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Effect of competition on the growth and crown form of lodgepole pine Bailey, Gordon Raymond 1964

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EFFECT OF COMPETITION ON THE GROWTH AND CROWN FORM OF LODGEPOLE PINE by GORDON RAYMOND BAILEY B. S c . ( F o r e s t r y ) , U n i v e r s i t y of Aberdeen, 1952 A THESIS SUBMITTED IN PARTIAL FULFILMENT OP THE REQUIREMENTS FOR THE DEGREE OP MASTER OP FORESTRY i n the Department of F o r e s t r y We accept t h i s t h e s i s as conforming to the re q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA A p r i l , 196^ In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study. I f u r t h e r agree that per-m i s s i o n f o r extensive copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s r e p r e s e n t a t i v e s . I t i s understood t h a t - c o p y i n g or p u b l i -c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n permission* Department of The U n i v e r s i t y of B r i t i s h Columbia, Vancouver 8, Canada i i ABSTRACT Tree growth and crown form of 131 open-grown and 63 f o r e s t -grown lodgepole pine were investigated. Areas sampled included repre-sentative s i t e s i n the I n t e r i o r , Lower Mainland and Vancouver Island i n B r i t i s h Columbia. Both graphical and multiple regression analyses were used. The best, but s t i l l inadequate, estimator of e i t h e r r a d i a l or basal area growth f o r the l a s t f i v e years was the growth f o r the period s i x to ten years ago. Standard errors of estimate ranged from 21.4- percent f o r basal-area growth of i n d i v i d u a l open-grown trees to ^3.5 percent f o r basal-area growth of i n d i v i d u a l forest-grown trees. More than 90 percent of the t o t a l v a r i a t i o n i n the crown width of open-grown lodgepole pine was accounted f o r by d.b.h. alone. For f o r e s t -grown trees only 56.8 percent waB accounted f o r by d.b.h. This per-centage may be increased to 81.1 percent by the addition of height-crown width ( H / C V ) , and to 68.^ percent by the a d d i t i o n of crown width/diam-eter (CW/D). Average value f o r CW/D was 0.99 f o r the forest-grown, and 2.13 f o r 90 open-grown trees ten years of age or older. Both H/CW and CW/D are s i g n i f i c a n t l y r e l a t e d to s i t e index and age. However, when d.b.h. i s taken i n t o account, only s i x percent of the v a r i a t i o n i n CV/D i s affected by s i t e index. Almost 50 percent of the height to the lowest dead branch, and over 90 percent of the height to the lowest l i v e branch could be ac-counted f o r by tree age, d.b.h. and height. One of four "competition f a c t o r s " , a l l r e l a t e d to distance to, and s i z e of, competing trees, i i i accounted f o r an ad d i t i o n a l 13.7 percent of the v a r i a t i o n i n height to dead branches. However, basal area, H/CW, and CW/D were of l i t t l e importance a f t e r the e f f e c t s of age, d.b.h. and height were accounted f o r . The maximum growth rate f o r open-grown trees was determined g r a p h i c a l l y f o r ages from 30 to 50 years by s i t e index classes. Comparison with normally grown trees showed that at l e a s t twice the normal yield-table-estimate of growth rate may be expected from open-grown trees. Using regression equations developed from.the data, a t h e o r e t i c a l conversion to lumber was made f o r a butt l o g from an open-grown tree. For boards, graded under the Western Pine Association's r u l e s , i t was shown that large knots may degrade lumber grown at the maximum r a t e . Therefore, use of an open-to-normal density model, which allows crowns to compete before excessive knot formation occurs, would be a desirable objective f o r management of lodgepole pine. ACKNOWLEDGEMENT Various members of the Faculty of Forestry, U n i v e r s i t y of B r i t i s h Columbia, have been of great assistance i n the preparation of t h i s t h e s i s . The constructive c r i t i c i s m and i n t e r e s t of Dr. J . H. G. Smith were gr e a t l y appreciated, p a r t i c u l a r l y f o r the l a t e r stages of the study. Mr. J . Hejjas and Dr. A. Kozak ex-pended considerable time and e f f o r t i n programming and operating the computer f o r analysis of these data. Attendance at the Univ e r s i t y was f a c i l i t a t e d by f i n a n c i a l assistance from the Van Dusen Foundation and the University Research Forest. Expenses incurred while c o l l e c t i n g part of. the data were met by funds made available by the National Research Council. With-out such assistance the completion of t h i s thesis would have been gr e a t l y delayed. i v TABLE OP CONTENTS Page TITLE PAGE ABSTRACT i i TABLE OP CONTENTS i v ACKNOWLEDGEMENT XIII INTRODUCTION 1 PURPOSE OP STUDY k REVIEW. OP LITERATURE 6 COLLECTION OP DATA 9 1. Location 9 2. Tree measurement 12 3. S i t e f a c t o r s measured 13 k. Descriptions of s i t e s sampled Ik ANALYSIS OP DATA 18 1. Radial growth of i n d i v i d u a l trees Open-grown 20 Forest-grown 2 7 Conclusion 31 i . Comparison of methods of desc r i b i n g crown development f o r r a d i a l growth estimation 31 i i . Correlations between D.b.h. and height and eight v a r i a b l e s 3k 2. Basal area growth of i n d i v i d u a l trees Open-grown % Forest-grown 39 Conclusion ^1 3. Analysis of crown width, crown width/diameter and height/crown width Introduction ^5 Analysis of crown width ^9 Estimation of D.b.h. from a e r i a l photographs 5^ Crown competition f a c t o r 55 Analysis of crown width/diameter and height/crown width i . Introduction 56 i i . Crown width/diameter 57 E f f e c t s of s i t e index and age 62 i i i . Height/crown width 63 k. Natural pruning of lodgepole pine Introduction 70 Tree competition f a c t o r 71 Analysis of factors a f f e c t i n g height to lowest dead branch 7^ Analysis of factors a f f e c t i n g height to lowest l i v e branch 77 GROWTH LIMITS OF LODGEPOLE PINE Introduction • 79 R e l a t i o n of s i t e index to s i t e f a c t o r s 80 Association between cumulative r a d i a l growth and aver-age s i t e index f o r sampling areas 82 Cumulative r a d i a l growth r e l a t e d to s i t e index 86 Growth comparisons 95 Marginal tree s i z e ..; 97 vi L i m i t a t i o n s o f Maximum Growth R a t e 99 Knot s i z e 100 S p e c i f i c g r a v i t y and f i b r e l e n g t h 107 SUMMARY AND CONCLUSIONS 110 LITERATURE CITED 116 APPENDIX ' 119 v i i REFERENCE LIST OF TABLES Table . V Page 1. Gross volumes i n MM cubic f e e t of commercial f o r e s t growing on a l l s i t e s i n B r i t i s h . Columbia i n 1957 1 2. Sound wood volume i n MM cubic feet of accessible stands 12 inches or more i n D.b.h. 2 3. Species cut, a l l products, 19&2, i n cubic f e e t 2 k. D.b.h., t o t a l height, age, s i t e index and basal area by s i t e s e r i e s 19 •  5. Summary of basic data f o r open-grown trees 21 6. Summary of data, and simple 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 analyses of r a d i a l and basal area growth of 83 i n d i v i d u a l open-grown trees 23 7. Linear regression equations f o r estimation of r a d i a l growth f o r the l a s t f i v e years f o r open-grown trees ........ 2k 8. Association between r a d i a l growth and 10 v a r i a b l e s f o r 90 open-grown trees 26 9. Summary of data, and simple 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 the analyses of r a d i a l and basal area growth of 63 i n d i v i d u a l forest-grown trees 28 10. Linear regression equations f o r the estimation of r a d i a l growth f o r the l a s t f i v e years f o r 63 i n d i v i d u a l forest-grown trees 29 11. Correlations between past r a d i a l growth and'crown indices 32 12. Comparisons of c o r r e l a t i o n s between D.b.h. and height and each of eight v a r i a b l e s 3k 13. Linear regression equations f o r the estimation of basal area growth f o r the l a s t f i v e years f o r 83. i n d i v i d u a l open-grown trees 38 1^. Linear regression equations f o r the estimation of basal area growth f o r the l a s t f i v e years f o r 63 i n d i v i d u a l forest-grown trees kO v i i i Table .' Page 15. A s s o c i a t i o n between basal area growth and ten v a r i a b l e s , k2 16. A s s o c i a t i o n between crown width and s i x v a r i a b l e s f o r open-grown and forest-grown trees k7 17. Simple c o r r e l a t i o n s between CW/D and H/CW r a t i o s and nine v a r i a b l e s ^8 18. Regression equations f o r the estimation of CW/D from H/CW or H/CW from CW/D k9 19a. Relationships between crown width and d.b.h., height, height/crown width and crown width/diameter f o r open-grown trees 50 b. Relationships between crown width and d.b.h., height, height/crown width and crown width/diameter f o r forest-grown trees 51 c. Estimation of d.b.h. from height, crown width and height/crown width 5k 20. Relative v a r i a t i o n of data used f o r crown width, crown/width/diameter, and height/crown width analyses 58 21. R e l a t i o n of CW/D to d.b.h., crown width, height and H/CW f o r 111 open-grown trees 60 22. R e l a t i o n of CW/D to d.b.h., s i t e index, age and H/CW f o r 63 forest-grown trees 60 23. Relation of H/CW to height, crown width, age and s i t e index f o r 111 open-grown trees 65 2k. Relation of H/CW to height, crown width, age and s i t e index f o r 57 forest-grown trees 65 25. Basic data used f o r the an a l y s i s on natural pruning of 57 forest-grown trees 73 26. Simple c o r r e l a t i o n c o e f f i c i e n t s between average height to lowest dead branch and average height to the lowest l i v e branch and four tree competition factors 7k 27. Linear regression equations f o r average height to lowest dead branch on each of four sides 75 i x * Table Page 28. Linear regression equations f o r average height to lowest l i v e branch on each of four sides 78 29. Linear and parabolic regression equations f o r cumulative r a d i a l growth of open-grown lodgepole pine on age, f o r each s i t e s e r i e s 84-30. Average d.b.h. at age 50 i n r e l a t i o n to average s i t e index f o r open-grown trees 86 31. Linear and parabolic regression equations f o r cumulative r a d i a l growth of forest-grown lodgepole pine on age, f o r each s i t e s e r i e s 87 32. Average d.b.h. of open-grown and forest-grown lodgepole pine at ages 30, ^0, and 50 years 96 33« Number of years required f o r open-grown and forest-grown lodgepole pine to reach a s p e c i f i e d diameter 96 3^. D i s t r i b u t i o n of lumber width by l o g s i z e 10^ 35. Lumber grade recovery by l o g diameter f o r forest-grown lodgepole pine 10**-36. Comparison of growth rates of lodgepole pine with Douglas f i r f o r open-grown and forest-grown trees 105 FIGURES No. Page 1. Location of sampling areas 11 2. Relation of crown width to diameter k6 3. Relation of s i t e index to s i t e f a c t o r s f o r sampling areas 81 k. Diameter on age f o r open-grown lodgepole pine of s i t e index c l a s s 31 to 50 89 5; Diameter on age f o r open-grown lodgepole pine of s i t e index cl a s s 51 to 70 90 6. Diameter on age f o r open-grown lodgepole pine of s i t e index cl a s s 71 to 90 91 7. Diameter on age f o r open-grown lodgepole pine of s i t e index class 91 to 110 92 8. Influence of s i t e index on open-grown tree s i z e 93 9. Diameter of open-grown lodgepole pine f o r ages 30 to 50 years 9^  APPENDIX Page 1,. Simple c o r r e l a t i o n matrices f o r selected v a r i a b l e s a. 90 open-grown trees 119 b. I l l open-grown trees 120 c. 83 open-grown trees 120 d. 63 forest-grown trees 121 e. 57 forest-grown trees 122 2. Cumulative r a d i a l growth of i n d i v i d u a l trees presented g r a p h i c a l l y f o r each s i t e s e r i e s a. 100 open-grown - Lac l a Hache 123 b. 200 open-grown - Manning Park 124 c. 300 open-grown - Lower Mainland - peat 125 d. 600 open-grown - Prince George 126 e. 800 + 1200 forest-grown - Lower Mainland - peat ... 127 f . (1000 forest-grown - Vancouver Island - moist. 128 ( 1100 forest-grown - Vancouver Island - wet " x i i ABBREVIATIONS USED IN TEXT D.B.H., dbh, d.b.h.diameter outside bark at breast height, i n inches double bark thickness at breast height i n inches, from two measurements diameter outside bark, i n inches Dbk D.o.b H Age SI C¥ CW/D H/CW Lc$ HDbr HLbr LDbr LLbr BrBTT R g6-10, B a g6-10 t o t a l tree height, i n feet unless otherwise s p e c i f i e d , t o t a l tree age, i n years s i t e index, t o t a l tree height at age 100 years the widest part of the crown, average of two measurements i n feet r a t i o of crown width/d.b.h. r a t i o of t o t a l height/crown width percentage l i v e crown, Lc/H, expressed as a percentage, where Lc i s the average distance from the lowest l i v e branch of any s i z e on each of four sides to the t i p of the tree average height, i n f e e t , to the lowest dead branch of any size on each of four sides average height, i n f e e t , to the lowest l i v e branch of any s i z e on each of four sides average of the maximum h o r i z o n t a l length of dead branches on each of four sides, measured i n feet average of the maximum ho r i z o n t a l length of l i v e branches on each of four sides, measured i n feet diameter i n inches, outside bark, of the base of the larg e s t l i v e branch on the tree r a d i a l growth i n inches, and basal area growth i n square inches, f o r the l a s t f i v e years, measured at breast height r a d i a l growth i n inches, and basal area growth i n square inches, f o r the period s i x to ten years ago, measured at breast he ights TC tree competition f a c t o r . An index i n v o l v i n g the d.b.h. and distance to competing trees 1 INTRODUCTION Lodgepole pine (Pinus c o n t o r t a , Dougl.) occurs throughout much o f the Province o f B r i t i s h Columbia and has been found a t a l l e l e v a t i o n s from sea l e v e l t o t i m b e r l i n e . I n 1957 i * was estimated t o form approximately 15 percent o f the t o t a l commercial f o r e s t on a l l s i t e s . However, a d i s p r o p o r t i o n a t e l y h i g h percentage o f lodgepole pine i s i n the s m a l l e r diameter c l a s s e s (Table l ) . TABLE 1 GROSS VOLUMES IN MM CUBIC FEET OF COMMERCIAL FOREST, GROWING ON ALL SITES IN BRITISH COLUMBIA IN 195? ( l ) D.b.h. A l l Species Lodgepole pine /f" _ 9» 81,526 . 26,970 (33$) 10" and l a r g e r 388,197 45,.517 (11.770 469,723 75,^ 87 (15.5$) Xl) Based on B.C. Forest S e r v i c e (1957). Despite i t s general d i s t r i b u t i o n , lodgepole pine i s mainly a s s o c i a t e d w i t h the I n t e r i o r o f the P r o v i n c e . A c c e s s i b l e stands 12" or l a r g e r i n d.b.h. provide approximately 18 percent of the t o t a l volume o f s i m i l a r stands f o r the I n t e r i o r ; f o r the Coastal r e g i o n , the percentage i s n e g l i g i b l e (Table 2 ) . 2 TABLE 2 SOUND WOOD VOLUME IN MM CUBIC FEET OF ACCESSIBLE STANDS 12 INCHES OR MORE IN D.B.H. ( l ) A l l Species Lodgepole pine Interior 48,513 8,676 (17.9$) Coast 19,641 38 ( 0.2$) 68,154 8,714 (12.7$) (1) B.C. Forest Service (1957). Lodgepole pine i s not yet a major contributor to the forest economy of Bri t i s h Columbia. In 1962, the volume cut i n the Interior for a l l purposes amounted to only 9*5 percent of the total Interior cut reported by the Bri t i s h Columbia Forest Service (Table 3). TABLE 3 SPECIES CUT, ALL PRODUCTS, 1962, IN CUBIC FEET ( l ) A l l Species Lodgepole pine Interior 559,586,467 52,940,145 (9.5$ Coast 783,349,910 20,706 * 1,342,936,377 52,960,851 (3.9$; 7JT5 From report of B.C. Forest Service (1962). * 0,0000 3$ The main reason for this low cut i s the generally small size of lodgepole pine trees. However, the annual cut w i l l probably increase i n 3 the near future. One of the results of the increasing necessity for operators to consider u t i l i z i n g small logs i n order to stay i n "business has been the establishment of stud mills manufacturing eight foot lengths of small dimension lumber. Many of these mills are designed to u t i l i z e only small logs. Several pulp mills are planned for the Interior i n the near future. Availability of a chip market w i l l promote harvesting of small logs. These developments by industry, plus the desirability of obtaining additional information concerning the effect of certain factors on the growth rate and crown form of lodgepole pine, have led to the present study. PURPOSE OF THE STUDY The study was made to determine - from measurements made on "both f u l l y open-grown and forest-grown individual lodgepole pine trees - how tree growth and crown form may be adequately expressed and related mathematically. The complex of factors that jointly result i n a particular growth rate i s expressed i n the statement that, "the growth rate of individual trees of the same species on the same site i s dependent upon the competition exerted towards each and the a b i l i t y of each to withstand this competition"' (Spurr, 1952). Tree-to-tree variation in response to competition was related only to environmental factors. Possible variation due to genetic differences could not be separated from experimental error i n any of the analyses made. Total competition may be regarded as having two components, crown competition for l i g h t , and root competition for water and nutrients. The assumption that crown competition adequately accounts for the effects of root competition has been made by most workers i n this f i e l d , (Van Slyke, 196k). While collecting data for this study the extent of the lateral root system of 55 lodgepole pine was investigated as part of a project for Dr. J.H.G. Smith, of the Faculty of Forestry. Average root spread was found to be well correlated with crown width and tree height. A correlation having been demonstrated, a l l analyses involving tree competition u t i l i z e d only crown data. Particular attention was paid to crown ratios, on the premise they provide a way of conveniently describing the to t a l i t y of competition on 5 the t r e e . Through t h i s approach i t was hoped to develop p o t e n t i a l l y u s e f u l r e l a t i o n s h i p s t h a t could be employed i n photogrammetric and management a p p l i c a t i o n s . Smith (1963) i n d i c a t e d how a knowledge of crown development may be used i n the manipulation of stands to achieve s p e c i f i c o b j e c t i v e s of management. Spacing c o n t r o l through m a i n t a i n i n g appropriate crown r a t i o s not only c o n t r o l s t r e e s i z e , r a t e of n a t u r a l pruning and knot s i z e , but a l s o the p r o p o r t i o n of bole wood to crown wood, the pro-p o r t i o n of summerwood and hence aspects of wood q u a l i t y such as spe-c i f i c g r a v i t y and f i b r e l e n g t h (Wellwood and Smith, 1962). I t was not considered appropriate i n a mensuration t h e s i s of t h i s type to expand the study of v a r i a t i o n o f Coast and I n t e r i o r lodgepole pine along the l i n e s used by L. Roche. The i n t e r e s t e d reader i s there-f o r e r e f e r r e d to h i s U n i v e r s i t y of B r i t i s h Columbia Master's Thesis on tha t t o p i c . 6 REVIEW OF LITERATURE Bright (1914) working with western yellow pine (Pinus ponderosa) found a distinct relation "between crown areas of normally shaped dominant trees and their stem diameter. Although concluding that root competition was not severe, he suggested that for determining required growing space an additional allowance - varying with diameter class - "be made to actual crown widths. Working on brush disposal from logged stands of western yellow pine Mclntyre (1931) using f u l l y stocked sample plots up to ten acres i n size, found a correlation between both crown width and crown length and board foot volume per acre. He concluded that for western yellow pine crown length was the better index. Chisman and Schumacher (19^0) related growing space to tree diameter and basal area through a quadratic expression i n developing their tree area ratio index. When studying the relationship of crown form to the development of young western white pine (Pinus monticola). Arnold (19^9) found correlations between the growing space ratio (crown width/stem diameter) and percentage li v e crown and the current growth rate. He found a combination of crown length and width (crown length times crown width) was the best estimator of current basal area growth (7^ percent of the total variation being accounted f o r ) . More recently, i n 1957, Krajicek and Brinkman, i n developing an index to express stand density based on the crown development of f u l l y 7 open-grown t r e e s , found a s t r o n g l i n e a r r e l a t i o n s h i p between crown width and stem diameter f o r open-grown Oak (Quercus s p . ) , h i c k o r y (Carya ovata) and Norway spruce ( P i c e a e x e l s i o r ) . The crown com p e t i t i o n f a c t o r which they developed f o r forest-grown t r e e s used t h i s r e l a t i o n s h i p . V e z i na (1962) found comparable l i n e a r r e g r e s s i o n s r e l a t i n g crown width t o stem diameter f o r white spruce ( P i c e a glauca) and balsam f i r ( A bies balsamea). I n 19&3 he r e l a t e d crown width and stem diameter f o r s m a l l open-grown jackpine (Pinus banksiana). Smith, Ker and Csizmazia (1961) have shown th a t the r a t i o s of crown width/diameter and t r e e height/crown width are u s e f u l i n e x p r e s s i n g stand d e n s i t y when used w i t h average stand diameter. Working w i t h Douglas f i r (Pseudotsuga m e n z i e s i i ) . western hemlock (Tsuga heterophy11a) and western r e d cedar (Thuya p l i c a t a ) they found t h a t about 90 percent of. the crown width v a r i a t i o n can be accounted f o r by stem diameter f o r open-grown t r e e s . This estimate can be improved t o 98 percent w i t h the i n c l u s i o n o f the crown width/diameter r a t i o . Apsey (1961), Pearson (1962J and Johnson (1962) demonstrated that a good r e l a t i o n s h i p e x i s t s between crown width and d.b.h. f o r open-grown and forest-grown t r e e s of the species a l d e r (Alnus r u b r a ) , b l a c k c o t t o n -wood (Populus t r i c h o c a r p a ) , Engelman spruce ( P i c e a Engelmanni) and I n t e r i o r Douglas f i r . The e f f e c t of competition on crown growth was i n v e s t i g a t e d by Smith et a l . (l96l) f o r Douglas f i r , hemlock and western red cedar. Be-tween 53 percent and 85 percent of the v a r i a t i o n i n c l e a r b o l e l e n g t h o f i n d i v i d u a l t r e e s could be accounted f o r by diameter, age and height - w i t h 8 age being the most important v a r i a b l e . By the a d d i t i o n of a d e n s i t y measure, b a s a l area per acre, to the three f a c t o r s r e f e r r e d t o , 5^ per cent t o 76 percent of the t o t a l v a r i a t i o n i n height t o the lowest l i v e branch could be accounted f o r . Diameter, height and crown width/diameter were found to be the most important v a r i a b l e s i n accounting f o r l e n g t h of l i v e crown, 58 percent to 66 percent of the t o t a l v a r i a t i o n being account-ed f o r . Percentage of l i v e crown was found to be s i g n i f i c a n t l y a s s o c i a t e d o n l y w i t h b a s a l area per acre and the height/crown width r a t i o . The v a r i a t i o n i n competition from s i d e - t o - s i d e of i n d i v i d u a l t r e e s was i n v e s t i -gated by comparison of the average values on a l l sides f o r heights t o dead and to l i v e branches w i t h the corresponding values f o r "open" and "dense" s i d e s . No s i g n i f i c a n t d i f f e r e n c e s were found f o r heights to e i t h e r dead or l i v e branches between averages f o r "dense" and " a l l " s i d e s . Values f o r the "open" sides showed s i g n i f i c a n t l y l e s s n a t u r a l pruning than f o r " a l l " o r "dense" s i d e s . I t i s evident t h a t v a r i a t i o n i n stand d e n s i t y - as an expression of t r e e competition - a f f e c t s the growth r a t e and crown form of the f o r e s t -grown t r e e . I f e f f e c t s due t o stand d e n s i t y d i f f e r e n c e s can be removed, then the f r e e growth of the i n d i v i d u a l t r e e may be s t u d i e d and the i n t e r -dependence of v a r i o u s stem and crown parameters determined i n the complete absence of t r e e competition. I f forest-grown t r e e s are s t u d i e d which have been subjected to v a r y i n g degrees of t r e e competition i t should be p o s s i b l e to determine not only the e f f e c t s of t r e e competition on i n d i -v i d u a l t r e e development but a l s o t o f i n d out how t r e e competition a f f e c t s the interdependence of the v a r i o u s t r e e f a c t o r s commonly used i n the d e s c r i p t i o n of forest-grown t r e e s . 9 COLLECTION OP DATA I t had been planned o r i g i n a l l y to c o l l e c t data on f o r e s t and open-grown t r e e s from a p a r t i c u l a r s i t e , and by o b t a i n i n g a d d i t i o n a l data from p a i r e d groups over a range of s i t e s the comparison o f the e f f e c t of d e n s i t y and s i t e d i f f e r e n c e s would have been f a c i l i t a t e d . However, i t was not p o s s i b l e to f o l l o w the planned approach due t o the d i f f i c u l t y of f i n d i n g enough f u l l y open-grown tre e s i n c l o s e p r o x i m i t y to forest-grown t r e e s , and a l s o due to the l a c k o f time to o b t a i n forest-grown samples from those areas where open-grown t r e e s were l o c a t e d . LOCATION I t was important to s e l e c t f o r the open-grown t r e e s , only u n d i s -turbed t r e e s that were f u l l y open-grown. The f o l l o w i n g c r i t e r i a were e s t a b l i s h e d to determine whether a p a r t i c u l a r t r e e was s u i t a b l e f o r the purpose intended: 1. No t r e e w i t h i n a r a d i u s equal t o t r e e height 2. The lowest p a r t of the crown should g e n e r a l l y be the widest 3. Free from disease 4. No v i s i b l e signs of g r a z i n g 5. No past i n t e r f e r e n c e by man w i t h e i t h e r bole or crown. Data f o r open-grown t r e e s were obtained mainly from three areas, near Lac l a Hache i n the I n t e r i o r , from the eastern boundary of Manning Park on the Hope-Princeton highway, and from L u l u I s l a n d near Vancouver. Information on forest-grown t r e e s was obtained from stands on L u l u I s l a n d and near Coquitlam on the Lower Mainland, and from 10 P a r k s v i l l e on Vancouver I s l a n d . Areas from which a d d i t i o n a l data were obtained a l s o are shown on the accompanying map ( F i g . l . ) . I t was a n t i c i p a t e d t h a t open-grown lodgepole pine meeting the r e q u i r e d above s p e c i f i c a t i o n s would be found i n parks, along the edge of f o r e s t e d areas, i n cemeteries and gardens, and along rights-of-way. Most of the t r e e s used were those found growing on l a n d that had been c l e a r e d at one time by man and had r e v e r t e d t o a n a t u r a l c o n d i t i o n . Many otherwise d e s i r a b l e t r e e s had been pruned t o make way f o r telephone or t r a n s m i s s i o n l i n e s or had been used as fence-posts. The f o u r t h c r i t e r i o n mentioned above, i . e . No.4 on the previous page,was ignored f o r the Lac l a Hache area which i s r a n c h i n g country. There a l l data on dead branches were ignored because c a t t l e had rubbed against the lower p o r t i o n o f most stems. A. few open-grown t r e e s from g o l f courses were i n c l u d e d i n c e r t a i n analyses but due t o the i m p o s s i b i l i t y of o b t a i n i n g increment cores were not completely s a t i s f a c t o r y . 11 Figure I- Location of Sampling Areas-12 TREE MEASIH3EMENT The f o l l o w i n g measurements were recorded f o r 131 open-grown and 63 forest-grown t r e e s where p o s s i b l e : Diameter at breast height T o t a l height Crown width - average of two measurements of the widest p a r t of the crown Height to the lowest dead branch of any s i z e on each of f o u r s i d e s Height to lowest l i v e branch of any s i z e on each of f o u r s i d e s Maximum h o r i z o n t a l l e n g t h of l i v e branches on each of f o u r sides Branch diameter outside bark at the base of the l a r g e s t l i v e branch on a t r e e Double bark t h i c k n e s s at breast height R a d i a l growth of wood, 1 - 5 y e a r s , 6 - 10, 11 - 15, and 16 - 20 years ago, then 21 - 30, 31 - k0 e t c . at breast height In a d d i t i o n to the above measurements the f o l l o w i n g data were ob-t a i n e d from a l i m i t e d number of open-grown t r e e s : Crown height - height t o the p o i n t at which crown width was measured Branch bark t h i c k n e s s at the base of the l a r g e s t l i v e branch on a t r e e Stem diameter outside bark 9 1 from the ground For a l l forest-grown t r e e s the crown c l a s s was noted. A measure of b a s a l area per acre was obtained u s i n g a prism w i t h a b a s a l area f a c t o r o f ten. I n a d d i t i o n , the d.b.h., d i r e c t i o n and distance t o a l l t r e e s w i t h i n a p l o t o f r a d i u s approximately equal to three times the crown width of the sample t r e e were recorded. This procedure g e n e r a l l y 13 r e s u l t e d i n the measurement of t r e e s i n a d d i t i o n to those t h a t were v i s i b l y a f f e c t i n g the crown growth of the sample t r e e . I t was considered d e s i r a b l e t o i n c l u d e these a d d i t i o n a l t r e e s to ensure t h a t a complete enumeration of a l l p o s s i b l e competitive t r e e s was made. SITE FACTORS MEASURED No exhaustive a n a l y s i s of s i t e was intended i n the study. How-ever, t o r e l a t e any r e s u l t s to other s t u d i e s each major area was c l a s s i f i e d on the b a s i s of the ground v e g e t a t i v e cover. Depth o f s o i l and the moisture regime were recorded f o r each area. I t a l s o had been planned to rec o r d aspect, p r o f i l e and contour o f slope f o r each sample t r e e , but i t became evident e a r l y i n the study t h a t r e c o r d i n g these f a c t o r s would not be of much value due to the d i f f i c u l t y o f o b t a i n i n g an adequate range o f va l u e s . Yalues f o r s i t e index, defined as t o t a l t r e e height at age 100, were derived from each i n d i v i d u a l t r e e by i n t e r p o l a t i o n i n the height/age curves used by the B r i t i s h Columbia Forest S e r v i c e (Forest Club, 1959). The r e s u l t i n g values were f e l t t o be r e l i a b l e f o r the data on f o r e s t -grown t r e e s , a l l dominant or co-dominant. However, a p p l y i n g the same method to the open-grown t r e e s almost c e r t a i n l y introduced an undeter-mined b i a s due to the assumption that every open-grown t r e e was dominant. Fo r young t r e e s , the g u i d i n g curves f o r 60 and 80 s i t e i n d i c e s were used t o provide a sheaf of s i m i l a r curves f o r the remaining s i t e q u a l i t i e s . T his again would introduce e r r o r s , due e i t h e r t o the assumption of anamorpnic height/age curves or through e r r o r s i n e x t r a p o l a t i o n . I n s h o r t , the average s i t e index values t h a t were determined f o r each s i t e sampled f o r the open-grown t r e e s almost c e r t a i n l y o/vlerstated Ik t h e i r p r o d u c t i v i t y . Average s i t e index determined f o r the s i t e s from which the forest-grown data were obtained would be more r e l i a b l e . Despite the f a c t t h a t d i r e c t comparison could only be made from the L u l u I s l a n d data - which are not t y p i c a l o f s i t e s where the bulk o f lodgepole pine i s t o be found - i t was p o s s i b l e t o draw v a l i d conclusions r e g a r d i n g s i t e e f f e c t s by the method o f r e g r e s s i o n a n a l y s i s used. The r e l a t i v e importance of any f a c t o r may be determined from a n a l y s i s and the ap p r o p r i a t e conclusions made. DESCRIPTION OF SITES SAMPLED The i n d i v i d u a l t r e e s measured were c l a s s i f i e d i n t o seven major s i t e s e r i e s on the b a s i s of f o r e s t s i t e c h a r a c t e r i s t i c s . Use of the " s i t e s e r i e s " code number f a c i l i t a t e d l a t e r i d e n t i f i c a t i o n o f the i n d i v i d u a l t r e e s . A l l data on c l i m a t e were obtained from Climate o f B r i t i s h Columbia (Dept. o f A g r i c , 1962). OPEN-GROWN TREES  S i t e s e r i e s 100 Number of t r e e s - 3 3 L o c a t i o n : 2 to 5 m i l e s south of Lac l a Hache, Cariboo Forest r e g i o n ( H a l l i d a y , 1958): M 2 Montane C e n t r a l Douglas f i r s e c t i o n . Forest s i t e type ( i l l i n g w o r t h and A r l i d g e , i960): Calamagrostis-A r c t o s t p h y l o s type S o i l : sandy loam - 12" t o 20" i n depth t o 'C' h o r i z o n , dry moisture regime T e r r a i n : f l a t to g e n t l y r o l l i n g r anching country Annual p r e c i p i t a t i o n - 1^ .16" - f i v e year average o 0 0 o Monthly temperature F: range 17 t o 59 average - 39 E l e v a t i o n : 2,670' S i t e s e r i e s 200 Number of trees - 28 Location: Eastern border of Manning Park, on Hope-Princeton highway-Forest region: S.A.2. - I n t e r i o r Sub-alpine (Halliday, 1958) Forest s i t e type: Cornus-moss type ( i and A., i960) T e r r a i n : River bench S o i l : Gravelly s i l t y loam - 16" or more i n depth to the 'C horizon. Moisture regime moist Annual p r e c i p i t a t i o n : 47.83" - four year average Monthly temperature °F: range - 19° to 53° average - 39° E l e v a t i o n : 4,000' S i t e s e r i e s 300 Number of trees - 35 - plus 10 young trees l e s s than 4.5 f t . i n height Peat or peaty s o i l s . This c l a s s i f i c a t i o n includes trees from Lulu Island, Coquitlam and the U n i v e r s i t y of B r i t i s h Columbia Endowment Lands, a l l near Vancouver Forest region: C; - Southern Coast Section Forest s i t e type - Lodgepole pine - labrador tea - peat moss (Forest Club, 1959) T e r r a i n : P l a t , low-lying swampy areas S o i l : peat to loamy peat, 16" or more i n depth. Wet to satur-ated moisture regime Annual p r e c i p i t a t i o n : 40.91" - 23 year average Monthly temperature °P: range - 36° to 64° average - 50° E l e v a t i o n : sea l e v e l (Dept. of A g r i c , 1962) S i t e s e r i e s 600 Number of trees - 9 16 Location: 20 miles to the south of Prince George, near Cale Creek Forest region: M.4. - Montane T r a n s i t i o n section (Halliday, 1958) Forest s i t e type: Calamagrostis ( I . and A., 1958) Te r r a i n : River bench, f l a t S o i l : Pine view clay a s s o c i a t i o n ( K e l l y and Frastad, 1946). Moisture regime moist with 16" or more s o i l depth Annual p r e c i p i t a t i o n : 24.15" - 18 year average O O O O Monthly temperature F: range 11 to 59 average - 38 El e v a t i o n : 2,200' (Dept. of A g r i c , 1962) S i t e s e r i e s 700. 500 and 400 Number of trees - 16 In addition to the above s e r i e s three open-grown trees were measured i n the Okanagan area near Vernon, four at Bear Lake located 50 miles north of Prince George, and nine from two g o l f courses i n Vancouver. Owing to the l i m i t e d number of trees and the i m p o s s i b i l i t y of obtaining increment cores from the "golf-course" trees these samples were not used i n the d i r e c t determination of s i t e d i f f e r e n c e s . FOREST-GROWN TREES S i t e s e r i e s 800 and 1200 Number of trees - 33 Obtained from Lulu Island and Coquitlam areas r e s p e c t i v e l y Peat s o i l s as previously described S i t e s e r i e s 1000 Number of trees - 10 Location: 3 miles west of P a r k s v i l l e , Vancouver Island 17 Forest r e g i o n : C . l . - Madrona Oak T r a n s i t i o n s e c t i o n ( H a l l . 1958) Forest type: Douglas f i r s a l a l a s s o c i a t i o n ( F o r e s t Club, 1959) T e r r a i n : F l a t S o i l : G r a v e l l y sandy loam, 7" to 9" i n depth. Moisture regime moist Annual p r e c i p i t a t i o n : 41.37" - 14 year average o o o o Monthly temperature F: .range - 34 to 63 average - 48 E l e v a t i o n : Sea l e v e l S i t e , s e r i e s 1100 Number of t r e e s - 16 S i m i l a r l o c a t i o n , depth o f s o i l and s o i l type to 1000 s i t e s e r i e s but c l a s s i f i e d as a wet moisture regime. S i t e s e r i e s 900 Number of t r e e s - 4 Two forest-grown t r e e s were measured i n the P r i n c e George area (open-grown 600 s e r i e s ) and two from an area approximately 100 m i l e s n o r t h o f P r i n c e George, near the P a r s n i p r i v e r . Due to the l i m i t e d sample these were not used f o r i n v e s t i g a t i o n of s i t e d i f f e r e n c e s . 18 ANALYSIS OF DATA P r e l i m i n a r y graphic i n t e r p r e t a t i o n was used f o r some analyses t o o b t a i n an understanding of b a s i c r e l a t i o n s h i p s and to a s s i s t i n determining the homogeneity of the s e l e c t e d groups of data. C a l c u l a t i o n s of m u l t i p l e r e g r e s s i o n equations and d e s c r i p t i v e s t a t i s t i c s were made u s i n g the I.B.M. 1620 of the Computing Centre at the U n i v e r s i t y of B r i t i s h Columbia. Most r e g r e s s i o n analyses were made u s i n g an a v a i l a b l e l i b r a r y programme No.603 th a t provided m u l t i p l e r e g r e s s i o n equations w i t h successive e l i m i n a t i o n s of the l e a s t important v a r i a b l e . This was defined as the f a c t o r t h a t c o n t r i b u t e d the l e a s t , a l g e b r a i c a l l y , to that p o r t i o n of v a r i a n c e c o r r e l a t e d by the r e g r e s s i o n . The r e s i d u a l v a r i a t i o n and m u l t i p l e c o r r e l a t i o n co-e f f i c i e n t squared (R ) were c a l c u l a t e d at each stage. Mean v a l u e s , standard d e v i a t i o n s , and matrices of v a r i a n c e and covariance, and simple c o r r e l a t i o n c o e f f i c i e n t s were a l s o c a l c u l a t e d by the programme. Analyses of v a r i a n c e were made to determine the s i g n i f i c a n c e of each added v a r i a b l e when used i n r e g r e s s i o n . Tables of some of the more important r e g r e s s i o n equations are presented. Although up to twenty i n -dependent v a r i a b l e s were used i n some analyses, most equations s e l e c t e d c o n t a i n two, three or f o u r v a r i a b l e s only. Most analyses were made on both open-grown and forest-grown se t s o f data. TABLE 4 AVERAGE DIAMETERj HEIGHT, AGE, SITE INDEX AND BASAL AREAS OP SITE SERIES Site No.of D.b.h. Height Age Site Basal series trees index area/ac. Units inches feet years H@100 yrs . sq.ft. Open-grown 100 33 Av. 14.52 43.18 58.45 62.12 S.D. 5.56 15.93 26.00 13.92 -Min. 5.60 20.00 18.00 35 — Max. 29.50 75.00 120 90 200 28 Av. ie.30 31.68 30.61 74.64 S.D. 4.50 10.99 9.46 12.32 -Min. 2.6 14 13 40 _ Max. 18.3 55 k5 100 -300 35 Av. 3.79 16.63 18.00 77.15 S.D. 4.42 14.72 15.70 16.25 -Min. 0.4 6 6 40 — Max. 15.5 46 51 80 -600 9 Av. 7.21 30.56 26.11 84.44 S.D. 3.83 15.56 16.95 10.14 -Min. 0.7 6 6 70 -Max. 13.6 55 63 100 -Forest-grown '800 + ) 31 Av. 6.13 5^ .1 39.55 93.87 9^ .52 [ 1200) S.D. 2.60 23.88 10.50 22.46 44.18 Min. 1.4 14 11 60 30 Max. 12.7 100 5k .150 190 1000 10 Av. 7.7^  79.50 44.40 130 142 S.D. 1.64 4.38 3.17 12.47 39.67 Min. 5.5 75 38 120 70 Max. 10.6 85 50 160 210 1100 16 Ave. 14.02 103.75 71.69 117.50 186.25 S.D. 2.60 6.71 4.81 9.31 48.29 Min. 9.6 90 61 100 110 Max. 18.6 110 77 130 240 20 RADIAL GROWTH OF INDIVIDUAL TREES OPEN-GROWN TREES For the data from 90 i n d i v i d u a l open-grown trees, r a d i a l growth over the l a s t f i v e years, was r e l a t e d to sixteen v a r i a b l e s . Some of these variables were of no d i r e c t i n t e r e s t at t h i s stage of the study, but were included to provide information of value p r i o r to more s p e c i f i c analyses. The independent v a r i a b l e s used were d.b.h. double bark thickness, height, crown width (CW), crown width/d.b.h. (CW/D), t o t a l age, r a d i a l growth s i x to ten years ago (RG^ ), height/crown width (H/CW), aver-age height to the lowest dead branch on each of four sides (HDbr), average height to the lowest l i v e branch on each of four sides (HLbr) butt diameter of the la r g e s t l i v e branch (BrBTT), percentage of l i v e crown (Lc$), crown width squared (CW 2), crown width squared times l i v e crown length (CW^.Lc), and the t o t a l height at 100 years ( s i t e index) (Table 5). . The single v a r i a b l e best correlated with r a d i a l growth over the l a s t f i v e years was the r a d i a l growth f o r the period s i x to ten years ago (r=.?79). Age was the v a r i a b l e next most c l o s e l y associated with r a d i a l growth f o r the l a s t f i v e years (r= -.576). Of the more impor-tant v a r i a b l e s , age was most c l o s e l y associated with the r a d i a l growth f o r the period s i x to ten years ago (r= -.486). P r e c i s i o n i n estimating r a d i a l growth f o r the l a s t f i v e years may be improved by the addition of height. Height and the v a r i a b l e TABLE 5 SUMMARY OF BASIC DATA FOR OPEN-GROW TREES Number of trees = 111 Number of trees = 90 Item Units Average SD Max. Min. Average SD Max. Min. Rg 1-5 inches 0.66 0.28 1.3 0.0 0.72 0.27 1.3 0.3 ^6-10 inches 0.?1 0.37 1.45 0.0 0.7^ 0.3^ 1.45 0.25 D.b.h. inches 9.17 6.46 29.5 0.0 11.17 5.60 29.5 0.9 Dbk inches 0.64 0.44 2.4 0.05 0.74 0.42 2.4 0.1 H feet 30.5 17.^ 75 <K5 35.9 15.2 75.0 9 C¥ feet 18.57 10.84 56 2.9 22 9.k 56 3.9 CW/D - 2.76 1*53 9.6 1.4 2.13 0.56 9S 1.4 Age yeaxs 35.12 24.87 120 2 41.9 23.1 120 10 H/CW - 1.72 0.43 3.0 0.9 1.67 0.37 3.0 0.9 HDbr feet 0.51 0.59 5.0 0.0 0.57 0.63 5.0 0.0 HLbr feet 2.30 1.70 7.0 0.0 2.90 1.96 7.0 0.0 LLbr feet 9.09 5.15 32.0 1.4 10.62 .^55 32.0 1.5 BrBTT inches 2.82 1.89 11.0 0.40 3.33 1.75 11.0 0.65 Lc$ - 93.6 5.0 100 82 93.6 k.7 100 82 SI ft© 72.14 15.86 100 40 68.55 15.35 100 40 100 yrs. 22 Rg^ ^ combined account f o r 66.5 percent of the t o t a l v a r i a t i o n (R= .816). The a d d i t i o n of a t h i r d v a r i a b l e , Lc$, although s i g n i f i c a n t , only i n -creased the percentage of v a r i a t i o n i n the r a d i a l growth over the l a s t f i v e years t h a t could be accounted f o r to 68.3 percent (R= .826)(Table 7). A second r e g r e s s i o n a n a l y s i s was made w i t h the v a r i a b l e , Rg£_^Q and v a r i a b l e s that were not r e q u i r e d f o r e s t i m a t i o n of r a d i a l growth e l i m -i n a t e d . The e i g h t v a r i a b l e s r e t a i n e d were diameter, CW, CW/D, H, Ldfo, age, H/CW, and s i t e index (Table 6). Data from seven of the i n d i v i d u a l t r e e s were r e j e c t e d f o r t h i s a n a l y s i s as the r a d i a l growth data had been obtained by a d i f f e r e n t method from t h a t of the remaining 83 t r e e s . E x c l u d i n g these data from the previous a n a l y s i s would not have a f f e c t e d the conclusions drawn. However, f o r the second a n a l y s i s i t was p r e f e r r e d to r e s t r i c t the r a d i a l growth data to those t r e e s t h a t were d e f i n i t e l y known to have been measured i n a c o n s i s t e n t manner. With the v a r i a b l e Rg^_]_Q e l i m i n a t e d , a l l e i g h t v a r i a b l e s used j o i n t l y accounted f o r 61.0 percent of the t o t a l v a r i a t i o n i n r a d i a l growth over the l a s t f i v e y e a r s . Next to age, the s i n g l e v a r i a b l e best c o r r e l a t e d w i t h past r a d i a l growth (Rg^ ) was height (r= -.521). The percentage o f the t o t a l v a r i a t i o n t h a t could be accounted f o r by age alone was 37.3 percent; by h e i g h t , 27.1 percent; by Lc$, 16.6 percent and by diameter, 16.0 percent. When combining s i n g l e v a r i a b l e s w i t h age, the a d d i t i o n of height was found t o have no s i g n i f i c a n t c o n t r i b u t i o n i n r e g r e s s i o n t o the per-centage of v a r i a t i o n removed. The a d d i t i o n of Lc$ was s i g n i f i c a n t , TABLE 6 SUMMARY OP DATA, AND SIMPLE CORRELATION COEFFICIENTS, FOR ANALYSES OF RADIAL AND BASAL AREA GROWTH OF 83 INDIVIDUAL OPEN-GROWN TREES Item U n i t s Average SD Simple c o r r e l a t i o n c o e f f i c i e n t w i t h B A g l _ 5 R g 1 - 5 **l-5 inches 0.?1 .27 - 1.000 D.b.h. inches 11.90 5.20 .652 -.400 H f e e t 37.77 14.21 .386 -.521 CW f e e t 23.14 8.73 .539 -.454 CW/D - 2.02 0.37 -.5^0 Age years 44.24 22.52 .313 -.610 H/CW - 1.67 .38 -.265 -.068 Ldfo * 92.12 4.48 .044 .408 SI H @ 100 68.43 15.28 -.042 .296 B A%- 5 s q . i n s . 21.5 10.3 1.000 -r nc.= 0.213 ; Not s i g n i f i c a n t values u n d e r l i n e d TABLE 7 LINEAR REGRESSION EQUATIONS FOR THE ESTIMATION OF RADIAL GROWTH FOR THE LAST FIVE YEARS FOR INDIVIDUAL OPEN-GROWN TREES Number of trees Age Independent variables H hdfo SI D.b.h. R 3V° 90 .2580 .6274 .4704 .5634 -.2866 .5360 Regression coefficients -.00460 -.00427 .00826 .606 .665 .683 24.3 22.6 22.1 83 1.0369 1.061 -.5406 -.275 .956 -.4496 .658 -.00733 -.00654 -.00370 -.00640 -.00768 -.00174 -.00156 -.00484 -.00777 .0174 .0137 .0147 .00141 .00259 .00407 -.0186 .373 .375 .438 .418 .415 .444 .212 30.2 30.4 28.9 29.4 29.4 29.0 34.1 25 i n c r e a s i n g the percentage of v a r i a t i o n accounted f o r to 41.8 percent, while the combination of age and s i t e index, also s i g n i f i c a n t , increased . 2 N the percentage of v a r i a t i o n accounted f o r a s i m i l a r amount (R = .415). I f the variables age, height and Lcfo are combined t h e i r j o i n t i nfluence accounts f o r 43.8 percent of the t o t a l v a r i a t i o n i n r a d i a l growth over the l a s t f i v e years. Using t h i s combination, an estimate of past r a d i a l growth would have a standard error of estimate of 29.0 percent. With age excluded from a combination, the p r e c i s i o n of e s t i -mation decreases appreciably. For example, diameter and s i t e index together account f o r only 21.2 percent of the t o t a l v a r i a t i o n i n r a d i a l growth (R= .460, SEg = 34.2#) (Table ? ) . I t i s of i n t e r e s t to note that i f s i t e index i s added to the com-b i n a t i o n of age, height and Lc$ the added contribution i s not s i g n i f -i c a n t , although when added to age alone a s i g n i f i c a n t increase i n p r e c i s i o n of estimation i s obtained. (This i s due to s i t e index being defined as a fun c t i o n of height and age). When both height and age are used i n combination the ad d i t i o n of s i t e index i s of l i t t l e value. In t h i s analysis r a d i a l growth over the past f i v e years has been r e l a t e d to current values of stem and crown measurements. Radial growth over the l a s t f i v e years, Rg 1_^, i s highly s i g n i f i c a n t l y correlated with r a d i a l growth over the previous f i v e year period (r= .779). I t may be i n f e r r e d that the r a d i a l growth over the next f i v e year period w i l l s i m i l a r l y be correlated with that of the l a s t f i v e years. This i n f e r -ence i s supported by a consideration of the asso c i a t i o n between i n d i -v i d u a l tree parameters and r a d i a l growth. Inspection of the appropri-ate c o r r e l a t i o n c o e f f i c i e n t s indicates that there i s a comparable a s s o c i a t i o n between fa c t o r s i n f l u e n c i n g r a d i a l growth i n the two growth p e r i o d s (Table 8). TABLE 8 ASSOCIATION BETWEEN RADIAL GROWTH AND 10 VARIABLES FOR 90 OPEN-GROWN TREES 6-10 Dbh H CW CW/D Age H/CW Lc$ SI cw2 2 CW. Lc Simple c o r r e l a t i o n c o e f f i c i e n t s R g 1 .5 -779 -.368 -.473 -.415 -.055 -.576 -.055 .377 .298 -.403 -.395 -10 ^ -.218 -.311 -.244 -.224 -.486 -.087 .282 .294 -.302 -.343 r.05 " • 2 0 5 ; r.01 = * 2 6 7 Not s i g n i f i c a n t values u n d e r l i n e d I f age determination could be made q u i c k l y and conveniently then the reduced p r e c i s i o n i n e s t i m a t i o n o f r a d i a l growth may be acceptable. As age i s g e n e r a l l y found by d r i l l i n g i n t o the t r e e , i t would be p r e f e r -able to use r a d i a l growth over the l a s t f i v e years t o provide a more r e l i a b l e estimate o f r a d i a l growth f o r the next f i v e year p e r i o d . FOREST-GROWN TREES The r a d i a l growth f o r the past f i v e years of 63 forest-grown t r e e s was r e l a t e d to seventeen independent v a r i a b l e s (Table 9), b a s a l area per acre being i n c l u d e d w i t h the v a r i a b l e s used i n the a n a l y s i s o f the data on open-grown t r e e s . One s u b s t i t u t i o n was made, the v a r i a b l e , average l e n g t h of dead branches r e p l a c e d the v a r i a b l e , b u t t diameter o f the l a r -gest branch. The s u b s t i t u t i o n was made merely f o r convenience, the v a r i a b l e s themselves being o f no i n t e r e s t i n t h i s p a r t i c u l a r a n a l y s i s . The s i n g l e v a r i a b l e best a s s o c i a t e d w i t h r a d i a l growth f o r the l a s t f i v e years ( B g ; ^ ) was the v a r i a b l e Rg£_1Q, accounting f o r 55.6 per cent o f the t o t a l v a r i a t i o n i n Rg-[_5 (r= .746). A d d i t i o n o f Ldfo f o l -lowed by s i t e index increased t h i s percentage t o 61.8 percent and 64.4 percent r e s p e c t i v e l y (Table 10). Improvement i n the p r e c i s i o n of e s t i -mation i s s m a l l . Using the two a d d i t i o n a l v a r i a b l e s r e s u l t s i n a r e d u c t i o n i n the standard e r r o r o f estimate from approximately 32 per-cent to 29 percent. I t i s evident that combining Rg^ w i t h a d d i t i o n a l v a r i a b l e s does not m a t e r i a l l y i n c r e a s e the p r e c i s i o n of e s t i m a t i o n . A g a i n of s i x percent i n the percentage o f the v a r i a t i o n i n past r a d i a l growth that can be accounted f o r might w e l l warrant the use of one ad-d i t i o n a l v a r i a b l e . Since Lc$ i s not p a r t i c u l a r l y convenient t o use, the disadvantages outweigh the advantages. A second a n a l y s i s was made r e l a t i n g Eg^_^ to ten v a r i a b l e s , d.b.h. h e i g h t , CW, CW/D, age, H/CW, LC$, s i t e index, b a s a l area per acre and crown c l a s s . With the v a r i a b l e e l i m i n a t e d , the percentage of v a r i a t i o n t h a t could be accounted f o r was g r e a t l y reduced. A l l ten v a r i a b l e s TABLE 9 SUMMARY OF DATA , AND SIMPLE CORRELATION COEFFICIENTS, FOR THE ANALYSES OF RADIAL AND BASAL AREA GROWTH OF 63 INDIVIDUAL FOREST-GROWN TREES Simple correlation coefficient with Item Units Average SD Min. Max. B A g l - 5 R *l-5 inches 0.27 0.13 0.05 0.45 .114 1.000 V l O inches 0.28 0.13 0.05 0.70 .746 B A e l - 5 sq.ins. 5.99 5.18 1.5 23.4 1.000 -B A e6 - 1 0 sq.ins. 6.14 5.70 0.71 32.8 .857 -.001 D.b.h. inches 8.23 4.25 0.8 18.6 • 533 .048 Dbk inches 0.85 0.68 0.05 2.80 .439 -.piz H feet 69.03 29.50 8.0 110 .520 - .02Z CW feet 6.9 2.64 1.8 15.0 .429 .262 CW/D - 0.99 0.47 0.41 3.21 .377 •222 Age years 48.84 16.10 11 77 .474 -.216 H/CW - 10.38 4.43 3.1 22.3 .279 -.362 HDbr feet 3.9 5.3 0.0 50.0 .278 -.001 HLbr feet 39.9 20.8 2.5 95.0 - -.222 LLbr feet 3.47 1.32 0.9 12.0 .424 .250 LDbr feet 2.72 1.32 0.25 12.7 .128 .220 Lofo - 45.37 13.92 19 86 -.217_ .386 2 CW sq.ft. 54.54 42.63 - .461 .281 2 CW.Lc cu.ft. 1989 2352 - - .471 .3H SI H@iee f t . 102.1 27.8 15 160 .416 .049 BA/ac. sq.ft. 123.2 59.6 20 240 .477 -.144 Cr.Cl. — 1.35 0.48 1 2 .029 -.244 r . 0 5 = 0.245 5 Not significant values underlined TABLE 10 LINEAR REGRESSION EQUATIONS FOR THE ESTIMATION OF RADIAL GROWTH FOR THE LAST FIVE YEARS FOR 63 INDIVIDUAL FOREST-GROWN TREES Inter-cept ^ 6 - 1 0 Ldfo Independent variables CW/D SI Cr.Cl. H/CW CW H 2 R SE^S Regression coefficients .06373 .7264 - - - - - - .556 31 .7 - . 0 2 7 3 0 .6796 .00230 - - - . 6 1 8 29.6 -.0311 .7035 .00134 .0409 - - - - - . 6 3 0 29.4 - . 1 6 3 7 .6736 .00177 .0657 .00095 - - . 6 5 7 28 .6 .1082 - .00349 - - - - - .149 4 3 . 8 .1889 - .00327 -.0522 - - . 188 43.1 .2527 • - .00250 - . 0 4 7 4 -.00344 - - . 194 4 3 . 4 .0847 - .00277 .00205 - . 0 2 4 7 -.0115 - - .310 4 0 . 5 .3091 - - -.00910 .00769 - . 095 4 5 . 7 .3252 - - - . 0 1 3 2 .00329 .000676 .171 4 3 . 8 ro combined accounted f o r only 34.1 percent. Only those v a r i a b l e s t h a t i n c o r p o r a t e d a crown measurement were s i g n i f i c a n t l y c o r r e l a t e d w i t h the r a d i a l growth over the l a s t f i v e y e a r s . The most c l o s e l y a s s o c i a t e d s i n g l e v a r i a b l e was Lcfo (r= .386), followed by H/CW (r= .262) and CW . (r= .262). Crown c l a s s and CW/D were other v a r i a b l e s r e l a t e d to the crown t h a t approached s i g n i f i c a n c e at the 95 percent confidence l e v e l . Age, which next to the v a r i a b l e Bg^_1G was the s i n g l e v a r i a b l e most c l o s e l y a s s o c i a t e d w i t h r a d i a l growth f o r the l a s t f i v e years f o r the open-grown t r e e s , approaches s i g n i f i c a n c e but i s subordinate to the crown v a r i a b l e s . o I n s p e c t i o n of the values f o r R , the percentage o f the t o t a l v a r i a t i o n that i s accounted f o r by the v a r i a b l e s concerned, i n d i c a t e s the e f f e c t of combining v a r i a b l e s s u c c e s s i v e l y w i t h Lc$. The fou r v a r i a b l e s that j o i n t l y account f o r 31 percent o f the t o t a l v a r i a t i o n i n %2-5 a 2 c e n o * convenient to use. Apart from crown c l a s s , the d e t e r -m i n a t i o n o f which i s not completely o b j e c t i v e , each v a r i a b l e r e q u i r e s two measurements. Of the remaining v a r i a b l e s crown width alone i s s i g n i f i c a n t l y c o r r e l a t e d w i t h past r a d i a l growth, accounting f o r 6.7 percent of the t o t a l v a r i a t i o n i n Rg]__5 When combined w i t h H/CW a 2 s m a l l but s i g n i f i c a n t i n c r e a s e i n p r e c i s i o n i s obtained (E = .095). Combining height w i t h crown width and H/CW r e s u l t s i n 17.1 percent of the t o t a l v a r i a t i o n being accounted f o r . I f the h i g h standard e r r o r of estimate ( S E ^ = 43.8) were acceptable, t h i s combination may be of va l u e f o r photogrammetric a p p l i c a t i o n . Prom the analyses made u s i n g the data from forest-grown t r e e s i t i s evident that only when one f i v e year growth p e r i o d can be used to estimate the growth i n the succeeding f i v e years can r a d i a l growth be adequately estimated f o r i n d i v i d u a l t r e e s . CONCLUSIONS FROM. RADIAL GROWTH ANALYSES Simple c o r r e l a t i o n c o e f f i c i e n t s between past r a d i a l growth and the independent v a r i a b l e s used are given i n Table 6 f o r the data from 83 open-grown t r e e s . Simple 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 a l l v a r i -a b les used i n the analyses are g i v e n i n Appendix l c . Comparison of the degree of a s s o c i a t i o n between important v a r i a b l e s w i l l a s s i s t i n e v a l u a t i n g the r e l a t i v e importance of each v a r i a b l e . Comparison of methods of d e s c r i b i n g crown development f o r r a d i a l  growth e s t i m a t i o n . Indices used i n the a n a l y s i s f o r d e s c r i b i n g crown s i z e were 2 ' average crown w i d t h , (average crown width) and (average crown width)' times l i v e - c r o w n l e n g t h . The p r o p o r t i o n o f crown to stem was expres-sed as crown width/diameter CW/D, height/crown width H/CW, and per-centage of l i v e crown Lcfo. Two measures of r a d i a l growth were a v a i l a b l e , r a d i a l growth f o r the past f i v e y e a r s , and r a d i a l growth f o r the p e r i o d s i x to ten years ago. C o r r e l a t i o n s between each of these s i x crown f a c t o r s and each of the two r a d i a l growth periods may be compared i n Table 11. 32 TABLE 11 CORRELATIONS BETWEEN PAST RADIAL GROWTH AND CROW INDICES Number o f trees Growth period CW 2 CW 2 CW.Lc CW/D H/CW Lc$ Simple c o r r e l a t i o n c o e f f i c i e n t s 90 open- E g l - 5 -.42 -.40 -.40 -.06 .06 .38 (1) grown trees ^6-10 -.24 -.30 -.34 -.22 -.02. .28 63 f o r e s t - .26 .28 .31 .23 -.36 .38 (2) grown trees 1-5 6-10 .38 .40 .40 -.02 -.29 •12 ( l ) r = .205 ; (2) r = .25 Not s i g n i f i c a n t values underlined Radial growth f o r the past f i v e years increases with crown width, 2 2 (crown width) , and (crown width) times crown length f o r forest-grown trees, but has a negative c o r r e l a t i o n with these crown indices f o r open-grown trees. This apparent decrease may be accounted f o r by con-s i d e r i n g the e f f e c t s of age and diameter on r a d i a l growth and crown growth. A l l three crown indices increase with age and diameter f o r both forest-grown and open-grown trees. For the data from forest-grown trees neither age nor diameter i s s i g n i f i c a n t l y associated with r a d i a l growth f o r the past f i v e years, but f o r open-grown trees inspection of the simple c o r r e l a t i o n c o e f f i c i e n t s (Appendix I a) shows that increase i n e i t h e r age or diameter i s associated with a decrease i n r a d i a l growth over the past f i v e years. From the data f o r open-grown trees i t has been shown that, with the exception of r a d i a l growth f o r the period s i x to ten years ago, age i s the most important s i n g l e v a r i a b l e i n accounting f o r r a d i a l growth over the past f i v e y e a r s . This i n f l u e n c e o f age masks that of any of the crown i n d i c e s f o r open-grown t r e e s . There appears t o be l i t t l e advantage i n u s i n g C¥^ or C\/f *Lc i n -stead of CW i n r e l a t i o n t o r a d i a l growth f o r e i t h e r open-grown or f o r e s t -grown t r e e s . Crown width i s the simplest of the crown i n d i c e s t o de-termine and i s e i t h e r s i g n i f i c a n t l y , or h i g h l y s i g n i f i c a n t l y , r e l a t e d t o r a d i a l growth i n a l l cases t e s t e d . Percentage of l i v e crown would appear to be c o r r e l a t e d s i m i l a r -l y w i t h r a d i a l growth over the past f i v e years f o r both open-grown and forest-grown t r e e s . I t w i l l be r e c a l l e d that t h i s v a r i a b l e was found to be s i g n i f i c a n t when in c l u d e d i n the r e g r e s s i o n equations developed (Tables 7 and 1 0 ) . The two crown r a t i o s , (CW/D) and (H/CW), appear to be p o o r l y c o r -r e l a t e d w i t h open-grown r a d i a l growth. This i s not s u r p r i s i n g as i n the absence of competitive t r e e s these r a t i o s represent the n a t u r a l development of the crown i n r e l a t i o n to stem c h a r a c t e r i s t i c s . With the forest-grown data, both r a t i o s appear t o be of p o t e n t i a l importance w i t h regard t o r a d i a l growth over the past f i v e y e a r s , H/CW having a h i g h l y s i g n i f i c a n t c o r r e l a t i o n and CW/D having a c o r r e l a t i o n coef-f i c i e n t t hat i s j u s t short of being s i g n i f i c a n t at the 95$ confidence l e v e l . N e i t h e r r a t i o i s apparently c o r r e l a t e d w i t h r a d i a l growth f i v e t o ten years ago. The reason f o r t h i s i s obscure. I t may be t h a t a p e r i o d of f i v e years i s s u f f i c i e n t time t o permit enough expansion of crowns and increase o f diameter growth t o mask any previous c o r r e l a t i o n w i t h f i v e - y e a r r a d i a l growth. This would imply that the changes i n the environment are such that i n c r e a s e s i n crown width are accompanied con-c u r r e n t l y or w i t h i n a very short p e r i o d of time by s m a l l e r r e l a t i v e i n -crease i n diameter growth. Furt h e r , t h i s increase i n crown width i s accompanied by e i t h e r no height increase or a p r o p o r t i o n a t e l y smaller h e i g h t increment. C o r r e l a t i o n s between D.B.H. and Height and 8 v a r i a b l e s . E s t i m a t i o n of volume may be made adequately u s i n g d.b.h. and height alone (Smith and Ker, 1957). I t i s of i n t e r e s t t o determine how these volume parameters are a f f e c t e d by c e r t a i n v a r i a b l e s . Prom the c o r r e l a -t i o n s given (Table 12) the r e l a t i v e usefulness of each o f the e i g h t v a r i a b l e s f o r the p r e d i c t i o n of d.b.h. and height may be considered. Of the two crown i n d i c e s CW/D appears to be more s t r o n g l y c o r -r e l a t e d w i t h d.b.h. than i s H/CW. This i m p l i e s that of the crown r a t i o s H/CW and CW/D, H/CW would be p r e f e r a b l e f o r combination w i t h TABLE 12 COMPARISONS OP THE CORRELATION BETWEEN D.B.H. AND HEIGHT AND EACH OP EIGHT VARIABLES Dbh H Age SI CW BA CW/D H/CW Simple c o r r e l a t i o n c o e f f i c i e n t s 90 open- Dbh 1.00 .87 .88 - .11 .95 _ -.61 -.18 (1) grown t r e e s H .87 1.00 .83 .11 .85 — -.52 .21 63 f o r e s t - Dbh 1.00 .90 .84 .63 .75 .65 -.64 .32 (2) grown t r e e s -.76 .64 H .90 1.00 .83 .82 .57 .75 ( l ) r 0c-= .205 ; r = .250 Not s i g n i f i c a n t values u n d e r l i n e d diameter f o r e s t i m a t i o n purposes. However, t h i s c o n c l u s i o n would not n e c e s s a r i l y be v a l i d . For open-grown t r e e s , age i s w e l l c o r r e l a t e d w i t h most of the important v a r i a b l e s used i n t h i s study (Appendixes l a , b and c ) , i n c l u d i n g CV//D (r= .473), but i s not c o r r e l a t e d w i t h H/CW (r= -.070)-. I f the dependent v a r i a b l e being estimated i s i t s e l f c o r r e l a t e d w i t h age, and i f age i s not used as one of the independent v a r i a b l e s , then the as-s o c i a t i o n between CW/D and age w i l l probably r e s u l t i n CW/D being o f more importance than H/CV i n combination w i t h d.b.h. A l t e r n a t i v e l y , i f age i s not c o r r e l a t e d w i t h the dependent v a r i a b l e , or i f age i s in c l u d e d i n an estimate, then the g r e a t e r independence of H/CV on diameter w i l l r e s u l t i n i t s i n f l u e n c e b e i n g g r e a t e r than the more c l o s e l y a s s o c i a t e d crown CW/D when used w i t h d.b.h. For forest-grown t r e e s , both crown r a t i o s are c o r r e l a t e d w i t h age and d.b.h. (Appendixes I d and e ) . T h e i r added i n f l u e n c e i n account-i n g f o r v a r i a t i o n i n a dependent v a r i a b l e w i l l depend on r e l a t i v e cor-r e l a t i o n s between d.b.h. and/or age and the dependent v a r i a b l e . BASAL AREA GROWTH OP INDIVIDUAL TREES OPEN-GROWN TREES Regression and c o r r e l a t i o n analyses were made u s i n g data from 83 open-grown t r e e s . Basal area growth f o r the l a s t f i v e years was r e l a t e d to nine v a r i a b l e s : d.b.h., h e i g h t , crown width (CW), crown width/diameter CW/D, age, height/crown width (H/CW), percentage l i v e crown ( L c $ ) , s i t e index, and b a s a l area growth over the p e r i o d s i x to t e n years ago ( B A g ^ _ 1 0 ) . Next to b a s a l area growth f o r the p e r i o d s i x to ten years ago, (r= .896), d.b.h. was the s i n g l e v a r i a b l e most c l o s e l y a s s o c i a t e d w i t h b a s a l area growth f o r t h e ' l a s t f i v e years (r= .652). Except f o r s i t e index and percentage l i v e crown a l l other v a r i a b l e s used were cor-r e l a t e d e i t h e r s i g n i f i c a n t l y or h i g h l y s i g n i f i c a n t l y w i t h BAg^ (Table 6). A l l nine v a r i a b l e s used together i n r e g r e s s i o n accounted f o r 84.5 percent of the t o t a l v a r i a t i o n i n b a s a l area growth f o r the l a s t f i v e y e a r s . The v a r i a b l e BAg alone accounts f o r most of t h i s v a r i a t i o n 6-10 2 (R = .802). Combining BAg, ,,. w i t h a d d i t i o n a l v a r i a b l e s i s o f minor 6-10 value f o r the improvement of the p r e c i s i o n o f estimate (Table 13). An a n a l y s i s made with the v a r i a b l e BAg, ,„ e l i m i n a t e d showed 6-10 t h a t s i g n i f i c a n t improvements i n the p r e c i s i o n of estimate could be ob-t a i n e d by combining a d d i t i o n a l v a r i a b l e s w i t h d.b.h. Of combinations i n v o l v i n g two v a r i a b l e s , the j o i n t e f f e c t of d.b.h. and age was found to provide the best estimate of BAg^ (R = .694, SEg = 36.4$). With a t h i r d v a r i a b l e , s i t e index, i n c l u d e d 72.0 percent of the t o t a l v a r i a t i o n i n b a s a l area growth f o r the l a s t f i v e years could be accounted f o r w i t h a standard e r r o r o f estimate of 25.8 percent. Regression equations u s i n g crown width, height/crown width and height were developed f o r p o s s i b l e use f o r e s t i m a t i o n from a e r i a l photo-graphs. The best two-variable combination was found to be CW and H/CW, (R = .300, SEg = 40.5$). No advantage i s gained by i n c l u d i n g height w i t h these two v a r i a b l e s , i n f a c t the standard e r r o r of estimate increases s l i g h t l y t o 40.7 percent. Of the two crown r a t i o s , CW/D was more e f f e c t i v e than H/CW i n combination w i t h d.b.h. (Table 13). This may be accounted f o r by c o n s i d e r -i n g the i n f l u e n c e of age. The a d d i t i o n o f age t o d.b.h. has been shown to be h i g h l y s i g n i f i c a n t i n estimates of b a s a l area growth f o r the l a s t f i v e y e a r s . Age i s h i g h l y c o r r e l a t e d w i t h CW/D f o r the data (r= .473 but i s not c o r r e l a t e d w i t h the r a t i o H/CW (r= -.070). With age e l i m i n a t e d , the i n -f l u e n c e o f CW/D w i l l be g r e a t e r than that of H/CW when combined with d.b.h. f o r the e s t i m a t i o n of b a s a l area growth f o r the l a s t f i v e y e a r s . TABLE 13 LINEAR REGRESSION EQUATIONS FOR THE ESTIMATION OF BASAL AREA GROWTH FOR THE LAST FIVE YEARS FOR 83 INDIVIDUAL OPEN-GROWN TREES Independent v a r i a b l e s H/CW Lcfo Age SI CW H R 2 SEj£ E. Regression c o e f f i c i e n t s 5.5859 .8581 - - - - - - .802 21.4 14.679 .7931 - -3.8977 - - - - .817 20.6 12.018 .7500 0.1750 -3.2159 - - - .821 20.5 -4.6299 - 0.8714 -10.503 -9.259 .5698 - - .593 31.3 45.664 - 0.7942 -10.604 -7.272 _ - - .539 34.4 24.856 - 1.0063 7.5643 - - - - .479 34.9 13.628 - 1.2336 '- -4.063 - - - .446 35.9 6.1888 - 1.2890 - - . - - - .425 36.4 2.155 - 1.3178 - - - .05393 - .431 36.5 5.850 - 3.1098 - - -.4823 - - .694 26.8 15.080 - 3.3198 - - -.5556 -.1240 - .720 25.8 12.538 - - - -2.8592 - - .5948 .05266 .300 40.7 14.389 - - - -3.9834 - - .5100 .300 40.5 I n t e r - BAg. Dbh CW/D cept 6-!° FOREST-GROWN TREES Analyses were made u s i n g the data from forest-grown t r e e s i n a s i m i l a r manner to t h a t from open-grown t r e e s . A d d i t i o n a l independent v a r i a b l e s were b a s a l area per acre and crown c l a s s . As i n the previous a n a l y s i s the v a r i a b l e f o r the growth i n the previous p e r i o d , BAg^ was the s i n g l e v a r i a b l e most c l o s e l y a s s o c i -ated w i t h b a s a l area growth f o r the l a s t f i v e years (r= .857), f o l -lowed by d.b.h. (r= .533), height (r= ,520)and b a s a l area per acre (r= .477) (Table 9). With the v a r i a b l e BAg, , r t e l i m i n a t e d , a l l remaining t e n v a r i -6-10 ables accounted f o r 41.3 percent of the t o t a l v a r i a t i o n i n b a s a l area growth w i t h a standard e r r o r o f estimate o f 72.5 percent. V a r i a b l e s were used w i t h e i t h e r d.b.h. or b a s a l area per acre i n a s e r i e s o f combinations (Table 14). Of combinations that i n c l u d e d d.b.h. the best equation developed w i t h two v a r i a b l e s used d.b.h. and H/GW to account f o r 29.7 percent of the t o t a l v a r i a t i o n i n b a s a l area growth. Almost as good and more convenient t o use was the combination d.b.h. and height accounting f o r 29.3 percent o f the t o t a l v a r i a t i o n . With three v a r i a b l e s the best equation of those t r i e d combined age and s i t e index w i t h d.b.h. (R = .302, SE^= 74.2$). The most e f f e c t i v e v a r i a b l e to combine w i t h b a s a l area per acre was crown width (R =.313, s E g = 73.0$). The subsequent a d d i t i o n o f the v a r i a b l e H/CV increased the percentage o f v a r i a t i o n accounted f o r t o 34.5 percent. The best estimate obtained from the r e g r e s s i o n equations developed u s i n g any two v a r i a b l e s , except f o r BA , was given by S 6-10 TABLE 14 LINEAR REGRESSION EQUATIONS FOR THE ESTIMATION OF BASAL AREA GROWTH FOR THE LAST FIVE YEARS FOR 63 INDIV-IDUAL FOREST-GROWN TREES Independent v a r i a b l e s 2 I n t e r - BAg, D.b.h. BA/ac. Age SI CW H/CW H R SRjfo cept ^ 0 ; _ f 1.2078 .7784 . - -Regression c o e f f i c i e n t s - - .733 43.5 -.1399 .7032 .2200 - - - - - .758 41.4 .6385 - .6500 - - - - - .284 73.8 -.009840 - .4196 - - - - .03686 .293 74.0 -.4060 - .6033 - - - .1377 - .297 73.8 -1.0728 - .2070 - - .2678 - .05080 .300 74.3 -9.8373 - .6916 - - 1.6709 1.1596 -.1948 .368 71.2 -1.6260 - - - - .3866 - .07160 .297 73.8 -5.7756 - - - - 1.0121 .4596 - .331 71.9 -8.9269 - - - - I.6O69 .8416 -.07132 .341 71.9 .8842 - - .04144 - .6066 - - .227 76.7 -2.2614 - - .03295 - .8443 - - .313 73.0 -5.0105 - - .01578 - - • .3103 - .345 71.9 -.03940 - .5649 - .02661 - - - .286 74.4 -1.0643 - .5474 - - .02494 - - .295 73.8 -2.6867 _ .2529 - .05194 .0315? - - .302 74.2 the combination of crown width and H"/CW (R = .331, SE = 71.9$). This E was developed p r i m a r i l y f o r i t s p o t e n t i a l u sefulness f o r photo-gram-m e t r i c a p p l i c a t i o n . The a d d i t i o n o f height t o t h i s combination d i d 2 not increase the p r e c i s i o n o f estimate s i g n i f i c a n t l y (R = .3^1, SEg = 71.9$. I t i s evident from the a n a l y s i s , as from the analyses of r a d i a l growth, that growth f o r the p e r i o d s i x to t e n years ago provides the best estimate o f growth f o r the l a s t f i v e years when used e i t h e r alone or i n combination. Estimates f o r the b a s a l area growth over the l a s t f i v e years f o r i n d i v i d u a l t r e e s that do not i n v o l v e the v a r i a b l e BAg^ ^ ( are u n r e l i a b l e . Even the combination o f b a s a l area per acre and R/C¥, both measures of stand d e n s i t y , does not provide an estimate of com-parable p r e c i s i o n t o the use of b a s a l area growth f o r the p e r i o d s i x t o t e n years ago. CONCLUSIONS FROM BASAL AREA ANALYSIS In the a n a l y s i s made on the data from the open-grown and f o r e s t -grown trees r e l a t i n g b a s a l area growth to c e r t a i n v a r i a b l e s , simple c o r r e l a t i o n c o e f f i c i e n t s were c a l c u l a t e d f o r the v a r i a b l e s used. These are presented f o r comparative purposes i n Table 15. 42 TABLE 15 ASSOCIATION BETWEEN BASAL AEEA GROWTH AND TEN VARIABLES BAg Dbh H CW CW/D Age H/CW LC$ SI Rg Rg 6 - l 0 1-5 6-10 Simple c o r r e l a t i o n c o e f f i c i e n t s 83 open-grown t r e e s B A«i_5 '90 .65 .39 .54 -.54 .31 -.27 .04 .04 - - ( l ) BAg 6 1 Q 1.00 .64 .40 .55 -.48 .28 .29 -.02 -.02 - -63 open-grown t r e e s B A g 1 - 5 .86 .53 .52 ,.43 -.38 .47 .28 -.22 .42 .11 .12 (2) B A g6-10 •'*8 ' 3 1 " * 3 8 * 3 7 , 3 ^ ^ * — ( l ) r = .213 ; (2) r = .25 Not s i g n i f i c a n t values u n d e r l i n e d .05 .05 When e v a l u a t i n g the importance o f each v a r i a b l e by comparing r e l -a t i v e c o r r e l a t i o n s w i t h b a s a l area growth, the c o r r e l a t i o n s between the v a r i a b l e s themselves should be considered. For example, height has a simple c o r r e l a t i o n w i t h BAg^ of 0.520 f o r the forest-grown data, hence height alone would account f o r 27 percent o f the v a r i a t i o n i n b a s a l area growth. However most of the i n f l u e n c e of height i n e s t i m a t i o n i s due to i t s h i g h l y s i g n i f i c a n t c o r r e l a t i o n w i t h diameter ( r = .900) (Appendix I d ) . A p o s s i b l e c o r r e l a t i o n between past r a d i a l and b a s a l area growth was not t e s t e d f o r the data from open-grown t r e e s owing t o the e x c l u s i o n o f the v a r i a b l e s , Rg^ and Rg^ from the independent v a r i a b l e s used i n these analyses. The analyses were concerned w i t h the i n f l u e n c e o f environmental f a c t o r s on b a s a l area growth. I t had been intended to exclude these v a r i a b l e s from the analyses made u s i n g the data from the forest-grown t r e e s . T h e i r inadvertent i n c l u s i o n complicated the r e -g r e s s i o n a n a l y s i s , but d i d provide a t e s t of the a s s o c i a t i o n between r a d i a l and b a s a l area growth f o r forest-grown t r e e s (Table 15). The simple c o r r e l a t i o n c o e f f i c i e n t s between e i t h e r Rg or Rg, and each 1-5 6-10 of the two b a s a l area growth periods were not s i g n i f i c a n t . A s i g n i f -i c a n t c o r r e l a t i o n between the corresponding v a r i a b l e s f o r data on the open-grown t r e e s would be u n l i k e l y both on the b a s i s of t h i s r e s u l t and on t h e o r e t i c a l grounds. With regard t o the negative c o r r e l a t i o n w i t h the crown r a t i o , CW/D, i n c r e a s e i n b a s a l area growth i s a s s o c i a t e d w i t h decrease i n the CW/D r a t i o . As the CW/D r a t i o i s a f u n c t i o n of the space a v a i l a b l e f o r crown spread i n terms of d.b.h., an increase i n d.b.h. i s u s u a l l y as-s o c i a t e d w i t h a decrease i n CW/D (r= .643) (Appendix I d ) . However, t o conclude that i t i s t h e r e f o r e necessary t o grow t r e e s i n such a way as to minimize the numerical value of the r a t i o CW/D would be i n -c o r r e c t . Obviously g r e a t e r diameter growth i s d e s i r a b l e , and as one would expect, increase i n crown width i s a s s o c i a t e d w i t h increase i n diameter (r= .753). Reference t o the r e g r e s s i o n equations and the e f f e c t o f added v a r i a b l e s on the percentage of v a r i a t i o n removed w i l l a i d i n i n t e r -p r e t a t i o n o f the v a r i a b l e s i n v o l v e d . The preceding analyses i l l u s t r a t e the d i f f i c u l t y o f o b t a i n i n g an adequate estimate f o r r a d i a l o r b a s a l area growth of i n d i v i d u a l lodgepole pine t r e e s u s i n g only environmental f a c t o r s . Best estimates are made when the growth r a t e immediately preceding the growth p e r i o d b e i n g determined i s known. Even then e s t i m a t i o n i s imprecise. D i f f e r e n c e s i n age, stem and crown parameters, and s i t e s , as measured by s i t e index, were taken i n t o account i n a l l analyses. For the forest-grown t r e e s , changes i n stand d e n s i t y , assessed by such i n d i c e s as b a s a l area per acre, height/crown width, crown width/diam-e t e r and t o a l i m i t e d extent by crown width i t s e l f and percentage o f l i v e crown, were a l s o u t i l i z e d i n a r r i v i n g at estimates of t r e e growth. More s e n s i t i v e parameters perhaps i n c l u d i n g s u b j e c t i v e estimates of t r e e v i g o u r might have been used to describe the i n d i v i d u a l t r e e , s i t e and stand d e n s i t y d i f f e r e n c e s . These might have improved the estimates obtained. E r r o r s i n measurement, whether systematic, o r random, would a l s o increase the percentage o f growth v a r i a t i o n that could not be accounted f o r . Probably most of the unaccountable v a r i a -t i o n i s normal t r e e - t o - t r e e v a r i a t i o n t h a t i s at a maximum i n a study based on i n d i v i d u a l t r e e s . 4 5 ANALYSES OP C R O W N WIDTH, CROWN WIDTH/DIAMETER AND HEIGHT/CROWN W I D T H INTRODUCTION Reference has p r e v i o u s l y been made to the usefulness o f a know-ledge o f crown and stem c h a r a c t e r i s t i c s of open-grown t r e e s f o r pre-d i c t i n g the r e s u l t of stand manipulation (Smith, Ker and Csizmazia, 1961; Smith, I963). R e l a t i o n s h i p s between crown width and d.b.h., h e i g h t , H/CW and CW/D f o r open-grown and forest-grown lodgepole pine are presented i n Table 16. Regression equations are given f o r two s e t s of data on open-grown t r e e s , the f i r s t f o r a l l open-grown t r e e s sampled, the second w i t h those t r e e s l e s s than ten years o f age at breast height e l i m i n a t e d (Table 19)• The r e g r e s s i o n o f crown width to d.b.h. i s pre-sented g r a p h i c a l l y t o emphasize the d i s t i n c t d i f f e r e n c e that e x i s t s be-tween open-grown and forest-grown trees ( P i g . 2). D.b.h., h e i g h t , CW/D, age and H/CW have s i m i l a r simple c o r r e l -a t i o n c o e f f i c i e n t s w i t h crown width f o r both groups of data on open-grown t r e e s (Table 16). However, the a s s o c i a t i o n between s i t e index and crown width, not s i g n i f i c a n t f o r the data on 90 open-grown t r e e s , i s h i g h l y s i g n i f i c a n t f o r the l a r g e r group. The a d d i t i o n a l t r e e s were a l l l e s s than t e n years o f age at breast height w i t h correspondingly small crowns. They were on s i t e s having an average value f o r s i t e index g r e a t e r than those o f the remaining 90 tre e s (Table 5). This combination of r e d u c t i o n i n average crown s i z e and increase i n average s i t e index r e -s u l t e d i n the l a r g e r group having the s i g n i f i c a n t negative c o r r e l a t i o n found between s i t e index and crown width f o r the data. k6 Both CW/D and H/CW have simple c o r r e l a t i o n c o e f f i c i e n t s w i t h CW t h a t are not q u i t e s i g n i f i c a n t at the 95 percent confidence l e v e l f o r the group o f 63 forest-grown t r e e s . The apparent p o s i t i v e s i g n i f i c a n t c o r r e l a t i o n between crown width and s i t e index f o r the data from forest-grown t r e e s i s due to the i n f l u e n c e o f age. The c o r r e l a t i o n of age wi t h s i t e index i s h i g h l y s i g -n i f i c a n t f o r the data c o l l e c t e d (r= .397)» the o l d e r t r e e s growing on the b e t t e r s i t e s . As increase i n crown width i s a s s o c i a t e d w i t h i n -crease i n age (r= .496), an increase i n crown width i s as s o c i a t e d w i t h an i n c r ease i n s i t e index. On t h e o r e t i c a l grounds the reverse would be t r u e . For t r e e s o f equal h e i g h t , those growing on poorer s i t e s w i l l be o l d e r and thus have a l a r g e r crown. Consequently increase i n s i t e i n -dex would be a s s o c i a t e d w i t h decrease i n crown width. TABLE 16 ASSOCIATION BETWEEN CROWN WIDTH AND SIX VARIABLES FOR OPEN-GROWN AND FOREST GROWN TREES No. o f tree s D.b.h. H CW/D Age H/CW SI Simple c o r r e l a t i o n c o e f f i c i e n t s Open-grown (1) 111 .969 .905 -.641 .900 -.319 -.389 90 .949 .846 -.452 .854 -.295 -.149 (2) Forest-grown 63 .753 .568 -.223 .496 -.222 .410 (3) (1) - .191 (2) r < ( ) 5 - .205 (3) r . 0 5 * .255 Values not s i g n i f i c a n t u n d e r l i n e d . 48 E v a l u a t i o n o f the r e l a t i o n s h i p between each o f the crown r a t i o s , CW/D and H/CW, and nine v a r i a b l e s may be made w i t h reference t o t h e i r r e s p e c 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 (Table 17). The a s s o c i a t i o n be-tween ba s a l area per acre and both r a t i o s i s of i n t e r e s t , the simple c o r r e l a t i o n c o e f f i c i e n t between b a s a l area per acre and each of the r a t i o s , CW/D and H/CW being h i g h l y s i g n i f i c a n t . SIMPLE CORRELATIONS BETWEEN CW/D AND H/CW AND EACH OP NINE VARIABLES TABLE 17 Dbh H Age SI CW CW/D H/CV BA/ac CcCl Simple c o r r e l a t i o n c o e f f i c i e n t s 90 open-grown t r e e s -.61- -.52 -.47 .12 -.45 1.00 -.12 --.18 i 2 l .07. .48 -.30 -.12 1.00 - - (1) 111 open-grown t r e e s -.69 -.67 -.59 .38 -.64 1.00 .02 --.24 .02 -.16 .48 -.32 .02 1.00 - (2) 63 forest-grown t r e e s -.64 -.76 -.70 -.59 -.22 1.00 -.72 -.56 -.04 (3) .33 .64 .47 .63 -.22 -.72 1.00 .60 .24 (1) r # Q 5 = .205 ; s(2) r > Q 5 = .170 ; (3) .255 Not s i g n i f i c a n t values u n d e r l i n e d The simple c o r r e l a t i o n c o e f f i c i e n t s between CW/D and diameter f o r both open-grown and forest-grown t r e e s are s i m i l a r . The f o r e s t -grown tr e e s measured were s e l e c t e d over a wide range of stand den-s i t i e s , as assessed by b a s a l area per acre. This suggests .that i f i t were p o s s i b l e to use CW/D as a c o n t r o l of stand d e n s i t y i n any manip-u l a t i o n o f stands then estimates of d.b.h.., from CW/D would l i k e l y have a c o n s i s t e n t standard e r r o r of estimate from f o r e s t to open-grown t r e e s . The a s s o c i a t i o n between the H / C W and CW/D r a t i o s from the data on forest-grown t r e e s permits the e s t i m a t i o n o f one i n terms o f the other (Table 18). TABLE 18 REGRESSION EQUATIONS FOR ESTIMATION OF CW/D FROM H / C W OR H / C V FROM C W / D ^ • • i ' Dependent Independent v a r i a b l e v a r i a b l e I n t e r c e p t CW/D R"/CW R Regression c o e f f i c i e n t s C W / D 1.7833 - .07624 .524 32,7 H / C W 17.204 -6.880 - .524 30.2 ( l ) Based on 63 forest-grown t r e e s . ANALYSIS OF CROWN WIDTH Crown width was r e l a t e d t o diameter, h e i g h t , CW/D, and H/CW f o r both open-grown and forest-grown t r e e s (Tables 19a,19b). About 94 per-cent of the t o t a l v a r i a t i o n i n the crown width of a l l the open-grown t r e e s , and about 90 percent when the younger t r e e s were excluded, could be accounted f o r by d.b.h. alone. For the forest-grown t r e e s only TABLE 19 a RELATIONSHIPS BETWEEN CROWN WIDTH AND D.B.H., HEIGHT, HEIGHT/CROWN WIDTH AND CROWN WEDIH/DIAMBrEE FOR OPEN-GROWN TREES Number of t r e e s I n t e r -cept D.b.h. H Independent v a r i a b l e s H/CW CW/D SI Age R 2 SE/ 0 ; Regression c o e f f i c i e n t s 111 3.6483 1.6271 - - - .939 14.4 3.2456 1.4985 .05180 - - .940 14.4 2.1746 1.6835 - .3468 - .940 14.4 8.2001 . 1.5887 - -2.448 - .948 13.3 10.913 .9467 .2431 -4.922 - .962 11.5 1.372 - .5647 - - .818 24.6 3.841 1.624 - -.00193 - .954 12.8 3.564 1.491 - - .0381 .940 14.4 90 4.238 1.585 - - - .902 13.4 3.778 1.471 .0484 - - .903 13.4 17.745 .5198 .4043 -9.6290 - .962 8.4 TABLE 19 b RELATIONSHIPS BETWEEN CROWN WIDTH AND D.B.H., HEIGHT, HEIGHT/CROWN WIDTH AND CROWN WIDTH/DIAMETER FOR FOREST-GROWN TREES Number Independent v a r i a b l e s 2 o f I n t e r - D.b.h. H H/CW CW/D SI Age R SEjS t r e e s oept _ Regression c o e f f i c i e n t s 3.054 .4685 - - - .568 25.4. 3.955 .791 -.0517 - - .629 23.6 -.9215 .6469 - - 2.527 .684 21.8 5.416 .5740 - -.3113 - .811 16.9 5.640 -.0422 .1146 -.6065 - .902 12.3 3.395 - .05091 - - .323 31.7 5.607 — .1075 -.5894 _ — .902 12.1 56.8 percent of the t o t a l crown width v a r i a t i o n could be r e l a t e d to changes i n d.b.h. The major p o r t i o n of the increase i n . v a r i a t i o n that could not be accounted f o r , between 33.4 percent and 37»1 percent, i s the r e s u l t of the influence of stand density changes. Combining CW/D with d.b.h. accounted f o r 68.4 percent of the t o t a l v a r i a t i o n i n crown width, while the j o i n t e f f e c t of H/CW and d.b.h. accounted f o r 8.1.1 percent. I t may be concluded that H"/CW i s more e f f e c t i v e i n combination with d.b.h. i n accounting f o r the t o t a l v a r i a t i o n i n crown widths of forest-grown lodgepole pine. The super-i o r i t y of H/CW i s not s u r p r i s i n g . I t has been shown that H/CW i s l e s s c l o s e l y associated with diameter than i s CV /D. Height v a r i a t i o n i s l e s s than diameter v a r i a t i o n with change i n stand density. Consequently change i n crown width would be more c l o s e l y associated with change i n H/CW than with v a r i a t i o n i n CW/D. In a p p l i c a t i o n , using H/CW i n preference to CW/D requires an a d d i t i o n a l measurement that i s not convenient to make accurately. An-other disadvantage i s that fl/CW alone does not provide as much i n f o r -mation as does CW/D. Number of trees per acre may be r e l a t e d to aver-age crown width, providing c e r t a i n assumptions concerning crown c l o s -ure, spacing pattern and'stand d i s t r i b u t i o n are made. The number of trees per acre i s therefore i n d i r e c t l y proportional to CW/D and s i m i -l a r l y i s d i r e c t l y proportional to H/CW, so e i t h e r r a t i o may be used f o r comparative purposes on s i m i l a r s i t e s . However, CW/D i n addition provides an estimate of t o t a l basal area per acre (basal area per 2 2 acre i n s q . f t . = (15.4 / (CV / D ) ) . The crown r a t i o H/CW cannot be manipulated i n a s i m i l a r manner without using a height-to-d.b.h. r e -l a t i o n s h i p which w i l l vary f o r d i f f e r e n t H/CW r a t i o s . As one i l l u s t r a t i o n , the height o f a f u l l y open-grown tree i s approximately 40 percent of the height of a forest-grown tree of the same d.b.h. (based on data obtained i n t h i s study). This a d d i t i o n a l information that can be gained through use of CW/D plus the eli m i n a t i o n of the tree height measurement suggests that CW/D i s a more p r a c t i c a l measure of density despite the greater pre-c i s i o n that may be obtained through the use of H/CW. Average d.b.h. has been shown to be more convenient than s i t e and age f o r the d e s c r i p t i o n of stands. McArdle, Meyer and Bruce (1949) found y i e l d estimates to be more precise when based on average d.b.h. than when s i t e index and age were used. Average d.b.h. i s of major importance i n the cost of logging and m i l l i n g . Information regarding any change i n d.b.h. that may be a s s o c i -ated with a change i n density i s not provided d i r e c t l y through H/CW but must f i r s t be expressed i n terms of crown width changes and then r e l a t e d through crown width to d.b.h. Change i n CW/D, although over a narrower numerical range, takes change i n d.b.h. d i r e c t l y into account. In comparing stands of d i f f e r e n t d e n s i t i e s , H/CW alone w i l l not take i n t o account any dif f e r e n c e s i n average diameter. For ease of comparison CW/D i s preferable. It should also be pointed out that the r a t i o H/CW i s more close-l y r e l a t e d to s i t e , i n c r e a s i n g on the better s i t e s . Both r a t i o s f o r forest-grown trees have hig h l y s i g n i f i c a n t simple c o r r e l a t i o n c o e f f i -ents with s i t e index (Table 1?), a f t e r allowing f o r the influence of d.b.h. The e f f e c t of s i t e index accounts f o r only an a d d i t i o n a l 6.0 percent of the v a r i a t i o n i n CW/D, while f o r H/CW combining s i t e index w i t h d.b.h. accounts f o r an a d d i t i o n a l 30.0 percent o f the t o t a l v a r i a -t i o n (Table 22). E s t i m a t i o n of d.b.h. from a e r i a l photographs. Reference has been made p r e v i o u s l y to l i n e a r r e g r e s s i o n equa-t i o n s that have been developed i n the analyses w i t h independent v a r i -ables t h a t are photo-measurable. T h e i r a p p l i c a t i o n i s r e s t r i c t e d due to t h e i r g e n e r a l l y h i g h standard e r r o r o f estimate. The equations developed to provide estimates of d.b.h. however, have standard e r r o r s o f estimate that are low enough to permit a u s e f u l estimate o f d.b.h. to be made. TABLE 19 c ESTIMATION OF D.B.H. FROM HEIGHT, CROWN WIDTH AND HEIGHT/CROWN WIDTH ^ In t e r c e p t H CW H/CW 2 R SE/o Regression c o e f f i c i e n t s Hi 111 open-grown t r e e s -1.5506 - .5774 - .939 17.4 -1.8675 .08929 .4476 - .950 15.9 -1.8697 .08924 .4477 .001206 .950 16.0 63 f o r e s t -grown t r e e s -.723 .1297 - - .811 22.7 .7972 .1686 - -.4053 .916 15.3 1.317 .1786 -.09279 -.45996 .917 15.3 ( l ) Based on data from 111 open-grown and 63 forest-grown t r e e s . Both t r e e height and crown width measurements may conveniently be made on a e r i a l photographs. For the forest-grown t r e e s the com-b i n a t i o n of height and H/CW appears to provide an adequate estimate. Crown Competition F a c t o r . The crown competition f a c t o r (CCF) developed by K r a j i c e k , and Brinkman i n 1957, uses the r e l a t i o n o f the crown widths of open-grown tr e e s to t h e i r diameters as a b a s i s f o r comparing stand d e n s i t i e s . The independence of CCF values from age has been i n v e s t i g a t e d by Vezina (1962,1963). He concluded that the crown competition f a c t o r d i d not appear to be r e l a t e d to age, but suggested the need f o r c o n f i r m a t i o n by a d d i t i o n a l t e s t s . The e v a l u a t i o n o f the independence of CCF values from s i t e and age d i f f e r e n c e s r e q u i r e s c o n s i d e r a t i o n of the e f f e c t s o f these d i f f e r -ences on the d i s t r i b u t i o n o f d.b.h. of- forest-grown t r e e s over a range of d e n s i t i e s . However, p o s s i b l e e f f e c t s of s i t e and age d i f f e r e n c e s on crown widths of open-grown t r e e s should a l s o be considered. I n s p e c t i o n o f the simple c o r r e l a t i o n c o e f f i c i e n t s given i n Table 16 shows that there i s a s i g n i f i c a n t a s s o c i a t i o n between crown width and both s i t e i n -dex and age f o r open-grown t r e e s . I t has been shown that d.b.h. alone accounts f o r 93.3 percent o f the t o t a l v a r i a t i o n i n the crown widths of 111 open-grown t r e e s (Table 19a). Therefore any increases i n the per-centage of v a r i a t i o n that could be accounted f o r by the a d d i t i o n of another v a r i a b l e would n e c e s s a r i l y be s m a l l . Two analyses of v a r i a n c e were made, the f i r s t u s i n g age as an a d d i t i o n a l v a r i a b l e to d.b.h. the second combining s i t e index w i t h d.b.h. The a d d i t i o n o f age was not s i g n i f i c a n t r e s u l t i n g i n only a n e g l i g i b l e r e d u c t i o n i n the r e s i d u a l v a r i a n c e . However the a d d i t i o n o f s i t e index was found t o be h i g h l y s i g n i f i c a n t , although accounting f o r only a s m a l l p o r t i o n of the t o t a l v a r i a t i o n (Table 19a). I n c l u d i n g s i t e index i n an estimate of crown width does not r e s u l t i n any important change i n the value f o r crown width. By i n s e r t i n g appropriate values i n the two regression equations given that r e l a t e crown width to d.b.h. and to d.b.h. and s i t e index, i t w i l l be found that even with extreme values f o r s i t e index any change i n an estimate of crown width i s exceedingly small, of the order of two to three tenths of a f o o t . Such a minor e f f e c t would be of small import-ance i n determining the crown competition f a c t o r f o r a f o r e s t stand. So f o r a l l p r a c t i c a l purposes, s i t e or age differences that may a f f e c t t h i s stand density measure are r e l a t e d o nly to the influence of these d i f -ferences on the growth of fo r e s t stands. ANALYSIS OF CROWN WIDTH/DIAMETER AND HEIGHT/CROWN WIDTH Introduction. The merit of CW/D or H/CW f o r use with other v a r i a b l e s as a method of assessing stand density has been discussed i n general i n the preced-i n g analysis of crown width. However, to provide more s p e c i f i c informa-t i o n to a i d evaluation of these two crown r a t i o s , regression analyses were made, using the data on both open-grown and forest-grown trees. CW/D and Il/CW were each r e l a t e d to d.b.h., height, crown width, age and s i t e index of open-grown trees. A s i x t h v a r i a b l e , basal area per acre, was included i n the analyses on the forest-grown trees. I t had been planned to use i d e n t i c a l data f o r a l l analyses of crown development. However, due to the l i m i t e d time that could be reserved f o r use of the I.B.M. 1620 computer i n preparation of t h i s t h e s i s the analysis of the H/CW r a t i o s f o r forest-grown trees was combined with that using natural pruning data obtained from 57 of the 63 forest-grown trees sampled (Table 25). The e a r l i e r analysis f o r CW/D r e l a t i o n s h i p s used data from a l l trees. Comparison of the simple c o r r e l a t i o n c o e f f i c i e n t matrices i n d i c a t e s t h a t d i f f e r e n c e s are minor (Appendixes 1 (e) and ( f ) ) . In a few cases an a s s o c i a t i o n becomes j u s t s i g n i f i c a n t or not q u i t e s i g n i f i -c ant. Some of the more important r e g r e s s i o n equations that combined two or three v a r i a b l e s were r e c a l c u l a t e d manually u s i n g the appropriate v a r i a n c e and covariances a v a i l a b l e from previous analyses. I n none of the seven r e g r e s s i o n s t e s t e d , was a s i g n i f i c a n t l y d i f f e r e n t r e s u l t found. Consequently r e s u l t s from the two analyses may be d i r e c t l y com-pared. To a i d d i s c u s s i o n of the r e s u l t s o f the analyses, Table 20 should be examined. Despite d i f f e r e n c e s between average, minimum and maximum values of the data f o r d.b.h. h e i g h t , and crown width, the co-e f f i c i e n t s o f v a r i a t i o n are very s i m i l a r f o r both forest-grown and open-grown t r e e s . Comparison of the c o e f f i c i e n t s o f v a r i a t i o n f o r C¥/D and H/CW i n d i c a t e s t h a t the d i s t r i b u t i o n o f the crown r a t i o data from the forest-grown t r e e s i s r e l a t i v e l y twice as v a r i a b l e as that from the open-grown t r e e s . I t i s t h i s a d d i t i o n a l v a r i a b i l i t y caused by crown compe-t i t i o n that i s the subject o f the analyses. Crown Width/Diameter Of the v a r i a b l e s used, the s i n g l e v a r i a b l e most c l o s e l y asso-c i a t e d w i t h the CW/D r a t i o f o r open-grown t r e e s was d.b.h. which account-ed f o r 47.3 percent o f the t o t a l v a r i a t i o n i n CW/D. A l l of the v a r i a b l e s used were s i g n i f i c a n t l y c o r r e l a t e d w i t h CW/D, height accounting f o r 44.2 percent of the t o t a l v a r i a t i o n , crown width f o r 41.0 percent, age f o r 35»1 percent and s i t e index, when used by i t s e l f accounting f o r 14.5 percent. Successive a d d i t i o n s of crown width, h e i g h t , o r age to d.b.h. d i d not s i g n i f i c a n t l y i n c r e a s e the percentage of v a r i a t i o n t h a t could be accounted f o r (Table 2 l ) . S i t e index when combined with a l l other v a r i a b l e s was found to be h i g h l y s i g n i f i c a n t , but when added to TABLE 20 RELATIVE VARIATION OP DATA USED PGR GROWN WIDTH, CROWN WIDTH/DIAMETER, AND HEIGHT/CROWN WIDTH ANALYSES No. of D.b.h. H CW CW/D H/CW Age SI trees Units inches feet feet - - years H@100 yr. Open-grown 111 Av. SD CV$ 9.2 6.0 65.0 30.5 17.4 55.5 18.6 10.8 58.1 2.8 0.8 28.5 1.7 0.4 23.5 35.1 24.9 71.0 72.1 15.9 22.1 90 Av. SD CV$ 11.2 5.6 50.3 35.9 15.2 42.3 22.0 9.4 42.5 2.13 0.56 26.3 1.67 0.37 22.1 41.9 23.1 68.6 15.4 22.4 Forest--grown 63 Av. SD cv$ 8.2 4.2 51.7 69.0 29.5 42.7 6.9 2.6 38.2 0.99 0.47 47.2 10.4 4.4 42.7 48.8 16.1 33.0 102.0 27.8 27.2 57 Av. SD CV$ 8.6 4.2 48.9 72.5 28.2 38.9 7.0 2.6 37.2 0.95 0.44 46.5 10.8 4.4 40.7 49.4 16.3 33.0 106.9 23.3 21.6 d.b.h. d i d not increase s i g n i f i c a n t l y t h a t p o r t i o n o f the v a r i a t i o n that could he accounted f o r . The a n a l y s i s demonstrated that w i t h d.b.h. taken i n t o account the remaining v a r i a b l e s have no s i g n i f i c a n t i n f l u e n c e on the CW/D r a t i o e i t h e r alone or i n combination. For the forest-grown t r e e s , the h i g h l y s i g n i f i c a n t simple c o r r e l -a t i o n between b a s a l area per acre and CW/D (r= .555) i n d i c a t e s that approximately 25 percent of the t o t a l v a r i a t i o n i n the CW/D r a t i o i s a s s o c i a t e d w i t h stand d e n s i t y , assessed as b a s a l area per acre. I n i n c r e a s e i n stand d e n s i t y i s associated w i t h a decrease i n the CW/D r a t i o . D.b.h. alone (r= -.643) accounts f o r 41.3 percent o f the v a r i a -t i o n . Adding b a s a l area t o d.b.h. has no s i g n i f i c a n t e f f e c t . The s i n g l e v a r i a b l e that i s most c l o s e l y a s s o c i a t e d w i t h CW/D i s h e i g h t , accounting f o r 58.4 percent o f the t o t a l v a r i a t i o n (r= -.764). S i t e index and age were each combined w i t h height and then w i t h d.b.h. (Table 22).. N e i t h e r s i t e nor age c o n t r i b u t e d s i g n i f i c a n t l y t o the per-centage o f v a r i a t i o n that could be accounted f o r by height alone. The a d d i t i o n of e i t h e r s i t e index or age, to d.b.h. was s i g n i f i c a n t . S i t e index and d.b.h. accounted f o r 47.3 percent while the combination of age and d.b.h. accounted f o r 49.8 percent o f the t o t a l v a r i a t i o n . An independent t e s t of the extent to which CV/D measures stand d e n s i t y i s d i f f i c u l t t o de v i s e . The e f f e c t o f s i t e index and age on the CW/D r a t i o i s r e a d i l y determined (Table 22). But to f i n d a measure of stand d e n s i t y t h a t i s not r e l a t e d i n some way w i t h the index b e i n g t e s t e d i s not as s t r a i g h t f o r w a r d . The GW/D r a t i o has been shown to be r e l a t e d t o b a s a l area and number of stems per acre, e i t h e r alone or w i t h d.b.h. taken i n t o account. This means t h a t a determination of TABLE 2 1 RELATION OP CROWN WIDTH/DIAMETER TO D.B.H., CROWN WIDTH, HEIGHT AND HEIGHT/CROWN WIDTH FOR 1 1 1 OPEN-GROWN TREES I n t e r -cept D.b.h. Independent v a r i a b l e s CW H H/CW 2 R Regression c o e f f i c i e n t s 4 .24?8 -.1626 - - .473 40.5 4.0324 -.2585 .05897 - .484 40.2 4.1765 -.2161 .06651 - . 0 2 2 0 4 - .493 40.0 5.2251 - . 1 7 0 8 - -.5282 .495 39.8 TABLE 22 -RELATION OP CROWN WIDTH/DIAMETER TO D.B.H., SITE INDEX, AGE AND HEIGHT/ CROWN WIDTH FOR 63 FOREST-GROWN TREES I n t e r -cept D.b.h. Independent v a r i a b l e s SI Age H/CW R 2 Regression c o e f f i c i e n t s 1 . 5 7 4 1 -.07065 - - - .413 37.8 1.9336 -.0490 -.005265 - - .473 34.7 1.9821 - -.02025 - . 4 8 8 33.9 1.9282 -.0202 - r.01574 - .498 33.9 2.3631 - -.00629 -.01593 - .586 31.3 2.615 .03270 -.00805 -.0219 - .603 30.9 1.7833 - - - .07624 .525 32.8 2.0333 -.05006 - - -.06063 .711 25.8 the e f f e c t of crown width on the v a r i a t i o n i n CW/D a f t e r the combined i n f l u e n c e of s i t e index, age and d.b.h. have been taken i n t o account would b a s i c a l l y s t i l l be a s s e s s i n g crown width. A comparison made w i t h the average values of CV/D r a t i o s f o r both groups o f data would i n t r o -duce c i r c u l a r i t y i n t o the t e s t . The c o r r e l a t i o n between H/CW and crown width has been shown to be low - e i t h e r j u s t s i g n i f i c a n t or not qu i t e s i g n i f i c a n t , depending on which set of data i s being used. This provides a more s u i t a b l e b a s i s f o r t e s t i n g CW/D. A s u i t a b l e standard may be obtained by u s i n g the CW/D r e l a t i o n -s h i p s found f o r f u l l y open-grown t r e e s . The c o e f f i c i e n t s of v a r i a t i o n i n d i c a t e t h a t the r e l a t i v e v a r i a b i l i t y of the CW/D r a t i o s f o r the f o r e s t -grown t r e e s i s roughly twice t h a t f o r the open-grown. As the crown widths and d.b.h. o f both groups have s i m i l a r c o e f f i c i e n t s of v a r i a t i o n i t may be i n f e r r e d that the a d d i t i o n a l v a r i a b i l i t y i s due to tr e e comp-e t i t i o n alone. To t e s t the v a l i d i t y of t h i s i n f e r e n c e the v a r i a b l e H/CW, the r e l a t i o n of t r e e height to growing space, should be added to those v a r i a b l e s which when combined accounted f o r approximately the same percentage of the t o t a l v a r i a t i o n i n both groups of t r e e s . I f the added i n f l u e n c e o f t h i s d e n s i t y measure i s demonstrably g r e a t e r f o r the f o r e s t -grown t r e e s than f o r the open-grown, then the in f e r e n c e t h a t the a d d i t i o n -a l v a r i a t i o n i s due to the e f f e c t s o f tr e e competition w i l l have been shown t o be v a l i d . The v a r i a b l e H/CW i s not s i g n i f i c a n t l y c o r r e l a t e d w i t h the CW/D r a t i o f o r open-grown t r e e s (r= -.124, N = 90; r= .020, N= 131). When combined w i t h d.b.h. however, the added i n f l u e n c e of H/CW was j u s t 62 s i g n i f i c a n t at the 95$ confidence l e v e l , i n c r e a s i n g the percentage of the t o t a l v a r i a t i o n i n CW/D th a t could be accounted f o r to 49.5 percent, an increase o f 2.2 percent (Table 2 l ) . For the forest-grown t r e e s , the a d d i t i o n of H/CW to d.b.h. r e s u l t e d i n a h i g h l y s i g n i f i c a n t increase i n the percentage of t o t a l v a r i a t i o n o f the CW/D r a t i o s t h a t could be ac-counted f o r . The increase was from 41.3 percent to 71.1 percent - ap p r o x i -mately 30 percent (Table 22). E f f e c t o f Age and S i t e Index. B i c k f o r d e_t a l . (1957) suggested t h a t an i d e a l measure of d e n s i t y should be l a r g e l y u n r e l a t e d to the charac t e r and age of the stand and the q u a l i t y of the s i t e . N e i t h e r crown r a t i o meets these requirements. Both age and s i t e index have been shown to exert a s i g n i f i c a n t though r e l a -t i v e l y small i n f l u e n c e on the CW/D r a t i o o f forest-grown t r e e s , a f t e r the e f f e c t of d.b.h. has been taken i n t o account. I n the absence of d.b.h., age accounts f o r 48.8 percent o f the t o t a l v a r i a t i o n i n CW/D while s i t e index accounts f o r 35.3 percent. When combined, 58.6 percent o f the t o t a l v a r i a t i o n i n CW/D i s accounted f o r (Table 22). The pronounced e f -f e c t s of s i t e index and age are masked, however, when the e f f e c t o f height i s taken i n t o account. Height alone accounts f o r 58.2 percent o f the t o t a l v a r i a t i o n . An a n a l y s i s o f variance demonstrated t h a t the ad-d i t i o n of e i t h e r age or s i t e index or both to height has no s i g n i f i c a n t e f f e c t i n the percentage o f v a r i a t i o n accounted f o r . This strong i n f l u e n c e o f s i t e index and age n a t u r a l l y impairs the usefulness of CW/D as a d e n s i t y measure i f used alone. However the e f f e c t s o f age and s i t e index can be modified c o n s i d e r a b l y by u s i n g d.b.h. or of course, h e i g h t , c o n c u r r e n t l y w i t h the crown r a t i o . When CW/D i s used to r e l a t e stand d e n s i t i e s on s i m i l a r s i t e s as i n stand manipulation o f even-aged f o r e s t s then the problem does not a r i s e . H e i g h t / crown width. This r a t i o , c l o s e l y r e l a t e d to the r a t i o of t r e e height t o the average spacing d i s t a n c e , i s ' dependent f o r i t s usefulness as an index o f stand d e n s i t y on the r e l a t i v e response of crown width and t r e e height to changes i n t r e e competition. Average crown width f o r f o r e s t -grown t r e e s v a r i e s i n v e r s e l y w i t h the number of t r e e s per acre. I t , can be demonstrated t h a t (crown width) i s c l o s e l y r e l a t e d to the r e c i p r o c a l of b a s a l &rea per acre (CW^ K/B.A. ; where K= (15.4 times d b h ) 2 ) . Height growth of lodgepole p i n e , besides being r e l a t e d t o s i t e index and age, has been shown to be h i g h l y c o r r e l a t e d w i t h stand d e n s i t y (Smithers, 1961, Holmes and Tackle, 1962, Duffy, 1962). I n the present study, height was h i g h l y s i g n i f i c a n t l y c o r r e l a t e d w i t h b a s a l area and percent-age l i v e crown (Appendix 1 d ) . While much of the v a r i a t i o n i n height w i l l be taken i n t o account by s i t e index and age, p a r t o f the r e s i d u a l v a r i a t i o n w i l l be a f f e c t e d by changes i n stand d e n s i t y . Besides a f f e c t -i n g h e i g h t , s i t e index has been shown to be r e l a t e d t o the H/CW r a t i o i t s e l f . A t r e e o f a given height growing on a poor s i t e , w i l l be o l d e r , and t h e r e f o r e tend to have a l a r g e r crown. Consequently, g i v e n comp-ar a b l e stand d e n s i t i e s , an i n c r e a s e i n s i t e q u a l i t y i s a s s o c i a t e d w i t h an incre a s e i n the H/CW r a t i o (Spurr, 1952). The v a r i a t i o n i n the H/CW r a t i o s f o r open-grown t r e e s should be r e l a t e d to s i t e index, age, height and crown width. The v a r i a t i o n i n the H/CW r a t i o s f o r the forest-grown t r e e s , g r e a t e r due to the i n f l u -ence of t r e e c o m p e t i t i o n , should be s i m i l a r l y r e l a t e d t o the same v a r i a b l e s . The e f f e c t of stand d e n s i t y on height i s l e s s than i t s e f f e c t on d.b.h. growth. Hence the p r e c i s i o n w i t h which H/CW estimates stand 6k d e n s i t y may be determined by crown width. Crown width provides a d i r -e c t index o f the a e r i a l growing space u t i l i z e d by the t r e e and i s r e l a t e d to the number of t r e e s per acre. Two analyses were made. I n the f i r s t a n a l y s i s the i n f l u e n c e o f s i t e index and age was ignored. V a r i a t i o n i n height t h a t could have been the r e s u l t o f stand d e n s i t y changes was taken i n t o account. The a s s o c i a t i o n between the r e s i d u a l v a r i a t i o n and v a r i a t i o n i n crown width was then compared f o r the two groups o f data. I n the second a n a l y s i s , the e f f e c t s o f both age and s i t e index were taken i n t o account before c o n s i d e r a t i o n o f height and crown width v a r i a t i o n . Irom t h e . f i r s t a n a l -y s i s (Tables 23 and 2k) the i n f l u e n c e o f height on the H"/CW r a t i o s f o r the two groups of t r e e s was found t o be d i s t i n c t l y d i f f e r e n t . V a r i a t i o n i n height accounted f o r a n e g l i g i b l e percentage of the t o t a l v a r i a t i o n i n the H/CW r a t i o f o r open-grown t r e e s (r= .022) but accounted f o r Jk.k percent when the data from forest-grown t r e e s were used. The i n f l u e n c e o f v a r i a t i o n i n the crown widths of open-grown and forest-grown t r e e s accounted f o r 10.2 percent and 9*9 percent r e -s p e c t i v e l y o f the t o t a l v a r i a t i o n i n H / C W . However, the e f f e c t of these two v a r i a b l e s i n combination was most marked, accounting f o r 6k.2 percent and 91.6 percent r e s p e c t i v e l y o f the t o t a l v a r i a t i o n i n H/CW. Due t o the n e g l i g i b l e e f f e c t of h e i g h t , a l l v a r i a t i o n i n the H/CW r a t i o f o r the open-grown t r e e s accounted f o r may be r e l a t e d to the e f f e c t of crown width. When r e l a t e d to the crown r a t i o of the forest-grown t r e e s , crown width and height combined accounted f o r 91.6" percent of the t o t a l v a r i a t i o n i n H/CW. The added e f f e c t of 0 TABLE 23 RELATION OP HEIGHT/CROWN WIDTH TO HEIGHT, CROWN WIDTH, AGE AND SITE INDEX OP 111 OPEN-GROWN TREES I n t e r -cept SI Independent v a r i a b l e s Age CW H .7651 .5732 .7002 1.0004 .5582 1.2695 1.780 .01318 .01484 .0127 .01154 .01773 .007074 Regression c o e f f i c i e n t s ,002035 •002301 .02113 .006623 .005887 .006256 .04543 .07145 .07505 .03376 .04289 .234 .245 .253 .255 .491 .668 .642 22.2 21.9 22.1 22.0 18.3 14.8 15.3 TABLE 24 RELATION OP HEIGHT/CROWN WIDTH TO HEIGHT, CROWN WIDTH, AGE AND SITE INDEX OP 57 FOREST-GROWN TREES Independent v a r i a b l e s ? I n t e r - SI Age CW H R cept Regression c o e f f i c i e n t s 4.1942 - .09129 .344 33.2 9.1672 - - -1.4894 .16?6 .916 12.0 -2.310 .09115 .0684 - - .492 29.2 3.875 .01956 -.06741 - .1128 .593 26.3 7.8014 .0216 - -1.464 .1521 .920 11.8 6.3829 .03826 .03245 -1.455 .1241 .921 11.8 66 crown width t h e r e f o r e accounted f o r an a d d i t i o n a l 57«2 percent of the t o t a l v a r i a t i o n , approximately the same as f o r the open-grown data. I t could be claimed that t h i s percentage r e f e r s to the added e f f e c t o f height a f t e r v a r i a t i o n due to crown width had been removed. However, i t had been decided before the a n a l y s i s to e l i m i n a t e the e f f e c t of height before t h a t o f crown width. For the forest-grown data t h i s se-quence was e s s e n t i a l o f course, t o remove any p o s s i b l e e f f e c t ..of stand d e n s i t y on height growth. I t may be concluded t h a t when height v a r i a t i o n has been account-ed f o r , but without t a k i n g i n t o account s i t e index and age d i f f e r e n c e s , about two t h i r d s o f the v a r i a t i o n of the H / C W r a t i o f o r both open-grown and forest-grown t r e e s i s a s s o c i a t e d w i t h crown width. The d i f f e r e n c e between average values f o r the crown widths of open-grown and f o r e s t -grown t r e e s may be compared i n Table 20. This a n a l y s i s i n d i c a t e s o n ly the a s s o c i a t i o n between H/CW and crown width a f t e r h e i g ht d i f f e r e n c e s have been taken i n t o account. V a r i a t i o n s i n H / C V due to the i n f l u e n c e o f s i t e index were not con-s i d e r e d . From the second s e r i e s of analyses made (Tables 23 and 24) the e f f e c t s of s i t e index and age used s i n g l y or i n combination were found. Study o f values of R (the r a t i o o f the percentage o f v a r i a t i o n account-ed f o r ) w i l l a s s i s t i n c l a r i f y i n g the i n t e r r e l a t i o n s h i p s e x i s t i n g be-tween s i t e index, age, height and crown width o f the open-grown t r e e s . I t i s apparent that important i n t e r a c t i o n s e x i s t . The predetermined order 2 i n which the v a r i a b l e s were t o be combined was s i t e index ( r = »234), s i t e 2 2 index and age (R = .245), s i t e index, age and height (R = .253), f o l -2 lowed by the i n c l u s i o n of crown width (R = .668). Many i n t e r p r e t a t i o n s are p o s s i b l e . F o l l o w i n g t h i s sequence i t may be concluded t h a t the a d d i t i o n o f crown width t o the other three v a r i a b l e s used i n combination r e s u l t e d i n accounting f o r an a d d i t i o n a l 41.5 per-cent o f the t o t a l v a r i a t i o n . This n e c e s s i t a t e s the r e t e n t i o n of v a r i -ables that do not themselves c o n t r i b u t e s i g n i f i c a n t l y t o the p o r t i o n of the v a r i a n c e that i s removed by the r e g r e s s i o n s , but that have import-ant and h i g h l y s i g n i f i c a n t i n t e r a c t i o n s when other v a r i a b l e s are l a t e r added. With the forest-grown data, a s i m i l a r sequence demonstrates t h a t s i t e index alone accounts f o r 35.2 percent of the t o t a l v a r i a t i o n i n H/CW, s i t e index and age, 49.2 percent, and the combination s i t e index, age and h e i g h t , 59*3 percent. When crown width i s i n c l u d e d the t o t a l v a r i a t i o n accounted f o r i s 92.1 percent. As f o r the data from open-grown t r e e s the added e f -f e c t of s i t e index and age a f t e r height and crown width i s not s i g n i f -i c a n t . However i n the predetermined sequence, f o r the forest-grown data, the a d d i t i o n a l e f f e c t s o f each v a r i a b l e were h i g h l y s i g n i f i c a n t . The a d d i t i o n a l percentage of the t o t a l v a r i a t i o n i n H/CW r a t i o accounted f o r by crown width when combined w i t h s i t e index, age and height was 32.8 percent. I n comparing these r e s u l t s , i t should be r e c a l l e d that the co-e f f i c i e n t of v a r i a t i o n f o r H/CW i s almost twice as great f o r the f o r e s t -grown as f o r the open-grown t r e e s . The f o u r v a r i a b l e s used account f o r almost a l l (92.1$) o f t h i s g r e a t e r v a r i a t i o n i n H/CW f o r the f o r e s t -grown t r e e s , w h i le there i s s t i l l a t h i r d (33.2$) of the t o t a l v a r i a t i o n i n H/CW f o r the open-grown t r e e s that i s unaccounted f o r . This i m p l i e s t h a t when s i t e index, age and height have been taken i n t o account, although the a s s o c i a t i o n between crown width and R"/CW i s s l i g h t l y g r e a t e r f o r the open-grown t r e e s , the p r e c i s i o n w i t h which an estimate of crown width may be made i s grea t e r f o r the forest-grown t r e e s . With height and crown width only combined the e f f e c t o f s i t e index and age i s not s i g n i f i c a n t (Table 2k). The r e g r e s s i o n equation f o r e s t i m a t i o n of crown width u s i n g height and H/CW has been presented ear-l i e r (Table 19 b ) . I t may be concluded from the analyses made t o evaluate the u t i l -i t y o f H/CW as a measure o f stand d e n s i t y t h a t , i n terms of crown width (number of t r e e s ) , the use o f H/CW alone only p a r t l y assesses stand d e n s i t y . The i n f l u e n c e of s i t e index, age, and height on H/CW accounts f o r a s i g n i f i c a n t percentage of the t o t a l v a r i a t i o n . The combined use of h e i g h t and H/CW i s necessary i f an adequately p r e c i s e estimate of crown width i s to be made. I t i s i n t e r e s t i n g to speculate on another p o s s i b l e way i n which the r a t i o H/CW may be used. Basal area per acre may be shown to be equivalent t o the expres-2 2 / 2 s i o n , 15.4 • D / CW , given uniform, square spacing o f t r e e s . This 2/ 2 e x p r e s s i o n i n t u r n may be s t a t e d as K. D / CW , where K i s a constant. Munro (i960) i n developing an e m p i r i c a l y i e l d t a b l e f o r I n t e r i o r lodge-pole p i n e , used the v a r i a b l e , average height times b a s a l area per acre. T h i s v a r i a b l e was h i g h l y s i g n i f i c a n t l y c o r r e l a t e d w i t h volume per acre i n c u bic f e e t . I f the expression above i s equated w i t h Munro's v a r i -a b l e , i t becomes (K.D 2.H)/ CW2. This may be r e - w r i t t e n as K. D . H . D. CW CW The r a t i o , CW/D i s conve n i e n t l y regarded as being equal to u n i t y , . f o r forest-grown t r e e s , I n the present study the average value f o r t h i s r a t i o was 0.99. The term K i s a constant, so t h e r e f o r e volume per acre should be highly significantly correlated with the variable, (H.D)/C¥. As no stand data had been collected during the study, this could not be tested. It would be of interest to test this theoretical association, and i f significant, test a photogrammetric stand volume equation based on i t s use. NATURAL PRUNING OP LODGEPOLE PINE INTRODUCTION Observation o f open-grown lodgepole pine shows t h a t the degree of n a t u r a l pruning on t r e e s that are f u l l y open-grown i s extremely l i m i t e d . The t y p i c a l bee-hive or p a r a b o l i c shape of the crown of the open-grown t r e e extends very n e a r l y t o the ground f o r t r e e s o f a l l ages. The maximum average height t o the lowest l i v e branch on any of 131 open-grown t r e e s was seven f e e t on a t r e e 66 years o l d . Dead branches per-s i s t throughout the l i f e of the t r e e . Most of the open-grown t r e e s s t u d i e d had one or more dead branches w i t h i n s i x inches of the ground. The extent of pruned h e i g h t on forest-grown t r e e s was i n v e s t i -gated by r e g r e s s i o n analyses r e l a t i n g the hei g h t s t o both dead and l i v e branches t o a t o t a l o f nine v a r i a b l e s . N a t u r a l pruning was defined i n terms of the average height to the lowest dead branch on each o f f o u r s i d e s , and as the average height to the lowest l i v e branch on each of f o u r s i d e s . These average h e i g h t s were each r e l a t e d to d.b.h., h e i g h t , age, s i t e index, crown wid t h , CW/D, H/CW, bas a l area per acre and one of f o u r a d d i t i o n a l i n d i c e s of competition from neighbouring t r e e s r e f e r -red to as " t r e e competition f a c t o r s " . An e x p l a n a t i o n o f the d e r i v a t i o n o f these f a c t o r s w i l l c l a r i f y the i n t e n t o f t h e i r use. When the data on forest-grown t r e e s were c o l l e c t e d , d i r e c t i o n , d i s t a n c e s and the d.b.h. of a l l p o s s i b l e competing t r e e s were recorded on a p o l a r coordinate g r i d . The branching c h a r a c t e r i s t i c s of sample t r e e s were recorded f o r each o f f o u r s i d e s . I t was ther e f o r e p o s s i b l e t o r e l a t e t r e e competition to the sample t r e e on a quadrant b a s i s . E f f e c t i v e competition o f neighbouring t r e e s was regarded as a f u n c t i o n o f d.b.h. and di s t a n c e o n l y . P o s s i b l e i n f l u e n c e o f crown c l a s s or t r e e height was assumed t o be accounted f o r by d.b.h. The data on neighbouring t r e e s were analysed l a t e r to de t e r -mine fo u r " t r e e competition f a c t o r s " . These were simple mathematical expressions intended to represent the combined e f f e c t o f competing t r e e s i z e and d i s t a n c e on the t r e e s s t u d i e d f o r n a t u r a l pruning. I t was most u n l i k e l y t h a t the data represented o n l y competing t r e e s , -at one l o c a t i o n 26 neighbouring t r e e s had been recorded - so only a p o r t i o n o f the data was used to c a l c u l a t e the competition f a c t o r s . A t r e e was t e n t a t i v e l y d efined as competing i f any part of i t s crown was w i t h i n a c e r t a i n d i s t a n c e from the sample t r e e . This distance was de f i n e d as the average crown r a d i u s o f a f u l l y open-grown t r e e having the same d.b.h. as the sample t r e e . Of the t r e e s t h a t met t h i s r e -quirement , those having crowns that subtended an unobstructed angle at the sample t r e e were c l a s s i f i e d as competing t r e e s . I n most quadrants these r e s t r i c t i o n s r e s u l t e d i n only one t r e e being r a t e d as competing. I n no case d i d more than three t r e e s i n one quadrant q u a l i f y as com-p e t i n g t r e e s . Tree Competition F a c t o r . The distance to a competing t r e e was expressed i n terms of the crown width o f an open-grown t r e e having the same d.b.h. as the f o r e s t -grown sample t r e e . The appropriate crown width was found u s i n g the r e l -a t i o n s h i p found e a r l i e r i n the study, CW = 4.238 + 1.585 (d.b.h.). The measured distance was standardised by d i v i d i n g by one h a l f o f the open-grown crown width. The e f f e c t of distance i n competition was assumed t o f o l l o w an i n v e r s e square r e l a t i o n s h i p , so t h a t the term used t o express 2 the "competition distance" was (CW/2.distance) . This term, calculated f o r each competing tree, was combined with each of four i n d i c e s develop-ed to express tree s i z e . I f the d.b.h. of the sample tree i s repre-sented by Ds, and the d.b.h. of the competing tree by Dc, then the four tree competition f a c t o r s (TC) developed were, 2 T C 1 = (C¥) . (Ds + Dc) (2. distance; TC2 = (CW) 2 . (Ds . Dc) (2.distance) TC3 = (CW) 2 . (Ds 2. Dc 2) (2.distance) TC4 = (CW) 2 . (Ds . D c ) 2 _ _ _ _ _ _ _ _ _ _ _ _ _ i (2.distance) 100 The i n d i v i d u a l tree competition f a c t o r s were combined f o r each quadrant. I t had been planned to make an i n i t i a l a n a lysis on a quadrant b a s i s , to f i n d which of the four tree competition f a c t o r s had the most s i g n i f i c a n t e f f e c t on the v a r i a t i o n i n the height to the lowest dead branch, and height to the lowest l i v e branch, on each of four sides. A second analysis would then have been made using only the most s i g n i f i -cant tree competition f a c t o r on a tree b a s i s . Due to the lack of the necessary computer time t h i s approach had to be abandoned and the two analyses combined usi n g only average heights and a l l four competition f a c t o r s on a tree b a s i s . The simple c o r r e l a t i o n c o e f f i c i e n t s between each p a i r of va r i a b l e s used i n the analyses are given i n Appendix l e . For ease of comparison, the simple c o r r e l a t i o n c o e f f i c i e n t s between both average height to the TABLE 25 BASIC DATA USED FOR THE ANALYSIS OP NATURAL PRUNING OP 57 FOREST-GROWN TREES Item Average SD Min. Max. D.b.h. 8.63 4.2 1.4 18.6 H 72.49 28.21 14 110 CW 7.05 2.65 3.5 15.0 CW/D 0.95 0.45 0.41 3.21 Age 49.42 16.34 11 77 H/CW 10.81 4.39 3.1 22.3 HDbr 4.10 5.47 0.0 50.0 HLbr 42.01 20.09 2.5 95.0 SI 106.84 23.23 60 160 BA/ac. 128.57 59.57 30 240 TCI 158.52 154.87 0.0 530 TC2 709.15 848.89 0.0 3174 TC3 1510.6 1856 0.0 6825 TC4 893.7 1358 0.0 4747 lowest dead branch, HDbr, and average' height t o the lowest l i v e branch, HLbr, on each of f o u r s i d e s , and the fou r competition f a c t o r s are given i n Table 26. Of the f o u r f a c t o r s , TC4 was found to be most closely-a s s o c i a t e d w i t h HDbr. A l l f a c t o r s were s i m i l a r l y a s s o c i a t e d w i t h HLbr. Consequently TC4 was s e l e c t e d as the f a c t o r to be inc l u d e d w i t h the e i g h t v a r i a b l e s p r e v i o u s l y mentioned i n the r e g r e s s i o n analyses. TABLE 26 SIMPLE CORRELATION COEFFICIENTS BETWEEN AVERAGE HEIGHT TO THE LOWEST DEAD BRANCH AND AVERAGE HEIGHT TO THE LOWEST LIVE BRANCH AND FOUR TREE COMPETITION FACTORS Pruned height TCI TC2 TC3 TC4 HDbr .518 .576 .483 .703 HLbr .556 .537 -567 .546 r.05 " « 2 5 9 ANALYSIS OF FACTORS AFFECTING HEIGHT TO THE LOWEST DEAD BRANCH A l l nine v a r i a b l e s together accounted f o r 65.3 percent of the t o t a l v a r i a t i o n i n HDbr. The s i n g l e v a r i a b l e most c l o s e l y associated w i t h HDbr was the f a c t o r TC4 accounting f o r 49.4 percent of the t o t a l v a r i a t i o n . Age, the next most c l o s e l y a s s o c i a t e d v a r i a b l e accounted f o r 47.4 percent (Table 27). The combination age and TC4 r e s u l t e d i n a h i g h l y s i g n i f i c a n t i n c r e a s e , 56.8 percent of the t o t a l v a r i a t i o n b e i n g accounted f o r . The subsequent a d d i t i o n o f d.b.h., a l s o s i g n i f i -cant, r e s u l t e d i n 60.4 percent of the t o t a l v a r i a t i o n i n the average TABLE 2? LINEAR REGRESSION EQUATIONS FOR THE AVERAGE HEIGHT TO THE LOWEST DEAD BRANCH ON EACH OF FOUR SIDES I n d e p e n d e n t v a r i a b l e s I n t e r -c e p t Age D.b.h. H CW/D H/CW TC4 S I BA/ac, R 2 R e g r e s s i o n c o e f f i c i e n t s -7.2678 .2300 - - - - - .471 100.0 -7.0691 .2124 .07811 - - - - .472 101.0 -7.0915 .2096 .06542 .00373 - - - .472 101.0 -11.6659 .2420 -.04856 .02847 2.2771 - - .486 101.0 -7.4729 .1853 .4636 -.06041 .2585 - .484 102.0 -3.9261 .2040 -.7558 .02947 .002605 - - .608 88.8 -3.8286 .2258 -.6380 - .002543 - - .604 88.3 -3.7754 .1276 - - .001754 - - .568 91.4 1.5698 - - - .002831 - - .494 97.8 -7.2186 .2297 .004861 .01780 - - -.01060 .478 102.0 -13.6342 .3412 .1348 -.1278 - - - .08399 _ .479 102.0 76 height to the lowest dead branch being accounted f o r . The s m a l l ad-d i t i o n a l i n c r e a s e when s i t e index i s i n c l u d e d was not s i g n i f i c a n t . The e f f e c t o f the s e v e r a l stand d e n s i t y i n d i c e s on the v a r i a -t i o n i n c l e a r bole l e n g t h a f t e r the i n f l u e n c e o f age, diameter and h e i g h t had been taken i n t o account was determined by a d d i t i o n a l analyses. The a d d i t i o n to age of d.b.h., or of both d.b.h. and height had no s i g -n i f i c a n t e f f e c t . When the stand d e n s i t y i n d i c e s used i n the a n a l y s i s were each combined w i t h age, age and d.b.h., or age, d.b.h. and height o n l y the a d d i t i o n o f TCk r e s u l t e d i n a s i g n i f i c a n t i n f l u e n c e on HDbr. This a n a l y s i s demonstrated t h a t only when approximately h a l f o f the t o t a l v a r i a t i o n i n HDbr had been accounted f o r by TCk was a s i g -n i f i c a n t p o r t i o n of the r e s i d u a l v a r i a t i o n accounted f o r by d.b.h. or h e i g h t . E v i d e n t l y the e f f e c t of d.b.h. on c l e a r bole l e n g t h i s only p a r t l y accounted f o r by i t s i n c l u s i o n i n the f a c t o r TC4. The e f f e c t of age alone has been shown to mask any i n f l u e n c e on c l e a r bole l e n g t h of the stand d e n s i t y f a c t o r s . Only the t r e e competition f a c t o r TC4 had any s i g n i f i c a n c e a f t e r age had been taken i n t o account. Of the nine v a r i -a b les used only crown width was not c o r r e l a t e d s i g n i f i c a n t l y w i t h the average height to the lowest dead branch. Despite t h i s , i t was not p o s s i b l e to develop a r e g r e s s i o n equation to estimate HDbr w i t h ade-quate p r e c i s i o n . The most s i g n i f i c a n t r e g r e s s i o n equation, u s i n g TC4, a s p e c i a l l y d e r i v e d t r e e competition index, had a standard e r r o r o f estimate of almost 90$. Apart from TC4, which i s inconvenient to use i n p r a c t i c e , no measure of stand d e n s i t y was s i g n i f i c a n t when used i n combination w i t h age. The use of age alone i s not l o g i c a l . Age had no observed e f f e c t on the value of HDbr f o r open-grown t r e e s . With sample t r e e s obtained from stands t h a t are more f u l l y stocked i t i s . l i k e l y t h a t more s a t i s f a c t o r y r e l a t i o n s h i p s could be developed. ANALYSIS OF FACTORS AFFECTING HEIGHT TO THE LOWEST LIVE BRANCH In s p e c t i o n of the simple c o r r e l a t i o n c o e f f i c i e n t s (Appendix Ie) i n d i c a t e s t h a t a l l stand d e n s i t y i n d i c e s used are h i g h l y s i g n i f i c a n t l y a s s o c i a t e d w i t h the average height t o the lowest l i v e branch. The most c l o s e l y a s s o c i a t e d measure of d e n s i t y i s b a s a l area per acre ( r = .792), f o l l o w e d by H/CW ( r = .752), CW/D ( r = -.732) and TCk ( r = .5^6). How-ever, the s i n g l e v a r i a b l e that i s most c l o s e l y a s s o c i a t e d w i t h HLbr i s height ( r = .9^0), accounting f o r 88.3 percent of the t o t a l v a r i a t i o n . The a d d i t i o n of d.b.h. to h e i g h t , f o l l o w e d by age, r e s u l t s i n s i g n i f -i c a n t i n c r e a s e s of t h i s percentage to 93.7 percent and 9^ .3 percent r e s p e c t i v e l y . With these three v a r i a b l e s used i n combination the a d d i t i o n a l i n f l u e n c e of the d e n s i t y i n d i c e s i s d i s t i n c t l y d i f f e r e n t . When added to the combination n e i t h e r CW/D nor the t r e e competition f a c t o r TCk i n c r e a s e the percentage of the t o t a l v a r i a t i o n accounted f o r s i g n i f -i c a n t l y . H/CW and b a s a l area per acre both c o n t r i b u t e s i g n i f i c a n t l y t o the combination when each i s added, but the v a r i a t i o n i n HLbr accounted f o r by t h e i r i n c l u s i o n i s small (Table 28). This l a c k of importance of stand d e n s i t y i n e s t i m a t i o n of pruned height i s more apparent than r e a l . As both d.b.h. and height growth are a f f e c t e d by t r e e competition, the e f f e c t of stand d e n s i t y i s expressed i n d i r e c t l y . S i t e index, a l s o a f f e c t s t r e e growth, but w i t h both age and height i n c l u d e d , the a d d i t i o n a l i n f l u e n c e of s i t e index was i n s i g n i f i c a n t . TABLE 28 LINEAR REGRESSION EQUATIONS FOR THE AVERAGE HEIGHT TO THE LOWEST LIVE BRANCH ON EACH OP POUR SIDES Independent v a r i a b l e s I n t e r -cept H D.b.h. Age H/CW BA/ac. R 2 S E / o Regression c o e f f i c i e n t s -6.4998 .6692 - - - .883 16.5 -8.9500 .9927 - 2 . 4 3 4 1 - - .937 12.2 -11.9582 .9333 -2.8015 .2121 - . 9 4 3 11.7 -13.1771 .7283 -1.528? .1345 .8263 - .952 10.9 - 1 1 . 2 3 8 8 .8537 -2.4588 .09839 .05998 .956 10.4 -9.9254 .8710 -2.2750 - .06550 .955 10.4 -11.7368 .6981 -1.3366 .6991 .05533 .961 9.7 -11.5790 .7357 - 1 . 1 4 4 1 .9364 .950 11.0 -o / • V . GROWTH LIMITS OF LODGEPOLE PINE INTRODUCTION Smith, Ker and Csizmazia (l96l) concluded from their study of the economic and biological effects on tree growth in the Vancouver Forest District, that trees should be grown as rapidly as possible to a minimum merchantable limit of 12 inches in d.b.h. They suggested that under extensive management stands should be grown at open den-s i t i e s in youth and be allowed to approach a normal density at harvest size. Such stand manipulation would not at present be economically feasible for the widely occurring, less valuable lodgepole pine. However the increasing attention being paid to the species, particularly by speciality mills equipped to handle small-sized material, warrants an investigation into the maximum rate of growth that could be expected i f lodgepole pine were to be managed on an "open-grown" basis. Radial and basal area growth over the last five years has been studied earlier for both open-grown and forest-grown individual trees. Estimation was found to be inadequate, due mainly to the high tree-to-tree variation. For this portion of the study total or cumulative growth of groups of trees w i l l be related to site and density d i f f e r -ences. Any restrictions that may have to be made on maximum growth rates due to a deleterious effect on market value w i l l be determined and appropriate recommendations made. As site quality cannot be manipulated as readily as stand den-sity , the effect of site differences w i l l be discussed f i r s t . Site index w i l l be related to site differences and in turn related to cumulative radial growth. THE R E L A T I O N OF SITE INDEX TO SITE FACTORS The average s i t e index determined f o r each s i t e s e r i e s sampled was compared with the average depth to the "C" horizon and with the average moisture regime f o r each s i t e (Figure j). Three of the s i t e s e r i e s sampled ( s e r i e s 100, 200 and 600) were located within the area studied by Illi n g w o r t h f o r h i s lodgepole pine s i t e c l a s s i f i c a t i o n system ( i l l i n g w o r t h and A r l i d g e , i960). The average s i t e index f o r each of these s i t e s was compared with the average tree height at 100 years reported by I l l i n g w o r t h . For areas that he c l a s s i f i e d as the Calamagrostis - A r c t o s t -phylos s i t e type, Illi n g w o r t h found an average height of 65 feet at age. 100. This f i g u r e compares favourably with the average s i t e index of 62 determined i n the course of t h i s study f o r t h i s s i t e type. S i m i l a r l y with the 600 s i t e s e r i e s , a Calamagrostis type, the reported height at 100 years i s i d e n t i c a l with the average s i t e index derived f o r the s i t e s e r i e s . However with the 200 s i t e s e r i e s , c l a s s i f i e d as a Cornus-Moss type, there i s a discrepancy. Illi n g w o r t h found that the height at 100 f o r these s i t e s averages 86 f e e t . From the data c o l l e c t e d , average s i t e index of the 200 s i t e s e r i e s was found to be 75. This discrepancy may be due to the 200 s i t e s e r i e s not being a t y p i c a l Cornus - Moss type, or due to an accumulation of errors i n the method used to obtain values f o r s i t e index. This p o s s i b i l i t y has been discussed previously. Illin g w o r t h noted the importance of s o i l moisture i n determin-i n g the p r o d u c t i v i t y of a s i t e . The wetter s i t e s had the greater pro-d u c t i v i t y . The observations made i n the course of t h i s study support t h i s c o n c l u s i o n i n g e n e r a l . However on the wetter s i t e s sampled (peat bogs) the extreme moisture c o n d i t i o n s r e s u l t e d i n a r e d u c t i o n i n pro-d u c t i v i t y as measured by s i t e index. A s i m i l a r c u r v i l i n e a r r e l a t i o n -s h i p between t r e e growth and s o i l moisture was reported by Duffy (1962) i n h i s study of the r e l a t i o n s h i p s between s i t e f a c t o r s and the growth of the lodgepole p i n e . He found that growth increased w i t h increase i n s o i l moisture up to 5 to 6 inches of a v a i l a b l e s o i l moisture i n the surface 36 inches o f p r o f i l e . A d d i t i o n a l a v a i l a b l e moisture d i d not r e s u l t i n any f u r t h e r i n c r e a s e i n tree growth. The e f f e c t of s o i l depth was masked by the e f f e c t of moisture. Reference to Figure 3 i n d i c a t e s t h a t the most productive s i t e s of those s t u d i e d are, apparently, the most shallow. These shallow s o i l s were from two areas on Vancouver I s l a n d , one o f which was c l a s s i f i e d as "wet", the other as "moist". With the e f f e c t o f s o i l moisture e l i m i n a t e d i t i s probable t h a t the more productive s i t e s would be shown to be a s s o c i -ated w i t h the deeper s o i l s . ASSOCIATION BETWEEN CUMULATIVE RADIAL GROWTH AND AVERAGE SITE INDEX FOR  SAMPLING AREAS. Cumulative R a d i a l Growth Related to Sampling Areas. At the time of c o l l e c t i o n the data were segregated i n t o twelve s i t e s e r i e s , seven f o r the open-grown and f i v e f o r the forest-grown data. R e c l a s s i f i c a t i o n reduced t h i s number to f o u r open-grown and t h r e e forest-grown s i t e s . Each o f these seven s i t e s was based on ground v e g e t a t i o n , l o c a t i o n and s o i l s i m i l a r i t i e s . This s t r a t i f i c a t i o n was the b a s i s f o r the f i r s t a n a l y s i s , an attempt t o r e l a t e cumulative r a d -i a l growth to the average s i t e index determined f o r each p a r t i c u l a r s i t e s e r i e s . A summary of the more important data i s given i n Table 4. Data on r a d i a l growth were obtained from increment cores from 83 open-grown and 63 forest-grown trees. Growth was measured f o r the l a s t twenty-years at five-year i n t e r v a l s , and then at i n t e r v a l s of ten years to the p i t h . Age at breast height f o r each tree of a s i t e s e r i e s was assumed to be the average f o r that p a r t i c u l a r s e r i e s . Graphs were prepared r e -l a t i n g the cumulative r a d i a l growth of i n d i v i d u a l trees to t o t a l age f o r each s i t e sampled (Appendix 2, a - f ) . Two sets of l i n e a r and parabolic regression equations were f i t t e d to the data, one from breast height age to age 50, and the other from breast height age to the maximum age recorded f o r each s i t e . For the forest-grown data, s i m i l a r equations were also developed f o r r a d i a l growth up to ages of 25 and 30. The regression equations with t h e i r respective c o r r e l a t i o n co-e f f i c i e n t s and standard errors of estimate are l i s t e d i n Tables 29 and 31. For purposes of comparison the standard e r r o r of estimate i t s e l f i s preferable to i t s expression as a percentage of the t o t a l r a d i a l growth. Each equation i n each s e r i e s applies to a d i f f e r e n t range of values, consequently the average value f o r the t o t a l r a d i a l growth w i l l vary f o r each equation. Both l i n e a r and parabolic equations accounted f o r a s i m i l a r per-centage of the t o t a l v a r i a t i o n i n r a d i a l growth. The l i n e a r equations f o r the period, breast height age to maximum age, were chosen to ac-count f o r the r a d i a l growth of trees on a l l s i t e s . These equations were plotted on the appropriate graphs to a i d comparison. Average d.b.h. at age 50 and the average s i t e index values of TABLE 29 LINEAR AND PARABOLIC REGRESSION EQUATIONS FOR CUMULATIVE RADIAL GROWTH OF OPEN-GROWN TREES FOR SITE SERIES Site series No. of observts Range in age Equation type Inter-cept Regression coefficients Bl B2 E 2 SE„ E 100 171 6 - 5 0 linear - . 7 1 7 7 .1360 .804 .892 36.9 para. -.8809 .1545 -.0003746 .805 .8896 36.9 256 6 -120 linear -.2936 .1166 .853 1.176 29.4 para. -.8732 .1550 -.0004311 .863 1.1335 28.3 200 158 6-45 linear -1.3182 .2073 .917 .6726 24.3 para. -1.4422 .2226 -.0003496 .918 .6714 24.2 300 68 9 - 4 6 linear -1.35078 .1412 .865 .6611 31.1 para. -1.0861 .1154 +.0004996 .866 .6579 30.9 600 35 5 - 61 linear -.08294 .1123 .870 .5853 33.4 para -.8441 .2034 -.001643 .924 .4451 25.4 each of the open-grown s i t e s e r i e s are presented i n Table 30. A Duncan's Mult i p l e Range te s t confirmed that except f o r the average s i t e index f o r the 200 and 300 s i t e s which were not s i g n i f i c a n t l y d i f -f erent, average values f o r s i t e index were s i g n i f i c a n t l y d i f f e r e n t be-tween the s i t e s from which the data on open-grown trees were obtained. However, as inspection of Table 30 shows, there i s l i t t l e c o r r e l a t i o n between average s i t e index and average d.b.h. at age 50 f o r the open-grown s i t e s e r i e s . This i s s u r p r i s i n g as, i n the absence of tree competition, increase i n r a d i a l growth i s r e l a t e d to s i t e q u a l i t y , normally defined i n terms of s i t e index. The explanation may be that the r a d i a l growth data f o r the i n d i v i d u a l trees were very v a r i a b l e ; the average c o e f f i c i e n t of v a r i a t i o n f o r a l l four s i t e s was 82 per-cent, while the v a r i a t i o n i n s i t e index was d i s t i n c t l y l e s s (c.v. = 23.2$). This would imply that even although correlated there would be a wide range of r a d i a l growth values associated with the s i t e index of the i n d i v i d u a l trees. The range of s i t e index f o r the i n d i v i d u a l trees i s more than twice that f o r the s i t e s e r i e s themselves (Table 4). Consequently, s t r a t i f y i n g the growth data by s i t e s e r i e s r e s u l t s i n a decrease i n the range of s i t e index values and a corresponding increase i n the v a r i a b i l i t y of the growth data associated with each s i t e . This r e s u l t implies that the p r e c i s i o n with which a vegetative s i t e c l a s s i f i c a t i o n system assesses r a d i a l growth i s considerably l e s s than i f s i t e index i s used d i r e c t l y as a basis f o r s t r a t i f i c a t i o n . E f f e c t s of s i t e index on the growth rate of forest-grown trees are masked by the influence of stand density. Regression equation are given f o r the three s i t e s e r i e s analysed (Table 3 l ) . Comparison between the 1000 and 1100 s e r i e s shows that with greater basal area per acre r a d i a l growth i s l e s s despite an increase i n s i t e index. However, as f o r the data on open-grown trees, the s t r a t i f i c a t i o n by vegetation or physiographic s i t e may not have demonstrated a c o r r e l a t i o n between s i t e index and the growth r a t e . TABLE 30 AVERAGE D.B.H. AT AGE 50 IN RELATION TO AVERAGE SITE INDEX FOR OPEN-GROWN SITES S i t e Series Average S i t e Index D.b.h. at 50 years from regression equations 100 62 * 12.16 200 75 18.8 * 300 77 11.54 600 84 * 11.06 * S i g n i f i c a n t l y d i f f e r e n t values. CUMULATIVE RADIAL GROWTH RELATED TO SITE INDEX To provide an estimate of the e f f e c t of s i t e index on diameter growth, the open-growth data were s t r a t i f i e d d i r e c t l y into s i t e index classes and a grap h i c a l analysis made on the change of d.b.h. with age ( F i g s . 4-7). To reduce the time involved, data from increment cores were not used, the d.b.h. of each tree being p l o t t e d over t o t a l age. A l i n e a r regression were f i t t e d to the data on each s i t e c l a s s by the "short cut" method suggested by Ker and Smith (1955). TABLE 31 LINEAR AND PARABOLIC REGRESSION EQUATIONS FOR CUMULATIVE RADIAL GROWTH OF FOREST-GROWN TREES FOR SITE SERIES Site No. of Range Equation Inter- Regression coefficients R S E E series observts in age. type cept Bl B2 1000 29 6-25 linear -.7615 .1381 .867 .3902 34.3 para. -1.1144 .2003 -.002105 .873 .3822 33.5 39 6-30 linear -.5933 .1214 _ .833 .4903 32.0 para. -1.1259 .2048 -.002404 .846 .4717 30.8 71 6-?6 linear -.03328 .08486 _ .708 .7248 31.6 para. -1.0783 .1969 -.002190 .772 .6407 28.0 1100 48 5 - 25 linear -.6095 .1321 _ .901 .3346 29.5 para. -.8203 .1729 -.001413 .905 .3290 28.8 54 5-30 linear -.5656 .1274 _ .898 .3733 28.0 para. -.8133 .1718 -.001393 .903 .3650 27.4 89 5-50 linear -.3010 .1064 _ .853 .6734 28.0 para. -.6588 .1480 -.0007996 .860 .6569 27.8 159 5 - 75 linear +.1876 .08394 _ .702 1.2425 33.3 para. -.7269 .1551 -.0009104 .730 1.1824 31.7 800 lfi4 9-25 linear -1.0313 .1181 _ .875 .2605 33.4 + para. -1.3301 .1611 -.001338 .87? .2587 33.2 1200 156 9-30 linear -.8194 .1021 - .866 .3635 28.1 para. -1.266? .1545 -.001248 .873 .3547 27.5 209 9 - 5 0 linear -.7196 .09636 — .850 .5024 28.0 para. -1.0335 .1261 -.0005529 .854 .4961 27.5 217 9-56 linear -.7465 .09764 _ .861 .5163 27.2 para. -.8927 .1109 -.0002340 .862 .5148 27.2 Average d.b.h., values were extracted from these graphs and p l o t t e d over the average s i t e index of the four s i t e s f o r t o t a l ages 30, kO and 50 years ( F i g . 8). The best s t r a i g h t l i n e was f i t t e d to the p l o t t e d points f o r each age group using the standard r u l e s f o r curve f i t t i n g . The f i n a l d.b.h. over t o t a l age curves, grouped by s i t e index clas s e s , were found to be s l i g h t l y c u r v i l i n e a r . Straight l i n e s were f e l t to adequately express the regression of d.b.h. with age f o r each s i t e c l a s s . The r e s u l t i n g group of d.b.h./age curves ( F i g . 9) does not pur-port to be a precise d e f i n i t i o n of changes i n d.b.h. with age and s i t e index f o r open-grown trees. The assumption that the r e l a t i o n s h i p be-tween d.b.h. and both age and s i t e index i s l i n e a r and use of the "short cut" method i n f i t t i n g the o r i g i n a l d.b.h./age curves, both a f f e c t the s o l u t i o n . These assumptions may be j u s t i f i e d on two grounds: one, that use of a l i n e a r regression has been shown to adequately account f o r the d.b.h./age r e l a t i o n s h i p up to a t o t a l age of 50 years, and appears to account f o r the regression of d.b.h. with s i t e index f o r a s i m i l a r period, and two, the number of trees within each s i t e class was small, p a r t i c u l a r l y i n s i t e c l a s s 91 - 110 ( F i g . 7). A more pre-c i s e procedure did not appear warranted by the data. With these assumptions i n mind and with an appreciation that the f i n a l group of curves w i l l provide close approximations rather than precise estimates, the change i n d.b.h. with age of open-grown trees on d i f f e r e n t s i t e s may be d i r e c t l y compared with the growth rates of f o r -est-grown stands within the range covered by the data. 89 92 93 94 GROWTH COMPARISONS I t w i l l be r e c a l l e d that the forest-grown data c o l l e c t e d i n t h i s study were s e l e c t e d p a r t l y to provide samples from stands having a wide range i n d e n s i t y (Table k). Consequently, the data do not represent f u l l y stocked stands. To provide a comparison of r a t e s of growth on d i f f e r e n t s i t e s f o r f u l l y stocked stands, data from the B r i t i s h Columbia Forest S e r v i c e y i e l d t a b l e f o r lodgepole p i n e , d i s t r i b u t e d i n 19^7 were used ( F o r e s t Club, 1959, pp. kl6-kld). The a c c e l e r a t e d growth r a t e f o r the open-grown tr e e s may be compared w i t h the "normal" growth r a t e o f the f u l l y stocked stands i n Tables 32 and 33. Smith, Ker and Csizmazia (l96l) compared the estimated growth o f Douglas f i r and western hemlock grown at open d e n s i t i e s w i t h dense grown stands. They concluded t h a t f o r a l l s i t e q u a l i t i e s the time r e q u i r e d to reach a s p e c i f i e d d.b.h. i s halved i f t r e e s are f u l l y open-grown. Data s e l e c t e d from t h e i r estimates f o r Douglas f i r growth are compared w i t h s i m i l a r data on lodgepole pine (Table 36). Comparison between the two species i s complicated by t h e i r d i f f e r e n t height growth c h a r a c t e r i s t i c s . Lodgepole pine i s _ s h o r t e r and has an e a r l i e r growth cu l m i n a t i o n than Douglas f i r . A s i t e index o f 90 f o r lodgepole pine represents a s i t e o f above average q u a l i t y ; a Douglas f i r s i t e index o f 90 i n d i c a t e s one of the poorer s i t e s f o r the s p e c i e s . Re-le a s e from stand competition has a grea t e r e f f e c t on lodgepole pine growth than on f i r . Douglas f i r stands of s i t e index 90 take approxi-mately 120 years to a t t a i n a d.b.h. o f 12 in c h e s . Lodgepole pine grow-i n g on a lodgepole pine s i t e index of 90 r e q u i r e s a s i m i l a r l e n g t h of time. The time r e q u i r e d f o r the pine to reach an intermediate d.b.h. i s , 96 TABLE 3 2 AVERAGE D.B.H. OP OPEN-GROWN (O-G) AND FOREST-GROWN (F-G) LODGEPOLE PINE AT AGES 3 0 , 40, and 5 0 YEARS Height T o t a l age at age 30.YTS. 40yrs. 50yrs. 80 100 F-G 0-G F-G 0-G F-G 0-G 40 44 7.5 6.0 9.0 6.4 10.5 5 0 5 2 - 7.9 6.1 9 . 8 6.6 11.6 60 65 - 8.4 6.1 11.0 6.8 13.4 70 73 6.0 8.9 6.6 11.7 7 .2 14.5 80 87 6 .2 9.5 7.0 13.0 7.7 16.5 90 98 6 ) . 9 10.1 7.5 14.1 8 .2 18.0 TABLE 33 NUMBER OF YEARS REQUIRED FOR OPEN-GROWN Al© NORMALLY GROWN LODGEPOLE PINE TO REACH A SPECIFIED DIAMETER H@100 yrs. 44 52 6 5 73 87 98 80 yrs. 40 50 60 7 0 80 9 0 Av. i.b.h. F-G,J-• 0-G F-G 0-G F-G 0-G F-G 0-G F-G 0-G F-G 0-G 6 40 1 9 3 8 2 0 36 2 0 3 1 2 0 28 2 0 2 5 2 0 7 66 26 6 0 2 5 55 24 46 2 3 40 2 3 3 5 22 8 1 3 0 3 3 1 0 0 3 0 8 4 28 7 0 2 7 5 6 2 6 4 7 2 5 9 * 4 7 » 36 140 3 2 1 0 0 3 1 76 2 9 60 2 7 1 0 -* * 41 * 3 6 1 5 0 3 4 1 0 3 32 7 7 3 0 1 2 # # * 41 # 41 * 3 7 120 35 14 # * # * * * * 4 8 * 43 # 40 1 6 * * * •* * * 49 * 44 1. Based on B.C. Forest Service normal y i e l d table f o r lodgepole pine. of course, l e s s than f o r Douglas f i r . However, i f both species had been grown to the same d.b.h., but at open d e n s i t i e s the time taken would have been d i s t i n c t l y d i f f e r e n t . Douglas f i r requires between 60 and 70 years to reach a d.b.h. of 12 inches on s i t e s having an index o f 90. Lodgepole pine growing on a pine s i t e of index 90 requires only 35 to 40 years. This increased growth i s only matched, or ex-ceeded, by Douglas f i r when open-grown on the better Douglas f i r s i t e s . In short, the rate of growth of lodgepole pine grown at open d e n s i t i e s on a s i t e ranked as, say, "good" f o r the species, appears to be very much the same as f o r Douglas f i r s i m i l a r l y grown at open d e n s i t i e s on s i t e s classed as "good" f o r Douglas f i r growth. MARGINAL TREE SIZE Lodgepole pine as small as seven inches d.b.h. i s presently being harvested from timber sales i n the I n t e r i o r of B.C. Doyle (1957) and Doyle and Calvert (l96l) found marginal tree sizes of 6.4 and 7.4 inches d.b.h. r e s p e c t i v e l y f o r operations i n spruce and balsam f i r stands i n Nova S c o t i a , and 7.4 inches d.b.h. f o r operations i n jack pine i n Northern Ontario. Differences i n the logging methods studied may have aff e c t e d these s i z e s . Both areas practised horse skidding, but i n Nova S c o t i a cross-cut saws and hand-loading methods were used. In Northern Ontario, power saws and mechanical loading presumably r e s u l t e d i n a d i f -f e r e nt t o t a l cost structure. With the equipment presently used i n B r i t i s h Columbia, i t i s un-l i k e l y that any of these marginal tree s i z e s would apply. Nine inches d.b.h. would be a c l o s e r approximation. Methods of complete tree harvesting from stump to landing are c u r r e n t l y being investigated i n Eastern Canada. I f shown to be success-f u l i n reducing logging costs, then t h ^ s i z e of the marginal tree w i l l be a f f e c t e d . However, marginal tree s i z e denotes only the break-even point f o r a p a r t i c u l a r operation. The optimum tree s i z e , u t i l i z i n g equipment presently used f o r both logging and m i l l i n g operations i n many lodgepole pine operations i n the I n t e r i o r of B r i t i s h Columbia, would be between 15 and 16 inches d.b.h. Above t h i s s i z e conventional m i l l s would be more e f f i c i e n t ; be-low t h i s s i z e , costs per u n i t volume increase. Prom the information contained i n Tables 32 and 3 3 , i t would appear that i f c o n t r o l of density of lodgepole pine stands were econom-i c a l l y f e a s i b l e , then the production of open-grown trees should be encouraged. On the b e t t e r s i t e s , a forty-year r o t a t i o n would produce trees from 12 to 14 inches d.b.h., twice the s i z e of normally grown t r e e s . However, growing lodgepole pine on t h i s basis would not neces-s a r i l y be d e sirable, due to the incomplete u t i l i z a t i o n of s i t e , and the lower q u a l i t y of wood produced. LIMITATIONS ON MAXIMUM GROWTH RATES Growing t r e e s at themaximum r a t e p o s s i b l e f o r a p a r t i c u l a r s i t e i s n e c e s s a r i l y accompanied by a r e d u c t i o n i n the number o f stems per acre. This r e d u c t i o n p l u s the reduced height f o r any s p e c i f i e d d.b.h. r e s u l t s i n a t o t a l volume per acre c o n s i d e r a b l y l e s s than f o r normally grown stands o f the same d.b.h. A numerical example, u s i n g y i e l d t a b l e s , s i t e index curves and volume t a b l e s published by the Forest S e r v i c e , Department o f Lands, Forests and Water Resources o f the Pro-v i n c e o f B r i t i s h Columbia w i l l i l l u s t r a t e the extent o f the d i f f e r e n c e . I f 12 inches i s s e l e c t e d as the average d.b.h. o f the two stands, then the number of stems per acre, assuming a uniform, square spacing i s 2 g i v e n by 43,56o/CW • Using the r e l a t i o n e s t a b l i s h e d e a r l i e r (CW = 4.24 + 1.58 d.b.h) the number of tr e e s t h a t would be f u l l y open-grown and average 12 inches d.b.h. would be 81. Assuming a s i t e index ( r e f e r e n c e age of 80) of 90, the average t r e e height would be app r o x i -mately 45 f e e t . With c l o s e u t i l i z a t i o n , merchantable volume would be approximately 14 cubic f e e t per t r e e , or 1,134 cubic f e e t per acre. The merchantable volume of a normally grown stand o f equivalent d.b.h. i s approximately 9,000 cubic f e e t per acre. Smith et a l . (l96l) have suggested an "open-to-normal" model which progresses from i n i t i a l l y wide spacing t o the normal d e n s i t y at the d e s i r e d h a r v e s t i n g s i z e . By f o l l o w i n g t h i s model i t i s claimed a r e d u c t i o n i n the volume per acre would not be as s o c i a t e d w i t h an increas e d , though l e s s than-maximum, growth r a t e . The age at which the crowns are allowed to c l o s e i f t h i s model i s f o l l o w e d can be considered t o be the key i n c o n t r o l l i n g both the 100 growth r a t e and the degree of n a t u r a l pruning d e s i r e d . The e a r l i e r t h i s age i s s e t , the more c l o s e l y w i l l the stand approach a completely nor-m a l l y grown stand. Consequently, those aspects of wood q u a l i t y t h a t are a f f e c t e d by the r a t e of growth, the p e r s i s t e n c e of a l i v e crown or the degree of branchiness can be c o n t r o l l e d to a considerable extent. KNOT SIZE The r e d u c t i o n i n t o t a l volume on a area b a s i s , when lodgepole pine i s grown t o a s p e c i f i e d merchantable s i z e , has been discussed. The p o s s i b i l i t y of necessary r e s t r i c t i o n s on the growth r a t e due t o u n d e s i r a b l e e f f e c t s of a t e c h n i c a l or economic nature should a l s o be considered. Of the n a t u r a l f e a t u r e s of wood that i n f l u e n c e e i t h e r i t s value or i t s u s e f u l n e s s , r i n g width and the number, s i z e and type of knots are the two most obvious c h a r a c t e r i s t i c s a f f e c t e d by stand d e n s i t y . For c e r t a i n f o r e s t products other c h a r a c t e r i s t i c s o f wood may be of g r e a t e r importance. S i z e and s t r a i g h t n e s s of stem, always d e s i r a b l e , are of major importance f o r poles or p i l i n g . I n t e r n a l wood q u a l i t i e s such as f i b r e l e n g t h or s p e c i f i c g r a v i t y would assume g r e a t e r importance i f lodgepole pine i s to be grown f o r p u l p i n g . The d i s c u s s i o n of p o s s i b l e l i m i t a t i o n s t h a t may be necessary w i l l centre on the manufacture of lumber. F i r s t , because lumber i s the main product manufactured from lodgepole p i n e , and secondly, because a c o n s i d e r a t i o n of the e f f e c t of maximum growth r a t e on lumber values w i l l a s s i s t e v a l u a t i o n f o r other products. Lodgepole pine lumber from B r i t i s h Columbia i s marketed under the Standard Grading Rules of the Western Pine A s s o c i a t i o n , P o r t l a n d , 101 Oregon. C h a r a c t e r i s t i c s that are considered under the va r i o u s grades i n c l u d e the s i z e , frequency and k i n d of knot, check, shake, p i t c h pockets, sap s t a i n s , worm holes and manufacturing d e f e c t s , but not closeness of g r a i n . Of these " d e f e c t s " , the s i z e and number of knots may be c o n t r o l l e d p a r t i a l l y by manipulation of stand d e n s i t y . Allow-a b l e knot s i z e s f o r Common and Dimension grades of lumber only w i l l be considered. Very l i t t l e c l e a r lumber i s manufactured from f o r e s t or normally grown pine; even l e s s would be produced from open-grown stock without a r t i f i c i a l pruning. When gra d i n g f o r Common lumber appearance i s b e i n g evaluated f a r more than f o r Dimension lumber i n which high s t r u c t u r a l s t r e n g t h i s the c h i e f r e q u i s i t e . Knots, c l a s s i f i e d as sound or unsound, t i g h t or lo o s e , are permitted i n a l l Common and Dimension grades, the allowance depending on the s i z e of lumber and the purpose f o r which the wood i s intended. I n the b e t t e r grades of Common lumber, f o r example, knots are r e s t r i c t e d to e i t h e r s e v e r a l sound, t i g h t knots that are not over 3/4" i n diameter, or to a few l a r g e r ones. As an example, f o r a board 1" by s i x inches - 16 f e e t long, twelve 3/4" knots would be permitted, w h i l e f o r a board 8 inches wide up to f i v e s i m i l a r l y sound 2" knots would be allowed. The r e s t r i c t i o n s become p r o g r e s s i v e -l y l e s s r i g i d u n t i l i n the lower grades of Common lumber, a board ten inches wide w i t h a dozen l a r g e knots, 2 to 3 inches i n diameter w i l l be permited i n the No. 3 Common grade. Dimension grades are more s p e c i f i c w i t h regard t o knots. D e f i n i t e maximum knot s i z e s are e s t a b l i s h e d f o r each width i n each grade. For example, No. 1 Dimension admits sound knots up to 1 l / 2 " 102 f o r f o u r - i n c h widths, up to 2" f o r s i x - i n c h widths, 2 l / 2 " f o r e i g h t -i n c h widths, 2 3/4" f o r t e n - i n c h widths and ,up t o 3." knots f o r twelve-i n c h widths. No. 3 Dimension, the lowest grade of Dimension lumber commonly shipped, permits knot s i z e s up to 2 l / 2 " f o r f o u r - i n c h widths, 3 1/4" knots f o r s i x - i n c h widths, 3 3/4" f o r e i g h t - i n c h widths, 4 l / 2 " f o r t e n - i n c h and 5" knots f o r widths of lumber twelve inches or wider. With the importance of the s i z e of knot i n grading e s t a b l i s h e d , i t i s p o s s i b l e to evaluate the e f f e c t on lumber grades of p e r m i t t i n g t r e e crowns t o develop n a t u r a l l y i n the f u l l y open-grown stand. With regard to the production of lumber from h e a v i l y branched l o g s , McBride (1963) observed t h a t when small l o g s from tops of t r e e s are sawn i n t o lumber, the number and s i z e of knots i s u s u a l l y enough t o make the boards run h e a v i l y to No. 3 Common. This i l l u s t r a t e s not only the importance of knot s i z e and frequency, but a l s o the r e l a t i v e e f f e c t of lumber width on the permitted knot s i z e f o r the r e s p e c t i v e grades. In the course of the present study the r e l a t i o n s h i p between l i v e branch l e n g t h and l i v e branch diameter o u t s i d e bark of the l a r g e s t l i v e branch on a t r e e was e s t a b l i s h e d . I t may be expressed as: Branch d.o.b. = - 0.233 + 0.336 (LLbr) ; / = 0.837, SEJ> = 2?.2$ Using t h i s r e g r e s s i o n , and the r e l a t i o n s h i p between crown width and d.b.h., i t i s p o s s i b l e to estimate the s i z e of the b u t t diameter of the l a r g e s t branch of an open-grown t r e e f o r any s p e c i f i e d d.b.h. Double bark t h i c k n e s s at breast height f o r open-grown tr e e s was found to be r e l a t e d to d.b.h. by the expression: Dbk - 0.0708 + 0.0614 (d.b.h); r 2 = 0.814, S E ^ = 28.3$ By assuming that a s i m i l a r r e l a t i o n s h i p i s tru e f o r 'branch hark an e s t i -mate o f knot s i z e may be made. I f f o r i l l u s t r a t i v e purposes a d.b.h. of 12 inches i s assumed f o r a f u l l y open-grown t r e e , the estimated width of the crown i s about 23.2 f e e t . Average maximum l i v e branch l e n g t h may then be assumed to be approximately I I f e e t . Using t h i s value f o r the v a r i a b l e LLbr i n the equation given above r e s u l t s i n an estimated average maximum branch diameter outside bark o f approximately 3 l/2 inches. I f knot s i z e i s assumed t o be equivalent to branch diameter outside bark l e s s double bark t h i c k n e s s , then the estimated maximum knot s i z e i s approximately 3 l/k inches. This i s the s i z e o f the maximum knot i n the outermost l a y e r of wood. The average knot would be much s m a l l e r . The importance of maximum knot s i z e has been discussed above w i t h reference to the s p e c i f i c a t i o n s e s t a b l i s h e d by the W.P.A. f o r Common and Dimension lumber grades. The top diameter i n s i d e bark of a 16 fo o t butt l o g may be ap-proximated by deducting two inches from the d.b.h. outside bark. For the example t h i s would give a l o g s i z e of te n inches. Most of the boards developed from a l o g o f t h i s s i z e would be ei g h t inches i n width (Table 34). When graded f o r appearance an e i g h t - i n c h board w i t h a 3 l/4 i n c h l i v e knot on the graded face would be graded as e i t h e r No. 3 Common or No. 4 Common depending on the frequency o f a d d i t i o n a l knots. As i n t h i s case the lumber i s from open-grown tre e s w i t h l i v e branches extending almost t o the ground, the board w i l l probably be graded as No. 4 Common. However, very few of the boards manufactured would have a knot as l a r g e as 3 l/4 inches. Knots of t h i s s i z e would occur only i n the 104 TABLE 34 DISTRIBUTION OP LUMBER WIDTHS BY LOG SIZE Diameter Lumber widths i n inches developed i n s i d e bk. at small 4 6 8 10 end of 16ft. l o g ? b of widths developed 6 80 20 -7 36 64 -8 34 61 5 9 14 32 54 10 9 18 73 11. 9 21 24 46 ( l ) Based on McBride (1963). TABLE 35 LUMBER GRADE RECOVERY BY LOG DIAMETER FOR POREST-(1) GROWN LODGEPOLE PINE Diameter W.P.A. Grade f o r boards i n s i d e bk. at small fo Recovery-end of 16ft. C l e a r No.2 and No.3 No.4 l o g B e t t e r Common Common 6 51 41 8 7 38 55 7 8 57 41 2 9 41 54 5 10 42: IP 11 29 59 12 (1) based "on McBride (1963). 105 TABLE 36 COMPARISON OP GROWTH RATES OP LODGEPOLE PINE WITH DOUGLAS FIR FOR OPEN-GROWN AND FOREST-GROWN TREES Forest-grown Open-grown F i r PI F i r P I S i t e index 140 9 0 ( 1 ) (2) 90 v J 140 9 0 ( D 90 « D.b.h. Years to grow to d.b.h. shown V ™ . 6 33 54 25 21 32 20 8 44 72 47 26 41 . 25 10 53 96 77 31 53 30 12 65 123 120 37 66 35 (1) I n t e r p o l a t e d from published t a b u l a t e d data, Smith et al'e(l96l). (2) Reference age 80 y e a r s . outermost p o r t i o n of the l o g . Much of t h i s p a r t of the l o g i s removed i n the form of slabs or edgings. I f t h i s l o s s i s assumed equ i v a l e n t to a l o s s of one i n c h i n depth then the s i z e of the average maximum knot i s reduced t o about 2.9 inches (obtained through a r e p e t i t i o n of the previous c a l c u l a t i o n u s i n g a d.b.h. of 10 i n c h e s ) . I n p r a c t i c e r e -d u c t i o n i n knot s i z e could be consid e r a b l y g r e a t e r . Due to the pro-g r e s s i v e r e d u c t i o n i n knot s i z e towards the p i t h , the e f f e c t o f heavy s l a b b i n g could r e s u l t i n the l a r g e s t knots being reduced by as much as 1 l / 2 inches. This would mean the maximum knot would be reduced to about 1 3/4 inches i n diameter. The permitted p r a c t i c e of grading from { the best face f o r Common grades has a s i m i l a r e f f e c t i n decreasing any adverse e f f e c t on grade due to knot s i z e . With a 2-inch t h i c k board, cut t a n g e n t i a l l y , there would be a d i f f e r e n c e of more than an i n c h between the s i z e of a knot on the two f a c e s . As there would be very few dead branches on open-grown lodgepole p i n e , r e j e c t i o n from the b e t t e r to the poorer grades on account of dead or loose knots would be at a minimum. Co n s i d e r a t i o n o f these f a c t o r s supports the c o n c l u s i o n t h a t w hile lumber from open-grown t r e e s w i l l have bigger and more numerous l i v e knots than lumber from forest-grown t r e e s , the e f f e c t of these knots w i l l not n e c e s s a r i l y r e s u l t i n much degrade of most of the lumber. Grades of s i d e lumber w i l l be mainly a f f e c t e d , due t o the l a r g e r knots i n the outermost l a y e r o f wood i n the l o g . The average q u a l i t y o f lumber w i t h i n a grade w i l l be reduced, r e s u l t i n g i n a "low-l i n e " product. The marketing problems a s s o c i a t e d w i t h such a product th a t ^ a l t h o u g h meeting the requirements of the grading r u l e s , may have to compete w i t h lumber of a more p l e a s i n g appearance, would l i k e l y be almost as s i g n i f i c a n t as a c t u a l degrade. 107 I f the h y p o t h e t i c a l eight i n c h boards were to be used f o r s t r u c -t u r a l purposes, then both faces o f the board have to be considered. I t i s l i k e l y t hat as the maximum permitted knot s i z e f o r an e i g h t - i n c h wide board i s 2 l / 2 inches f o r No. 1 Dimension and 3 l / 2 f o r No. 2 Dimension most boards would be graded as No. 2 Dimension. Many m i l l s h a n d l i n g lodgepole pine are s p e c i a l t y m i l l s , designed to manufacture 2" by 4" studs. The maximum permitted l i v e knot s i z e f o r nominal f o u r - i n c h widths i s 1 l / 2 " f o r No. 1 Dimension, 2" f o r No. 2 and 2 l / 2 inches f o r No. 3. With a maximum s i z e of between two and three inches, much of the small dimension produced from open-grown trees would be graded as No. 3 Dimension. For these m i l l s knot s i z e i s evid e n t -l y more c r i t i c a l than f o r a more f l e x i b l e m i l l . I n the production of r a i l r o a d t i e s , knot s i z e may be a l i m i t i n g f a c t o r . Knots w i t h diameters up to one t h i r d of the face width are allowed i n a l l grades of t i e s , p r o v i d i n g they are sound and t i g h t . With a twelve-inch top diameter l o g , a 7" by 9" No. 1 t i e could be made. However, depending on t h e i r l o c a t i o n , l a r g e knots may r e s u l t i n such t i e s being r e j e c t e d or being of marginal q u a l i t y . E v i d e n t l y on the ba s i s of the examples given i t may be concluded that although growing lodgepole pine at f u l l y open d e n s i t i e s through-out the r o t a t i o n i s not accompanied by excessive r e d u c t i o n i n the aver-age grade of the product manufactured, there i s an important adverse e f f e c t , due to increased knot s i z e , on the o v e r - a l l q u a l i t y w i t h i n a p a r t i c u l a r grade. With the open-to-normal d e n s i t y model suggested e a r l i e r , the increase i n knot s i z e can be hel d to acceptable s i z e l i m i t s by c o n t r o l o f the average crown width through spacing c o n t r o l . A compromise between the advantages of r a p i d growth and the disadvantages of an excessive number and s i z e of knots has to be made. Consideration of the optimum time at which the crown canopy-should be allowed to cl o s e would be based on the end-product r e q u i r e d . I f fewer and s m a l l e r knots i n lumber are worth more than r e d u c t i o n i n the number of years r e q u i r e d to reach merchantable s i z e s , then the open-grown stage should be reduced. For the purpose of pulpwood pro d u c t i o n , other c o n s i d e r a t i o n s such as the maximum volume per a c r e , maximum pulp y i e l d per u n i t o f wood, - the maintenance of the maximum f i b r e l e n g t h and the d e s i r a b i l i t y of h i g h s p e c i f i c g r a v i t y would take precedence over the p e r m i s s i b l e s i z e o f knots. SPECIFIC GRAVITY AMD FIBRE LENGTH Lodgepole pine w i l l probably be used as pulpwood w i t h the es-tablishment of pulp m i l l s i n the I n t e r i o r of B r i t i s h Columbia. An in c r e a s e i n p u l p - y i e l d i s a s s o c i a t e d w i t h an increase i n s p e c i f i c g r a -v i t y . Both s p e c i f i c g r a v i t y and f i b r e l e n g t h are a s s o c i a t e d w i t h improved s t r e n g t h p r o p e r t i e s of pulp. I n view of the p o t e n t i a l use as pulpwood, p o s s i b l e e f f e c t s o f an increase i n growth r a t e on both these i n t e r n a l c h a r a c t e r i s t i c s of lodgepole pine should be considered. The e f f e c t of growth r a t e and seven other v a r i a b l e s , on the s p e c i f i c g r a v i t y of lodgepole pine was i n v e s t i g a t e d by Frood (1963). He r e l a t e d s p e c i f i c g r a v i t y t o coded s i t e c l a s s , latewood percent, growth r a t e , r i n g age, crown c l a s s , d.b.h., amount of heartwood and the amount and percentage of sapwood. A l l eight v a r i a b l e s used In com-b i n a t i o n accounted f o r 22.6 percent of the t o t a l v a r i a t i o n i n s p e c i f i c g r a v i t y . The r a t e of growth, the most important v a r i a b l e , accounted f o r 109 5.59 percent when used i n combination w i t h . a l l v a r i a b l e s . Frood concluded from h i s a n a l y s i s t h a t of the v a r i a b l e s used, r a t e o f growth was the most c l o s e l y associated v a r i a b l e w i t h s p e c i f i c g r a v i t y . He found the e f f e c t s of coded s i t e c l a s s and r i n g age, although s i g n i f i c a n t , were of only minor importance. From these r e s u l t s , reported by Frood, i t i s evident t h a t the r e d u c t i o n i n s p e c i f i c g r a v i t y as a r e s u l t of increased growth r a t e s w i l l be s m a l l . The lower costs a s s o c i a t e d w i t h e i t h e r a s h o r t e r r o t a t i o n or w i t h h a r v e s t i n g l a r g e r s i z e d timber w i l l more than compensate f o r the small decrease i n pulp y i e l d due to a f a s t e r growth r a t e . S a t i s f a c t o r y t o t a l volumes per acre can be achieved w i t h a f a s t e r than normal growth r a t e by f o l l o w i n g the open-to-normal d e n s i t y model d i s -cussed e a r l i e r . The r e d u c t i o n i n s p e c i f i c g r a v i t y r e s u l t i n g from r a p i d growth, although s m a l l , suggest an advantage i n lower t r a n s p o r t a t i o n c o s t s . T h i s e f f e c t would be of grea t e r value f o r shipment of lumber than f o r the t r a n s f e r of ch i p s . The author i s not acquainted w i t h any i n v e s t i g a t i o n s made on the p o s s i b l e i n f l u e n c e of growth r a t e s on the average f i b r e l e n g t h of lodgepole pine. By analogy w i t h analyses made by Smith e_t a l . (1961) 1 on the f i b r e l e n g t h o f Douglas f i r and Western hemlock i t i s pro-bable that although i n c r e a s e i n age and t r e e s i z e r e s u l t s i n longer average f i b r e l e n g t h , growth r a t e i t s e l f has no important i n f l u e n c e on f i b r e l e n g t h . I f the analogy i s v a l i d open-grown lodgepole pine t h a t has been grown to a s p e c i f i e d d.b.h., younger than forest-grown stands of the same average d.b.h., w i l l have a s h o r t e r average f i b r e l e n g t h . For both f i r and hemlock the number of r i n g s from the p i t h had the most i n f l u e n c e on f i b r e l e n g t h . However, c o n s i d e r a t i o n s of f i b r e l e n g t h alone, would not l i k e l y a f f e c t the management of lodgepole p i n e . 110 SUMMARY AND CONCLUSION Analyses o f f a c t o r s a f f e c t i n g t r e e growth and crown form o f i n d i v i d u a l lodgepole pine were made u s i n g data from 131 open-grown and 63 forest-grown t r e e s . The data were c o l l e c t e d by the author from v a r i o u s areas i n B r i t i s h Columbia covering a range of s i t e c o n d i t i o n s . Tree measurements made inc l u d e d d.b.h., h e i g h t , age, r a d i a l growth data, crown width, the diameter of the l a r g e s t branch, and f o r each of f o u r s i d e s of each i n d i v i d u a l t r e e , the average heights to the lowest dead, and lowest l i v e branches. S i t e f a c t o r s recorded were the v e g e t a t i v e s i t e c l a s s i f i c a t i o n , s o i l depth and the s o i l moisture regime. Although g r a p h i c a l methods f o r c e r t a i n phases of the study were necessary, the r e l a t i v e i n f l u e n c e of each v a r i a b l e on the t r e e character-i s t i c s i n v e s t i g a t e d was e s t a b l i s h e d by m u l t i p l e r e g r e s s i o n a n a l y s i s on an I.B.M. 1620. I n t e r p r e t a t i o n o f the r e s u l t s of these analyses was based l a r g e l y on c o n s i d e r a t i o n o f the d i f f e r e n c e s between the e f f e c t s o f v a r i -a b les from open-grown t r e e s and the e f f e c t s of the same v a r i a b l e s from forest-grown t r e e s . R a d i a l growth of i n d i v i d u a l t r e e s . R a d i a l growth f o r the l a s t f i v e ' years o f each o f 90 open-grown t r e e s was r e l a t e d t o the r a d i a l growth f o r the pe r i o d s i x to ten years ago, Rg£_-j_Q, and f i f t e e n independent v a r i a b l e s . A second a n a l y s i s was made w i t h Rg/- i r i and other v a r i a b l e s not considered important e l i m i n -6-10 f ated. Due to the great v a r i a t i o n between t r e e s a l l estimates f o r the r a d i a l growth f o r the l a s t f i v e years were found to be u n r e l i a b l e . The best s i n g l e v a r i a b l e was Rg^ 1 Q , accounting alone f o r 62 percent of the t o t a l v a r i a t i o n . Combination w i t h a d d i t i o n a l v a r i a b l e s r e s u l t e d i n only s m a l l increases i n t h i s percentage. For the forest-grown t r e e s a s i m i l a r , though even l e s s closely-a s s o c i a t e d r e l a t i o n s h i p was found. Rg, accounted f o r approximately p-10 56 percent of the t o t a l v a r i a t i o n i n the r a d i a l growth of forest-grown t r e e s f o r the l a s t f i v e y e a r s . Combination w i t h a d d i t i o n a l v a r i a b l e s increased t h i s f i g u r e s i g n i f i c a n t l y , but even w i t h Lc$, CW/D and s i t e index, the next most important v a r i a b l e s , the increase was only 10 per-cent. The standard e r r o r o f estimate was s l i g h t l y reduced from 31*7 percent to 28.6 percent. Without u s i n g Rg^ ^ the f o u r next most im-portant v a r i a b l e s , Lc$, H/CW, s i t e index and crown c l a s s accounted f o r only 31.0 percent of the t o t a l v a r i a t i o n . B a s a l area growth o f i n d i v i d u a l t r e e s . This a n a l y s i s , u s i n g the data from 83 open-grown and 63 f o r e s t -grown t r e e s , r e s u l t e d i n s i m i l a r conclusions to the a n a l y s i s of r a d i a l growth. Using BAg^ ^ alone accounted f o r 80.2 percent of the t o t a l v a r i a t i o n i n b a s a l area growth f o r the l a s t f i v e years f o r the open-grown t r e e s , and 73•3 percent f o r the forest-grown t r e e s . These percentages could not be a p p r e c i a b l y increased by the a d d i t i o n of other v a r i a b l e s . With the v a r i a b l e BAg,- n „ excluded from an estimate the o - l O best two-variable combination f o r the open-grown trees used d.b.h. and age. Together they accounted f o r 69.k percent of the v a r i a t i o n . Adding s i t e index increased t h i s f i g u r e to 72.0 percent w i t h a standard e r r o r o f 25.8 percent. The best two-variable combination f o r the forest-grown t r e e s , crown width and height/crown width ( r e l a t e d t o b a s a l area per acre and stand d e n s i t y ) accounted f o r only 33.1 percent. 112 Prom the preceding analyses, i t may be concluded that no s a t i s -f a c t o r y method of e s t i m a t i n g r a d i a l or b a s a l area growth f o r the l a s t f i v e years of i n d i v i d u a l t r e e s was found. The best growth e s t i m a t i o n was that f o r b a s a l area of open-grown t r e e s . I t s standard e r r o r of estimate was 21.4 percent. Crown width, crown width/diameter and height/crown width. More than 90 percent of the t o t a l v a r i a t i o n i n the crown width o f open-grown t r e e s , but only 56.8 percent f o r forest-grown t r e e s , could be accounted f o r by d.b.h. For the forest-grown t r e e s the combination of H/CW w i t h d.b.h. increased the percentage accounted f o r t o 81.1 percent. CW/D and d.b.h. together accounted f o r 68.4 percent of the v a r i a t i o n i n crown width. However w h i l e both H/CW and CV//D are a f f e c t e d by s i t e i n -dex, a f t e r the e f f e c t of d.b.h. on the v a r i a t i o n i n the two r a t i o s has been taken i n t o account, H/CW i s a f f e c t e d more than CW/D. As CW/D a l s o p r o v i d e s more i n f o r m a t i o n than H/CW i t s use w i t h d.b.h. i s p r e f e r a b l e . The value of these r a t i o s as d e n s i t y i n d i c e s was t e s t e d a f t e r e f f e c t s of age, s i t e index and height were accounted f o r . CW/D was test e d against H./CW and H/CW was t e s t e d against crown width. I t was concluded t h a t , although both crown r a t i o s assess stand d e n s i t y , the e f f e c t s of s i t e index and age, bei n g h i g h l y s i g n i f i c a n t , should be taken i n t o account when comparing d i f f e r e n t stands. N a t u r a l pruning of lodgepole pine. N a t u r a l pruning was d e f i n e d as the average height to the lowest dead, and t o the lowest l i v e y branch on each o f f o u r s i d e s . N a t u r a l p r u n i n g o f open-grown lodgepole pine was found to be non-existent f o r dead branches and very l i m i t e d f o r l i v e branches. For a l l open-grown tr e e s average height to l i v e branches was l e s s than three f e e t . For the forest-grown t r e e s , the p e r s i s t e n c e of dead branches was more v a r i -a ble ( c o e f f i c i e n t of v a r i a t i o n = 135$) than f o r l i v e ( c . v . = 52$). Average height to dead branches was approximately 4 f e e t and t o l i v e branches, 40 f e e t . Four " t r e e competition f a c t o r s " , each i n c o r p o r -a t i n g the d.b.h. o f , and d i s t a n c e to, ;competing t r e e s , were r e l a t e d to the two measures of pruned h e i g h t . The most c l o s e l y a s s o c i a t e d one, together w i t h b a s a l area per acre, H/CW and CW/D were combined w i t h age, d.b.h., s i t e index and height as independent v a r i a b l e s i n a r e -g r e s s i o n a n a l y s i s of pruned h e i g h t . Age alone accounted f o r 47.1 per-cent of the v a r i a t i o n i n height t o dead branches. Only the competition f a c t o r , of a l l remaining d e n s i t y v a r i a b l e s , accounted f o r any a d d i t i o n a l i v a r i a t i o n . None of the d e n s i t y i n d i c e s had any important e f f e c t on the v a r i a t i o n i n height to l i v e branches a f t e r age, t r e e height and d.b.h. were used i n combination. Growth l i m i t s of Lodgepole pine. Two g r a p h i c a l analyses were made to determine the cumulative r a d i a l growth r a t e of open-grown and forest-grown t r e e s 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 . I n the f i r s t a n a l y s i s the sampling areas were used as the b a s i s f o r s t r a t i f i c a t i o n . The average s i t e index f o r each s i t e s e r i e s was r e l a t e d to the average d.b.h. at age 50, determined from the l i n e a r r e g r e s s i o n equations c a l c u l a t e d f o r each s i t e s e r i e s . No a s s o c i -a t i o n was found. I t was concluded that s t r a t i f i c a t i o n by v e g e t a t i o n s i t e was not adequate. In the second a n a l y s i s the data were s t r a t i f i e d i n t o f o u r s i t e index c l a s s e s d i r e c t l y . A group of d.b.h. on age, by s i t e index curves was developed. D.b.h. of open-grown t r e e s between 30 and 50 years was compared w i t h the d.b.h. o f forest-grown t r e e s of the same age and s i t e . On the b e t t e r s i t e s open-grown tr e e s grow twice as f a s t . On the poorer s i t e s t h i s d i f f e r e n t i a l i n c r e a s e s . C u r r e n t l y the optimum t r e e s i z e f o r h a r v e s t i n g lodgepole pine i s about 15 to 16 inches d.b.h. Economically, marginal t r e e s i z e would l i k e l y be approximately 9 inches d.b.h. The maximum growth r a t e of lodgepole pine was found to be s i m i l a r to the maximum growth r a t e o f Douglas f i r f o r s i t e q u a l i t i e s of equal rank f o r each species. L i m i t a t i o n s on maximum growth r a t e . The r e d u c t i o n i n stand volume produced i f open-grown tr e e s are grown to the same d.b.h. as normally grown t r e e s was i l l u s t r a t e d by a numerical example. An average d.b.h. of 12 inches and s i t e index of 90 f e e t at 80 years was assumed. The stand volume o f a f u l l y open-grown stand would be approximately 13 percent of the normally grown stand. This r e d u c t i o n i n t o t a l volume may be avoided by f o l l o w i n g an "open-to-normal" d e n s i t y p a t t e r n o f growth. An increased growth r a t e a f f e c t s c e r t a i n n a t u r a l c h a r a c t e r i s t i c s o f wood. The most important of these are knot s i z e and frequency. Through r e l a t i o n s h i p s between crown width and d.b.h., bark t h i c k n e s s and d.b.h., and branch diameter and l i v e branch length developed i n t h i s study, i t i s p o s s i b l e t o estimate the maximum knot s i z e that would r e s u l t from growing f u l l y open-grown t r e e s to a s p e c i f i e d d.b.h. I n f u l l y open-grown t r e e s of 12 inches d.b.h., a few knots approximately 3 l/4 inches i n diameter would be formed. Although they w i l l be l i v e k n o ts, reference t o the Western Pine A s s o c i a t i o n s ' grades, shows that some boards w i l l be down-graded from No. 2 Common to No. 3 Common. However the average grade of lumber may not m a t e r i a l l y change, although much marginal lumber would be produced. I f graded as Dimension then they would meet the s p e c i f i c a t i o n f o r No. 2, unless manufactured i n t o 2 by 4's eight f e e t l o n g . Then, w i t h knots between 2" and 3", con-s i d e r a b l e degrade may be expected. The open-to-normal d e n s i t y p a t t e r n of growth permits c o n t r o l of knot s i z e . By not p e r m i t t i n g crowns to form e x c e s s i v e l y heavy branches, a compromise may be a t t a i n e d between r a p i d growth and s u i t a b l e wood q u a l i t y . S p e c i f i c g r a v i t y i s reduced by a f a s t e r growth r a t e , thereby re d u c i n g pulp y i e l d . The average f i b r e l e n g t h w i l l be s h o r t e r f o r young or smaller t r e e s . However, economies r e s u l t i n g from r a p i d growth outweigh these disadvantages. LITERATURE CITED Apsey, T. M. 1961. An e v a l u a t i o n of crovm widths of r e d a l d e r as an ai d to the p r e d i c t i o n of growth and y i e l d . 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On the t r e e - a r e a r a t i o and c e r -t a i n of i t s a p p l i c a t i o n s . Jour, of For. 38(f-) : 311 - 317. % Department of A g r i c u l t u r e . 1962. Climate of B r i t i s h Columbia. Queen's P r i n t e r , V i c t o r i a . • D u f f y , P.J.B. 1962. R e l a t i o n s h i p s between s i t e f a c t o r s and growth of lodgepole pine i n the f o o t h i l l s o f A l b e r t a . Ph.D. T h e s i s , Univ. of Minn., 94pp. Doyle, J . A. 1957* E f f e c t of t r e e s i z e o f spruce and balsam f i r on • h a r v e s t i n g and conversion t o lumber i n Nova S c o t i a . F.P.L. Can., Tech. Note No. 5, 30pp. Doyle, J . A. and W. W. C a l v e r t . I96I. E f f e c t of t r e e s i z e of jack pine on h a r v e s t i n g and conversion t o lumber i n Northern Ontario. F.P. Res. Br. Can., Tech. Note No. 19, 26 pp. H a l l i d a y , ¥. E. D. 1937. A f o r e s t c l a s s i f i c a t i o n f o r Canada. Dept. Res. and Dev., Dom. For. Ser., B u l l . 89. Holmes, J.R.B. and D. Tackle. I962. Height growth of lodgepole pine i n Montana r e l a t e d to s o i l and stand f a c t o r s . Mont. State Univ., School of F o r e s t r y , B u l l . No. 21, 12 pp. I l l u s . 117 Frood, G. D. 1963. Wood zone and growth zone r e l a t i o n s h i p s i n Pinus c o n t o r t a (dougl.) v a r . l a t i f o l i a (Engelm.). Unpublished B.S.F. Thesis, Univ. of B.C., Fac. of For., 43pp. I l l i n g w o r t h , K. and J.W. C. A r l i d g e . i960. I n t e r i m report on some f o r e s t s i t e types i n lodgepole pine and spruce-alpine f i r stands. Dept. of Lands and F o r e s t s , B.C.F.S., Res. Note No. 35 , 44pp. Johnson, C. I962. An e v a l u a t i o n of crown widths of open-grown Engel-mann spruce and i n t e r i o r Douglas f i r as an a i d to the p r e d i c t i o n of y i e l d and growth. Unpublished B.S.F. Thesis, Univ. of B.C., Fac. of For. 80pp. K e l l y , C.C. and L. F a r s t a d . 1946. S o i l survey of the P r i n c e George area, B r i t i s h Columbia. Dept. of A g r i c , B.C., Report No. 2, 58pp. I l l u s . Ker, J . W. and J . H. G. Smith. 1955- Advantages of the p a r a b o l i c ex-p r e s s i o n o f height-diameter. For. Chron. 3 l(3) * 236 - 246. K r a j i c e k , J . E. and K. A. Brinkman. 1957. Crown development : an i n -dex of stand d e n s i t y . C e n t r a l States For. Exp. S t a t . S t a t . , Note No. 108, l p . McArdle,. R. E., Meyer, W. H. and D. Bruce. 1949. The y i e l d o f Douglas f i r i n the P a c i f i c Northwest. U.S. Dept. of A g r i c . Tech. B u l l . No. 201, 74pp. McBride, C.F. I963. Sawing small l o g s . For. Chron. 39(2) : 175 - 182. Munro, D.M. i960. The growth and y i e l d of lodgepole pine on Tree Farm Licence No. 16. Unpublished B.S.F. T h e s i s , Univ. of B.C., Fac. of For. 43p.. Pearson, R.W. I962. An a n a l y s i s of crown widths of open-grown and f o r e s t -grown black cottonwood as an a i d i n the p r e d i c t i o n o f y i e l d and growth. Unpublished B.S.F. Thesis, Univ. of B.C., f a c . of For. 74pp. 2 Smith, J . H. G., and J . V/. Ker. 1957 • Timber volume depends on D H. B. C. Lumberman 41(9) : 28 - 30. Smith, J.H.G. and J.W. Ker. i960. Growing Douglas f i r and western hemlock t r e e s at d e s i r e d r a t e s . Univ. o f B.C. Fac. of For., Res. Note No. 24, 6pp. Smith, J.H.G., Ker, J.W. and J . Csizmazia. 1961. Economics of r e -f o r e s t a t i o n of Douglas f i r , western hemlock and western red cedar i n the Vancouver Forest D i s t r i c t . Univ. of B.C., Fac. of For., For. B u l l . No. 3 , 144 pp. Smithj J.H. G. 1958. B e t t e r y i e l d s through wider spacing. Jour, of For. 56(7); 492 - 497. Smith, J.H.G. 19^3. A n a l y s i s of crown development can e s t a b l i s h b i o l o g i c a l and economic l i m i t s to growth of t r e e s and. stands. Commonwealth For. Rev. 4 2 ( l ) : 2? - 33. Smithers, L.A. 1961. Lodgepole pine i n A l b e r t a . Dept. of For. Can., B u l l . 127, 153pp. Spurr, S.E. 1952. Forest Inventory. Ronald P r e s s . New York. Trappe, J.M. 1957. Experience w i t h b a s a l area e s t i m a t i o n by prism i n lodgepole p i n e . Pac. N.W. Res. and Range Exp. S t a t . , Res. Note No. 145, 6pp. U.B.C. Forest Club. 1959. F o r e s t r y Handbook f o r B r i t i s h Columbia. Univ. of B.C., Fac. of For., Forest Club, 800 pp. VanSlyke, A.L. 1964. Crown measures f o r coniferous t r e e s and stands. Unpublished r e p o r t , 40pp. Vezina, P.E. I962. Crown width-d.b.h. r e l a t i o n s h i p s f o r open-grown balsam f i r and white spruce i n Quebec. For. Chron. 38(4) : 463 - 473. . I963. More about the crown competition f a c t o r . For. Chron. 39(3) : 313-18. Wellwood, R.W. and J.H.G. Smith. 1962. V a r i a t i o n i n some important q u a l i t i e s of wood from young Douglas f i r and hemlock t r e e s . Univ. o f B.C., Fac. of For., Res. Pap. No. 50, 15pp. Western Pine A s s o c i a t i o n . 1956. Standard grading r u l e s . W.P.A., P o r t l a n d , Oregon. APPENDIX l a SIMPLE CORRELATION MATRIX FOR 90 OPEN-GROWN TREES Dbh .368 Dbk -.362 H - . 4 7 3 CW - . 4 1 5 CW/D - . 0 ^ 5 . Age -.576 Rg 6-10 . 7 7 8 H/CW HDbr -.219 HLbr - . 5 7 3 LLbr - . 4 1 5 BRBTT - . 3 3 8 Lc$ . 3 7 7 CW2 - . 4 0 3 CW^Lc - . 3 9 5 SI . 2 9 8 Dbh . 8 7 5 . 8 7 1 . 9 4 9 - . 6 1 4 . 8 8 4 - . 2 1 8 - . 1 7 7 . 3 1 3 .698 . 9 4 3 . 8 5 3 - . 3 2 4 . 8 9 9 . 8 3 7 - . 1 6 7 Dbk . 7 7 6 . 7 9 9 -.529 . 8 3 4 -.312 - . 1 0 1 . 1 8 7 . 5 9 0 . 7 8 8 . 7 4 0 - . 2 4 9 . 7 6 7 . 7 4 7 -.128 H . 8 4 6 -.523 . 8 3 1 -.311 . 2 1 4 . 3 8 3 . 6 8 1 . 8 4 6 .725 -.206 . 7 8 3 .796 . 1 0 6 CW -.452 . 8 5 4 - . 2 4 4 -.295 .325 .729 . 9 9 7 . 8 7 5 - . 3 5 5 . 9 5 8 . 8 7 2 - . 1 4 9 CW/D - . 4 7 3 - . 2 2 4 - . 1 2 4 - . 2 1 5 . - . 3 3 6 - . 4 3 6 - . 4 0 5 .256 - . 3 3 7 - . 2 8 8 . 1 2 2 Age - . 4 8 6 -.020 .299 . 7 6 5 . 8 5 6 . 7 7 8 - . 4 1 1 . 8 3 9 . 8 0 8 -.351 R g 6 - 1 0 - . 0 8 7 - . 1 1 6 - . 4 6 9 -.250 -.229 . 2 8 2 - . 3 0 2 - . 3 4 3 .294 H/CW •M -.112 - . 2 8 0 -.266 . 2 9 7 - . 2 7 8 - . 1 0 7 .477 HDbr . 4 9 9 . 3 5 5 .213 -.371 . 2 6 5 . 2 3 9 - . 0 4 1 HLbr . 7 2 4 .622 - . 7 8 3 . 6 5 9 . 5 7 4 -.350 LLbr . 8 7 8 - . 3 4 7 . 9 6 6 . 8 8 9 -.122 BrBTT - . 3 2 3 . 8 8 1 . 8 4 1 -.122 Lcfo - . 2 8 5 - . 1 6 6 . 5 3 5 CW2 . 9 5 9 - . 1 4 0 CW^Lc -.oil r Q c = 0 . 2 0 5 ; r 0 1= 0 . 2 6 7 Not s i g n i f i c a n t values u n d e r l i n e d APPENDIX l b SIMPLE CORRELATION MATRIX FOR 111 OPEN-GROWN TREES H CW CW/D Age H/CW Lcfo SI Dbh .920 .969 -.688 .921 -.234 -.482 -.399 H .905 -.665 .885 .022 -.409 -.205 CW -.641 .901 -.319 -.502 -.389 CW/D -.593 .020 .466 .381 Age -.161 -.521 -.509 H/CW .214 .484 Ltifo .548 r n,-= 0.191 ; Not s i g n i f i c a n t values u n d e r l i n e d APPENDIX l c SIMPLE CORRELATION MATRIX FOR 83 OPEN-GROWN TREES H CW CW/D Age H/CW L C $ SI BAg BAg 6-10 1-5 Dbh .839 .937 -.523 .871 -.187 -.2__ -.184 .642 .652 H .809 -.379 .807 .253 -.062 .121 .396 .387 CW -.254 .834 -.318 -.242 -.162 .554 .539 CW/D -.398 -.201 .008 .194 -.482 -.540 Age -.064 -.338 -.370 .284 .313 H/CW .326 .484 -.291 -.265 Lc$ .611 -.015 .044 SI -.070 -.042 MS6-10 : • -222. r.05 = 0.215 ; Not s i g n i f i c a n t values u n d e r l i n e d APPENDIX Id SIMPLE CORRELATION MATRIX FOR 63 FOREST-GROWN TREES Dbh Bfirj^ -048 Dbk -.017 H -.097 CW .262 CW/D _22_ Age -.216 % 6-10 .746 H/CW -.362 HDbr -.001 HLbr -.227 LLbr .249 LDbr .220 Ldfo .386 2 CW .281 2 CW.Lc .311 SI .049 BA/ac -.144 Dbh .891 .900 .753 -.643 .844 .187 .325 .602 .758 .760 .220 -.337 .732 .777 .629 .646 Dbk .773 .578 -.557 .784 .075 .319 .604 .646 .588 ._6 -.287 .572 .655 .489 .578 H .568 -.764 .834 .030 .639 .591 .945 .576 .087 -.591 .532 .583 .822 .748 CW -.223 .496 .375 -.222 .236 .364 .997 .623 -.023 .979 .803 .410 .316 CW/D -.699 -.029 -.724 -.408 -.763 -._4 .012 .668 -.1_6 -.236 -.594 -.555 Age -.o_2 .472 .692 .787 .508 -.011 -.518 .471 .510 .397 .694 RS6-10 -.289 -.022 -.098 .361 .241 .120 .401 .401 • i l Z -.093 H/CW .378 .779 -.214 -.414 -.717 -•225. -.13_ .630 .599 HDbr .551 .255 -.233 -.271 .218 .275 .309 .442 HLbr .368 -.112 -.774 .329 .368 .792 .795 LLbr .622 -.016 .976 .904 .412 .314 LDbr .277 .582 .531 .095 -.122 Lc$ .o_ .033 -.492 -.543 2 CW .951 .372 .294 CW^Lc .418 .315 si ;._ _ _ _ i r n,= 0.250 ; r = 0.325 Not s i g n i f i c a n t v alues u n d e r l i n e d APPENDIX l e SIMPLE CORRELATION MATRIX FOR THE NATURAL PRUNING DATA ON 57 FOREST-GROWN TREES H CW CW/D Age H/CW HDbr HLbr SI BA/ac T C I TC2 TC3 TC4 Dbh .890 .7^ 7 -.598 .877 .246 .616 .730 .576 .611 .680 .747 .760 .818 H .544 -.728 .881 .587 .615 .9^0 .797 .727 .622 .663 .651 .687 CW -.147 .517 -.315 .242 .322 .339 .269 .368 .460 .487 .483 CW/D -.715 -.699 -.416 -.732 -.516 -.506 --.429 -.425 -.420 -.418 Age .458 .686 .811 .441 .719 .610 .645 .638 .702 H/CW .366 .752 .593 .566 .277 .227 .215 • 210 HDbr .563 .340 .447 .518 .576 .483 .703 HLbr .784 .792 .556 .537 .567 .546 SI .496 .385 .404 .402 .398 BA/ac .450 .437 .529 .446 T C I .922 .872 .827 TC2 .842 .896 TC3 .824 TC4 1.000 r - 0.259 Not s i g n i f i c a n t values u n d e r l i n e d 123 125 126 lips -i-i-H-:-;+;+ I S S E xi+H+H± ±EEtbEx 4444-14444-+±b:l+b: ± | ± J : i ± i i t mm mm xcbtrrdrl -rrf-;+;-!-;-r ^#]:Hxr:|++xt!x: i i i i i l !-'-!-f \-\-\- ~r -rr\'\Jr ~r -r ^ | : E t i E : : : + ^ * . ^ j + E 4 T i + j+FE : + i-H-+i+ : l i4 : : feipls + + - i- i - i+i+ i + f II :thi:ix -!-!-!+ - i T " :pH:F+|:F+ :p."iX]j:|:jx :!xtjX-4-t-#B4BT!± :i±nx]q:pi: d:l:dxn±i: +i-!-:-i-i+i-i-+?! 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