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Yield and volume tables for aspen in central and northern Alberta MacLeod, William Kenneth 1952

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YIELD MD VOLUME TABLES FOR ASPEN IN CENTRAL AND NORTHERN ALBERTA by WILLIAM KENNETH MACLEOD A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF FORESTRY i n the F a c u l t y of GRADUATE STUDIES We accept t h i s t h e s i s as conforming to the standard r e q u i r e d from candidates f o r the degree of MASTER OF FORESTRY Members of the F a c u l t y of F o r e s t r y THE UNIVERSITY OF BRITISH COLUMBIA A p r i l , 1952 ABSTRACT E v e n - a g e d w e l l s t o c k e d a s p e n s t a n d s i n N o r t h e r n A l b e r t a were sampled i n o r d e r t o d e r i v e " n o r m a l " y i e l d s p e r a c r e f o r number and s i z e o f t r e e s , b a s a l a r e a , and v a r i o u s measures o f v o l u m e . The s t a n d s o c c u r c h i e f l y on t h r e e q u a l i t i e s o f s i t e w h i c h have been c l a s s i f i e d i n t o P a i r , Medium and Good by t h e a v e r a g e h e i g h t o f d o m i n a n t t r e e s a t 80 y e a r s . E x c e p t i o n a l l y h i g h m o r t a l i t y p e r decade i s c h a r - a c t e r i s t i c i n f u l l y s t o c k e d y o u n g aspen s t a n d s and t h e r e l a t i o n o f number o f t r e e s p e r a c r e t o a v e r a g e d i a m e t e r i s m a r k e d l y d i f f e r e n t f r o m t h e t r e n d s f o u n d by i n v e s t i g a t o r s f o r o t h e r s p e c i e s . , A t a b l e o f s t a n d d e n s i t y u n i t s was c o n s t r u c t e d t o p e r m i t the , r a p i d . c a l c u l a t i o n o f s t a n d - d e n s i t y i n d e x when a v e r a g e d i a m e t e r and number o f t r e e s p e r a c r e have been d e t e r - m i n e d . The mean a n n u a l c u b i c volume g r o w t h on medium s i t e s i s maximum a t age I4.O. F o r m e r c h a n t a b l e c u b i c and b o a r d f e e t , g r o w t h r e a c h e s a peak a t 85 and 130 y e a r s r e s p e c t i v e l y . D a t a f r o m two o t h e r r e g i o n s show t h a t t h e amount o f c u l l i s h i g h i n a s p e n t r e e s above 80 y e a r s o f age , t h i s i n d i c a t e s t h a t t h e wood s h o u l d be u t i l i z e d b e f o r e a s t a n d - a g e o f 130 y e a r s i s r e a c h e d i f maximum r e t u r n i n b o a r d f o o t vo lume i s d e s i r e d . By lij.0 y e a r s aspen s t a n d s show s i g n s o f b r e a k i n g u p . The hardwood stands measured were composed mainly of aspen but both white b i r c h and b l a c k p o p l a r o c c u r r e d on many of the p l o t s . The growth o f the b l a c k p o p l a r i s only s l i g h t l y l e s s than t h a t f o r the aspen. I t has c o n s i s t e n t l y lower volumes p e r tre e which permits the use of aspen volume t a b l e s when c o r r e c t i o n f a c t o r s are a p p l i e d . ' ACKNOWLEDGMENT The author' would l i k e to express h i s a p p r e c i a t i o n to the Department of Resources and Development, F o r e s t r y Branch, Ottawa, f o r p e r m i s s i o n to use the d a t a employed i n the development of the t a b l e s presented. TABLE OP CONTENTS -'' ' Page' INTRODUCTION 1 THE POPLAR FOREST. SAMPLED.-.. .: ' •• 2 ASPEN YIELD TABLES ' ' ' ' ' ' l± Height Growth and S i t e "Index - • 11. Number and S i z e of Trees 13 B a s a l Area Y i e l d s llj. Volume Y i e l d s . l l | . T o t a l Cubic Feet llj. Merchantable Cubic and Board Feet II4. Increment and R o t a t i o n Age 2I4. C u l l 25 D e n s i t y 28 BLACK POPLAR, PERCENTAGE COMPOSITION CHANGE 33 VOLUME TABLES FOR ASPEN AND BLACK POPLAR 36 Measurements and Computations 36 T o t a l Cubic Feet 37 Merchantable Cubic Feet 38 Merchantable Board Feet, Scribn'er Rule 39. VOLUME TABLES FOR WHITE BIRCH i|4 T o t a l Cubic Peet ' ' kk' Merchantable Cubic and Board Peet • )|)| APPENDIX ' 53 B a s i c Data 53 F i e l d Work O f f i c e Computations. 56 Method of A n a l y s i s 56 • BIBLIOGRAPHY . 65 ILLUSTRATIONS Table Page 1. Stand composition and frequency of occurrence of species on sample p l o t s . .. \x 2.. T o t a l . h e i g h t of average dominant aspen 5 3. T o t a l number of t r e e s per acre 0 .6-inch d.b.h. and l a r g e r 6 Jj.. Diameter of the average t r e e by age c l a s s and s i t e index • • • • 6 5. T o t a l b a s a l area per acre i n c l u d i n g a l l t r e e s 0.6-inch'd.b.h. and l a r g e r 7 6. Y i e l d per acre i n cubic f e e t , e x c l u d i n g bark, . f o r a l l t r e e s 0 .6-inch d.b.h. and l a r g e r ....... 7 7. Y i e l d per acre i n c u b i c f e e t of merchantable stem, e x c l u d i n g bark, from a 1-foot stump to a [(.-inch top i n s i d e bark; f o r a l l t r e e s Jj.-incb.es d.b.h. and l a r g e r • • • • • • • 16 8. Y i e l d s per acre i n c u b i c f e e t of merchantable stem, e x c l u d i n g bark, from a 1-foot stump to a ij.-inch top i n s i d e bark; f o r t r e e s J4.-II inches d.b.h. i n c l u s i v e ,, 16 9. Y i e l d s per acre i n c u b i c f e e t of merchantable stem, e x c l u d i n g bark, from a 1-foot stump to a ij.-inch top i n s i d e bark; f o r t r e e s 12-inches d.b.h. and l a r g e r 17 10. Y i e l d s per acre i n board f e e t , S c r i b n e r l o g r u l e , from a 1-foot stump to a 6-inch top i n s i d e ,bark; f o r a l l t r e e s 7-inches d.b.h. and l a r g e r 17 11. Y i e l d s per a c r e . i n board f e e t , S c r i b n e r l o g r u l e , from a 1-foot stump to a 6-inch top i n s i d e bark; f o r a l l t r e e s 12-inches d.b.h., and l a r g e r • 18 12. Conversion u n i t s a p p l i e d to t o t a l c u b i c volume "of w e l l stocked aspen stands to o b t a i n mer- chantable c u b i c volume of a l l t r e e s JL-inches d.b.h. and l a r g e r ......... ̂  ... 20 13. Conversion u n i t s a p p l i e d to t o t a l c u b i c volume of w e l l stocked aspen stands to o b t a i n merchant- able c u b i c volume of a l l t r e e s 12-inches d.b.h.. and l a r g e r 21 ILLUSTRATIONS Table Page. 111. Conversion u n i t s a p p l i e d to t o t a l c u b i c volume of w e l l stocked, aspen stands to o b t a i n merchantable board f o o t volumes, S c r i b n e r r u l e , of a l l t r e e s 7-inches d.b.h. and l a r g e r 21 15. Conversion u n i t s a p p l i e d to t o t a l c u b i c volume of w e l l stocked aspen stands to o b t a i n mer- chantable board f o o t volumes, S c r i b n e r r u l e , of a l l t r e e s 1 2-inches d.b.h. and l a r g e r 22 16. Mean and p e r i o d i c annual aspen growth per acre i n c u b i c f e e t , e n t i r e stem, e x c l u d i n g bark, a l l t r e e s 0 . 6 - i n c h d.b.h. and l a r g e r 22 17. Mean and p e r i o d i c annual aspen growth per acre i n cubic f e e t , merchantable stand, e x c l u d i n g bark, from a 1-foot stump t o . a 1 | -inch top i n s i d e bark; f o r a l l t r e e s [(.-inches d.b.h. and l a r g e r 23 18. Mean, and p e r i o d i c , annual aspen growth per acre i n board f e e t , S c r i b n e r r u l e , from a 1-foot stump to a 6-inch top i n s i d e bark; f o r a l l t r e e s 7-inches d.b.h. and l a r g e r 23 19. R o t a t i o n age to the n e a r e s t h a l f decade f o r maximum wood p r o d u c t i o n , according to p o r t i o n of stand and u n i t of volume considered, f o r three s i t e c l a s s e s 25 2 0 . C u l l percent, f o r t r e e s li-inches d.b.h. and l a r g e r , r e l a t e d to aspen t o t a l age f o r medium s i t e s .. 26 2 1 . Stand d e n s i t y u n i t s f o r aspen corresponding to average stand.diameters i n inches ' 31 2 2 . Percentage composition of b l a c k p o p l a r r e l a t e d to age 35 23. Volume t a b l e f o r aspen and b l a c k p o p l a r i n t o t a l cubic f e e t ' J4.9 2I4.. Volume t a b l e f o r aspen and b l a c k p o p l a r i n merchantable cu b i c f e e t 50 25. Volume t a b l e f o r aspen and b l a c k p o p l a r i n merchantable board f e e t 5 l ( ' ILLUSTRATIONS T a b l e Page 26. Volume t a b l e s f o r w h i t e b i r c h . . . . 52 27. P l o t d i s t r i b u t i o n by age and s i t e i n d e x c l a s s e s 53 '28. C o r r e c t i o n i n y e a r s t o be added, t o age d e t e r m i n e d f r o m i n c r e m e n t b o r i n g s o r stump c o u n t s , t o o b t a i n a spen t o t a l age 55 29. F r e q u e n c y d i s t r i b u t i o n o f . r e s i d u a l s and t h e p r o b i t s c o r r e s p o n d i n g t o t h e i r c u m u l a t i v e f r e q u e n c y p e r c e n t - = . . . . 59 30. S t a t i s t i c s i l l u s t r a t i n g r e l i a b i l i t y o f . y i e l d t a b l e s , and e f f e c t o f age, and s i t e and age, 6I4. Figur,e 1. Map showing l o c a t i o n o f sample p l o t s ; e a c h d o t marks a l o c a l i t y where one o r more p l o t s were t a k e n . . . 2 2. H e i g h t c u r v e s u s e d f o r s i t e c l a s s i f i c a t i o n ' 5 3« Number o f t r e e s p e r a c r e s h o w i n g t r e n d s w i t h age and s i t e i n d e x 8 I4.. D i a m e t e r o f t r e e o f a v e r a g e b a s a l a r e a ' a t b r e a s t h e i g h t , showing t r e n d s w i t h age and s i t e i n d e x 9 5» T o t a l b a s a l a r e a p e r a c r e f o r t r e e s o v e r 0 . 6 - i n c h d.b.h., showing t r e n d s w i t h age and s i t e i n d e x 9 6 . Y i e l d p e r a c r e i n c u b i c f e e t e x c l u d i n g b a r k , showing t r e n d s w i t h age and s i t e i n d e x 10 7. Y i e l d p e r a c r e i n c u b i c f e e t o f m e r c h a n t a b l e stem, e x c l u d i n g b a r k ( t o a [(.-inch t o p i n s i d e b a r k ) , showing t r e n d s w i t h age and s i t e i n d e x 18 8. Y i e l d p e r a c r e i n - b o a r d . f e e t , S c r i b n e r l o g r u l e ( t o a 6 - i n c h t o p i n s i d e b a r k ) , s howing t r e n d s w i t h age and s i t e i n d e x •••• 19 9. The r e l a t i o n s h i p between t h e m e r c h a n t a b l e c u b i c f o o t - t o t a l c u b i c f o o t volume r a t i o , t o a v e r a g e s t a n d d.b.h., where t h e m e r c h a n t a b l e s t a n d i n c l u d e s t r e e s I 4 . -inches and l a r g e r . 19 t ILLUSTRATIONS F i g u r e ' •Page 10. The r e l a t i o n s h i p between board f o o t - t o t a l cubic f o o t volume r a t i o , to average stand d.b.h., where the merchantable stand i n c l u d e s t r e e s 7-inches d.b.h. and l a r g e r 20 : 1 1 . The r e l a t i o n of t o t a l number of t r e e s per acre to average, stand d.b.h., f o r .78 f u l l y stocked aspen sample p l o t s 30 12. The r e l a t i o n of percentage composition, by b a s a l area, to t o t a l age f o r b l a c k p o p l a r on 61 sample p l o t s 35 13. ' The t r e n d of h e i g h t on d.b.h. w i t h i n each 10- f o o t h e i g h t c l a s s I4.5 Iij.. The- r e l a t i o n of board f o o t volume ( S c r i b n e r r u l e ) on d.b.h. by 1 0-foot h e i g h t c l a s s e s l\$ 15. The r e l a t i o n of board f o o t volume ( S c r i b n e r r u l e ) on t o t a l h e i g h t by 2-inch diameter c l a s s e s I4.6 16. Slope c o e f f i c i e n t s "b" f o r trend of S c r i b n e r board f o o t volume on t o t a l h e i g h t , p l o t t e d on diameter at b r e a s t h e i g h t ij.7 17. Adjusted volume r a t i o s ( b a s i s = 80 f e e t ) p l o t t e d over diameter at b r e a s t h e i g h t Itf 18. I n t e r c e p t c o e f f i c i e n t s "a" f o r trend of S c r i b n e r board f o o t volume on t o t a l h e i g h t , p l o t t e d on diameter at b r e a s t h e i g h t I4.8 19. The r e l a t i o n of the c o e f f i c i e n t s of v a r i a t i o n . .. and standard d e v i a t i o n s of dominant h e i g h t r e s i d u a l s to t o t a l age 57 20. The r e l a t i o n of the l o g a r i t h m of number of t r e e s to average d.b.h 58- 2 1 . The r e l a t i o n of s i t e index to age; no c o r - r e l a t i o n i s shown'-.: 60 22. Freehand curves showing i n (a) the average r e l a t i o n of volume to age; i n (b) the r e l a t i o n of the standard d e v i a t i o n of volume to age; and i n (c) the c o e f f i c i e n t of v a r i a t i o n of volume to age 63 23. : The r e l a t i o n between the f i r s t r e s i d u a l s of t o t a l c u b i c volume (expressed i n standard u n i t s f o r i t s age) and 'site -index' 61| YIELD AltfD VOLUME TABLES FOR ASPEN IN CENTRAL AND NORTHERN ALBERTA INTRODUCTION . / Aspen"'" (Populus tremuloides Mlchx. ) i s the most abundant t r e e of the f o o t h i l l and p l a i n s r e g i o n of A l b e r t a , but at present i t i s of general v a l u e only as a cover crop. L o c a l l y , i t ' i s important f o r fuelwood, f e n c e p o s t s , wagon stock, rough lumber, and l o g s f o r l o g c a b i n c o n s t r u c t i o n . T h i s s i t u a t i o n e x i s t s f o r many reasons, the most s i g n i f i c a n t ones being, (1) the range of aspen i s so extensive t h a t out- s i d e markets have adequate s u p p l i e s , (2) the more v a l u a b l e c o n i f e r o u s woods on t h i s c o n t i n e n t are s t i l l r e l a t i v e l y p l e n t i f u l , (3) the prevalence of h e a r t r o t i n aspen makes i t u n s u i t a b l e to an i n d u s t r y which i s geared to the p r o d u c t i o n of lumber only. The f u t u r e p o s s i b i l i t i e s f o r t h i s s p e c i e s are th e r e - f o r e subject to s p e c u l a t i o n , but the ever i n c r e a s i n g value of wood and i t s by-products s t r o n g l y i n d i c a t e s t h a t i t i s only a q u e s t i o n of time before aspen w i l l be important i n the p r o v i n c i a l f o r e s t economy. I t was i n a n t i c i p a t i o n of an i n c r e a s e d i n t e r e s t i n and u t i l i z a t i o n of aspen that t h i s study was undertaken. Other names i n use are: white p o p l a r , p o p l a r , popple, asp, aspen p o p l a r , quaking aspen, and smooth-barked p o p l a r . -2- THE POPLAR FOREST SAMPLED The area f o r which the prese n t y i e l d t a b l e s were c o n s t r u c t e d i s contained w i t h i n the l i m i t s of the B 18 r e g i o n d e s c r i b e d by H a l l i d a y ( 5 ) . The bulk of the sample p l o t s measured, however, are concentrated i n the v i c i n i t y of the Le s s e r Slave Lake sub-drainage where p o p l a r a t t a i n s optimum development. A d d i t i o n a l data were c o l l e c t e d west of Edmonton i n l o c a t i o n s .shown i n red i n the sketch map, F i g u r e 1. FIGURE 1 - Map showing l o c a t i o n of sample p l o t s ; each dot marks a l o c a l i t y where one or more p l o t s were taken. -3- Only a few of the r i v e r s and streams which wind through the e n t i r e r e g i o n are shown and, although a g e n t l y r o l l i n g country- sid e i s a f e a t u r e of the topography, the l a r g e r . s t r e a m s , c e n t r e s of r a t h e r deep U-shaped v a l l e y s , p r o v i d e abrupt r e l i e f to an otherwise r e g u l a r landscape. The f o r e s t cover i n g e n e r a l i s of a patchy nature due i n p a r t to the d e s t r u c t i o n caused by past f i r e s and to the heterogeneous mixtures of aspen w i t h white spruce ( P i c e a g l a u c a (Moench.) Voss), balsam f i r (Abies balsamea (L.) M i l l s ) , l odgepole pine (Pinus c o n t o r t a Dougl.) and jack pine (Pinus Banksiana Lamb.). The many swamps of b l a c k spruce ( P i c e a mariana ( M i l l . ) B.S.P.) but add to t h i s apparent p a t c h i n e s s . Of the hardwoods b l a c k p o p l a r 1 (Populus b a l s a m i f e r a L.) and white b i r c h ( B e t u l a p a p y r i f e r a Marsh. )•• are seldom e n t i r e l y absent. The former i s the more common p a r t i c u l a r l y i n moist h a b i t a t s , e x i s t i n g i n pure stands on the a l l u v i a l s o i l s of the r i v e r f l a t s , or as l a r g e i n d i v i d u a l s along creek margins. The s b l a c k p o p l a r competes s u c c e s s f u l l y w i t h aspen as a g e n e r a l r u l e but the degree of i t s success depends upon s o i l and moisture c h a r a c t e r i s t i c s . White b i r c h may be found growing i n almost pure stands of h i g h marketable value i n a few l o c a l i t i e s but such occurrences are not very, common. I t most f r e q u e n t l y e x i s t s i n the mixtures as a t w i s t e d s p i n d l y t r e e of r e l a t i v e l y l i t t l e commercial importance. The average percentage composition and frequency of occurrence of these deciduous species i n c l u d e d i n the p l o t s measured are shown i n Table 1, These f i g u r e s should not be taken as r e p r e s e n t a t i v e of the e n t i r e r e g i o n but of the p o p u l a t i o n sampled. "^"Other names i n use are: tealsam p o p l a r , balm, balm of G i l e a d , p o p l a r , tacamahac, and rough-barked p o p l a r . -k- TABLE 1 STAND COMPOSITION AND FREQUENCY OF OCCURRENCE OF SPECIES ON SAMPLE PLOTS ' Composition Frequency Common by of name S c i e n t i f i c name b a s a l area occurrence : ~ — — % % Aspen Populus tremuloldes Michx. 93.92 100.0 Black p o p l a r . P.opulus b a l s a m i f e r a L. 5.16 71.8 White b i r c h B e t u l a p a p y r i f e r a Marsh. 0 .92 28.2 ASPEN YIELD TABLES The y i e l d t a b l e s presented are d e r i v e d from stands estimated to be u t i l i z i n g f u l l y the growing c a p a c i t y of the l a n d . In such stands the aspen crowns form a f a i r l y complete canopy except i n the case of those under 30 years of age. Here the crowns become narrower and an apparent o v e r l a p p i n g i s c h a r a c t e r i s t i c . Y i e l d s obtained from such f u l l y stocked stands are commonly r e f e r r e d t o as "normal" y i e l d s . There are a number of obvious o b j e c t i o n s to both the b a s i s of sampling and the a p p l i c a t i o n of the r e s u l t i n g y i e l d t a b l e s but i t w i l l be g e n e r a l l y agreed that normal y i e l d t a b l e s have been and are u s e f u l d u r i n g e a r l y phases of f o r e s t r y development. Tables 2 to 6 i n c l u s i v e , show t o t a l h e i g h t o f . t h e average dominants, number of t r e e s , average s i z e of t r e e , b a s a l area, and volume of wood per acre f o r d i f f e r e n t ages and q u a l - i t i e s of s i t e . They are the r e s u l t of a p r o j e c t begun and completed d u r i n g the summer of 1950. In t h i s study y i e l d s of f u l l y stocked stands c o n t a i n i n g even-aged aspen between 10 and II4.O years were measured on 89 small' temporary sample areas - 5 - TABLE 2 TOTAL HEIGHT OP AVERAGE DOMINANT ASPEN T o t a l T o t a l h t . by s i t e index T o t a l T o t a l h t . by s i t e Index age 50 • 60 70 80 90 age $0 60 70 80 90 yea r s f t . f t . f t . f t . f t . y e a r s 10 10 l k 17 20 23 70 20 20 26 31 36 42 80 30 28 35 kl 1*8 55 9.0 ko 3k U2 k9 57 65 100 39 k7 56 6k 73 110 60 k3 52 61 10 79 120 f t . f t . f t . f t . f t kl 56 66 75 85 50 60 70 80 90 52 63 73 8k 9k 5k 65 76 86 97 56 67 78 89 90 58 69 80 91 102 1 t o t a l h e i g h t of average dominant aspen of 80 y e a r s FIGURE 2 - 'Height curves used f o r s i t e c l a s s i f i c a t i o n . - 6 - TABLE 3 TOTAL NUMBER OP TREES PER ACRE • 0 . 6 - INCH D.B.H. AND LARGER Total Trees per acre by s i t e index: age 5o ;, 60 70 80 90 (years) Number 10 10,000 4 8500 7700 6700 6050 20 6900 ' $800 5000 144.00 3750 • 30 14.700 3900 3300 2800 2500 ll-O 3250 2650 22^0 1900 1680 50 2200 I8I4.O 1550 1350 1180 60 1550 1300 1100 960 850 70 1100 930 : 800 705 630 80 790 690 600 525 kio 90 610 535 1*65 I4IO 370 100 U95 1*35 380 330 295 110 [j.20 . 365 320 280 214.5 120 370 , 315 276 224.0 210 • TABLE; h DIAMETER OP THE AVERAGE TREE .BY AGE CLASS AND SITE INDEX Total Diameter at breast height age \ , .-. ' by s i t e 'index: . 50 60 70 89 90 (years) " ; \ . : Inches 7~~ ~' 10 0.6 0.7 0.8 1.0 1.3 20 1.3 1.5 1.7 2.0 2.3 30 1.9 2.2 . 2 . 5 2.9 3.2 k-0 2 .5 - 2.9 . 3 .3 ' 3 . 8 ' I4..2 50 3.2 3.6 ' I4..I . I4..6 5.1 60 . , 3 . 8 I4..I4. k-9 • - 5-5 6.1 70 . lj.,6 ' 5 .2 5 . 9 ' 6 .5 7.1 80 S-k 6.1 6.8 7.6 8.3 90 6 .2 6.9 7 .8 8.6 9.1|. 1 ° ° 6 - 9 7.7 ' , 8.6 9.6 10.5 }\% I ' 5 9.14- 10.14. 11.5 1 2 ° 8 .0 9 .0 . 10.1 11..2 • 12.14. .-7- . TABLE 5 TOTAL BASAL AREA PER ACRE INCLUDING ALL TREES 0.6-INCH D.B.H., AND LARGER Total Basal area per acre by site index: age 50 60 70 80 . 90 (years) Square feet 10, l k 26 38 50 .61 20 66 78 91 103 I l k 30 9k 106 119 130 11*1 ko 111 122 136 11*7 158 50 118 . 130 11*3 155 168 60 122 131* lk8 160 172 70 12k 137 150 162 176 80 126 139 152 16k 177 90 128 llj.0 15k 165 178 100) 128 llj.0 151+ 166 178 110 128 llj.0 .151* 166 178 120 128 . llj.0 15k 166 178. TABLE 6 YIELD PER ACRE IN CUBIC FEET, EXCLUDING BARK, FOR ALL TREES 0*6-INCH D.B.H., AND LARGER Total Y i e l d per acre by s i t e index: age . t ; 50 6b 70 80 90 (years) Cubic feet 10 80 1-80 280 k20 570 20 620 ' 855 1120 11*15- 1715 30 llk5 lk80 1890 2315 2775 ko 1605 2030 2575 311*5 3775 50 1970 2k80 3115 3800 • k555 60 2270 2850 3560 1*31*5 5155 70 2525 3180 3925 k790 5685 80 2735 3l*k0 k2k0 5160 6115 90 2910 3650 k5io 51*60 6k75 100 3050 3805 1*730 5700 . 6760 110 3165 , 3920 lj.900 5900 6980 120 3255 .k030 ' 5035 • 6080 7170 -8- PIGTTRE 3 - Number of t r e e s per acre showing trends with age and s i t e index. • ¥ M-oi- - • • ...... .1 . _ - ... _ - ., .. .. J.0 ZO 30 4 0 SO 40 70 gC <?£> 100 110 ' LZO J Aspen total age - ijecrs j j ; FIGURE li --diameter of t r e e of average b a s a l area at brea h e i g h t , showing trends w i t h age and s i t e index. ! — - • < • > - ; II ; " " " " ! ' — ' ! ' 1 | " 1 " ' 1 " 1 — ' ' " — — — — i 20O| (-r- -+ ¥ { I • - : -. - - — S*r ! 0 \o 20 so 40 so &o 70 &c 90 too no tw\ Aspen toto; ^. s-^ears ' . — — — « — — , — , „ L FIGURE 5 - T o t a l b a s a l area per acre f o r trees over 0,6- inc h d.b.h., showing trends w i t h age and s i t e index. FIGURE 6 - Y i e l d per acre i a cubic f e e t e x c l u d i n g bark, showing trends with age and s i t e index. s c a t t e r e d throughout the r e g i o n 3hown i n F i g u r e 1. -For each p l o t age, s i t e q u a l i t y , number and siz,© of t r e e s and q u a n t i t y of wood were c a r e f u l l y determined. F u l l d e t a i l s of the analy- s i s and methods of measurement are d e s c r i b e d i n the Appendix. The v a r i a b l e s shown i n the t a b l e s were analysed and r e l a t e d to age and s i t e from'which y i e l d s per acre f o r each of the age and s i t e c l a s s e s shown were obtained. These y i e l d ? t a b l e s are s t r i c t l y only a p p l i c a b l e to the area sampled but i t i s b e l i e v e d they may be used with some assurance over the r e g i o n i n c l u d e d by Grande P r a i r i e , Peace R i v e r , Athabaska and Lac La Biche, South of Edmonton the p o p l a r has a scrubby appearance and from the few measurements a v a i l a b l e the height-diameter r e l a t i o n s h i p s have a d i f f e r e n t shape. T h i s evidence i s i n c o n c l u s i v e and does not permit l i m i t i n g the a r e a of a p p l i c a b i l i t y . I t does i n d i c a t e however, t h a t p o p l a r growth i n other p a r t s of A l b e r t a may not be comparable w i t h the y i e l d t a b l e v a l u e s . For stands with a d i f f e r e n t degree of s t o c k i n g from that shown i n the t a b l e s , p r e d i c t e d v a l u e s must be c o r r e c t e d according to standard procedures. The amount of t h i s c o r r e c t i o n w i l l be d e s c r i b e d l a t e r under " d e n s i t y . " Height Growth and S i t e Index The h e i g h t a t t a i n e d by the average dominant at 80 y e a r s was used as the index of s i t e q u a l i t y . T h i s age was chosen because aspen stands by t h i s time have a t t a i n e d m a t u r i t y , and because t h i s age has been used to develop s i t e curves f o r white spruce (6) which i s commonly a s s o c i a t e d with the p o p l a r . -12- The f o l l o w i n g i l l u s t r a t e s the r a t h e r s t r i k i n g s i m i l a r i t i e s between p l o t frequency occurrence percent f o r the three p r i n c i p a l s i t e c l a s s e s . S i t e c l a s s e s Frequency of p l o t occurrence aspen white spruce (percent) (percent) (height at 80 years) 70 70-80 60-70-80 F i g u r e 2 p o r t r a y s the t r e n d . o f average dominant h e i g h t w i t h age from which the v a l u e s i n Table 2 were d e r i v e d . The use of t h i s i n f o r m a t i o n to estimate s i t e q u a l i t y of an area f o l l o w s standard procedures when age and average dominant h e i g h t are known. In stands above 100 years of age, the aver- age height of the upper canopy may be used s i n c e dominants are d i f f i c u l t to r e c o g n i z e . F o r younger ages the average h e i g h t of from l\. to 8 dominants i s adequate, p a r t i c u l a r y i f the stand has a uniform appearance. F o r v a r i e d types of stands, l a r g e r samples should be taken. In t h i s study, the diameters of the dominants were averaged f o r each p l o t and used to o b t a i n dominant h e i g h t from the h e i g h t - d i a m e t e r curve. The d i f f e r e n c e between t h i s estimate and the average of a c t u a l h e i g h t s i s small and w i l l l i k e l y be unimportant i n p r a c t i c a l work. The mechanics of e s t i m a t i n g s i t e index may best be i l l u s t r a t e d by an example. I f the c r u i s e i n f o r m a t i o n shows the age of the stand to be 60 y e a r s and the average h e i g h t of the dominants to be 65 f e e t , what i s the s i t e index? R e f e r r i n g t o F i g u r e 1, opposite an age of 60 on the h o r i z o n t a l a x i s , a h e i g h t of 65 f e e t f a l l s between s i t e c l a s s 70 and 80, -'13- which may be i n t e r p o l a t e d by eye as. 7I4.. The same r e s u l t may be obtained from the use of Table 2. A h e i g h t of- 6 5 f e e t f a l l between the 70 and 80 s i t e index c l a s s , which c a l c u l a t e d p r e - c i s e l y i s , 70 / (l | / 9 x 10) or 7k'k' I n p r a c t i c e u s u a l l y only broad s i t e index c l a s s e s are used, so f o r convenience a de- s c r i p t i v e t i t l e has been gi v e n to each. S i t e Index Very best or e x c e l l e n t 90 Good ' •• 80 Medium 70 P a i r , 60 Poor ' 5 0 Number and S i z e of Trees F i g u r e 3> from which Table 3 was d e r i v e d , d e p i c t s the t o t a l number of t r e e s 0 , 6 - i n c h d.b.h., and l a r g e r by age c l a s s e s . Prom 10 to 5 0 years on mediiim s i t e s the number of t r e e s per acre decreases from 7700 to 1 5 0 0 , an average m o r t a l - i t y per decade of l 5 0 0 t r e e s . Prom ages 5 0 t o 100 y e a r s the m o r t a l i t y per decade decreases to 23I4. trees.. For Douglas f i r i n the P a c i f i c Northwest by comparison, the m o r t a l i t y i s only 36O and 60 per decade r e s p e c t i v e l y f o r the same p e r i o d s . S i m i l a r h i g h m o r t a l i t y f o r aspen has also been found i n the Lake S t a t e s ; Zehngraff (20) r e f e r s to " t h e ' e x c e p t i o n a l l y h i g h m o r t a l i t y r a t e o f the s p e c i e s " (aspen) as one of the u n d e r l y i n reasons e a r l i e r Lake S t a t e s estimates of volume y i e l d s were found to be too h i g h . The l a r g e number of t r e e s per acre i n the young age c l a s s e s are r e f l e c t e d i n the small average stand diameters - I I ] . - '(Figure I4. arid Table I4.). T h i s s i t u a t i o n l e a d s to an unexpected e f f e c t on diameter increment per decade s i n c e from $0 to 100 years i t i s s l i g h t l y g r e a t e r than from ages 10 to £0 y e a r s . Basal Area Y i e l d s The t r e n d of b a s a l area w i t h age f o r f i v e s i t e s i s shown i n F i g u r e 5 . The average v a l u e s f o r each s i t e and age c l a s s are shown i n Table. -5 . On medium s i t e s , age 5>0, II4.3 square f e e t of b a s a l area are. produced; t h i s . i n c r e a s e s to iSk- by age 100. Volume Y i e l d s T o t a l Cubic Peet F i g u r e 6 p o r t r a y s the t o t a l wood produced with i n c r e a s ing.age, i n c l u d i n g stump and top, i n a l l t r e e s 0 . 6 - i n c h d.b.h., and l a r g e r . Volumes f o r each s i t e and age c l a s s are g i v e n i n Table 6. Merchantable Cubic and Board Feet Y i e l d s i n merchantable c u b i c and board f o o t volume, by the S c r i b n e r l o g r u l e , f o r p o r t i o n s of stands on the d i f f e r - ent s i t e s , are presented i n Tables 7 to 11 i n c l u s i v e . F i g u r e s 7 and 8 show the y i e l d s at v a r i o u s ages by s i t e c l a s s e s i n c u b i c f e e t f o r t r e e s [(.-inches d.b.h. and l a r g e r , and i n board f e e t f o r t r e e s 7-inches d.b.h. and over. The merchantable t a b l e were computed from t o t a l c u b i c y i e l d v a l u e s by means of f a c t o r s obtained from the r a t i o of merchantable volume to t o t a l c u b i c volume, p l o t t e d over average stand diameter. -Figures 9 and 10 i l l u s t r a t e the r a t i o trends f o r cubic f e e t i n t r e e s I|.-inches d.b -15- and l a r g e r , and f o r board f e e t in.1 t r e e s 7-lnches d.b.h., and above, r e s p e c t i v e l y . The r a t i o s are of value f o r r a p i d c o n v e r s i o n i n t o the d e s i r e d u n i t s of measure. A f t e r the average diameter and t o t a l cubic volume, have been computed other volume measures may be obtained readily.. The accuracy of these converted volumes w i l l depend on the degree of s t o c k i n g and the d i s t r i b u t i o n of the stem diameters. I f the former i s average and the l a t t e r more'or l e s s r e g u l a r , no s e r i o u s i n a c c u r a c i e s should r e s u l t . The c o n v e r s i o n u n i t s used are presented i n Tables 12 to 15 i n c l u s i v e . -16- TABLE 7 YIELD PER ACRE IN CUBIC FEET OF MERCHANTABLE STEM, EXCLUDING BARK, FROM A l - F O O T STUMP TO A'k-INCH TOP'INSIDE BARK; FOR ALL TREES' k-INCHES. D.B.H. AND LARGER T o t a l age t 4 v r Y i e l d per acre by s i t e index: 1 : 50 60' 7.0; , 80 90 (years) Merchantable c u b i c f e e t 10 _ _ _ _ _ 20 - - - IkO 695 30 20 95 . 220' kho ko 185 385 '• 710 • 1230 1790 50 k95 860 Ikl5 2070 2825 -60 890 Ik55 • 2105 2900 3725 ' 70 1375 2010 2770 3600 kk80 80 1795 2k85 3270 ki85 . 5110 90 2125 2835 3695 k620 5620 100 2370 3100 J4.OOO k975 6ok5 110 2555 3290 k255 5255 6370 120 2690 3k55 5520 6655 TABLE 8 YIELDS PER ACRE IN CUBIC FEET OF MERCHANTABLE STEM, EXCLUDING' BARK, FROM A 1-FOOT STUMP TO A k-INCH TOP INSIDE BARK; FOR TREES k-11 INCHES D.B.H. INCLUSIVE : . T o t a l Y i e l d per acre by s i t e index: age ^ ^5 80 90 (years) MeTcl^nTable cubic f e e t 10 - - - - 20 30 20 95 ho 185 385 5o k95 860 60 890 ik55 70 1375 2010 .80 1795 . 2k85 90 2125: . 2835 100 2370 2880 110 2370 2815 120 23k5 2725 - IkO 220 kko 695 710 1230 1790 11*15 2070 2825 2105 2900 3725 2770 . 3600 kk20 3270 3925 kk25 3395 3855 kl70 33kO . 3560 3525 3155 31k5 2585 2875 25k5 1550 -17- TABLE 9 YIELDS PER ACRE IN CUBIC PEET OP MERCHANTABLE STEM, EXCLUDING BARK, PROM A 1-FOOT STUMP TO A I4.-INCH TOP INSIDE BARK; FOR TREES 12 INCHES D.B.H. AND LARGER 1 • i ; ; ; ; : : ; 1— T o t a l Y i e l d s per acre by s i t e Index: a S e 50 60 70 80 90 (Years) Merchantable c u b i c f e e t 10 - - - 20 - - - 30 - - - 1+.0 - - - 50 - - - - 60 - - - 70 - - - — 69 80 - - - 260 685 90 - - 300 765 ii*5o 100 - 220 660 11*15 2520 110 135 14-75 1100 2110 3785 120 275 730 1580 2975 5105 TABLE 10 YIELDS PER ACRE IN BOARD FEET, SCRIBNER LOG RULE, FROM A 1-FOOT STUMP TO A 6-INCH TOP INSIDE BARK; FOR ALL TREES 7-INCHES D.B.H. AND LARGER ~ i i i - . T o t a l Y i e l d per acre by s i t e index: age 50 60 70 80 90 rears) Board f e e t 10 — 20 30 - - - — 55 1*0 - - 90 375 755 50 1*0 200 560 1160 2070 60 270 725 11*05 2630 1*510 70 770 1560 3060 5270 8640 80 151*5 3010 51*70 9905 11+980 90 2705 1*965 9380 11*525 20395 100 1*150 7610 12580 I86I4.O 25215 110 5825 9880 151*35 21770 28550 120 7260 11725 17825 21;320 3101*5 -18- TA.BLE 11 YIELDS PER ACRE IN BOARD FEET, SCRIBNER LOG RULE, FROM A l-FOOT STUMP TO A 6-INCH TOP INSIDE BARK; FOR ALL TREES 12-INCHES D.B.H. AND LARGER T o t a l age Y i e l d per acre by s i t e index: 5o 60 70 ' 80 90 (years) Board f e e t 10 _ 20 - - — — -30 - - - - -- - - - -5o - - - — -60 - - — - — 70 - - - 190 655 80 - - 320 1060 229< 90 330 1130 2565 • 5635 100 275 855 2225 5815 11965 110 585 1590 1*265 99io l 8 8 k 5 120 960 25ko 7150 1I1650 25310 . —1 - 9 0 0 0 \ 1 — 1—&gj > —--"1 8 0 _ 3 ^ ' j 1 - ^ 4 0 0 0 Q ^^y^ ^^^^ ^ ^ " ^ ___L———' 6 0 - -t; 2.000 V S . x r / / / ^ ^ 1 0 10 ZC 30 40 SO 60 70 80 90 too 110 120 Mp&r rota! oge-yeors ' FIGURE 7 - Y i e l d per acre i n cubi c f e e t of merchantable s t ex c l u d i n g bark (to a k - i n c h top i n s i d e bark),showing trend with age and s i t e index. em, s -19- %• 1 " "n • "~ .90 « v. Z4000 - 7 2oooo -*§ L^ooo $ 1 is / On J 7 . L _ / _ 6 0 - - 4ooo» - j - • ; fr / / / " T5Q% . . .. : . c LO 23 30 40 So bo 70 80 Aspen total, age-years <90 LOO 110 120 FIGURE 8 - Y i e l d p e r acre i n board f e e t , S c r l b n e r r u l e (to a 6-inch top i n s i d e b a r k ) , showing tr e n d s with age and s i t e ' i n d e x . Average p.Q.H. ofptots-mches FIGURE 9 - The r e l a t i o n s h i p between the merchantable cubi c f o o t - t o t a l cubic f o o t volume r a t i o , to average stand d.b.h., where the merchantable stand i n c l u d e s t r e e s [{.-inches and l a r g e r . FIGURE 10 - The relat i o n s h i p between board f o o t - t o t a l cubic foot volume r a t i o , to average stand d.b.h., where the merchantable stand includes trees 7-inches d.b.h. and larger. TABLE 12 CONVERSION UNITS APPLIED TO TOTAL CUBIC VOLUME OF WELL STOCKED ASPEN STANDS TO OBTAIN MERCHANTABLE CUBIC VOLUME OF ALL TREES 4-INCHES D.B.H. AND LARGER Average 1 Average stand diameter,tenths of an inch stand 0.0 0.1 0.2 0.3 O-.lj. 0.5 0.6 0.7 O.B 0.9 ~ d.b.h. Conversion units, t o t a l cubic to mer. cubic v o l . , trees IL"J. .0)17 inches 1.0 - - - - -2.0 .033 .049 .065 .082 .099 ,116 3-0 .210 .230 .251 .275 .298 .322 4.0 435 • 455 .474 • 493 .511 .528 5.0 .606 ,620 .633 .645 .656 .667 6.0 .715 .723 .731 .738 .745 -752 7.0 .783 .788 .794 .799 .803 .807 8.0 .826 .830 .833 .836 .839 -843 9.0 .857 .860 .862 .865 .868 .870 .8^4 10.0 .883 .885 .887 .889 .891 11,0 .904 .906 .908 .910 .911 .913 12.0 .922 .924 .925 .926 .928 .930 -21- TABLE 13 CONVERSION UNITS APPLIED TO TOTAL CUBIC VOLUME OP WELL STOCKED ASPEN STANDS TO OBTAIN MERCHANTABLE CUBIC VOLUME OP ALL TREES 12-INCHES D.B.H.AND LARGER Average Average stand diameter,tenths of an i n c h stand 0.0 0 .1 0 .2 0.3 O.U 0.5 0.6 0.7 O.b1 0.9 d.b.h. Conversion u n i t s , t o t a l c u b i c t o mer.cubic v o l . t r e e s 12"+ (inches) " ' 6.0 - - - - - 7.0 .004 .011 .019 .026 .034 .042 .050 .058 .066 .075 8.0 .084 .094 .103 .112 .121 .131 .140 .150 .160 .170 9.0 .818 .191 .202 .213 .224 .236 .248 .260 .273 .286 10.0 .300 .314 .328 .343 .358 .373 .389 .405 .421 .437 11.0 .454 .472 .489 .506 .524 .542 .561 .580 .599 .618 12.0 .637 .656 .675 .694 .712 .729 .747 .764 .780 .796 TABLE 14 CONVERSION UNITS APPLIED TO TOTAL CUBIC VOLUME OP WELL STOCKED ASPEN STANDS TO OBTAIN MERCHANTABLE BOARD FOOT VOLUMES SCRIBNER RULE, OF ALL TREES 7-INCHES D.B.H. AND LARGER Average Average stand diameter,tenths of an i n c h stand 0.0 0 .1 0.2 0.3 0 . 4 6.5 0.6 0 .7 0 .8 0.9 d.b.h. Conversion u n i t s , t o t a l c u b i c v o l . to board f t . , t r e e s 7"^ (inches) " 3.0 - - .02 .04 .05 .06 .08 .10 .12 .14 4.0 .16 .18 .20 .23 .26 .28 .30 .34 .36 .40 5.0 .42 .k6 .49 .53 .56 .60 .64' .69 .73 .78 6.0 .82 .88 .93 .98 1.04 1.10 1.16 1.22 1.29 I . 3 6 7.0 I . 4 4 1.52 1.60 1.68 1.76 1.84 1.92 2.00 2 .08 2.16 8.0 2 .23 2.31 2.38 2.45 2 .52 2 .59 2.66 2.72 2 .79 2 .85 9.0 2 .91 2.97 3.03 3.09 3.15 3.21 3.27 3.32 3.38 3.43 10.0 3.49 3.54 3.59 3.64 3.69 3.73 3.78 3.82 3.86 3.90 11.0 3.93 3.97 4.00 4.03 4.06 4.09 4.12 4.15,4.18 4.21 12.0 4.23 4.26 4.29 4.31 4.33 4.35 4.38 4.40 4.42 4.44. -22- TABLE 15 CONVERSION UNITS APPLIED TO TOTAL CUBIC VOLUME OP WELL STOCKED ASPEN STANDS TO OBTAIN MERCHANTABLE BOARD FOOT VOLUMES, SCRIBNER RULE, OP ALL TREES 12-INCHES D.B.H., AND LARGER Average Average stand diameter, tenths of an inch stand 0.0 0.1 0.2 0.3 O.k 0.5 0.6 0.7 0.8 0.9 ~ d.b.h. Conversion u n i t s , t o t a l cubic v o l . to board ft,,trees 12JH (inches) ' 6.0 - 0.01 0.02 0.02 0.03 O.Oij. 0.05 0.06 0.05 0.09 7.0 0.10 0.12 0.13 0.15 0.16 0.18 0.20 0.22 0.25 0.27 8.0 0.30 0.32 0.35 O.38 O.I4.O O.I4J4. 0.it7 0.40 0.54 0.58 9.0 O.63 0.68 0.74 0.80 O.87 0.95 1.02 1.10 1.18 1.26 10.0 1.35- 1.1+2 1.50 1.59 1.68 1.77 1.86 1.95 2.0i+ 2.Ik 11.0 2.23 2.32 2.kl 2.51 2.61 2.70 2.80 2.89 2.99 3.O8 12.0 3.17 3.26 3.35 3.44 3.53 3.61 3.70 3.78 3.86 3.9k TABLE 16 MEAN AND PERIODIC ANNUAL ASPEN GROWTH PER ACRE IN CUBIC PEET, ENTIRE STEM, EXCLUDING BARK, ALL TREES 0.6- ^INCH D.B.H., AND LARGER / j / , 1 (years) 1 Mean and periodic 1 annual growth ' Total age Pair 60 Medium 70 Good 80 m.a.1. p. a. 1 m.a.1. p. a . i . m.a.1. p. a . i . Total cubic feet 10 18.0 _ 28.0 _ 42.0 — 20 k2.8 65.5 56.0 80.5 70.8 94.0 30 49.3 59.0 63.O 73.5 77.2 87.O 4o 50.8 50.0 64.4 62.0 78.6 75.0 50 49.6 41.0 62.3 49.0 76.0 59.5 60 47.5 35.0 59.3 39.5 72.4 49.0 70 45.4 29.5 56.1 34-0 68.4 40.5 80 43.0 23.0 53.0. 29.0 64.5 33.5 90 4o.6 18.0 50.1 24.5 60.7 26.5 100 38.0 13.5 47.3 20.0 57.0 22.0 110 35.6 11.0 44.5 15.0 53.6 18.5  -2k- Increment and r o t a t i o n age Tables 16, 1? and 18 show r a t e s of growth on P a i r , Medium and Good s i t e s i n terms o f p e r i o d i c and mean annual increment. Tables 16 and 17 show these growth val u e s In c u b i c f e e t f o r the e n t i r e stand and f o r the merchantable p o r t i o n . The values i n Table 18 are expressed i n board f e e t f o r the t r e e s 7-inches and over. The r o t a t i o n age i s u s u a l l y r e f e r r e d t o as the age at which p e r i o d i c and mean annual growth are the same. In p r a c t i c e , the number of years t h a t w i l l be r e q u i r e d to o b t a i n r e g e n e r a t i o n a f t e r the f i n a l cut, should be i n c l u d e d . Since aspen produces seed f r e q u e n t l y and abundantly and i s capable of p r o l i f i c coppice growth i t may s a f e l y be assumed t h a t a new crop w i l l come In immediately and no a d d i t i o n a l y e ars need be added. A stand cut at the r o t a t i o n age w i l l y i e l d the maximum volume r e t u r n per y e a r of growth. Rate of growth i s only one of a number of f a c t - ors to be e v a l u a t e d i n f i x i n g the proper age a t which to cut a given stand. The type of product d e s i r e d , the f i n a n c i a l aspects of f o r e s t management and the s i l v i c u l t u r a l f e a t u r e s of the f o r - e s t must a l l be taken i n t o account. N e v e r t h e l e s s , volume p r o - d u c t i o n alone i s an important item. I t w i l l be noted from the t a b l e s that the peak of mean annual growth i s i n f l u e n c e d by s i t e and measure of volume. The r o t a t i o n ages i n d i c a t e d by the d a t a c o l l e c t e d i n t h i s study are shown i n Table 19. F o r maximum p r o d u c t i o n of wood p e r acre, short r o t a - t i o n s of kO y e a r s are i n d i c a t e d . Since most of the t r e e s i n stands of t h i s age are below k-inches i n diameter, a kC—year -25 - rotation period i s of rather t h e o r e t i c a l i n t e r e s t at present. This low rotation age, however, i t i s in t e r e s t i n g to note, i s the same as that suggested by MacLeod (6) f o r aspen i n mixed- wood stands growing i n the same general area. When only trees k-inches d.b.h. and larger are considered, the r o t a t i o n period i s lengthened to 85 years. For board foot measure, trees 7- inches and above, a rotation i n t e r v a l of 130 years i s indicated. TABLE 19 ROTATION AGE TO THE NEAREST HALF DECADE FOR MAXIMUM WOOD PRODUCTION,ACCORDING TO PORTION OF STAND AND UNIT OF VOLUME CONSIDERED,FOR THREE SITE CLASSES When unit of volume and p:&rt of stand Is F a i r Med. Good 60 70 80 Total age in yrs. Total cubic volume, a l l trees l " + included kO ij.0 35 Merchantable cubic f e e t , a l l trees k" + included 90 85 80 Merchantable board f e e t , a l l trees 7" + included - (130) (125) (Scrib.rule) ( ) - bracketed figures are extrapolated. C u l l Unfortunately there i s no information on the amount of wood rot per tree f o r the area nor were any data taken i n th i s study. Some consideration must be given to thi s very important factor, however, which i n other areas i s the greatest single cause f o r c u l l in aspen. Although i t i s obviously unwise to apply c u l l percentages derived from studies made i n other regions, some of the dangers i n doing so may be more apparent than r e a l , p a r t i c u l a r l y when one pathogen, Fomes i g n i a r i u s , i s - 2 6 - th© most important rot causing agent throughout the entire range of poplar. Prom Black's data ( 1 ) , f o r aspen i n Northern Ontario, figures on percentage of c u l l related to diameter were used to estimate t o t a l rot i n percent f o r each plot measured i n Northern Alberta. The values shown i n Table 20 were read from a graph where these percentages were cor- related with age. TABLE 20 CULL 1 PERCENT, FOR TREES k-INCHES D.B.H. AND LARGER, RELATED TO ASPEN TOTAL AGE FOR MEDIUM SITES « f Total age C u l l Total age C u l l (years) (percent) (years) (percent) 30 1.0 80 9 .0 LL0 1.0 9 0 13.0 50 2.0 100 18.0 60 k . 0 110 2 2 . 0 70 6 .0 120 27 .0 Meineke (8) studied the pathology of aspen i n Utah i n 1 9 2 9 . The c u l l percentages shown i n h i s publ i c a t i o n are similar, when correlated with age, to the values i n Table 2 0 . The per- centages derived i n both regions are given below f o r comparison: Age C u l l as a percentage of merchantable volume f o r : Northern Ontario Utah 30 1.0% 1,0% 60 k .0# l.% 9 0 13.0^ 9 . 0 ^ 120 27.0$ 30.0$ It should be noted that the c u l l percentages shown f o r the two regions do not have a s t r i c t l y comparable basis. In Black's A l l portions of the merchantable stem having a rot diameter greater than 1-inch; based on Black's data (1) f o r aspen i n Northern Ontario. study, merchantable l e n g t h i n c l u d e d t h a t p o r t i o n of the stem from a 1-foot stump to a 3«5-inch top; any p o r t i o n of the stem with a r o t diameter g r e a t e r than 1-inch was c u l l e d . The volume of t h i s c u l l e d p o r t i o n was then expressed as a percentage of the t o t a l volume of each t r e e . Meinecke i n c l u d e d as merchant- abl e stem t h a t p o r t i o n between a 1-foot stump and a 2-inch top. He expressed the volume of the mass of decay as a percentage of the merchantable volume of each t r e e . B l a c k c o n s i d e r e d only t r e e s above 6-inches d.b.h., and although Meineke measured merchantable t r e e s , the lower diameter l i m i t employed i s not c l e a r . F o r l a r g e samples these d i f f e r e n c e s i n method are s m a l l , i n c r e a s i n g the p o s s i b i l i t y t h a t the s i m i l a r i t y of the p e r c e n t - ages shown above are not due to chance alone. Although these c u l l percentages are not s t r i c t l y a p p l i c a b l e to Northern A l b e r t a aspen, i t i s l i k e l y t h a t the e r r o r i n c u r r e d w i l l not be g r e a t i f they are a p p l i e d as a c o r r e c t i o n to volume estimates f o r t h a t r e g i o n . The c u l l f i g u r e s i n d i c a t e a l s o t h a t f o r stands o l d e r than 80 y e a r s , an allowance f o r r o t i s n e c e s s a r y i f volume estimates are to be of much value, and t h a t i t may be b e t t e r to employ the estimated deductions than to d i s r e g a r d them e n t i r e l y . A p p l i c a t i o n of the c u l l percentages g i v e n i n Table 20 to volume y i e l d s , changes the r o t a t i o n ages p r e v i o u s l y suggested very l i t t l e f o r both t o t a l and merchantable cub i c f e e t . For stands 120 years and o l d e r , amount of c u l l i s h i g h which should r e s u l t i n l o w e r i n g the r o t a t i o n p e r i o d g i v e n f o r board f e e t . Since these ages are beyond the range covered by the data an adjusted r o t a t i o n age cannot be determined. -28- D e n s i t y B a s a l area as a measure of d e n s i t y i n the a p p l i c a t i o n of normal y i e l d t a b l e s was found by Meyer (10) to be b e t t e r than any other y i e l d t a b l e measure. Ba s a l area can be obtained from f i e l d d ata and compared to the t a b u l a r value, . ( i n t e r p o l a t e d from the y i e l d t a b l e s according to age and s i t e index) i n o r d e r to o b t a i n a s t o c k i n g value f o r a f o r e s t . The r a t i o i s u s u a l l y expressed i n p e r c e n t . Thus, i n the case of aspen, i f the b a s a l area of a stand of s i t e q u a l i t y 80 and age 60 has been computed as 130 square f e e t per acre, i t i s compared wi t h a d e n s i t y of 160 square f e e t (from Table $ ) . The s t o c k i n g t h e r e f o r e , i s 130/160 x 100 or 8 l p e r c e n t . F o r f u t u r e p r e d i c t i o n s of growth i t i s u s u a l to assume that t h i s f i g u r e w i l l remain the same; thus at age 100 the b a s a l area w i l l be 166 x .81 or 134 square f e e t . Growth i n f o r m a t i o n from permanent p l o t s i n d i c a t e t h a t a trend towards n o r m a l i t y takes p l a c e i n overstocked and under- stocked stands. Use of the above assumption, t h e r e f o r e , i s to g i v e c o n s e r v a t i v e f u t u r e growth estimates f o r understocked stands (the most common) and o p t i m i s t i c f o r e c a s t s f o r stands which are overstocked. The extent of t h i s e r r o r w i l l depend upon s t o c k i n g , age of the stand and growth c h a r a c t e r i s t i c s of the p a r t i c u l a r s p e c i e s i n q u e s t i o n . Although b a s a l area has been suggested here as the measure to be used when e s t i m a t i n g d e n s i t y i n c o n j u n c t i o n w i t h the y i e l d t a b l e s , number of t r e e s per acre has been r e c e i v i n g g r e a t e r a t t e n t i o n by f o r e s t e r s when r e l a t e d to the diameter of the t r e e of average b a s a l area. Reineke (16) has shown t h a t f o r - 2 9 - a number o f s p e c i e s t h i s r e l a t i o n s h i p assumed a s t r a i g h t l i n e form when p l o t t e d on double l o g a r i t h m i c paper. Out of the 111 s p e c i e s that were t e s t e d the slop e s f o r 12 of these were the same. Employing an average d.b.h. of 10 inches as h i s index diameter and a sheaf of l i n e s p a r a l l e l t o the main guide l i n e , he was able to a s c r i b e a d e n s i t y number to any stand where the number of t r e e s p e r acre and the average stand diameter were known. T h i s stand d e n s i t y index i s t h e r e f o r e the number of t r e e s per acre at an index diameter of 10 i n c h e s . Mulloy (12) (13) has brought the stand d e n s i t y index concept to the a t t e n - t i o n of Canadian f o r e s t e r s and Spurr (19) a l s o has ex p l o r e d i t s p o s s i b i l i t i e s . Although stand d e n s i t y i n d i c e s have not been employed to develop any p o r t i o n of the y i e l d t a b l e s , they are prese n t e d here to f a c i l i t a t e comparison w i t h aspen growing i n othe r r e g i o n s where t h i s measure of s t o c k i n g i s used. I t w i l l a l s o be shown t h a t the slope of the r e g r e s s i o n l i n e of number of t r e e s on average diameter (on double l o g a r i t h m i c paper) may be q u i t e d i f f e r e n t f o r aspen than the one d e r i v e d by Reineke and used by Mulloy f o r s p e c i e s i n E a s t e r n Canada. To determine the r e g r e s s i o n l i n e , the average of the number of t r e e s p e r acre i n each 2 - i n c h average diameter c l a s s was p l o t t e d over average d.b.h. on l o g paper. These p o i n t s are shown i n F i g u r e 11, and a s t r a i g h t l i n e o b v i o u s l y f i t s the data b e s t . The equation was determined as l o g N = -I . 7 6 7 l o g D + k . 2 5 7 , where N equals the number of t r e e s p e r acre and D the b a s a l area of the average t r e e i n i n c h e s . When the p l o t d a t a were a l l converted t o l o g a r i t h m i c v a l u e s and f i t t e d by the method of l e a s t squares, a slope of -I.6I4.6 was obtained, a FIG-TTRE 11 - The, r e l a t i o n of t o t a l number of t r e e s per acre to average stand d.b.h., f o r ?3 f u l l y stocked aspen sample p l o t s . The slope of the f i t t e d r e g r e s s i o n l i n e i s compared with" that obtained by Reineke f o r a number of other s p e c i e s . - 3 1 - TAELE 21 STAND DENSITY UNITS FOR ASPEN CORRESPONDING TO AVERAGE STAND DIAMETERS IN INCHES Average Average stand d.b.h..' tenths of an inch stand 0 . 0 - '0-1 <K2 0^3 0i4 0.5 0^6 0.7 0.8 0.9 d * T ) , t u Stand density units (inches) 1.0 0.017 0.020 0.023 0-027 0.031 0.035 O.O39 0.043 0.048 0.053 2.0 0.058 O.O63 0.068 0.074 0.080 0.086 0.092 O.O98 0.105 0.112 3.0 0.119 0.126 O.I33 0.140 0.148 O.156 0.164 0.172 0.180 0.189 4.0 0.198 0.20? 0.216 0.225 0.234 0.244 0.254 0.264 0.274 0.284 5.0 0.294 O.305 O.316 O.327 0.338 O.349 O.360 O.371 O.382 0.394 6.0 0.406 0.418 O.43O 0.442 O.454 0.467 0.480 0.493 O.506 O.519 7.0 O.532 O.545 O.559 0.573 0.587 0.601 0.615 0.628 0.643 O.658 8.0 0.673 0.688 0.703 0.718 O.734 0.750 0.766 0.782 0.798 0.814 9.0 0.830 0.847 O.863 0.880 0.897 0.914 O.93I 0.948 O.965 0.982 10.0 1.000 1.018 I.O36 I.O56 1.074 1.092 1.110 1.128 1.146 1.164 U . 0 I .I83 1.202 1.221 1.240 1.259 1.278 1.298 I.3I8 I.338 I.358 12.0 I.378 1.498 1.418 1.439 1.460 1.481 1.502 I.523 1 .5^ 1.565 13.0 1.587 1.609 I.631 I.653 1.675 1.697 1.719 1.742 1.765 1.788 14.0 1.811 1.834 1.857 1.880 I.903 1.926 1.949 1.972 1.996 2.020 15.0 2.044 2.068 2.092 2.116 2.140 2.164 2.188 2.213 2.238 2.263 16.0 2.288 2.313 2.388 2.363 2.389 2.415 2.441 2.467 2.493 2.519 -32- somewhat lower slope than d e r i v e d by freehand methods. The reason f o r t h i s d i f f e r e n c e has been e x p l a i n e d by H. A. Meyer (9) as due to e r r o r s i n c u r r e d by the use of l o g a r i t h m s i n the p l a c e of n a t u r a l numbers. T h i s e r r o r i s a systematic one and may be c o r r e c t e d by use of the standard e r r o r . The l i n e f i t t e d by the method of l e a s t squares d i d not conform to the p l o t t e d averages of the data, but c o r r e c t i o n s were awkward to make when the standard e r r o r decreased w i t h an i n c r e a s e i n average stand diameter. The l i n e i l l u s t r a t e d i n F i g u r e 11, f i t t e d by freehand methods, was t h e r e f o r e assumed to be the best f i t and.employed i n the computations d e s c r i b e d l a t e r . I t i s not c l e a r whether Reineke obtained h i s curve by f i t t i n g the data by l e a s t squares or whether the wealth of d a t a analyzed r e v e a l e d the slope of -1.605 presented i n h i s paper by standard procedures of b a l a n c - i n g d a t a by freehand methods. Schnur (18) f o r Upland Oak found the slope to be somewhat f l a t t e r than the slope obtained by Reineke, while f o r aspen the slope appears much steep e r ( r e f e r to F i g u r e 11). I f t h i s l a s t i s true the e x p l a n a t i o n must l i e i n the r a t h e r e x c e s s i v e m o r t a l i t y of the aspen i n the e a r l y y e a r s . •- To be c o n s i s t e n t with the stand d e n s i t y index concept o u t l i n e d by Reineke, the r e g r e s s i o n l o g N = -I.767 l o g D + k.257 was converted to the 1000 t r e e l e v e l at an average d.b.h. of 10-Inches. The r e s u l t i n g f ormula i s expressed by, Log F = 1.767 l o g D + k .767. In order t h a t stand d e n s i t y i n d i c e s may be c a l c u l a t e d r a p i d l y , a t a b l e of stand d e n s i t y u n i t s (Table 21) was c o n s t r u c - ted f o r aspen s i m i l a r to the one d e r i v e d by Mulloy u s i n g Reineke 1s formula. The procedure adopted t o d e r i v e these t a b l e s i s as f o l l o w s . -33- The required average diameter values were converted to logarithmic numbers and the number of trees per acre calcut5- lated from the formula given above, log N = - 1 . 7 6 7 log D + k .767. The stand density units were obtained by d i v i d i n g the values f o r N into 1000. Prom these the stand density index may be computed quickly. I f the average diameter has been determined as 6.1 with 200 trees per acre, the stand density index w i l l be 0 . k l 8 x 200 or 8k. It i s admitted that the re- gression of number of trees over average diameter may be too steep either as a r e s u l t of bias i n the sample or as a result of below-normal stocking of the older stands. Since f i r e i s a major problem i n the area, i t i s conceivable that older stands i n the larger diameters have been subjected to f i r e at some period i n the past. BLACK POPLAR, PERCENTAGE COMPOSITION CHANGE Plots were chosen i n pure hardwood stands composed mainly of aspen, and although black poplar occurred on 7 1 . 8 per- cent of them, i t never exceeded 30 percent of the stand compo- s i t i o n . Since no r e s t r i c t i o n s were imposed to govern the number of stems allowable, s i g n i f i c a n t changes i n the amount of black poplar throughout the age classes can be mainly credited to differences i n growth between t h i s species and aspen. It i s conceivable, however, that the colour and texture of the black poplar bark, which i s almost black in older stands, would have some e f f e c t on the choice of plots made. The r e s u l t s which w i l l be presented may therefore be influenced by personal bias. Only those plots containing black poplar were used to -34- determine the regression of percentage composition and age by the method of least squares. The average percentage within each age class and the regression l i n e are shown i n Figure 12. An analysis of variance was made to test the r e l i a b i l i t y of the relationship. The figures obtained are given b&low: Degrees of ' Sum Mean ' Variance Source Freedom Squares Squares Ratio Var i a t i o n due to regression 1 221.71 221.71 4.55 Residual v a r i a t i o n 59 2877.25 48.76 Total v a r i a t i o n 60 3098.96 From tables shown by Fisher and Yates (3), the variance r a t i o at the 5 percent l e v e l is 3*97 compared with the 4*55 value determined. The regression, therefore of the two variables employed i s s i g n i f i c a n t at the 5 percent p r o b a b i l i t y l e v e l . The percentage composition of black poplar at ©ach 20-year age class i s given i n Table 22. The average change i s small (0.65 percent per decade) and w i l l not be introduced as correction i n the prediction of black poplar growth from the y i e l d tables. The relationship shown i n Figure 12 indicates the s i m i l a r i t y in basal area growth of aspen and black poplar where they exist i n close association. This j u s t i f i e s , somewhat, treating a l l species i n the hardwood mixture as one unit. This procedure has been followed i n the development of poplar y i e l d s described in t h i s thesis. - 3 5 - g 70 A* 5 10 20 30 40 SO &0 70 80 90 UX 110 120 Totol aye- years FIGURE 12" - The r e l a t i o n of percentage composition, by b a s a l area, to t o t a l age f o r b l a c k p o p l a r on 61 s a n p i e p l o t s . TABLE 22 PERCENTAGE COMPOSITION OF BLACK POPLAR RELATED TO AGE T o t a l age Composition by b a s a l are; (years) 20 kO 60 80 100 (percent) 9 . 3 8 . 1 6 . 7 5-4 4 . 1 - 3 6 - VOLUME TABLES FOR ASPEN AND BLACK POPLAR Measurements and Computations Aspen and b l a c k p o p l a r t r e e s were f e l l e d and measured d u r i n g y i e l d s t u d i e s conducted by the w r i t e r f o r mixedwood and pure p o p l a r stands growing i n Northern A l b e r t a . For each t r e e , diameters and bark t h i c k n e s s e s were recorded at the f o l l o w i n g p o i n t s : at a stump h e i g h t of 1-foot, at k.5 f e e t above ground and at the end of each e q u a l - l e n g t h e d l / 1 0 - s e c t i o n between b r e a s t h e i g h t and the t i p of the t r e e . Lengths of stem were accumulated from the base and t h i s accumulated h e i g h t at each p o i n t measured was p l o t t e d over the corresponding diameter i n s i d e bark. By j o i n i n g the p o i n t s w i t h a smoothed l i n e , a graph f o r each t r e e was obtained from which i t was p o s s i b l e to read measurements f o r the u t i l i z a t i o n d e s i r e d . The volume measures used i n A l b e r t a were t o t a l cubic feet,merchantable cubic f e e t (1-foot stump to a k - i n c h top i n s i d e bark) and board f e e t ( l - f o o t stump to a 6-inch top i n s i d e b a r k , S c r i b n e r r u l e ) . T o t a l c u b i c f o o t volume i n s i d e bark f o r each t r e e was c a l c u l a t e d u s i n g Smalian's formula; the p o r t i o n between ground and 1-foot stump h e i g h t was t r e a t e d as a c y l i n d e r . The mer- chantable volume was obtained by s u b t r a c t i n g the volume of stump and top. From the graphs of each t r e e , 16.3-foot l o g s were s c a l e d i n board f o o t volume. The top l o g c o u l d be 8 . 3 , 10 . 3 , 12 . 3 , 14»3, or 16 . 3 f e e t long depending on the l e n g t h of stem which remained from the l a s t 16.3-foot l o g . -37- Por analysis of volume, the measurements used f o r each aspen and black poplar tree were: 1. Diameter at breast height i n inches outside bark, 2. Total height i n feet, 3. Volume i n (a) t o t a l cubic feet, (b) merchantable cubic feet, (c) and merchantable board feet, Scribner rule. Total Cubic Feet The t o t a l cubic volume f o r each aspen tree was com- pared with volumes given i n a table constructed f o r t h i s 1 species i n eastern Canada . The table gave values which were consistently high. Adjusted volumes were obtained from a graph derived by p l o t t i n g actual volumes over tabular volumes on double logarithmic paper (Table 23). From a comparison made previously by the writer, i t was found that black poplar had a c h a r a c t e r i s t i c a l l y thicker bark and poorer form than the aspen. The volumes obtained therefore, when the black poplar trees were interpolated i n Table 23, were too high. A correction factor of 0.8L2 was determined and applied. The estimate of the actual volumes which resulted proved to be sa t i s f a c t o r y . The aggregate d i f f erence was small and the average deviation did not increase beyond that obtained f o r the aspen. 1 Dominion Form Class Volume Tables, page 182, 19k8. -38- 'Merchantable Cubic Feet No aspen volume t a b l e s a p p l i c a b l e to the merchantable l i m i t s used i n A l b e r t a were l o c a t e d . I t was necessary t h e r e - f o r e , t o c o n s t r u c t a new t a b l e . The method employed i n the a n a l y s i s was e s s e n t i a l l y that suggested by Dwight (2). T h i s method i s an improvement on standard g r a p h i c a l techniques because the r e l a t i o n s h i p of h e i g h t - t o - d i a m e t e r w i t h i n each h e i g h t c l a s s i s taken i n t o account. The group of curves i n t h i s step (Figure 13) are f i t t e d c o n c u r r e n t l y w i t h those ob- t a i n e d by p l o t t i n g volume over diameter by h e i g h t c l a s s e s . The volumes and h e i g h t s read f o r each 2 - i n c h c l a s s are next used to d e r i v e the r e l a t i o n s h i p of volume to h e i g h t by diameter c l a s s e s . F o r the aspen d a t a these curves proved to be' a f a m i l y of s t r a i g h t l i n e s , most of them r a d i a t i n g from a common o r i g i n . Although the curves may be harmonized i n t h i s p a r t of the a n a l y s i s , volume was r e p l o t t e d over diameter by h e i g h t c l a s s e s i n order to f a c i l i t a t e r e a d i n g of volume f o r 1-inch diameter i n t e r v a l s . From these curves the v a l u e s shown i n Table 2k were obtained. The b l a c k p o p l a r t r e e d a t a f o r merchantable c u b i c f e e t were now compared wi t h volumes i n t e r p o l a t e d f o r diameter and h e i g h t i n Table 2k. The t a b u l a r v a l u e s obtained were again too h i g h . M u l t i p l y i n g by a c o r r e c t i o n f a c t o r of 0.817 r e s u l t e d i n a much improved estimate w i t h but a s l i g h t i n c r e a s e i n the average d e v i a t i o n p e r c e n t over t h a t obtained f o r the aspen. -39- Merchantable Board F e e t , S c r i b n e r Rule A s i m i l a r a n a l y s i s f o r diameter, h e i g h t and board f o o t volume was c a r r i e d out f o r the aspen up to and i n c l u d i n g the step of p l o t t i n g volume over h e i g h t by d.b.h. c l a s s e s . F i g u r e s 13 and l k i l l u s t r a t e the f i r s t two steps (the number of t r e e s used to weight each p o i n t on the graphs are o m i t t e d ) . F i g u r e 15 shows the p r e l i m i n a r y group of s t r a i g h t l i n e s f i t t e d to the data. The spacing and s l o p e s of these l i n e s f o r each diameter c l a s s are harmonized by an a d a p t a t i o n of a method o u t l i n e d by Meyer (11). Since volume i n board f e e t f o r any one diameter c l a s s i s d i r e c t l y r e l a t e d to t o t a l h e i g h t , i t may be expressed by the f o l l o w i n g f o r m u l a : V = a + bH where V = board f o o t volume, a - i n t e r c e p t , b = slope, H = t o t a l h e i g h t i n f e e t . The slope of the l i n e f o r each diameter c l a s s was determined. These v a l u e s p l o t t e d over diameter were f i t t e d by a freehand curve (Figure 16). T h i s r e l a t i o n s h i p i s a s t r a i g h t l i n e f o r 1 3-inch diameters and l a r g e r , w i t h a slope of b" = -5.65 + 0.612D. Below 1 3-inches the r e l a t i o n of slope to diameter i s curved, and a d i f f e r e n t procedure i s r e q u i r e d - F o r the p r e s e n t i t may be noted t h a t i n d i v i d u a l slope v a l u e s may be read from the curve i n F i g u r e 16 f o r diameters between 7 and 1 2-inches. -ko- In the next step, an adjusted volume f o r a standard h e i g h t c l a s s of 80-feet was computed f o r each 2-inch diameter, where the adjusted volume = the average volume f o r the d.b.h. c l a s s - b" (average h e i g h t f o r the d.b,h. c l a s s ) - 80, and b" = -5.65 + 0.612D. The average volumes and h e i g h t s were obtained by c a l c u l a t i n g weighted averages f o r each 2-inch c l a s s . Adjusted volumes were then p l o t t e d over diameter and a curve f i t t e d as shown i n F i g u r e 17. Again the r e g r e s s i o n proved to be a s t r a i g h t l i n e f o r diameters 13-inches and l a r g e r , the r e s u l t i n g r e g r e s s i o n i s expressed by the equation, a d j . v o l . = -236 + 28.5D. F o r diameters below 13-inches, i t may be noted t h a t a d j u s t e d volume may be read f o r any d.b.h. from the curve. From the slope equation and adjusted volume equation f o r a standard h e i g h t of 80-feet the f o l l o w i n g i s t r u e : 1. A d j . volume (V) = -236.0 f 28.5D 2. -bH = -5.65+ 0.612D) 80 or k52.0 - I4.9.OD by adding (1) and (2) V-bH = + 216.0 - 20.5D a - 4- 216.0 - 20.5D s i n c e V = a + bH and a = V - bH. For e s t i m a t i n g volumes of t r e e s with diameters 13-inches and above, there are now three equations; A General e x p r e s s i o n V* = a + bH B The slope e x p r e s s i o n b = _ 5,65 + 0.612D C The i n t e r c e p t e x p r e s s i o n a = + 216.0 - 20.5D - k l - 'Since slope "b" and i n t e r c e p t "a" are changing i n a c u r v i l i n e a r manner f o r diameters below 1 3-inches, equations B and G are not a p p l i c a b l e to the s m a l l e r diameters. While slope v a l u e s may be obtained from F i g u r e 16, c o r r e s p o n d i n g f i g u r e s f o r the i n t e r c e p t are s t i l l r e q u i r e d i n order to d e r i v e i n d i v i d u a l equations f o r each 1-inch diameter c l a s s . T h i s d i f f i c u l t y was overcome, by c a l c u l a t i n g v a l u e s of 'a' and p l o t t i n g these over diameter as shown i n F i g u r e 18. The computations f o r 'a' were made from the e x p r e s s i o n , a = volume at chosen h e i g h t - b x (chosen h e i g h t ) where volume may be read from F i g u r e 17 and slope v a l u e s from F i g u r e 16. An i n d i v i d u a l e q u a t i o n t h e r e f o r e , was determined f o r the diameters r e q u i r e d . From the equations shown below the val u e s f o r the board f o o t volumes shown i n Table 25 were o b t a i n e d . Group I - Diameters at b r e a s t h e i g h t from 7-12 inches i n c l u s i v e 7" - V = : - 8.8 + 0.22H 8" - V = • - 13.6 0.50H 9" - V : : - 18.5 + 0.79H 10" - V = : - 2k.1 i T 1.12H 11" - V = : - 31.0 + l.k6H 12" - V = : - kO.O 1.87H Group I I - Diameters at b r e a s t h e i g h t f o r t r e e s 13-inches and l a r g e r . General e x p r e s s i o n V = a + bH The slope e x p r e s s i o n b = -5.65 * 0.612D The i n t e r c e p t expres- s i o n a = + 216.0 - 20.5D -1+2 - Examples of a p p l i c a t i o n F o r c l a r i t y , volumes i n board f e e t are c a l c u l a t e d f o r examples o c c u r r i n g i n Group I and Group I I . 1. Wanted: t o determine the volume i n board f e e t f o r a 10- i n c h t r e e of h e i g h t 63 f e e t . From Group I the eq u a t i o n i s : V = - 2 k.l + 1.12H S u b s t i t u t i n g f o r H V z - 2k.1 + 1.12 x 63 V = k6.5 board f e e t . 2. Wanted: to determine the board f o o t volume f o r a 1 9-inch t r e e of h e i g h t 9k f e e t . From Group I I the g e n e r a l e q u a t i o n i s : V = a + bH to determine the slope s u b s t i t u t e 19 f o r D i n b = - 5»65 + 0.612D b = -5.65 + 0.612 x 19 = +5.98 to determine the i n t e r c e p t s u b s t i t u t e 19 f o r D i n a = +216.0- 20.5D a = + 216.0 - 20.5 x 19 = - 173.5 s u b s t i t u t i n g f o r b, a, and H i n the g e n e r a l equation V = -173.5 + 5.98 x 9k «*• 388.6 board f e e t . To apply the v a l u e s i n Table 25 to estimate b l a c k p o p l a r volumes the t a b u l a r f i g u r e s were reduced by m u l t i p l y i n g them by O.787. -43- The method employed above to harmonize a family of straight l i n e s was o r i g i n a l l y suggested by W.H. Meyer to develop volume tables i n board feet where the r a t i o of volume/ diameter plotted over diameter by height classes, form a series of straight l i n e s . The aspen data plotted t h i s way indicated c u r v i l i n e a r i t y f o r diameters above 20-inches. The explanation may be that larger diameters are found mainly i n understocked stands and are usually trees of poorer form. It was f e l t therefore, that Meyer's method could not be j u s t i f i - ably employed. Adapting the method described, o f f e r s l i t t l e advantage to those who are f a m i l i a r with the systems of crosscurving, but f o r those who are not, the introduction of this semi- mathematical system may f a c i l i t a t e the harmonization of both slope and spacing. Another feature of the method i s that i t may be employed f o r other relationships where a system of straight l i n e s i s applicable. In cert a i n cases, some advantage may be gained by a mathematical control of tabular and i n t e r - mediate values. The weakness l i e s i n the manner o r i g i n a l averages have been obscured by previous curving. This would seem to be no more serious however, than the weaknesses involved i n any m u l t i c u r v i l i n e a r method. -kk- VOLUME TABLES FOR WHITE BIRCH T o t a l Cubic F e e t Height measurements f o r 93 b i r c h t r e e s were taken by MacLeod (6) as they o c c u r r e d i n mixedwood stands through- out the same r e g i o n as t h i s study. The t o t a l c u b i c volumes shown i n Table 26 are taken from h i s r e p o r t . Merchantable Cubic and Board F e e t To d e r i v e merchantable t a b l e s , aspen volumes i n cub i c and board f e e t were i n t e r p o l a t e d f o r the diameters and h e i g h t s g i v e n i n Table 26, To the volume shown f o r each d.b.h. c l a s s , the r a t i o of aspen t o t a l c u b i c volume to that f o r b i r c h was a p p l i e d as a c o r r e c t i o n . To assume a s p e n - b i r c h t o t a l volume r a t i o s were the same f o r merchantable measures p r o v i d e d the o n l y b a s i s p o s s i b l e under the circumstances s i n c e no b i r c h t r e e s were measured f o r volume. The amount of b i r c h p r e s e n t i n the stands measured was small however, and any e r r o r s t h a t might a r i s e from i n c o r r e c t volume t a b l e s f o r t h i s s p e c i e s cannot s e r i o u s l y a f f e c t the r e s u l t s . -45- -120 -WO t£ 80 \ \ eo -20 — V Sol 8 12 16 20 24 Di'ometer; Breast Height, I Vir?ches)__ I O O 90 28 1 FIGURE 13 - The trend of height on d.b.h, w i t h i n each 1 0-foot height c l a s s . FIGURE - ll). The r e l a t i o n of board f o o t volume (Scribner r u l e ) on d.b.h. by 10-foot height c l a s s e s . -1+6- l^Mal^hlilhl ^f5'°\0f,.hClld f ° o t V o l u r a s ( S c r i b n e r r u l e ) on t o t a l h e i g h t by 2-inch diameter c l a s s e s . -hi- top o f — 2-o • 0 A 8 I Diameter. \ 1 2 i Qreat 6 2 0 z iht- 4 26 1J I 1 1 FIGURE 16 - Slope c o e f f i c i e n t s "b" f o r t r e n d of S c r i b n e r board f o o t volume on t o t a l h e i g h t , p l o t t e d on diameter at b r e a s t h e i g h t . — 600 <-> 500 tQ 4O0 1 -v§ Zoo -\Zoo / • 0 4 6 I Diameter. E. 1, z 1 breast 6 2 Heiqh fi FIGURE 17 - Adjusted volume r a t i o s ( b a s i s = 80 f e e t ) p l o t t e d over diameter at b r e a s t h e i g h t . 160 WO $ 1 ^ oo £o — -40 — •10 0 2 4 1 < I > 8 1 eter, Breast l 0 i Height-, 2 14 I in.) \ i FIGURE 18 - I n t e r c e p t c o e f f i c i e n t s "a" f o r trend of S c r i b n e r board f o o t volume on t o t a l h e i g h t , p l o t t e d on diameter at b r e a s t h e i g h t . TABLE 23 VOLUME TABLE Aspen (P. tremuloides Michx.) and Black Poplar (P.balsamifera L.) Total Cubic foot Volume Central and Northern Alberta Total Height - feet d. b.h. i n . 10 20 30 40 50 60 70 80 90 100 110 Total peeled volume i n cubic feet Basis number of trees 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 2? 0.06 0.21 0.04 0.13 0.28 0.47 0.85 I .36 0 .07 , 0.29 I 0»37 0.66 0.85 1.19 1.53 1.90 I 2.44 2.75 3.55 4.86 6.38 8.10 0-.45 J_04 1.871 2.98 *-35 5.97 7.84 10.00 12.3 14.8 17.5 20.4 23.5 26.9 30.3 2.21 3.52 5.15 7.09 9.30 11.8 14. _____ 17. 20.5 24.0 27.8 31.6 _ _ _ _____ 44.6 ^9.5 5 .̂7 8.20 10.76 13.6 16.7 20.0 23.6 27.6 31.9 36.3 40.9 46.1 1 9 0 1 _±_L 56T9 62.9 68.8 74.7 12.22 15.5 18.9 22.6 26.7 31.2 36.0 41.1 46.3 52.2 58.1 64.4 71.0 77.6 84.2 13.7 17.3 21.1 25.2 29.8 34.8 40.1 45.8 51.6 58.2 64.8 32.9 38.4 44.2 50.5 _£__ 90.8 97.4 104.0 110.6 117.2 64.2 ____. 71.9__2_i 79.2 87.3 86.5 95.3 93.8 103.3 101.11111.3 _________ 115.7 127.3 -23T0I135.3 130.3 145; 3 62.2 70.2 78.2 86.7 95.5 104.2 112.9 121.6 130.3 139.0 147.7 156.4 2 4 9 13 13 6 9 10 5 6 8 5 7 8 7 11 11 8 5 4 6 4 1 2 1 Basis num- ber of «g trees 8 15 18 16 29 39 28 - I65 1 f o r Black Poplar multiply tabular volumes by 0.842 - basis, 46 trees. Heavy line indicates the extent of the original data. Volumes include entire stem inside bark. Table was prepared by adjusting aspen volume table, page 196, Dominion Form Class Volume Tables, 1948. Aspen i Aggregate difference, table 0.267 percent high • Average deviation 4 6.15 percent Black Poplar : Aggregate difference, table 0.023 percent low : Average deviation 4 6.09 percent - 5 0 - TABLE 24 VOLUME TABLE Aspen (P.tremuloides Michx.) and Black Poplar 1 ' (P.balsamifera L.) Merchantable Cubic Peet Central and Northern Alberta d.b.h. in. Total Height Ft. 30 40 50 60 ' 70 80 90 100 110 Merchantable volume i n cubic' feet Basis number of trees 4 0.15 0.45 0.75 10 5 1.05 1.50 1.93 2.40 13 6 2.40 3.05 3.70 •̂35 6 7 3.90 4.80 5.70 6.60 7.50 9 8 5.50 6.70 7.80 9.00 10.1 11.2 10 9 6.95 8.60 10.25 11.90 13.55 15.2 5 10 8.20 10.50 12.9 15.2 17.5 19.8 6 11 12.5 15.4 18.4 21.3 24.3 8 12 14.6 18.2 21.9 25.5 29.4 5 13 16.6 21.1 25.6 30.1 3^7 39.2 7 14 18.6 24.1 29.6 35.1 40.6 46.1 8 15 27.1 33.5 39.9 46.3 52.7 7 16 30.5 37.7 44.9 52.1 59.3 66.5 11 17 33.6 41.8 50.0 58.2 66.£ 74.6 11 18 37.9 46.0 55.1 64.2 73.3 82.4 8 19 40.2 50.2 60.2 70.2 80.2 90.2 5 20 43.9 54.7 65.5 76.2 87.0 97.8 4 21 58.8 70.5 82.3 94.0 105.7 6 22 63.O 75.6 88.2 100.7 113.3 4 23 80.6 94.2 107.7 121.3 1 24 85.6 100.2 114.8 129.4 - 25 90.6 106.2 121.7 137.3 2 26 95.6 112.2 1 128.7 145.2 1 27 118.2 135.7 153.2 28 142.7 161.2 Basis,num- ber of trees - 10 18 16 29 39 28 7 - 147 for Black Poplar multiply tabular volumes by 0.817 - basis,number of trees 46. Heavy line indicates the extent of the original data. Volumes include stem from l«foot stump to a 4-inch top, inside bark. Table was prepared for aspen by mult-curvilinear methods. Correction term 0.817 was applied to table values for estimating Black Poplar volumes. Aspen : Aggregate difference, table 0.462 percent low. : Average deviation + 6.18 percent Black Poplar : Aggregate difference, table 0.114 percent high : Average deviation + 6.49 percent. -51- TABLE 25 VOLUME TABLE * Aspen (P.tremuloides Michx.) and Black Poplar' (P. balsamif era L.) Merchantable Board (Scrib.) inside bark-Central and Northern Alberta Total Height Peet Basis d.b.h. • i n . 40 50 ' 60 70 ' 80 ' 90 ' 100 1 110 - Number of Merchantable volume in board feet .(Scribe) 1 trees 7 2 4 7 9 3 8 11 16 21 26 31 9 9 21 29 37 45 53 5 10 32 43 54 66 77 6 11 42 57 71 86 100 8 12 72 91 109 128 5 13 88 U l 134 157 180 7 14 104 133 I63 192 221 8 15 120 156 191 226 262 7 16 136 178 219 261 302 11 17 1 152 200 248 295 342 390 11 18 169 223 277 330 384 438 8 19 185 245 305 365 424 434 5 20 201 267 333 399 465 531 4 21 290 362 434 506 578 6 22 312 390 468 546 624 4 23 419 1503 588 672 1 24 447 538 628 718 25 476 1572 669 765 2 26 504 606 709 812 1 27 641 750 858 -28 791 906 - Basis number of trees - - 9 28 39 28 7 - 111 for Black Poplar multiply tabular volumes by 0.787 - basis 46 trees. Heavy line indicates the extent of the original data. Volumes include stem from 1-foot stump to a 6-inch top inside bark. Table prepared for aspen by multi-curvilinear methods. Correction term 0.787 was applied to tabular values to estimate Black Poplar volumes. Aspen : Aggregate difference, table 0.126 percent high : Average deviation + 12.65 percent Black Poplar : Aggregate difference,table 0,029 percent low : Average deviation + 14.84 percent -52- TABLE 26 VOLUME TABLES White Birch (B. Papyrifera Marsh.) Central and Northern Alberta . / / ' . i d.b.h. Total Volumes inside bark (inches) Height Total Merch. (feet) cubic cubic feet feet Merch. Board feet (Scrib.) 1 13 0.07 - - 2 22 0.35 - - 3 30 0 . 8 8 • - - k 38 1.76 0.11 - 5 k$ 3 . 0 0 l . k 6 - 6 51 k . 6 l 3.25 - 7 56 6.63 5.33 3 8 61 9.12 7 . 6 k 15 9 65 11.9 . 10.k 31 10 69 15.1 13.7 k9 11 73 , 1 8 . 9 17 .5 68 12 76 2 2 . 9 21.6 92 13 78 27.1 25.9 115 80 31.7 30.9 U 3 Based on a height /d.b.h. curve f o r 93 trees. Total cubic volume interpolated from volume table f o r white birch, in Quebec (Dominion Form Class Volume Tables, page I82,19k8). Volumes i n merchantable cubic and merchantable board feet (Scrib.) obtained by adjusting corresponding aspen volumes f o r these measures by a r a t i o equal to: t o t a l cubic volume f o r aspen divided by corresponding white b i r c h t o t a l cubic volume. Merchantable cubic volumes include stem from 1-foot stump to a k-inch top inside bark. Merchantable board foot volumes include stem from 1-foot stump to a 6-inch top inside bark. APPENDIX Ba s i c Data I t i s d i f f i c u l t to o b t a i n measurements i n f o r e s t s f o r every age and s i t e q u a l i t y , but c o n s i d e r i n g the small s i z e of the sample a f a i r d i s t r i b u t i o n among the p o s s i b l e combinations of age and s i t e q u a l i t y was obtained. T h i s i s i l l u s t r a t e d i n Table 27. The f i e l d method f o l l o w e d was to s e l e c t f u l l y stocked or normal p l o t s from the b e s t , the medium and the poor p o r t i o n s of stands of each age c l a s s . T h i s procedure was s a t i s f a c t o r y where a range i n s i t e e x i s t e d . Some stands however, were very uniform-and i n such cases two p l o t s r e p r e s e n t i n g the average c o n d i t i o n were measured. F o r e s t s of other s i t e q u a l i t i e s then, had to be sought out d u r i n g the progress of the study. An average guide curve of dominant h e i g h t over age p r e v i o u s l y prepared by the w r i t e r f o r the aspen i n mixedwood stands o f f e r e d some a s s i s t a n c e i n keeping a r e c o r d of the approximate d i s t r i b u t i o n of the s i t e q u a l i t i e s sampled. TABLE 27 PLOT DISTRIBUTION BY AGE AND SITE INDEX CLASSES .Totals 5 8 11 9 9 9 7 8 9 3 T o t a l s 3 13 32 23 7 78 - 5 V F l e l d Work For the most part,' aspen i n Northern A l b e r t a does not n a t u r a l l y occur i n u n i f o r m w e l l stocked stands extending over l a r g e areas but r a t h e r i n s m a l l patches. I n d i v i d u a l p l o t s t h e r e f o r e had to be s e l e c t e d r a t h e r than composite p l o t s such as taken by McArdle (7). The p l o t boundaries were surveyed w i t h a compass and s t e e l tape. Most p l o t s were r e c t a n g u l a r but a few were taken w i t h acute angles never l e s s than 60 degrees. A minimum of 100 t r e e s i n the main stand was r e q u i r e d on each p l o t . Size t h e r e f o r e v a r i e d from l e s s than l / l O acre to over l / 2 acre from young to o l d stands. A l l l i v i n g t r e e s were c a l i p e r e d and recorded by i n c h c l a s s e s a c c o r d i n g to s p e c i e s . Small t r e e s of the u n d e r s t o r y which were found i n some stands above 80 years of age were recorded by i n c h c l a s s e s . Those measur- i n g l e s s than 0 . 6 of an i n c h were recorded i n two h e i g h t groups, 6 inches to 3 f e e t and 3 f e e t p l u s . These s m a l l e r t r e e s were not i n c l u d e d i n the y i e l d computations. F o r each p l o t , t o t a l h e i g h t was measured w i t h s t e e l tape and Abney l e v e l except i n dense young stands where t r e e s were f e l l e d and measured d i r e c t l y . Two h e i g h t s f o r each 1- i n c h diameter c l a s s were taken f o r stands below 80 y e a r s and f o r each 2 - i n c h diameter c l a s s i n o l d e r stands. Diameters and h e i g h t s of dominants were recorded s e p a r a t e l y ; they v a r i e d i n number from If. to 8 t r e e s per p l o t . Age d e t e r m i n a t i o n s were made by c o u n t i n g the annual r i n g s . I t was found t h a t c o n s i s t e n t estimates could only be obtained by counting the r i n g s on the b u t t of the t r e e a f t e r - 5 5 - f e l l i n g . I t was necessary t o make a very s l o p i n g cut w i t h a sharp axe i n or d e r that minute r i n g s c o u l d be d i s c e r n e d . Though the average age of the dominants was taken as p l o t age, the procedure adopted f o r each stand was f i r s t to make age counts throughout t o a s c e r t a i n i f a l l t r e e s c o u l d be cons i d e r e d even-aged. Such a c o n d i t i o n was found to be gen- e r a l l y true f o r t h i s s p e c i e s . Since age de t e r m i n a t i o n s were u s u a l l y made at s e v e r a l f e e t above the ground l e v e l , i t was necessary to add the ages obtained at these h e i g h t s the num- ber of years r e q u i r e d to r e a c h the h e i g h t of the stump. The values i n Table 28 based on some 300 measurements of domin- ant aspen s e e d l i n g s were used to convert the r i n g count t o t o t a l age. TABLE 28 CORRECTION-IN YEARS TO BE ADDED TO AGE DETERMINED PROM INCREMENT BORINGS OR STUMP COUNTS, TO OBTAIN ASPEN TOTAL AGE Di s t a n c e from D i s t a n c e from average ground A S e average ground Age l e v e l to b o r i n g C o r r e c t i o n l e v e l to b o r i n g C o r r e c t i o n or top of stump or top of stump (inches) (years) (inches) (years) 1 1 10 2 2 1 12 3 3 1 18 3 k 1 2k k 5 1 30 k 6 2 36 5 7 2 k2 5 8 2 k8 5 9 2 Skr 5 -56- O f f i c e Computations The b a s a l area per p l o t f o r each diameter c l a s s was. now computed and a h e i g h t diameter curve drawn. The average h e i g h t of each d.b.h. c l a s s and average dominant were o b t a i n - ed. In t h i s l a s t case, the h e i g h t was read from the curve c o r r e s p o n d i n g to the average of the dominant diameters recorded. T h i s average was c a l c u l a t e d by b a s a l area. T o t a l c u b i c , merchantable c u b i c and S c r i b n e r board f o o t volumes f o r each diameter c l a s s were now computed with the a i d of volume t a b l e s (Tables 23 to 26 i n c l u s i v e ) . T o t a l s were then taken f o r each of f i v e items (number of t r e e s , b a s a l area and the three volumes) and converted to an acre b a s i s . The b a s a l area of the average t r e e s f o r each p l o t was c a l c u l a t e d by d i v i d i n g the t o t a l b a s a l area by the t o t a l number of t r e e s . A r a t i o ( t o t a l volume d i v i d e d by b a s a l area) adopted to p r o v i d e a cross-check between volume and b a s a l area i n the l a t e r a n a l y s i s was a l s o computed. Method of A n a l y s i s The method of a n a l y s i s employed was e s s e n t i a l l y t h a t d e s c r i b e d by Osborne and Schumacher (15). To o b t a i n curves of average dominant h e i g h t over age by s i t e index c l a s s e s , the standard d e v i a t i o n and c o e f f i c i e n t of v a r i a t i o n w i t h i n each age c l a s s was c a l c u l a t e d f i r s t . These s t a t i s t i c s p l o t t e d on age, F i g u r e 19, p r o v i d e d the b a s i s w i t h which to c o n s t r u c t the sheaf of curves I l l u s t r a t e d e a r l i e r i n F i g u r e 2, By means of t h i s graph a s i t e index value could be g i v e n to each p l o t -57- c 30 93 O I " §20 *-o ^ 1 <i Coefficient of \ 'ariafion of Dominant Height Residuals to Age s i > Co ef fi ci en t of  Co ef fi ci en t of  ) e Co ef fi ci en t of  Age - ) 'ears JO 1' 10 IJ Co ef fi ci en t of  10 20 30 40 50 60 ' 70 80 90 100 11 o 120 \i Standard Deviations of Dominant Height Residuals to Age Q Age - Years - ' i 10 20 30 40 50 60 70 8C 90 100 II 0 120 130 140 150 i i r- PIGfURE. 19 - The r e l a t i o n of the c o e f f i c i e n t s of v a r i a t i o n and standard d e v i a t i o n s of dominant h e i g h t r e s i d u a l s to t o t a l age. - 5 8 - a c c o r d i n g to i t s age a n d doxJiFhant h e i g h t . Next, i t was found necessary to r e j e c t 6 p l o t s i n the IkO y e a r age g r o u p . T h i s r a t h e r a r b i t r a r y a c t i o n was cons i d e r e d expedient from t h e r e s u l t of f i e l d o b s e r v a t i o n s . The a s p e n stands found at t h i s age c o u l d not be considered t r u l y f u l l y stocked and i n many cases evidence of breakup was o b v i o u s l y apparent. I n c l u s i o n of such u n s a t i s f a c t o r y p l o t s to develop n o r m a l y i e l d s was t h e r e f o r e considered t o be of l i t t l e v a l u e , p a r t i c u l a r l y w h e n no stands i n the 120 and the 130 year age c l a s s e s were l o c a t e d . To ensure u n i f o r m i t y of d e n s i t y i n the remaining p l o t s the r e l a t i o n of number of t r e e s to average diameter was used to t e s t the data. The number of t r e e s per acre was converted t o l o g a r i t h m s , g r o u p e d i n t o 2 - i n c h c l a s s e s and p l o t t e d over average stand diameter. The curve f i t t e d to the p l o t t e d p o i n t s i s i l l u s t r a t e d i n F i g u r e 2 0 . Average D.B.fir of plot$~'wcfte$ FIGURE 20 - The r e l a t i o n of the l o g a r i t h m of number of t r e e s to average d.b.h. - 5 9 - To t e s t f o r n o r m a l i t y 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 f r o m t h e c u r v e was f i r s t o b t a i n e d . T h e s e were c o n v e r t e d t o c u m u l a t i v e f r e q u e n c y p e r c e n t a g e s f o r each o f w h i c h , a p p r o p - r i a t e p r o b i t v a l u e s were e x t r a c t e d f r o m t a b l e s g i v e n by P i s h e r and Y a t e s ( 3 ) . The d i s t r i b u t i o n was now c h e c k e d by p l o t t i n g t h e u p p e r c l a s s l i m i t s shown i n t h e f i r s t c o lumn o f T a b l e 29 o v e r t h e p r o b i t v a l u e s g i v e n i n t h e l a s t c o l u m n . The s l i g h t l y s i g m o i d a l c u r v e i n d i c a t e d , r e v e a l e d k u r t o s i s , b u t n o t s t r o n g l y enough t o a f f e c t t h e b a l a n c e o f t h e p r o c e d u r e t o any e x t e n t . TABLE 29 FREQUENCY DISTRIBUTION OP RESIDUALS AND THE PROBITS CORRESPONDING TO THEIR CUMULATIVE FREQUENCY PERCENT C l a s s C u m u l a t i v e i n t e r v a l P l o t s f r e q u e n c y P r o b i t s l o g a r i t h m s number p e r c e n t u n i t s •0.20-0.22 1 1.2 2.74 +0.17-0.19 1 2 .4 3.02 40.14-0.16 1 3.6 3.20 +0.11-0.13 5 9.6 3.70 +0.08-0.10 5 15.7 3.99 +0.05-0.07 8 25.3 4 .33 +0.02-0.04 14 4 2 . 2 4 .80 - 0 . 0 1 - 0 . 0 1 15 60.2 5.26 - 0 . 0 4 - 0 . 0 2 11 73-5 5 .63 -o.07-0.05 7 82.0 5-92 - 0 . 1 0 - 0 . 0 8 5 87.9 6.17 - 0 . 1 3 - 0 . 1 1 6 95.2 6.66 - 0 . 1 6 - 0 . 1 4 1 96.3 6„79 - 0 . 1 9 - 0 . 1 7 1 97.6 6 .98 - 0 . 2 2 - 0 . 2 0 1 98.8 7.26 - 0 . 3 4 - 0 . 3 2 1 100.0 8.72 + T o t a l 83 - - The s t a n d a r d d e v i a t i o n of 0.089 l o g number o f t r e e s was c a l c u - l a t e d and f o l l o w i n g 5 t h e a c c e p t e d p r o c e d u r e , a l l p l o t s f a l l i n g o u t s i d e of two s t a n d a r d d e v i a t i o n s (2 x 0.089) were d i s c a r d e d . T h i s meant a t o t a l o f 5 p l o t s were r e j e c t e d , 4 u n d e r s t o c k e d and 1 o v e r s t o c k e d . The r e m a i n i n g 78 were employed i n t h e - 6 0 - a n a l y s i s d e s c r i b e d below. To ensure t h a t the independent v a r i a b l e s , age and s i t e were not c o r r e l a t e d , t h e i r i n t e r r e l a t i o n was t e s t e d by means of a s c a t t e r diagram, F i g u r e 21, and the "Corner t e s t of A s s o c i a t i o n " d e s c r i b e d by Olmstead and Tukey ( I k ) . No s i g n i f i c a n t c o r r e l a t i o n between them was found. 000^' — inn " go — w c 0 o o o 0 O 0 oo 0 < o o 0 — r 1_ rt O O o • o 0 0 o o Q O 60 o 0 2 -+ O O 1 • - 5o An 0 0 1 £> 20 3 o 4 o 50 (iO "70 80 90 1.00 uo u \Aspen fotol age-years FIGURE 21 - The r e l a t i o n of s i t e index to age; no c o r r e l a t i o n i s shown. -61- The d a t a f r o m e a c h p l o t were now s o r t e d i n t o 10- y e a r age c l a s s e s . The a v e r a g e v a l u e s p l o t t e d on age f o r m e d t h e b a s i c g u i d e c u r v e s f o r number o f t r e e s , a v e r a g e diameter"*", b a s a l a r e a , t o t a l c u b i c v o l u m e / b a s a l a r e a and t o t a l c u b i c volume. A method o f c r o s s - c h e c k i n g i s c o n v e n i e n t l y p r o v i d e d by t h i s s y s t e m o f c u r v e s . The b a s a l a r e a p e r a c r e r e a d f r o m t h e mean c u r v e f o r a g i v e n age, s h o u l d e q u a l t h e p r o d u c t o f t h e c o r r e s p o n d i n g number o f t r e e s p e r a c r e and t h e a v e r a g e b a s a l a r e a p e r t r e e . A l s o t h e p r o d u c t o f t h i s b a s a l a r e a and t h e v o l u m e / b a s a l a r e a r a t i o w i l l g i v e t h e c o r r e s p o n d i n g t o t a l c u b i c volume p e r a c r e . The a v e r a g e g u i d e c u r v e s were a l l b r o u g h t i n t o agreement by means o f t h i s c r o s s - c h e c k i n g p r o c e s s . To o b t a i n c u r v e s o f s i t e i n d e x t h e r e s i d u a l s f r o m t h e s e a v e r a g e c u r v e s were o b t a i n e d and t h e s t a n d a r d d e v i a t i o n and c o e f f i c i e n t o f v a r i a t i o n were computed f o r e a c h age c l a s s . Prom t h e r e l a t i o n o f t h e s e two m e a s u r e s w i t h age a b a s i s was p r o v i d e d t o d e r i v e o t h e r c u r v e s o f s i t e q u a l i t y a b o u t the a v e r a g e . The c u r v e s were b r o u g h t i n t o c o i n c i d e n c e as b e f o r e by t h e c r o s s - c h e c k i n g o f i n t e r r e l a t e d v a l u e s . F i g u r e s 22 and 23 a r e shown t o i l l u s t r a t e t h e t r e n d s o f s t a n d a r d d e v i a t i o n and c o e f f i c i e n t o f v a r i a t i o n w i t h age, and s t a n d a r d u n i t s w i t h s i t e i n d e x , o b t a i n e d when d e r i v i n g t o t a l c u b i c volume y i e l d f o r d i f f e r e n t age and s i t e c l a s s e s . S i m i l a r c u r v e s were ''"average d i a m e t e r = a v e r a g e b a s a l f o r e a c h age c l a s s d i v i d e d by t h e c o r r e s p o n d i n g a v e r a g e number o f t r e e s . T h e s e v a l u e s d i d n o t c o i n c i d e w i t h t h e mean o f the a v e r a g e d i a m e t e r s them- s e l v e s . T h e r e f o r e the c o r r e s p o n d i n g v a l u e s were p l o t t e d on d o u b l e l o g p a p e r and a l i n e f i t t e d . T h i s r e g r e s s i o n was u s e d as a b a s i s t o a d j u s t t h e a v e r a g e d i a m e t e r ( s q . f t . ) f o r e a c h p l o t . -62- c o n s t r u c t e d f o r e a c h o f t h e f i v e v a r i a b l e s d e s c r i b e d above. The y i e l d t a b l e s d e r i v e d f r o m t h e s e c u r v e s were c h e c k e d a g a i n s t t h e d a t a f r o m w h i c h t h e y were c o n s t r u c t e d . The s t a t i s t i c s o b t a i n e d a r e g i v e n i n T a b l e 30. I t w i l l be n o t e d t h a t o n l y f o r t h e number o f t r e e s i t e m d o e s t h e v a r i a - t i o n a c c o u n t e d f o r become s m a l l e r when t h e a f f e c t o f s i t e i s t a k e n i n t o a c c o u n t . The r e a s o n f o r t h i s was f o u n d t o e x i s t i n s t a n d s 30 y e a r s and y o u n g e r . I n t h e s e , o t h e r i n f l u e n c e s o v e r w e i g h th e e f f e c t o f s i t e . When t h e p l o t s were d i v i d e d i n t o two age g r o u p s , 10-30 and k0-110, t h e v a r i a t i o n a c c o u n t e d f o r by s i t e now i n c r e a s e d by 9.1 p e r c e n t i n t h e o l d e r age c l a s s . The r e s u l t s o f t h e c o m p u t a t i o n s a r e g i v e n b e l o w : I t e m Age o n l y Age and S i t e Number o f t r e e s - §ge c l a s s 10-30 y e a r s V a r i a t i o n a c c o u n t e d f o r , p e r c e n t 67.2 53»5 Number o f t r e e s - age c l a s s k0-110 y e a r s V a r i a t i o n a c c o u n t e d f o r , p e r c e n t 80. 3 89.k- I n T a b l e 30 t h e f i g u r e s show t h a t b a s a l a r e a i s t h e l e a s t s e n s i t i v e and t o t a l volume t h e most s e n s i t i v e t o t h e i n f l u e n c e o f s i t e . The r e s u l t s a r e i n g e n e r a l , c o m p a r a b l e w i t h t h o s e o b t a i n e d by i n v e s t i g a t o r s who have p r e s e n t e d y i e l d t a b l e s f o r o t h e r s p e c i e s . -63- oC ~> ZO 0 _ _ • : i ' : iiT«iri_ii ' : 'O— 3 to io 30 40 So _o 70 8o go LOO no* j2o * FIGURE 22 - Freehand curves showing i n (a) the average r e l a t i o n of volume to age; i n (b) the r e l a t i o n of the standard d e v i a t i o n of volume to age; and i n (c) the c o e f f i c i e n t of v a r i a t i o n of volume t o age. -6k- +t6 FIGURE 23 - The r e l a t i o n between the f i r s t r e s i d u a l s of t o t a l cubic volume (expressed i n standard u n i t s f o r i t s age) and s i t e index. TABLE 30 STATISTICS ILLUSTRATING RELIABILITY OF YIELD TABLES, AND EFFECT OF AGE, AND SITE AND AGE Item Age only Age and S i t e NUMBER OF TREES Aggregate d i f f e r e n c e , percent Standard e r r o r , number V a r i a t i o n accounted f o r , percent AVERAGE DIAMETER (Inches) Aggregate d i f f e r e n c e , percent Standard e r r o r , inches V a r i a t i o n accounted for,percent BASAL AREA (Square-feet) Aggregate d i f f e r e n c e , p e r c e n t Standard e r r o r , square f e e t V a r i a t i o n accounted f o r , percent TOTAL CUBIC VOLUME Aggregate d i f f e r e n c e , percent Standard e r r o r , cubic f e e t V a r i a t i o n accounted f o r , percent +0.776 691 88.3 + 0.953 785 84.6 + 0.563' 3.7 81,7 + 0.687 2.8 93-7 -0.311 23 69 .4 - 0.725 20 76.0 - 0 . 0 k 3 819 76.0 + 0.139 514 94.4 - 6 5 - BIBLIQGRAPHY (1) Black, R.L., Interim Report on the Decay of Trembling Aspen (Populus tremuloides Michx.) i n the Upper Pic Region of Northern Ontario. Unpublished report, Canada Dept. A g r i c , Dominion Forest Pathology, Toronto, Ontario, 1951. (2) Dwlght, T.W., Refinements of P l o t t i n g and Harmonizing Freehand Curves, Forestry Chronicle-, June, 1937. (3) Fisher, R.A., and Frank Yates, S t a t i s t i c a l Tables for B i o l o g i c a l , A g r i c u l t u r a l and Medical Research. Hafner Publishing Company, New York, 1949. (4) Garland, Hereford, Aspen f o r Veneer, U.S. Dept. A g r i c , Lake States For, Expt. Sta., Aspen Report 13, 1948* (5) Halliday, W.E.D., A Forest C l a s s i f i c a t i o n f o r Canada, Dept. Mines and Resources, Dom.For.Serv. Bui,89,1937- (6) MacLeod, W.K., Yi e l d s of Spruce-poplar Stands i n Northern Alberta. Unpublished report, Canada Dept, Resources and Development, For. Br,, Ottawa, 1951. (7) McArdle, R.E., Walter H. Meyer, and Donald Bruce, The Y i e l d of Douglas F i r i n the P a c i f i c Northwest. U.S, Dept. A g r i c , Tech. Bui 201. Revised Oct. 1949. (8) Meineke, E.P., Quaking Aspen. U.S. Dept. A g r i c , Tech. Bui. 155,1929. (9) Meyer, H.A., A Correction f o r Systematic Error Occurring i n the Application of the Logarithmic Volume Equation. Perm. State Forest School Res. Paper 7, 1941. (10) Meyer, W.H., A study of the Relation Between Actual and Normal Yields of Immature Douglas F i r Forests, Jour. A g r i c Res., V o l . k l , No. 9, 635-665,1.930. (11) Meyer, W.H., A Method of Volume-diameter Ratios for Board-foot Volume Tables. Jo u r . Forestry,, l\2t 185-189,1944. (12) Mulloy, G.A., Empirical Stand Density Y i e l d Tables. Canada Dept. Mines and Resources, Dom.For,Serv., S i l v . Res. Note 73, 1944. (13) Mulloy, G.A., Empirical Stand Density Y i e l d Tables, Canada Dept. Mines and Resources, Dom. For.Serv., S i l v . Res. Note 82 ,1947, -66- BIBLIOG-RAPHY ( l k ) O l m s t e a d , P.S., and J.W. Tukey, A C o r n e r T e s t f o r A s s o c i a t i o n . A n n a l s of v M a t h e m a t i c a l S t a t i s t i c s , 18: k95,19k7. (15) O s b o r n e , J . C , and F. X. Schumacher, The C o n s t r u c - t i o n o f N o r m a l - y i e l d and S t a n d T a b l e s f o r E v e n - aged T i m b e r S t a n d s . J o u r . A g r i c , Res., V o l . 5l> No. 6, 547-56k, 1935.- (16) R e i n e k e , L.H., P e r f e c t i n g a S t a n d - d e n s i t y I n d e x f o r E v e n - a g e d F o r e s t s . J o u r . A g r i c . Res., Vol.4 . 6 , No, 7,627-638, 1933. (17) S c h a f e r , E.R., Aspen f o r P u l p and P a p e r . U.S. D e p t . A g r i c , Lake S t a t e s F o r . E x p t . S t a . , A s p e n R e p o r t 13,1947. (18) S c h n u r , G.L., Y i e l d , S t a n d , and Volume T a b l e s f o r E v e n - a g e d U p l a n d Oak F o r e s t s . U.S. D e p t . A g r i c , T e c h . B u i . N c 560, 1937. (19) S p u r r , S.H., F o r e s t I n v e n t o r y . The R o n a l d P r e s s Company, New Y o r k , 1952. 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