UBC Theses and Dissertations

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UBC Theses and Dissertations

Variation in growth efficiency of selected western hemlock (Tsuga heterophylla (RAF.) Sarg.) 1979

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VARIATION IN GROWTH EFFICIENCY OF SELECTED WESTERN HEMLOCK (TSUGA HETEROPHYLLA (RAF.) SARG.) TREES by GARY LEE NELSON B S c , Colorado S t a t e U n i v e r s i t y A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF FORESTRY i n THE FACULTY OF GRADUATE STUDIES F a c u l t y o f F o r e s t r y We accept t h i s t h e s i s as c o n f o r m i n g to the r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA August, 1979 © G a r y Lee N e l s o n , 1979 I n 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 o f t h e r e q u i r e m e n t s f o r an a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e 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 r e f e r e n c e and s t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by t h e Head o f my D e p a r t m e n t o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . D e p a r t m e n t n f hore.s +sy The U n i v e r s i t y o f B r i t i s h C o l u m b i a 2075 W e s b r o o k P l a c e V a n c o u v e r , C a n a d a V6T 1W5 - i i - ABSTRACT E i g h t y w e s t e r n hemlock t r e e s , i n t h e age range o f 15 t o 48 y e a r s , .were s e l e c t e d on t h r e e Crown Z e l l e r b a c h t r e e farms i n n o r t h w e s t e r n Oregon and s o u t h w e s t e r n Washington t o sample t h e range o f v a r i a t i o n i n g r owth e f f i - c i e n c y . Growth e f f i c i e n c y i s d e f i n e d as t h e a b i l i t y o f t h e crown t o p r o - duce t h e maximum amount of wood i n r e l a t i o n to. i t s crown s u r f a c e a r e a . S e l e c t i o n o f t h e t r e e s was based on t h e crown i n d e x r a t i o ( l i v e crown l e n g t h / crown w i d t h ) . The o b j e c t i v e s o f t h e s t u d y were t o e s t i m a t e : 1) t h e range o f v a r i a t i o n i n growth e f f i c i e n c y o f i n d i v i d u a l t r e e s , 2) how v a r i a t i o n i n growth e f f i c i e n c y o f i n d i v i d u a l t r e e s c o u l d be u t i l i z e d t o maximize volume on a u n i t a r e a , and 3) t h e e f f i c i e n c y o f narrow crown w e s t e r n hemlock t r e e s as wood p r o d u c e r s . R e s u l t s from r e g r e s s i o n a n a l y s i s showed t h a t t h e r e was s u f f i c i e n t v a r i a - t i o n i n growth e f f i c i e n c y , w i t h a range o f t h e s t a n d a r d i z e d r e s i d u a l s ex- c e e d i n g a t l e a s t ±2.0 s t a n d a r d e r r o r s of t h e e s t i m a t e f o r a l l t h r e e r e g r e s - s i o n models. Based on t h i s r ange i t i s s u g g e s t e d t h a t s e l e c t i o n o f t e n y e a r b a s a l a r e a i n c r e m e n t o r g r o s s stem volume f o r w e s t e r n hemlock i n r e l a - t i o n t o crown s u r f a c e a r e a o r sapwood b a s a l a r e a may be w o r t h w h i l e . The s i g n i f i c a n c e o f t h e v a r i a t i o n i n growth e f f i c i e n c y becomes appa- r e n t when t h e h i g h e r growth e f f i c i e n c y c l a s s e s a r e s e l e c t e d . I t i s e s t i - mated t h a t s e l e c t i o n o f t h e h i g h e r growth e f f i c i e n c y c l a s s e s r a t h e r t h a n t h e a v e r a g e may i n c r e a s e t e n y e a r b a s a l a r e a i n c r e m e n t / h e c t a r e by 39 t o 45 p e r c e n t . I t a p p e ars from t h e t r e e s measured t h a t t h e r e i s l i t t l e r e l a t i o n s h i p between growth e f f i c i e n c y and t h e degree o f s l e n d e r n e s s o f t h e crown. - i i i - TABLE OF CONTENTS Page INTRODUCTION 1 LITERATURE REVIEW 3 MATERIALS AND METHODS 9 RESULTS AND DISCUSSION . . . - 18 1. Range o f V a r i a t i o n i n Growth E f f i c i e n c y 1§ a. Model One: Growth E f f i c i e n c y - R e l a t i n g G r o s s Stem Volume/Crown S u r f a c e A r e a t o Age 23 b. Model Two: Growth E f f i c i e n c y - R e l a t i n g Ten Y e a r B a s a l A r e a Increment t o Crown S u r f a c e A r e a .. 27 c. Model Th r e e : Growth E f f i c i e n c y - R e l a t i n g Ten Y e a r B a s a l A r e a Increment t o Sapwood B a s a l A r e a .. 30 2. U t i l i z a t i o n o f V a r i a t i o n i n Growth E f f i c i e n c y 36 3. E f f i c i e n c y o f Narrow-Crown W e s t e r n Hemlock T r e e s . ... 53 SUMMARY 59 LITERATURE CITED 61 APPENDICES ' 64 I . W estern Hemlock Comb Form 64 I I . W e stern Hemlock F l a t - B r a n c h e d Form 65 I I I . W e s t e r n Hemlock S t e e p l e Form 66 IV. W e s t e r n Hemlock Cedar Form 67 - i v - LIST OF TABLES T a b l e Page 1 Measurements and E s t i m a t i o n s o f V a r i o u s P a r a m e t e r s on t h e 80 S e l e c t e d T r e e s 19 2 C u m u l a t i v e P e r c e n t Under t h e Normal and Observed D i s t r i b u t i o n s 40 3 S t a n d a r d i z e d R e s i d u a l s and R a n k i n g o f t h e 80 O b s e r v a t i o n s . 45 4 P r e d i c t e d Ten Y e a r B a s a l A r e a I n c r e m e n t / H e c t a r e a t V a r i o u s Sapwood B a s a l A r e a s and C l a s s e s o f E f f i c i e n c y 50 - v - LIST OF FIGURES F i g u r e Page 1 L o c a t i o n o f C l a t s o p , C a t h l a m e t , and T i l l a m o o k T r e e Farms i n Oregon and Washington 13 2 C l a t s o p T r e e Farm 14 3 T i l l a m o o k T r e e Farm 15 4 C a t h l a m e t T r e e Farm 16 5 Method of C a l c u l a t i n g Crown S u r f a c e A r e a / T r e e 17 6 Model 1: V a r i a t i o n i n Growth E f f i c i e n c y 24 7 Model 1: V a r i a t i o n i n Growth E f f i c i e n c y R e p r e s e n t e d by S t a n d a r d i z e d R e s i d u a l s . 26 8 Model 2: V a r i a t i o n i n Growth E f f i c i e n c y 28 9 Model 2: V a r i a t i o n i n Growth E f f i c i e n c y R e p r e s e n t e d by S t a n d a r d i z e d R e s i d u a l s 29 10 R e g r e s s i o n o f Crown S u r f a c e A r e a on Sapwood B a s a l A r e a ..... 32 11 Model 3: V a r i a t i o n i n Growth E f f i c i e n c y 33 12 Model 3: V a r i a t i o n i n Growth E f f i c i e n c y R e p r e s e n t e d by S t a n d a r d i z e d R e s i d u a l s 35 13 C u m u l a t i v e Normal and Observed D i s t r i b u t i o n s f o r Model 1 .. 37 14 C u m u l a t i v e Normal and Observed D i s t r i b u t i o n s f o r Model 2 .. 38 15 C u m u l a t i v e Normal and Observed D i s t r i b u t i o n s f o r Model 3 .. 39 16 Model 1: S e l e c t i o n o f E f f i c i e n t l y Growing I n d i v i d u a l s .... 42 17 Model 2: S e l e c t i o n o f E f f i c i e n t l y Growing I n d i v i d u a l s .... 43 18 Model 3: S e l e c t i o n o f E f f i c i e n t l y Growing I n d i v i d u a l s .... 44 19 Ten Y e a r B a s a l A r e a I n c r e m e n t / H e c t a r e f o r V a r i o u s Sapwood B a s a l A r e a s and C l a s s e s o f E f f i c i e n c y 54 - v i - F i g u r e Page 20 R e g r e s s i o n o f S t a n d a r d i z e d R e s i d u a l s from M o d e l 1 on t h e Crown Index R a t i o 56 21 R e g r e s s i o n of S t a n d a r d i z e d R e s i d u a l s f r o m Model 2 on t h e Crown Index R a t i o 57 22 R e g r e s s i o n o f S t a n d a r d i z e d R e s i d u a l s f r o m Model 3 on t h e Crown Index R a t i o 58 - v i i - ACKNOWLEDGEMENTS I am v e r y g r a t e f u l t o Dr. 0. S z l k l a i , F a c u l t y o f F o r e s t r y and s u p e r - v i s o r o f my t h e s i s committee, f o r a s s i s t a n c e and encouragement i n t h e p r e - p a r a t i o n o f t h i s t h e s i s . Thanks a r e a l s o extended t o Dr. D. L e s t e r , Crown Z e l l e r b a c h C orp., f o r h i s s u p p o r t and i n s i g h t i n t h e p r e p a r a t i o n o f t h i s t h e s i s . G r a t i t u d e i s a l s o e xtended t o Dr. D. W i l l i a m s and Dr. J . Demaer- s c h a l k , F a c u l t y o f F o r e s t r y , f o r r e v i e w i n g t h e t h e s i s and c o n t r i b u t i n g t h e i r a d v i c e . I n a d d i t i o n , acknowledgement and th a n k s a r e extended t o Mr. M. A. E l - S h a r k a w i , Ms. S. P h e l p s , and Ms. G. Ho f o r t h e i r a s s i s t a n c e and ti m e i n computing. I am g r e a t l y i n d e b t e d t o Crown Z e l l e r b a c h C o r p o r a t i o n and t h e Western F o r e s t G e n e t i c s A s s o c i a t i o n f o r t h e i r f i n i c i a l s u p p o r t i n t h e fo r m o f t h e F o r e s t G e n e t i c s R e s e a r c h F o u n d a t i o n S c h o l a r s h i p w h i c h made t h i s r e s e a r c h p o s s i b l e . Thanks a r e a l s o e xtended t o Mr. Y. E l - K a s s a b y , Mrs. A. F a s h l e r , and Mrs. M. A. D e V e s c o v i f o r t h e i r s u p p o r t and encouragement. F i n a l l y , my most s i n c e r e t h a n k s t o my w i f e , K a r e n , f o r h e r u n f a i l i n g s u p p o r t and l o v e . - 1 - VARIATION IN GROWTH EFFICIENCY OF SELECTED WESTERN HEMLOCK (TSUGA HETEROPHYLLA (RAF.) SARG.) TREES INTRODUCTION Western hemlock (Tsuga h e t e r o p h y l l a ( R a f . ) Sarg.) i s one o f t h e most I m p o r t a n t c o m m e r c i a l t r e e s p e c i e s i n t h e P a c i f i c N o r t h w e s t . I t i s n o t o n l y a p r i m a r y lumber p r o d u c e r , b u t one o f t h e major s p e c i e s used f o r pulpwood on the c o a s t . I t s o c c u r r e n c e ranges a l o n g t h e P a c i f i c c o a s t f r o m s o u t h e a s t e r n A l a s k a t o n o r t h e r n C a l i f o r n i a , and i n the' R o c k y M o u n t a i n s f r o m t h e -southern h a l f o f B r i t i s h C o l u m b i a t h r o u g h n o r t h e r n Idaho, t o n o r t h w e s t e r n Montana (Harlow and H a r r a r , 1 9 6 9 ) . I n t h e l a s t s e v e r a l y e a r s , w e s t e r n hemlock has come i n t o i n c r e a s i n g demand i n t h e p l a n t i n g programs o f p r i v a t e and p u b l i c a g e n c i e s ; and t h i s t r e n d i s e x p e c t e d t o c o n t i n u e a t an a c c e l e r a t e d r a t e ( P i e s c h , 1 9 7 4 ) . However, l i t t l e a t t e n t i o n has been g i v e n t o t h e s t u d y o f w e s t e r n hemlock g e n e t i c s (Meagher,1976), b e c a u s e f o r many y e a r s i t was c o n s i d e r e d t h e l e a s t d e s i r a b l e among c o m m e r c i a l c o n i f e r s p e c i e s i n t h e P a c i f i c N o r t h w e s t . Even though i t s p o t e n t i a l f o r management as an e f f i c i e n t volume p r o d u c e r has l o n g been r e - c o g n i z e d (Hogue, 1929; and Dimock, 1 9 5 8 ) , i t i s j u s t r e c e n t l y b e i n g u t i l i z e d . F o r e s t t r e e improvement i s a p r a c t i c a l e x t e n s i o n o f g e n e t i c s , w i t h t h e o b j e c t i v e o f o b t a i n i n g g e n e t i c a l l y b e t t e r t r e e s f o r p l a n t i n g ( W r i g h t , 1 9 6 2 ) . R e s e a r c h r e l a t e d t o f o r e s t t r e e improvement and g e n e t i c s has been i n p r o g r e s s f o r 150 y e a r s , b u t o n l y i n t h e p a s t 25 y e a r s has r e s e a r c h been i n t e n s i v e ( W r i g h t , 1 9 7 6 ) . F o r w e s t e r n hemlock t h i s r e s e a r c h began about a decade ago, - 2 - w i t h s t u d i e s i n i t i a t e d i n 1968, i n d e p e n d e n t l y by P i e s c h (1974) and Meagher (1976). P r i o r t o t h a t t i m e a s m a l l number o f p l u s t r e e s had been s e l e c t e d i n B r i t i s h C o l u m b i a ( W a l t e r s e t a l . , 1 9 6 0 ) . Western hemlock appears w e l l s u i t e d t o g e n e t i c improvement e f f o r t s ( P i e s c h , 1976). Wellwood (1960) r e p o r t e d v a r i a t i o n i n t r a c h e i d l e n g t h , and t r e e s h a v i n g t r a c h e i d s e i t h e r s h o r t e r o r l o n g e r t h a n a v e r a g e r e t a i n e d t h a t f e a t u r e as t h e y c o n t i n u e d t o grow. A p p r e c i a b l e v a r i a t i o n was a l s o r e p o r t e d i n h e i g h t o f t w o - y e a r - o l d s e e d l i n g s , b o t h w i t h i n and between p o p u l a t i o n s o f w e s t e r n hemlock ( P i e s c h , 1 9 7 4 ) . Meagher (1976) found t h a t w e s t e r n hemlock p o p u l a t i o n s d i f f e r e n t i a t e r a p i d l y w i t h l o c a l i t y and e l e v a t i o n . T h i s i n v e s t i g a t i o n d e a l s w i t h t h e v a r i a t i o n and s e l e c t i o n o f growth e f f i c i e n c y o f i n d i v i d u a l w e s t e r n hemlock t r e e s . The o b j e c t i v e s o f t h e s t u d y were t o e s t i m a t e : 1) the range o f v a r i a t i o n i n growth e f f i c i e n c y o f i n d i v i d u a l t r e e s : a) r e l a t i n g g r o s s stem volume/crown s u r f a c e a r e a t o age, b) r e l a t i n g t e n y e a r b a s a l a r e a i n c r e m e n t t o crown s u r f a c e a r e a , and c) r e l a t i n g t e n y e a r b a s a l a r e a i n c r e m e n t t o sapwood b a s a l a r e a , 2) how v a r i a t i o n i n growth e f f i c i e n c y o f i n d i v i d u a l t r e e s c o u l d be u t i l i z e d t o maximize volume p e r u n i t a r e a , and 3) t h e e f f i c i e n c y o f narrow- crown w e s t e r n hemlock t r e e s as wood p r o d u c e r s . - 3 - LITERATURE REVIEW The i m p o r t a n c e of crown v a r i a t i o n i n r e l a t i o n t o wood q u a l i t y and q u a n t i t y has l o n g been r e c o g n i z e d by f o r e s t g e n e t i c i s t s . Emphasis i s u s u a l l y p l a c e d on v a r i a t i o n i n t h e b r a n c h i n g c h a r a c t e r i s t i c s s u c h as b r a n c h a n g l e and b r a n c h d i a m e t e r ( B a r b e r and R e i n e s , 1956; R u d o l p h , 1956; C a m p b e l l , 1961; Stephenson and Snyder, 1969; and Dorman, 1976), t h a t i s , c h a r a c t e r i s t i c s a f f e c t i n g wood q u a l i t y . The p r i m a r y o b j e c t i v e s of a t r e e improvement program i n most coun- t r i e s , i s t o s e l e c t and b r e e d t r e e s w i t h i n c r e a s e d g r o w t h r a t e s , d e s i r - a b l e stem form, and i n c r e a s e d r e s i s t a n c e t o i n s e c t s and d i s e a s e s . F o r w e s t e r n hemlock, volume s u p e r i o r i t y i s t h e s i n g l e most i m p o r t a n t t r a i t among stem s t r a i g h t n e s s , s p i r a l g r a i n , b r a n c h s i z e c o n s i d e r a t i o n s , s p e c i f - i c g r a v i t y , and c e l l u l o s e c o n t e n t (Thomas and S t e v e n s , 1977). There a r e many f a c t o r s w h i c h i n f l u e n c e t h e g r o w t h o f i n d i v i d u a l t r e e s on a g i v e n s i t e , however, c o m p e t i t i o n i s p r o b a b l y t h e s i n g l e most i m p o r t a n t f a c t o r (Brown and Goddard, 1961). C o m p e t i t i o n i s d e f i n e d as t h e a c t i v e demand by two o r more or g a n i s m s f o r a common r e s o u r c e . T h e r e- f o r e , i f t r e e s a r e s e l e c t e d f o r s u p e r i o r growth r a t e o r volume w i t h o u t c o n s i d e r a t i o n of t h e degree of c o m p e t i t i o n t o w h i c h t h e y have been sub- j e c t e d , i t may be f ound t h a t t h e y a r e g r o w i n g no more t h a n s h o u l d be ex- p e c t e d w i t h t h e g r o w i n g space a v a i l a b l e t o them (Brown and Goddard, 1961). I t seems l o g i c a l t o assume t h a t t h e s i z e o f t h e crown s h o u l d be an i n d i c a t i o n of t h e c o m p e t i t i o n a t r e e has undergone. Brown and Goddard s t a t e d t h a t : " t h e s e a r c h f o r p l u s phenotypes c e n t e r s around t h e p r e m i s e t h a t c e r t a i n t r e e s a r e i n h e r e n t l y more e f f i - c i e n t t h a n o t h e r s i n t h e m a n u f a c t u r e and u t i l i z a t i o n o f p h o t o s y n t h a t e s . S t a t e d somewhat d i f f e r e n t l y , a p l u s t r e e by a. p r i o r i r e a s o n i n g p o s s e s s e s t h e p o t e n t i a l i t y o f p r o d u c i n g more i n c r e m e n t p e r u n i t crown s i z e and grow i n g space t h a n competing n e i g h b o r i n g t r e e s o f t h e same age." T h e i i m p o r t a n c e o f l e a f i n e s s i n d r y - m a t t e r p r o d u c t i o n has l e d t o t h e a s s u m p t i o n t h a t crown d i m e n s i o n s s h o u l d be r e l a t e d t o i n c r e m e n t (Matthews, 1963). There a r e many examples o f t h e p o s i t i v e r e l a t i o n s h i p between crown w i d t h and stem d i a m e t e r ( H o l s o e , 1948; M i n o r , 1951; Toda, 1954; B e r l y n , 1962; and V e z i n a , 1962), and crown w i d t h and b a s a l a r e a i n c r e m e n t (Week, 1944; and H o l s o e , 1948). The c l o s e n e s s o f t h e r e l a t i o n between crown d i a m e t e r and stem d i a m e t e r o r b a s a l a r e a i n c r e m e n t i n many s p e c i e s does n o t p r e c l u d e t h e e x i s t e n c e o f t r e e s t h a t have crowns s m a l l e r o r l a r g e r t h a n a v e r a g e f o r a g i v e n stem d i a m e t e r o r b a s a l a r e a i n c r e m e n t (Matthews, 1963). S t u d - i e s o f M o l l e r (1945) i n Denmark w i t h beech and s p r u c e showed t h a t t h e same q u a n t i t y o f f o l i a g e can pro d u c e d i f f e r e n t q u a n t i t i e s o f stem v o l - ume. T h e r e f o r e , i f t h e c o n v e r s e s t a t e m e n t i s t r u e , t h a t t h e same quan- t i t y o f stem volume can be produced by d i f f e r e n t q u a n t i t i e s o f f o l i a g e , t h e r e a r e o b v i o u s a d v a n t a g e s t o be g a i n e d f r o m i d e n t i f y i n g t h o s e t r e e s w h i c h a r e e f f i c i e n t wood p r o d u c e r s i n r e l a t i o n t o t h e q u a n t i t y o f f o l i - age and t h e s i z e o f t h e i r crown d i a m e t e r s (Matthews, 1963). A t t h e same t i m e , q u a l i t y c h a r a c t e r i s t i c s s u c h as s p e c i f i c g r a v i t y , c e l l u l o s e c o n t e n t , s t r a i g h t n e s s , s p i r a l g r a i n , and b r a n c h s i z e s h o u l d be c o n s i d e r - ed f o r t h e s e l e c t e d t r e e . Though t r e e s w i t h s m a l l crown d i a m e t e r s may n o t pro d u c e stem v o l - - 5 - umes e q u a l t o wide-crown t r e e s , t h e i r e f f i c i e n c y may be g r e a t e r . Assman (1970) found t h a t i n t r e e s o f t h e same s p e c i e s and dbh, i n d i v i d u a l s h a v i n g s l e n d e r crowns o r a low crown f u l l n e s s r a t i o (crown w i d t h / c r o w n l e n g t h ) were more p r o d u c t i v e on a l a n d a r e a b a s i s t h a n t r e e s h a v i n g w i d e crowns. I n o r d e r t o a s c e r t a i n t h e shape and s i z e of crown most c o n d u c i v e t o a h i g h r a t e of g rowth, t h e b e s t p l a n i s t o r e l a t e t h e c a p a c i t i e s of i n d i v i d - u a l t r e e s t o t h e i r r e s p e c t i v e crown s u r f a c e a r e a (Assman, 1970). Matthews (1963) and o t h e r s ( R u d o l p h , 1956; C a m p b e l l and R e d i s k e , 1966; and Morgen- s t e r n e t a l . , 1975) have e x p r e s s e d t h e s i m i l a r i d e a t h a t s e l e c t i o n f o r g rowth r a t e s h o u l d be d i r e c t e d toward f i n d i n g n o t t h e l a r g e s t t r e e , b u t t h e t r e e t h a t has u t i l i z e d g r o w i n g s p a c e , l i g h t , and n u t r i e n t s most e f f i c i e n t l y . T h i s r e q u i r e s f i n d i n g t h e t r e e w i t h t h e b e s t g r o w t h i n r e l a t i o n t o i t s l e a f s u r f a c e a r e a ( M o r g e n s t e r n e t a l . , 1975). Though two t r e e s may have t h e same q u a n t i t y o f f o l i a g e o r crown s u r - f a c e a r e a , t h e e f f i c i e n c y of t h e n e e d l e s t o c o n v e r t c a r b o n d i o x i d e and w a t e r i n t h e p r e s e n s e o f c h l o r o p h y l l and s u n l i g h t i n t o p h o t o s y n t h a t e s may d i f f e r g r e a t l y due t o d i f f e r e n t m o r p h o l o g i c a l crown f o r m s . D i f f e r e n c e s i n e f f i c i e n c y of t h e n e e d l e s may be d i r e c t l y due t o t h e c a p a b i l i t i e s of a t r e e ' s genome t o s y n t h e s i z e p h o t o s y n t h a t e s , o r i n d i r e c t l y as a consequence o f a t r e e ' s m o r p h o l o g i c a l crown form, where one f o r m may be more advantageous because o f t h e o r i e n t a t i o n of t h e n e e d l e s t o t h e suns r a y s . A l e x a n d r o v (1971) o b s e r v e d four, b a s i c m o r p h o l o g i c a l forms o f Norway s p r u c e w i t h 24 t r a n s i t i o n a l f o r m s . The f o u r f o r m s , comb, b r u s h , compact, and f l a t - b r a n c h e d , a r e made a p p a r e n t by t h e b r a n c h i n g c h a r a c t e r i s t i c s and r e f l e c t t h e e c o l o g i c a l c o n d i t i o n s . The comb s p r u c e r e c e i v e d i t s name because of t h e s t r u c t u r e o f t h e s e c o n d - o r d e r b r a n c h e s , w h i c h hang down i n a c o m b - l i k e c u r t a i n . The name -6- b r u s h s p r u c e i s g i v e n because o f t h e b r u s h - l i k e s t r u c t u r e o f t h e second- o r d e r b r a n c h e s w h i c h grow i n a l l d i r e c t i o n s . The compact s p r u c e i s s i m i - l i a r t o t h e b r u s h s p r u c e , b u t t h e s e c o n d - o r d e r b r a n c h e s r e m a i n h o r i z o n t a l because o f t h e i r s h o r t l e n g t h , c o n s i d e r a b l e t h i c k n e s s , and s t u r d i n e s s t o form a compact mass. The f l a t - b r a n c h e d f o r m r e c e i v e s i t s name because t h e f i r s t - , s e c o n d - , and t h i r d - o r d e r b r a n c h e s d e v e l o p i n t h e same h o r i z o n t a l p l a n e . A l e x a n d r o v (1971) made no a t t e m p t i n h i s s t u d y t o d e t e r m i n e t h e g r o w t h e f f i c i e n c y w i t h i n and between t h e f o u r f o r m s . However, i t i s l i k e l y t h a t each f o r m may have t h e same q u a n t i t y o f f o l i a g e o r : c r o w n s u r f a c e a r e a , b u t d i f f e r i n t h e i r e f f i c i e n c y t o s y n t h e s i z e p h o t o s y n t h a t e s because o f t h e e c o l o g i c a l c o n d i t i o n s , t h e o r i e n t a t i o n o f t h e n e e d l e s on t h e s e c o n d - o r d e r b r a n c h e s , o r t h e g e n e t i c a b i l i t y o f t h e t r e e i t s e l f t o s y n t h e s i z e p h o t o - s y n t h a t e s even under optimum c o n d i t i o n s . Measurements of f o l i a g e mass o r l e a f s u r f a c e a r e a f o r f o r e s t t r e e s a r e o f t e n u s e d by f o r e s t e r s , e c o l o g i s t s , p h y s i o l o g i s t s , and o t h e r s i n t e r e s t - ed i n t r e e g r o w t h t o e s t i m a t e p h o t o s y n t h e t i c p o t e n t i a l . Such measurements a r e i m p o r t a n t as w e l l i n s t u d i e s o f e v a p o r a t i o n , t r a n s p i r a t i o n , and i n t e r - c e p t i o n o f p r e c i p i t a t i o n . G e n e r a l l y , t h e l e a f s u r f a c e a r e a o r f o l i a g e mass i s t h e p r e f e r r e d measurement, and methods have been d e v e l o p e d t o e s t i m a t e t h e s e f o r some s p e c i e s . By u s i n g r e g r e s s i o n a n a l y s i s , C a b l e (1958) f o u n d a r e l a t i o n s h i p between l e a f s u r f a c e a r e a and ovendry w e i g h t o f i n d i v i d u a l p o n d e r o s a p i n e f a s c i c l e s . F o r s e v e r a l hardwoods and s h o r t l e a f p i n e , t o t a l q u a n t i t y o f f o l i a g e was found by e s t i m a t i n g e q u a t i o n s f o r t h e number o f l e a v e s by b o t h t r e e and b r a n c h d i a m e t e r ( R o t h a t c h e r et. a l . , 1954). Many o f t h e s e e s t i m a t e s a r e time- c o n s u m i n g , hence f o r some s t u d i e s -7- o t h e r i n d i c a t o r s o f p h o t o s y n t h e t i c a r e a a r e u s e d . Among t h e s e , crown r a d - i u s X crown l e n g t h , crown d i a m e t e r X crown l e n g t h , and crown s u r f a c e a r e a have been found t o be h i g h l y c o r r e l a t e d w i t h t r e e g r o wth. One a p p r o a c h i n s e l e c t i n g f o r g r o w t h e f f i c i e n c y i s t o d e t e r m i n e i n each s t a n d t h e r e g r e s s i o n o f b r e a s t - h e i g h t d i a m e t e r s q u a r e d X h e i g h t on crown d i a m e t e r X crown l e n g t h ( R u d o l p h , 1956). T r e e s above t h e r e g r e s s i o n l i n e r e f l e c t s p e c i a l v i g o r and can be s e l e c t e d . A s i m i l a r p r o c e d u r e used by Brown and Goddard (1961) f o r l o b l o l l y p i n e , i s t o measure b a s a l a r e a i n c r e m e n t d u r i n g t h e l a s t t e n y e a r s , and r e l a t e t h i s t o t h e p r o d u c t o f crown l e n g t h X crown r a d i u s . They found a c o r r e l a t i o n c o e f f i c i e n t o f b a s a l a r e a i n c r e a s e on crown l e n g t h X crown r a d i u s t o be 0.83. A g a i n , t r e e s above t h e g e n e r a l r e g r e s s i o n l i n e a r e c a n d i d a t e s f o r s e l e c t i o n . A more r e l i a b l e i n d i c a t i o n of g r o w t h c a p a b i l i t i e s w o u l d be t h e use o f crown s u r f a c e a r e a (Brown and Goddard, 1961). H o l s o e (1948) found t h a t t h e r e g r e s s i o n o f t e n y e a r b a s a l a r e a i n c r e m e n t on crown s u r f a c e a r e a i n r e d oak and w h i t e a s h gave c o r r e l a t i o n c o e f f i c i e n t s o f 0.962 and 0.899, r e s p e c t i v e l y . S i n c e crown d i a m e t e r measurements a r e l a b o r i o u s and t i m e - c o n s u m i n g , t h e y a r e o n l y made i f t h e c a n d i d a t e t r e e meets minimum r e q u i r e m e n t s i n crown and b r a n c h c h a r a c t e r i s t i c s and i s f r e e o f damage from i n s e c t s and d i s e a s e s (Brown and Goddard, 1961). R e c e n t l y , c o n i f e r f o l i a g e mass was found t o be h i g h l y c o r r e l a t e d w i t h t h e c r o s s - s e c t i o n a l a r e a o f c o n d u c t i n g t i s s u e (sapwood) measured a t 1.3m above ground f o r D o u g l a s - f i r , n o b l e f i r , and p o n d erosa p i n e ( G r i e r and W a r i n g , 1974). The sapwood b a s a l a r e a and f o l i a g e a r e a a r e r e l a t e d s i n c e w a t e r t r a n s p o r t t o t h e f o l i a g e w i t h i n t h e t r e e stem i s c o n f i n e d t o t h e -8- sapwood (Whitehead, 1978). T h e r e f o r e , i t may be w o r t h w h i l e t o r e l a t e b a s a l a r e a i n c r e m e n t t o sapwood b a s a l a r e a , w h i c h would be a d i r e c t measurement o f a t r e e ' s l e a f a r e a . T r e e s above t h e r e g r e s s i o n l i n e r e p r e s e n t e f f i c i e n t wood p r o d u c e r s and a r e c a n d i d a t e s f o r s e l e c t i o n . F o r s e l e c t i o n , t h e a p proaches mentioned above a r e a p p l i c a t i o n s of a method c a l l e d b a s e - l i n e s e l e c t i o n ( E i n s p a h r ej: a l . , 1964; and M o r g e n s t e r n ej; a l . , 1975). To e v a l u a t e t h e g r o w t h of an i n d i v i d u a l t r e e a d e q u a t e l y , i t i s n e c e s s a r y n o t o n l y t o have i n f o r m a t i o n on age, stem d i a m e t e r a t b r e a s t h e i g h t , crown l e n g t h , crown w i d t h , and sapwood b a s a l a r e a , b u t t h e r e must be s t a n d a r d s o r b a s e - l i n e s w i t h w h i c h t o compare t h e g r o w t h r a t e s of i n d i v i d u a l t r e e s . The r e g r e s s i o n o f t h e dependent v a r i a b l e (stem volume o r b a s a l a r e a i n c r e m e n t ) on t h e i n d e p e n d e n t v a r i a b l e (crown s u r f a c e a r e a , crown l e n g t h X crown r a d i u s , o r sapwood b a s a l a r e a ) d e t e r m i n e s t h e b a s e - l i n e . C a n d i - d a t e t r e e s must exceed t h e mean o f t h e base p o p u l a t i o n by a c e r t a i n amount, f o r example, by two s t a n d a r d d e v i a t i o n s ( M o r g e n s t e r n e t a l . , 1975). There i s l i m i t e d i n f o r m a t i o n o f t h i s s u b j e c t p e r t a i n i n g t o w e s t e r n hemlock. A p o s i t i v e r e l a t i o n s h i p was f ound between crown w i d t h and stem d i a m e t e r ( S m i t h and K e r , 1960). V a r i a t i o n i n e f f i c i e n c y of b o l e volume/ crown volume was r e p o r t e d between t h e s p e c i e s w e s t e r n hemlock, D o u g l a s - f i r , and w e s t e r n r e d c e d a r , w i t h hemlock s u p e r i o r t o b o t h i n terms o f a v e r a g e e f f i c i e n c y o f wood p r o d u c t i o n ( S m i t h e t a l . , 1961). Thomas and S t e v e n s (1977) e v a l u a t e d g r o w t h e f f i c i e n c y i n w e s t e r n hemlock by r e l a t i n g f i v e y e a r b a s a l a r e a i n c r e m e n t t o crown a r e a . They used b a s e - l i n e s e l e c t i o n t e c h n i q u e s w i t h s e l e c t i o n o f p l u s t r e e s based d i r e c t l y on t h e s i z e o f t h e r e s i d u a l . -9- MATERIALS AND METHODS E i g h t y w e s t e r n hemlock t r e e s were s e l e c t e d a l o n g l o g g i n g r o a d s on Crown Z e l l e r b a c h t r e e farms i n Oregon and Washington. The l o c a t i o n o f t h e t r e e farms C l a t s o p , C a t h l a m e t , and T i l l a m o o k , and t h e 80 s e l e c t e d t r e e s , a r e shown i n F i g u r e s 1-4. The t r e e s were s e l e c t e d t o sample t h e range o f v a r i a t i o n i n g r o wth e f f i c i e n c y o f i n d i v i d u a l t r e e s i n t h e age range of 15 t o 40 y e a r s . I n i t - i a l s e l e c t i o n was based on t h e l i v e crown l e n g t h / c r o w n w i d t h r a t i o term- ed crown i n d e x (Assman, 1970). T h i s r a t i o g i v e s an i n d i c a t i o n o f t h e s l e n d e r n e s s o r roundness o f t r e e crowns. A h i g h r a t i o i n d i c a t e s a s l e n - d er crown. F o r w e s t e r n hemlock, an a v e r a g e r a t i o was d e t e r m i n e d t o be 2.5 (Walkup, 1978). The o b j e c t i v e was t o g e t a range of crown i n d e x r a t i o s as w i d e as p o s s i b l e . By u s i n g t h e crown i n d e x r a t i o , i t was p o s s i b l e t o sample t h e range o f v a r i a t i o n i n growth ' e f f i c i e n c y , ' - a n d a l s o t o d e t e r m i n e t h e e f f i - c i e n c y o f n a r r o w crown w e s t e r n hemlock t r e e s as wood p r o d u c e r s . The c h a r a c t e r s measured on each t r e e were t o t a l h e i g h t ^ (m), stem d i a m e t e r (cm) a t 1.3 m above ground ( d b h ) , t h r e e t o f i v e upper stem d i a - m e t e r s (cm) a t t h e i r r e s p e c t i v e stem h e i g h t s , b a r k t h i c k n e s s (mm) a t dbh, age, l i v e crown l e n g t h (m), crown w i d t h s (m) a t t h r e e d i f f e r e n t i n d i v i d u a l t r e e h e i g h t s , t e n y e a r r a d i a l i n c r e m e n t (cm) a t dbh, sapwood r a d i a l l e n g t h (cm) a t dbh, and t o t a l r a d i a l l e n g t h (cm) a t dbh. T o t a l h e i g h t , upper stem d i a m e t e r s , and l i v e crown l e n g t h were t o t a l h e i g h t was measured t o t h e n e a r e s t c e n t i m e t e r as i f t h e d r o o p i n g l e a d e r were s t r a i g h t measured by a S p i e g e l - R e l a s k o p . The l i v e crown l e n g t h i s d e f i n e d as t h e d i s t a n c e from t h e t i p o f t h e t e r m i n a l l e a d e r t o t h e l o w e s t l i v e b r a n c h - es o f a f u l l w h o r l . D i a m e t e r a t stump h e i g h t and dbh were measured by a d i a m e t e r t a p e . Crown w i d t h s were d e t e r m i n e d by m e a s u r i n g f o u r r a d i i and d i v i d i n g by two. Measurements were made f r o m t h e c e n t e r o f t h e stem t o r i g h t ang- l e s o f b r a n c h t i p s . Three crown w i d t h s were measured a t v a r i o u s h e i g h t s on t h e t r e e . The f i r s t crown w i d t h measured was al w a y s t h e base crown w i d t h . The base crown w i d t h was d e t e r m i n e d by t h e w i d t h o f t h e l o w e s t l i v e b r a n c h e s o f a f u l l w h o r l o f t h e t r e e crown. The r e m a i n i n g two crown w i d t h s were a r b i t r a r i l y chosen a t d i f f e r e n t h e i g h t s where t h e t r e e crown would v a r y i n shape, t h a t i s , d e v i a t e f r o m a c o n i c a l shape. Crown w i d t h s were d e t e r m i n e d as f o l l o w s : t h e r a d i u s a t t h e w i d e s t p a r t o f t h e l i v e crown b a s e was measured, t h e n t h r e e crown r a d i i were measured a t 90 degree i n t e r v a l s around t h e stem. The f o u r r a d i i were a v e r a g e d t o g i v e a crown w i d t h . Measurements o f t h e o t h e r two crown w i d t h s was n o t n e c e s s a r i l y a t i t s w i d e s t p o i n t , b u t made d i r e c t l y above o r p a r a l l e l t o i t s b a s e crown r a d i i . A g a i n , f o u r r a d i i were measured f o r each o f t h e two crown w i d t h s and a v e r a g e d . Ten y e a r r a d i a l i n c r e m e n t was d e t e r m i n e d by t a k i n g t h e a v e r a g e 10 y e a r r a d i a l i n c r e m e n t o f t h r e e c o r e s e x t r a c t e d a t 120 degree a n g l e s a t dbh. I f o n l y two c o r e s were t a k e n , they.were e x t r a c t e d , at.-90jdegree ang-7 l e s a t dbh. A f t e r t e n y e a r r a d i a l i n c r e m e n t was d e t e r m i n e d f o r each c o r e , t h e y were s t a i n e d t o d e t e r m i n e t h e r a d i a l sapwood t h i c k n e s s . S i n c e w e s t e r n hemlock does n o t have a v i s i b l e sapwood-heartwood boundry, a s t a i n i n g - 1 1 - s o l u t i o n o f 40 ml g l y c e r i n : 3 0 ml m e t h y l a l c o h o l : 6 0 ml c o n c e n t r a t e d h y d r o - c h l o r i c a c i d was used t o d e t e r m i n e t h e r a d i a l sapwood t h i c k n e s s . The s t a i n r e a c t s w i t h l e u c o a n t h o c y a n i d i n s , w h i c h a r e p r e s e n t i n t h e sapwood, r e s u l t i n g i n a pink-to-mauve c o l o r sapwood and a g r e e n i s h heartwood ( B a r - t o n , 1973). Age was d e t e r m i n e d by t a k i n g an i n c r e m e n t c o r e a t stump h e i g h t , and b a r k t h i c k n e s s a t dbh was d e t e r m i n e d by a b a r k meter t a k i n g t h e a v e r a g e o f t h r e e r e a d i n g s a t 120 degr e e a n g l e s . T o t a l h e i g h t , d i a m e t e r a t stump h e i g h t , dbh, t h r e e t o f i v e upper stem d i a m e t e r s , and b a r k t h i c k n e s s were used i n c a l c u l a t i n g t o t a l g r o s s stem volume i n s i d e b a r k . T h e r e f o r e , t h e stem was d i v i d e d i n t o f i v e , s i x , o r s e v e n s e c t i o n s , and t h e volume f o r each s e c t i o n was c a l c u l a t e d by S m a l i a n ' s f o r m u l a and summed. The l i v e crown l e n g t h and crown w i d t h s were used i n c a l c u l a t i n g crown s u r f a c e a r e a f o r each i n d i v i d u a l t r e e . The crown was d i v i d e d i n t o t h r e e s e c t i o n s and t h e s u r f a c e a r e a f o r each s e c t i o n was computed and summed as seen i n F i g u r e 5. Ten y e a r r a d i a l i n c r e m e n t and t o t a l r a d i a l l e n g t h were use'd i n c a l - c u l a t i n g t e n y e a r b a s a l a r e a i n c r e m e n t . L i k e w i s e , r a d i a l sapwood t h i c k - n e ss and t o t a l r a d i a l l e n g t h were used i n c a l c u l a t i n g sapwood b a s a l a r e a . Three models were employed u s i n g l e a s t s q u a r e r e g r e s s i o n t e c h n i q u e s t o d e t e r m i n e t h e range o f v a r i a t i o n i n growth e f f i c i e n c y o f i n d i v i d u a l w e s t e r n hemlock t r e e s . They a r e i n o r d e r : 1) g r o s s stem volume/crown s u r f a c e a r e a = a + b ( a g e ) , 2) t e n y e a r b a s a l a r e a i n c r e m e n t = a + b ( c r o w n s u r f a c e a r e a ) , and 3) t e n y e a r b a s a l a r e a i n c r e m e n t = a + b(sapwood b a s a l a r e a ) . -12- S c a t t e r diagrams of t e n y e a r b a s a l a r e a i n c r e m e n t on crown s u r f a c e a r e a and t e n y e a r b a s a l a r e a i n c r e m e n t on sapwood b a s a l a r e a , showed V- shaped d i s t r i b u t i o n s i n b o t h c a s e s w i t h t h e v a r i a n c e s i n c r e a s i n g l i n e a r l y w i t h t h e i n d e p e n d e n t v a r i a b l e . T h e r e f o r e , w e i g h t e d l e a s t s q u a r e r e g r e s s i o n t e c h n i q u e s were used i n t h e second and t h i r d models. The measurement of g r o w t h e f f i c i e n c y was based on t h e d e v i a t i o n o f an o b s e r v a t i o n f r o m t h e r e g r e s s i o n l i n e , t h a t i s , t h e s i z e of t h e r e s i d u a l s . B a s e l i n e s e l e c t i o n w i t h two s e l e c t i o n i n t e n s i t i e s o f 1/50 and 1/100 were employed t o s e l e c t f o r s u p e r i o r i n d i v i d u a l s f o r g r o w t h e f f i c i e n c y f o r a l l t h r e e r e g r e s s i o n models. T h e r e f o r e , o n l y t h o s e i n d i v i d u a l s whose s t a n d a r d - i z e d r e s i d u a l exceeded 2.054 (1/50) o r 2.33 (1/100) were s e l e c t e d . Ten y e a r b a s a l a r e a i n c r e m e n t / h e c t a r e f o r v a r i o u s sapwood b a s a l a r e a s was e s t i m a t e d f r o m t h e p r o d u c t of t e n y e a r b a s a l a r e a i n c r e m e n t / t r e e and t h e number of t r e e s / h e c t a r e f o r t h e c o r r e s p o n d i n g sapwood b a s a l a r e a . By r e l a t i n g t h e base crown w i d t h t o sapwood b a s a l a r e a t h e number o f t r e e s / h e c t a r e can be e s t i m a t e d . To d e t e r m i n e t h e e f f i c i e n c y o f n a rrow crown w e s t e r n hemlock t r e e s as wood p r o d u c e r s , t h e s t a n d a r d i z e d r e s i d u a l (measure o f g r o w t h e f f i c i e n c y ) f o r a l l t h r e e r e g r e s s i o n models was r e l a t e d t o t h e crown i n d e x r a t i o . O 2 0 4 0 M i l e s S C A L E il—i i -14- FIGURE 2 CLATSOP TREE FARM -15- FIGURE 3 TILLAMOOK TREE FARM  FIGURE 5: METHOD OF CALCULATING CROWN SURFACE AREA/TREE where z^ + z^ + = crown s u r f a c e a r e a ; (m ) D = crown w i d t h s h t = t r e e h e i g h t s w i t h i n crown RESULTS AND DISCUSSION 1. Range o f V a r i a t i o n i n Growth E f f i c i e n c y The t h r e e methods employed u s i n g l e a s t s q u a r e r e g r e s s i o n t e c h n i q u e s d e t e r m i n e d t h e range o f v a r i a t i o n i n g r o w t h e f f i c i e n c y o f i n d i v i d u a l w e s t e r n hemlock t r e e s . Growth e f f i c i e n c y i s d e f i n e d as t h e a b i l i t y o f t h e crown t o p r o d u c e t h e maximum amount o f wood i n r e l a t i o n t o i t s crown s u r f a c e a r e a . The measurement o f growth e f f i c i e n c y was based on t h e d e v i a t i o n o f an ob- s e r v a t i o n from t h e r e g r e s s i o n l i n e , t h a t i s , t h e s i z e o f t h e r e s i d u a l . T h e r e - f o r e , t h e range o f v a r i a t i o n i n growth e f f i c i e n c y i s d e t e r m i n e d f r o m t h e upper and l o w e r v a l u e s o f t h e r e s i d u a l s o r t h e s t a n d a r d i z e d r e s i d u a l s . The measurements t a k e n on t h e 80 i n d i v i d u a l o b s e r v a t i o n s w i t h com- p u t a t i o n s o f g r o s s stem volume, crown s u r f a c e a r e a , e t c . , a r e shown i n T a b l e 1. I t i s a p p a r e n t f r o m T a b l e 1 t h a t f o r n e a r l y t h e same b a s a l a r e a i n c r e m e n t o r t h e same age and n e a r l y t h e same g r o s s stem volume, t h e r e e x i s t s l a r g e d i f f e r e n c e s i n crown s u r f a c e a r e a . T h e r e f o r e , s i m p l e r e g r e s s i o n t e c h n i q u e s were used t o r a n k t h e t r e e s a c c o r d i n g t o t h e s i z e of t h e i r r e s i d u a l , most p r o d u c t i v e i n volume growth o r t e n y e a r b a s a l a r e a i n c r e m e n t , and t h e n l a t e r s e l e c t e f f i c i e n t l y g r o w i n g i n d i v i d u a l s by b a s e - l i n e s e l e c t i o n . S e l e c t i o n o f e f f i c i e n t l y g r o w i n g i n d i v i d u a l s i s based on t h e a s s u m p t i o n t h a t a l l t r e e s measured a r e e q u a l i n o t h e r p h e n o t y p i c t r a i t s o f i n t e r e s t . An a d d i t i o n a l a s s u m p t i o n i s t h a t t h e r e i s no major v a r i a t i o n i n c l i m a t i c and e d a p h i c i n - f l u e n c e s between t h e 80 o b s e r v a t i o n s . The d i f f e r e n c e s i n g r o s s stem volume or t e n y e a r b a s a l a r e a i n c r e m e n t f o r i n d i v i d u a l s w i t h n e a r l y t h e same crown s u r f a c e a r e a may be due t o d i f f e r - ences i n crown shape o r form; t h e r e b y c a u s i n g d i f f e r e n c e s i n t h e e f f i c i e n c y -19- TABLE l : MEASUREMENTS AND ESTIMATIONS 1 DF VARIOUS PARAMETERS 1 ON THE 8 0 SELECTED TREES TREE CROWN TEN YEAR GROSS CROWN TEN YEAR SAPWOOD AGE NO. INDEX BASAL AREA STEM SURFACE BASAL AREA BASAL PATIO INCREMENT VOLUME AREA INCREMENT* AREA (cm ) (m3) (m2) (cm ) (cm ) 1 2 . 9 7 2 7 C . 9 6 0 . 3 6 5 4 1 2 7 . 2 6 1 2 7 0 . 9 8 2 9 9 . 4 3 2 > 2 4 . 1 1 2 4 4 . 5 3 0 . 1 5 6 5 5 6 . 3 0 4 2 8 4 . 2 4 3 1 8 . 1 4 1 9 3 1 . 5 9 . 1 5 4 . 1 2 C . C 4 4 1 5 3 . 5 9 8 1 5 4 . 1 2 1 1 3 . 6 2 1 5 4 2 . 5 9 3 2 3 . 5 4 0 . 2 2 5 9 1 5 3 . 2 0 3 3 2 3 . 5 4 3 6 2 . 5 8 2.1 5 2 . 6 8 4 6 0 . 7 9 0 . 8 2 0 3 1 2 3 . 5 1 4 4 6 0 . 7 9 6 0 3 . 5 8 3 0 e 3 . 8 3 1 4 4 . 7 6 0 . 0 8 2 4 4 5 . 8 9 6 1 4 4 . 7 6 1 3 3 . 9 4 2 4 7 2.66 1 1 5 . C 7 C . C 5 3 0 3 3 . 1 5 3 1 1 5 . 0 7 1 1 4 . 7 8 2 0 8 1 . 7 5 4 1 7 . 9 3 0 . 3 1 7 4 1 4 8 . 5 9 3 4 1 7 . 9 3 4 1 4 . 2 6 2 1 q 2.55 2 1 9 . 0 2 0 . 1 3 0 9 4 2 . 1 4 2 2 1 9 . 0 2 2 1 6 . 2 0 1 9 IC 1 . 9 2 4 8 7 . 7 5 0 . 3 7 9 4 1 0 3 . 9 1 7 4 8 7 . 7 5 4 2 6 . 3 3 1 3 1 1 3.24 3 2 9 . 9 3 0 . 1 2 5 9 5 1 . 9 1 0 3 2 9 . 9 3 3 2 5 . 2 4 1 9 1 2 2 . 6 6 3 C 9 . 5 7 C . 1 2 9 2 6 3 . 0 7 0 3 0 9 . 5 7 2 7 7 . 7 6 2 1 1 2 2 . 1 2 2 0 7 . 9 3 0 . C 8 9 2 8 4 . 1 9 1 2 0 7 . 9 3 1 9 8 . 0 6 1 9 14 3 . 9 2 2 1 4 . 3 6 0 . 2 C 1 3 6 4 . 2 0 5 2 1 4 . 3 6 2 5 8 . 8 2 2 7 15 1.92 4 3 9 . 4 8 G.2259 9 2.758 4 3 9 . 4 8 4 8 4 . 6 1 2 1 16 2.08 1 7 8 . 0 4 0 . C 7 9 3 83.191 1 7 8 . 0 4 1 7 9 . 9 7 2 0 1 7 2.44 319.. IC 0. 1840 4 4 . 5 3 5 3 1 9 . 1 0 3 9 7 . 7 3 2 2 I £ 2.57 156.35 C. 1029 30.563 164 ,C3 206.75 22 I S 3.57 245.46 0 . 1743 43.293 245.46 3 * 5 . 7 . 5 2 7 /X 2.42 16 6.69 0.J005 50.506 166.S9 351.96 2 7 * Occasionally some increment cores did not stain to determine sapwood thickness. To be consistent only those cores which were used to measure sapwood thickness were used to determine ten year basal area increment for regression model 3. -20- TABLE I (CONT.) T SEE CROWN NO. INDEX R A T I G 21 22 23 24 25 26 27 26 29 3C 31 32 33 34 35 36 :37 •38 39. 4C 2.70 2.S7 3.33 3.14 2.64 2.21 1.43 2.25 2.23 2.97 2.83 2.22 1.69 2 .52 2.75 2 .40 2.49 2 .95 2.6 1 2 ,C3 TEN: YEAR BASAL AREA INCREMENT (cm ) 106. 17 120.56 312.24 137. 12 122.72 223.24 1C5.28 197.51 3 14.82 31.37 121.96 337.95 113.97 115.00 247.71 101.6 1 207.C9 62. 75 IC2.33 424.2C GPCSS STEM VCLUME (m ) 0.1580 0. 1376 0.4603 0.2362 0.1258 C.3182 0.C491 0.C747 C. 1527 0.C223 C. 129C 0.1503 0.C597 0.C413 0. 1057 0.C503 0. 1926 0.C4 91 C.C7C5 G . 3635 CROWN SURFACE AREA (m2) 41.258 40.276 70.424 44.820 27.738 33.629 4C.526 50.396 81. 158 39.014 46.991 52.301 54.624 55.306 76.290 72. 130 59.560 28.411 37.309 16 1.316 TEN YEAR BASAL AREA INCREMENT (cm2) 106.17 120.56 312.24 137.12 122.72 223.24 105.28 175.64 314.82 81.37 12L.96 395.8C 113.97 115.00 247.71 101.61 207.09 82.75 102.33 424.20 SAPWOOD BASAL AREA (cm ) 210.59 220.51 375.98 363.72 227.61 360.49 110.49 169.35 283.90 80.77 157.19 372.02 110.91 103.78 205.81 87.80 258.77 97.06 95.69 471.49 AGE 26 23 32 27 35 29 48 24 25 17 24 21 16 17 I 7 16 24 23 <!0 41 - 2 1 - TABLE I (CONT.) TREE Wo. CROWN" TEN YEAR GRCSS INDEX BASAL AREA STEM RATIO INCREMENT VOLUME u 1 42 43 45 46 47 49 49 50 / 5 1 52 53 54 55 56 5 7 53 59 60 2.14 3.31 3.73 2.92 2.83 2.74 2.45 3.04 4.26 2.72 2.96 2.29 2.65 2. 13 2.28 2.C4 2.43 3.10 2.96 2 .64 (cm ) 156. 13 1C1.64 223.30 159.59 17 4.56 1C4.63 199.86 222.43 266.00 136.C6 96.71 57.71 69.C8 19C .96 4C5.96 34 1. 14 158.62 333.97 I 7 C . 4 7 374.71 t  3̂  (m ) C. 1098 C.C769 0. 1430 C. 1306 0.1244 0.C481 0. 1234 C.2004 0. 1485 0.C564 0.C439 0.C359 C. C567 0. 1456 C.2699 0. 1655 G . 1414 0.2432 0.105 1 0.2126 CRCWN SURFACE AREA (m2) 46.064 63.231 92.057 38.362 41.609 30.025 71.933 58.734 118.238 51.276 26.019 15.090 2 8.7 85 46. 147 95.331 92.393 2 7.807 104. 965 58.184 128.532 TEN YEAR BASAL AREA INCREMENT (cm ) 137.61 101.84 218.81 159.59 174.56 104.83 199.86 222.43 266.CO 136.C8 96. 71 57.71 69.08 190.96 4C5.98 241.14 158.62 330.97 170.47 374.71 SAPWOOD BASAL AREA (cm ) 144.83 103.69 208.33 175.83 164.30 85.57 170.55 250.42 275.85 136.93 95.00 55.96 94.43 241.53 520.10 326.06 197.95 362.42 147.38 398.93 AGE 18 18 17 18 16 16 16 19 21 16 17 17 24 28 24 21 26 20 18 23 - 2 2 - T A B L E 1 ( C O - N T . - 1 T R E E C R C W N T E i \ V E A R G R O S S N O . I N C E X B A S A L A R E A S T E M R A T I O I N C R E M E N T V O L U M E C R C W N T E N Y E A R S A P W O O D A G E S U R F A C E B A S A L A R E A B A S A L A R E A I N C R E M E N T A R E A 6 1 6 2 6 3 6 5 6 6 6 7 6 8 6 9 7 C 7 1 7 2 7 3 7 4 7 5 7 6 7 7 7 8 7 9 3 . 7 6 3 . 4 1 3 . 9 2 2 . 5 3 2 . S 3 2 . 9 9 2 . 3 3 3 . 3 C 3 . 3 8 3 . 5 3 3 . 1 9 2 . 5 7 4 . 4 7 4 . 7 6 3 . 0 0 3 . 6 6 5 . 0 6 5 . 2 4 4 . 1 9 6 . CC (cm ) 3 5 3 . 7 4 1 5 2 . 8 3 1 2 G . 6 7 2 0 2 . 0 1 2 5 6 . 8 7 2 4 1 . 5 7 3 7 5 . 5 3 1 4 4 . 1 3 2 1 8 . 5 8 2 8 8 . C 5 8 4 . 1 4 1 7 4 . 3 4 1 3 9 . 0 2 3 4 5 . 3 1 1 1 2 . 8 2 I C O . 1 6 2 6 2 . 1 6 1 5 C . 5 6 1 4 2 . 7 C 3 5 2 . 4 8 (m3) C . 3 7 3 8 0 . 2 9 1 8 C . 1 8 2 9 0 . 2 1 3 0 0 . 2 4 4 3 0 . 1 5 6 C 0 . 4 1 8 0 C . 1 2 5 4 0 ^ 1 5 3 5 0 . 1 5 4 1 0 . 0 9 9 1 0 . 1 1 2 1 0 . 2 2 2 2 0 . 4 4 6 6 0 . C 9 9 5 0 . C 5 7 7 0 . 3 6 6 3 C . 2 4 3 7 C. 1 7 4 3 •J . 6 5 4 5 (m2) 8 1 . 0 9 8 9 6 . 8 9 3 6 1 . 3 0 7 4 1 . 4 0 8 5 6 . 4 4 9 5 3 . 2 9 6 8 1 . 0 3 0 7 6 . 5 8 9 6 3 . 7 5 5 5 7 . 6 3 6 2 2 . 8 8 3 3 9 . 4 6 5 8 4 . 6 4 7 1 3 7 . 2 1 4 2 9 . 5 1 3 2 6 . 0 4 4 1 0 0 . 3 1 3 6 9 . 1 4 9 7 2 . 0 2 6 1 4 0 . 5 4 7 (cm2) 3 5 3 . 7 4 1 5 2 . 6 3 1 2 0 . 6 7 2 C 2 . 0 1 2 9 6 . 8 7 2 2 7 . 5 1 3 7 5 . 5 3 1 1 5 . 8 9 2 1 8 . 5 3 2 8 8 . 0 5 8 4 . 1 4 1 7 4 . 3 4 1 4 6 . 9 4 3 4 9 . 3 1 1 1 2 . 8 2 1 0 0 . 1 6 2 6 2 . 1 6 1 5 0 . 9 6 1 4 2 . 7 0 3 0 C . 7 6 (cm ) 4 2 5 . 5 1 2 3 8 . 0 1 2 2 8 . 7 1 3 1 7 . 8 7 3 8 0 . 2 1 3 4 3 . 6 6 4 8 6 . 9 7 1 3 0 . 3 8 1 8 6 . 2 5 3 1 1 . 0 4 1 2 1 . 7 8 1 5 3 . 9 3 2 0 0 . 3 9 4 8 4 . 3 0 1 4 6 . 1 9 9 8 . 0 5 3 3 5 . 4 5 3 0 9 . 7 8 1 8 2 . 2 0 3 7 6 . 8 4 2 5 2 7 2 9 2 8 2 6 2 6 2 7 1 9 2 1 2 5 3 0 2 1 2 8 3 1 1 9 1 8 2 2 2 6 2 3 2 7 -23- o f t h e crowns t o s y n t h e s i z e p h o t o s y n t h a t e s . F o u r d i s t i n c t m o r p h o l o g i c a l crown forms o f w e s t e r n hemlock were o b s e r v e d on a l l t h r e e t r e e f a r m s , however, t h e e f f i c i e n c y w i t h i n and between t h e f o u r forms was n o t d e t e r m i n e d . The crown forms a r e made d i s t i n c t by t h e b r a n c h i n g c h a r a c t e r i s t i c s . The f o u r forms and t h e i r d e s c r i p t i o n a r e : 1) comb form: second o r d e r b r a n c h e s hang down i n a c o m b - l i k e c u r t a i n ( A p pendix I ) , 2) f l a t - b r a n c h e d form: second and t h i r d o r d e r b r a n c h e s d e v e l o p i n t h e same h o r i z o n t a l p l a n e (Appendix I I ) , 3) s t e e p l e form: t h e m a j o r i t y o f t h e f i r s t o r d e r b r a n c h e s i n t h e upper h a l f o f t h e t r e e crown droop s t r a i g h t down ( a v e r a g e w i d t h approx. 1 m.), w h i l e t h e l o w e r h a l f o f t h e crown have l o n g b r a n c h e s more o r l e s s a t r i g h t a n g l e s t o the stem (Appendix I I I ) , 4) c e d a r form: f u l l n e s s o f t h e crown r e s e m b l e s a c e d a r crown w i t h d r o o p i n g b r a n c h e s (Appendix I V ) . D i f f e r e n c e s i n crown s u r f a c e a r e a a r e p a r t l y due t o e n v i r o n m e n t and p a r t l y due t o h e r e d i t y . The magnitude o f t h e s e components a r e n o t d e f i n e d f o r w e s t e r n hemlock, b u t crown w i d t h w h i c h w i l l i n f l u e n c e crown s u r f a c e a r e a i s u s u a l l y i n f l u e n c e d more by s t o c k i n g . a) Model One: Growth E f f i c i e n c y - R e l a t i n g G r o s s Stem Volume/Crown S u r f a c e A r e a t o Age The range o f v a r i a t i o n i n growth e f f i c i e n c y by r e l a t i n g g r o s s stem v o l - 3 2 ume (m )/crown s u r f a c e a r e a (m ) t o age f o r t h e 80 i n d i v i d u a l o b s e r v a t i o n s i s shown i n F i g u r e 6. O b s e r v a t i o n s above t h e r e g r e s s i o n l i n e i n d i c a t e e f f i c i e n t  wood p r o d u c e r s i n r e l a t i o n t o t h e i r crown s u r f a c e a r e a and age, w h i l e o b s e r - v a t i o n s below t h e r e g r e s s i o n l i n e a r e l e s s e f f i c i e n t f o r wood p r o d u c t i o n i n r e l a t i o n t o t h e i r crown s u r f a c e a r e a and age. Of t h e 80 o b s e r v a t i o n s , 35 o c c u r r e d above t h e r e g r e s s i o n l i n e , w h i l e 45 o c c u r r e d b e l o w t h e r e g r e s s i o n l i n e . F i g u r e 7 shows a p l o t o f t h e s t a n d a r d i z e d r e s i d u a l s w i t h a v a r i a b l e range o f 4.189 f o r t r e e #26 t o -3.422 f o r t r e e #,27.' The r e g r e s s i o n e q u a t i o n , y = .00002 + .000124(x) where y = g r o s s stem volume/crown s u r f a c e a r e a , and x = age, t a k e s i n t o a c c o u n t t h e c o m p e t i t i v e i n f l u e n c e t o w h i c h a t r e e has been sub- j e c t e d , and a c c o r d i n g t o L e d i g (1974) i s t h e o r e t i c a l l y a sound approach. I f t h e crown s u r f a c e a r e a can be c o n s i d e r e d a good i n d i c a t i o n o f t h e c o m p e t i t i o n a t r e e has undergone, t h e n s e l e c t i o n o f g r o s s stem volume a t a g i v e n age s h o u l d be based on i n d i v i d u a l s w h i c h produced t h e l a r g e s t g r o s s stem volume i n r e l a t i o n t o t h e i r crown s u r f a c e a r e a . Based on t h e above o b s e r v a t i o n s , a c o r r e l a t i o n c o e f f i c i e n t o f .46 was c a l c u l a t e d between t h e i n d e p e n d e n t v a r i a b l e , age, and t h e dependent v a r i a b l e , g r o s s stem volume/crown s u r f a c e a r e a . The r e g r e s s i o n i s s i g n i f i c a n t a t t h e .01 l e v e l o f s i g n i f i c a n c e . R e f e r r i n g a g a i n t o F i g u r e s 6 and 7, i t i s a p p a r e n t t h a t t h e r e i s a w i d e r a n g e o f v a r i a t i o n i n growth e f f i c i e n c y when g r o s s stem volume/crown s u r f a c e a r e a i s r e l a t e d t o age. A c o e f f i c i e n t o f v a r i a t i o n o f 48.6% was computed by t h i s r e g r e s s i o n model. I t i s n o t unreasonable- t o s u s p e c t t h a t a t l e a s t p a r t o f t h i s v a r i a t i o n FIGURE 7 MODEL 1: VARIATION IN GROWTH IN GROWTH EFFICIENCY REPRESENTED BY STANDARDIZED RESIDUALS 3.E + 2.7 + I .a h4 CO w p4 Q W 0.0 3 _ 0.3 H CO ~ i .a -2.7 + -3.E f T T II I ON I -+- -+- 0 0 IS 20 2S 30 35 H0 HE TREE NUMBER 50 55 E0 E5 70 75 80 -27- i s due t o h e r i t a b l e f a c t o r s . T h e r e f o r e , s e l e c t i o n f o r g r o s s stem volume i n r e l a t i o n t o crown s u r f a c e a r e a and age c o u l d be w o r t h w h i l e , b) Model Two: Growth E f . f i c . i . e n c y r R e l a t i n g Ten Y e a r B a s a l A r e a Increment t o Crown S u r f a c e A r e a The range o f v a r i a t i o n i n growth e f f i c i e n c y by r e l a t i n g t e n y e a r b a s a l 2 2 a r e a i n c r e m e n t (cm ) t o crown s u r f a c e a r e a (m ) f o r t h e 80 i n d i v i d u a l o b s e r - v a t i o n s i s shown i n F i g u r e 8. A s c a t t e r d i a g r a m o f t e n y e a r b a s a l a r e a i n c r e - ment on crown s u r f a c e a r e a showed a V-shaped d i s t r i b u t i o n w i t h t h e v a r i a n c e s i n c r e a s i n g l i n e a r l y w i t h crown s u r f a c e a r e a . T h e r e f o r e , a w e i g h t e d l e a s t s q u a re r e g r e s s i o n t e c h n i q u e was used i n t h e a n a l y s i s . F o r t h i s r e g r e s s i o n model crown s u r f a c e a r e a a c c o u n t e d f o r 52 p e r c e n t o f the v a r i a n c e o f t e n y e a r b a s a l a r e a i n c r e m e n t . The r e g r e s s i o n i s s i g n i f i - c a n t a t t h e .01 l e v e l o f s i g n i f i c a n c e . O b s e r v a t i o n s above t h e r e g r e s s i o n l i n e i n F i g u r e 8 i n d i c a t e t r e e s e f f i c i e n t i n r a d i a l growth i n r e l a t i o n t o t h e i r crown s u r f a c e a r e a , w h i l e o b s e r v a t i o n s b e l o w t h e r e g r e s s i o n l i n e i n d i c a t e t r e e s w h i c h a r e l e s s e f f i c i e n t i n r a d i a l growth i n r e l a t i o n t o t h e i r crown s u r f a c e a r e a . Of t h e 80 o b s e r v a t i o n s , 36 o c c u r r e d above t h e r e g r e s s i o n l i n e , w h i l e 44 o c c u r r e d below. F i g u r e 3 shows a p l o t o f t h e s t a n d a r d i z e d r e s i d u a l s w i t h a v a r i a b l e range o f 2.541 f o r t r e e #17 t o -1.659 f o r t r e e #36. A g a i n , t h e r e g r e s s i o n e q u a t i o n , y = 51.55 + 2 . 4 9 5 ( x ) , where y = x = t e n y e a r b a s a l a r e a i n c r e m e n t , and crown s u r f a c e a r e a , FIGURE 8 MODEL 2: VARIATION IN GROWTH EFFICIENCY O—. CO 6 o IT). o UJ en (_) a C E l q . d COO SH- CE LU >- o w 2 H 0.0 Y = 51.55 + 2.495(X) SE = 1.05 (weighted) F = 83.9 r 2 = .52 i 00 I 25.0 50.0 75.0 100.0 125.0, CROWN SURFACE RREfl 0 0 150.0 ~ l 175.0 200.0 FIGURE 9 MODEL 2: VARIATION IN GROWTH EFFICIENCY REPRESENTED BY STANDARDIZED RESIDUALS 3.0 T . 2.4 + . B + 1.2 + w S 0.0 +i SI M -0.E + -1.2 + -I . B -2.H I N3 I -3.0 — i — 25 — i — 30 — t — 35 0 0 — i — 20 H0 MS TREE NUMBER £0 55 E0 E5 70 75 B0 -30- t a k e s i n t o a c c o u n t t h e c o m p e t i t i v e i n f l u e n c e t o w h i c h a t r e e has been sub- j e c t e d . The use o f t e n y e a r b a s a l a r e a i n c r e m e n t as the dependent v a r i a b l e i n s t e a d o f g r o s s stem volume has s e v e r a l advantages o v e r t h e l a t e r . F i r s t , crown s u r - f a c e a r e a i s an e s t i m a t e o f p a s t growth p o t e n t i a l f o r a s h o r t span o f t i m e . T h e r e f o r e , p r e s e n t crown s u r f a c e a r e a may n o t be a good r e p r e s e n t a t i o n o f g r o s s stem volume w h i c h i s an a c c u m u l a t i o n o f p a s t growth. Assuming t h a t t h e c u r - r e n t crown i s n o t much d i f f e r e n t from t h e crown a t t h e s t a r t o f t h e t e n y e a r p e r i o d , and t h a t t h e d u r a t i o n o f t h e p e r i o d has n o t seen major changes i n t h e s t a t u s o f t h e crown; th e n t h e p r e c e e d i n g t e n y e a r p e r i o d o f growth i s ad^ vantageous o v e r g r o s s stem volume. A second advantage i s t h e r e l a t i v e ease t o measure t e n y e a r b a s a l a r e a i n c r e m e n t r a t h e r t h a n g r o s s stem volume. R e f e r r i n g a g a i n t o F i g u r e s 8 and 9, i t i s a p p a r e n t t h a t t h e r e i s a w i d e range o f v a r i a t i o n o f t e n y e a r b a s a l a r e a i n c r e m e n t i n r e l a t i o n t o crown s u r - f a c e a r e a . F o r t h e o b s e r v a t i o n s measured a c o e f f i c i e n t o f v a r i a t i o n o f 16.3% was computed. A g a i n , i t i s n o t u n r e a s o n a b l e t o s u s p e c t t h a t a t l e a s t p a r t o f t h i s v a r i a t i o n i s due to h e r i t a b l e f a c t o r s . T h e r e f o r e , s e l e c t i o n o f growth e f f i c i e n c y by r e l a t i n g t e n y e a r b a s a l a r e a i n c r e m e n t t o crown s u r f a c e a r e a may be w o r t h - w h i l e . c) Model Three: Growth E f f i c i e n c y - R e l a t i n g Ten Y e a r B a s a l A r e a Increment t o Sapwood B a s a l A r e a As mentioned i n t h e l i t e r a t u r e r e v i e w , sapwood b a s a l a r e a i s a d i r e c t measurement o f a tree'rs l e a f a r e a o r crown s u r f a c e a r e a . P r e v i o u s r e g r e s s i o n s u s i n g sapwood b a s a l a r e a t o p r e d i c t p r o j e c t e d f o l i a g e a r e a (Whitehead, 1978) and f o l i a g e mass ( G r i e r and Wa r i n g , 1974) were f o u n d t o be h i g h l y c o r r e l a t e d . The r e g r e s s i o n o f crown s u r f a c e a r e a on sapwood b a s a l a r e a f o r t h e 80 - 3 1 - o b s e r v a t i o n s i s shown i n F i g u r e 10. T h i s r e l a t i o n s h i p has a c o r r e l a t i o n c o - e f f i c i e n t o f .63 and i s s i g n i f i c a n t a t t h e .01 l e v e l o f s i g n i f i c a n c e . The c o r r e l a t i o n c o e f f i c i e n t o f .63 i s l o w e r t h a n t h o s e o b s e r v e d by W h i t e - head (1978) f o r S c o t s p i n e (r=.98, n = l l ) , and G r i e r and W a r i n g (1974) f o r Doug- l a s - f i r (r=.98, n=33), n o b l e f i r (r=.99, n=10), and p o n d e r o s a p i n e (r=.98, n=9). T h i s may be due t o a h i g h e r r e l a t i o n s h i p between sapwood b a s a l a r e a and f o l i a g e a r e a o r mass, t h a n sapwood b a s a l a r e a and crown s u r f a c e a r e a . The d i f f e r e n c e may a l s o be due t o d i f f e r e n c e s i n shade t o l e r a n c e . Western hemlock i s c o n - s i d e r e d a shade t o l e r a n t s p e c i e s , whereas D o u g l a s - f i r , p o n d e r o s a p i n e , S c o t s p i n e , and n o b l e f i r a r e c o n s i d e r e d shade i n t o l e r a n t ( F o w e l l s , 1965). However, t h i s does n o t n e g a t e t h e use o f s u b s t i t u t i n g sapwood b a s a l a r e a f o r crown s u r f a c e a r e a t o p r e d i c t t e n y e a r b a s a l a r e a i n c r e m e n t . The use o f sapwood b a s a l a r e a a t 1.3 m e t e r s above ground r a t h e r t h a n crown s u r f a c e a r e a t o p r e d i c t t e n y e a r b a s a l a r e a i n c r e m e n t has an o b v i o u s a d v a n t a g e i n measurement. S i n c e t h r e e i n c r e m e n t c o r e s have a l r e a d y been e x t r a c t e d t o measure t e n y e a r b a s a l a r e a i n c r e m e n t t h e s t a i n i n g and m e a s u r i n g o f t h e s e same t h r e e c o r e s t o d e t e r m i n e sapwood b a s a l a r e a p r e s e n t s more ease and l e s s t i m e t h a n m e a s u r i n g t h e l i v e crown l e n g t h and t w e l v e crown r a d i i t o d e t e r m i n e crown s u r f a c e a r e a . The range o f v a r i a t i o n i n growth e f f i c i e n c y by r e l a t i n g t e n y e a r b a s a l a r e a 2 2 i n c r e m e n t (cm ) t o sapwood b a s a l a r e a (cm ) f o r t h e 80 o b s e r v a t i o n s i s shown i n F i g u r e 11. A s c a t t e r d i a g r a m o f t e n y e a r b a s a l a r e a i n c r e m e n t on sapwood b a s a l a r e a showed a V-shaped d i s t r i b u t i o n w i t h t h e v a r i a n c e s i n c r e a s i n g l i n e a r l y w i t h sapwood b a s a l a r e a . A g a i n , a w e i g h t e d l e a s t s q u a r e r e g r e s s i o n t e c h n i q u e was used i n t h e a n a l y s i s . F o r t h i s r e g r e s s i o n model, sapwood b a s a l a r e a a c c o u n t e d f o r 82 p e r c e n t o f t h e v a r i a n c e o f t e n y e a r b a s a l a r e a i n c r e m e n t . T h i s r e g r e s s i o n model i s   -34- a l s o s i g n i f i c a n t a t t h e .01 l e v e l o f s i g n i f i c a n c e . A g a i n , o b s e r v a t i o n s above t h e r e g r e s s i o n l i n e i n d i c a t e t r e e s e f f i c i e n t i n r a d i a l growth i n r e l a t i o n t o t h e i r sapwood b a s a l a r e a , w h i l e o b s e r v a t i o n s b e l o w t h e r e g r e s s i o n l i n e i n d i - c a t e t r e e s w h i c h a r e l e s s e f f i c i e n t i n r a d i a l growth i n r e l a t i o n t o t h e i r s a p - wood b a s a l a r e a . Of t h e 80 o b s e r v a t i o n s , 42 o c c u r r e d above t h e r e g r e s s i o n l i n e , w h i l e 38 o c c u r r e d b e l o w t h e r e g r e s s i o n l i n e . F i g u r e 12 shows a p l o t o f t h e s t a n d a r d - i z e d r e s i d u a l s w i t h a v a r i a b l e range o f 2.361 f o r t r e e #10 t o -2.979 f o r t r e e #24. S i n c e sapwood b a s a l a r e a i s r e l a t e d t o crownvjsurfa'ce a r e a t h e ' r e g r e s s i o n e q u a t i o n , y = 25.64 + .7554(x) where y = t e n y e a r b a s a l a r e a i n c r e m e n t , and x = sapwood b a s a l a r e a , t a k e s i n t o a c c o u n t t h e c o m p e t i t i v e i n f l u e n c e t o w h i c h a t r e e has been sub- j e c t e d . A g a i n , i t a p p e a r s i n F i g u r e s 11 and 12 t h a t t h e r e i s a w i d e range o f v a r i a t i o n o f t e n y e a r b a s a l a r e a i n c r e m e n t i n r e l a t i o n t o sapwood b a s a l a r e a . A c o e f f i c i e n t o f v a r i a t i o n o f 3.1% was computed by t h i s r e g r e s s i o n model. T h e r e f o r e , as i n t h e o t h e r two r e g r e s s i o n models, i t i s n o t u n r e a s o n - a b l e t o s u s p e c t t h a t a t l e a s t p a r t of t h i s v a r i a t i o n i s due t o h e r i t a b l e f a c t o r s . T h e r e f o r e , s e l e c t i o n f o r t e n y e a r b a s a l a r e a i n c r e m e n t i n r e l a t i o n t o sapwood b a s a l a r e a c o u l d be w o r t h w h i l e . FIGURE 12 MODEL 3: VARIATION IN GROWTH EFFICIENCY REPRESENTED BY STANDARDIZED RESIDUALS 3.0 T 2.H § 0. E M W w Pi @ 0.0 N I—I g -0.E -I.B + -2.H + -3.0 0 i 00 I 0 IS 20 25 30 35 H0 MS TREE NUMBER £0 55 E0 E5 70 75 B0 -36- 2. U t i l i z a t i o n o f V a r i a t i o n i n Growth E f f i c i e n c y Knowing t h a t a s u f f i c i e n t range o f v a r i a t i o n i n growth e f f i c i e n c y e x i s t s f o r a l l t h r e e r e g r e s s i o n models, we s h o u l d c o n s i d e r how t o u t i l i z e t h i s v a r i a - t i o n . I n o r d e r t o l o c a t e s u p e r i o r phenotypes t o be t e s t e d f o r g e n e t i c s u p e r - i o r i t y a s t a t i s t i c a l r e l a t i o n s h i p between t h e o b s e r v a t i o n s and t h e mean o f t h e p o p u l a t i o n i s n e c e s s a r y t o p r e d i c t t h e degree o f improvement t h a t can be ex- . . p e c t e d . There a r e d i f f e r e n t methods t o u t i l i z e t h i s i n f o r m a t i o n , b u t one ap- p r o a c h i s t h e use o f b a s e - l i n e s e l e c t i o n . As mentioned i n t h e l i t e r a t u r e r e v i e w , b a s e - l i n e s e l e c t i o n p r o v i d e s s t a n d a r d s w i t h w h i c h t o compare t h e growth e f f i c i e n c y o f i n d i v i d u a l t r e e s . The r e g r e s s i o n o f t h e dependent v a r i a b l e on t h e i n d e p e n d e n t v a r i a b l e can be c o n s i d e r e d t h e b a s e - l i n e . The b a s e - l i n e , w h i c h i s t h e r e g r e s s i o n l i n e , s e r v e s as an e n v i r o n m e n t a l r e f e r e n c e and t h e r e s i d u a l v a r i a t i o n i s e q u a t e d w i t h g e n e t i c v a r i a n c e . T h e r e f o r e , s e l e c t i o n f o r growth e f f i c i e n c y o f t h e measured t r e e s i s based on i n d i v i d u a l s w i t h r e s i d u a l s above a d e s i r e d s t a n d - a r d s u c h as two s t a n d a r d e r r o r s o f t h e e s t i m a t e . I n o r d e r t o use s t a n d a r d e r r o r s of t h e e s t i m a t e t o s e l e c t f o r e f f i c i e n t - l y g r o w i n g t r e e s , t h e f r e q u e n c y d i s t r i b u t i o n o f t h e r e s i d u a l s s h o u l d be n o r - mal. The r e s i d u a l s from a l l t h r e e r e g r e s s i o n models a p p r o x i m a t e a n o r m a l d i s t r i b u t i o n . F i g u r e s 13, 14, and 15 show th e p l o t t i n g of t h e c u m u l a t i v e n o r - mal and o b s e r v e d d i s t r i b u t i o n f o r t h e t h r e e r e g r e s s i o n models. T a b l e 2 shows t h e c u m u l a t i v e p e r c e n t under t h e n o r m a l and o b s e r v e d d i s t r i b u t i o n s a t v a r i o u s s t a n d a r d e r r o r s o f t h e e s t i m a t e . A l t h o u g h t h e o b s e r v e d d i s t r i b u t i o n s f o r each model a r e skewed t o some d e g r e e , a t - t e s t f o r skewness showed t h a t t h e d i s t r i b u t i o n s were n o t s i g n i f i c a n t l y d i f f e r e n t from normal a t t h e .05 l e v e l o f s i g n i f i c a n c e . FIGURE 13 CUMULATIVE NORMAL AND OBSERVED DISTRIBUTIONS FOR MODEL 1 100 4- -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 STANDARD ERROR OF THE ESTIMATE FIGURE 14 CUMULATIVE NORMAL AND OBSERVED DISTRIBUTIONS FOR MODEL 2 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2. STANDARD ERROR OF THE ESTIMATE FIGURE 15 CUMULATIVE NORMAL AND OBSERVED DISTRIBUTIONS FOR MODEL 3. -40- T A B L E 2: C U M U L A T I V E PERCENT UNDEB T E E NORMAL AND OBSERVED D I S T R I B U T I O N S STANDARD ERROR % NORMAL % OBSERVED D I S T R I B U T I O N OF THE E S T I M A T E D I S T R I B U T I O N MODEL 1 MODEL 2 MODEL 3 - 2 . 5 0,62 1-25 0-0 1. 25 - 2 . 0 2. 28 1-25 0.0 3.15 - 1 . 5 6.68 2-50 2-50 8. 7 5 -1.0 15. 87 6.25 1 5 . 0 0 1 5 . 00 - 0 . 5 3 0 . 8 5 3 0 . 0 0 3 3 . 8 5 2 5 . 00 0.0 5 0 . 0 0 5 6 , 25 5 5 . 0 0 4 7 . 5 0 0.5 6 9 - 1 5 7 3 . 7 5 7 1 . 2 5 6 7 . 50 1.0 8 4 . 13 8 6 - 2 5 8 1 . 2 5 8 6 . 2 5 1.5 9 3 . 3 2 9 3 . 7 5 9 1 . 2 5 9 3 . 75 2.0 9 7 - 72 9 7 - 5 0 . S 6 - 2 5 98- 75 2. 5 9 9 - 3 8 9 8 - 7 5 9 8 . 7 5 100-CO - 4 1 - A c c o r d i n g t o t h e needs o f a p a r t i c u l a r t r e e improvement program any l e v e l o f s t a n d a r d e r r o r s o f e s t i m a t e c a n be employed as a s e l e c t i o n g u i d e - l i n e . I n a l l t h r e e r e g r e s s i o n models, +2.054 and +2.33 s t a n d a r d e r r o r s o f t h e e s t i m a t e , w h i c h i s e q u i v a l e n t t o s e l e c t i o n i n t e n s i t i e s o f one i n f i f t y and one i n a hundred r e s p e c t i v e l y , a r e used as s e l e c t i o n g u i d e l i n e s f o r growth e f f i c i e n c y . T h e r e f o r e , o n l y t h o s e t r e e s whose s t a n d a r d i z e d r e s i d u a l exceeds 2.054 o r 2.33 w i l l be s e l e c t e d f o r growth e f f i c i e n c y . F i g u r e 16 shows t h e s e l e c t i o n o f e f f i c i e n t i n d i v i d u a l s f o r t h e f i r s t r e g r e s s i o n model o f g r o s s stem volume/crown s u r f a c e a r e a on age. A s e l e c t i o n i n t e n s i t y o f one i n f i f t y w i l l s e l e c t t r e e s #5 and #26 w h i c h have s t a n d a r d - i z e d r e s i d u a l s o f 2.075 and 4.189 r e s p e c t i v e l y , w h i l e o n l y t r e e #26 w i l l be s e l e c t e d a t an i n t e n s i t y o f s e l e c t i o n o f one i n a hundred. F o r t h e second r e g r e s s i o n model, F i g u r e 17, o f t e n y e a r b a s a l a r e a i n c r e m e n t on crown s u r f a c e a r e a , o n l y t h r e e t r e e s w i l l be s e l e c t e d w i t h a s e l e c t i o n i n t e n s i t y o f one i n f i f t y , namely t r e e s #11, 17 and 32. F o r t h i s r e g r e s s i o n model, two t r e e s had s t a n d a r d i z e d r e s i d u a l s g r e a t e r t h a n 2.33. Hence, t r e e s #17 and #32 a r e s e l e c t e d a t t h e s e l e c t i o n i n t e n s i t y o f one i n a hundred. The s e l e c t i o n o f e f f i c i e n t i n d i v i d u a l s by t h e l a s t r e g r e s s i o n model o f t e n y e a r b a s a l a r e a i n c r e m e n t on sapwood b a s a l a r e a i s shown i n F i g u r e 18. Only one t r e e i s s e l e c t e d , t r e e #10, whose s t a n d a r d i z e d r e s i d u a l exceeds b o t h l e v e l s o f i n t e n s i t y . T a b l e 3 shows t h e s t a n d a r d i z e d r e s i d u a l and r a n k i n g o f t h e 80 i n - d i v i d u a l o b s e r v a t i o n s f o r a l l t h r e e r e g r e s s i o n models. A l l t h r e e r e g r e s s i o n models of e v a l u a t i n g growth e f f i c i e n c y a r e p l a u s i b l e and w i l l l o c a t e s u p e r i o r phenotypes t o be t e s t e d f o r g e n e t i c s u p e r i o r i t y , b u t t h e r e a p p ears t o be a wide r a n g e o f v a r i a t i o n between t h e r a n k i n g o f t h e o b s e r v a t i o n s by t h e t h r e e r e g r e s s i o n models.    -45- T A B L E 3 : S T A N D A R D I Z E D R E S I D U A L S A N D R A N K I N G O F T H E 80 O B S E R V A T I O N S T R E E M O D E L 1 R A N K M O D E L 2 R A N K M O D E L 3 R A N K N O . <STD. R E S I D U A L S T D . R E S I D U A L S T D . R E S I D U A L 1 - 0 . 0 9 3 3 7 - 1 . 0 6 0 69' 0 . 3 8 5 2 9 2 0 . 2 8 8 2 6 0 . 7 5 8 2 0 0 . 3 5 7 3 1 3 - 0 . 7 5 9 6 6 - 0 . 4 6 2 5 3 1 . 3 9 2 7 A - 0 . 3 2 7 6 3 - 0 . 9 6 6 6 3 0 . 4 3 9 2 7 5 2 . 0 7 5 * 2 C . 9 8 5 1 6 - 0 . 2 9 4 5 4 6 - 0 . 8 6 5 6 9 - 0 . 3 4 1 4 2 0 . 5 4 0 2 6 7 - 0 . 6 4 9 6 1 - 0 . 3 6 2 4 4 0 . 0 8 9 3 3 8 - 0 . 3 5 3 5 1 - 0 . 0 3 9 3 7 1 . 3 5 7 6 9 0 . 5 2 2 2 1 1 . 0 4 1 1 5 0 . 7 1 1 " 1 8 1 0 1 . 0 0 1 1 1 1 . 8 8 2 4 2 . 3 6 1 * * 1 1 1 C . C 3 3 3 5 2 . 2 3 9 * 3 1 . 1 3 1 1 1 1 2 - 0 . 4 1 6 5 3 1 . 3 7 4 1 3 1 . 5 4 7 4 1 3 - 0 . 9 4 7 7 3 - 0 . 6 3 5 5 6 0 . 8 0 8 1 6 1 4 - 0 . 1 7 1 4 1 0 . 0 3 5 3 5 - C . 1 4 7 4 7 1 5 - 0 . 1 3 8 39 1 . 7 6 2 5 0 . 7 5 5 1 7 1 6 - 1 . 1 1 2 7 7 - 0 . 9 6 4 6 7 0 . 4 2 7 2 8 1 7 0 . 9 8 9 1 2 2 . 5 4 1 * * 1 - 0 . 1 2 2 4 5 1 8 0 . 4 4 2 23 C . 5 6 0 2 3 - 0 . 4 3 0 5 9 1 9 0 . 4 6 8 2 2 1 . 4 1 5 9 - 0 . 6 4 2 6 4 2 0 i . 8 4 8 3 - 0 . 13:5 3 8 - 2 . 2 7 4 7 8 * exceeds s e l e c t i o n i n t e n s i t y o f 1/50 e x c e e d s s e l e c t i o n i n t e n s i t y o f 1/100 -46- T A B L E 3 ( C O N T . ) T R E E M O D E L 1 R A N K M O D E L 2 R A N K f l O O E L 3 R A N K N O . S T D . R E S I D U A L S T D . R E S I D U A L S T D . R E S I D U A L 21 0 . 4 1 6 2 5 - 0 . 8 1 6 6 4 - 1 . 8 8 3 7 7 2 2 - 0 . 0 5 9 3 6 - 0 . 5 3 8 5 4 - 1 . 6 7 9 7 4 2 3 1 . 8 2 2 4 1 . 0 9 8 1 4 0 . 0 4 7 4 0 2 4 1 . 3 6 1 5 - 0 . 4 2 5 4 9 - 2 . 9 7 9 8 0 2 5 C . 1 2 0 3 3 0 . 0 4 0 3 4 - i . 7 2 6 7 5 2 6 4 . 1 8 9 * * 1 1 . 6 4 1 6 - 1 . 3 6 9 7 3 2 7 - 3 . 4 2 2 8 0 - 0 . 8 0 7 6 2 - 0 . 1 2 6 4 6 2 8 - 1 . 0 8 9 7 6 0 . 3 0 9 2 3 0 . 5 9 0 2 2 2 5 - 0 . 8 9 1 7 1 0 . 7 3 1 2 1 1 . 5 4 3 5 3 0 - 1 . 1 1 7 7 8 - 1 . 1 7 2 7 5 - 0 . 2 0 4 5 0 3 1 - 0 . 1 8 3 4 2 - 0 . 7 4 1 5 9 - 0 . 6 2 2 6 3 3 2 0 . 1 7 7 2 9 2 . 3 3 8 * * 2 1 . 6 0 8 3 3 3 - 0 . 6 5 4 6 3 - 1 . 0 8 4 7 0 0 . 1 5 C 3 6 3 4 - 0 . 9 9 3 7 5 - 1 . 0 8 7 7 7 0 . 2 4 0 3 2 3 5 - 0 . 5 3 4 5 8 0 . 0 7 2 3 3 1 . 6 1 5 2 3 6 - 0 . 5 3 9 7 2 - 1 . 6 5 9 8 0 0 . 3 5 8 3 0 3 7 0 . 1 6 7 3 0 0 . 0 9 7 3 2 - 0 . 3 0 3 5 5 3 8 - C . 8 2 3 6 7 - 0 . 3 0 3 6 3 - 0 . 5 7 2 6 2 3 9 - C . 4 3 9 5 4 - C . 7 5 1 6 0 C . 1 5 7 3 5 4 0 - 1 . 9 6 3 7 9 - 0 . 2 5 5 4 1 0 . 6 7 9 1 9 T A B L E 3 ( C O N T . ) T R E E M O D E L 1 R A N K M O D E L 2 R A N K M O D E L 3 R A N K N O . S T D . R E S I D U A L S T D . R E S I D U A L S T D . R E S I D U A L 4-1 0 . 0 9 3 34 - 0 . 1 3 4 3 9 0 . 0 7 4 3 9 4 2 - 0 . 7 4 5 6 5 - 1 . 4 6 6 7 8 - 0 . 0 7 3 4 4 4 3 - Q . 4 1 4 5 2 - 0 . 6 5 5 5 7 0 . 8 6 3 1 4 4 4 0 . 8 2 3 1 4 0 . 2 1 5 2 9 C . 0 3 0 4 1 4 5 0 . 7 0 6 1 8 0 . 3 2 2 2 7 0 . 6 7 3 2 0 4 6 - 0 . 2 8 9 4 7 - 0 . 4 2 8 5 0 0 . 5 4 7 2 4 4 7 - 0 . 2 0 8 4 3 - 0 . 4 0 0 4 6 1 . 2 0 9 1 0 4 8 0 . 7 4 1 1 6 0 . 3 4 4 2 6 0 . 1 6 8 3 4 4 9 - 0 . 9 8 4 7 4 - 0 . 8 0 5 6 1 0 . 6 7 0 2 1 5 0 - 0 . 6 5 0 6 2 - 0 . 6 5 8 5 8 0 . 2 0 8 3 3 5 1 - 0 . 3 1 8 4 8 - 0 . 4 2 0 4 8 - 0 . 0 2 5 4 3 5 2 ' 0 . 1 8 2 2 8 - 0 . 8 7 9 6 5 - 0 . 4 7 4 6 0 5 3 - 0 . 7 3 5 6 4 - 1 . 0 9 7 7 2 - 0 . 9 9 8 6 8 5 4 - 0 . 2 4 6 4 5 0 . 3 8 7 2 5 - C . 3 8 3 5 7 55 Q . 6 3 C 2 0 1 . 2 9 4 1 2 - 0 . 1 9 1 4 9 56 - 0 . 6 0 C 5 9 0 . 6 6 6 2 2 1 . 3 3 3 3 57 1 . 3 1 6 6 0 . 7 7 5 1 9 - C . 4 0 9 5 8 58 - 0 . 1 3 4 3 3 0 . 1 3 5 30 C . 5 7 7 2 3 55 - C . 3 2 1 4 5 - 0 . 3 7 3 4 5 0 . 9 6 0 1 2 6C - 0 . 8 7 7 7 0 0 . 0 2 3 36 C . 8 3 1 1 5 -48- T A 6 L E 3 ( C O N T . i T R E E K Q D E L I N O . S T D . R E S I C I U L R A N K M O D E L 2 S T D . R E S I D U A L R A N K M O D E L 3 S T D . R E S I D U A L R A N K 6 1 6 2 6 3 6 4 6 5 6 6 6 7 6 8 6 9 7 C 7 1 7 2 7 3 7 4 7 5 7 6 7 7 7 8 7 9 8G 1 . 0 6 4 • Q . 2 6 C •0 . 4 5 8 1 . 1 8 C C . 7 7 4 • C . 2 3 1 1 . 2 8 C 0. 5 3 2 0. 1 5 8 0. 1 6 6 C . 4 1 6 0 . 1 5 4 • C . 6 2 6 • 0 . 4 4 2 0 . 7 1 2 1 . 0 7 5 0 . 6 4 5 0 . 1 9 7 0 . 3 2 7 0 . 9 2 0 1 0 4 6 5 6 8 1 5 4 4 7 5 7 4 0 3 1 2 4 3 2 6 0 5 5 1 7 9 1 9 2 7 5 0 1 3 1 . 2 0 2 - 1 . 5 4 8 - 1 . 1 6 1 0 . 7 9 4 1 . 5 0 8 0 . 8 5 3 1 . 4 6 7 - 1 . 2 2 1 0 . 1 0 8 1 . 3 1 4 - 0 . 5 5 6 0 . 4 2 0 - 1 . 4 5 9 - 0 . 4 1 3 - 0 . 2 4 7 - 0 . 3 4 8 - 0 . 4 3 0 - C . 9 ' 5 4 - 1 . 1 3 2 - C . 4 5 5 1 3 7 9 7 4 1 8 7 1 7 8 7 6 3 1 1 1 5 5 2 4 7 7 4 7 4 0 4 3 5 1 66 7 3 52 G . 1 1 3 - 1 . 1 8 6 • 1 . 7 8 8 - 1 . 2 4 4 • 0 . 2 8 5 • 1 . 0 8 3 • 0 . 2 8 3 - C . 2 5 1 1 . 3 3 2 0 . 5 4 2 - 1 . 0 5 6 G . 9 0 9 - 0 . 7 3 9 • 0 . 6 7 2 - 0 . 6 6 9 C . 0 1 6 - 0 . 3 2 0 - 2 . 1 4 9 • 0 . 5 3 0 • 0 . 1 7 1 3 7 7 1 7 6 7 2 5 3 7 0 5 2 5 1 9 2 5 6 9 1 3 6 7 6 6 6 5 4 2 5 6 7 9 6 1 4 8 -49- To d e t e r m i n e w h i c h v a r i a b l e s and r e g r e s s i o n model i s b e s t t o e v a l u - a t e t h e growth e f f i c i e n c y o f i n d i v i d u a l t r e e s w i l l r e s t on t h e outcome o f i n h e r i t a n c e s t u d i e s . However, t h e l a s t r e g r e s s i o n model t h a t i s r e l a t i n g t e n y e a r b a s a l a r e a i n c r e m e n t t o sapwood b a s a l a r e a , i s t h e d e s i r e d model t o e v a l u a t e growth e f f i c i e n c y . T h i s i s b a s e d on t h e ease o f measurement o f t h e two v a r i a b l e s and t h e h i g h c o r r e l a t i o n between them. The s i g n i f i c a n c e o f t h e v a r i a t i o n i n growth e f f i c i e n c y becomes a p p a r - en t i n T a b l e 4 w h i c h shows p r e d i c t e d t e n y e a r b a s a l a r e a i n c r e m e n t / h e c t a r e (m 2) f o r v a r i o u s sapwood b a s a l a r e a s . Ten y e a r b a s a l a r e a i n c r e m e n t / h e c t a r e was e s t i m a t e d f r o m t h e p r o d u c t o f t e n y e a r b a s a l a r e a / t r e e (Model 3) and t h e number o f t r e e s / h e c t a r e four. the< c o r r e s p o n d i n g sapwood b a s a l a r e a . By r e - l a t i n g t h e v a r i a b l e base crown w i d t h t o sapwood b a s a l a r e a , t h e number o f t r e e s / h e c t a r e can be e s t i m a t e d f o r a g i v e n sapwood b a s a l a r e a . The r e g r e s s i o n i s s i g n i f i c a n t a t t h e .01 l e v e l o f s i g n i f i c a n c e and has a c o r r e l a t i o n c o - e f f i c i e n t o f .56. F o r each g i v e n sapwood b a s a l a r e a , t h e t e n y e a r b a s a l a r e a i n c r e m e n t / h e c t a r e was c a l c u l a t e d f o r f i v e c l a s s e s o f growth e f f i c i e n c y b a s e d on Model 3. The c l a s s e s a r e d e f i n e d a s — low growth e f f i c i e n c y : t r e e s w h i c h a r e -2.33 s t a n d a r d e r r o r s o f t h e e s t i m a t e f r o m t h e r e g r e s s i o n l i n e medium low growth e f f i c i e n c y : t r e e s w h i c h a r e -2.054 s t a n d a r d e r r o r s o f t h e e s t i m a t e f r o m t h e r e g r e s s i o n l i n e a v e r a g e growth e f f i c i e n c y : t r e e s on t h e r e g r e s s i o n l i n e medium h i g h growth e f f i c i e n c y : t r e e s w h i c h a r e +2.054 s t a n d - a r d e r r o r s o f t h e e s t i m a t e f r o m t h e r e g r e s s i o n l i n e h i g h growth e f f i c i e n c y : t r e e s w h i c h a r e +2.33 s t a n d a r d e r r o r s o f t h e e s t i m a t e f r o m t h e r e - g r e s s i o n l i n e -50- T A B L E 4 : P R E D I C T E D T E N Y E A R B A S A L A R E A I N C R E M E N T / H E C T A R E A T V A R I O U S S A P W O O D B A S A L A R E A S A N D C L A S S E S O F E F F I C I E N C Y S A P W O O D C L A S S E S O F E F F I C I E N C Y B A S A L A R E A LOW M E D . L O W A V E , M E D . H I G H H I G H (cm ) (m ) (m ) (m ) (m 2) (m 2) 6 0 2 . 7 3 . 6 1 0 . 2 1 6 . 8 1 7 . 7 7 0 3 . 1 4 . 1 1 0 . 9 1 7 . 8 1 8 . 7 8 0 3 . 5 4 . 5 1 1 . 6 1 8 . 7 1 9 . 6 9 0 3 . 9 4 . 9 1 2 . 2 1 9 . 5 2 0 . 4 1 0 0 4 . 3 5 . 3 1 2 . 7 2 0 . 1 2 1 . 1 1 1 0 4 . 7 5 . 7 1 3 . 2 2 0 . 8 2 1 . 8 1 2 0 5 . 1 6 . 1 1 3 . 7 2 1 . 3 2 2 . 3 1 3 0 5 . 4 6 . 5 1 4 . 1 2 1 . 8 2 2 . 9 1 4 0 5 . 8 6 . 8 1 4 . 5 2 2 . 3 2 3 . 3 1 5 0 6 . 1 7 . 2 1 4 . 9 2 2 . 7 2 3 . 7 1 6 0 6 . 4 7 . 5 1 5 . 3 2 3 . 0 2 4 . 1 1 7 0 6 . 7 7 . 8 1 5 . 6 2 3 . 4 2 4 . 4 1 8 0 7 . 0 8 . 1 1 5 . 9 2 3 . 6 2 4 . 7 1 9 0 7 . 3 8 . 4 1 6 . 1 2 3 . 9 2 4 . 9 2 0 0 7 . 6 8 . 6 1 6 . 4 2 4 . 1 2 5 . 2 2 1 0 7 . 9 8 . 9 1 6 . 6 2 4 . 3 2 5 . 4 2 2 0 8 . 1 9 . 1 1 6 . 8 2 4 . 5 2 5 . 5 2 3 0 8 . 4 9 . 4 1 7 . 0 2 4 . 7 2 5 . 7 2 4 0 8 . 6 9 . 6 1 7 . 2 2 4 . 8 2 5 . 8 2 5 0 8 . 8 9 . 8 1 7 . 4 2 4 . 9 2 5 . 9 - 5 1 - T A B L E 4 I C O N T . I S A P W O O D C L A S S E S O F E F F I C I E N C Y B A S A L A R E A LOW M E D . L O W A V E . M E D . H I G H H I G H (cm ) (m 2) (m 2) (m 2) (m 2) (m 2) 2 6 0 9 . 0 1 0 . 0 1 7 . 5 2 5 . 0 2 6 . 0 2 7 0 5 . 2 1 0 . 2 1 7 . 6 2 5 . 1 2 6 . 1 2 8 0 5 . 4 1 0 . 4 1 7 . 8 2 5 . 2 2 6 . 2 2 9 0 9 . 5 1 0 . 5 1 7 . 9 2 5 . 2 2 6 . 2 3 0 0 5 . 7 1 0 . 7 1 8 . 0 2 5 . 2 2 6 . 2 3 1 0 9 . 9 1 0 . 8 1 8 . 1 2 5 . 3 2 6 . 3 3 2 0 1 0 . 0 1 1 . 0 1 8 . 1 2 5 . 3 2 6 . 3 3 3 0 1 0 . 1 1 1 . 1 1 8 . 2 2 5 . 3 2 6 . 3 3 4 0 1 0 . 3 1 1 . 2 1 8 . 3 2 5 . 3 2 6 . 3 3 5 0 1 0 . 4 1 1 . 3 1 8 . 3 2 5 . 3 2 6 . 2 3 6 0 1 0 . 5 1 1 . 4 1 8 . 4 2 5 . 3 2 6 . 2 3 7 0 1 0 . 6 1 1 . 6 1 8 . 4 2 5 . 2 2 6 . 2 3 8 0 I C . 7 1 1 . 7 1 8 . 4 2 5 . 2 2 6 . 2 3 9 0 1 0 . 8 1 1 . 8 1 8 . 5 2 5 . 2 2 6 . 1 4 0 0 1 G . 9 1 1 . 8 1 8 . 5 2 5 . 1 2 6 . 0 4 1 0 1 1 . 0 1 1 . 9 1 8 . 5 2 5 . 1 2 6 . 0 4 2 0 1 1 . 1 1 2 . 0 1 8 . 5 2 5 . 1 2 5 . 9 4 3 0 1 1 . 2 1 2 . 0 1 8 . 5 2 5 . 0 2 5 . 8 4 4 0 1 1 . 2 1 2 . 1 1 8 . 5 2 4 . 9 2 5 . 8 4 5 0 1 1 . 3 1 2 . 2 1 8 . 5 2 4 . 9 2 5 . 7 -52- T A B L E 4 I C O N T . ) S A P W O O D B A S A L A R E A (cm ) 4 6 0 4 7 0 4 8 0 4 9 0 5 0 0 5 1 0 5 2 0 5 3 0 5 4 0 5 5 0 5 6 0 5 7 0 5 8 0 5 9 0 6 0 0 6 1 0 6 2 0 6 3 0 6 4 0 C L A S S E S O F E F F I C I E N C Y LOW ( m 2 ) 1 1 . 4 1 1 . 4 1 1 . 5 1 1 . 6 1 1 . 6 1 1 . 7 1 1 . 7 1 1 . 7 1 1 . 8 1 1 . 8 1 1 . 8 1 1 . 9 1 1 . 9 1 1 . 9 1 1 . 9 1 1 . 9 1 1 . 9 1 2 . 0 1 2 . 0 M E D . L O W ( m 2 ) 1 2 . 2 1 2 . 3 1 2 . 3 1 2 . 4 1 2 . 4 . 1 2 . 5 1 2 . 5 1 2 . 5 1 2 . 5 1 2 . 6 1 2 . 6 1 2 . 6 1 2 . 6 1 2 . 7 1 2 . 7 1 2 . 7 1 2 . 7 1 2 . 7 1 2 . 7 A V E . ( m 2 ) M E D . H I G H H I G H 1 8 . 5 1 8 . 5 1 8 . 5 1 8 . 5 1 8 . 5 1 8 . 4 1 8 . 4 1 8 . 4 1 8 . 3 1 8 . 3 1 8 . 3 1 8 . 2 1 8 . 2 1 8 . 2 1 8 . 1 1 8 . 1 1 8 . 0 1 8 . 0 1 8 . 0 ( m 2 ) 2 4 . 8 2 4 . 7 2 4 . 6 2 4 . 6 2 4 . 5 2 4 . 4 2 4 . 3 2 4 . 3 2 4 . 1 2 4 . 1 2 4 . 0 2 3 . 9 2 3 . 8 2 3 . 7 2 3 . 6 2 3 . 5 2 3 . 4 2 3 . 3 2 3 . 2 ( m 2 ) 2 5 . 6 2 5 . 6 2 5 . 5 2 5 . 4 2 5 . 3 2 5 . 2 2 5 . 1 2 5 . 1 2 4 . 9 2 4 . 8 2 4 . 8 2 4 . 6 2 4 . 6 2 4 . 5 2 4 . 4 2 4 . 2 2 4 . 1 2 4 . 0 2 4 . 0 -53- • The s i g n i f i c a n c e o f t h e v a r i a t i o n i n growth e f f i c i e n c y i s r e a l i z e d when p e r c e n t d i f f e r e n c e s a r e c o n s i d e r e d between medium h i g h o r h i g h g r o w th e f f i c i e n c y c l a s s e s and t h e ave r a g e growth e f f i c i e n c y . By s e l e c t i n g t r e e s f o r growth e f f i c i e n c y w h i c h a r e +2.054 o r +2.33 s t a n d a r d e r r o r s o f t h e e s t i - mate f r o m t h e r e g r e s s s i o n l i n e f o r a g i v e n sapwood b a s a l a r e a , t h e t e n y e a r b a s a l a r e a i n c r e m e n t / h e c t a r e may i n c r e a s e by a p p r o x i m a t e l y 39 t o 45% r e s p e c t - i v e l y . These v a l u e s a r e based on t h e a s s u m p t i o n t h a t a h e c t a r e i s f u l l y s t o c k e d w i t h u n i f o r m s p a c i n g . These r e s u l t s c a n be seen more c l e a r l y i n F i g u r e 19. 3. E f f i c i e n c y o f Narrow Crown We s t e r n Hemlock T r e e s The t h i r d o b j e c t i v e o f t h i s s t u d y was t o d e t e r m i n e t h e e f f i c i e n c y o f narrow crown w e s t e r n hemlock t r e e s as wood p r o d u c e r s . I f t h e same amount o f wood can be added t o t h e b o l e by a s l i m m e r , more e f f i c i e n t crown r a t h e r t h a n a w i d e r crown, t h e n more t r e e s c o u l d be m a i n t a i n e d on a u n i t a r e a and hence the p r o d u c t i o n o f wood p e r u n i t a r e a may i n c r e a s e . The crown i n d e x r a t i o was used as a measurement of s l e n d e r n e s s o r broadn e s s o f a t r e e crown. The h i g h e r t h e r a t i o , t h e slimmer t h e crown. F o r t h e t r e e s measured, an ave r a g e crown i n d e x r a t i o o f 2.94 was computed. C o n s i d e r i n g Walkup's (1978) a v e r a g e r a t i o o f 2.5, a 17.6% i n c r e a s e i s sub- s t a n t i a l when t h e d i f f e r e n c e i n t h e number o f t r e e s p e r u n i t a r e a i s co n - s i d e r e d . F o r example, by i n c r e a s i n g t h e r a t i o f r o m 2.5 t o 2.94 f o r t r e e s a t age 20, w i t h a l i v e crown, l e n g t h / t o t a l h e i g h t r a t i o o f 40% on a s i t e i n - dex o f 115 (base 5 0 ) , 38% more t r e e s c o u l d be m a i n t a i n e d on a h e c t a r e . To d e t e r m i n e t h e e f f i c i e n c y o f narrow crown w e s t e r n hemlock t r e e s as wood p r o d u c e r s , a s i m p l e l i n e a r r e g r e s s i o n o f t h e s t a n d a r d i z e d r e s i d u a l s f r o m t h e t h r e e p r e v i o u s r e g r e s s i o n s were r e l a t e d t o t h e crown i n d e x r a t i o . The p l o t s o f t h e t h r e e r e g r e s s i o n s a r e shown i n F i g u r e s 20, 21, and 22. FIGURE 19 TEN YEAR BASAL AREA INCREMENT/HECTARE FOR VARIOUS SAPWOOD BASAL AREAS AND CLASSES OF EFFICIENCY // -High E f f i c i e n c y -Medium High E f f i c i e n c y // Average E f f i c i e n c y Medium Low E f f i c i e n c y Low E f f i c i e n c y 1 1 1 1 1 1 1 1 0.0 80.0 160.0 240.0 320.0 400.0 0 480.0 560.0 64 SAPWOOD BfiSflL AREA (cm 2) -55- O n ly t h e s t a n d a r d i z e d r e s i d u a l s o r e f f i c i e n c y f r o m t h e f i r s t r e g r e s s i o n model ( F i g u r e 20) showed an i n c r e a s e as t h e crown i n d e x r a t i o i n c r e a s e d . However, t h e c o e f f i c i e n t o f d e t e r m i n a t i o n was o n l y 2.0%, and t h e r e g r e s s i o n v- was n o t s i g n i f i c a n t a t t h e .05 l e v e l o f s i g n i f i c a n c e . F o r t h e o t h e r two r e g r e s s i o n models ( F i g u r e s 21 and 2 2 ) , t h e e f f i c i e n c y d e c r e a s e d as t h e crown 2 i n d e x r a t i o i n c r e a s e d . B o t h r e g r e s s i o n s have v e r y l ow r v a l u e s , 4.2% ( F i g u r e 21) and 8.2% ( F i g u r e 2 2 ) . F i g u r e 21 i s a l s o n o t s i g n i f i c a n t a t t h e .05 l e v e l o f s i g n i f i c a n c e , whereas F i g u r e 22 i s s i g n i f i c a n t . I n v i e w o f a l l t h r e e r e g r e s s i o n s , i t a p p e a r s t h a t n a rrow crown w e s t - e r n hemlock t r e e s a r e l e s s e f f i c e n t f o r r a d i a l growth t h a n w i d e r crown t r e e s . I t i s p o s s i b l e t h a t t h e n a r r o w crown t r e e s measured i n t h i s s t u d y , t r e e s w i t h r a t i o s g r e a t e r t h a n 4.0, may have been s u p p r e s s e d t o some de- g r e e . A l t h o u g h t h e growth e f f i c i e n c y ( s t a n d a r d i z e d r e s i d u a l s ) i n c r e a s e d as t h e crown i n d e x r a t i o i n c r e a s e d i n F i g u r e 20, t h e i n c r e a s e i s n o t s u b s t a n t i a l . F u r t h e r m o r e , t h e crown i n d e x r a t i o f o r a l l t h r e e r e g r e s s i o n s a c c o u n t s f o r o n l y a s m a l l p a r t o f t h e v a r i a n c e i n growth e f f i c i e n c y . T h e r e f o r e , i n t h e s e l e c t i o n p r o c e s s o f e f f i c i e n t l y g r o w i n g t r e e s , s e - l e c t i o n f o r t r e e s w i t h e f f i c i e n t crowns s h o u l d be based o n l y on t h e a b i l i t y o f t h e crown t o produce wood e f f i c i e n t l y , and n o t on t h e d e g r e e of s l e n d e r n e s s o f t h e crown. -56- FIGURE 20 REGRESSION OF STANDARDIZED RESIDUALS FROM MODEL 1 ON THE CROWN INDEX RATIO in in CM' in • — i . i in in m . i + 4> 4>4> 4> E f f i c i e n c y = -.49 + .17(X) .99 .02 SE 2 r = ~1 —I 1— 2.0 3.0 4.0 CROWN INDEX RATIO 5.0 0.0 1.0 6.0 -57- -58- -59- SUMMARY The e f f i c i e n c e s o f t h e crown s u r f a c e a r e a f o r t h e i n d i v i d u a l t r e e s s h o u l d o n l y be a p p l i e d t o t h e g e o g r a p h i c r e g i o n i n w h i c h t h e y were s e l e c t e d . D i f f e r e n c e s i n e f f i c i e n c y o f g i v e n l e a f q u a n t i t i e s may f l u c t u a t e i n d i f f - e r e n t c l i m a t e s , because t h e l e s s f a v o r a b l e t h e c l i m a t e , t h e l a r g e r t h e l e a f q u a n t i t i e s w i l l be r e q u i r e d t o produce e q u a l q u a n t i t i e s o f wood ( A s s - man, 1970). Three models, 1) g r o s s stem volume/crown s u r f a c e a r e a = a^ + b ^ ( a g e ) , 2) t e n y e a r b a s a l a r e a i n c r e m e n t = a^ + b^(crown s u r f a c e a r e a ) , and 3) t e n y e a r b a s a l a r e a i n c r e m e n t = a^ + b^(sapwood b a s a l a r e a ) , were employed u s i n g l e a s t s q u a r e r e g r e s s i o n t e c h n i q u e s t o d e t e r m i n e t h e range of v a r i a t i o n i n growth e f f i c i e n c y o f i n d i v i d u a l w e s t e r n hemlock t r e e s . Growth e f f i c i e n c y i s d e f i n e d as t h e a b i l i t y o f t h e crown t o pro d u c e t h e maximum amount o f wood i n r e l a t i o n t o i t s crown s u r f a c e a r e a . The measure o f growth e f f i c i e n c y was based on t h e s i z e o f t h e s t a n d a r d i z e d r e s i d u a l . I t a p p e a r s t h a t f o r a l l t h r e e r e g r e s s i o n models, t h e r e i s a s u f f i c i e n t r a nge o f v a r i a t i o n i n g r o w t h e f f i c i e n c y f o r w e s t e r n hemlock t o make s e l e c t i o n w o r t h w h i l e . T h i s i s based on t h e range o f s i z e s o f t h e s t a n d a r d i z e d r e s i d u a l s and t h e c o e f f i c i e n t s o f v a r i a t i o n o f 48.6% f o r model 1, 16.3% f o r model 2, and 3.1% f o r model 3. Though t h e c o e f f i c i e n t o f v a r i a t i o n f o r model 3 i s s m a l l i t s h o u l d n o t be assumed t h a t s e l e c t i o n o f t r e e s w i t h l a r g e t e n y e a r b a s a l a r e a i n c r e m e n t i s due t o a c o r r e s p o n d i n g l y l a r g e sapwood b a s a l a r e a . The crown s u r f a c e a r e a o r sapwood b a s a l a r e a , w h i c h i s r e l a t e d t o crown s u r - f a c e a r e a , i s assumed t o be a i n d i c a t i o n o f t h e c o m p e t i t i o n a t r e e has under- -60- gone. T h e r e f o r e , a l l t h r e e r e g r e s s i o n models o f e v a l u a t i n g growth e f f i c i e n c y a r e p l a u s i b l e s i n c e t h e s i z e o f t h e crown s u r f a c e a r e a i s a c c o u n t e d f o r i n t h e r e g r e s s i o n models. The l a s t r e g r e s s i o n model o f r e l a t i n g t e n y e a r b a s a l a r e a i n c r e m e n t t o sapwood b a s a l a r e a i s t h e d e s i r e d model t o e v a l u a t e g r o w t h e f f i c i e n c y . T h i s i s based on t h e ease o f measurement o f t h e two v a r i a b l e s and t h e h i g h c o r r e l a t i o n between them. T h e r e f o r e , when s e l e c t i n g f o r p l u s t r e e s i t may be a d v i s a b l e t o i n c l u d e t h e sapwood b a s a l a r e a measurement a l o n g w i t h o t h e r t r a i t s o f i n t e r e s t . I n a l l t h r e e r e g r e s s i o n models, +2.054 and +2.33 s t a n d a r d e r r o r s o f t h e e s t i m a t e w h i c h i s e q u i v a l e n t t o s e l e c t i o n i n t e n s i t i e s o f one i n f i f t y and one i n a hundred, r e s p e c t i v e l y , were used as s e l e c t i o n g u i d e l i n e s f o r growth e f f i c i e n c y . By s e l e c t i n g t r e e s w h i c h a r e +2.054 o r +2.33 s t a n d a r d e r r o r s o f the e s t i m a t e from t h e r e g r e s s i o n l i n e i n s t e a d o f t r e e s on t h e r e g r e s s i o n l i n e i n model 3, t h e r e may be an i n c r e a s e i n t e n y e a r b a s a l a r e a i n c r e m e n t / h e c t a r e o f a p p r o x i m a t e l y 39 t o 45 p e r c e n t f o r t h e o b s e r v a t i o n s measured. The i n c r e a s e i n t e n y e a r b a s a l a r e a i n c r e m e n t / h e c t a r e d e m o n s t r a t e s t h e i m p o r t a n c e o f s e l e c t i n g f o r growth e f f i c i e n c y by e v a l u a t i n g t h e c o m p e t i t i o n t o w h i c h a t r e e has been s u b j e c t e d . Though t h e r e i s l i t t l e r e l a t i o n s h i p between growth e f f i c i e n c y and t h e degre e o f s l e n d e r n e s s o f t h e crown, i t a p p e a r s t h a t n a rrow crown w e s t e r n hem- l o c k t r e e s a r e l e s s e f f i c i e n t f o r r a d i a l growth t h a n w i d e r crown t r e e s . T h e r e - f o r e , s e l e c t i o n o f t r e e s w i t h e f f i c i e n t crowns s h o u l d be based o n l y on t h e a b i l i t y o f t h e crown t o pro d u c e wood e f f i c i e n t l y and n o t on t h e degree of s l e n d e r n e s s o f t h e crown. - 6 1 - LITERATURE CITED A l e x a n d r o v , A. 1971. The oc c u n s e n c e o f forms o f Norway s p r u c e based on b r a n c h i n g h a b i t . S i l v a e G e n e t i c a 20: 204-208. Assman, E. 1970. The p r i n c i p l e s o f f o r e s t y i e l d s t u d y . Pergamon P r e s s ; 506 pp, O x f o r d . B a r b e r , J.C. and M. R e i n e s . 1956. 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F i r s t o r d e r b r a n c h e s o f comb form, n o t i c e t h e second o r d e r b r a n c h e s h a n g i n g down i n a c o m b - l i k e f a s h i o n  Top s e c t i o n c u t o f f from s t e e p l e form, n o t i c e t h e d r o o p i n e s s o f t h e f i r s t o r - d e r b r a n c h e s -67- APPENDIX IV. WESTERN HEMLOCK CEDAR FORM

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