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A framework for evaluating the impact of planting strategies on wood supply Erdle, Thomas Alan 1984

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A FRAMEWORK FOR EVALUATING THE IMPACT OF PLANTING STRATEGIES ON WOOD SUPPLY BY THOMAS ALAN ERDLE B . S c . F . , The U n i v e r s i t y o f New B r u n s w i c k , 1979 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENT FOR THE DEGREE OF MASTER OF FORESTRY i n THE FACULTY. OF GRADUATE STUDIES (Department of Forestry) We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA May 1984 © Thomas A. E r d l e , 1984 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of Forestry  The University of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date August 1, 1984 DE-6 (3/81) i ABSTRACT To e f f e c t i v e l y meet wood supply objectives, design of reforestation efforts based on planting requires selec-tion of both the rate and density at which plantations are to be established. An a n a l y t i c a l framework to aid in making these decisions is constructed and employed in a case study of an i n d u s t r i a l forest holding in northwest New Brunswick. The case study reveals how planting t a c t i c s can be evaluated at the forest level in measures relevant to the forest man-agement goals reforestation is meant to serve. To demonstrate t h i s , stand level responses to planting, forecast with a plantation growth simulator, are used as input for a whole forest productivity model. Simu-lations with the forest model are performed over a range of plantation establishment options to generate forest level performance indicators of magnitude and cost of immediate harvest increase, magnitude and cost of future harvest i n -crease, required seedling supply, and to t a l cost of planta-tion establishment. Data generated by several hundred such simulation t r i a l s are condensed and presented in nomogram format. In this form, the results cl e a r l y demonstrate the s e n s i t i v i t y of planting effects on wood supply to forest structure and stand operability constraints and highlight the trade-offs between (1) capturing short term versus long term gains; (2) level of risk and level of harvest; (3) increased har-i i vest and i t s associated cost; and (4) stand operability constraints and increased harvest. This information may greatly influence decision making but is not available when assessment of planting options is r e s t r i c t e d to stand level performance. The an a l y t i c a l framework presented must be coupled with the decision maker's values and objectives to be of most value in t a i l o r i n g plantation t a c t i c s to wood supply goals. i i i TABLE OF CONTENTS Page ABSTRACT i i LIST OF TABLES v LIST OF FIGURES v i ACKNOWLEDGEMENTS i x INTRODUCTION 1 DETAILS OF THE ANALYSIS 5 O b j e c t i v e s 5 Components and I n d i c a t o r s 5 Bounds on P e r s p e c t i v e 7 LITERATURE REVIEW 10 PLANTING STRATEGY AND WOOD SUPPLY 16 The N a t u r e o f t h e R e l a t i o n s h i p Between P l a n t i n g and Wood S u p p l y 16 R e q u i r e m e n t s f o r A n a l y s i n g P l a n t i n g E f f e c t s on Wood S u p p l y 22 THE CASE STUDY 24 The Company 24 The F o r e s t 25 S t a n d D e v e l o p m e n t 28 E x i s t i n g S t a n d s 31 U n t r e a t e d P o s t - H a r v e s t S t a n d s 32 P l a n t e d P o s t - H a r v e s t S t a n d s 32 H a r v e s t R u l e .• 39 O p e r a t i o n a l C o n s t r a i n t s 40 P l a n t a t i o n C o s t s 44 F o r e s t D e v e l o p m e n t Model 45 RESULTS 48 Wood S u p p l y W i t h No P l a n t i n g 48 How Many H e c t a r e s t o P l a n t ? . . 51 What P l a n t a t i o n D e n s i t y t o E s t a b l i s h ? 63 C h a n g i n g O p e r a b i l i t y C o n s t r a i n t s 74 CONCLUSION 83 LITERATURE CITED • 86 i v L I S T OF TABLES Page T a b l e 1 . C o m p a r i s o n o f a c t u a l b a l s a m f i r ( b F ) s t a n d s ( B a s k e r v i 1 l e , u n p u b l i s h e d d a t a ) and s i m u l a t e d b l a c k s p r u c e ( b S ) s t a n d s ( E r d l e 1 9 8 0 ) i n n o r t h w e s t New B r u n s w i c k . C u r v e n u m b e r s r e f e r t o t h o s e c o n t a i n e d i n F i g u r e 8 38 T a b l e 2 M i n i m u m and ( y e a r s ) w h i c h dow f o r e a c h t y p e s p r e s e n t e s t . G r o w t h t h o s e d e f i n e d t e x t maximum s t a n d a g e s bound t h e o p e r a b l e w i n -o f t h e e i g h t g r o w t h on t h e F r a s e r I n c . f o r -t y p e n u m b e r s r e f e r t o on p a g e s 25 and 27 i n 41 T a b l e 3 . O p e r a b i l i t y s t a t i s t i c s f o r e i g h t p l a n t a t i o n d e n s i t i e s u n d e r o p e r a b i l -i t y 115 o n s t r a i n t s o f s e v e n N/m and m /ha. 43 T a b l e 4 T a b l e 5, P l a n t i n g c o m p o n e n t c o s t s ( 1 9 8 2 d o l l a r s ) f o r e i g h t p l a n t a t i o n d e n s i -t i e s . S o u r c e s : R. S p e e r and C. H a r d i n g , N . B . D e p . N a t . R e s . ( p e r s . comm. ) and L o g a n (1 9 8 2 ) , P l a n t i n g c o s t s ( 1 9 8 2 p l a n t a t i o n d e n s i t i e s . $ / h a ) f o r e i g h t 46 46 v LIST. OF FIGURES Page F i g u r e 1A. General r e l a t i o n s h i p between stand d e n s i t y and merchantable volume 12 F i g u r e 1B. General r e l a t i o n s h i p between stand d e n s i t y and average p i e c e - s i z e 12 F i g u r e 2. Stand development c h a r a c t e r i z e d by merchantable volume per h e c t a r e (above) and stems per c u b i c metre (below) 19 F i g u r e 3. D e t e r m i n a t i o n of minimum time to stand o p e r a b i l i t y and the width of the o p e r a b l e window 20 F i g u r e 4. L o c a t i o n of the F r a s e r I n c . f r e e -h o l d f o r e s t used f o r the wood sup-p l y a n a l y s i s 26 F i g u r e 5, F i g u r e 6, F i g u r e 7 F i g u r e 8 Age c l a s s s t r u c t u r e and a s s o c i a t e d y i e l d s f o r the e i g h t growth types on the F r a s e r I nc. f o r e s t . S o l i d l i n e s are c u r r e n t y i e l d s ; dashed l i n e s are p o s t - h a r v e s t y i e l d s . ... 29 Comparison of s i m u l a t e d ( E r d l e 1980) and a c t u a l ( S t i e l l and Be r r y 1973) merchantable volume d e v e l o p -ment f o r white spruce p l a n t a t i o n s at 1.8 m s p a c i n g (SI = Dominant h e i g h t (m) at age 50).„ , Comparison of s i m u l a t e d ( E r d l e 1980) and a c t u a l ( S t i e l l and Berry 1973) diameter d i s t r i b u t i o n s f o r white spruce p l a n t a t i o n s at 1.8 m s p a c i n g when average DBH i s 15 cm. Comparison of s i m u l a t e d ( E r d l e 1980) and a c t u a l diameter d i s t r i b u -t i o n f o r 22 year o l d , 1.9 m x 1.9 m whit e spruce p l a n t a t i o n i n n o r t h -west New Brunswick. < 35 35 37 v i Page F i g u r e 9. Comparison of p i e c e - s i z e d e v e l o p -ment f o r s i m u l a t e d b l a c k spruce ( E r d l e 1980) and a c t u a l balsam f i r s t a n d s ( B a s k e r v i 1 1 e , u n p u b l i s h e d data) of comparable d e n s i t y and volume per h e c t a r e at age 55. (See F i g u r e 10, F i g u r e 11. F i g u r e 12, F i g u r e 13. F i g u r e 14, F i g u r e 15 F i g u r e 16, F i g u r e 17, Table 1 ) . Merchantable volume (above) and p i e c e - s i z e development (below) f o r b l a c k spruce p l a n t a t i o n s at f i v e d e n s i t i e s . Dashed v e r t i c a l l i n e s r e p r e s e n t minimum time r e q u i r e d to j o i n t l y s a t i s f y o p e r a b i l i t y t h r e s h -o l d s o f 115 m-V ha and seven N/m3. Growing s t o c k p r o f i l e f o r the F r a -ser Inc . f o r e s t under no h a r v e s t . 37 42 49 Growing s t o c k p r o f i l e f o r the F r a -s e r I n c . f o r e s t under annual har-v e s t r a t e s of 500 000, 400 000 and 335 000 m3 49 Cost per c u b i c metre of a l l o w a b l e cut e f f e c t versus h e c t a r e s p l a n t e d per year 53 R e l a t i o n s h i p between number of hec-t a r e p l a n t e d (§ 2500 N/ha) per year and maximum s u s t a i n a b l e h a r v e s t 53 M a r g i n a l b e n e f i t of p l a n t i n g , ex-pressed as c u b i c metres of a l l o w -able cut e f f e c t per h e c t a r e p l a n t e d 54 Mechanism behind n o n - l i n e a r i t y and s a t u r a t i o n of the a l l o w a b l e cut e f f e c t 54 R e l a t i o n s h i p between c h a r a c t e r i s -t i c s of average st a n d s h a r v e s t e d and the a l l o w a b l e cut e f f e c t a t -t r i b u t a b l e to v a r i o u s p l a n t i n g r a t e s 57 v i i Page F i g u r e 18. R e l a t i o n s h i p between o p e r a b l e grow-i n g s t o c k , t i m e , and area p l a n t e d per year at 2500 N/ha 61 F i g u r e 19. R e l a t i o n s h i p between p l a n t a t i o n d e n s i t y , p l a n t i n g r a t e and maximum s u s t a i n a b l e h a r v e s t 66 F i g u r e 20. Nomogram of s i x i n d i c a t o r v a r i a b l e s v e r s u s p l a n t i n g r a t e and p l a n t a t i o n d e n s i t y 70 F i g u r e 21. R e l a t i o n s h i p between maximum su s -t a i n a b l e h a r v e s t , p l a n t a t i o n den-s i t y and p i e c e - s i z e c o n s t r a i n t s when minimum merchantable volume c o n s t r a i n t i s 115 mVha 77 F i g u r e 22. R e l a t i o n s h i p of maximum s u s t a i n a b l e h a r v e s t v e r s u s p l a n t a t i o n d e n s i t y and p i e c e - s i z e c o n s t r a i n t s at v a r -i o u s minimum merchantable volume per h e c t a r e t h r e s h o l d s 81 v i i i ACKNOWLEDGEMENTS I am i n d e b t e d to s e v e r a l people and agencies f o r t h e i r a s s i s t a n c e d u r i n g the p r e p a r a t i o n of t h i s t h e s i s . D r s . G. F. Weetman, T. H. H a l l , and D. Haley of the U n i v e r -s i t y o f B r i t i s h Columbia and Dean G. L. B a s k e r v i l l e of the U n i v e r s i t y of New Brunswick p r o v i d e d u s e f u l d i s c u s s i o n along the way and c o n s t r u c t i v e comments on the t h e s i s d r a f t s . F r a s e r I n c . was most c o - o p e r a t i v e i n a l l o w i n g me to use t h e i r f o r e s t h o l d i n g and i n v e n t o r y data f o r the case s t u d y . To E r i k Wang of F r a s e r I n c . , I am p a r t i c u l a r l y g r a t e f u l f o r the t i m e , a d v i c e , and i n t e r e s t he committed to my work. I acknowledge w i t h thanks the f i n a n c i a l support p r o v i d e d me by the U n i v e r s i t y of B r i t i s h Columbia and Mac-M i l l a n - B l o e d e l L i m i t e d d u r i n g my r e s i d e n c e at u n i v e r s i t y . Mary Ann Casey's t y p i n g of the t h e s i s i s g r e a t l y appre-c i a t e d . F i n a l l y , I o f f e r s p e c i a l thanks to Dean G. L. Bas-k e r v i l l e who sparked i n me the i n t e r e s t i n stand and f o r e s t dynamics which made t h i s t h e s i s r e a l l y fun to w r i t e . T. A. E. i x INTRODUCTION In 1980, the Canadian forestry sector reforested nearly 200 000 ha of land by planting. An increase in this s i l v i c u l t u r a l effort to 700 000 ha annually has been pro-posed as part of a Canadian strategy designed to avert future wood supply shortages, maintain or increase the pro-ductivity of the forest base, and enhance the nation's role as a supplier in world forest products markets (Federal For-est Sector Strategy Committee 1981). The situation well i l l u s t r a t e s the cl a s s i c link between forest management and s i l v i c u l t u r e . In an attempt to secure a certain wood supply future, the forestry sector has addressed a forest management problem. In planting trees, i t has, in part, opted for a s i l v i c u l t u r a l solution to that problem. Thus, s i l v i c u l t u r e is the means chosen to s a t i s f y the desired management end of a secure wood supply. It l o g i c a l l y follows that design and evaluation of s i l v i c u l -t u r a l t a c t i c s should, therefore, be based on how well they serve to sa t i s f y wood supply goals. This evaluation concept follows that discussed by Baskeryille (1981) under the term strategic study. He de-scribed strategic studies as being "most useful where they are aimed at finding the best combination of individual stand level s i l v i c u l t u r a l treatments that gives the desired objectives for the whole forest". With respect to a planting e f f o r t , the "best com-1 bination" includes, at least (1) the amount of area to treat; (2) the timing of the treatment; (3) the density at which stands are established; and (4) selection of appro-priate species to plant. Currently, some analytical methods systematically assess amount and timing of treatment in light of the overall wood supply objectives the treatments are intended to satisfy. In New Brunswick, for example, es-tablishment of new Crown Licenses involved designing, on a license by license basis, s i l v i c u l t u r a l programs speci f i -cally tailored to sustain selected long term harvest levels associated with the forest structure peculiar to each license. There is scant evidence to suggest, however, that similar analyses have been performed to address the third issue of plantation density in the context of its s i g n i f i -cance to wood supply. This is particularly troubling be-cause of the large costs involved in planting and since the density question is one of the most fundamental one with which, the s i l v i c u l t u r i s t must grapple. Further, sugges-tions have been made that selection of optimal densities has yet to be satisfactorily resolved (Painter 1980). Nonethe-less, decisions with respect to plantation density, satis-factory or otherwise, are made by the score continually with the annual planting of hundreds of thousands of hectares in Canada. This forces two c r i t i c a l questions. F i r s t , on what basis are current decisions made? Second, can this 2 p r o c e s s be b o l s t e r e d t o h e l p ensure t h a t the m i l l i o n s of d o l l a r s a n n u a l l y a l l o c a t e d e f f i c i e n t l y a c h i e v e the wood s u p p l y b e n e f i t s f o r which they are i n t e n d e d ? P l a n t a t i o n d e n s i t y i s most e a s i l y , and perhaps most commonly, p e r c e i v e d as f a l l i n g e x c l u s i v e l y i n the do-main of s i l v i c u l t u r e . I f so, i t f o l l o w s t h a t e v a l u a t i o n of a l t e r n a t i v e d e n s i t i e s be made on grounds most r e l e v e n t to the s i 1 v i c u l t u r i s t . These grounds are d e s c r i b e d by terms i n c l u d i n g diameter d i s t r i b u t i o n , r o t a t i o n age, mean annual increment and y i e l d per h e c t a r e . I f the s i 1 v i c u l t u r i s t has an economic a d v i s o r , then f i n a n c i a l r o t a t i o n , v a l u e per c u b i c metre or m a r g i n a l b e n e f i t may be added to the e v a l u a -t i o n c r i t e r i a . A l l of these v a r i a b l e s are d i r e c t l y a f f e c t e d by p l a n t a t i o n d e n s i t y and t h e i r importance i n d e c i s i o n making i s o b v i o u s . In f a c t , s o p h i s t i c a t e d a l g o r i t h m s u s i n g dynamic or l i n e a r programming have been designed to enable s e l e c t i o n o f d e n s i t y l e v e l s which o p t i m i z e a s e l e c t e d set of these i n -d i c a t o r s to a s s i s t the s i l v i c u l t u r i s t i n making the best c h o i c e (Hann and B r o d i e 1980). <I f , however, c o n s i d e r a t i o n i s r e s t r i c t e d s o l e l y to the i n d i v i d u a l s t and and to st a n d l e v e l measures of p e r f o r -mance, the s i l v i c u l t u r a l s o l u t i o n i s c a s t a d r i f t of the o r i -g i n a l f o r e s t management problem. That i s , the stand i s con-c e p t u a l l y e x t r a c t e d from the f o r e s t , an o p t i m a l s o l u t i o n f o r sta n d r e g u l a t i o n d e v i s e d , then the st a n d i s r e - i n s e r t e d to the f o r e s t . T his c a r r i e s w i t h i t the i m p l i c i t e x p e c t a t i o n 3 that the stand level optimality w i l l somehow translate into optimality at the forest and wood supply l e v e l s . The contention here is that current practises in New Brunswick assess plantation density in this manner and, to answer the second previously posed question, that the approach can indeed be strengthened. S p e c i f i c a l l y , analysis of alternative densities for plantations can be made more t e l l i n g by viewing stands within the forest context and accounting for how they develop, not as isolated e n t i t i e s , but as constituents of a complex forest, comprised of thou-sands of stands, whose c o l l e c t i v e development define the dynamics of the forest in a fashion which is not simply additive. In this l i g h t , the relevant indicators of per-formance are no longer stand measures, but forest measures such as annual harvest lev e l s , cost per increment of har-vest, continuity and value of wood flow, and potential for i n d u s t r i a l expansion. Such a procedure enables e x p l i c i t and direct translation of the effect of plantation density control on forest development and the associated wood supply. 4 DETAILS OF THE ANALYSIS OBJECTIVES The o v e r a l l o b j e c t i v e of t h i s t h e s i s i s to d e s i g n an a n a l y t i c a l framework which p r o v i d e s i n s i g h t i n t o how v a r -i o u s p l a n t a t i o n d e n s i t i e s i n f l u e n c e wood s u p p l y . More spe-c i f i c o b j e c t i v e s are to app l y t h i s mechanism, i n a case s t u d y , t o a p a r t i c u l a r f o r e s t h o l d i n g i n New Brunswick to p r o v i d e t h i s i n s i g h t and to d i s c u s s the r e s u l t s w i t h r e f e r -ence t o t h e i r i m p l i c a t i o n s to d e c i s i o n making. The s p e c i f i c f o r e s t to be used i s the 300 000 ha f r e e h o l d l i m i t of F r a s e r I n c . , l o c a t e d i n northwest New Brunswick. The f o r e s t i s a major spruce ( P i c e a spp.) and f i r (A b i es balsamea, (L.) M i l l . ) s u p p l y source f o r the Company and i t s s t r u c t u r e i s r e p r e s e n t a t i v e of New Brunswick f o r e s t c o n d i t i o n s i n gen-e r a l . COMPONENTS AND INDICATORS To e f f e c t i v e l y t r e a t the i n t e r a c t i o n of p l a n t a t i o n d e n s i t y and wood s u p p l y , the f o l l o w i n g a n a l y s i s w i l l proceed t h r o u g h t h r e e s t a g e s . S ince management has s e l e c t e d p l a n t -i n g as a s i l v i c u l t u r a l o p t i o n to pursue, i t i s faced w i t h d s e l e c t i n g a d e s i r e a b l e p l a n t a t i o n e s t a b l i s h m e n t r a t e , as w e l l as w i t h c h o o s i n g an a p p r o p r i a t e p l a n t a t i o n d e n s i t y . The f i r s t s t a g e w i l l focus on v a r y i n g the annual p l a n t i n g r a t e , w i t h i n i t i a l p l a n t a t i o n d e n s i t y s e t at 2500 stems per hec-t a r e (N/ha). Immediate h a r v e s t g a i n s , the cost of r e a l i z i n g 5 them, and the potential for future harvest increase w i l l be assessed as forest level measures of planting program per-formance. The second stage w i l l vary the annual planting rate, as well as the plantation density. I n i t i a l density w i l l be systematically considered over the range of 500 to 4000 N/ha. Performance measures examined w i l l include those stated above, plus nursery stock requirements and the cost of future harvest increases. The third part of the analysis w i l l be a sensitiv-it y test, designed to reveal how varying the operability constraints of piece-size and merchantable volume, jointly and separately, influence the wood supply associated with alternative plantation densities. Immediate increases in annual harvest w i l l be examined as the measure of density performance as the operability constraints are systemati-cally altered. Past trends and current developments accentuate the likelihood that operability constraints w i l l change con-siderably.in the future. This is apt to have profound sig-nificance on density selection because the spacing of stems so strongly influences piece-size and merchantable volume per hectare - two fundamental determinants of stand opera-b i l i t y . It also confounds density selection by injecting considerable uncertainty regarding the conditions which w i l l prevail in the future when today's new plantations reach harvestable form. 6 These three components of the analysis constitute the a n a l y t i c a l framework for assessing the impact of planta-tion density on wood supply in terms relevant and useful to management in evaluating i t s s i l v i c u l t u r a l options. Rather than view this as an optimization problem or an economic study of the issue, this framework simulates what happens to the forest, and the quantity and cost of the associated wood supply, when a selected policy is followed with respect to stand level s i l v i c u l t u r a l regimes. In addition, the analy-s i s w i l l reveal the s e n s i t i v i t y of the results to changes in constraints and conditions over which the manager has s i g n i -ficant control. BOUNDS DN PERSPECTIVE To keep the analysis concise and tractable, bounds w i l l be placed on the aspects considered. F i r s t , the time horizon over which forest development w i l l be tracked has been limited to 80 years. This allows s u f f i c i e n t time for lagged effects to surface and eliminates the p o s s i b i l i t y of a short term, exploitative assessment of matters. It is not so long, however, to become cumbersome computationally, nor meaningless operationally. The analysis w i l l include only spruce and balsam f i r since these species are predominant in economic impor-tance, not only on the forest li m i t studied, but for New Brunswick as a whole. Quality of the wood supply w i l l only be dealt with in terms of piece-size. Data for plantation 7 development i n New Brunswick are i n s u f f i c i e n t to a l l o w i n -c l u s i o n o f k n o t i n e s s , branch s i z e , or o t h e r measures of q u a l i t y i n a r e a s o n a b l e manner. Economic c o n s i d e r a t i o n s w i l l be r e s t r i c t e d to the e s t a b l i s h m e n t and t e n d i n g c o s t s of p l a n t a t i o n s . Value of p r o d u c t h a r v e s t e d , and the c o s t of h a r v e s t i n g i t , c r e a t e added u n c e r t a i n t y i n f o r e c a s t i n g . A l t h o u g h t h e i r importance cannot be d e n i e d , a d d r e s s i n g them at t h i s p o i n t would i n -f l a t e the scope of the a n a l y s i s to an unmanageable l e v e l and c l o u d the i s s u e h e r e , which i s to f o r e c a s t what i s happening to the f o r e s t . There i s no o b s t a c l e , however, to appending them i n . a f u t u r e , expanded study based on the mechanism set f o r t h h e r e . In f a c t , a s s e s s i n g the p h y s i c a l nature of the wood s u p p l y i s an a b s o l u t e p r e r e q u i s i t e to the i m p o r t a n t economic c o n s i d e r a t i o n s o f h a r v e s t v a l u e and c o s t , which must be made to complete the d e c i s i o n making p i c t u r e . The wood flo w o b j e c t i v e can t a k e , a v a r i e t y of forms, depending on management p h i l o s o p h y . S u s t a i n e d y i e l d , or some v a r i a n t a l l o w i n g c o n s i d e r a b l e f l u c t u a t i o n might both be r e a s o n a b l e c oncepts to pursue. The r e s t r i c t i o n h e r e , however, w i l l be made to s u s t a i n e d y i e l d . The reasons f o r t h i s are t w o - f o l d . F i r s t , s u s t a i n e d y i e l d i s perhaps the most c o n d u c i v e to p a i n t i n g a c l e a r p i c t u r e of the c o m p l e x i -t i e s of f o r e s t dynamics and the r o l e p l a n t a t i o n d e n s i t y p l a y s as they u n f o l d . S e c o n d l y , s u s t a i n e d y i e l d i s the New Brunswick f o r e s t management p o l i c y on Crown Lands. T h i s i s not to say t h a t s u s t a i n e d y i e l d i s s a c r o -8 sanct, nor that this analysis method has limited u t i l i t y under alternate management philosophies. Other harvest pro-f i l e s could quite easily be dealt with, needing only speci-fication of the desired harvest profile. 9 LITERATURE REVIEW Numerous efforts have addressed the matter of desired stand density l e v e l s . These may be conveniently sorted into three general categories: (1) empirical studies; (2) qua l i t a t i v e discussions; and (3) quantitative analyses. Empirical investigations have been conducted in which stands of various inter-tree spacings have been estab-lished and their development monitored over time. These t r i a l s have been carried out for many species in both plan-tation conditions and those of spaced natural stands. The issue of density control and i t s impact on wood supply is the same for the two situations. Although the thrust of this thesis is towards plantation establishment, i t is a small matter to extend the approach to include spacing natural stands. The objective of density control is to get the desired number of stems in the ground, in the desired s p a t i a l arrangement. Whether this is effected by adding trees to the s i t e via planting or by removing excess trees through spacing is of l i t t l e consequence. Of the empirical t r i a l s in Canada, the works of Baskerville (1965) and S t i e l l and Berry (1973) are perhaps the best known. The essence of their findings is that (1) within l i m i t s , merchantable volume per hectare is d i r e c t l y related to stand density; and (2) the relationship between 10 average stem s i z e and d e n s i t y i s an i n v e r s e one. These con-c l u s i o n s conform to c o n v e n t i o n a l f o r e s t r y wisdom and are c o r r o b o r a t e d by s t u d i e s i n spaced balsam f i r (Ker 1981), l o d g e p o l e p i n e ( P i n u s c o n t o r t a Dougl.) (Johnstone 1981) and r e d pine ( P i n u s r e s i n o s a A i t . ) (Lundgren 1981). The r e l a t i o n s h i p s of p i e c e - s i z e and volume per h e c t a r e to stand d e n s i t y are i l l u s t r a t e d i n F i g u r e s 1(A) and 1 ( B ) , r e s p e c t i v e l y . Up to the p o i n t of extreme c r o w d i n g , where s t a g n a t i o n s e t s i n , i n c r e a s i n g stand d e n s i t y y i e l d s i n c r e a s i n g volume per h e c t a r e . This r e s u l t s because h i g h e r d e n s i t i e s , or c l o s e r t r e e s p a c i n g s , r e t a i n a g r e a t e r p r o p o r -t i o n of the p o t e n t i a l growing space i n support of t r e e growth f o r a l o n g e r p e r i o d of time than do lower d e n s i t i e s . Reducing d e n s i t y a f f o r d s i n d i v i d u a l stems more growing space and r e s o u r c e s c o n d u c i v e to more r a p i d p i e c e - s i z e d e v e l o p -ment. These r e l a t i o n s h i p s are g e n e r a l l y accepted as v a l -i d q u a l i t a t i v e l y a l t h o u g h q u a n t i f i c a t i o n has proven d i f f i -c u l t and v a r i e s c o n s i d e r a b l y w i t h s p e c i e s and s i t e . None-t h e l e s s , q u a l i t a t i v e l y , F i g u r e 1 r e v e a l s an obvious and im-p o r t a n t c o n f l i c t between s i m u l t a n e o u s a t t a i n m e n t of h i g h volumes per h e c t a r e and l a r g e p i e c e - s i z e s . Both are d e s i r e -a b l e o b j e c t i v e s b u t , c l e a r l y , an e f f o r t to g a i n on one f r o n t i s i n e s c a p a b l y accompanied by a s a c r i f i c e on the o t h e r . T h i s poses a b a s i c t r a d e - o f f which has p r o b a b l y t r i g g e r e d much of the h i g h d e n s i t y v e r s u s low d e n s i t y debate common to the second c a t e g o r y of d e n s i t y s e l e c t i o n study - the q u a l i -i 11 Merchantable Volume (m3/ha) Increasing Stand Density Figure 1 A . General relationship between stand density and merchantable volume. 12 t a t i v e discussions. In 1943 a stated Canadian forest policy advocated a high volume per hectare and, therefore, a high density stand establishment stance (Wiksten 1968). Suggested den-s i t y t a c t i c s were debated through the 1950's and 1960's. An interesting exchange was carried in the "For Sake of Argue-ment" section of the Forestry Chronicle (1965-1968) and was recently resurrected by Smith (1983). This f l u r r y co-in-cided with the realized imminence of operational scale planting and the heightened urgency for the need to identif y the appropriate t a c t i c s to practice. Proponents of lower densities argued on the grounds of e f f i c i e n c i e s in harvesting (Baskerville 1966, Wiksten 1966 and 1968), reduced stand establishment cost (Stafford 1931, Smith 1958, Cayford 1966), increased speci-f i c gravity of wood (Kennedy 1966), and higher value return per hectare (Smith 1958). Advocates of higher densities cited the advantages of shorter rotations (Vincent 1966), reduced knotiness and branch size (Wilde 1965, Farrar 1966) and higher wood quality and s p e c i f i c gravity (Farrar 1966). In the higher density position, an ethical flavour emerges around the d e s i r e a b i l i t y of maintaining each hectare of forest in i t s most productive state. There are vali d points made from both positions and the r e l a t i v e strength of any particular argument is d i r -ectly determined by the quality, quantity, and value of the material sought by any s p e c i f i c agency. 1 3 The t h i r d area o f r e s e a r c h i n d e n s i t y s e l e c t i o n sheds a more q u a n t i t a t i v e l i g h t on the i s s u e . Osborne (1967) used pr e s e n t net worth c a l c u l a t i o n s to measure the c o s t per u n i t of wood produced under v a r i o u s d e n s i t i e s to su p p o r t a wide s p a c i n g p h i l o s o p h y . Wiksten (1968) proposed l i n e a r programming methods as advantageous i n stand l e v e l assessment. Hann et a l . ( 1 9 8 3 ) , B r o d i e and Kao (1979), and many o t h e r s have used dynamic programming a l g o r i t h m s which enable o p t i m i z a t i o n of d e n s i t y at the stand l e v e l . Buongiorno and Teeguarden (1978) l i n k e d s i m u l a t i o n and l i n e a r programming models to help r a t i o n a l i z e a l a r g e s c a l e r e f o r e s t a t i o n program, which i n c l u d e d s p e c i f i c c o n s i d e r a t i o n of i n i t i a l d e n s i t y . T h e i r work i s more comprehensive than o t h e r e f f o r t s i n t h a t s i m u l t a n e o u s a c c o u n t i n g i s made of many areas p o t e n t i a l l y a v a i l a b l e f o r r e f o r e s t a t i o n . How-e v e r , i t does f a i l to i n c o r p o r a t e the remainder of the f o r e s t i n e x i s t i n g s t a n d s at other than c u t - o v e r stages of development. D e s p i t e t h i s r i c h body of i n v e s t i g a t i o n , i n t e r p r e -t a t i o n and a n a l y t i c a l t o o l s , concerns s t i l l a r i s e t h a t den-s i t y c o n t r o l remains i l l - r e s o l v e d . P a i n t e r (1980), f o r ex-ample, s u g g e s t s t h a t c u r r e n t p r a c t i s e s are founded more on t r a d i t i o n a l grounds than r i g o r o u s a n a l y s i s w i t h l i t t l e e v i -dence t h a t they are c r i t i c a l l y r e v i e w e d . The common denominator to the bulk of e f f o r t s u ndertaken and arguments posed i s the f i x a t i o n on e v a l u a t -i n g s t a n d d e n s i t y on st a n d l e v e l c r i t e r i a of performance. 14 At best, this approach dangerously over-simplifies the interplay of stand composition, stand mangement, and forest structure in governing forest dynamics, and consequently, in governing wood supply. At worst, i t isolates s i l v i c u l t u r e from the forest management goals i t is meant to serve and is the l i t e r a l embodiment of "not seeing the forest for the trees". In fact, Lundgren (1973) had i d e n t i f i e d this as a fundamental weakness of much of past forest analysis: "That weakness l i e s in overemphasizing analyses of individual stand treatments (such as pruning, thinning and planting) as though they were isolated events with no outside e f f e c t s . The impact of a program of individual stand treatments on the overall economic position of the entire forest management operation has been underemphasized or ignored." It is hardly the case that the .need to evaluate s i l v i c u l t u r a l t a c t i c s at the forest level has not been rea-l i z e d . Several authors, Baskerville (1981), Wiksten (1966), Cayford (1966) and Smith (1966) have a l l c l e a r l y recognized the need and endorsed the concept. The issue is that l i t t l e has been done in this regard in a thorough analytical approach to plantation density. 15 PLANTING STRATEGY AND WOOD SUPPLY The Nature of the Relationship Between Planting and Wood  Supply Before s p e c i f i c a l l y examining the effects of planta-tion density on wood supply, i t is worth reviewing the rationale which supports any planting e f f o r t . From this re-view, the components required for the analysis presented here can be i d e n t i f i e d and the pieces assembled. Regulating the harvest from a forest is achieved through balancing the liquidation of mature stands with the development of immature ones. Under a sustained yield ob-je c t i v e , an upper threshold is placed on the liquidation rate by the entry of young stands into economically harvest-able condition. Harvesting beyond this rate depletes the mature reserve prior to the a v a i l a b i l i t y of replacement stands. Such a harvest level would create a hiatus in wood flow, leaving the sustained yield objective u n f u l f i l l e d . Any actions which hasten, or retard, the rate at which young stands become available for harvest have obvious implications to the rate at which mature ones can be har-vested. Relatively rapid development of young stands serves to increase the available harvest, r e l a t i v e l y slow develop-ment acts to decrease i t . Rate of development can be visu-alized as having two controls, a bi o l o g i c a l one and a tech-ni c a l one. 1 6 Through p l a n t i n g , c u t - o v e r s i t e s are i m m e d i a t e l y r e - s t o c k e d w i t h d e s i r e a b l e s p e c i e s , s p a t i a l l y arranged by d e s i g n t o u t i l i z e as much of the s i t e as p o s s i b l e and to m i n i m i z e i n t r a - s p e c i e s c o m p e t i t i o n . Rapid growth i s promo-t e d i n t h i s way, thus p l a n t a t i o n development exceeds t h a t f o r any u n t r e a t e d stands which do not m a n i f e s t immediate r e -g e n e r a t i o n and good stem d i s t r i b u t i o n a c r o s s the s i t e . Under the r e a s o n a b l e assumption t h a t most u n t r e a t e d stands do not possess these q u a l i t i e s , the r a t i o n a l e f o r p l a n t i n g s u r f a c e s . The more r a p i d development of p l a n t e d stands t r a n s l a t e s i n t o a g r e a t e r l i q u i d a t i o n r a t e of mature s t a n d s , and, t h e r e f o r e i n t o i n c r e a s e d wood s u p p l y . As shown i n F i g -ure 1 and d i s c u s s e d above, c o n s i d e r a b l e c o n t r o l can be e x e r -c i s e d i n p l a n t a t i o n development by r e g u l a t i n g d e n s i t y . T r a n s i t i v e r e a s o n i n g r e v e a l s , t h e n , t h a t p l a n t a t i o n d e n s i t y c o n t r o l w i l l e x e r t c o n s i d e r a b l e i n f l u e n c e on wood s u p p l y . T h i s i s the b i o l o g i c a l aspect of p l a n t a t i o n development. The t e c h n i c a l aspect of p l a n t a t i o n development r e -v o l v e s around the manager's d e f i n i t i o n of the minimum char-a c t e r i s t i c s which a stand must possess to be c o n s i d e r e d eco-n o m i c a l l y a v a i l a b l e f o r h a r v e s t . Geographic a c c e s s a b i l i t y i s not the i s s u e i n New Brunswick, r a t h e r the s t r u c t u r a l t r a i t s o f stands are the i m p o r t a n t c o n s i d e r a t i o n . Two key q u a l i t i e s which determine economic a v a i l a b i l i t y are the q u a n t i t y of merchantable wood present i n the s t a n d , and the pa c k a g i n g of t h a t wood, t h a t i s the p i e c e - s i z e or volume per t r e e ( B a s k e r v i l l e 1978). These two c h a r a c t e r i s t i c s may be 17 defined in terms of merchantable volume per hectare (nrr/ha) and stems per cubic metre (N/m3), respectively. Figure 2 schematically depicts how these stand variables characteris-t i c a l l y change with age for the species in this study area. Economic a v a i l a b i l i t y , more aptly termed operability, is de-fined as the s a t i s f a c t i o n of minimum merchantable volume per hectare and maximum stems per cubic metre levels imposed by the u t i l i z a t i o n practises of wood consumers (Baskerville 1 978). The stand age at which both constraints are f i r s t met i s defined here as the minimum time to o p e r a b i l i t y . Figure 3 represents this analysis? determination of minimum time to o p e r a b i l i t y . If, for example, the mini-mum volume per hectare required to make a harvest economi-c a l l y worthwhile i s 100 m3, the stand is f i r s t operable at age 40 and becomes inoperable at age 90. If i t is addition-a l l y required that stems be large enough that there are no more than ten N/m3, the time to operability is increased to age 50. By choosing to adjust these constraints, the oper-a b i l i t y window can be opened and closed and the minimum time to operability be raised or lowered. This adjustment is a technical regulator which appears to operate on stand devel-opment, in that tightening operability constraints delays stand a v a i l a b i l i t y and relaxing them accelerates i t . Further, reference to Figure 1 reveals that plan-tation density plays a key role in regulating the patterns displayed in Figure 2 and, therefore, the determiniation of minimum time to operability and, e f f e c t i v e l y , the rate of 18 250 200 M e r c h a n t a b l e Volume (m 3/ha) 150 100 50 40 60 80 100 Stand Age ( y e a r s ) 14 12 Average P i e c e - s i z e (N/m 3) 10 8 6 40 60 80 100 Stand Age ( y e a r s ) F i g u r e 2. Stand development c h a r a c t e r i z e d by merchantable volume per h e c t a r e (above) and stems per c u b i c metre ( b e l o w ) . 1 9 250 Average Piece-size (N/m3) 14 12 10 40 60 Stand Age 80 (years) 100 Figure 3. Determination of minimum time to stand operability and the width of the operable window. 20 development of stands. Thus, i t is evident, that there is both a b i o l o g i c a l and technical basis for examining planta-tion density as a control mechanism to influence wood supply. The manner by which this mechanism affects wood supply i s one i l l u s t r a t i o n of the allowable cut effect (ACE). ACE has been defined by Schweitzer et_ £l_. ( 1 972) as "the immediate increase in today's allowable cut which i s attributable to expected future increases in yie l d s " . The concept has been the center of considerable controversy, the bulk of which relates to use of ACE as an economic analysis tool (Teeguarden 1 973, Schweitzer et_ a l . 1973, Lundgren 1 973 , Bell et_ al_. 1 975). Despite this controversy, ACE w i l l be used in this analysis because i t s role is re s t r i c t e d to the physical nature of wood supply. Further, ACE is an integral component of forest management strategy in New Brunswick (Baskerville 1982). Its use seems quite legitimate in the New Brunswick case in l i g h t of the s i g n i f i c a n t impending volume decline associated with mature stands in the Province. ACE can be employed to of this potential mortality and re-direct i t use at the m i l l . This benefit has not been c r i t i c s of ACE. There are, of course, limits to the the achievable increase in wood supply attributable to planting via ACE. These are imposed by the a v a i l a b i l i t y of mature and near, mature stands from which the increased capture much for economic addressed by magnitude of 21 harvest i s to be taken. This a v a i l a b i l i t y , a function of the forest age class structure and i t s change over time, is a prime regulator of the way in which a planting strategy influences wood supply. This i s the crux of the argument here, that examination of s i l v i c u l t u r e t a c t i c s is most meaningfully performed when stands to be treated are retained within the context of the entire forest structure to which they contribute. Stands grow, stands deteriorate and stands are harvested. Each process acts to change the forest structure over time. Because the forest structure constrains the way in which plantation growth affects l i q u i d a t i o n rate, i t becomes essential to consider not only the current forest structure, but i t s dynamic nature as well. Requirements For Analysing Planting Effects on Wood Supply In light of the previous discussion, six required ingredients can be i d e n t i f i e d for analysing the influence of plantation density on wood supply. F i r s t , a particular for-est must be selected for which planting and planting density are to be examined. Second, data for that forest must be available and amenable to description of the existing age class structure and to forecasting i t s future development. Age structure is a t r a i t unique to a s p e c i f i c forest; conse-quently, so are the responses of the forest. One size does not f i t a l l . Third, there must be s u f f i c i e n t information 22 available to describe how a l l of the constituent stands are l i k e l y to develop. This applies not only for a l l existing stands, but also for those (both unplanted and planted at various densities) which result after harvesting. Fourth, an accounting system is needed which can (1) keep track.of constituent stand development; (2) compile and compute the c o l l e c t i v e effects into measures of forest level develop-ment; (3) accommodate the imposition of various harvest lev e l s and harvest p r i o r i t y rules; and (4) allow the imple-mentation of a series of alternative s i l v i c u l t u r a l regimes in terms of area and density of established plantations. F i f t h , a strategy by which stands w i l l be queued for harvest must be defined. Lastly, d e f i n i t i o n s of pre-v a i l i n g o p e r a b i l i t y constraints and seedling a v a i l a b i l i t y are required . 23 THE CASE STUDY THE COMPANY The previously stated ingredients have been assem-bled and knit together to perform wood supply analyses for the private forest holding of Fraser Inc., based in Edmund-ston, New Brunswick. Fraser Inc. was selected as desirable for the study because of i t s progressive attitude towards managing with the aid of such analyses. Their forest holding was deemed suitable because i t is managed as a sustained supply unit, is part of an intensive s i l v i c u l t u r a l program, and is described by a more comprehensive data base than perhaps any other holding in New Brunswick. The company operates two sawmills and two pulp-mills whose tota l annual consumption rate averages 2.85 mi l l i o n cubic metres. Spruce and balsam f i r are the primary species u t i l i z e d , and together comprise over 90 % of the t o t a l wood volume consumed. Free market roundwood and chip purchases, the Res-tigouche-Tobique Crown Land License, and the Company's p r i -vate forest holding are major contributors to the to t a l wood supply. The l a t t e r source provides 15 - 20% of the t o t a l . The 1980 re-allocation of Crown Land in New Brun-swick revealed that maximum consumptive demand of the Fraser Inc. m i l l s outstripped the sustainable wood supply by 24 approximately six percent. The Company, therefore, has a very real interest in any measures which could be employed to increase their maximum sustainable harvest. THE FOREST The Fraser Inc. freehold limit contains approxi-mately 300 000 ha of productive forest land. The holding f a l l s in Madawaska, Restigouche, V i c t o r i a , and Carleton Counties in northwest New Brunswick (Figure 4). Its forest i s classed in the Maritime Uplands and Restigouche-Bras d'or Ecoregion Zones (Loucks 1962). Spruce and f i r stand types predominate, followed by spruce-fir-hardwood, hardwood-spruce-fir , and hardwood types, in order of decreasing abundance. In the following analysis, and subsequent discussions, the hardwood stand types (softwood component is less than 25 percent of the stand) w i l l be eliminated from consideration. Their minimal spruce-fir volume e f f e c t i v e l y excludes them as contributors to the spruce-fir supply base, which is the major concern here. To describe the forest structure, and to 0 forecast i t s development over time, eight growth types were i d e n t i -f i e d . On the basis of species composition and s i t e produc-t i v i t y (Hall 1981), each stand on the l i m i t was assigned to one of these eight types: 1. High s i t e : well stocked f i r overtopped by shrubs and intolerant hardwoods. 25 Figure 4. Location of the Fraser Inc.freehoId forest used for the wood supply analysis. 2 6 2. High s i t e : f i r predominates with some spruce. 3. High s i t e : spruce predominates with some f i r . 4. Low s i t e : spruce predominates with some f i r . 5. High s i t e : poorly stocked f i r overtopped by shrubs and intolerant hardwoods. 6. High s i t e : f i r and some spruce in equal mix with hardwoods. 7. Low s i t e : poorly stocked f i r overtopped by shrubs and intolerant hardwoods. 8. Low s i t e : f i r and some spruce in equal mix with hardwoods. Yield curves associated with the types are presented in Fig-ure 5 . This aggregation of inventory data greatly reduces the computational burden and compilation complexity associ-ated with tracking thousands of stands i n d i v i d u a l l y . At the same time, i t increases comprehension of forest dynamics and retains and accounts for the unique c h a r a c t e r i s t i c s of stand development which are manifest in terms of (1) rate and magnitude of merchantable volume accumulation; (2) persis-tence of volume in the stand; (3) timing and rate of volume decline due to natural forces which contribute to stand dec-adence; and (4) stand formation and growth response follow-ing harvesting. Stands assigned to each growth type were further sorted by age class (on the basis of their developmental stage) and distributed across an age axis to r e f l e c t where 27 they currently reside with respect to their expected future development. This two way sorting provides a succinct, yet powerfully descriptive, picture of the structure of the Fra-ser Inc. forest holding (Figure 5). Data used to construct Figure 5 were supplied by Erik Wang of Fraser Inc. and stem from considerable sampling and analysis of their l i m i t . As such, they constitute the most reasonable obtainable de-s c r i p t i o n of that forest's structure. Figure 5 reveals the present forest to have an ir r e g u l a r structure, with a preponderance of mature and over-mature stands, a moderate presence of very young regen-erating stands, and a paucity of stands between the two ex-tremes. Clearcut harvesting during the past t h i r t y years has given r i s e to the substantial presence of stands at early stages of development. The spruce budworm (Choriston- eura fumif erana (Clem..)) has played a s i g n i f i c a n t role in the development of spruce-fir forests in northern New Brun-swick. Its impact is evidenced by the broken forest struc-ture containing a disproportionally large component in the 60 to 80 year age classes, which originated from the 1913 -1919 budworm outbreak. The reader is referred to C l i f f o r d (1981) for a more comprehensive explanation of the c o l l e c -t i v e forces which contributed to formation of the forest structure shown in Figure 5. STAND DEVELOPMENT To forecast the development of the forest over 28 100 Growth Type 3 Area (km 2) 50 rflr-h Ilk Merch Vol (m 3/ha) 200 100 100 50 Growth Type 4 _ JD. 20 40 60 80 100 120 l 4 o Stand Age (years) Merch Vol (m 3/ha) 200 100 20 40 60 80 100 120 140 Stand Age ( y e a r s ) F i g u r e 5. Age c l a s s s t r u c t u r e and a s s o c i a t e d y i e l d s f o r the e i g h t growth types on th F r a s e r Inc. f o r e s t . S o l i d l i n e s are c u r r e n t y i e l d s ; dashed l i n e s are post h a r v e s t y i e l d s . 100 Area (km 2) 50 Growth Type 5 Arei (km' 1 00 50 Growth Type 6 , fTrrnx JTCEL U O L O Arej (km' 100 50 Growth Type 7 100 Area (km 2) 50 IQjllLlU-X-C Growth Type 8 LlXl 20 40 60 St and 80 Age 100 120 (ye a r s ) 140 F i g u r e 5. Continued. 200 Merch Vol (m 3/ha) 100 200 Merch Vol (m 3/ha) 100 200 Merch Vol (m 3/ha) 100 200 Merch 20 40 60 80 100 120 140 Stand Age ( y e a r s ) time and to evaluate the imposition of various harvest levels and s i l v i c u l t u r a l treatments, i t i s f i r s t necessary to describe the development of the forest's constituent growth types. This must be done for a l l currently existing types, those which w i l l regenerate, untended, following future harvesting, and those .which w i l l be created with s i l -v i c u l t u r a l measures (Hall 1981). The development of growth types is most conven-i e n t l y expressed in the form of merchantable volume yield curves, which depict merchantable volume per hectare on the Y-axis and time (or stand age) on the X-axis. EXISTING STANDS From stand sampling data and harvest scale re-ports, yield curves of spruce-fir volume for existing stands have been constructed (Wang 1983, l e t t e r to author). In Figure 5, these are shown, together with the corresponding age class structures, for the eight growth types previously described. Forest structure and stand y i e l d , arranged in this manner, characterize the forest as a series of stands at various stages of development along their respective yield patterns. Age is used here to provide a scale on the hori-zontal axis, but the important point is that c r i t i c a l points on the y i e l d curve (and area d i s t r i b u t i o n ) are separated by an appropriate number of years. It is not the absolute age of a stand which is important, but i t s position r e l a t i v e to 31 the yield curve. Once this position is established, age can be used to link the current structure with yield to provide the future pattern of forest development. Age should not be interpreted in the s t r i c t chronological sense ( C l i f f o r d 1981). UNTREATED POST-HARVEST STANDS Predicted yields from untreated future cut-overs are represented by broken lines in Figure 5 . These curves were estimated on the basis of experience and professional judgement through consultation with Fraser Inc. personnel (Wang, pers. comm.). In being shifted to the right on the age axis, they r e f l e c t delayed regeneration and retarded i n i t i a l growth caused by competition from hardwood and shrub species, however, equivalent peak volumes indicate a return of spruce and f i r stocking to the pre-cut l e v e l . These con-ditions are common to many of Fraser Inc. recently cut-over s i t e s and can reasonably be expected to prevail on future cut-overs as well. PLANTED POST-HARVEST STANDS Development of planted stands is p a r t i c u l a r l y d i f -f i c u l t to handle because of the dearth of empirical evidence regarding plantation growth in northwest New Brunswick. The oldest plantations of any consequence in the area are less than twenty years old. Further, t r i a l s of various planting densities have not been conducted. To f i l l this information 32 gap, yield curves were constructed from forecasts of planta-tion growth made using a plantation development simulation model designed and constructed by the author (Erdle 1980). The model was developed in 1980 s p e c i f i c a l l y for black and white spruce plantations in northwest New Brun-swick. It's design e x p l i c i t l y accounts for the effects of stand structure and intra-species competition on tree growth and, consequently, i t can be used to evaluate a range of i n i t i a l densities and thinning interventions. Major assumptions b u i l t into the model structure are that (1) in the absence of any competition, tree height and diameter growth are bounded by inherent upper li m i t s which are functions of species and site type; (2) realized growth, a reduction from these thresholds, is regulated by stand density and the competitive status of individuals of a particular size and position within the stand; (3) planted stems are uniformly spaced across the s i t e ; and (4) compe-t i t i o n control measures w i l l be undertaken to minimize the influence of undesireable vegetation, leaving intra-species competition as the sole source of tree growth interference. The model views the stand in terms of a diameter and height d i s t r i b u t i o n , uses this d i s t r i b u t i o n to calculate density and competitive status factors for each size class and applies the factors to potential dimension increment in calculation of actual increments. Stems in each size class are then advanced in accordance with their computed realized growth values. The growth estimation process is i t e r a t i v e 33 (one year time steps), each year taking into account the changing stand structure in the computation of density and competitive status growth regulation factors. In this way, the model is s u f f i c i e n t l y dynamic to grow stands in a re a l -i s t i c manner and to allow incorporation of planting density a l t e r n a t i v e s . Further, the diameter d i s t r i b u t i o n approach provides information on not only t o t a l merchantable y i e l d , but on the piece-size composition of that yield as well, thus the model s a t i s f i e s the data needs for operability de-termination, as previously discussed. L i t t l e plantation data is available in New Brun-swick against which model forecasts can be compared. How-ever, three meaningful checks have been made as a way of p a r t i a l l y assessing the model's performance. To determine i f merchantable volume trends generated by the model are r e a l i s t i c , comparisons were made for white spruce between simulation results and density t r i a l plantings at the Cana-dian Forestry Service Research Laboratory at Petawawa, Ontario ( S t i e l l and Berry 1973). The simulated yield curves (for 1.8 m square spacing) nicely sheath those for actual stands at the same spacing (Figure 6). Also, the quantity of volume production ranks consistently and l o g i c a l l y with the s i t e index associated with each curve. Forecasts of piece-size development were evaluated in three fashions. F i r s t , diameter dist r i b u t i o n s for white spruce, planted at 1.8 x 1.8 m spacing, were compared be-tween the Petawawa plantations and simulated r e s u l t s . 34 Petawawa Plantations 15 20 25 30 35 40 45 50 Stand Age (years) Figure 6. Comparison of simulated (Erdle 1980) and actual ( S t i e l l and Berry 1973) merchantable volume development for white spruce plantations at 1.8 m spacing. (SI = Dominant height (m) at age 50) . 10 Stem Dis t r i b u t i o n (?o) Petawawa Simulated Plantations r i i 11 13 15 17 DBH 19 21 ob < c m) 23 25 27 Figure 7. Comparison of simulated (Erdle 1980) and actual ( S t i e l l and Berry 1973) diameter distributions for white spruce plantations at 1.8 m spacing when average DBH i s 15 cm. 35 Figure 7 shows good correspondence between the two. Second, a 22 year old black spruce plantation, located in northwest New Brunswick, was sampled to construct i t s diameter d i s t r i -bution. I n i t i a l i z a t i o n data, r e f l e c t i n g that plantation's density and s i t e quality, were assembled and input to the model. A forecast of stand development to age 22 was made and the resulting diameter d i s t r i b u t i o n plotted against that found for the actual plantation (Figure 8). The results compare favourably. Third, a check of change in average piece-size was made with permanent sample plot data for balsam f i r near the Fraser Inc. l i m i t . Stems per merchantable cubic metre was derived from a 20 year data set for four f i r stands (Basker-v i l l e , unpublished data). The same variable was extracted from growth simulations of stands which paralleled the mer-chantable volume per hectare and stem counts for the f i r stands at age 35 (Table 1). Plots of stems per merchantable cubic metre versus stand age are shown for the actual and simulated stands in Figure 9. The more negative slope at years 35 to 45 in the empirical data may be largely attributable to the very high stem counts f i r stands contained in their early stages of development (Baskerville, pers. comm.) as opposed to almost constant density plantations. If t h i s , in fact, explains the disparity over the f i r s t half of the plotted range, the results suggest reasonable model forecasts of the piece-size s t a t i s t i c s . 36 Actual Plantation Simulated Plantation 10 Stem 8 Dis t r i b u t i o n ( ? o ) 6 4 2 3 5 7 9 11 13 15 17 19 21 23 DBH Q b (cm) Figure 8. Comparison of simulated (Erdle 1980) and actual diameter d i s t r i b u t i o n for 22 year old 1.9 x 1.9 m white spruce plantation in northwest New Brunswick. 3 \ Average Piece-si ze (N/m3) 30 35 40 45 50 55 Stand Age (years) Figure 9. Comparison of piece-size development for simu-lated black spruce (Erdle 1980) and actual bal-sam f i r stands (Baskervi11e, unpublished data) of comparable density and volume per ha at age 55. (See Table 1.) I I r 1 F "1 . _ J "~1 37 Table 1. Comparison of a c t u a l balsam f i r (bF) st a n d s (Bas-k e r v i l l e , u n p u b l i s h e d data) and s i m u l a t e d b l a c k (bS) s t a n d s ( E r d l e 1980) i n i northwest New Brun-s w i c k . Curve numbers r e f e r to those c o n t a i n e d i n F i g u r e 8. Curve Merch m^/ha N/ha Number at Age 50 y r s at Age 35 y r s S p e c i e s Data Type 1 268 3235 bS S i m u l a t e d 2 261 2598 bS S i m u l a t e d 3 324 2965 bF E m p i r i c a l 4 339 2965 bS S i m u l a t e d 5 345 3163 bF E m p i r i c a l 6 329 2416 bS S i m u l a t e d 7 338 2866 bF E m p i r i c a l 8 334 2570 bF E m p i r i c a l 38 In t o t a l , outcomes of. the three checks give very l i t t l e cause to suspect unacceptable model performance. These assessments, however, do not form the rigorous bench-mark tests that normally pre-date use of model forecasts. Nonetheless, the patterns produced by the model are qualita-t i v e l y consistent with i n t u i t i v e reasoning, and are quanti-t a t i v e l y in accord with what scant evidence is available and the considered opinions of local foresters. It is therefore used as the basis for generating plantation development in this analysis. It would obviously be preferable to have more substantive plantation growth data available. If i t be-comes available over time, the planting density versus wood supply evaluation technique presented in this thesis does not change in principle or design, the additional informa-tion merely serves to reduce the uncertainty which bounds the r e s u l t s . HARVEST. RULE The harvest rule defines the sequence in which the harvest w i l l progress through the operable stands. In this analysis a strategy which harvests the physiologically old-est stands f i r s t w i l l be employed. Stands are sorted in a harvest queue by decreasing future volume loss. In this way, those stands which, i f l e f t unharvested, would suffer the greatest mortality are harvested f i r s t . This oldest f i r s t rule minimizes mortality and maximizes growth of the 39 forest as a whole and promotes a over time. high sustainable harvest OPERATIONAL CONSTRAINTS For the following analysis two types of con-s t r a i n t s . must be recognized and quantified. The f i r s t are constraints which define the l i m i t s of stand oper a b i l i t y . Establishment of these l i m i t s is performed in consideration of minimum acceptable piece-size and minimum acceptable mer-chantable volume per hectare. Fraser Inc. personnel have estimated that the current l i m i t s of operability for the eight growth types are s a t i s i f i e d between the stand ages l i s t e d in Table 2 (Wang, pers. comm.). The operable windows these ages define for each growth type are defined by the arrows in the yield curves in Figure 5. A maximum of seven N/m3 and a minimum merchantable volume of 115 m3/ha were assumed to be minimally acceptable for plantation operability given existing u t i l i z a t i o n standards (Wang, pers. comm.). To define operable ages for plantations the plantation growth model was run for establishment densities of 500 to 4000 N/ha (at increments of 500). Figures 10A and 10B display the resulting piece-size and merchantable volume per hectare s t a t i s t i c s . Application of the stated operability requirements sets the ope r a b i l i t y l i m i t s for each density as shown by the dashed v e r t i c a l lines . 40 Table 2. Minimum and maximum stand ages (years) which bound the operable window for each of the eight growth types present on the Fraser Inc. forest. Growth type numbers refer to those defined on pages 25 and 27 in text. Minimum Maximum Stand Age Stand Age Growth Type (years) ( years) 1 65 120 2 45 100 3 50 135 4 55 115 5 65 115 6 50 95 7 70 115 8 50 90 The time and merchantable volume per hectare when ope r a b i l i t y i s f i r s t met are presented in Table 3. Of i n -terest in the tabulation is that low density plantations generally become operable sooner than high density ones, but this early operability is accompanied by substantially re-duced volumes. Selecting a density t a c t i c to employ is a matter of trading these two variables off since early opera-b i l i t y and high yield cannot be simultaneously achieved. The second type of constraint relates s p e c i f i c a l l y to the planting program. Both planting stock a v a i l a b i l i t y and planting s i t e a v a i l a b i l i t y place bounds on the alterna-tives considered. The Fraser Inc. nursery has a current 41. 280 240 25 30 35 40 -45 50 Plantation Age (years) Figure 10. Merchantable volume (above) and piece-size de-velopment (below) for black spruce plantations at five densities. Dashed v e r t i c l e lines represent minimum time required to j o i n t l y sat-i s f y o p e r a b i l i t y thresholds of 115 m^/ha and seven N/m\ 42 Table 3. Operability s t a t i s t i c s for eight plantation densities under operability constraints of seven N/ha and 115 m3/ha. Plantation Density (N/ha) Piece-size Constraint met (years) Merch. Vol. Constraint met (years) Minimum Time to Operability (years) Merch . Vol . at Operability (m3/ha) 500 a 33 44 44 115 1000° 36 33 36 128 1500° 39 30 39 1 74 2000° 43 29 43 209 2500b 46 28 46 234 3000 b 49 28 49 256 3500b 51 27 51 270 4000 b 53 27 53 284 a b Merchantable volume per ha constraint is Piece-size constraint is limiting factor limiting factor of o p e r a b i l i t y . of o p e r a b i l i t y . capacity of seven million seedlings per year which sets the upper l i m i t on considered planting alternatives. Available planting area is regulated by the rate at which harvesting proceeds and, therefore, the rate at which cut-over sites are generated. As such, this constraint is not fixed but is consequent to and automatically set by the imposed harvest l e v e l . It is assumed that any cut-over can be planted. PLANTATION COSTS Cost indicators of alternative planting regimes are derived from annual planting costs which are calculated as: PCL = HCi * ? k i [ 1 ] where: PC^ = annual plantation cost for density alternative i . HC^ = per hectare plantation cost for density alternative i . PA^ = hectares planted per year using density alternative i . Annual area planted is a management decision variable, which is systematically tested in the following analysis, bounded by the stock and planting s i t e constraints set out above. Per hectare planting cost is composed of both fixed costs and variable costs which are a function of seed-lings per hectare of planting. It can be expressed as: HCi = S T + SP + (PS*N/ha) + (PC*N/ha) [2] 44 where: ST = stand tending cost per hectare (considered here to be only competition control.) SP = s i t e preparation cost per hectare. PS = planting stock cost per seedling. PC = planting cost per seedling. N/ha = seedlings planted per hectare. In deference to Fraser Inc. c o n f i d e n t i a l i t y r i g h t s , unit cost values have been derived from the New Brunswick Department of Natural Resources s i l v i c u l t u r a l cost s t a t i s t i c s . Table 4 summarizes and explains the applicable values. Total cost per hectare for each considered planta-tion density was calculated by applying these values in .equation [2]. The results are contained in Table 5. FOREST DEVELOPMENT MODEL Forecasting forest development under various har-vest and planting interventions is performed using a compu-ter coded (FORTRAN IV) simulation model. The Wood Supply Model (WSM) was modified by the author for the sp e c i f i c s of this analysis from one designed and written by Erik Wang of Fraser Inc. Its concept p a r a l l e l s that of WOSFOP (WOod Supply and FOrest Productivity model) which has seen exten-sive use within New Brunswick and several other provinces (Cuff and Baskerville 1982). Several publications describe i t s concept, mechanics and applications (Hall 1978, Hall 1981, Baskerville 1978, C l i f f o r d 1981, Wang 1982). Conse-quently, i t w i l l be reviewed only b r i e f l y here. 45 Table 4. Planting component costs (1982 dollars) for eight plantation densities. Sources: R. Speer and C. Harding, N. B. Dep. Nat. Res. (pers. comm.) and Logan (1982). Density (N/ha) Herbicide** ($/ha) Stock1' ($/seedling) Planting ($/seedling) Scarification L" ($/ha) 500 124 0.095 0.104 76 1000 124 0.095 0.095 86 1500 124 0.095 0.086 97 2000 124 0.095 0.078 108 2500 124 0.095 0.078 108 3000 124 0.095 0.078 108 3500 124 0.095 0.078 108 4000 124 0.095 0.078 108 a Two a e r i a l applications of herbicide. D Black spruce container stock. c C & H plow. Table 5. Planting costs (1982 $/ha) for eight plantation densities. Density (N/ha) Herbicide ($/ha) Stock ($/ha) Planting ($/ha) Scarification ($/ha) Total ($/ha) 500 124 48 52 76 300 1000 124 95 95 86 400 1500 124 143 129 97 493 2000 124 190 156 108 578 2500 124 237 195 108 664 3000 124 285 234 108 751 3500 124 332 273 108 837 4000 124 380 312 108 924 46 The WSM accepts as input an array of growth types which constitute a selected forest, their associated areas, age class structures, yield functions (for existing, post-harvest untreated and post-harvest treated stands) and oper-a b i l i t y l i m i t s . At two year i t e r a t i o n intervals i t advances the age class structures along their respective yield curves and calculates informative forest level s t a t i s t i c s including t o t a l operable growing stock, volume lost to mortality and the changing forest structure. User specified harvest rates, harvest rules, and s i l v i c u l t u r a l e f f o r t s are incor-porated to harvest the forest and to channel stands off to new stages of development and yield functions. The WSM is a simple bookkeeping tool which tracks the forest dynamics resulting from various management a l t e r -natives in terms germane to the information needs of deci-sion makers faced with selecting the most desirable option. 47 RESULTS Wood Supply With No Planting The imbalanced age class structure combined with the spruce-fir yield patterns shown in Figure 5 form the core of the wood supply management problem posed by the Fraser Inc. holding. Clearly, the bulk of the stands on this forest have futures marked by substantial volume de-c l i n e , which w i l l translate into an overall growing stock decline for the forest. . To i l l u s t r a t e t h i s , a simulation t r i a l was per-formed for the forest in the absence of any harvest what-soever. Figure 11 reveals the resulting growing stock pro-f i l e to be quite unstable with the nadir occurring about 60 years into the future. The structure of the forest at the occurrence of the growing stock nadir provides the con-st r a i n t on sustainable wood flow; therefore, the manner in which harvesting and s i l v i c u l t u r e regulate the forest struc-ture and the timing and level of the nadir i t creates, are the keys in determining their d e s i r e a b i l i t y with respect to wood suppply. To establish a baseline against which planting contribution to wood supply can be measured, the maximum sustainable harvest, without any s i l v i c u l t u r e , was deter-mined. As a starting point, an annual harvest of 500 000 m3/year was imposed on the forest. Its impact on the grow-ing stock p r o f i l e is presented in Figure 12. This harvest 48 Operable Growing Stock 6 (m3 10" 6) 4 2 20 40 60 80 Years from Now Figure 11. Growing stock p r o f i l e for Fraser Inc. forest under no harvest . 20 40 60 80 Years from Now Figure 12. Growing stock p r o f i l e for Fraser Inc. forest under annual harvest rates of 500 000, 400 000 and 335 000 m3-49 l e v e l drives the nadir of operable growing stock to zero after approximately 25 years and, thus, does not s a t i s f y the forest level goal of sustained y i e l d . Reduction of the annual harvest to 400 000 m3 delays the nadir's occurrence for an additional 15 years, but i t too depletes the growing stock and i s unsustainable. It is not u n t i l the harvest is lowered to 335 000 m-Vyear that a sustainable level i s reached. The growing stock nadir occurs 70 years into the future and is main-tained at a s u f f i c i e n t l y high volume and with a forest structure that allows continuation of the 335 000 m3/year harvest. The dashed line present at 65 years in Figure 12 marks the change in growing stock d i s t r i b u t i o n between old stands (those existing at present) and new stands (those post harvested stands created from now on). The new stands do not contribute to the operable growing stock u n t i l about year 65; that i s , their minimum time to operability is 65 years. Planting, by reducing this minimum time, pushes the dashed lin e interface between the old and new forest, shown in Figure 12, nearer in time. Consequently, the tr a n s i t i o n between reliance of the harvest on old versus new growth occurs e a r l i e r , thereby allowing an accelerated li q u i d a t i o n of the old growth and an immediate increase in sustainable harvest. In planning a program to effect this increase, the most pressing questions become: (1) How many hectares should be established? and (2) What should be the density 50 target? How Many Hectares to Plant? In examining these issues, attention w i l l f i r s t be focussed on the number of hectares treated. For purposes of i l l u s t r a t i o n , the plantation density considered w i l l be 2500 N/ha and l i m i t s for plantation operability w i l l be fixed at 115 m3/ha minimum volume and a maximum of seven N/m3. Results from the plantation growth model show that, for 2500 N/ha, this condition is f i r s t s a t i s f i e d at 46 years (Table 3). By d e f i n i t i o n , the minimum time to plantation op e r a b i l i t y i s 46 years. This compares favourably to that of 65 years for untreated post-harvest stands and should provide a sustainable harvest above 335 000 mVyear. To establish the relation between plantation ef f o r t and wood supply, area planted was set at zero and i n -creased at 500 ha intervals u n t i l the t o t a l available nur-sery stock of 7 000 000 seedlings per year was consumed. At each 500 ha level (1) the maximum sustainable harvest over an 80 year time horizon was determined; (2) the total cost of the plantation program calculated; and (3) the cost per cubic metre of increase in harvest (attributable to plant-ing) calculated. The harvests and costs associated with each plantation effort are shown in Figures 14 and 13, respectively. The pattern shown in Figure 14 possesses two very revealing c h a r a c t e r i s t i c s . With plantation establishment at 51 less than 2000 ha/year, increasing the planting rate allows increasing the immediate sustainable harvest l e v e l . This benefit of planting i l l u s t r a t e s the allowable' cut effect, or ACE, (Schweitzer et a l . 1 972) and can be used as p a r t i a l j u s t i f i c a t i o n of planting expense. Of interest here, how-ever, i s that the relationship is non-linear; the slope of the curve is decreasing at an increasing rate. This means that the marginal hectares planted are progressively less e f f e c t i v e in promoting an increased harvest. The trend is more s t r i k i n g when expressed as cubic metres, of increased harvest per hectare of increased planting (Figure 15). The figure reveals that the 1750 t n hectare planted per year i s merely one quarter as e f f e c t i v e as the 250 t n hectare, in terms of i t s contribution to the allowable cut e f f e c t . Of course, the 1750 t h planted hectare is growing no d i f f e r e n t l y than the 250 t n, therefore, the non-linearity de-picted in Figure 14 must be ascribed to some feature of the mature forest from which the allowable cut effect is rea-l i z e d . Consideration of the existing forest age struc-ture, harvest sequence and stand yield patterns provides the explanation. Under the harvest rule used in the analysis, stands are sorted for harvest p r i o r i t y by decreasing volume decline. Each year, the harvest begins at the top of this queue and proceeds back through i t u n t i l the harvest quota i s s a t i s f i e d . For a simplified one stand type forest, the pro-52 30 25 Cost per m3 of ACE ($) 20 15 10 1000 2000 3000 Ha Planted per Year 4000 Figure 13, Cost per cubic metre of allowable cut effect versus hectare planted per year. 450 Max. Sust. Harvest (1000 m 3/yr) 425 400 375 350 325 1000 2000 3000 Ha Planted per Year 4000 Figure 14. Relationship between number of hectares planted (S 2500 N/ha) per year and maximum sustainable harvest. 53 80 of ACE Per Ha Planted 40 20 500 1000 1500 2000 2500 Ha Planted per Year Figure 15. Marginal benefit of planting, expressed as cubic metres of allowable cut effect per hectare planted. Harvest Progression Stand Age (years) Figure 16. Mechanism behind non-linearity and saturation of the allowable cut effe c t . 54 gression of harvest under this rule can be visualized as s t a r t i n g with the oldest stands and moving back through successively younger ones (Figure 16). When the harvest is set very low, stands develop along the growth curve (bottom arrow) at a rate equal to, or greater than the rate at which they are harvested (top arrow). That i s , the average age of harvested stands increases. As the harvest is increased the pattern begins to s h i f t so that the rate of harvest progres-sion along the top arrow exceeds the rate of stand growth progression along the bottom arrow and the average age of harvested stands decreases. Continued increase of the harvest level eventually pushes the harvest past the threshold at point A on Figure 16. Beyond this point, no stands exist to the right of point A (they have been previously harvested) and the har-vest i s drawn solely from stands which are s t i l l accumulat-ing volume; thus, there is a positive feedback in which the forest growing stock i s being eroded both by increased har-vest, and reduced growth. This, in turn, shrinks the base from which the harvest can be drawn, reduces the rate at which the harvest level can be increased, and gives rise to the decreasing marginal benefit of planting. As the harvest is accelerated s t i l l further, point B i s reached and the a v a i l a b i l i t y of operable stands is ex-hausted. If then becomes impossible to sustain any addi-t i o n a l harvest l e v e l , unless steps are taken to reduce the time to stand operability ( i e . s h i f t point B in Figure 16 to 55 the l e f t ) . Application of this explanation to the actual pattern presented in Figure 14 i s presented in Figures 17A and 17B. For the Fraser holding, the harvest can be i n -creased to 375 000 m-Vyear by planting 500 ha/year (at 2500 N/ha). Planting above this level allows a harvest rate high enough so that stands younger than the point A threshold in Figure 17A are taken in the harvest. At point A, harvesting has altered the forest structure, so that no stands reach the point of maximum mean annual volume increment. The dashed lines link the two conditions that occur simultan-eously. As soon as the harvest moves into stands to the l e f t of point A in Figure 17A, the non-linear portion of the curve in Figure 17B is entered and the marginal benefit of planting begins to decline. As planting increases up to 2000 ha/year, the har-vest increases but is forced into stands closer and closer to point B, and consequently at lower and lower mean annual increments, thereby continually eroding the growing stock base. The erosion is reflected in the decreasing slope of the sustainable harvest curve (Figure 17B). F i n a l l y , at 2000 ha/year planted, the harvest is so high, 420 000 m-Vyear, that point B is reached and additional operable stands are no longer available to sustain a higher harvest. When this occurs, the slope of the curve in Figure 17B be-comes horizontal and the allowable cut effect is saturated. Under a sustained yield policy planting additional 56 M e r c h a n t a b l e Vo1 urn e (m 3/ha) F i g u r e 17A, Max. S u s t . H a r v e s t ( 1 000 m 3/yr) 450 425 400 375 350 325 F i g u r e 17B. F i g u r e 17. 1000 2000 3000 Ha P l a n t e d p e r Year 4000 R e l a t i o n s h i p between c h a r a c t e r i s t i c s o f a v e r a g e s t a n d s h a r v e s t e d and a l l o w a b l e c u t e f f e c t a t t r i b u t a b l e t o v a r i o u s p l a n t i n g r a t e s . 57 hectares, above the 2000 ha/year rate, has no effect whatso-ever in increasing the immediate harvest rate, although i t w i l l permit an increased harvest in the future. This is represented by the horizontal li n e segment in figure 17B for planting rates above 2000 ha/year. The harvest benefits from a planting program in this range can only be realized at some future date. With the information of the effect of planting on wood supply at hand, the decision-maker can begin to l o g i -c a l l y select an appropriate plantation e f f o r t . The size of the program selected w i l l depend upon decision-maker's econ-omic objectives. It is interesting to note that the New Brunswick policy for Crown Lands is to set the planting rate for each license at the point which just saturates the allowable cut e f f e c t . This policy maximizes the short-term sustainable harvest but does so at a very dear price. The last units of harvest bought by planting come at a point where the mar-ginal benefit is very near zero. If i t is reasonable to assume that the marginal cost of planting is constant, then the cost per unit of immediate increase in harvest escalates rapidly. This occurrence is shown in Figure 13 for the Fra-ser Inc. forest. Traditional economic theory seeks to equate mar-ginal benefits and marginal costs. By saturating the allow-able cut e f f e c t , the New Brunswick policy drives planting well past this point to where marginal costs greatly exceed 58 marginal benefits, when the latte r are measured in terms of an immediate increase in harvest. The non-linearity of planting benefits might be used to argue that a re-alloca-tion of planting dollars would be adviseable. Maintaining the planting effort at levels well below those required to saturate the ACE would free up monies for use in alternative s i l v i c u l t u r a l t a c t i c s . It must be borne in mind, however, that so far marginal benefit has only been expressed as an immediate harvest increase. Planting also acts to buy a future i n -crease in both the forest growing stock and the harvest i t can sustain. This provides the base for the tr a n s i t i o n to future i n d u s t r i a l expansion which might well be a part of the decision-maker's objectives. Thorough examination of future harvest increases attributable to planting requires numerous analyses in which both the timing and magnitude of increases are varied. How-ever, this does not leave planting in the context of the fu-ture forest structure. Alternatively, an indicator of fu-ture harvest expansion can be had by examining the forest's growing stock p r o f i l e over time. The la t t e r approach is used here because i t reveals the planting effect on forest structure and growing stock data are provided by the anal-yses already performed. The maximum sustainable harvest associated with each planting level from 500 to 4000 ha/year was determined on the Fraser Inc. holding in order to generate a series of 59 80 year growing stock p r o f i l e s . Figure 18 presents the results of this in the form of a contoured surface in which the "elevation" i s volume of operable growing stock available at any combination of hectares planted per year and time into the future. The surface possesses two interesting features, both of which are relevant to selecting a planting effort under the consideration of future harvest increase. F i r s t , a "valley" traverses the surface between 40 and 70 years on the time axis. This represents the nadir in growing stock shown in two dimensions in Figures 11 and 12. To the right of the valley, growing stock change is extremely sensitive to both time ( p a r a l l e l to the X-axis) and to number of hec-tares planted per year ( p a r a l l e l to the Y-axis). To the l e f t of the valley, growing stock is again sensitive to time but very insensitive to hectares planted. The l a t t e r is true because the minimum time to o p e r a b i l i l t y for 2500 N/ha plantations i s 46 years (Table 3) therefore, their volume production is not reflected in the operable growing stock u n t i l 46 years has elapsed. The slight change which is present stems from the higher harvest rate, and faster l i q u i d a t i o n of the growing stock, associated with expanding planting from zero to 2000 ha/year. As previously discussed the forest structure cre-ating the nadir, or valley bottom in Figure 18, is the con-str a i n t on expanding the harvest. The valley i t produces is s i g n i f i c a n t here because i t indicates when future harvest 60 OPERABLE: GROWING STOCK CMILLION CUBIC METRES? FIGURE 18 RELATIONSHIP BETWEEN OPERABLE GROWING STOCK _ TIME, AND AREA PLANTED PER YEAR AT 3500 N/HA 61 increases w i l l f i r s t become available. At best then, the decision maker cannot expect to realize future gains in har-vest volume, beyond the immediate allowable cut effect, for almost 50 years. The second relevant feature is that once the 50 years has elapsed, c l e a r l y superior gains are provided by planting more hectares per year. At age 60, the growing stock for 4000 ha/year planted is six times greater than that for 500 ha/year and 2.5 times greater than that for 2000 ha/year and the forest structure is more stable. This reveals that once an increase in harvest, above the current ACE, i s sustainable, the magnitude of the increase expands considerably i f a larger effort in planting has been made i n i t i a l l y . It can be concluded that extensive planting pro-grams (over 2500 ha/year for the example) more e f f i c i e n t l y y i e l d sizeable, long-term harvest gains, while more modest ef f o r t s show considerable advantage for short term (ACE) gains. The re l a t i v e importance the decision-maker places on long versus short-term benefits w i l l determine how he trades off the advantages of various planting options in the selection of the program which best suits his forest and objectives. Further, since the structure of the existing forest plays such a dominant role in regulating the benefits of planting, i t is clear that planting program design must be made for the sp e c i f i c forest holding in question. 62 What Plantation Density to Establish? To c l e a r l y i l l u s t r a t e the impact of various rates of plantation establishment on wood supply, consideration has thus far been r e s t r i c t e d to a plantation density of 2500 N/ha. The decision-maker's problem, however, also includes plantation density s e l e c t i o n . To address t a c t i c s from this perspective, the following analyses were performed in which both the density and rate of planting were examined. The reasonable extremes of plantation density con-sidered were set at a minimum of 500 and a maximum of 4000 N/ha. Analyses were performed including these two extremes and the six 500 N/ha intervals between them. The plantation growth model was run for each of the eight selected densities to generate stand development data. Results were examined to determine when the current Fraser Inc. operability constraints (piece-size of seven N/m3 and merchantable volume of 115 m^/ha) would be s a t i s -f i e d . The time required to meet the more stringent of the two constraints for each density was set as the minimum time to o p e r a b i l i l t y . Figure 10 presents the r e s u l t s . It i s interesting to note how the constraint on o p e r a b i l i t y switches from merchantable volume per hectare, at a density of 500 N/ha, to piece-size at higher densi-t i e s . This, of course, makes good i n t u i t i v e sense. But, as w i l l be shown l a t e r , i t has profound implications in select-ing plantation density in the event that the constraints change over time. 63 To examine changing both plantation density and area planted per year, 64 wood supply analyses were per-formed using the wood supply model. For each of the eight plantation densities, eight planting rates were established, ranging from zero to 4000 ha/year, at 500 ha in t e r v a l s . The following variables were tracked for each t r i a l : (1) max-imum sustainable harvest; (2) annual cost of the planting program; (3) seedlings planted per year; and (4) operable growing stock. In addition, cost per cubic metre of allow-able cut effect and cost per cubic metre of expanded growing stock volume at year 60 were derived from (1) and (2), and (2) and '(4), respectively. Figure 19 i s a contour surface of maximum sustain-able harvest versus plantation density and area planted per year. Several s i g n i f i c a n t features are evident in the f i g -ure. F i r s t , the asymptote shown for the maximum harvest curve for 2500 N/ha in Figure 14 reappears as a set of hori-zontal contours across a l l densities in Figure 19. The planting rate at which the horizontal contours are reached varies substantially between each plantation density. For example, i t appears at 1 500 ha/year for 4000 N/ha, 2000 ha/year at 2500 N/ha, and 3000 ha/year at 1500 N/ha. This shows that at higher plantation densities, and therefore longer times to op e r a b i l i t y , the allowable cut effect i s saturated at lower planting rates. The explanation is obvious i f reference is made back to Figure 16. The longer times to operability e f f e c t i v e l y s h i f t the B threshold in 64 Figure 16 to the r i g h t . Thus, the progression of harvest through operable stands depletes the operable growing stock sooner and quickly bounds harvest gains resulting from i n -creased planting. Secondly, the elevation (maximum sustainable har- . vest) at saturation of the allowable cut effect varies d i r -ectly with time to plantation o p e r a b i l i t y . Therefore, small ACE volumes are available using high plantation densities ( 3000 to 4000 N/ha) and using very low ones (500 N/ha). This occurs because long times to o p e r a b i l i t y , whether due to slow piece-size or merchantable volume development, re-tard the rate at which plantations become available for har-vest and, consequently, reduce the rate at which existing operable stands can be liquidated. Figure 19 shows that the maximum harvest which can be obtained via planting i s 480 000 m3/year and arises from planting approximately 1250 N/ha at a rate of 3000 ha/year. This peak on the surface corresponds to the plantation den-s i t y which has the lowest time to operability and the plant-ing rate which saturates the allowable cut effect at that density. It might be tempting to conclude that the best combination of options for this forest is that which yields the 480 000 m^/year harvest. However, the shape of the sur-face which surrounds the peak cautions against jumping to that conclusion. This is the third feature of interest in Figure 19. Movement off the peak toward increased plantation 65 MAXIMUM SUSTAINABLE HARVEST CTHOUSANDS CUBIC METRES PER YEAR5 340 360 1 000 2000 3000 4000 PLANTING RATE CHA/YR5 FIGURE 19 RELATIONSHIP BETWEEN PLANTATION DENSITY, PLANTING RATE, AND MAXIMUM SUSTAINABLE HARVEST 66 density causes the maximum sustainable harvest to slid e down a gentle slope. In the other d i r e c t i o n , toward decreased plantation density, the maximum sustainable harvest plunges down a much steeper slope, as indicated by the t i g h t l y packed contours. These slopes r e f l e c t the s e n s i t i v i t y and robustness of the harvest to plantation density changes and is a factor to consider in decision making. The 1250 N/ha at 3000 ha/year combination is perched right at the edge of the precipice. If this option i s selected, sub-standard plantation, performance resulting from low seedling s u r v i v a l , poor competition control, or i n e f f e c t i v e protection could have disastrous consequences. Such occurrences would push the sustainable harvest over the brink and either (1) a severely reduced sustainable harvest would be realized; or (2) an unexpected hiatus in wood flow would result from following a harvest rate set in accordance with plantation yields which never, in fact, materialize. Alternatives in this high s e n s i t i v i t y zone might be choices of the risk-takinq decision-maker. A more conservative philosophy might opt for a higher plantation density (2000 to 3000 N/ha), accepting a s l i g h t l y lower harvest in order to reside in the less sensitive decision area which, by d e f i n i t i o n , is more forgiving of fai l u r e s in plantation per-formance. Movement to the l e f t of the high point is through widely spaced contours, indicating small marginal losses in harvest associated with reductions in the rate of planting. 67 As previously discussed, i t might be economically e f f i c i e n t to move in this direction and re-allocate the saved funds elsewhere. Additional considerations are relevant in select-ing a plantation regime to follow. Cost variables, resource a v a i l a b i l i t y and potential future expansion may greatly i n -fluence the decisions made. To allow simultaneous consider-ation of these other factors, Figure 19 is shown as one nom-ogram in a set (Figure 20) which includes the effects of plantation density and planting rate on (1) seedlings re-quired per year; (2) cost per cubic metre of ACE; (3) operable growing stock 60 years hence; (4) cost per unit of operable growing 60 years hence; (5) t o t a l annual planting cost; and (6) maximum sustainable harvest. The nomogram presentation format is p a r t i c u l a r l y useful for option evaluation when two decision variables are to be assessed via their control over several indicator var-iables (Peterman 1975). Here the decision variables are plantation density and rate of planting while the indicator variables are the six items l i s t e d in the previous paragraph and contoured in Figure 20. Figure 20F reveals total planting cost to be l i n -early related to both plantation density and planting rate. If, however, cost effectiveness is measured by dividing t o t a l cost by volume of extra harvest purchased (ACE) by planting, quite another pattern results (Figure 20B). The cost l i n e a r i t y dissappears altogether. Very low densities, 68 with very low planting rates yield the cheapest extra wood largely because the numerator (total cost) is kept small by the modest planting program. While additional wood acquired by the low plantation density, low plantation rate option is very cheap ($5/m 3), the actual quantity bought is extremely small (360 000-335 000 = 25 000 m3/year ) (Figure 20A). Thus, i f a larger ACE is desired, an escalating cost per additional unit must be accepted. L i t t l e is to be gained by increasing density while keeping planting rates low (less than 1000 ha/year) as i s evidenced by the near v e r t i c a l contours in Figure 20A. However, substantial har-vest increases are available i f the area planted per year is increased at almost any of the plantation densities. Pro-ceeding up the valley, which p a r a l l e l s the X-axis at 1000 N/ha, in Figure 20B, appears to be the most cost e f f i c i e n t way to effect this gain. However, alternatives in this mar-ginal cost depression reside very near the c l i f f in Figure 20A and therefore are accompanied by substantial risk in the event of poor plantation performance. The marginal cost s e n s i t i v i t y to moving out of the cost trough, by increasing density, is r e l a t i v e l y low u n t i l a rate of approximately 2500 ha/year is reached. The con-servative decision-maker might accept the increaseed margin-al cost and move towards a higher density, perceiving the increased cost as an insurance policy against poor planta-tion performance. Cost per cubic metre of ACE escalates rapidly as 69 MAX HARVEST C 1 000 M3/YR3 < r z 38Q 30 20 •40 30 20 10 COST PER M3 OF ACE C*5 30 -40 50 S0 70 80 1 0 20 FIGURE 20B 30 -40 s H H W Z u 0 z 0 H h < h Z < J Q. OGS 0> YR 80 CMILLIONS M3? •40 30 20 1 0 1 0 FIGURE 20C 20 30 •40 STOCK REQUIRED CM OF SUPPLY5 •40 30 20 1 0 50 1 50 200 25 1 75 1 25 7 5 20 30 •40 COST/M3 OGS o? YR ea C*D •40 30 1 0 30 -40 10 20 FIGURE 20D 30 -40 •40 30 20 1 0 PLANTING COST CS/YR3 5 10 15 20 25 30 35 1 0 FIGURE 20E P L A N T I N G R A T E C 1 0 0 H A / Y R 5 1 0 FIGURE 20F 20 30 •40 FIGURE 20 NOMOGRAM OF SIX INDICATOR VARIABLES VERSUS PLANTING RATE AND PLANTATION DENSITY 70 high densities and high planting rates are approached. This steep region corresponds closely to the horizontal contour portion of the Figure 20A surface. The pattern results from continued planting program cost increase (Figure 20F) and s t a l l e d sustainable harvest increase (Figure 20A). Thus, when viewed only from the ACE perspective, high density, high planting rates are not only i n e f f e c t i v e , they are ex-ceedingly expensive. Figures 20C and 20D contain information relevant to future increases. They are somewhat analogous to the 20A, 20B pair, but refer to the future, rather than immedi-ate, supply and cost pictures. The operable growing stock at age 60 (OGS 60) does not increase appreciably u n t i l r e l a -t i v e l y high planting rates are employed (Figure 20C). Fur-ther, the planting rate at which the escalation begins is lower for high densities and higher at low densities and the location of the sharp rise co-incides with the start of the horizontal contour area in Figure 20A. This correspondence makes i n t u i t i v e sense because as long as the sustainable harvest i s increasing most of the plantations which become operable are quickly harvested to sat i s f y the increased har-vest; thus, build-up of the growing stock is in h i b i t e d . Once the allowable cut effect is saturated however, addi-ti o n a l planting acts to "bank" a substantial volume of wood which surfaces in the i n f l a t e d growing stock in Figure 20C. This bank of wood then provides the basis for an increased harvest in the future. 7 1 The largest future supply and, therefore, largest future harvest expansion occurs at planting 2500 N/ha and 4000 ha/year. It f a l l s off as density decreases because individual stand volume is quite low (Figure 10). Si m i l a r l y , operable growing stock declines with densities above 2500 N/ha because the time to operability is protracted by piece-size development, resulting in a small portion of the established plantations being operable and able to contribute to the tota l operable growing stock. Starting at low planting rates for any density, the marginal cost of 0GS 60 (annual cost of program divided by 0GS 60) climbs, peaks and then declines as planting rates increase. The 0.35 $/m3 ridge in Figure 20D highlights the pattern. Once again, the ridge corresponds to the start of the horizontal contour surface in Figure 20A. To the l e f t of the ridge marginal cost f a l l s off because the low planting rates incur small annual costs (Figure 20F). To the right of the ridge, the marginal costs drops in response to the rapidly r i s i n g operable growing stock. The lowest cost for any appreciable increase in growing stock co-in-cides with the 1000 N/ha, 4000 ha/year planting combina-t i o n . This option buys an eight m i l l i o n m3 growing stock at age 60. Considerably . more could be had (11 mi l l i o n m3) by maintaining the 4000 ha/year rate, but increasing density to 2500 N/ha (Figure 20C). The associated cost increase is 25 percent (0.25 versus 0.20 $/m3), which compares favorably with the volume gain of 37.5 percent (11 versus eight 72 m i l l i o n m-5). From this perspective, a higher plantation density i s advantageous over that density which yields the largest, cheapest immediate gain. Freedom to select between the plantation density, planting rate alternatives is somewhat r e s t r i c t e d by the Fraser Inc. current nursery capacity of seven m i l l i o n seed-lings per year. How do the various options relate to seed-l i n g a v a i l a b i l i t y ? The answer l i e s in Figure 20E which is a contour surface of required seedling supply. Current seed-l i n g a v a i l a b i l i t y i s s u f f i c i e n t to serve a l l options to the l e f t of the 100 percent contour; those to the right of that l i n e would require nursery expansion. If the low plantation density, high planting rate i s selected to maximize immediate benefits, the Fraser Inc. seedling production could shrink by approximately 40 per cent to 4.2 m i l l i o n seedlings per year. Increasing the planting density and maintaining a high rate, to achieve long-term gains and move away from the high risk zone in Figure 20A could be performed with s l i g h t , i f any, expansion above the current capacity. In either case, Figure 20 contains very l i t t l e evidence to suggest that a major nursery expansion program would be warranted. None of the options requiring substan-t i a l l y more than seven m i l l i o n seedlings per year manifest any real advantages (in fact they show major disadvantages) in either the short-term (ACE) or long-term (expansion) aspects which might be important to the decision-maker. 7 3 Changing Operability Constraints Thus far, the assumption has been made that cur-rent operability constraints (seven N/m3 and 115 m3/ha.) w i l l continue into the future. Past changes in u t i l i z a t i o n and common sense indicate this to be a rather remote p o s s i b i l -i t y . If, in fact, they do continue to change, what are the implications to plantation density selection? To examine this question an additional series of simulations were performed for the Fraser Inc. forest. A l l input data were kept as before except the imposition of ope r a b i l i t y constraints on plantation development. Con-st r a i n t s could change in either, or both, of two ways; changing piece-size requirements and changing merchantable volume per hectare thresholds. As the forest products i n -dustry is moving toward a fibre and re-constituted product orientation i t i s unlikely that piece-size constraints w i l l be tightened to any great extent. For this reason, the range of piece-size requirements to be tested was bounded at six N/m3 on the tight side and 14 N/m3 on the relaxed side. Intervals at two N/m3 were used. Merchantable volume constraints, on the other hand might conceivably move in either d i r e c t i o n . Expensive, sophisticated harvesting systems of the future, coupled with the geographic dispersion of plantations resulting from today's harvest pattern, might necessitate very high volumes per hectare for cost e f f i c i e n t operation. Conversely, har-vesting systems might become so e f f i c i e n t as to make very 74 low volumes per hectare economical to harvest. To account for both of these p o s s i b i l i t i e s , four merchantable volume thresholds were examined, 70, 115, 160, and 205 m3/na. Establishment of minimum time to operability for each plantation density (500 to 4000 N/ha) under each of the twenty different combinations of piece-size and merchantable volume constraints was performed as before. The time at which each constraint was met was noted with that for the more stringent of the two being set as the minimum time to o p e r a b i l i t y . P o t e n t i a l l y , there are four decision variables i n -volved in this analysis: (1) plantation density; (2) plantation establishment rate; (3) piece-size constraint changes; and (4) merchantable volume per hectare constraint changes. To reduce the ungainliness of controlling four variables simultaneously, the planting rate was fixed at the rate which saturates the allowable cut effect for each den-s i t y a lternative. In addition, the minimum merchantable volume constraint was i n i t i a l l y held at i t s current value of 115 m3/ha. This allowed varying only plantation density and piece-size constraints, for which there are 48 unique com-binations (eight for density and six for piece-size). For each of these 48 pairs, wood supply analyses were performed to establish the associated maximum sustainable harvest. The results are presented as a contour surface in Figure 21. Several interesting inferences can be drawn from i t . F i r s t , i t is clear that the d e s i r a b i l i t y of a l -75 ternative densities, with respect to wood supply, varies considerably depending on the piece-size constraints which are imposed. Under the stringent requirement of six and seven N/m3, plantation densities of 1000 and 1500 N/ha provide the maximum sustainable harvest (480 000 m^/year). At progressively higher densities, the sustainable harvest declines rapidly because the crowding of stems retards piece-size development and, thereby, protracts the minimum time to ope r a b i l i t y . At lower densities, site u t i l i z a t i o n i s so low that a considerable delay is incurred in reaching the merchantable volume threshold of 115 m^/ha, even though the six stems N/m3 is quickly attained. However, as the piece-size constraint is relaxed, Figure 21 reveals that not only does the maximum sustainable harvest increase, but so does the plantation density at which the maximum i s realized. This is evidenced by the ridge which passes through points A, B, C and D in the sur-face. That the surface rises with relaxed piece-size con-s t r a i n t s is a re f l e c t i o n of the decreased time to operabil-i t y they allow and the consequent effect this has on wood supply, as previously discussed. That points A, B, C and D reside progressively higher on the plantation density axis is indicative of the e a r l i e r achievement of operability thresholds by higher den-s i t y plantations when the constraint on piece-size is re-duced. In fact, the position of the ridge corresponds to those densities which s a t i s i f y the operability constraints 76 MAXIMUM SUSTAINABLE HARVEST AT MINIMUM MERCHANTABLE VOLUME CONSTRAINT OP 115 M3/HA CTHOUSANDS CUBIC METRES? 420 -4-40 -480 6 3 10 12 1-4 MAXIMUM STEMS PER CUBIC METRE FIGURE 21 RELATIONSHIP BETWEEN MAXIMUM SUSTAINABLE HARVEST, PLANTATION DENSITY„ AND PIECE-SIZE CONSTRAINTS WHEN MINIMUM MERCHANTABLE VOLUME CONSTRAINT IS «15 M3/HA 77 in the minimum time. Solely from ACE perspective then, the densities on the ridge might be considered most desirable for the associated operability constraints. Further examination of Figure 21 sheds more light than that, however. The two very different patterns appar-ent in the slopes which the ridge separates allow other im-portant interpretations. The portion of the surface below the ridge is almost wholly composed of horizontal contours, s i g n i f y i n g complete i n s e n s i t i v i t y of wood supply to piece-size constraints for the associated plantation density l e v e l s . The i n s e n s i t i v i t y r e f l e c t s the fact that minimum merchantable volume (115 m3/ha) is the over-riding con-strai n t at these plantation densities, taking longer to sat-i s f y than any of the piece-size l e v e l s . In fact, the start of a horizontal contour for any density co-incides exactly with the point at which the constraining factor switches from piece-size to merchantable volume. As w i l l be dis-cussed l a t e r , this has major implications in the event of merchantable volume constraint changes. It i s noteworthy that the contours in the lower slope are quite densely packed. This creates a high risk zone, similar to that evident in Figure 20A, which the con-servative decision-maker might wish to avoid. Nonetheless, should a density in this zone be selected, there is at least some assurance that piece-size constraint changes, or unex-pectedly slow stem development, w i l l have minimal impact on sustainable harvest l e v e l s . 78 The portion of the surface above the ridge pre-sents an altogether d i f f e r e n t s i t u a t i o n . The contours re-veal that changes in required piece-size substantially effect wood supply and do so in a non-linear fashion. Here, wood supply levels are responsive, because with higher den-s i t y plantations, rapid stand volume growth is acquired at the expense of stem development. Therefore, the tight con-st r a i n t i s piece-size and, when i t is relaxed, the minimum time to operability drops, allowing the sustainable harvest to r i s e . The rise is non-linear because piece-size develop-ment is non-linear. At low stems per cubic metre, the f l a t -ness of the lower curve in Figure 10 defines major reduc-tions in time to operability for small changes in piece-size requirements. The translation of this effect on wood supply appears in the close contour packing associated with low stems per cubic metre in Figure 21, and their gradual dis-persion as this variable increases. For decision making this implies that i t is of l i t t l e consequence i f uncertainty about future constraints varies between ten and 12 N/m3, but i t is of extreme conse-quence i f the same magnitude of uncertainty i s bounded by six and eight N/m3. Piece-size constraint changes are not the sole source of uncertainty the decision-maker must contend with, in evaluating plantation density alternatives. There is also the matter of variable minimum merchantable volume per 79 hpntare thresholds. To add this element to the picture, three sets of wood supply analyses were performed i d e n t i -c a l l y to that just presented, except that minimum merchant-able volume constraints were set at 70, 160 and 205 m"Vha. The results are combined with those for 115 m3/ha and pre-sented as a nomogram set in Figure 22. The four surfaces possess several similar qualita-ti v e t r a i t s . F i r s t , there are obvious trends of increased sustainable harvest with decreases in piece-size con-s t r a i n t s . This is evidenced by the general r i s e in contours with movement to the right , p a r a l l e l to the stems per cubic metre axis. Second, each surface is divided into two parts by a ridge which increases on the stems per cubic metre axis as the plantation density is increased. Third, the areas below each ridge manifest i n s e n s i t i v i t y of wood supply to piece-size changes and high s e n s i t i v i t y to plantation density. F i n a l l y , the surface areas above each ridge show the reverse patt ern; low s e n s i t i v i t y of wood supply to plantation den-s i t y and high s e n s i t i v i t y to piece-size constraints. Quantitatively, the surfaces contain some very im-portant differences. The most obvious is the rise in sus-tainable harvest which accompanies progressive relaxation of the merchantable volume constraint from 205 to 70 m3/ha. For example, the maximum contours for Figure 22 A, B, C and D are 560, 540 , 500 and 460 thousand m-Vyear, respectively. Further, the plantation density which provides the maximum 80 MAX SUST HARV AT MIN MERCH VOL. CONSTRAINT OF 70 M3/HA C1000 M3/YR3 MAX SUST HARV AT MIN MERCH VOL. CONSTRAINT OF t15 M3/HA C1000 M3/YR3 < r \ Z 0 0 (9 > I-H z Id Q Z 0 H h < H Z < J -40 35 30 25 20 1 5 1 0 5 440460 •440-460 430 e s FIGURE 22A 10N 12 14 e 8 FIGURE 22B 10 12 14 40 35 30 25 20 1 5 1 0 5 MAX SUST HARV AT MIN MERCH VOL CONSTRAINT OF 160 M3/HA C1000 M3/YR5 440460 40 460 :420 :380 1 0 MAX SUST HARV AT MIN MERCH VOL CONSTRAINT OF 205 M3/HA C1000 M3/YR3 440460 -420 -400 -360 6 8 FIGURE 22C 1 0 1 Z 1 4 M A X I M U M FIGURE 22D S T E M S P E R 1 0 M3 1 2 1 4 FIGURE 22 RELATIONSHIP OF MAXIMUM SUSTAINABLE HARVEST VERSUS PLANTATION DENSITY AND PIECE-SIZE CONSTRAINTS AT VARIOUS MINIMUM MERCHANTABLE VOLUME PER HECTARE THRESHOLDS 8 1 harvest level on each surface increases s i g n i f i c a n t l y with an increased constraint on merchantable volume per hectare. F i n a l l y , consistently higher harvests are a v a i l -able from high plantation density options when piece-size is held constant and the merchantable volume constraints tight-ened. The exception l i e s in the high density, low piece-size combinations found in the upper l e f t of each figure. Here, the 360, 380, 400 and 420 thousand m-Vyear contours are configured i d e n t i c a l l y for a l l four surfaces. This de-fines a region of i n s e n s i t i v i t y of wood supply to merchant-able volume constraints. It is not surprising. At these combinations, any of the tested merchantable volume thresh-olds are quickly s a t i s f i e d , while those for piece-size are not. Thus, piece-size is the stringent constraint and i n -s e n s i t i v i t y of the wood supply to merchantable volume con-s t r a i n t s r e s u l t s . Together, these patterns hold considerable rele-vence to decision-making. F i r s t , major wood supply gains are to be had with the design of systems which can economi-c a l l y harvest low volume stands. Second, the merchantable volume which is in fact required for an economic harvest, impinges d i r e c t l y on the d e s i r e a b i l i t y of various planting d e n s i t i e s . Expectations of high required volumes would argue for high density options, while the reverse would pre-sent a strong case for lower plantation densities. 82 CONCLUSION By design, discussion thus far has provided no firm recommendations of optimal planting densities or plant-ing rates. None w i l l be made here either. This absence should not be perceived as a short-coming of the analyses presented. What has been provided is a systematic, informa-tive approach to embedding plantation a c t i v i t i e s into the development of the entire forest and the translation of re-sultant effects into measures relevant to forest manage-ment. While this analysis has focussed e n t i r e l y on wood flow volumes and s i l v i c u l t u r e costs, i t must be emphasized that wood value is a c r i t i c a l component in the decision-making process. To include i t simply requires one step be-yond what has been presented here: the decision-maker must place values on stems of various size and quality in r e l a -tion to his s p e c i f i c product strategies and economic objec-t i v e s . With this information available, plantation yield and wood flow from the forest under any planting densities and rates would be translated into economic terms, and a l l volume measure outcomes replaced by dollar measures. Addressing wood values then becomes a straightforward change in measurements units, for which the framework presented here remains appropriate. But c l e a r l y , whether the perspective is value or volume, plantation program design goes far beyond determina-tion of optimality at the stand level and application of 83 that optimum to a l l planted stands in the forest. Different planting alternatives at the stand level have been shown to generate dramatically different forest level outcomes because of the forest level interactions. In exercising planting options, the decision-maker can gain substantial control over his wood supply future. However, in doing so, he must be prepared to make d i f f i c u l t decision concessions. The results reveal trade-offs to be inescapable, especially (1) between capturing short versus long term gains; (2) between level of risk and level of harvest; (3) between i n -creased harvest and cost of increased harvest; and (4) be-tween operability constraints and increased harvest. Inescapable as they may be, compromises associated with trade-offs can be lessened i f planting program design incorporates more than one density option. While this may be unorthodox in New Brunswick forestry, there is ample ev i -dence here to suggest that simultaneous establishment of both low and high density plantations is an attractive a l -ternative. Such a scheme would be tailo r e d to serve short and long term goals, with low density stands addressing the former and high density stands addressing the l a t t e r . In plantation program design, the decision-maker must also contend with the uncertainty of future operability constraints. These have been shown to have a profound im-pact on the nature of the wood supply and the effectiveness of planting alternatives in serving that supply. Uncertain-ty regarding operability constraints which w i l l prevail in 84 the future must be addressed now, with today's establishment of the future forest. The a n a l y t i c a l system discussed here does l i t t l e to reduce that uncertainty. Nonetheless the re-sults are valuable in directing attention to where uncer-tainty has pronounced impact, and providing a measure of the sign i f i c a n c e of that uncertainty. As a package, the ana l y t i c a l method, and results produced from i t , form a rich body of decision-making assis-tance. They w i l l be of value i f the decision-maker applies to them his philosophy, persuasions and i n t e l l e c t to nego-t i a t e through the trade-offs and uncertainty to select the options which most e f f e c t i v e l y serve his purpose. 85 L I T E R A T U R E C I T E D B a s k e r v i l l e , G. L. 1965. Dry matter production in immature balsam f i r stands. For. Sci. Mono. No. 9, 42 pp. B a s k e r v i l l e , G. L. per acre 1966. Grow large trees and high volumes For. Chron 42 (1): 101-102. Baskerville, G. L. 1978. decisions. Univ sources , 73 pp. Forest New Brunswick, dynamics and management Dep. Forest Re-Baskerville, G. L. 1981. Strategic studies - A Discussion Paper. In: An Industrial assessment of forestry research in Canada (Vol. I I ) , Present Status and needs of Canadian Forestry Research, K. M. Thomp-son (ed) PPRIC, October 1981, 175 pp. Baskerville, G. L. 1982. Brunswick. N.B. The spruce/fir wood supply in New Dep. Nat. Resourc, 15 pp. B e l l , E. , R. Fight and R. Randall. 1975. ACE edged sword. 3. For. 73(10): 642-642. The two-Brodie, 3. D. and C. Kao. 1979. Optimizing thinning in Douglas-fir with three descriptor dynamic pro-gramming to account for accelerated diameter growth. For. S c i . 25(4): 665-674. Buongiorno, 3. and D. E. Teeguarden. 1978. Operations re-search techniques in the management of large-scale reforestation programs. In operational forest management planning methods: proceedings, meeting • of Steering Systems Project Groups, IUFR0. U.S.D.A. For. Ser. Gen. Tech. Rep. PSW-32: 36-44. Cayford, 3. H. 1966. Grow small or Chron. 42(2): 206-207. large trees? For C l i f f o r d , W. L. tion. swic k. T. 1981. Master's 83 pp . Wood supply analysis by simula-Thesis. Universify - of New Brun-86 Cuff, W. and G. L. Baskerville. 1982. Ecological modelling and management of spruce budworm i n f e s t e d f i r -spruce forest of New Brunswick, Canada. Paper presented at 3 r c' Int. Conf. on State-of-the-Art in Ecological Modelling, Colorado State Univ., May 24-28, 1982, 5 pp. Erdle, T. A. 1980. A plantation yield forecasting system for black and white spruce in the Black Brook for-est d i s t r i c t . 0. D. Irving Woodlands Internal Rep.,89pp. Farrar, 3. L. 1966. Crowding can improve wood quality. For. Chron. 42(2): 204. Federal Forest Sector Strategy Committee. 1981. A forest sector strategy for Canada. Can. Dep. Envir., 59 PP • H a l l , T. H. 1978. Toward a fremework for forest management decision-making in New Brunswick. N. B. Dep. Nat. Res., Fredericton, N. B. Rep. No. TRI-78, 83 PP • H a l l , T. H. 1981. Forest management decision making: art or science. For. Chron. 57(5): 233-238. Hann, D. W. and 3. D. Brodie. 1980. Even-aged management: basic managerial questions and available or poten-t i a l techniques for answering them. U.S.D.A, For. Serv. Gen. Tech. B u l l . INT-83, 29 pp. Hann, D. W., 3. D. Brodie and K. H. R i i t t e r s . 1983. Opti-mum stand prescriptions for ponderosa pine. 3 For. 81(9): 595-598. Johnstone, W. D. 1981. Effects of spacing 7-year-old lodgepole pine in west-central Alberta. Can. For. Serv., NFRC Inf. Rep. NOR-X-236, 18 pp. Kennedy, R. W. 1966. Wide spacing results in better qual-i t y . For. Chron. 42(3): 317. 87 Ker, M. F. 1981. Early response of balsam f i r to in northwestern New Brunswick. Can. For. MFRC Inf. Rep. M-X-129, 36 pp. spacing Serv. , Logan, A. 1982. S i l v i c u l t u r a l s t a t i s t i c s - Crown Lands, 1981-1982. N. B. Dep. Nat. Res., Fredericton, N. B., 41 pp. Loucks, 0. L. 1962. A forest c l a s s i f i c a t i o n for the Mari-time Provinces. Proc. N. S. Inst. S c i . , Vol. 25: 85-167. Lundgren, A. L. 1973. The allowable cut ef f e c t : Some fur-ther extensions. 3. For. 71(6): 357-360. Lundgren, A. L. 1981. The effect of i n i t i a l number of trees per acre and thinning densities on timber yields from red pine plantations in the Lake States. U.S.D.A. For. Serv. Res. Pap. NS-193, 25 pp. Osborne, 3. E. 1967. Plant them wide, George For. Chron. 43(4): 389-392. Painter, M. F. 1980. Eight for the eighties. For. Chron. 56(4): 168-170. Peterman, R. M. 1975. New techniques for policy evaluation in ecological systems: Methodology for a case study of P a c i f i c salmon f i s h e r i e s . 3. Fish. Res. Board of Canada, 32: 2179-2188. Schweitzer, D. L., R. W. Sassaman and C. H. Schallau. 1972 Allowable cut ef f e c t . 3. For. 70(7): 415-418. Schweitzer, D. L., R. W. Sassaman, C. H. Schallau. 1973. The allowable cut ef f e c t : A reply. 3. For. 71(4): 22 7. Smith, 3. H. G. 1958. Better yields through wider spac-ing. 3. For. 56(7): 492-497. 88 Smith, 3. H. G. 1966. Continuing and e f f i c i e n t production of desirable forest products should be our aim. For. Chron. 42(1): 5, 13. Smith, 3. H. G. 1983. . Planning for intensive forest man-agement must use price/size gradients. For. Chron. 59(5): 218. Stafford, E. 1931. Skeletal planting. 3. For. 29(1): 41-47. S t i e l l , W. and A. B. Berry. 1973. Development of unthinned white spruce plantations to age 50 a Petawawa For-est Experiment Station. Can. For. Serv. Publ. 1317, 18 pp. Teeguarden, D. E. 1973. ment. 3. For. The allowable cut 71(4): 224-226. effect : A corn-Vincent, A. B. 1966. Grow a maximum acre. For. Chron. 42(1): 101. of cellulose per Wang, E. C. 1982. Wood supply analysis - a forest manage-ment t o o l . Paper presented at CP.P.A. Maritime Section meeting Moncton, N. B., March, 1982, 19 pp. Wiksten, A. 1966. Grow timber for greatest total benefit. For. Chron. 42(2): 204-206. o Wiksten, A. 1968. On spacing - "Plant them wide, George". For- Chron. 44(2): 71-72. Wilde, S. A. 1965. Plantation spacing and site condi-tions. .Tree Planter's Notes No. 65: 12-13. 89 

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