of P e r r y (1985) and C a n n e l l e t a l . (1984) a p p l y to red p ine and to a l a r g e range of i n i t i a l s p a c i n g s , the onset o f c o m p e t i t i o n ( i . e . , when t r e e s composing a s tand reach a s i z e such t h a t c o m p e t i t i o n causes a r e d u c t i o n i n growth) must be e s t i m a t e d f o r the v a r i o u s s p a c i n g s . D e t e r m i n i n g when c o m p e t i t i o n takes p l a c e i n a s tand i s not an easy task because i t i s not a measurable q u a n t i t y . One p o s s i b l e way c o n s i s t s o f a n a l y s i n g the d i f f e r e n c e i n growth ra te between a s tand-grown t r e e and a t r e e f r e e o f c o m p e t i t i o n ( C u r t i s 1970; P e r r y 1985; P i e n a a r 1965) . The same p r i n c i p l e may be a p p l i e d by comparing v e r y dense s tands w i t h o t h e r s o f low d e n s i t y . I f there i s no s i g n i f i c a n t d i f f e r e n c e among these s tands a t young ages , i t i s p o s s i b l e to conc lude t h a t c o m p e t i t i o n has not y e t had an impact on growth. When s i g n i f i c a n t d i f f e r e n c e s b e g i n to appear p r o g r e s s i v e l y from the c l o s e s t to the w i d e s t s p a c i n g s , i t becomes p o s s i b l e to determine when c o m p e t i t i o n b e g i n s . 71 D e t e r m i n i n g the exac t age o f the onset o f c o m p e t i t i o n f o r a p a r t i c u l a r s p a c i n g was d i f f i c u l t because not a l l the t r e e s o f a g i v e n s tand become s u b j e c t to c o m p e t i t i o n a t the same t i m e . A l s o , because the f i v e narrowes t s p a c i n g s d i d not d i f f e r much i n d e n s i t y , the onse t s o f c o m p e t i t i o n i n these s p a c i n g s p r o b a b l y o c c u r r e d w i t h i n a r e l a t i v e l y s h o r t p e r i o d of t i m e . The absence o f s i g n i f i c a n t d i f f e r e n c e s i n DBH among s p a c i n g s at ages 13 and 14 ( T a b l e 4 .2) suggests t h a t c o m p e t i t i o n had not y e t taken p l a c e . (As ment ioned above , c o n c l u d i n g t h a t compe-t i t i o n had not y e t o c c u r r e d at these ages w i t h i n the c l o s e s t s p a c i n g s i s based on the absence o f s i g n i f i c a n t d i f f e r e n c e s when compar i sons are made w i t h s tands c h a r a c t e r i z e d by l a r g e i n i t i a l s p a c i n g s ) . Even though s i g n i f i c a n t d i f f e r e n c e s i n DBH AGR were found at age 13, none were o b t a i n e d f o r b a s a l a r e a AGR, DBH and b a s a l a r e a RGRs ( T a b l e s 4 . 6 , 4 . 7 , 4 .10 , 4 . 1 1 ) . Because s i g n i -f i c a n t d i f f e r e n c e s began to appear at age 15, the onset o f compe-t i t i o n was assumed to occur at t h i s age f o r at l e a s t the two c l o s e s t s p a c i n g s . As p r e v i o u s l y ment ioned , the m a j o r i t y o f t r e e s i n a l l the s p a c i n g s a t these two ages were c h a r a c t e r i z e d by h i g h crown r a t i o v a l u e s ( F i g u r e 1 o f Appendix 2 ) . I t i s a t age 15 t h a t the two c l o s e s t s p a c i n g s s t a r t e d h a v i n g h i g h p r o p o r t i o n s of t r e e s w i t h crown r a t i o s lower than 85%. The d e c l i n e i n RGR w i t h t r e e s i z e and the n e g a t i v e c o r r e -l a t i o n c o e f f i c i e n t s f o r e v e r y s p a c i n g at age 13 c o r r e s p o n d e d w i t h the absence o f c o m p e t i t i o n i n any s p a c i n g ( F i g u r e s 4 . 9 . 1 and 4 . 1 0 . 1 ; T a b l e 4 . 1 2 ) . A t age 18, the two narrowes t s p a c i n g s showed an i n c r e a s e i n RGR w i t h t r e e s i z e ( F i g u r e s 4 . 9 . 2 and 4 . 1 0 . 2 ) . They showed a r e l a t i v e l y c o n s t a n t r e l a t i o n s h i p w i t h t r e e s i z e a t ages 16 and 17 r e s p e c t i v e l y because t h e i r 72 c o r r e l a t i o n c o e f f i c i e n t s were not s i g n i f i c a n t l y d i f f e r e n t from z e r o . The 1.8 m s p a c i n g showed l i t t l e v a r i a b i l i t y i n DBH and b a s a l a r e a RGRs w i t h t r e e s i z e a t age 17 ( T a b l e 4 . 1 2 ) . Other than the two s m a l l e s t DBH c l a s s e s , the 2.1 m s p a c i n g remained r e l a t i v e l y c o n s t a n t w i t h t r e e s i z e at age 18. For these two s p a c i n g s , mean DBH, b a s a l a r e a AGR, and DBH and b a s a l area RGRs became s i g n i f i c a n t l y d i f f e r e n t from the l a r g e s t s p a c i n g (6 .0 m) a t age 16 ( T a b l e s 4 . 2 , 4 . 7 , 4 .10 , and 4 . 1 1 ) . However, o n l y some t r e e s had a crown r a t i o lower than 85% at age 16 ( F i g u r e 1 of Appendix 2 ) . As the p r o p o r t i o n o f t r e e s w i t h crown r a t i o v a l u e s g r e a t e r than 85% d e c r e a s e d d r a s t i c a l l y a t age 17 f o r the 1.8 m and 2.1 m s p a c i n g s , i t appears t h a t c o m p e t i t i v e s t r e s s was o c c u r r i n g o n l y on some t r e e s a t age 16 and t h a t many o ther t r e e s were c l o s e to the l i m i t o f b e i n g a f f e c t e d by c o m p e t i t i o n . F i n a l l y , the f o u r w i d e s t s p a c i n g s s t i l l showed a d e c l i n e i n RGR w i t h DBH at age 18. The c o m p e t i t i v e c o n d i t i o n o f the four w i d e s t s p a c i n g s i s more d i f f i c u l t to e v a l u a t e . A t age 16, mean DBHs of the 2.4 m, 3.0 m, and 4.3 m s p a c i n g s d i d not d i f f e r s i g n i f i c a n t l y , the 4.3 m and 6.0 m ones d i d , but the 3.0 m and 6.0 m ones d i d not (Tab le 4 . 2 ) . T h i s sugges t s t h a t s i g n i f i c a n t d i f f e r e n c e s between the 4.3 m and 6.0 m s p a c i n g s d i d not n e c e s s a r i l y i m p l y t h a t the former s p a c i n g was a f f e c t e d by c o m p e t i t i o n , but t h a t a t r e n d of low v a l u e s e x i s t i n g b e f o r e the onset o f c o m p e t i t i o n remained e f f e c t i v e a few y e a r s a f t e r the onset o f c o m p e t i t i o n . In f a c t , the 4.3 m s p a c i n g showed lower v a l u e s than the 3.0 m s p a c i n g up to age 20. A l s o , none o f these s p a c i n g s d i f f e r e d s i g n i f i c a n t l y f o r b o t h DBH and b a s a l a r e a RGRs ( T a b l e s 4.10 and 4 . 1 1 ) . The 2.4 m s p a c i n g began to d i f f e r from the 6.0 m s p a c i n g a t age 16 73 f o r b a s a l a r e a AGR and 17 f o r DBH and b a s a l a r e a RGR. However, a l l the t r e e s o f t h a t s p a c i n g had a crown r a t i o g r e a t e r than 85% at ages 17 and 18. T h i s p r o p o r t i o n was around 35% at age 19. D e s p i t e s i g n i f i c a n t d i f f e r e n c e s at ages 17 and 18, i t appears t h a t t r e e s i n the 2.4 m s p a c i n g became a f f e c t e d by c o m p e t i t i v e s t r e s s at age 19, and t h a t RGR became i n v a r i a n t w i t h t r e e s i z e at age 21 ( T a b l e 4 . 1 2 ) . I f a d e c l i n e i n RGR w i t h DBH i n d i c a t e s f o r wide as w e l l as f o r narrow s p a c i n g s t h a t c o m p e t i t i o n i s n o n - e x i s t e n t or not v e r y s e v e r e , then the w i d e s t t h r e e s p a c i n g s d i d not appear to be under heavy s t r e s s a t age 24. DBH and b a s a l a r e a RGRs of the 3.0 m s p a c i n g s t a r t e d d i f f e r i n g from the 6.0 m s p a c i n g around age 20 when t r e e s began to have crown r a t i o s lower than 85% ( F i g u r e 1 of Appendix 2 ) . R e l a t i v e growth r a t e became i n v a r i a n t w i t h t r e e s i z e a t age 30 ( F i g u r e s 4 .9 .4 and 4 . 1 0 . 4 ; T a b l e 4 . 1 2 ) . On ly the two w i d e s t s p a c i n g s showed a d e c l i n e i n RGR w i t h t r e e s i z e a t age 30 ( F i g u r e s 4 . 9 . 4 and 4 . 1 0 . 4 ; T a b l e 4 . 1 2 ) . However, the crown r a t i o s o f these two s p a c i n g s began to show v a l u e s lower than 85% at ages 26 and 30 r e s p e c t i v e l y . In summary, the onset o f c o m p e t i t i o n appeared to occur at age 15 f o r the 1.2 m and 1.5 m s p a c i n g s , 1.6 f o r the 1.8 m and 2.1 m s p a c i n g s , 19 f o r the 2.4 m s p a c i n g , 20 f o r the 3.0 m s p a c i n g , 26 f o r the 4.3 m s p a c i n g , and 30 f o r the 6.0 m s p a c i n g . The p a t t e r n o f change r e l a t e d to the onset o f c o m p e t i t i o n as sugges ted by C a n n e l l e t a l . (1984) and P e r r y (1985) i s a p p l i c a b l e to the f i v e c l o s e s t s p a c i n g s . However, the decrease i n RGR w i t h i n c r e a s e i n t r e e s i z e does not e x c l u s i v e l y i n d i c a t e the absence of c o m p e t i t i o n , and c o m p e t i t i o n does not b e g i n o n l y when RGR 74 shows l i t t l e v a r i a b i l i t y w i t h t r e e s i z e . The f i r s t age o f the o c c u r r e n c e o f l i t t l e v a r i a b i l i t y o f RGR w i t h t r e e s i z e took p l a c e 1 year a f t e r the onset o f c o m p e t i t i o n f o r the 1 . 2 m , 1 . 5 m , and 1.8 m s p a c i n g s , 2 y e a r s f o r the 2.1 m and 2.4 m s p a c i n g s , and 10 y e a r s f o r the 3.0 m s p a c i n g . A t age 30, the 4.3 m and 6.0 m s p a c i n g s were s t i l l c h a r a c t e r i z e d by a decrease i n RGR w i t h t r e e s i z e . The p r o p o r t i o n s o f t r e e s a l r e a d y s u b j e c t to c o m p e t i t i o n were 75%, 52%, 60%, 51%, 95%, and 100% f o r the 1.2 m, 1.5 m, 1.8 m, 2.1 m, 2.4 m, and 3.0 m s p a c i n g s r e s p e c t i v e l y when RGR became i n v a r i a n t . However, the c o m p e t i t i v e s t r e s s between the age o f the onset o f c o m p e t i t i o n and the o c c u r r e n c e o f l i t t l e v a r i a b i l i t y o f RGR w i t h t r e e s i z e was p r o b a b l y not i m p o r t a n t because the crown r a t i o v a l u e s o f the t r e e s were s t i l l r e l a t i v e l y h i g h d u r i n g t h i s t r a n s i t i o n ( F i g u r e 1 o f Appendix 2 ) . The i n c r e a s e i n the d e l a y observed between the age o f the onset o f c o m p e t i t i o n and the age when RGR began to show l i t t l e v a r i a b i l i t y w i t h t r e e s i z e i n c r e a s e d from one year to two y e a r s between the 1.2 m and 2.4 m s p a c i n g s . T h i s sugges ts t h a t the t r a n s i t i o n from decrease i n RGR w i t h t r e e s i z e to i n c r e a s e o c c u r r e d s lower as s p a c i n g was i n c r e a s e d . T h i s c o u l d be r e l a t e d to the f a c t t h a t s e l f - t h i n n i n g proceeds more s l o w l y as s tand d e n s i t y i s d e c r e a s e d ( R a d o s e v i c h and Os teryoung 1987) . However, the d e l a y o f 10 y e a r s f o r the 3.0 m s p a c i n g i s s u r p r i s i n g l y h i g h compared to the o t h e r s p a c i n g s . T h i s l o n g e r p e r i o d might be r e l a t e d to the t ime o c c u r r i n g between the onset o f c o m p e t i t i o n ( i . e . , when t r e e s began to have crown r a t i o v a l u e s lower than 85%) and the t ime where a l l t r e e s appeared to be a f f e c t e d by c o m p e t i t i v e s t r e s s ( a l l crown r a t i o v a l u e s lower than 85%). T h i s was t h r e e y e a r s f o r the f i v e c l o s e s t s p a c i n g s and the 4.3 m 75 s p a c i n g and 5 y e a r s f o r the 3.0 m s p a c i n g . Examin ing the changes i n the r e l a t i o n s h i p between RGR and t r e e s i z e to e s t i m a t e when c o m p e t i t i o n b e g i n s i n even-aged s tands has advantages over o t h e r methods. The method of O'Connor (1935) ( i . e . , c o r r e l a t e d curve t r e n d ) c o n s i s t s o f d e r i v i n g a graph showing c u r v e s of mean t r e e volume f o r d i f f e r e n t i n i t i a l s t o c k i n g s a t s e v e r a l remeasurement p e r i o d s . Then , a S - c u r v e s e p a r a t i n g a f r e e - g r o w t h zone and a s u p p r e s s i o n zone i s d e r i v e d . The f r e e - g r o w t h zone i s d e f i n e d as the s e c t i o n on the graph where a r e d u c t i o n i n the number of t r e e s does not a f f e c t the mean volume of the t r e e s , and the s u p p r e s s i o n zone i s the s e c t i o n where c o m p e t i t i o n i s c o n s i d e r e d to o c c u r . The M-V curve i s then d e r i v e d by drawing a curve j o i n i n g the i n f l e c t i o n p o i n t s of the c u r v e s o f the mean t r e e volume f o r d i f f e r e n t i n i t i a l s tand d e n s i t i e s a t s e v e r a l remeasurement p e r i o d s . T h i s curve p r o v i d e s an e s t i m a t e o f the maximum number of t r e e s r e q u i r e d to o b t a i n a maximum i n c r e a s e i n mean t r e e volume at any age . Other a u t h o r s a p p l i e d the same a p p r o a c h , but used mean s tand DBH or mean s tand growth ( P i e n a a r 1965) . P i e n a a r (1965) found i t d i f f i c u l t to a p p l y the approach of O'Connor because o f the need to a n a l y s e a wide range o f i n i t i a l s p a c i n g s w i t h remeasurement d a t a . Working w i t h p a r t o f the d a t a se t o f O'Connor (1935) , P i e n a a r (1965) c o n s i d e r e d t h a t c o m p e t i t i o n began i n the h i g h d e n s i t y s tands when the mean DBH d i f f e r e d by more than 1.25 mm (0 .05 i n c h e s ) from low d e n s i t y s t a n d s . However, he d i d not g i v e any j u s t i f i c a t i o n for t h i s l i m i t . 76 S i m i l a r approaches based on the s e l f - t h i n n i n g r u l e were a l s o developed. One of the best examples i s the stand d e n s i t y mana-gement diagram developed by Drew and F l e w e l l i n g ( 1 9 7 9 ) f o r D o u g l a s - f i r . On" a graph of mean t r e e volume f o r d i f f e r e n t stand d e n s i t i e s , they d e l i m i t e d zones showing d i f f e r e n t i n t e n s i t i e s of co m p e t i t i v e s t r e s s . These diagrams are a l s o used to p r e d i c t the e f f e c t of t h i n n i n g . A s i m i l a r approach was adopted by Smith and Brand ( 1 9 8 8 ) f o r red p i n e . The c o r r e c t a p p l i c a t i o n of these methods r e q u i r e s the ana l y s e s of stands f o r a wide range of i n i t i a l d e n s i t y and at s e v e r a l remeasurements. Such data do not e x i s t f o r a l l commer-c i a l s p e c i e s and f o r d i f f e r e n t s i t e q u a l i t i e s . My r e s u l t s show th a t the occurrence of l i t t l e v a r i a b i l i t y of RGR wit h t r e e s i z e corresponds c l o s e l y w i t h the onset of c o m p e t i t i o n f o r a wide range of s p a c i n g s . T h i s can be used f o r a s s e s s i n g the onset of co m p e t i t i o n f o r red pine stands on d i f f e r e n t s i t e s without making comparisons w i t h open-grown t r e e s or stands w i t h d i f f e r e n t s pacings on the same s i t e . The occurrence of l i t t l e v a r i a b i l i t y of RGR wit h t r e e s i z e at the begin n i n g of c o m p e t i t i o n probably occurs f o r other s p e c i e s as w e l l . The r e s u l t s of Pe r r y ( 1 9 8 5 ) suggest t h a t t h i s correspondance i s true f o r D o u g l a s - f i r . 4 . 5 . 1 . 2 - Development i n Height 4 . 5 . 1 . 2 . 1 - Cumulative Increment Compared to DBH, mean h e i g h t d i d not d i f f e r much among spacing s ( F i g u r e 4 . 1 1 ; Table 1 of Appendix 2 ) . F i g u r e 4 . 1 1 completes the graph of S t i e l l and Ber r y ( 1 9 7 7 ) up to age 3 3 , and shows the same l i n e a r t r e n d . More d e t a i l s can be found i n Figure 4 . 1 2 which i l l u s t r a t e s how t o t a l h e i g h t i n c r e a s e d w i t h DBH s i z e 77 FIGURE 4.11: MEAN HEIGHTS FOR ALL SPACINGS OVER AGE 16.001 13 16 19 22 25 28 31 34 TOTAL AGE 78 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 1 .30 Vr / / / // /4 L E G E N D ' a = S P A C I N G : 1 . 2 X 1 . 2 M « = S P A C I N G : 1 . 5 X 1 . 5 M * = S P A C I N G : 1 . 8 X 1 . 8 M 0 - S P A C I N G : 2 . 1 X 2 . 1 M V = 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 o = S P A C I N G : 6 . 0 X 6 . 0 M i • i 1 i • i • i • i 10 12 14 It 18 20 DBH SIZE CLASS (CM) FIGURE 4 . 1 2 . 3 : A G E 2 4 6 8 DBH SIZE CLASS (CM) FIGURE 4 . 1 2 . 4 : A G E 30 12.70 1 1 .98 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 DBH SIZE CLASS (CM) 30 1 r J L E G E N D / 6 = S P A C I N G : 1 . 2 X 1 . 2 M / 0 = S P A C I N G : 1 . 5 X 1 . 5 M < / S P A C I N G : 1 . 8 X 1 . 8 M 'i / 0 = S P A C I N G : 2 . 1 X 2 . 1 M / \ / V = S P A C I N G : 2 . 4 X 2 . 4 M ' i / • = S P A C I N G : 3 . 0 X 3 . 0 M / * • * = SPACING: 4 . 3 X 4 . 3 M ,1 o = S P A C I N G : 6 . 0 X 6 . 0 M • fl i i i" 10 14 18 22 26 30 34 38 DBH SIZE CLASS (CM) 79 c l a s s . The 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 i n the n e s t e d anova ( T a b l e 4 . 1 3 ) . W h i l e no s i g n i f i c a n t d i f f e r e n c e s were o b t a i n e d among s p a c i n g s a t ages 13 and 18, mean h e i g h t v a r i e d a t ages 24, 30, and 33 ( T a b l e 4 . 1 3 ) . The Tukey m u l t i p l e comparisons t e s t f a i l e d to 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 f o r ages 24 and 30. T h i s s i t u a t i o n may be a t t r i b u t e d to the f a c t t h a t the s t a t i s t i c a l t e s t s r e s u l t e d i n v a l u e s j u s t a t the l i m i t o f s i g n i f i c a n c e . The 6.0 m s p a c i n g was found to s i g n i f i c a n t l y d i f f e r from the 2.4 m, 3.0 m, and 2.1 m s p a c i n g a t age 33. However, these d i f f e r e n c e s can h a r d l y be a t t r i b u t e d to the e f f e c t o f c o m p e t i t i o n because the w i d e s t and the c l o s e s t s p a c i n g s d i d not s i g n i f i c a n t l y d i f f e r . T h i s p a t t e r n c o r r e s p o n d s to what has been g e n e r a l l y observed f o r red p i n e : mean h e i g h t i s not s i g n i f i c a n t l y a f f e c t e d by s p a c i n g f o r a t l e a s t the f i r s t 15 to 20 y e a r s ( B e l l a and De F r a n c e s c h i 1974; B e r r y 1969; Bramble et a l . 1949; S t i e l l 1964) . As the s t a n d became o l d e r , no c o n s i s t e n t t r e n d w i t h s p a c i n g appeared . . A l t h o u g h mean h e i g h t has been found to i n c r e a s e w i t h s p a c i n g (Bramble e t a l . 1949; Byrnes and Bramble 1949; R a l s t o n 1954) , the absence o f c o r r e l a t i o n w i t h s tand d e n s i t y has a l s o been r e p o r t e d ( B e l l a and De F r a n c e s c h i 1980; Lemmien 1950; S t i e l l and B i c k e r s t a f f 1959) . 4 . 5 . 1 . 2 . 2 - A b s o l u t e Growth Rate A l t h o u g h t h e r e were l a r g e o s c i l l a t i o n s , AGR i n c r e a s e d w i t h t r e e s i z e : the l a r g e r the t r e e , the f a s t e r i t grew ( F i g u r e 4 . 1 3 ) . T h i s t r e n d i s c o n f i r m e d by the r e s u l t s o f the anova i n which the 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 ( T a b l e 4 . 1 4 ) . 80 T a b l e 4 .13 : T w o - l e v e l - n e s t e d anova t e s t s f o r mean h e i g h t (m). Age S p a c i n g s i n c l u d e d (m) DBH c l a s s S p a c i n g D . F . F D . F . F 13 a l l 54/395 8.13* 6/54 0 . 3 3 n . s . 18 a l l 95/409 58.84* 7/95 0 . 9 9 n . s . 24 a l l 108/373 23.10* 7/108 2.18* 30 a l l 118/349 13.67* 7/118 2.71* 33 a l l 113/342 10.78* 7/113 5.34* * : 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 o f 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 d i f f e r e n c e . Comparison of mean h e i g h t s among the spacings Tukey's m u l t i p l e range t e s t s Age s p a c i n g (m) 1.2 1.5 1.8 2.1 2.4 3.0 4.3 6.0 24 9 .64a* 10 .19a 10.05a 10.47a 10 .32a 10 .47a 9.36a 9.51a 30 13 .15a 13 .36a 13 .29a 14 .16a 13.92a 14.02a 12.92a 13.02a 33 15.07ab 14.58ab 14.37ab 15.66a 15 .36a 15.59a 14.32ab 13.89b * : the 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 not 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 o f 0 .05 . 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 . 9 5 0 0 . 8 8 5 0 . 8 2 0 c t o < b J >-\ 0 2 7 5 5 6 9 0 ( — 0 . 6 2 5 I o U 0 . I oo. < 5 6 0 4 9 5 0 . 4 JO 0 . 3 6 5 0 . 3 0 0 DBH SIZE CLASS (CM) FIGURE 4.13.3: AGE 24 DBH SIZE CLASS (CM) FIGURE 4.13.4: AGE 30 0 . 9 0 0 H 0 . 8 2 7 i 0 . 7 5 4 tC 0 . 6 8 1 • >-\ 0 . 2 h O . I o U o I QC O O . < 6 0 8 J 5 3 5 - ^ 4 6 2 -3 8 9 i 0 . 8 0 0 0 . 7 2 6 0 . 3 1 6 0 . 2 4 3 -0 . 1 7 0 L'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 i l l Mi i 0 . 0 6 0 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 i vw 10 15 2 0 2 3 3 0 10 2 6 DBH SIZE CLASS (CM) I 18 2 2 DBH SIZE CLASS (CM) 3 0 3 4 3 8 82 T a b l e 4 .14: T w o - l e v e l nes ted anova t e s t s f o r AGR i n h e i g h t ( m / y e a r ) . Age S p a c i n g s i n c l u d e d (m) DBH c l a s s D . F . F S p a c i n g D . F . F 13 a l l 18 a l l 24 a l l 30 a l l 54/392 5.55* 93/408 1.82* 107/370 2.16* 114/341 1.70* 6/54 3.10* 7/93 12.54* 7/107 1 .14n . s 7/114 11.58* * : 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 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 d i f f e r e n c e . Comparison of mean h e i g h t s among the s p a c i n g s Age T u k e y ' s m u l t i p l e range t e s t s S p a c i n g (m) 1.2 1.5 1.8 2.1 2.4 3.0 4.3 6.0 13 0 .62a* 0 .74a 0 .75a 18 0 .44a 0.55bc 0.50b 30 0 .45abc 0 .38abc 0.36c 0.76a 0.73a 0.76a 0.54bc 0 .62cd 0.65d 0.45abc 0.45abc 0.51ab 0.59a 0 .56bcd 0.45a 0.57ab 0.29 * : the 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 not 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 .05 . 83 Even though t h e r e were s i g n i f i c a n t d i f f e r e n c e s , mean AGR d i d not show any t r e n d of v a r i a t i o n w i t h s p a c i n g ( T a b l e 4 . 1 4 ) . Whi le the main f a c t o r o f the anova was s i g n i f i c a n t a t age 13, the m u l t i p l e compar i son t e s t f a i l e d to d e t e c t which means d i f f e r e d s i g n i f i c a n t l y . S i g n i f i c a n t d i f f e r e n c e s were a l s o found at ages 18 and 30. However, the m u l t i p l e range t e s t showed t h a t there was no t r e n d of v a r i a t i o n i n AGR w i t h s p a c i n g . F i n a l l y , no s i g n i f i c a n t d i f f e r e n c e s were d e t e c t e d at age 24. I t i s g e n e r a l l y a c c e p t e d t h a t mean h e i g h t growth does not v a r y over a wide range o f s p a c i n g ( C l u t t e r e t a l . 1983; Shepherd 1986) , except when the s t a n d i s v e r y open or v e r y c l o s e d ( D a n i e l e t a l . 1979) . The r e s u l t s r e p o r t e d above su p p or t t h i s . Even though i t was d i f f i c u l t to demonstrate s i g n i f i c a n t d i f f e r e n c e s at age 13, the w i d e s t s p a c i n g tended to d i f f e r from the i n t e r m e d i a t e s p a c i n g s . A t age 18, s l i g h t d i f f e r e n c e s were found among the i n t e r m e d i a t e s p a c i n g s compared to the w i d e s t and narrowes t ones . The same t r e n d a l s o o c c u r r e d a t age 30. The absence o f 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 24 c o r r e s p o n d e d to c l o s e r v a l u e s i n mean AGR than f o r the o t h e r y e a r s . There was a good correspondance between i n c r e a s e s i n h e i g h t AGR and i n c r e a s e s i n d e g r e e - d a y s compared to the p r e v i o u s year at ages 17, 20, 24, and 26 ( F i g u r e 4 . 1 4 ) . However, t h e r e appeared to be a d e l a y e d r e l a t i o n s h i p between i n c r e a s e s i n p r e c i p i t a t i o n and i n c r e a s e s i n AGR at ages 17, 20, and 24. For each of these y e a r s , the p r e v i o u s growing season was c h a r a c t e r i z e d by h i g h p r e c i p i t a t i o n . T h i s d e l a y e d e f f e c t r e f l e c t s the f a c t t h a t shoot e l o n g a t i o n i s a two-year p r o c e s s , e s p e c i a l l y f o r a s p e c i e s such as red p i n e ( D a n i e l e t a l . 1979) . A c c o r d i n g to Assmann (1970) , D a n i e l e t a l . (1979) , and Lanner (1985) , the f o r m a t i o n of the 84 FIGURE 4 . 14 HEIGHT AGR DATA SUPERIMPOSED CL IMATIC VARIABLES o . s o o 0 . 7 4 8 0 . 6 9 S O . S 4 4 \ 0 . 5 9 2 h ^ " 0 . 5 4 0 g 0 . 4 8 8 ^ 0 . 4 3 6 0 . 3 8 4 0 . 3 3 2 0 . 2 8 0 A V E R A G E A O R ( H E I G H T ) ' O R A L L S P A C I N G S O V E R A C E 1 - 2 X 1 . 2 M 1 . 5 X I S M 1 . 9 X 1 . 8 M — 2 . 1 X 2 - 1 M — 2 . 4 X 2 . 4 M — 3 . 0 X 3 . 0 M — 4 - . 3 X 4 . 3 M — e . o X 6 . 0 M 1 2 1 » 1 8 2 1 2 4 2 7 2 4 . 0 2 2 . 4 .— . 2 0 . S CO ^ g 1 9 . 2 <~> 25 OO F 1 7 * U J U J ce co ^ O 1 e o 2 a | 1 4 . 4 =S 1 1 . 2 e.e 8.0 L E G E N D A — M E A N M A X I M U M T E M P E R A T U R E O — M E A N M I N I M U M T E M P E R A T U R E © — M E A N T E M P E R A T U R E 1 2 1 5 2 7 2 1 2 4 T O T A L A G E 3 3 85 FIGURE 4 . 1 4 : (CONTINUED) A V E R A G E A O R ( H E I G H T ) F O R A L L S P A C I N G S O V E R A G E 2 . 4 X 2 . 4 M 3 . 0 X 3 . 0 M 4 . 3 X 4 . 3 M S . O X C O M 1 S 1 8 2 1 2 4 2 7 3 0 3 3 1 5 2 1 2 4 T O T A L A G E 3 0 3 3 86 m e r i s t e m a t i c bud i n the p r e v i o u s season i s i n f l u e n c e d by s o i l m o i s t u r e c o n d i t i o n s , n u t r i t i o n a l s t a t u s , and t e m p e r a t u r e . When m e r i s t e m a t i c a c t i v i t y beg ins i n the c u r r e n t s eason , shoot e l o n -g a t i o n i s a l s o i n f l u e n c e d by the p r e v a i l i n g c l i m a t i c c o n d i t i o n s . 4 . 5 . 1 . 2 . 3 - R e l a t i v e Growth Rate D e s p i t e l a r g e f l u c t u a t i o n s , h e i g h t RGR d e c r e a s e d w i t h age ( F i g u r e 4 . 1 5 ) . A t age 13, i t g e n e r a l l y d e c r e a s e d w i t h t r e e s i z e w i t h i n a l l s p a c i n g s ( F i g u r e 4 . 1 6 . 1 ) . F i v e y e a r s l a t e r , the d e c r e a s i n g r a t e o f RGR w i t h t r e e s i z e f o r the narrowes t spac ings was r e d u c e d . The same t r e n d i s more n o t i c e a b l e a t age 24. When the s t a n d reached 30 y e a r s , RGR i n c r e a s e d w i t h t r e e s i z e i n the c l o s e s t s p a c i n g s , w h i l e i t s t i l l d e c r e a s e d i n the w i d e s t ones . Compared to DBH and b a s a l a r e a ( F i g u r e s 4.9 and 4 . 1 0 ) , there were more f l u c t u a t i o n s and the change i n the r e l a t i o n s h i p between RGR and t r e e s i z e o c c u r r e d s l o w l y . The v a r i a t i o n i n RGR w i t h t r e e s i z e i s c o n f i r m e d i n T a b l e 4.15 i n which the 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 ages . The same p a t t e r n of v a r i a t i o n was o b s e r v e d by C a n n e l l e t a l . (1984) i n a c o m p e t i t i o n exper iment i n v o l v i n g s e e d l i n g s o f S i t k a spruce and l o d g e p o l e p i n e . In t h i s s t u d y , 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 were found o n l y at ages 18 and 24. The m u l t i p l e range t e s t s showed t h a t h e i g h t RGR d i d not v a r y much w i t h s p a c i n g , and t h a t most o f the s p a c i n g s were not s i g n i f i c a n t l y d i f f e r e n t , b e i n g p a r t i t i o n e d i n t o o n l y two g r o u p s . Even though f l u c t u a t i o n s w i t h c l i m a t e were l e s s pronounced than those o f AGR, t h e r e appeared to be a correspondance between i n c r e a s e s i n RGR and i n c r e a s e s i n d e g r e e - d a y s a t ages 17, 20, and 24 ( F i g u r e 4 . 1 7 ) . Except f o r age 20, an i n c r e a s e i n RGR was 87 FIGURE 4.15: MEAN HEIGHT RGRs FOR ALL SPACINGS OVER AGE 0.240 0.218 0.196 0.174 < Id >-0.152-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 .0.130-I o u I O cr 0.108 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 i i i — i — i — ' — i — > i 13 16 19 22 25 TOTAL AGE 28 31 88 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 0.340 0.316 0.292< 2 \ 0 2 268 244 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 0.220 H I S2o. LI i c c o . o 196 172 0. 148 0. 124 0 . 100 DBH SIZE CLASS (CM) FIGURE 4.16.3: AGE 24 0. 20 0. 18 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 - SPACING: 2.4X2.4 M = SPACING: 3.0X3.0 M = SPACING: 4.3X4.3 M = SPACING: 6.0X6.0 M 6 8 10 12 14 DBH SIZE CLASS (CM) FIGURE 4.16.4: AGE 30 0.130 o . o o o 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 v o = SPACING: 6.0X6.0 M £ 0 10 15 20 25 DBH SIZE CLASS (CM) 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 .0000 ' 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 DBH SIZE CLASS (CM) 89 T a b l e 4 .15 : T w o - l e v e l n e s t e d anova t e s t s f o r RGR i n h e i g h t ( m / y e a r / m ) . Age S p a c i n g s i n c l u d e d (m) 13 a l l 18 a l l 24 a l l 30 a l l DBH c l a s s D . F . F S p a c i n g D . F . F 54/392 8.88* 93/408 4.58* 107/370 2.88* 114/341 1.52* 6/54 0 .81n . s 7/93 5.36* 7/107 1 .07n . s 7/114 10.16* * : 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 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 . Age Comparison o f mean RGRs i n h e i g h t among the s p a c i n g s T u k e y ' s m u l t i p l e range t e s t s S p a c i n g (m) 1.2 1.5 1.8 2.1 2.4 3.0 4.3 6.0 18 0 .07a* 24 0 .03ab 0.08b 0.03b 0.07a 0.02b 0.08b 0.03ab 0.09b 0.03ab 0.10b 0 .03a 0.10b 0.03a 0.07a 0.02b * : The 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 not 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 0.05. 90 FIGURE 4 . 1 7 : HEIGHT RGR DATA SUPERIMPOSED CL IMATIC VARIABLES 0 . 2 4 0 0 . 2 1 8 O. 1 9 6 O. 1 7 4 O. 1 5 2 O. 1 3 0 O. 1 O S O . O S S 0 . 0 8 4 0 . 0 4 2 0 . 0 2 0 A V E R A G E R O R ( H E I G H T ) F O R A L L S P A C I N G S O V E R A G E L E G E N D A — 1 . 2 X 1 . 2 M O — 1 .3 X 1 .S M — 1 . 8 X 1 . 8 M o — 2 . 1 X 2 . 1 M V — 2 . 4 X 2 . 4 M • — 3 . 0 X 3 . 0 M — 4 . 3 X 4 . 3 M — « . 0 X 6 . 0 M 1 2 21 2 4 .2 7 3 0 2 4 . 0 2 2 . 4 2 0 . S 1 9 . 2 6 £2 o 1 6 . o 1 4 . 4 LP 1 2 8 1 1 . 2 9 . 6 8 . 0 L E G E N D A — M E A N M A X I M U M T E M P E R A T U R E O — M E A N M I N I M U M T E M P E R A T U R E o — M E A N T E M P E R A T U R E 3— 3 b 3 3 1 2 21 2 4 T O T A L A G E 91 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 c i p i t a t i o n d u r i n g the p r e v i o u s g r o w i n g season. The same reasons as mentioned f o r AGR may e x p l a i n t h i s d e l a y e d e f f e c t . 4 . 5 . 1 . 3 - Development i n Volume 4 . 5 . 1 . 3 . 1 - C u m u l a t i v e Increment The g e n e r a l t r e n d was an i n c r e a s e i n the mean t r e e volume w i t h s p a c i n g ( T a b l e 4 . 1 6 ) . Except a t age 1 3 , t h e r e were 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 ( T a b l e 4 . 1 7 ) . The DBH n e s t i n g f a c t o r i n the anova i n d i c a t e d a s i g n i f i c a n t r e l a t i o n s h i p between t r e e volume and DBH ( T a b l e 4 . 1 7 ) . There appears t o be an expo-n e n t i a l r e l a t i o n s h i p between DBH and volume ( F i g u r e 4 . 1 8 ) . T h i s s u g g e s t s t h a t the 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 the s e n s i t i v i t y o f DBH t o d e n s i t y because h e i g h t growth was n ot found t o be much a f f e c t e d by s p a c i n g . 4 . 5 . 1 . 3 . 2 - A b s o l u t e Growth Rate C o n t r a r y t o DBH and b a s a l a r e a , the t r e n d i n volume AGR was an i n c r e a s e from age 13 t o age 2 3 , and then a s t a b i l i z a t i o n or a s l i g h t r e d u c t i o n ( T a b l e 4 . 1 8 ) . Except a t age 1 3 , 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 were found a t a l l ages ( T a b l e 4 . 1 9 ) . The g e n e r a l t r e n d was an i n c r e a s e i n AGR w i t h s p a c i n g . The 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 e v e r y age; the l a r g e r the t r e e , the g r e a t e r AGR. A t age 1 3 , the r e l a t i o n s h i p between DBH and volume AGR was l i n e a r f o r the w i d e s t s p a c i n g s ; f o r the narrow s p a c i n g s , i t was e x p o n e n t i a l ( F i g u r e 4 . 1 9 ) . Above age 1 3 , the r e l a t i o n s h i p s were a l l l i n e a r . 93 TABLE 4 .16: Mean volumes per t r e e (m 3 ) f o r a l l s p a c i n g s over age . S p a c i n g (m) 13 18 Age 23 28 33 1 .2x1 .2 Mean N -0 .004841 83 0 .021800 61 0 .047590 55 0 .085120 46 0 .134100 37 1 .5x1 .5 Mean N 0 .006861 66 0 .027996 62 0 .060310 58 0 .092080 56 0 .124120 54 1 .8x1 .8 Mean N 0 .006919 63 0 .032480 58 0 .070682 57 0 .113120 54 0 .147410 54 2 .1x2 .1 Mean N 0 .007388 63 0 .037179 61 0 .090677 59 0 .146110 57 0 .211770 54 2 .4x2 .4 Mean N 0 .007273 58 0 .039879 58 0 .106000 58 0 .177510 57 0 .249300 56 3 . 0x3 .0 Mean N 0 .007683 60 0 .047819 59 0 .141000 58 0 .251160 58 0 .353940 58 4 .3x4 .3 Mean N 0 .006982 62 0 .041389 58 0 .140250 56 0 .285650 56 0 .432260 53 6 . 0x6 .0 Mean N - 0 .059785 95 0 .194800 94 0 .413490 94 0 .634690 92 Table 4.17: Two-level nested anova t e s t s f o r t o t a l volume (m 3). Age Spacings i n c l u d e d (m) DBH c l a s s Spacing D . F . F D . F . F 13 a l l 54/394 199.88* 6/54 0.29n.s. 18 a l l 95/409 175.73* 7/95 4.30* 23 a l l 110/377 113.67* 7/110 16.93* 28 a l l 111/359 80.72* 7/111 35.20* 33 a l l 113/339 59.47* 7/113 48.17* *: 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 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 d i f f e r e n c e . 94 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 10 * 0.0138 * 2 UJ 0.01 15 2 D 0.0092 0.0069 0.0046 0.0023 0.0000 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 3 4 5 6 7 DBH SIZE CLASS (CM) FIGURE 4.18.3: AGE 23 10 0. I 10 0.099 0.088 0.077 10 » 0 066 * 2 —^' LI 0 055 2 D 044 O > 0 033 0.022 0.011 0.000 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 6 8 10 12 DBH SIZE CLASS (CM) FIGURE 4.18.4: AGE 28 14 16 18 20 0.280 0.252 0.224 0. 196 10 » 0. 168 UJ 0. 140 2 D 0.112 0.084 0.056 0.028 0.000 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 6 8 10 12 14 16 18 20 22 24 26 28 DBH SIZE CLASS (CM) 0.550 0. 495 0. 440 0.383 0.055 0.000 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 7 4 11 f/f 12 15 18 21 24 27 30 33 36 DBH SIZE CLASS (CM) 95 TABLE 4 .18: Mean AGRs i n volume ( m 3 / y e a r ) f o r a l l s p a c i n g s over age . S p a c i n g Ages (m) 13 18 23 28 1 .2x1 .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 .8x1 .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 58 0 .013220 58 0 .013950 57 0 .013804 56 3 .0x3 .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 T a b l e 4 .19 : T w o - l e v e l - n e s t e d anova t e s t s f o r AGR i n volume ( m 3 / y e a r ) . Age S p a c i n g s i n c l u d e d (m) DBH c l a s s S p a c i n g 13 a l l 18 a l l 23 a l l 28 a l l D . F . F D . F . F 54/356 62.44* 6/54 2 . 2 2 n . s . 89/398 39.59* 7/89 26.13* 103/367 17.65* 7/103 72.55* 106/346 6.66* 7/106 103.21* * : 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 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 . 96 FIGURE 4. 19 VOLUME AGRs AS A FUNCTION OF DBH SIZE CLASS FIGURE 4.19.1: AGE 13 FIGURE 4.19.2: AGE 18 0 .016B 0.0151 0.0135 : 0.0115 2 >-">0 .0102 ,0.0085 LEGEND : SPACING: 1.2X1.2 M SPACING: 1.5X1.5 M S^PACING: 1.8X1.8 M S^PACING: 2.1X2.1 M • SPACING: 2.4X2.4 M • SPACING: 3.0X3.0 M • SPACING: 4.3X4.3 M o. oo 1 9 0.0002 3 4 5 B 7 8 9 10 DBH SIZE CLASS (CM) FIGURE 4.19.3: AGE 23 0.040 0.036 0.032 # * 2 028 024 0.020 O O . :> g o . < 016 012 0.008 0.004 0.000 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 10 12 14 16 18 20 DBH SIZE CLASS (CM) FIGURE 4.19.4: AGE 28 0.0540 0.0486-0.04321 % 0.0378^ ^>0.0324J 0.0054 0.0000 / 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 ,*"*\ } I / 0.060 0.054 0.048 \o. 042 036 ,0 .030 _ l O 0 > et o o < 024 018 0.012 0.006 0 . 0 0 0 * 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 • J 9 12 15 18 21 24 27 30 33 36 DBH SIZE CLASS (CM) DBH SIZE CLASS (CM) 97 4 . 5 . 1 . 3 . 3 - R e l a t i v e Growth Rate Mean volume RGR d e c r e a s e d w i t h age ( T a b l e 4 . 2 0 ) . S i g n i -f i c a n t d i f f e r e n c e s were found at a l l ages ( T a b l e 4 . 2 1 ) . The g e n e r a l t r e n d c o n s i s t e d o f an i n c r e a s e i n RGR w i t h s p a c i n g . The r e s u l t s o f the anova i n d i c a t e d t h a t RGR v a r i e d s i g n i f i c a n t l y w i t h t r e e d i a m e t e r ( T a b l e 4 . 2 1 ) . I t d e c r e a s e d as DBH i n c r e a s e d at age 13 ( F i g u r e 4 . 2 0 . 1 ) . When the s tands were 18 y e a r s o l d , the RGR at the n a r r o w e s t s p a c i n g i n c r e a s e d w i t h DBH, remained c o n s t a n t at s p a c i n g s o f 1.5 m and 1.8 m ( a p a r t from the lowest c l a s s e s ) , and d e c r e a s e d w i t h i n c r e a s i n g DBH at the w i d e s t s p a c i n g s ( F i g u r e 4 . 2 0 . 2 ) . The same t r e n d c o n t i n u e d at ages 23 and 28 ( F i g u r e s 4 .20 .3 and 4 . 2 0 . 4 ) . E s s e n t i a l l y , volume RGR showed the same p a t t e r n s as those o f d iameter and b a s a l a r e a . T h e r e f o r e , the i n t e r p r e t a t i o n i n terms of e f f i c i e n c y i s the same. 4 . 5 . 2 - F u n c t i o n a l A p p r o a c h As p r e v i o u s l y ment ioned , the f u n c t i o n a l approach may be used to complement the c l a s s i c a l approach and to b e t t e r v i s u a l i z e the development o f i n d i v i d u a l t r e e s . For i n s t a n c e , i t i s p o s s i b l e to observe p r e c i s e l y how the RGR ( i . e . , e f f i c i e n c y ) o f i n d i v i d u a l t r e e s v a r i e s b e f o r e and a f t e r the onset o f c o m p e t i t i o n . E q u a -t i o n s have been f i t t e d to i n d i v i d u a l t r e e s by d i f f e r e n t r e s e a r -c h e r s ( e . g . , P i e n a a r and T u r n b u l l 1973, Sweda 1984, and Yang et a l . 1978) . However, no s t u d i e s were found i n which growth i n d i c e s , such as AGR or RGR were d e r i v e d and used to compare the development o f i n d i v i d u a l t r e e s . 98 TABLE 4 .20: Mean RGRs i n volume ( m 3 / y e a r / m 3 ) f 0 r a l l s p a c i n g s over age . S p a c i n g Ages (m) 13 18 23 28 1 .2x1 .2 Mean N 0. 255830 61 0 .128140 55 0 .075880 46 0 .053640 37 1 .5x1 .5 Mean N 0. 281900 62 0 .137070 58 0 .073086 56 0 .048586 54 1 .8x1 .8 Mean N 0. 311860 58 0 .147990 57 0 .078509 54 0 .047720 54 2 .1x2 .1 Mean N 0. 342040 61 0 .171400 59 0 .083402 57 0 .061938 54 2 .4x2 .4 Mean N 0. 366340 58 0 .204300 58 0 .100070 57 0 .065037 56 3 . 0x3 .0 Mean N 0. 406490 59 0 .229120 58 0 .120700 58 0 .070599 58 4 .3x4 .3 Mean N 0. 369140 58 0 .268200 56 0 .151270 56 0 .088417 55 6 . 0x6 .0 Mean N - 0 .245860 94 0 .153690 94 0 .087128 92 T a b l e 4 . 2 1 : T w o - l e v e l n e s t e d anova t e s t s f o r RGR i n volume (m 3 / y e a r / m 3 ) . Age S p a c i n g s i n c l u d e d (m) 13 a l l 18 a l l 23 a l l 28 a l l DBH c l a s s D . F . F S p a c i n g D . F . F 54/356 8.05* 89/398 12.05* 103/367 6.52* 106/346 4.49* 6/54 16.91* 7/89 30.89* 7/103 45.80* 7/106 24.93* * : 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 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 . 99 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 0.563 N0 .526 10 2 0.489 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 7 8 9 DBH SIZE CLASS (CM) FIGURE 4.20.3: AGE 23 0.440 0.399 0.358 ^ 0 . 3 1 7 C£ fi 0.276 \ 10 0.071 0.030 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 " x -^ ,o = SPACING: 6.0X6.0 M \\\ DBH SIZE CLASS (CM) FIGURE 4.20.4: AGE 28 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 0.150 0.010 cure 0.015 0.000 6 8 12 13 18 21 24 DBH SIZE CLASS (CM) 27 30 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 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) 100 4 . 5 . 2 . 1 - C u m u l a t i v e Increment A l l the f u n c t i o n s 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 of d e t e r m i n a t i o n ( T a b l e 1 of Appendix 3 ) . The p r e d i c t e d v a l u e s of DBH were c l o s e to the o b s e r v a t i o n s ( F i g u r e 1 o f Appendix 3 ) . On ly a few t r e e s were b a d l y r e p r e s e n t e d by the d e r i v e d f u n c t i o n s . The e q u a t i o n s f o r some t r e e s showed a d e c l i n e around 33 y e a r s of age . Even though the f i t was good, t h i s s i t u a t i o n i s not r e p r e -s e n t a t i v e o f growth a t t h i s age . I t i s p o s s i b l e t h a t a n o n l i n e a r f u n c t i o n ( i . e . , the W e i b u l l f u n c t i o n ) might have produced b e t t e r r e s u l t s (Payandeh 1983) . D e s p i t e these s h o r t c o m i n g s , i t was s t i l l p o s s i b l e to make comparisons among t r e e s . W h i l e the range o f i n i t i a l DBHs was a p p r o x i m a t e l y the same at age 13, t r e e s reached g r e a t e r v a l u e s a t age 33 as s p a c i n g was i n c r e a s e d . T h i s t r e n d was apparent i n the parameters f o r age which i n c r e a s e d w i t h s p a c i n g ( T a b l e 1 o f Appendix 3 ) . In g e n e r a l , the t r e e s kept t h e i r s o c i a l s t a t u s . The l a r g e r the t r e e a t a young age, the l a r g e r i t was a t o l d e r ages . However, by age 33 the m a j o r i t y o f the t r e e s had changed t h e i r rank s l i g h t l y . T h i s may be seen i n T a b l e 1 (Appendix 3) by comparing the ranks f o r DBH at ages 13 and 33. Most of the d i f f e r e n c e s between ranks are 0 or 1. Seven t r e e s out o f 80 had a d i f f e r e n c e o f 2, 7 had a d i f f e r e n c e o f 3, 4 had a d i f f e r e n c e o f 4, and o n l y 1 had a d i f f e r e n c e as l a r g e as 5. 4 . 5 . 2 . 2 - A b s o l u t e Growth Rate E q u a t i o n s f o r AGR were o b t a i n e d as the f i r s t d e r i v a t i v e of the growth f u n c t i o n s ( T a b l e 2 and F i g u r e 2 o f Appendix 3 ) . Nega-t i v e v a l u e s appeared f o r some t r e e s around age 33. T h i s o c c u r r e d because the model used d i d not r e p r e s e n t a d e q u a t e l y the r a t e o f 101 d e c l i n e i n growth at t h i s age. However, the equations showed the major trends i n such a way t h a t i t was p o s s i b l e to make compa-r i s o n s because a l l the t r e e s kept the same p o s i t i o n s r e l a t i v e to each o t h e r . As s p a c i n g i n c r e a s e d , AGR i n c r e a s e d ( F i g u r e 2 of Appendix 3 ) . The parameters f o r age, which c o n s t i t u t e the s l o p e s of the f u n c t i o n s , i n c r e a s e d i n a b s o l u t e value with s p a c i n g (Table 2 of Appendix 3 ) . T h i s suggests t h a t the r a t e of decrease i n AGR o c c u r r e d a l i t t l e more r a p i d l y with a r e d u c t i o n i n stand d e n s i t y . The examination of the DBHs at ages 13 and 33 by d e c r e a s i n g order of AGR showed t h a t low AGRs were g e n e r a l l y a s s o c i a t e d with small t r e e s and h i g h AGRs wit h l a r g e ones ( F i g u r e 2 of Appendix 3 ) . However, there were no t a b l e e x c e p t i o n s : at both ages, l a r g e t r e e s may have low AGRs, and small t r e e s h i g h AGRs. The ranks f o r AGR show t h a t there was no c o n s i s t e n t r e l a t i o n s h i p with age (Table 2 of Appendix 3 ) . For every p l o t , the mean d i f f e r e n c e i n rank f o r AGR between ages 13 and 33 i s higher than t h a t f o r cumu-l a t i v e increment, and most of the d i f f e r e n c e s were g r e a t e r than 3 . T h i s i n d i c a t e s t h a t the t r e e s d i d not keep the same s o c i a l s t a t u s i n AGR with age. 4 . 5 . 2 . 3 - R e l a t i v e Growth Rate As p r e v i o u s l y s t a t e d , the RGR equations were d e r i v e d by computing the f i r s t d e r i v a t i v e of the equations o b t a i n e d by f i t t i n g the n a t u r a l l o g a r i t h m of DBH over time (Table 3 of Appendix 3 ) . Even though the p r e d i c t e d v a l u e s f o r RGR were very c l o s e to the o b s e r v a t i o n s , n e g a t i v e v a l u e s around the ages 30 and 33 were o b t a i n e d ( F i g u r e 3 of Appendix 3 ) . As was the case f o r AGR, t h i s was a problem r e l a t e d to the r e g r e s s i o n model. 102 S i m i l a r trends to AGR were e v i d e n t ; RGR at any age i n c r e a s e d w i t h s p a c i n g , and i t s r a t e of decrease over age i n c r e a s e d . The same p a t t e r n o c c u r r e d w i t h i n every p l o t . At age 13, the s m a l l e r the t r e e , the g r e a t e r the RGR. Subsequently, the t r e e s reached a p o i n t where the RGRs had very c l o s e v a l u e s . T h i s took p l a c e between the ages 22 and 23 f o r the 1.2 m s p a c i n g , 25 and 26 f o r the 1.8 m s p a c i n g s , and 27 and 28 f o r the 3.0 m s p a c i n g . For the 6.0 m s p a c i n g , o n l y one set of t r e e s had very c l o s e v a l u e s i n RGR by age 31 ( F i g u r e 3.4 of Appendix 3 ) . F o l l o w i n g t h i s p e r i o d , the r e l a t i o n s h i p between t r e e s i z e and RGR was r e v e r s e d ; the l a r g e r the t r e e , the g r e a t e r the RGR. However, not a l l the t r e e s f o l l o w e d the p a t t e r n d e s c r i b e d above. Some small t r e e s had lower RGRs than l a r g e r t r e e s at age 13, and v i c e v e r s a • T h i s was l e s s pronounced than f o r AGR; RGR was c h a r a c t e r i z e d by a more sy s t e m a t i c p a t t e r n of change than AGR. A l l the t r e e s shown were a f f e c t e d by the same type of change; h i g h l y e f f i c i e n t t r e e s at age 13 became compa r a t i v e l y l e s s e f f i c i e n t at age 33 and v i c e v e r s a . These o b s e r v a t i o n s were supported by the mean d i f f e r e n c e s between the ranks f o r RGR at both ages (Table 3 of Appendix 3 ) . For the three v a r i a b l e s , mean d i f f e r e n c e s were mostly between 1 and 2 ( i . e . , s m a l l e r than those of AGR). Only a few v a l u e s were g r e a t e r than 3. 4.5.3- E s t i m a t i o n of the P o t e n t i a l Growth Rate of Stand-Grown Trees from Open-Grown Trees When a s i n g l e - t r e e distance-dependent model i s used i n s i m u l a t i o n , a major step c o n s i s t s of e s t i m a t i n g p o t e n t i a l growth ra t e ( A l i g et a l . 1984; Ek and Monserud 1975; Loucks et a l . 1982; Smith and W i l l i a m s 1980). The m a j o r i t y of these models have been based upon Newnham's (1964) assumptions (Ek and Monserud 1975; 103 Loucks et a l . 1981). One of these concerns the e s t i m a t i o n of the p o t e n t i a l growth rate of t r e e s . Although w i d e l y used i n s i m u l a t i o n , t h i s assumption has never been t e s t e d . The main o b j e c t i v e of t h i s s e c t i o n i s to t e s t not o n l y t h i s assumption, but a l s o a l t e r n a t i v e ones. Except f o r the f i r s t four t r e e s , the open-grown t r e e s measured a l l appeared to have the same ge n e r a l t r e n d , at l e a s t f o r the f i r s t 3 5 years (Table 4 . 2 2 , F i g u r e 4 . 2 1 ) . The equation of Ek ( 1 9 7 1 ) , developed from open-grown red pine t r e e s i n Minnesota, i s a l s o i n c l u d e d i n F i g u r e 4 . 2 1 . I t i s l o c a t e d near the middle of the group formed by t r e e s 5 to 1 3 . The f i r s t four t r e e s were r e j e c t e d f o r the purposes of t h i s study because they departed c o n s i d e r a b l y from the m a j o r i t y of the t r e e s and from Ek's e q u a t i o n . T h i s d e c i s i o n was supported by the f a c t t h at these four t r e e s were not l o c a t e d as c l o s e to the s p a c i n g t r i a l as the remaining t r e e s . The W e i b u l l f u n c t i o n was used to d e r i v e a l o c a l growth equ a t i o n f o r DBH as a f u n c t i o n of age at b r e a s t h e i g h t from open-grown t r e e s 5 to 1 3 (Table 4 . 2 3 ) . T h i s e q u a t i o n was a l s o l o c a t e d near the middle of the group formed by t r e e s 5 to 1 3 ( F i g u r e 4 . 2 2 ) . Both Ek's e q u a t i o n and the d e r i v e d e q u a t i o n e s t i m a t e d DBH v a l u e s c l o s e l y f o r at l e a s t the f i r s t 3 0 y e a r s . Beyond t h i s p o i n t , s u b s t a n t i a l d i f f e r e n c e s o c c u r r e d because asymptotic v a l u e s were a t t a i n e d at d i f f e r e n t ages. For t h i s reason, o n l y the f i r s t 3 5 years are shown on the graph. Even though the equations d i d not d i f f e r g r e a t l y w i t h i n the range of age c o n s i d e r e d , i t was d e c i d e d to perform t e s t s u s i n g both e q u a t i o n s when i t was p o s s i b l e to do so. (They w i l l be d e s i -gnated as the d e r i v e d e q u a t i o n and Ek's e q u a t i o n , r e s p e c t i v e l y ) . 1 0 4 TABLE 4 . 2 2 : B a s i c growth i n f o r m a t i o n on the open-grown t r e e s . Tree DBH T o t a l h e i g h t Crown Crown B r e a s t h e i g h t numbe r ( cm) (in) w i d t h (m) l e n g t h (m) age 1 5 6 . 7 1 7 . 9 8 . 8 1 2 . 2 8 4 2 5 3 . 9 1 7 . 2 9 . 3 1 3 . 4 7 7 3 5 4 . 9 1 5 . 2 9 . 8 1 2 . 4 7 9 4 5 0 . 0 1 6 . 6 9 . 2 1 2 . 8 7 0 5 5 0 . 5 1 2 . 1 9 . 7 1 1 . 4 3 7 6 5 1 . 3 1 5 . 1 1 1 . 0 1 4 . 2 3 5 7 4 9 . 8 1 4 . 1 9 . 2 1 3 . 3 3 6 8 3 9 . 7 1 1 . 0 9 . 3 1 0 . 0 2 7 9 6 5 . 7 1 6 . 0 9 . 7 1 3 . 9 7 8 1 0 4 3 . 5 1 3 . 5 8 . 5 1 2 . 5 3 0 1 1 3 8 . 7 1 5 . 0 1 0 . 0 1 3 . 8 2 5 1 2 4 6 . 5 1 3 . 9 9 . 0 1 2 . 3 3 5 1 3 5 9 . 2 1 6 . 2 1 0 . 3 1 2 . 7 5 5 1 0 5 FIGURE 4.21: DBH = F(AGE) FOR OPEN-GROWN TREES 55.0 49 . 5 44 . 0 38 . 5 33.0 CJ I 00 Q 27.5-22.0-16.5 11.0-5.5-0.0 LEGEND A = TREE| 1 0= TREEf 2 0= TREEf 3 0 = TREEf 4 V= TREE* 5 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 • 1 1 1 1 1 1 1 1 1 1 • i • 1 1 1 • 1 1 1 10 15 20 25 30 35 AGE AT BREAST HEIGHT 106 T a b l e 4 .23 : Comparison of v a l u e s between DBHs o b t a i n e d from E k ' s e q u a t i o n and the d e r i v e d e q u a t i o n . E k ' s e q u a t i o n : -0 .045913xAGE) 1.469047 DBH (cm) = 59 .721242(1-E ) E q u a t i o n d e r i v e d : 1.238790 - (0 .034162xAGE) DBH (cm) - 63 .014384(1-E ) DBH (cm) Age E k ' s e q u a t i o n D e r i v e d e q u a t i o n 1 0.6 0.9 2 1.6 2.2 3 2.9 3.6 4 4.3 5.1 5 5.7 6.7 6 7.3 8.2 7 8.8 9.8 8 10.4 11.4 9 11.9 13.0 10 13.6 14.6 11 15.1 16.2 12 16.7 17.8 13 18.2 19.3 14 19.7 20.8 15 21.2 22.3 16 22.6 23.7 17 24.0 25.2 18 25.4 26.6 19 26.7 27.9 20 27.9 29.2 21 29.2 30.5 22 30.4 31.8 23 31.6 33.0 24 32.7 34.2 25 33.8 35.3 26 34.8 36.4 27 35.8 37.5 28 36.8 38.5 29 37.8 39.6 30 38.7 40.5 31 39.5 41.5 32 40.4 42.4 33 41.2 43.3 34 41.9 44.1 35 42.7 44.9 107 FIGURE 4.22: DBH = F(AGE) FOR OPEN-GROWN TREES O 5 10 15 20 25 30 35 AGE AT BREAST HEIGHT 108 The f i r s t s t e p c o n s i s t e d o f t e s t i n g the h y p o t h e s i s of Ford ( 1 9 7 9 , 1 9 8 4 ) f o r open-grown t r e e s ( i . e . , a l l the t r e e s have the same RGR b e f o r e the on s e t o f c o m p e t i t i o n ) . I n e f f e c t , stand-grown t r e e s b e f o r e the on s e t of c o m p e t i t i o n a r e open-grown t r e e s . DBH RGR o f open-grown t r e e s ( d o t t e d l i n e s ) a r e shown t o g e t h e r w i t h stand-grown d a t a b e f o r e the on s e t of c o m p e t i t i o n ( s o l i d l i n e s ) on F i g u r e 4 . 2 3 f o r the 4 . 3 m s p a c i n g and on F i g u r e 4 . 2 4 f o r the 6 . 0 m s p a c i n g . B oth f i g u r e s show s u b s t a n t i a l d i f f e -r e n ces a t e v e r y age among the RGRs o f i n d i v i d u a l open-grown t r e e s . The h y p o t h e s i s o f Ford ( 1 9 7 9 , 1984) must a g a i n be r e j e c t e d . These f i g u r e s a l s o show t h a t the RGRs o f stand-grown t r e e s a r e c o n t a i n e d w i t h i n the l i m i t s d e f i n e d by the RGRs of open-grown t r e e s . T h e r e f o r e , o t h e r h y p otheses e s t i m a t i n g the p o t e n t i a l growth r a t e o f stand-grown t r e e s can be c o n s i d e r e d . The f o l l o w i n g two hyp o t h e s e s were t e s t e d : (1) the p o t e n t i a l i n c r e m e n t o f 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 of an open-grown t r e e o f the same DBH, and ( 2 ) the p o t e n t i a l i n c r e m e n t o f a stand-grown t r e e i n terms o f RGR i s e q u a l t o t h a t of an open-grown t r e e o f the same DBH. The in c r e m e n t o f open-grown t r e e s was computed from the d e r i v e d e q u a t i o n and Ek's e q u a t i o n by s o l v i n g the 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 the stand-grown t r e e s compared. R e s u l t s a r e l i s t e d i n T a b l e s 4 . 2 4 and 4 . 2 5 f o r the 4 . 3 m and 6 . 0 m s p a c i n g f o r a 1-year growth p e r i o d . I n g e n e r a l , the d e r i v e d e q u a t i o n and the e q u a t i o n of Ek ( 1 9 7 1 ) r e s u l t e d i n n e a r l y e q u a l v a l u e s . W i t h r e s p e c t 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 were found between the c a l c u l a t e d AGR o f stand-grown t r e e s and the v a l u e s computed from the e q u a t i o n s f o r t he 4 . 3 m and 6 . 0 m s p a c i n g r e s p e c t i v e l y ( T a b l e s 4 . 2 4 and 4 . 2 5 ) . For RGR, o n l y one s i g n i f i c a n t d i f f e r e n c e was 109 FIGURE 4 .23 : RGR(DBH) = F(AGE) FOR O P E N - G R O W N TREES AND STAND-GROWN TREES BEFORE THE ONSET OF COMPETITION (SPACING: 4 .3 M) LEGEND = STAND-GROWN TREE « = STAND-GROWN TREE $ = STAND-GROWN TREE = STAND-GROWN TREE = STAND-GROWN TREE-= OPEN-GROWN TREE! 5 = OPEN-GROWN TREES 6 o 7 8 9 10 11 = OPEN-GROWN TREE = OPEN-GROWN TREE = OPEN-GROWN TREE = OPEN-GROWN TREE = OPEN-GROWN TREE = OPEN-GROWN TREE! 12 = OPEN-GROWN TREEf 13 = STAND-GROWN TREES = OPEN-GROWN TREES 3 4 5 AGE AT BREAST HEIGHT LEGEND = STAND-GROWN TREE; : STAND-GROWN TREE) = STAND-GROWN TREE = STAND-GROWN TREE) • STAND-GROWN TREEJ • OPEN-GROWN TREE) = OPEN-GROWN TREE) • OPEN-GROWN TREEj : OPEN-GROWN TREE OPEN-GROWN TREEj OPEN-GROWN TREE OPEN-GROWN TREE OPEN-GROWN TREE OPEN-GROWN TREE 33 35 38 82 99 5 6 7 8 9 10 11 12 13 = STAND-GROWN TREES = OPEN-GROWN TREES AGE AT BREAST HEIGHT TIT R G R ( D B H ) ( C M / Y E A R / C M ) CO o rr: r-o to O J ro O « > -O-O Ca-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 O I I O O o o II II II COCO CO II II co co m o o o I I I o o o S 3 S 3 S3 O O O i 2 2 2 I I O O S 3 S 3 O O O © O O O cn CO o O 00 OO Cn -T CT) R G R ( D B H ) ( C M / Y E A R / C M ) p p p o o ^ '—• ' - ^ ro ro —' -c- o 0-1 - J CT) cn O J 1 '—W 1 w ,W " S i — p ro CD ro p CD O ro CO —H m m O 00 ro II II II 11 11 11 CO CO CO CO 2 2 2 2 2 2 Z I I I I I I O O O O O O . _ S3 S3 S 3 S 3 S3 S 3 Q O Q Q O O Q * * * * * * * Z 2 2 2 Z 2 Z ^ —H — l - j —I —I —I —I —I S 3 S 3 S 3 S 3 S 3 S 3 S 3 S 3 S 3 rnrnrrir^rHrnrnrn rn OO I I O O S 3 S 3 O O S 3 0 0 1 1 0 0 S3 S 3 O O ; * * : z z S 3 S 3 m m co m o S 3 o * z —I S 3 3) O L 7 1 C '73 > z o m O J) O 3D -—GO „ -ODD >m~n Q3> ^ 3 i s 0 0 5-« d m d m 0 0 0 z > z o £~!rororo — — TABLE 4 . 2 4 : Comparison of observed AGRs and RGRs i n DBH of the s tand-grown t r e e s from the 4 . 3 m s p a c i n g be fore the onset of 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 t r e e v a l u e s as d e f i n e d by the second 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 R e l a t i v e growth ra t e (cm/year) (cm/year /cm) De r i v e d E k ' s D e r i v e d E k ' s Tree # Observed e q u a t i o n e q u a t i o n Observed e q u a t i o n e q u a t i o n 1 1 . 8 0 1 . 5 7 1 . 5 7 0 . 2 2 3 0 0 . 1 9 5 9 0 . 1 9 5 0 2 1 . 8 7 1 . 6 0 1 . 6 0 0 . 1 6 6 9 0 . 1 4 1 3 0 . 1 4 1 4 3 1 . 7 5 1 . 6 0 1 . 5 7 0 . 2 0 7 8 0 . 1 8 9 0 0 . 1 8 8 4 4 1 . 8 5 1 . 6 0 * 1 . 5 7 * 0 . 2 0 5 6 0 . 1 7 8 6 0 . 1 7 8 2 5 1 . 6 5 1 . 6 0 1 . 5 7 0 . 1 9 4 7 0 . 1 8 5 9 0 . 1 8 5 5 7 1 . 6 2 1 . 5 7 1 . 5 7 0 . 2 0 8 2 0 . 2 0 3 5 0 . 2 0 2 4 8 1 . 6 5 1 . 6 0 1 . 6 0 0 . 1 5 1 8 0 . 1 4 6 3 0 . 1 4 6 4 9 1 . 8 0 1 . 6 0 1 . 6 0 0 . 1 6 2 5 0 . 1 4 3 8 0 . 1 4 3 9 12 1 . 6 5 1 . 5 5 1 . 5 2 0 . 2 6 4 9 0 . 2 4 8 5 0 . 2 4 5 3 16 1 . 7 5 1 . 5 7 1 . 5 7 0 . 2 5 6 9 0 . 2 2 5 8 0 . 2 2 3 7 17 1 . 8 5 1 . 6 0 1 . 6 0 0 . 1 6 3 7 0 . 1 4 1 9 0 . 1 4 1 9 27 0 . 5 7 1 . 3 3 * 1 . 2 0 * 0 . 3 3 1 0 0 . 6 6 8 4 * 0 . 6 2 5 9 * 30 1 . 6 7 1 . 5 7 1 . 5 5 0 . 2 5 8 4 0 . 2 3 7 3 0 . 2 3 4 7 31 1 . 6 5 1 . 5 2 1 . 5 0 0 . 3 1 5 9 0 . 2 9 1 0 0 . 2 8 5 1 32 1 . 9 2 1 . 6 0 * 1 . 6 0 * 0 . 1 8 3 6 0 . 1 5 2 8 0 . 1 5 2 8 33 1 . 8 2 1 . 6 0 1 . 5 7 0 . 2 0 3 7 0 . 1 7 7 6 0 . 1 7 7 3 35 1 . 5 0 1 . 5 2 1 . 5 0 0 . 2 9 9 0 0 . 3 0 1 6 0 . 2 9 5 2 36 1 . 6 7 1 . 5 7 1 . 5 2 0 . 2 6 2 8 0 . 2 4 4 5 0 . 2 4 1 6 37 1 . 2 5 1 . 5 0 * 1 . 4 2 * 0 . 3 3 2 3 0 . 3 8 1 3 0 . 3 6 8 5 38 1 . 58 1 . 5 7 1 . 5 5 0 . 2 2 5 6 0 . 2 2 4 9 0 . 2 2 3 1 42 1 . 5 7 1 . 6 0 1 . 6 0 0 . 1 4 3 8 0 . 1 4 3 9 0 . 1 4 4 1 46 1 . 7 3 1 . 6 0 1 . 6 0 0 . 1 5 4 0 0 . 1 4 2 9 0 . 1 4 3 0 53 1 . 9 2 1 . 6 0 1 . 6 0 0 . 1 8 5 5 0 . 1 5 3 4 0 . 1 5 3 4 54 1 . 8 3 1 . 5 5 1 . 5 3 0 . 3 4 1 5 0 . 2 6 5 3 0 . 2 6 0 2 64 1 . 5 3 1 . 4 7 1 . 4 0 0 . 4 0 5 7 0 . 3 9 2 0 0 . 3 7 7 6 65 1 . 4 7 1 . 5 0 1 . 4 7 0 . 3 1 7 8 0 . 3 6 2 7 0 . 3 1 6 6 74 1 . 6 3 1 . 50 1 . 4 0 0 . 3 8 0 4 0 . 3 6 2 2 0 . 3 5 1 4 82 1 . 6 0 1 . 5 2 1 . 4 7 0 . 3 4 0 8 0 . 3 1 6 2 0 . 3 0 8 3 98 1 . 2 0 1 . 4 3 1 . 4 0 0 . 3 6 6 2 0 . 4 2 9 1 0 . 4 1 2 5 99 1 . 2 2 1 . 4 7 1 . 4 2 0 . 3 2 8 6 0 . 3 8 9 3 0 . 3 7 5 9 * : s i g n i f i c a n t d i f f e r e n c e 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 5 112 TABLE 4 . 2 5 : Comparison of ob s e r v e d AGRs and RGRs i n DBH of the stand-grown t r e e s from the 6 . 0 m s p a c i n g b e f o r e the onse 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 t r e e v a l u e s as d e f i n e d by the second 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 R e l a t i v e growth r a t e (cm/year) (cm/year/cm) D e r i v e d Ek's D e r i v e d Ek' s Tree # Observed e q u a t i o n e q u a t i o n Observed e q u a t i o n e q u a t i o n 1 1 . 8 5 1 . 5 5 1 . 5 3 * 0 . 1 0 7 2 0 . 0 8 9 1 0 . 0 8 8 4 2 1 . 9 3 1 . 5 5 * 1 . 5 5 * 0 . 1 2 0 0 0 . 0 9 7 1 0 . 0 9 6 7 3 1 . 7 5 1 . 6 0 1 . 6 0 0 . 1 5 4 2 0 . 1 4 2 3 0 . 1 4 2 2 4 1 . 6 5 1 . 5 5 1 . 5 2 0 . 0 9 3 3 0 . 0 8 7 1 0 . 0 8 6 5 5 1 . 6 5 1 . 5 8 1 . 5 7 0 . 1 1 6 4 0 . 1 1 1 2 0 . 1 1 1 1 6 1 . 5 3 1 . 5 8 1 . 5 8 0 . 1 0 9 5 0 . 1 1 2 7 0 . 1 1 2 6 7 1 . 8 7 1 . 5 3 * 1 . 5 2 * 0 . 1 0 4 8 0 . 0 8 6 6 0 . 0 8 5 9 8 1 . 8 5 1 . 4 8 1 . 4 7 0 . 0 9 1 8 0 . 0 7 3 9 0 . 0 7 2 8 9 1 . 9 5 1 . 5 7 * 1 . 5 5 * 0 . 1 2 4 8 0 . 1 0 0 0 0 . 0 9 9 6 10 1 . 8 5 1 . 5 7 * 1 . 5 7 * 0 . 1 2 2 7 0 . 1 0 4 9 0 . 1 0 4 6 11 1 . 9 5 1 . 5 5 * 1 . 5 3 * 0 . 1 1 6 9 0 . 0 9 3 1 0 . 0 9 2 6 12 1 . 8 8 1 . 5 7 1 . 5 7 0 . 1 2 9 7 0 . 1 0 9 5 0 . 1 0 9 3 13 2 . 0 3 1 . 5 7 * 1 . 5 7 * 0 . 1 3 1 1 0 . 1 0 2 7 0 . 1 0 2 4 14 1 . 8 2 1 . 5 2 1 . 5 0 0 . 0 9 9 8 0 . 0 8 3 7 0 . 0 8 2 9 15 2 . 0 7 1 . 5 3 * 1 . 5 0 * 0 . 1 1 3 5 0 . 0 8 4 6 0 . 0 8 3 8 16 1 . 7 3 1 . 5 5 1 . 5 3 0 . 1 0 2 7 0 . 0 9 1 7 0 . 0 9 1 2 17 1 . 9 2 1 . 5 5 * 1 . 5 3 * 0 . 1 1 5 5 0 . 0 9 3 2 0 . 0 9 2 6 18 1 . 6 3 1 . 5 7 1 . 5 7 0 . 1 0 8 4 0 . 1 0 4 1 0 . 1 0 3 8 19 1 . 8 5 1 . 5 5 1 . 5 3 0 . 1 0 6 5 0 . 0 8 8 9 0 . 0 8 8 2 20 1 . 8 3 1 . 5 2 * 1 . 4 8 * 0 . 0 9 5 1 0 . 0 7 8 5 0 . 0 7 7 4 21 1 . 5 3 1 . 5 5 1 . 5 5 0 . 0 9 1 9 0 . 0 9 3 2 0 . 0 9 2 7 22 1 . 8 2 1 . 5 5 * 1 . 5 5 * 0 . 1 1 1 1 0 . 0 9 6 4 0 . 0 9 5 9 23 1 . 8 3 1 . 5 7 * 1 . 5 7 * 0 . 1 2 1 9 0 . 1 0 6 0 0 . 1 0 5 8 24 1 . 8 0 1 . 5 2 1 . 5 0 0 . 0 9 5 3 0 . 0 8 0 4 0 . 0 7 9 5 25 1 . 8 2 1 . 5 7 1 . 5 5 0 . 1 1 3 3 0 . 0 9 7 8 0 . 0 9 7 4 26 1 . 6 7 1 . 5 5 1 . 5 3 0 . 0 9 8 6 0 . 0 9 0 9 0 . 0 9 0 3 27 1 . 7 7 1 . 5 3 1 . 5 2 0 . 0 9 7 7 0 . 0 8 4 8 0 . 0 8 4 0 28 2 . 0 7 1 . 5 0 * 1 . 4 7 * 0 . 1 0 3 5 0 . 0 7 5 6 0 . 0 7 4 5 29 1 . 8 5 1 . 5 5 1 . 5 2 0 . 1 0 6 5 0 . 0 8 8 2 0 . 0 8 7 6 30 2 . 0 3 1 . 5 7 * 1 . 5 7 * 0 . 1 3 2 9 0 . 1 0 4 7 0 . 1 0 4 4 *: s i g n i f i c a n t d i f f e r e n c e 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 5 113 f o u n d . The computa t ion o f AGR and RGR f o r a 5 -year p e r i o d d i d not r e s u l t i n s i g n i f i c a n t l y g r e a t e r e r r o r s than f o r 1-year growth p e r i o d ( T a b l e 4 . 2 6 ) . The next h y p o t h e s i s t e s t e d c o n s i s t e d of the assumpt ion f i r s t used i n s i m u l a t i o n by Newnham (1964): the p o t e n t i a l d iameter increment o f a s tand-grown t r e e i n terms of AGR i s e q u a l to t h a t o f an open-grown t r e e o f the same s i z e and age . T h i s h y p o t h e s i s was a l s o t e s t e d w i t h RGR. T h i s se t of hypotheses i m p l i e s t h a t v a r i o u s open-grown t r e e s reach d i f f e r e n t s i z e s at a g i v e n age because o f d i s t i n c t g e n e t i c c h a r a c t e r i s t i c s , s i t e , a n d / o r m i c r o -c l i m a t i c c o n d i t i o n s . The development o f the p o t e n t i a l growth f u n c t i o n was based upon the e q u a t i o n d e r i v e d w i t h the d a t a d i s p l a y e d i n F i g u r e 4 .22 . A se t o f c u r v e s was o b t a i n e d by v a r y i n g the a s y m p t o t i c parameter ( F i g u r e 4 . 2 5 ) . They r e f l e c t the d i f f e r e n t growth r a t e s reached by v a r i o u s open-grown t r e e s a t the same age . The t r e e s i n F i g u r e 4.22 do not a l l have the same shape as the c u r v e s i n F i g u r e 4 .25 . However, i t was b e l i e v e d t h a t the e r r o r r e s u l t i n g from the comp-u t a t i o n o f the p o t e n t i a l growth r a t e would be v e r y s m a l l , e spe-c i a l l y a t young ages . T h i s approach i s s i m i l a r to t h a t used by Newnham ( 1964 ) . For AGR, 17 and 8 s i g n i f i c a n t d i f f e r e n c e s were found between o b s e r v a t i o n s and the d e r i v e d v a l u e s from open-grown t r e e s f o r the 4.3 m and 6.0 m s p a c i n g s r e s p e c t i v e l y and f o r a 1 -year p e r i o d ( T a b l e s 4.27 and 4 . 2 8 ) . On the o t h e r hand , no s i g n i f i c a n t d i f f e -rences were found f o r RGR. R e l a t i v e l y c l o s e v a l u e s were o b t a i n e d f o r the 5 -year growth p e r i o d on the 6.0 m s p a c i n g (Tab le 4 . 2 9 ) . 114 TABLE 4 . 2 6 : Comparison of observed AGRs and RGRs i n DBH of the s tand-grown 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 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 t r e e v a l u e s as d e f i n e d by the second 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 R e l a t i v e growth ra t e (cm/5 y e a r s ) (cm/5 y ears / cm) D e r i v e d E k ' s D e r i v e d E k ' s Tree # Observed e q u a t i o n e q u a t i o n Observed e q u a t i o n e q u a t i o n 1 8 . 9 7 . 7 7 . 6 0 . 4 7 8 5 9 0 . 4 2 4 7 7 0 . 4 2 1 7 1 2 9 . 5 7 . 8 7 . 7 0 . 5 4 5 3 4 0 . 4 6 5 6 0 0 . 4 6 3 5 3 3 8 . 8 8 . 0 8 . 0 0 . 7 0 4 7 1 0 . 6 5 4 9 2 0 . 6 5 5 2 4 4 8 . 3 7 . 7 7 . 6 0 . 4 4 5 2 1 0 . 4 1 6 7 6 0 . 4 1 3 4 8 5 8 . 2 7 . 9 7 . 8 0 . 5 3 8 2 7 0 . 5 2 0 6 9 0 . 5 1 9 6 8 6 7 . 6 7 . 9 7 . 8 0 . 5 0 7 3 4 0 . 5 2 0 6 9 0 . 5 1 9 6 8 7 9 . 4 7 . 7 7 . 6 0 . 4 9 7 0 3 0 . 4 2 2 0 7 0 . 4 1 8 9 4 8 9 . 1 7 . 5 7 . 3 0 . 4 2 6 6 8 0 . 3 6 2 2 8 0 . 3 5 7 3 8 9 9 . 5 7 . 8 7 . 8 0 . 5 5 8 4 9 0 . 4 7 8 4 4 0 . 4 7 6 6 4 10 9 . 1 7 . 8 7 . 8 0 . 5 5 7 2 7 0 . 4 9 5 3 2 0 . 4 9 3 8 6 11 9 . 6 7 . 7 7 . 7 0 . 5 3 4 0 8 0 . 4 5 0 3 3 0 . 4 4 7 9 0 12 9 . 2 7 . 8 7 . 8 0 . 5 8 0 1 6 0 . 5 1 3 2 2 0 . 5 1 2 0 9 13 1 0 . 3 7 . 8 7 . 8 0 . 6 1 5 8 6 0 . 4 9 8 8 2 0 . 4 9 7 4 2 14 8 . 9 7 . 6 7 . 5 0 . 4 5 8 5 0 0 . 4 0 3 9 1 0 . 4 0 0 2 8 15 1 0 . 2 7 . 6 7 . 6 0 . 5 2 1 5 1 0 . 4 1 4 1 4 0 . 4 1 0 7 9 16 8 . 6 7 . 7 7 . 7 0 . 4 7 8 8 9 0 . 4 3 8 6 8 0 . 4 3 5 9 7 17 9 . 4 7 . 7 7 . 7 0 . 5 2 5 4 2 0 . 4 5 0 3 3 0 . 4 4 7 9 0 18 8 . 2 7 . 8 7 . 8 0 . 5 1 0 8 3 0 . 4 9 1 8 7 0 . 4 9 0 3 4 19 8 . 9 7 . 7 7 . 6 0 . 4 7 5 9 8 0 . 4 2 2 0 7 0 . 4 1 8 9 4 20 8 . 8 7 . 5 7 . 4 0 . 4 2 7 4 4 0 . 3 7 5 4 2 0 . 3 7 0 9 4 21 7 . 6 7 . 7 7 . 6 0 . 4 3 1 1 4 0 . 4 3 5 8 4 0 . 4 3 3 0 6 22 9 . 2 7 . 8 7 . 7 0 . 5 2 8 8 4 0 . 4 6 2 4 8 0 . 4 6 0 3 4 23 9 . 2 7 . 8 7 . 8 0 . 5 6 9 0 9 0 . 5 0 2 3 5 0 . 5 0 1 0 2 24 8 . 9 7 . 6 7 . 5 0 . 4 4 4 5 2 0 . 3 8 9 2 8 0 . 3 8 5 2 2 25 9 . 0 7 . 8 7 . 7 0 . 5 2 2 9 7 0 . 4 6 5 6 0 0 . 4 6 3 5 3 26 8 . 1 7 . 7 7 . 6 0 . 4 4 8 8 0 0 . 4 3 0 2 5 0 . 4 2 7 3 3 27 8 . 6 7 . 6 7 . 5 0 . 4 4 6 0 3 0 . 4 0 3 9 1 0 . 4 0 0 2 8 28 1 0 . 1 7 . 5 7 . 4 0 . 4 7 2 9 9 0 . 3 7 0 9 6 0 . 3 6 6 3 4 29 9 . 1 7 . 7 7 . 6 0 . 4 8 9 7 7 0 . 4 2 7 5 0 0 . 4 2 4 5 1 30 1 0 . 2 7 . 8 7 . 8 0 . 6 1 5 1 9 0 . 5 0 2 3 5 0 . 5 0 1 0 2 115 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 and RGRs i n DBH of the stand-grown t r e e s from the 4 . 3 m s p a c i n g b e f o r e the ons 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 t r e e v a l u e s as d e f i n e d by the t h i r 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 R e l a t i v e growth r a t e (cm/yea r) (cm/year/cm) D e r i v e d D e r i v e d Tree # Observed e q u a t i o n Observed e q u a t i o n 1 1 . 8 0 2 . 0 7 0 . 2 2 3 0 0 0 . 2 4 8 8 7 2 1 . 8 7 2 . 3 2 * 0 . 1 6 6 8 8 0 . 2 0 0 5 7 3 1 . 7 5 2 . 1 5 * 0 . 2 0 7 8 2 0 . 2 4 8 8 7 4 1 . 8 5 1 . 8 0 0 . 2 0 5 5 9 0 . 2 0 0 5 7 5 1 . 6 5 1 . 7 0 0 . 1 9 4 6 7 0 . 2 0 0 5 7 7 1 . 6 2 1 . 9 7 * 0 . 2 0 8 2 3 0 . 2 4 8 8 7 8 1 . 6 5 2 . 2 5 * 0 . 1 5 1 8 2 0 . 2 0 0 5 7 9 1 . 8 0 2 . 2 7 * 0 . 1 6 0 4 7 0 . 2 0 0 5 7 12 1 . 6 5 1 . 5 5 0 . 2 6 4 9 4 0 . 2 4 8 8 7 16 1 . 7 5 3 . 7 5 * 0 . 2 5 6 9 5 0 . 4 8 6 4 7 17 1 . 8 5 2 . 3 0 0 . 1 6 3 7 3 0 . 2 0 0 5 7 27 0 . 5 7 1 . 0 3 * 0 . 3 3 1 0 8 0 . 5 6 0 9 2 30 1 . 6 7 2 . 2 0 * 0 . 2 5 8 3 7 0 . 3 2 7 3 8 31 1 . 6 5 1 . 7 5 0 . 3 1 5 9 2 0 . 3 2 7 3 8 32 1 . 9 2 2 . 7 0 * 0 . 1 8 3 6 3 0 . 2 4 8 8 7 33 1 . 8 2 5 . 0 0 * 0 . 2 0 3 6 9 0 . 4 8 6 4 7 35 1 . 5 0 2 . 6 2 * 0 . 2 9 9 0 6 0 . 4 8 6 4 7 36 1 . 6 7 2 . 1 2 * 0 . 2 6 2 8 0 0 . 3 2 7 3 8 37 1 . 2 5 0 . 7 2 * 0 . 3 3 2 2 8 0 . 2 0 0 5 7 38 1 . 5 7 2 . 3 5 * 0 . 2 2 5 5 6 0 . 3 2 7 3 8 42 1 . 5 7 2 . 8 7 0 . 1 4 3 8 4 0 . 2 4 8 8 7 46 1 . 7 2 2 . 2 7 * 0 . 1 5 4 0 5 0 . 2 0 0 5 7 53 1 . 9 2 2 . 7 2 * 0 . 1 8 5 4 8 0 . 2 4 8 8 7 54 1 . 8 2 3 . 1 2 0 . 3 4 1 5 2 0 . 4 8 6 4 7 64 1 . 5 2 1 . 9 0 0 . 4 0 5 6 7 0 . 4 8 6 4 7 65 1 . 4 7 1 . 5 2 0 . 3 1 7 8 1 0 . 3 2 7 3 8 74 1 . 6 3 2 . 5 0 0 . 3 8 0 3 9 0 . 5 6 0 9 2 82 1 . 6 0 1 . 6 0 0 . 3 4 0 8 3 0 . 3 2 7 3 8 98 1 . 2 0 2 . 0 0 * 0 . 3 6 6 2 0 0 . 5 6 0 9 2 99 1 . 2 2 1 . 1 7 0 . 3 2 8 5 8 0 . 3 2 7 3 8 *: s i g n i f i c a n t d i f f e r e n c e 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 / 117 TABLE 4 .28: Comparison of observed AGRs and RGRs i n DBH of the s tand-grown t r e e s from the 6.0 m s p a c i n g b e f o r e the the onset 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 t r e e v a l u e s as d e f i n e d by the t h i r 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 R e l a t i v e growth ra te (cm/year) (cm/year /cm) D e r i v e d D e r i v e d Tree # Observed e q u a t i o n Observed e q u a t i o n 1 1.85 1.97 0.10719 0.11221 2 1.93 2.07 0.12001 0.12783 3 1.75 1.67 0.15416 0.14786 4 1.65 2.00 0.09327 0.11221 5 1.65 1.82* 0.11637 0.12783 6 1.53 1.58 0.10953 0.11221 7 1.87 2.67* 0.10477 0.14786 8 1.85 2.32 0.09185 0.11221 9 1.95 2.35 0.12479 0.14786 10 1.85 1.93 0.12272 0.12783 11 1.95 1.90 0.11697 0.11221 12 1.88 1.87 0.12967 0.12783 13 2.03 1.98 0.13111 0.12783 14 1.82 2.08 0.09977 0.11221 15 2.07 2.07 0.11354 0.11221 16 1.73 2.18* 0.10275 0.12783 17 1.92 1.90 0.11552 0.11221 18 1.63 1.93* 0.10836 0.12783 19 1.85 1.95 0.10655 0.11221 20 1.83 2.18 0.09509 0.11221 21 1.53 2.15 0.09193 0.12783 22 1.82 2.08* 0.11112 0.12783 23 1.83 1.93 0.12194 0.12783 24 1.80 1.90 0.09530 0.09967 25 1.82 2.05 0.11328 0.12783 26 1.67 1.92 0.09856 0.11221 27 1.77 2.35* 0.09769 0.12783 28 2.07 2.25 0.10353 0.11221 29 1.85 2.25* 0.10655 0.12783 30 2.03 1.70* 0.13292 0.11221 * : s i g n i f i c a n t d i f f e r e n c e a t the l e v e l o f p r o b a b i l i t y of 0.05 118 TABLE 4 . 2 9 : Comparison 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 from the 6 . 0 m s p a c i n g b e f o r e the ons 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 t r e e v a l u e s as d e f i n e d by the t h i r 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 R e l a t i v e growth r a t e (cm/ 5 y e a r s ) (cm/ 5 years/cm) D e r i v e d D e r i v e d Tree # Observed e q u a t i o n Observed e q u a t i o n 1 8 . 9 1 0 . 0 0 . 4 7 8 5 9 0 . 5 2 2 6 6 2 9 . 5 1 0 . 5 0 . 5 4 5 3 4 0 . 5 9 0 3 7 3 8 . 8 8 . 6 0 . 7 0 4 7 1 0 . 6 7 5 2 0 4 8 . 3 1 0 . 2 0 . 4 4 5 2 1 0 . 5 2 2 6 6 5 8 . 2 9 . 3 0 . 5 3 8 2 7 0 . 5 9 0 3 7 6 7 . 6 7 . 9 0 . 5 0 7 3 4 0 . 5 2 2 6 6 7 9 . 4 1 4 . 1 0 . 4 9 7 0 3 0 . 6 7 5 2 0 8 9 . 1 1 1 . 7 0 . 4 2 6 6 8 0 . 5 2 2 6 6 9 9 . 5 1 2 . 2 0 . 5 5 8 4 9 0 . 6 7 5 2 0 10 9 . 1 9 . 8 0 . 5 5 7 2 7 0 . 5 9 0 3 7 11 9 . 6 9 . 3 0 . 5 3 4 0 8 0 . 5 2 2 6 6 12 9 . 2 9 . 4 0 . 5 8 0 1 6 0 . 5 9 0 3 7 13 1 0 . 3 9 . 7 0 . 6 1 5 8 6 0 . 5 9 0 3 7 14 8 . 9 1 0 . 5 0 . 4 5 8 5 0 0 . 5 2 2 6 6 15 1 0 . 2 1 0 . 2 0 . 5 2 1 5 1 0 . 5 2 2 6 6 16 8 . 6 1 1 . 3 0 . 4 7 8 8 9 0 . 5 9 0 3 7 17 9 . 4 9 . 3 0 . 5 2 5 4 2 0 . 5 2 2 6 6 18 8 . 2 9 . 9 0 . 5 1 0 8 3 0 . 5 9 0 3 7 19 8 . 9 1 0 . 0 0 . 4 7 5 9 8 0 . 5 2 2 6 6 20 8 . 8 1 1 . 3 0 . 4 2 7 4 4 0 . 5 2 2 6 6 21 7 . 6 1 1 . 3 0 . 4 3 1 1 4 0 . 5 9 0 3 7 22 9 . 2 1 0 . 6 0 . 5 2 8 8 4 0 . 5 9 0 3 7 23 9 . 2 9 . 7 0 . 5 6 9 0 9 0 . 5 9 0 3 7 24 8 . 9 9 . 5 0 . 4 4 4 5 2 0 . 4 6 7 2 7 25 9 . 0 1 0 . 5 0 . 5 2 2 9 7 0 . 5 9 0 3 7 26 8 . 1 9 . 8 0 . 4 4 8 8 0 0 . 5 2 2 6 6 27 8 . 6 1 2 . 3 0 . 4 4 6 0 3 0 . 5 9 0 3 7 28 1 0 . 1 1 1 . 5 0 . 4 7 2 9 9 0 . 5 2 2 6 6 29 9 . 1 1 1 . 6 0 . 4 8 9 7 7 0 . 5 9 0 3 7 30 1 0 . 2 8 . 2 0 . 6 1 5 1 9 0 . 5 2 2 6 6 *: s i g n i f i c a n t d i f f e r e n c e 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 5 119 The f o u r t h se t o f hypotheses may be s t a t e d a s : the p o t e n -t i a l increment o f a s tand-grown t r e e i n terms of AGR i s equa l to t h a t o f an open-grown t r e e o f the same age, but a d j u s t e d by the r e s p e c t i v e d i a m e t e r s o f both t r e e s . The same t e s t s were a l s o per formed f o r RGR. C o n t r a r y to the f i r s t h y p o t h e s i s , s l i g h t d i f f e r e n c e s were observed between the d e r i v e d e q u a t i o n and E k ' s (1971) e q u a t i o n . R e s u l t s are shown i n T a b l e s 4 .30 , 4 . 3 1 , and 4 .32 . For the AGR of the 4.3 m s p a c i n g , 18 and 26 s i g n i f i c a n t d i f f e r e n c e s out o f 30 were found between the v a l u e s computed from s tand-grown t r e e s and those c a l c u l a t e d from the d e r i v e d e q u a t i o n and E k ' s (1971) e q u a t i o n ( T a b l e s 4 . 3 0 ) . For the 6.0 m s p a c i n g , the 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 were 11 and 18 r e s p e c t i v e l y ( T a b l e 4 . 3 1 ) . The c o r r e s p o n d i n g numbers f o r RGR were: 8, 8, 14, and 23 ( T a b l e s 4.30 and 4 . 3 1 ) . For the 5 -year growth p e r i o d , c l o s e v a l u e s were o b t a i n e d f o r some t r e e s between observed RGRs and AGRs and the v a l u e s from the d e r i v e d e q u a t i o n and E k ' s e q u a t i o n , w h i l e o t h e r t r e e s showed s u b s t a n t i a l d i f f e r e n c e s (Table 4.32) . The l a s t s e t o f hypotheses was t h a t the p o t e n t i a l increment of a s tand-grown t r e e i n terms of AGR or RGR i s e q u a l to t h a t of an open-grown t r e e o f the same age, but a d j u s t e d by i t s e f f i -c i e n c y . For AGR, the o n l y s i g n i f i c a n t d i f f e r e n c e found was f o r the 4.3 m s p a c i n g ( T a b l e s 4.33 and 4 . 3 4 ) . No s i g n i f i c a n t d i f f e -rence c o u l d be d e t e c t e d f o r RGR. The v a l u e s computed from the d e r i v e d e q u a t i o n and E k ' s (1971) e q u a t i o n d i f f e r e d o n l y s l i g h t l y . Of the s e t s o f hypotheses examined, the f i f t h se t performed b e t t e r t h a t the o t h e r s because n e i t h e r AGR nor RGR s i g n i f i c a n t l y d i f f e r e d (except i n 1 c a s e ) . T h i s was f o l l o w e d by the second s e t . The t h i r d and f o u r t h s e t s had many more s i g n i f i c a n t d i f f e -120 TABLE 4 .30: Comparison o f observed AGRs and RGRs i n DBH of the s tand-grown t r e e s from the 4.3 m s p a c i n g b e f o r e the onset 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 t r e e v a l u e s as d e f i n e d by the 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 r a t e R e l a t i v e growth ra te (cm/year) (cm/year /cm) D e r i v e d E k ' s D e r i v e d E k ' s Tree # Observed e q u a t i o n e q u a t i o n Observed e q u a t i o n e q u a t i o n 1 1 .80 2 .07 2 .35 0 .22300 0 .33249 0 .44143 2 1 .87 2 .32* 2 .62* 0 .16688 0 .29782* 0 .37825* 3 1 .75 2 .15* 2 .42* 0 .20782 .0 .34742 0 .46180* 4 1 .85 1 .80 2 .00* 0 .20559 0 .22931 0 .29077 5 1 .65 1 .70 1 .92* 0 .19467 0 .21901 0 .27783 7 1 .62 1 .97* 2 .22* 0 .20823 0 .31912 0 .42430 8 1 .65 2 .25* 2 .50* 0 .15182 0 .28785* 0 .36572* 9 1 .80 2 .27* 2 .52* 0 .16047 0 .29290* 0 .37224* 12 1 .65 1 .55 1 .77 0 .26494 0 .24923 0 .33004 16 1 .75 3 .75* 4 .47* 0 .25695 1 .50161 2 .45965 17 1 .85 2 .30 2 .60* 0 .16373 0 .29696* 0 .37931* 27 0 .57 1 .03* 1 .27* 0 .33108 0 .46534 0 .77510 30 1 .67 2 .20* 2 .55* 0 .25837 0 .49915 0 .70983 31 1 .65 1 .75 2 .02* 0 .31592 0 .38220 0 . 54069 32 1 .92 2 .70* 3 .07* 0 .18363 0 .44371* 0 .59067 33 1 .82 5 .00* 6 .00* 0 .20369 2 .09149 3 .45335 35 1 . 50 2 .62* 3 .12* 0 .29906 1 .02340 1 .67056 36 1 .67 2 .12* 2 . 47* 0 .26280 0 .48113 0 .68435 37 1 .25 0 .73* 0 .83* 0 .33228 0 .08999* 0 .11340* 38 1 .58 2 . 35* 2 .72* 0 .22556 0 .53977 0 .77062 42 1 .58 2 .88* 3 .27* 0 .14384 0 .47894 0 .63914 46 1 .72 2 .27* 2 . 57* 0 .15405 0 .29513* 0 .37516* 53 1 .92 2 .72* 3 .07* 0 .18548 0 .44087* 0 .58661* 54 1 .82 3 .12 3 .75* 0 .34152 1 .14550 1 .84105 64 1 .52 1 .90 2 .25 0 .40567 0 .68773 1 .10509 65 1 .47 1 .52 1 .75* 0 .31786 0 . 33126 0 .46885 74 1 .63 2 .50 3 .03* 0 .38039 1 .10878 1 .83932 82 1 .60 1 .60 1 .85* 0 .34083 0 .34242 0 .48296 98 1 .20 2 .00* 2 .37* 0 .36620 0 .87454 1 .44956 99 1 .22 1 .18 1 . 37 0 .32858 0 .25934 0 .36682 * : s i g n i f i c a n t d i f f e r e n c e a t the l e v e l o f p r o b a b i l i t y o f 0.05 121 TABLE 4 .31 : Comparison o f observed AGRs and RGRs i n DBH of the s tand-grown 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 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 t r e e v a l u e s as d e f i n e d by the 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 r a t e R e l a t i v e growth i ra t e (cm/year) (cm/year /cm) D e r i v e d E k ' s D e r i v e d Ek' s Tree # Observed e q u a t i o n e q u a t i o n Observed e q u a t i o n e q u a t i o n 1 1.85 1.97 2.10 0 .10719 0.13990 0.16140* 2 1.93 2.07 2.25* 0 .12001 0.16787 0.19765* 3 1.75 1.67 1.80 0 .15416 0.15398 0.18565 4 1.65 2.00 2 .15* 0 .09327 0.14301* 0.16511* 5 1.65 1.82* 1.98* 0 .11637 0.14743 0.17364* 6 1.53 1.58 1.70* 0 .10953 0.11178 0.12896 7 1.87 2.67* 2.92* 0 .10477 0.25401* 0.30732* 8 1.85 2.32 2.48* 0 .09185 0.16503* 0.19052* 9 1.95 2.35* 2.58 0 .12479 0.22101* 0.26698* 10 1.85 1.93 2.12* 0 .12272 0.15594 0.18360* 11 1.95 1.90 2.03 0 .11697 0.13405 0.15456 12 1.88 1.87 2.03 0 .12967 0.14942 0.17584 13 2.03 1.98 2.15 0 .13111 0.15886 0.18691 14 1.82 2.08 2.23* 0 .09977 0.14796* 0.17076* 15 2.07 2.07 2.22 0 .11354 0.14634 0.16876* 16 1.73 2.18* 2.38* 0 .10275 0.17767* 0.20941* 17 1.92 1.90 2.03 0 .11552 0.13401 0.15452 18 1.63 1.93* 2.10* 0 .10836 0.15749* 0.18557* 19 1.85 1.95 2.10 0 .10655 0.14019 0.16175* 20 1.83 2.18* 2.38* 0 .09509 0.15712* 0.18140* 21 1.53 2.15* 2.33* 0 .09193 0.17581* 0.20740* 22 1.82 2.08* 2.28* 0 .11112 0.16937* 0.19956* 23 1.83 1.93 2.08* 0 .12194 0.15436 0.18176* 24 1.80 1.90 2.02 0 .09530 0.12125 0.13751* 25 1.82 2.05 2.23* 0 .11328 0.16692* 0.19662* 26 1.67 1.92 2.07* 0 .09856 0.13750 0.15870* 27 1.77 2.35* 2.57* 0 .09769 0.19120* 0.22545* 28 2.07 2.25 2.43 0 .10353 0.16170* 0.18658* 29 1.85 2.25* 2.48* 0 .10655 0.18379* 0.21654* 30 2.03 1.70* 1.83 0 .13292 0.11988 0.13813 * : s i g n i f i c a n t d i f f e r e n c e a t the l e v e l o f p r o b a b i l i t y o f 0.05 122 TABLE 4 .32: Comparison o f observed AGRs and RGRs i n DBH of the s tand-grown 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 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 t r e e v a l u e s as d e f i n e d by the 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 R e l a t i v e growth ra t e (cm/5 y e a r s ) (cm/5 years / cm) D e r i v e d E k ' s D e r i v e d Ek' s Tree # Observed e q u a t i o n e q u a t i o n Observed e q u a t i o n e q u a t i o n 1 8.9 10.0 10.8 0.47859 0.66199 0.76655 2 9 .5 10.5 11.6 0.54534 0.78536 0.92932 3 8.8 8.3 9.3 0.70471 0.70354 0.85454 4 8.3 10.2 11.1 0.44521 0.67568 0.78241 5 8.2 9.3 10.2 0.53827 0.68944 0.81582 6 7.6 7.9 8.6 0.50734 0.52502 0.60795 7 9.4 14.1 15.8 0.49703 1.19438 1.45072 8 9.1 11.7 12.8 0.42668 0.78069 0.90400 9 9.5 12.2 13.7 0.55849 1.03894 1.26193 10 9.1 9.8 10.8 0.55727 0.73141 0.86547 11 9.6 9.3 10.2 0.53408 0.62090 0.71897 12 9.2 9.4 10.4 0.58016 0.70143 0.83000 13 10.3 9.7 10.7 0.61586 0.72541 0.85838 14 8.9 10.5 11.4 0.45850 0.69851 0.80884 15 10.2 10.2 11.1 0.52151 0.68025 0.78770 16 8.6 11.3 12.4 0.47889 0.83932 0.99317 17 9.4 9.3 10.2 0.52542 0.62090 0.71897 18 8.2 9.9 10.9 0.51083 0.73740 0.87257 19 8.9 10.0 10.9 0.47598 0.66655 0.77187 20 8.8 11.3 12.3 0.42744 0.75330 0.87228 21 7.6 11.3 12.5 0.43114 0.84531 1.00026 22 9.2 10.6 11.7 0.52884 0.79136 0.93641 23 9.2 9.7 10.7 0.56909 0.71942 0.85129 24 8.9 9.5 10.2 0.44452 0.56945 0.64744 25 9.0 10.5 11.6 0.52297 0.78536 0.92932 26 8.1 9.8 10.7 0.44880 0.65286 0.75598 27 8.6 12.3 13.6 0.44603 0.91725 1.08539 28 10.1 11.5 12.5 0.47299 0.76243 0.88286 29 9.1 11.6 12.8 0.48977 0.86330 1.02154 30 10.2 8.2 9.0 0.61519 0.54785 0.63439 123 TABLE 4 .33 : Comparison of observed AGRs and RGRs i n DBH of the s tand-grown t r e e s from the 4.3 m s p a c i n g b e f o r e the onset of 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 t r e e v a l u e s as d e f i n e d by the f i f 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 r a t e R e l a t i v e growth ra te (cm/year) (cm/year /cm) D e r i v e d E k ' s D e r i v e d E k ' s Tree # Observed e q u a t i o n e q u a t i o n Observed e q u a t i o n e q u a t i o n 1 1.73 1.73 1.70 0.18518 0.20189 0.19991 2 1.77 1.77 1.77 0.14061 0.15363 0.15220 3 1.73 1.60 1.60 0.18120 0.18414 0.18234 4 1.83 1.77 1.70 0.17966 0.18633 0.18460 5 1.60 1.60 1.57 0.16665 0.17846 0.17681 7 1.63 1.47 1.43 0.18509 0.18165 0.17988 8 1.60 1. 53 1. 50 0.13401 0.13742 0.13615 9 1.80 1.63 1.63 0.14631 0.14456 0.14323 12 1.60 1.57 1.57 0.21494 0.23488 0.23256 16 1.60 1.40 1.40 0.19349 0.18909 0.18691 17 1.77 1.73 1.73 0.14061 0.15047 0.14908 27 0.65 0.45 0.45 0.32837 0.23936 0.23657 30 1.57 1.47 1.47 0.20045 0.21460 0.21234 31 1.60 1.43 1.43 0.24587 0.26215 0.25938 32 1.83 1.73 1.73 0.15487 0.16033 0.15875 33 1.73 1.47 1.43 0.16858 0.15185 0.15013 35 1.50 1.17* 1.17* 0.24692 0.21794 0.21545 36 1.63 1.43 1.43 0.21525 0.21658 0.21430 37 1.27 1.20 1.17 0.27277 0.30205 0.29924 38 1. 57 1.33 1.33 0.19530 0.18461 0.18268 42 1.47 1.37 1.37 0.12155 0.12326 0.12206 46 1.70 1.57 1.57 0.13851 0.13896 0.13767 53 1.83 1.87 1.87 0.15621 0.17051 0.16884 54 1.43 1.90 1.90 0.19255 0.28050 0.27724 64 1.40 1.50 1.50 0.26812 0.31789 0.31427 65 1.50 1.33 1.30 0.26527 0.26645 0.26366 74 1.85 1.20 1.20 0.36066 0.27334 0.27014 82 1.53 1.50 1.47 0.25516 0.28945 0.28638 98 1.30 1.10 1.00 0.32839 0.27807 0.27481 99 1.30 1.10 1.10 0.29083 0.27378 0.27190 * : s i g n i f i c a n t d i f f e r e n c e at the l e v e l o f p r o b a b i l i t y 0.05 124 TABLE 4 .34: Comparison of observed AGRs and RGRs i n DBH of the s tand-grown 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 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 t r e e v a l u e s as d e f i n e d by the f i f 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 r a t e R e l a t i v e growth ra t e (cm/year) (cm/year /cm) D e r i v e d E k ' s D e r i v e d Ek' s Tree # Observed e q u a t i o n e q u a t i o n Observed e q u a t i o n e q u a t i o n 1 1.78 1.82 1.82 0.09572 0.10209 0.10130 2 1.70 1.90 1.88 0.10907 0.11310 0.11218 3 1.76 1.68 1.68 0.14094 0.14276 0.14155 4 1.66 1.64 1.64 0.08904 0.08977 0.08908 5 1.64 1. 58 1.58 0.10766 0.10829 0.10742 6 1.52 1.44 1.44 0.10147 0.10190 0.10111 7 1.88 1.80 1.76 0.09941 0.09803 0.09720 8 1.82 1.82 1.80 0.08534 0.08783 0.08716 9 1.90 1.88 1.86 0.11170 0.11682 0.11583 10 1.82 1.78 1.76 0.11145 0.11425 0.11333 11 1.92 1.94 1.94 0.10682 0.11241 0.11155 12 1.84 1.90 1.90 0.11603 0.12499 0.12399 13 2.06 2.02 2.00 0.12317 0.12478 0.12378 14 1.78 1.80 1.78 0.09170 0.09544 0.09470 15 2.04 2.08 2.06 0.10430 0.10974 0.10890 16 1.72 1.68 1.68 0.09578 0.09670 0.09593 17 1.88 1.94 1.94 0.10508 0.11241 0.11155 18 1.64 1.58 1.56 0.10217 0.10142 0.10061 19 1.78 1.82 1.82 0.09520 0.10151 0.10073 20 1.76 1.76 1.76 0.08549 0.08942 0.08873 21 1.52 1.46 1.46 0.08623 0.08582 0.08513 22 1.84 1.74 1.72 0.10577 0.10292 0.10210 23 1.84 1.74 1.72 0.11382 0.11254 0.11163 24 1.78 1.78 1.78 0.08891 0.09186 0.09118 25 1.80 1.80 1.78 0.10459 0.10755 0.10668 26 1.62 1.66 1.66 0.08976 0.09498 0.09425 27 1.72 1.72 1.70 0.08920 0.09202 0.09128 28 2.02 2.04 2.02 0.09460 0.09909 0.09833 29 1.82 1.84 1.80 0.09796 0.10186 0.10104 30 2.04 1.98 1.98 0.12304 0.12632 0.12535 * : s i g n i f i c a n t d i f f e r e n c e a t the l e v e l o f p r o b a b i l i t y 0.05 125 r e n c e s . However, the number of 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 f o r t h e s e t h r e e h y p otheses when RGR was used i n s t e a d of AGR. The p o o r e r performance o f t h e s e t h r e e h y p o t h e s i s s e t s when AGR was used may be e x p l a i n e d by the f a c t t h a t two t r e e s o f the same s i z e and f r e e from c o m p e t i t i o n may not have the same i n c r e m e n t because of d i f f e r e n t g e n e t i c c h a r a c t e r i s t i c s , s i t e , or m i c r o c l i m a t i c c o n d i t i o n s . The d i f f e r e n c e s among stand-grown and open-grown t r e e s d i m i n i s h e d when RGR was used perhaps because i t a d j u s t e d f o r g e n e t i c , s i t e , or o t h e r e n v i r o n m e n t a l d i f f e r e n c e s . These r e s u l t s s u g g e s t t h a t a measure o f e f f i c i e n c y based on RGR may be u s e f u l f o r e s t i m a t i n g the p o t e n t i a l growth r a t e o f stand-grown t r e e s . However, t h i s p a r t of the s t u d y was not d e f i n i t i v e . As p r e v i o u s l y m entioned, comparisons were made between open-grown t r e e s and stand-grown t r e e s 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 . When a growth s i m u l a t o r i s d e v e l o p e d , the growth of e v e r y t r e e must be e s t i m a t e d u n t i l c o m p e t i t i o n o c c u r s . The l a r g e r the s p a c i n g , the l o n g e r the p o t e n t i a l growth r a t e c o n s t i t u t e s the r e a l i n c r e m e n t . The n e x t l o g i c a l s t e p would be t o t e s t t h e s e h y p o t h e s e s i n s i m u l a t i o n i n o r d e r t o d e t e r m i n e i f the h y p o t h e s i s t h a t was the most s u c c e s s f u l w i t h stand-grown t r e e s 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 would a l s o be the most s u c c e s s f u l t o p r e d i c t the p o t e n t i a l growth r a t e of stand-grown t r e e s t h a t were a f f e c t e d by c o m p e t i t i o n . E x i s t i n g f o r e s t growth s i m u l a t o r s do not d i s t i n g u i s h between t r e e s t h a t were never s u b j e c t e d t o c o m p e t i t i o n and tho s e t h a t were g r o w i n g under c o m p e t i t i v e s t r e s s , and th e n r e l e a s e d a t a c e r t a i n age. I n o t h e r words, i t i s assumed t h a t two t r e e s of the same s i z e but o r i g i n a t i n g from the two c o n d i t i o n s j u s t d e s c r i b e d 126 would have the same p o t e n t i a l growth r a t e . A c c o r d i n g to Newnham (1964) , t h i s as sumpt ion does not take i n t o c o n s i d e r a t i o n the p o s s i b l e p h y s i o l o g i c a l s t r e s s the t r e e was u n d e r g o i n g b e f o r e r e l e a s e . He assumed t h a t the e r r o r s r e s u l t i n g from not c o n s i -d e r i n g t h i s e f f e c t would be n e g l i g i b l e . 4 . 6 - Summary and C o n c l u s i o n s The f i r s t o b j e c t i v e of t h i s c h a p t e r was to compare the deve-lopment i n AGR and RGR b e f o r e and a f t e r the onset o f c o m p e t i t i o n f o r red p i n e growing under a wide range o f s p a c i n g s . The p e r f o r -mance o f these two types o f growth r a t e d i f f e r e d . 1- W h i l e AGR was always p o s i t i v e l y c o r r e l a t e d w i t h t r e e s i z e , RGR showed d i f f e r e n t r e l a t i o n s h i p s b e f o r e and a f t e r the onset of c o m p e t i t i o n . When c o m p e t i t i o n began or was not too s e v e r e , RGR was n e g a t i v e l y r e l a t e d to t r e e s i z e . Smal l t r e e s were more e f f i c i e n t than b i g t r e e s . One to f o u r y e a r s a f t e r the onset o f c o m p e t i t i o n , t h e r e was no v a r i a t i o n w i t h t r e e s i z e . F i n a l l y , RGR became p o s i t i v e l y r e l a t e d to t r e e s i z e . The h y p o t h e s i s t h a t a l l t r e e s have the same RGR b e f o r e the onset o f c o m p e t i t i o n was r e j e c t e d . The second o b j e c t i v e , which was to de termine i f RGR r e p r e s e n t s the changes i n the c o m p e t i t i v e s t a t u s of s tands b e t t e r than AGR, was f u l l y met: 2- RGR r e f l e c t e d the onset of c o m p e t i t i o n b e t t e r than AGR. The f a c t t h a t RGR had a g r e a t e r a b i l i t y than AGR to r e t a i n the same s o c i a l s t a t u s from ages 13 to 33 sugges ts t h a t i t has a more s p e c i f i c and p r e d i c t a b l e p a t t e r n o f change i n the course of s t a n d growth than AGR. My r e s u l t s c l e a r l y i n d i c a t e t h a t RGR i s b e t t e r a s s o c i a t e d w i t h the c o m p e t i t i v e s t a t u s o f t r e e s of d i f f e -127 r e n t s i z e s composing a s tand than AGR. AGR o n l y i n d i c a t e d a t e v e r y age t h a t l a r g e t r e e s grow f a s t e r than s m a l l ones . The d i f f e r e n t p a t t e r n s shown by RGR at d i f f e r e n t ages c o u l d not o n l y be a s s o c i a t e d w i t h the change i n the c o m p e t i t i v e s t a t u s , but c o u l d a l s o be i n t e r p r e t e d i n terms of b i o l o g i c a l c a u s e s , i . e . , the e f f i c i e n c y o f t r e e s to produce new b iomass . More s p e c i -f i c a l l y , t h i s r e l a t e s to the e q u i l i b r i u m between p h o t o s y n t h e s i s and r e s p i r a t i o n . W h i l e i t might be d i f f i c u l t to s tudy these b a s i c p h y s i o l o g i c a l p r o c e s s e s i n the f i e l d , o t h e r approaches such as e s t i m a t i n g the e f f i c i e n c y o f t r e e s to produce new m a t e r i a l per u n i t o f r e s o u r c e s accumulated ( e . g . , c h l o r o p h y l l , n u t r i e n t s , water) c o u l d be u n d e r t a k e n i n o r d e r to b e t t e r u n d e r s t a n d the changes i n e f f i c i e n c y . The t h i r d and f o u r t h o b j e c t i v e s concerned the e s t i m a t i o n of the p o t e n t i a l growth r a t e o f s tand-grown t r e e s from open-grown t r e e s . 3- Hypotheses based on RGR performed b e t t e r than hypotheses based on AGR f o r e v e r y s e t . These r e s u l t s suggest t h a t RGR i s p r o m i s i n g f o r use w i t h s i n g l e - t r e e mode l s . T h i s i s a l s o s u p p o r t e d by the f a c t t h a t RGR measures the e f f i c i e n c y o f t r e e s a t u s i n g r e s o u r c e s and t h a t s i n g l e - t r e e models at tempt to p r e d i c t the r e l a t i v e p a r t i t i o n o f r e s o u r c e s . A major problem o c c u r r i n g when the c o m p e t i t i v e s t r e s s o f i n d i v i d u a l t r e e s i s e s t i m a t e d i n s i n g l e - t r e e models i s to s e p e r a t e the e f f e c t o f c o m p e t i t i o n from the p h y s i o l o g i c a l c h a r a c -t e r i s t i c s ( i . e . , g e n e t i c i n h e r i t a n c e ) . The i n c r e a s e i n s i z e of a p a r t i c u l a r t r e e depends on i t s g e n e t i c p o t e n t i a l , the m i c r o c l i -m a t i c c o n d i t i o n s , and the amount o f c o m p e t i t i o n . AGR expres se s the e f f e c t o f a l l these f a c t o r s . I f RGR expres se s the increment 128 of t r e e s i n d e p e n d e n t l y o f g e n e t i c i n h e r i t a n c e or m i c r o c l i m a t i c c o n d i t i o n s (as sugges ted by Buchman and Benz i e (1988) , Kramer and K o z l o w s k i (1974) , L e d i g (1974) , and R a d o s e v i c h and Osteryoung (1987) ) , i t w i l l v e r y p r o b a b l y r e f l e c t the e f f e c t o f c o m p e t i t i o n i n s i n g l e - t r e e mode l s . The next l o g i c a l s t ep b e f o r e d e v e l o p i n g growth models would be to s tudy the development of i n d i v i d u a l t r e e s i n more d e t a i l . A c o m b i n a t i o n o f the f u n c t i o n a l approach and the methodology used by Smith (1966) , which examined the e f f e c t of s e v e r a l crown p a r a -meters and s t a n d v a r i a b l e s on i n d i v i d u a l t r e e s , might produce good r e s u l t s . 129 CHAPTER 5 CROWN DEVELOPMENT STUDY 5 . 1 - I n t r o d u c t i o n The dependence o f stem growth upon crown development has been r e c o g n i z e d by s e v e r a l r e s e a r c h e r s ( e . g . , Assmann 1970, C u r t i n 1970, F o r d 1985, Harper 1977, K o z l o w s k i 1971, K u u l u v a i n e n 1988, and Zedaker e t a l . 1987) . The major impact o f c o m p e t i t i o n o c c u r s a t the canopy l e v e l through the i n f l u e n c e o f c o m p e t i t o r s on crown d i m e n s i o n and s t r u c t u r e ( P e r r y 1985) . However, the number of s t u d i e s f o l l o w i n g crown development over time under d i f f e r e n t s t a n d d e n s i t y c o n d i t i o n s i s s m a l l . F u r t h e r m o r e , crown development has m o s t l y been s t u d i e d w i t h a b s o l u t e measures ( e . g . , crown w i d t h ) . V e r y l i t t l e use has been made of measures o f e f f i -c i e n c y . O ' H a r a (1988) c o n s i d e r e d t h a t a measure o f e f f i c i e n c y based on a r a t i o o f stem increment to a measure o f growing space such as crown p r o j e c t i o n (measure o f the h o r i z o n t a l a r e a o c c u p i e d by the crown) p r o v i d e s a b e t t e r measure o f how t r e e s o f d i f f e r e n t s o c i a l p o s i t i o n s u t i l i z e the r e s o u r c e s of the s i t e than comparing o n l y the dominance c l a s s e s . The f i r s t o b j e c t i v e o f t h i s phase o f the s tudy i s to examine v a r i o u s measures o f e f f i c i e n c y based on crown c h a r a c t e r i s t i c s f o r a wide range o f s p a c i n g s and ages and to de termine i f they are b e t t e r c o r r e l a t e d w i t h the onset o f c o m p e t i t i o n than a b s o l u t e measures . In the l a s t c h a p t e r , i t was observed t h a t RGR changed b e f o r e and a f t e r the onset o f c o m p e t i t i o n . I t was c o n c l u d e d t h a t s m a l l t r e e s were more e f f i c i e n t than b i g t r e e s b e f o r e c o m p e t i t i o n and t h a t the e f f e c t o f c o m p e t i t i v e s t r e s s was to decrease the e f f i c i e n c y o f the t r e e s g r e a t l y a f f e c t e d by c o m p e t i t i o n . I f the 130 v a r i o u s forms o f r e l a t i o n s h i p s between RGR and t r e e s i z e r e a l l y i n d i c a t e a change i n the e f f i c i e n c y of t r e e s , the same t r e n d s s h o u l d a l s o o c c u r w i t h measures o f e f f i c i e n c y based on crown c h a r a c t e r i s t i c s . Thus, the second o b j e c t i v e o f t h i s phase of the s t u d y i s t o d e t e r m i n e i f t h e r e i s a s i m i l a r i t y between the changes i n RGR and the changes i n r e l a t i v e growth measures based on crown d i m e n s i o n s . F o l l o w i n g a l i t e r a t u r e r e v i e w and a d e s c r i p t i o n o f m a t e r i a l and methods, b a s i c r e l a t i o n s h i p s between 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. Then, the a b s o l u t e measures, r e l a t i v e measures, and r e l a t i v e growth measures are examined s u c c e s s i v e l y . R e s u l t s t h a t were c o n s i d e r e d as l e s s i n t e r e s t i n g a f t e r a n a l y s i s a r e i n c l u d e d i n Appendix 4 . 5 . 2 - L i t e r a t u r e Review Crown development o f r e d p i n e i s v e r y s e n s i t i v e t o s t a n d d e n s i t y and t h e r e i s a c l o s e r e l a t i o n s h i p between crown w i d t h and stem d i a m e t e r ( S t i e l l 1 9 7 0 ; S t i e l l and B e r r y 1 9 7 7 ) . The expe-r i m e n t s u n d e r t a k e n by S t i e l l ( 1 9 7 0 ) suggest t h a t c o m p e t i t i o n a t the crown l e v e l i s more l i m i t i n g than below-ground s t r e s s f o r red p i n e a t Petawawa. Three methods have been used t o a n a l y s e the s p a t i a l c h a r a c -t e r i s t i c s o f crowns. The f i r s t one i n v o l v e s m e asuring 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 branches such as l e n g t h , d i a m e t e r , l o c a t i o n , or f o l i a g e c o n t e n t ( B e a d l e e t a l . 1 9 8 2 ; Cochrane and For d 1 9 7 8 ; F o r d 1 9 8 2 ; Gary 1 9 7 8 ; I l o n e n e t a l . 1 9 7 9 ; K e l l o m a k i 1 9 8 0 , 1 9 8 6 ; K i n e r s o n and F r i t s c h e n 1 9 7 1 ; S t i e l l 1 9 6 2 , 1 9 6 6 ) . The second method c o n s i s t s of measuring the d i s t r i b u t i o n o f f o l i a g e i n terms o f mass or l e a f a r e a a l o n g the stem ( H a l l 1 9 6 5 , 1 9 6 6 ; Stephens 1 9 6 9 ) . The t h i r d method c o n s i s t s o f measuring crown 131 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 ( C u r t i n 1 9 7 0 ; C u r t i s and Reukema 1 9 7 0 ; S t i e l l and B e r r y 1 9 7 7 ) . A l l t h e s e parameters a re d e f i n e d as a b s o l u t e measures. A l t h o u g h v e r y r i c h i n d e t a i l , the f i r s t two methods a re not p r a c t i c a l f o r s t u d i e s o f s t a n d growth i n v o l v i n g remeasurement d a t a from many t r e e s . Because c o l l e c t i n g the n e c e s s a r y i n f o r -m a t i o n i s v e r y l a b o r i o u s and c o n s i s t s o f d e s t r u c t i v e measurement, v e r y few t r e e s g e n e r a l l y a r e a n a l y s e d . I t i s t h e r e f o r e d i f f i c u l t t o o b t a i n r e l i a b l e i n f o r m a t i o n a p p l i c a b l e t o o t h e r t r e e s . The t h i r d method i s not as b i o l o g i c a l l y i n f o r m a t i v e , but crown d i m e n s i o n s a r e e a s i l y measureable i n a n o n - d e s t r u c t i v e manner. A l s o , r e l i a b l e r e l a t i o n s h i p s a p p l i c a b l e t o o t h e r t r e e s o f t e n can be d e r i v e d . Two major t y p e s o f s t u d i e s have used b a s i c crown d i m e n s i o n s . The f i r s t t y p e a d d r e s s e d r e l a t i o n s h i p s between crown w i d t h and the DBH o f open-grown t r e e s . T h i s u s u a l l y h i g h l y s i g n i f i c a n t r e l a t i o n s h i p i s independent o f s i t e q u a l i t y and age ( D a n i e l e t a l . 1 9 7 9 ) . I t was used by K r a j i c e k e t a l . ( 1 9 6 1 ) t o d e r i v e the crown c o m p e t i t i v e f a c t o r , and by McMinn ( 1 9 8 6 ) t o d e r i v e p r i s m f a c t o r s f o r q u a n t i f y i n g crown c o m p e t i t i o n i n a l o b l o l l y p i n e ( P i n u s t a e d a L.) s t a n d . T h i s r e l a t i o n s h i p has 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 growth models t o e s t i m a t e the zone of i n f l u e n c e o f each t r e e (Alemdag 1 9 7 8 ; Loucks e t a l . 1 9 8 1 ) . E q u a t i o n s have been d e v e l o p e d by Alemdag ( 1 9 7 8 ) f o r w h i t e s p r u c e , A l e x a n d e r ( 1 9 7 1 ) f o r Engelmann s p r u c e , Ek ( 1 9 7 1 ) f o r r e d p i n e , Ek ( 1 9 7 4 ) f o r s e v e r a l s o f t w o o d and hardwood s p e c i e s , Leech ( 1 9 8 4 ) f o r l o b l o l l y p i n e , A r n e y ( 1 9 7 2 ) and Newnham ( 1 9 6 4 ) f o r D o u g l a s - f i r , Newnham ( 1 9 6 6 ) f o r red and w h i t e p i n e s , Tabbush and White ( 1 9 8 8 ) f o r s i t k a s p r u c e , V e z i n a ( 1 9 6 2 , 1963) f o r balsam 132 f i r , whi te s p r u c e , and Jack p i n e , and Ze ide ( 1 9 8 6 ) f o r red oak and l o b l o l l y p i n e . A s u b s t a n t i a l rev iew was p r e p a r e d by Honer ( 1972) . The second type addres sed r e l a t i o n s h i p s between crown d imens ions and DBH of s tand-grown t r e e s . L i n e a r e q u a t i o n s r e l a t i n g crown w i d t h to DBH are most common. A f r e q u e n t o b j e c -t i v e was to de termine the e f f e c t o f s tand d e n s i t y on t h i s r e l a -t i o n s h i p . W h i l e Bonnor ( 1 9 6 4 ) c o n c l u d e d t h a t s tand d e n s i t y d i d not a f f e c t t h i s r e l a t i o n s h i p f o r l o b l o l l y p i n e , Smith and B a i l e y ( 1 9 6 4 ) found a s i g n i f i c a n t impact f o r D o u g l a s - f i r and l o d g e p o l e p i n e . In t h e i r s t u d y , the s l o p e c o e f f i c i e n t was c l o s e l y r e l a t e d to s p a c i n g and the i n t e r c e p t c o e f f i c i e n t was a s s o c i a t e d w i t h the age and s i z e o f the t r e e s . C u r t i s and Reukema ( 1 9 7 0 ) found a s i g n i f i c a n t d i f f e r e n c e o n l y between the i n t e r c e p t c o e f f i c i e n t s f o r D o u g l a s - f i r . They a l s o extended t h e i r s tudy to o t h e r crown d i m e n s i o n s . 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 were found o n l y between i n t e r c e p t s f o r crown l e n g t h v e r s u s DBH r e l a t i o n -s h i p s . On the o t h e r hand, bo th the s l o p e s and i n t e r c e p t s s i g n i -f i c a n t l y d i f f e r e d among s p a c i n g s f o r crown volume and s u r f a c e a r e a v e r s u s DBH. These s t u d i e s , however, were per formed o n l y for one age . Other s t u d i e s were made s o l e l y to d e r i v e e q u a t i o n s t h a t c o u l d be used to de termine the crown d imens ions ( w i d t h , l e n g t h , h e i g h t to the base o f the crown, volume, s u r f a c e ) . Good examples are the s t u d i e s o f Beekhuis ( 1 9 6 5 ) , Bonnor ( 1 9 6 8 ) , C o l e and Jensen ( 1 9 8 2 ) , C u r t i n ( 1 9 6 4 , 1 9 7 0 ) , Dyer and B u r k h a r t ( 1 9 8 7 ) , K e l l o m a k i ( 1 9 8 6 ) , R i t c h i e and Hann ( 1 9 8 7 ) , S e i t z ( 1 9 8 6 ) , S p r i n z and B u r k h a r t ( 1 9 8 7 ) , W i l e ( 1 9 6 4 ) , and Z a r n o v i c a n ( 1 9 8 2 ) . 133 Crown development can a l s o be s t u d i e d i n terms of e f f i -c i e n c y . Two t y p e s of crown e f f i c i e n c y measures a r e : (1) r a t i o o f crown s i z e t o crown d i m e n s i o n ( e . g . , crown w i d t h t o crown l e n g t h ) or stem s i z e and ( 2 ) r a t i o o f i n c r e m e n t t o crown s i z e . These a re measures of e f f i c i e n c y because t h e y a re based on r a t i o s t h a t e x p r e s s the growth o f stems or crowns r e l a t i v e t o o t h e r d i m e n s i o n s s e n s i t i v e t o s i t e c o n d i t i o n s . The most common e f f i -c i e n c y measure o f the f i r s t type i s crown r a t i o ( r a t i o of crown l e n g t h t o t r e e h e i g h t ) . I t e s t i m a t e s the p h o t o s y n t h e t i c c a p a c i t y of a t r e e ( o r a b i l i t y t o p r o v i d e p h o t o s y n t h a t e t o the d i f f e r e n t p a r t s o f the t r e e ) ( F a r r a r 1 9 8 4 ; Smith 1 9 8 6 ; S p r i n z and B u r k h a r t 1 9 8 7 ) , and c o n s t i t u t e s a measure o f i t s v i g o r (Chapman 1 9 5 3 ; Smith 1 9 8 6 ) . A c c o r d i n g t o Holdaway ( 1 9 8 6 ) , crown r a t i o d e c r e a s e s as c o m p e t i t i o n f o r l i g h t i n t e n s i f i e s w i t h i n a s t a n d , and i s i n v e r s e l y r e l a t e d t o t r e e s i z e . However, a p a r t i c u l a r t r e e can grow a t i t s maximum c a p a c i t y as l o n g as i t s crown r a t i o i s g r e a t e r t h a n 50% ( F a r r a r 1 9 8 4 ) . The e f f e c t o f v a r i o u s i n i t i a l s p a c i n g s arid/or t h i n n i n g t r e a t m e n t s on the crown r a t i o of Norway s p r u c e , S i t k a s p r u c e , and D o u g l a s - f i r a t age 15 was performed by Kramer ( 1 9 6 6 ) . R e s u l t s showed t h a t i t i n c r e a s e d w i t h s p a c i n g and the i n t e n s i t y of t h i n n i n g . The e f f e c t o f v a r i o u s i n i t i a l s p a c i n g s was a l s o r e p o r t e d by Smith ( 1 9 7 7 , 1 9 8 7 ) , Reukema and Smith ( 1 9 8 7 ) and W a l t e r s and Smit h ( 1 9 7 3 ) f o r D o u g l a s - f i r , w e s t e r n hemlock (Tsuga  h e t e r o p h y l l a ( R e f . ) S a r g . ) , and w e s t e r n r e d c e d a r ( T h u j a p l i c a t a Donn). The crown r a t i o was found t o i n c r e a s e w i t h s p a c i n g a t ages 1 6 , 2 0 , 2 5 , and 5 5 . T h i s measure of e f f i c i e n c y was a l s o computed by K u u l u v a i n e n ( 1 9 8 8 ) and Z a r n o v i c a n ( 1 9 8 2 ) i n t h e i r s t u d i e s . 134 Other s t u d i e s d e v e l o p e d e q u a t i o n s f o r p r e d i c t i n g the crown r a t i o o f i n d i v i d u a l t r e e s ( e . g . , D e l l e t a l . (1979) f o r s l a s h p i n e , Dyer and B u r k h a r t (1987) f o r l o b l o l l y p i n e , Holdaway (1986) f o r v a r i o u s softwood and hardwood s p e c i e s , and Ward (1964) f o r red oak) or i t s mean s tand v a l u e ( e . g . , C o l e and Jensen 1982) . F o l l o w i n g t h i n n i n g t rea tment s i n l o b l o l l y p i n e p l a n t a t i o n s , B u r t o n and S h o u l d e r s (1983) deve loped e q u a t i o n s p r e d i c t i n g the mean increment i n b a s a l a r e a , DBH, and volume w i t h crown w i d t h , crown volume, and crown r a t i o as independent v a r i a b l e s . The use o f the l a s t v a r i a b l e p r o v i d e d b e t t e r r e s u l t s than the f i r s t two. Crown r a t i o was a l s o used by Graham (1980) to p r e d i c t the p r o b a -b i l i t y o f m o r t a l i t y of t r e e s i n whi te p i n e s t a n d s . T h i s measure o f e f f i c i e n c y was a l s o used i n two s i n g l e - t r e e d i s t a n c e - i n d e -pendent growth models ( i . e . , STEMS - B e l c h e r 1981, 1983; Holdaway 1984 - and PROGNOSIS - Stage 1973, 1975; Wykoff e t a l . 1982) . Other r a t i o s i n v o l v i n g crown d imens ions have been d e v e l o p e d . For i n s t a n c e , crown w i d t h to crown l e n g t h ( a l s o c a l l e d crown shape or crown f u l l n e s s r a t i o ) , crown width to DBH ( a l s o c a l l e d crown p r o j e c t i o n r a t i o ) , and crown w i d t h to stem h e i g h t ( Z a r n i v o c a n 1982) . The crown f u l l n e s s r a t i o was computed by K u u l u v a i n e n (1988) m a i n l y to examine i t s e f f e c t on mean need le mass d e n s i t y . Smith (1969) recommended the use o f crown w i d t h to DBH and h e i g h t to crown w i d t h r a t i o s . In young D o u g l a s - f i r and l o d g e p o l e p i n e s t a n d s , they would r e s p e c t i v e l y be around 2 and 3 under open c o n d i t i o n s , 1 and 5 under normal c o n d i t i o n s , and 0.7 and 0.8 under dense c o n d i t i o n s . A c c o r d i n g to Smith (1963) , the crown w i d t h to DBH r a t i o can be r e l a t e d to the number o f r i n g s per u n i t o f l e n g t h . In a p a r t i c u l a r D o u g l a s - f i r s p a c i n g t r i a l r a n g i n g from 1.21 m to 9.4 m, Smith (1977) r e p o r t e d t h a t the 135 crown w i d t h to DBH r a t i o i n c r e a s e d w i t h s p a c i n g a t age 2 0 , w h i l e the h e i g h t to crown w i d t h r a t i o d e c r e a s e d . A t age 5 5 , however, the l a t t e r r a t i o was found to i n c r e a s e w i t h s p a c i n g up to 3 . 6 6 m, and then d e c r e a s e . W a l t e r s and Smith ( 1 9 7 3 ) a l s o computed the same r a t i o s f o r D o u g l a s - f i r , wes tern r e d c e d a r , and wes tern hemlock a t age 1 6 . Even though not much v a r i a t i o n w i t h s p a c i n g was e v i d e n t , the crown w i d t h to DBH r a t i o i n c r e a s e d w i t h s p a c i n g f o r D o u g l a s - f i r and wes tern hemlock, w h i l e i t s l i g h t l y d e c r e a s e d f o r wes tern r e d c e d a r . For a l l these s p e c i e s , the h e i g h t to crown w i d t h r a t i o d e c r e a s e d w i t h s p a c i n g . For the same t h r e e s p e c i e s , Reukema and Smith ( 1 9 8 7 ) computed the crown f u l l n e s s r a t i o at age 2 5 . W h i l e no v a r i a t i o n was n o t i c e a b l e f o r wes tern r e d c e d a r , i t d e c r e a s e d w i t h s p a c i n g f o r wes tern hemlock, and i n c r e a s e d o n l y up to a 2 . 7 m s p a c i n g f o r D o u g l a s - f i r . Another measure o f e f f i -c i e n c y used i s the r a t i o o f crown s u r f a c e to crown volume ( C u r t i s and Reukema 1 9 7 0 ) . F o r d ( 1 9 8 5 ) ment ioned t h a t the c o n t r o l of t h i s r a t i o has a d i r e c t e f f e c t on s tand p r o d u c t i v i t y . The o t h e r type o f crown measure e f f i c i e n c y i s based on the r a t i o o f b o l e increment to crown s i z e . H a m i l t o n ( 1 9 6 9 ) used the r a t i o o f volume increment per u n i t o f crown p r o j e c t i o n to compare r e l e a s e d 23 y e a r - o l d S i t k a spruce t r e e s w i t h o t h e r t r e e s a c t i n g as c o n t r o l s . For both c a t e g o r i e s , t h i s measure o f e f f i c i e n c y was a s s o c i a t e d w i t h the s i z e o f the t r e e . However, r e l e a s e d t r e e s were more e f f i c i e n t than u n r e l e a s e d t r e e s i n e v e r y DBH c l a s s , and r e l e a s e d t r e e s o f a s m a l l DBH c l a s s were found to be more e f f i -c i e n t than u n r e l e a s e d t r e e s o f l a r g e r DBH c l a s s e s . The same r a t i o was used by O ' H a r a ( 1 9 8 8 ) f o r a n a l y s i n g the e f f e c t o f t h i n n i n g t r e a t m e n t s i n a 6 4 - y e a r - o l d D o u g l a s - f i r s t a n d . He c o n c l u d e d t h a t , compared to an u n t h i n n e d s t a n d , t a l l t r e e s from 136 t h i n n e d s tands w i t h s m a l l crowns used the growing space more e f f i c i e n t l y than those w i t h l a r g e r crowns. C i t i n g the s tudy of Badoux (1945) , Assmann (1970) r e p o r t e d t h a t volume increment per ground cover (crown p r o j e c t i o n ) , crown s u r f a c e a r e a , and crown volume i n a 88 y e a r - o l d Sco t s p i n e s tand i n c r e a s e d w i t h the s o c i a l s t a t u s , but d e c r e a s e d w i t h t r e e s i z e ( thus crown s i z e ) w i t h i n each t r e e c l a s s . These t h r e e s t u d i e s c o n c l u d e d t h a t v e r y e f f i c i e n t t r e e s are c h a r a c t e r i z e d by deep narrow crowns. The same c o n c l u s i o n was reached by K u u l u v a i n e n (1988) f o r Norway spruce ( P i c e a a b i e s ( L . ) K o r s t . ) . A b s o l u t e growth r a t e measures can a l s o be used i n c o n j u n c -t i o n w i t h f o l i a g e d a t a as a measure of e f f i c i e n c y to e v a l u a t e the c o m p e t i t i v e s t r e s s e x p e r i e n c e d by i n d i v i d u a l t r e e s (Waring 1983; Waring and S c h l e s i n g e r 1985; Waring e t a l . 1980) . F o r d (1982) used the r a t i o o f b a s a l a r e a increment to f o l i a g e weight w h i l e s t u d y i n g a 1 5 - y e a r - o l d S i t k a spruce s t a n d . Based upon t h i s measure o f v i g o r , he c o n c l u d e d t h a t a l l the t r e e s have the same e f f i c i e n c y up to the onset o f c o m p e t i t i o n . Then , t h i s r a t i o becomes i n v e r s e l y r e l a t e d to the e f f e c t o f c o m p e t i t i o n ; a low v a l u e , which means t h a t f o l i a g e has a low c a p a c i t y to produce new m a t e r i a l , i n d i c a t e s t h a t a t r e e i s under severe c o m p e t i t i v e s t r e s s . War ing e t a l . (1980) and Waring e t a l . (1981) proposed a s i m i l a r r a t i o , stem increment per u n i t o f l e a f a r e a . In two d i f f e r e n t s t u d i e s on D o u g l a s - f i r s t a n d s , they used the r a t i o s of stem biomass increment to l e a f a r e a and of volume increment to l e a f a r e a . These two measures are v e r y s i m i l a r i n concept to RGR. 137 V e r y s i g n i f i c a n t r e l a t i o n s h i p s (wi th r e l a t i v e l y narrow c o n f i d e n c e l i m i t s ) can n o r m a l l y be d e r i v e d between f o l i a g e weight or l e a f a r e a and DBH or b a s a l a r e a (Cable 1 9 5 8 ; F o r d 1 9 8 2 ; Kaufmann et a l . 1 9 8 2 ; Waring e t a l . 1 9 7 8 ; Whitehead 1978) or sapwood a r e a ( G r i e r and Waring 1 9 7 4 ; Kaufmann and T r o e n d l e 1 9 8 1 ; Long and Smith 1 9 8 4 ; Marchand 1 9 8 4 ; Waring e t a l . 1 9 8 2 ; Whitehead 1 9 7 8 ) . These r e l a t i o n s h i p s can be used to e s t i m a t e f o l i a g e weight or l e a f area of o t h e r t r e e s ( F o r d 1 9 8 2 ) . The e s t i m a t i o n o f l e a f area or f o l i a g e weight from sapwood area r e l a t e to the p i p e - m o d e l t h e o r y d e v e l o p e d by S h i n o z a k i et a l . ( 1 9 6 4 a , 1 9 6 4 b ) . More r e c e n t l y , V a l e n t i n e ( 1 9 8 8 ) d e v e l o p e d a growth model i n t e g r a t i n g the c a r b o n - b a l a n c e budget , the p i p e - m o d e l t h e o r y , and the s e l f - t h i n n i n g r u l e . Some measures o f e f f i c i e n c y p a r t i a l l y or e n t i r e l y based on q u a l i t a t i v e crown c h a r a c t e r i s t i c s have a l s o been d e v e l o p e d . The crown v i g o r index used by F a i r w e a t h e r ( 1 9 8 6 ) i n hardwood s tands i n v o l v e d crown s i z e , f u l l n e s s , d e p t h , and c o l o r . Smith ( 1 9 8 0 a ) d e v e l o p e d indexes based on c o l o u r and v i g o r o f the crown and a p p l i e d them to D o u g l a s - f i r , wes tern hemlock, and wes tern r e d c e d a r . To the bes t o f my knowledge, such measures of e f f i -c i e n c y have not been a p p l i e d to red p i n e . 5 . 3 - Hypotheses A l t h o u g h some of the measures of e f f i c i e n c y mentioned above have been computed on many o c c a s i o n s , t h e i r p o t e n t i a l r e l a t i o n -s h i p s to s t a n d dynamics have not been d e t e r m i n e d because they i have been used i n a r e l a t i v e l y narrow range o f a n a l y t i c a l s i t u a t i o n s . More s p e c i f i c a l l y , i t has never been shown how they v a r y b e f o r e and a f t e r the onset o f c o m p e t i t i o n f o r a wide range 138 of s p a c i n g s and ages and f o r t r e e s o f d i f f e r e n t s i z e s . A l t h o u g h crown r a t i o and the r a t i o o f crown width to DBH have been computed by Smith (1977, 1987) , Reukema and Smith (1987) , and W a l t e r s and Smith (1973) w i t h d a t a o r i g i n a t i n g from s p a c i n g t r i a l s , i t was o n l y f o r a few ages . F u r t h e r m o r e , these s t u d i e s d i d not show how these r a t i o s v a r i e d w i t h the c o n d i t i o n s mentioned above . The f o l l o w i n g hypotheses w i l l be t e s t e d i n t h i s c h a p t e r : H 5 . 1 - B e f o r e the onset o f c o m p e t i t i o n i n even-aged s tands of red p i n e , a l l the t r e e s have the same e f f i c i e n c y i n terms of crown deve lopment . H 5 . 2 - When c o m p e t i t i o n takes p l a c e , low e f f i c i e n c y v a l u e s are a s s o c i a t e d w i t h t r e e s e x p e r i e n c i n g h i g h l e v e l s o f c o m p e t i t i o n , w h i l e h i g h e f f i c i e n c y v a l u e s are a s s o c i a t e d w i t h low c o m p e t i t i v e s t r e s s . These hypotheses are s i m i l a r to those t e s t e d i n the l a s t c h a p t e r because the measures of e f f i c i e n c y based on crown c h a r a c t e r i s t i c s are s i m i l a r i n concept to RGR. They a l s o r e f l e c t the c o n c l u s i o n s o f F o r d (1979, 1982, 1984) . The r e s u l t s o b t a i n e d i n the l a s t c h a p t e r suggest t h a t the f i r s t h y p o t h e s i s w i l l be r e j e c t e d . T h u s , the f o l l o w i n g h y p o t h e s i s w i l l be c o n s i d e r e d as w e l l : H 5 . 3 - B e f o r e the onset o f c o m p e t i t i o n i n even-aged s t a n d s , s m a l l t r e e s are more e f f i c i e n t than l a r g e ones . Three types o f crown measures w i l l be d e r i v e d : a b s o l u t e measures , r e l a t i v e measures , and r e l a t i v e growth measures . These w i l l be d e f i n e d i n the next s e c t i o n . A b s o l u t e and r e l a t i v e 1 3 9 measures w i l l be compared, and i t w i l l be d e t e r m i n e d i f the r e l a t i v e measures show the same t r e n d s as the r e l a t i v e growth measures . 5 . 4 - M a t e r i a l and Methods The d a t a employed were d e s c r i b e d i n Chapter 3. As mentioned above , the crown c h a r a c t e r i s t i c s s t u d i e d can be grouped i n t o t h r e e d i f f e r e n t c l a s s e s : a b s o l u t e measures , r e l a t i v e measures , and r e l a t i v e growth measures . The l a t t e r two can be c o n s i d e r e d as measures o f e f f i c i e n c y . A b s o l u t e measures c o n s i s t of crown w i d t h , crown l e n g t h , crown p r o j e c t i o n , crown s u r f a c e a r e a , crown volume, f o l i a g e w e i g h t , and b r a n c h w e i g h t . Crown w i d t h and crown l e n g t h were measured d i r e c t l y i n the f i e l d . Crown p r o j e c t i o n was computed as the s u r f a c e o f the c i r c l e d e l i m i t e d by crown w i d t h . A c c o r d i n g to S p r i n z and B u r k h a r t (1987) , crown p r o j e c t i o n c o n s t i t u t e s an i n d i r e c t measure o f p h o t o s y n t h e t i c a r e a . As sugges ted by the s t u d i e s o f S t i e l l (1962, 1966) , the form of the crown was assumed to be p a r a b o l o i d . T h e r e f o r e , the crown s u r f a c e a r e a was computed w i t h the f o l l o w i n g f o r m u l a : 2 4 1.5 4 1.5 Crown s u r f a c e a r e a where R i s the r a d i u s o f the crown and L i t s l e n g t h . The f o l l o w i n g f o r m u l a was used to compute crown volume: Crown volume 2 0 . 5 x I I x R x L . 140 The f o l i a g e weight of e v e r y t r e e was computed w i t h the f o r m u l a d e r i v e d by S t i e l l and B e r r y ( 1 9 7 7 ) : F o l i a g e weight (kg) = 0 . 4 9 8 8 x crown l e n g t h (m) x crown width (m) 2 R - 0 . 9 9 Because o f the r e l a t i v e l y l i m i t e d range o f da ta used to d e v e l o p t h i s e q u a t i o n , a compar i son was made w i t h an e q u a t i o n d e r i v e d from the d a t a c o l l e c t e d by Alemdag and S t i e l l ( 1 9 8 2 ) . T h i s d a t a se t was c o l l e c t e d i n the same a r e a and was c h a r a c t e -r i z e d by a much wider range of t r e e s i z e and age . There was no s i g n i f i c a n t d i f f e r e n c e between the e q u a t i o n s . F i n a l l y , the biomass of branches o f e v e r y t r e e was p r e d i c t e d from an e q u a t i o n a l s o d e r i v e d from the s tudy of Alemdag ( 1 9 8 3 ) and Alemdag and S t i e l l ( 1 9 8 2 ) : Biomass o f branches (kg) • 0 . 6 6 3 1 4 x Crown w i d t h (m) x Crown l e n g t h (m) 2 R - 0 . 9 1 The f i r s t r e l a t i v e measure computed was the r a t i o o f crown w i d t h to crown l e n g t h . T h i s was c a l l e d the crown f u l l n e s s r a t i o by Assmann ( 1 9 7 0 ) . When t h i s r a t i o i n c r e a s e s , the shape o f the crown becomes more rounded . The second r e l a t i v e measure c a l c u -l a t e d was the r a t i o o f crown s u r f a c e to crown vo lume. The c l o s e r the s p a c i n g , the l a r g e r the r a t i o ( C u r t i s 1 9 7 0 ) . The t h i r d measure used was the r a t i o of f o l i a g e biomass to b r a n c h b iomass . T h i s r a t i o r e p r e s e n t s the p r o p o r t i o n of p h o t o s y n t h e t i c t i s s u e per u n i t o f r e s p i r a t o r y t i s s u e ( P e r r y 1 9 8 5 ) . The r a t i o o f f o l i a g e biomass to crown volume was a l s o d e r i v e d . I t was used by K u u l u v a i n e n ( 1 9 8 8 ) as a measure o f need le d e n s i t y . I t a l s o r e f l e c t s the e f f i c i e n c y of the p h o t o s y n t h e t i c t i s s u e , g i v e n the 141 space a l l o c a t e d . The o t h e r r e l a t i v e measures c a l c u l a t e d were based upon both crown and b o l e d i m e n s i o n s . The r a t i o o f crown w i d t h to DBH ( a l s o c a l l e d crown p r o j e c t i o n r a t i o ) measures the degree to which crown w i d t h exceeds stem d iameter (Assmann 1 9 7 0 ) . The r a t i o o f crown w i d t h to stem h e i g h t i s a measure o f spread (Assmann 1 9 7 0 ) . Crown r a t i o , which was d i s c u s s e d e x t e n s i v e l y i n S e c t i o n 5 . 1 , was a l s o c a l c u l a t e d . These r a t i o s are s i m i l a r i n concept to the l e a f a r e a r a t i o ( l e a f a r e a / s t e m biomass) which r e f l e c t s the p r o p o r t i o n of p h o t o s y n t h e t i c t i s s u e to r e s p i r a t o r y t i s s u e (Hunt 1 9 8 2 ) . As i t was d e c i d e d to a p p l y t h i s concept to o t h e r crown d i m e n s i o n s , the f o l l o w i n g r a t i o s a l s o were computed: crown l e n g t h to DBH, crown p r o j e c t i o n to DBH and h e i g h t , crown s u r f a c e to DBH and h e i g h t , crown volume to DBH and h e i g h t , and f o l i a g e biomass to DBH and h e i g h t . The RGR measures s t u d i e d were based on the increment i n DBH, b a s a l a r e a , and h e i g h t . The crown c h a r a c t e r i s t i c s r e t a i n e d were: crown w i d t h , crown l e n g t h , crown p r o j e c t i o n , crown s u r f a c e a r e a , crown volume, and f o l i a g e b iomass . The computa t ion o f every r a t i o was based upon the e q u a t i o n p r o v i d e d by Hunt ( 1 9 8 2 ) f o r u n i t l e a f r a t e : _ W(2) - W(l) L n [ C R ( 2 ) ] - L n [ C R ( l ) ] RATIO •» x T ( 2 ) - T ( l ) CR ( 2 ) - CR ( 1 ) where W i s DBH, b a s a l a r e a , or h e i g h t , and CR one o f the crown c h a r a c t e r i s t i c s ment ioned above , and T the age . The r a t i o s based on f o l i a g e biomass r e f l e c t the RGR a d j u s t e d f o r p r o d u c t i v e m a t e r i a l (sapwood area) because o f the r e l a t i o n s h i p t h a t e x i s t s between the sapwood a r e a and l e a f area or biomass (Waring e t 142 a l . 1981) . As the emphasis was on comparing s p a c i n g e f f e c t s , data from the two sample p l o t s f o r a g i v e n s p a c i n g were merged. Trees from each s p a c i n g were d i v i d e d i n t o 1 cm d iameter c l a s s e s . These d i a m e t e r c l a s s e s c o n s t i t u t e d the n e s t i n g f a c t o r i n a nes ted anova . T h i s d e s i g n was used to compare the s p a c i n g s , and t e s t whether the crown parameters a n a l y s e d d i f f e r e d f o r t r e e s of v a r i o u s s i z e s . I t a l s o was used f o r t e s t i n g some o f the crown parameters based on measures of e f f i c i e n c y f o r v a r i a b i l i t y be fore the onset o f c o m p e t i t i o n . 5 . 5 - R e s u l t s and D i s c u s s i o n 5 . 5 . 1 - R e l a t i o n s h i p s between Crown Dimensions and Bo le S i z e s L i n e a r r e g r e s s i o n e q u a t i o n s were d e r i v e d to r e l a t e crown d imens ions to stem deve lopment . Except f o r the 1.5 m s p a c i n g , the s l o p e s o f the r e l a t i o n s h i p between crown w i d t h and d iameter f o r the f i r s t s i x s p a c i n g s d i d not d i f f e r s i g n i f i c a n t l y (Tab le 5 . 1 ) . The s l o p e s o f the 4.3 m and 6.0 m s p a c i n g s were much g r e a t e r than those o f the f i r s t s i x s p a c i n g s . The i n t e r c e p t s i n c r e a s e d w i t h s p a c i n g . The e f f e c t o f s tand d e n s i t y on the r e l a t i o n s h i p between crown w i d t h and DBH has been s t u d i e d f o r o t h e r s p e c i e s . For D o u g l a s - f i r , C u r t i s and Reukema (1970) d i d not o b t a i n any s i g n i -f i c a n t d i f f e r e n c e among s l o p e s , but the i n t e r c e p t was found to i n c r e a s e w i t h s p a c i n g . The same t r e n d was a l s o n o t i c e d by C u r t i n (1964, 1970) f o r E u c a l y p t u s o b l i q u a L ' H e r i t . Stand d e n s i t y was found to a f f e c t the s l o p e o f the r e l a t i o n s h i p s f o r D o u g l a s - f i r and l o d g e p o l e p i n e (Smith and B a i l e y 1964) . The r a t e o f change 143 T a b l e 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 o f DBH (cm) f o r a l l ages and e v e r y s p a c i n g . Form of e q u a t i o n : crown width - a + bxDBH Spacing (m) a b n 2 r SEE 1.2 0.855- 0.125ab* 901 0.69 0.316 1.5 1.017 0.119b 963 0.61 0.359 1.8 1.026 0.129ab 915 0.66 0.398 2.1 1.060 0.132a 950 0.77 0.362 2.4 1.288 0.133a 916 0.81 0.357 3.0 1.536 0.132a 924 0.86 0.348 4.3 1.410 0.162 893 0.93 0.357 6.0 1.003 0.182 1127 0.96 0.297 *: spacings w i t h the same l e t t e r do not 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 of 0 . 0 5 . SEE: standard e r r o r of es t i m a t e . Note: Both 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 every spacing at the l e v e l of p r o b a b i l i t y of 0 . 0 5 . T a b l e 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 o f DBH (cm) f o r a l l ages and e v e r y s p a c i n g . 2 Form of e q u a t i o n : crown l e n g t h = a + bxDBH + cxDBH 2 Spacing (m) a b c n r SEE 1.2 1.151 0.461 -0.011 896 0.72 0.591 1.5 1.556 0.438 -0.012 961 0.64 0.585 1.8 1.4 56 0.453 -0.011 915 0.72 0.556 2.1 0.982 0.570 -0.015 948 0.81 0.538 2.4 0.911 0.604 -0.016 917 0.82 0.560 3.0 0.333 0.662 -0.015 924 0.86 0.623 4.3 0.479 0.553 -0.009 910 0.93 0.607 6.0 0.278 0.482 -0.005 1229 0.90 0.649 SEE: standa r d e r r o r of es t i m a t e . Note: the three 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 every spacing at the l e v e l of p r o b a b i l i t y of 0.05. 144 o f crown w i d t h w i t h d i a m e t e r i n c r e a s e d as s t a n d d e n s i t y d e c r e a s e d u n t i l a maximum was reached w i t h open-grown t r e e s . They c o n c l u d e d t h a t the i n t e r c e p t was dependent upon the age and s i t e o f 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 used t o r e l a t e crown l e n g t h t o DBH ( T a b l e 5 . 2 ) . L i t t l e d i f f e r e n c e e x i s t e d among the s p a c i n g s from DBH = 0 t o DBH = 15 cm ( F i g u r e 5 . 1 ) . Beyond t h i s l i m i t , the s m a l l e r the s p a c i n g , the lower the c o r r e s p o n d i n g , c u r v e l e v e l e d o f f , e x c e p t f o r the f i r s t two s p a c i n g s . T h i s s u g g e s t s 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 or not v e r y s e v e r e , crown l e n g t h does not v a r y much among s t a n d s of d i f f e r e n t s p a c i n g s . When c o m p e t i -t i o n i n t e n s i f i e s , the r e d u c t i o n i n l i g h t p e n e t r a t i o n i n d u c e s mor-t a l i t y o f the l o w e s t b r a n c h e s , and thus o c c u r s f a s t e r as s t a n d d e n s i t y i s i n c r e a s e d . T h i s i s why crown l e n g t h d e c r e a s e s as s p a c i n g i s i n c r e a s e d f o r the same DBH. More e x t e n s i v e r e s u l t s f o r crown l e n g t h w i l l be examined below. 5 . 5 . 2 - A b s o l u t e Measures The mean v a l u e s o f crown w i d t h , crown l e n g t h , crown p r o j e c -t i o n , crown s u r f a c e , crown volume, f o