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Growth simulation of trees, shrubs, grasses and forbs on a big-game winter range Quenet, Robin Vincent 1973

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C ' GROWTH SIMULATION OF TREES, SHRUBS, GRASSES AND FORBS ON A BIG-GAME WINTER RANGE by ROBIN V. QUENET A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in the department of Zoology We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA JULY, 1973 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 fo r scholarly purposes may be granted by the Head of my Department or by h i s 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 The University of B r i t i s h Columbia Vancouver 8, Canada - i - ABSTRACT Plant growth, production, competition and, to a limited degree, secondary succession have been simulated for a mixed species forest eco- system operating on a big-game winter range. The simulation was based on empirically derived relationships. The major plant species investi- gated included Pseudotsuga menziesii (Mirb.) Franco (Douglas-fir)"'", Amelanchier a l n i f o l i a , Ceanothus sanguineus, Shepherdia canadensis, Prunus virginiana, Rosa nutkana, Symphoricarpos albus, Agropyron spicatum, Poa compressa and scabrella, Calamagrostis rubescens and Koeleria cristata. Distinction was not made among forb species. The simulation model predicts plant community development and production by species for a maximum period of 100 years following estab- lishment, with up to 20 calculation intervals. Individual plants form the basic simulation unit. Variable data inputs include simulation period, calculation interval, species composition, density, inherent biological v a r i a b i l i t y and site quality. Output i s expressed in terms of wood production, weight of annual twig production of shrubs, current annual growth and carry-over of grasses, and current annual growth, of forbs. Designed to be used on the Wigwam big-game winter range in the East Kootenay d i s t r i c t of British Columbia, the model provides a quantitative comparison of the land's capability to produce wood, browse, grasses and forbs. It also provides a basis for the solution of forestry-wildlife A l l other common and scie n t i f i c names with authorities are l i s t e d in Appendix I. - i i - conflicts, such as assessment of the implications of management for wood production on ungulate food production, and formulation and testing of strategies designed to increase yields of wood, browse, grass and forbs. - i i i - ACKNOWLEDGEMENTS The author gratefully acknowledges his indebtedness to the faculty and staff of the Departments of Zoology, Forestry and Agriculture and the Institute of Animal Resource Ecology of the University of British Columbia, especially Dr. C. J. Walters, Dr. C. S. Holling, Dr. H. C. Nordan, Dr. F. L. Bunnell, Dr. J. H. G. Smith, Dr. V. C. Brink, and Dr. J. F. Bendell. Their helpful advice and guidance are greatly appreciated. Very special thanks are extended to Dr. P. J. Bandy, of the B. C. Fish and Wildlife Branch, for his unfailing support, guidance and enthusiasm as project supervisor, to Mr. K. M. Magar, Mr. F. Heywood, and Mr. J. Inkster for their invaluable assistance in programming, and to Mr. J. F. Dronzek of the Canadian Forestry Service for f i e l d assistance. Assistance and equipment in establishment of the climatological network was provided by Mr. J. R. Marshall, B. C. Department of Agriculture, Agroclimatology Sector, Canada Land Inventory. The author is grateful to the Canadian Forestry Service for educational leave to undertake graduate studies, financial assistance while attending university, and use of department f a c i l i t i e s , and to the B. C. Fish and Wildlife Branch for the provision of equipment. - iv - TABLE OF CONTENTS Page ABSTRACT i ACKNOWLEDGEMENTS i i i TABLE OF CONTENTS iv LIST OF TABLES v i LIST OF FIGURES v i i INTRODUCTION 1 JUSTIFICATION FOR THE STUDY 1 OBJECTIVES 2 METHODS 3 The Approach 3 The Variables 4 The System 5 The Components 7 The Functions • • 7 The Analytical Methods 10 THE STUDY AREA 12 ANALYSIS OF PLANT GROWTH 18 COMPONENTS OF TREE GROWTH 18 Height Growth 18 Crown Growth 21 Diameter Growth 26 Volume Growth 27 - v - Page COMPONENTS OF SHRUB GROWTH 27 Crown Diameter Growth 29 Annual Twig Production 35 COMPONENTS OF GRASS AND FORB GROWTH 39 Rate and Pattern of Growth 39 Total Grass and Forb Production 44 ANALYSIS OF PLANT COMPETITION 46 Components of Tree Competition 46 Components of Shrub Competition 48 Components of Grass and Forb Competition 53 THE MODEL 60 STRUCTURE 60 The Main Program 61 Simulation of Tree Growth 64 Simulation of Understory Growth 73 CURRENT STATUS OF THE MODEL 86 OUTPUT 86 Validation 88 Tree Growth Simulation 89 The Vegetative Community Simulation 99 POTENTIAL FOR APPLICATION 115 BIBLIOGRAPHY 117 APPENDIX I 120 APPENDIX II 122 APPENDIX III 123 - v i - LIST OF TABLES Table Page 1. The degree of var i a b i l i t y found on seven 1/10-th acre Douglas-fir sample plots 16 2. The degree of var i a b i l i t y found within a 1/10-th acre Douglas- f i r plot having a density of 500 stems per acre 16 3. Maximum and minimum densities found for the most commonly occurring shrub species 17 4. Variability found in current annual growth for Agropyron, Poa and forbs in the absence of tree and shrub shade 17 5. Comparative productivity of Agropyron, Poa and forbs growing in association with Amelanchier, Ceanothus and Shepherdia. . . . 57 6. Output at lowest level of detail for shrubs, grasses and forbs. . 87 7. Comparison of simulated and actual stand volumes measured on the study area 98 8. Comparison of selected mean tree parameters for calculation intervals of 2 and 10 years 99 9. Comparative productivities of wood, Amelanchier, Agropyron and forbs for two Douglas-fir stands with 2224 and 247 stems per acre and site index 60 113 - v i i - LIST OF FIGURES Figure Page 1. The system and i t s levels of organization 6 2. Components of the system 8 3. Study area showing the location and extent of the Pseudotsuga- Agropyron and Pseudotsuga-Poa communities 14 4. Relationship between height and age for dominant Douglas-fir . 20 5. Height frequency distribution for 20-year-old open-grown Douglas-fir 21 6. Relationship between branch length and height above branch base 22 7. Relationship between horizontal branch length and total branch length 23 8. Relationship between height to maximum crown width and total tree height 24 9. Relationship between height to base of l i v e crown and maximum crown width 25 10. Relationship between diameter at breast height and the product of crown area and tree height minus 4.5 feet 26 11. Measurement of shrub height 28 12. Crown diameter to age relationship for Amelanchier 31 13. Simulated population of Amelanchier 32 14. Crown diameter to age relationship for Ceanothus 32 15. Simulated population of Ceanothus 33 16. Crown diameter to age relationship for Shepherdia 33 17. Relationship of shrub diameter to age. A: Symphoricarpos B: Rosa C: Prunus 34 18. Relationship between weight of annual twig production and shrub area. A: Amelanchier B: Ceanothus C: Shepherdia 36 - v i i i - Figure Page 19. Relationship between weight of annual twig production and shrub diameter. A: Prunus B: Rosa C: Symphoricarpos 37 20. Current annual growth of Agropyron by weekly intervals. . . . 41 21. Current annual production of forbs by weekly intervals. . . . 41 22. Selected relationships between current annual growth and carry- over for Agropyron. A: Production for weeks 2, 5 and 10 B: Production for weeks 16 and 17 and the control plots. . . . 42 23. Plot of the 'a' and 'b' variables from the equation GAG = a x TANH (Co x b) expressed as a function of weeks since the i n i t i a t i o n of spring growth. . 43 24. Relationship between the number of Ceanothus and crown closure of trees 50 25. Relationship between the number of Symphoricarpos and crown closure of trees 50 26. Theoretical relationship between number of Prunus and Rosa and crown closure of trees 51 27. Relationship between Agropyron production and crown closure of trees 54 28. Relationship between forb production and crown closure of trees 54 29. Relationship between combined Calamagrostis, Koeleria and Bromus production and crown closure of trees 54 30. Definition of zones of influence for large shrub species. . . . 56 31. Response of Agropyron and forb production to Prunus density. . . 59 32. Flow chart of subroutines showing optional pathways 62 33. Simplified flow chart of main program showing i t s control over optional pathways through the model 63 34. Simplified flow chart of tree growth subroutines 65 35. Array coding for two Douglas-fir trees occupying growing space. . 70 - ix - Figure Page 36. Graphic representation of the return of portions of tree crowns crossing the plot boundary 72 37. Arrangement of arrays showing the relationship between tree, shrub and grass and forb arrays 74 38. Simplified flowchart of shrub, grass and forb growth (understory subroutines) 76 39. Relationship between Agropyron production and Prunus density by shrub age 85 40. Comparison between simulated volume and DBH and B.C. Forest Service volume and DBH taken from V.A.C. 1012, medium site . . 91 41. Comparison between simulated volume and DBH and B.C. Forest Service volume and DBH taken from V.A.C. 1013, low site. . . . 92 42. Comparison of Goulding's and my simulated gross cubic foot volume per acre for site index 150 94 43. Comparison of Goulding's and my simulated gross cubic foot volume per acre for site index 120 95 44. Comparison of Goulding's and my simulated gross cubic foot volume per acre for site index 90 96 45. Comparison of Goulding's and my simulated mean DBH for site index 120 97 46. Simulated effect of tree crown closure on Amelanchier number and production 103 47. Simulated response of shrub mortality and production response to changing crown closure for a shade intolerant and an intermediate shade tolerant species. A: Prunus B: Symphoricarpos 104 48. Comparison of simulated Agropyron production for site index 60 with 2224, 1112 and zero trees per acre 105 49. Comparison of simulated forb and Calamagrostis and Koeleria production response to tree crown closure in the presence and absence of shrubs 107 50. Effect of forest stand density and site index on forest crown closure 109 - X - Figure Page 51. Trade-off between wood and Agropyron production 110 52. Trade-off between Agropyron production and annual twig production of Amelanchier I l l - 1 - GROWTH SIMULATION OF TREES, SHRUBS, GRASSES AND FORBS ON A BIG-GAME WINTER RANGE INTRODUCTION The purpose of the study i s to develop a means of predicting the effect of plant community development on ungulate food production. The method used i s computer simulation of plant growth and competition. Abstract mathe- matical representation of the system in a computer allows (1) incorporation of an otherwise prohibitive number of inter-relationships, (2) manipulation and study not feasible in real l i f e , and (3) representation of years of plant community development in seconds. The simulation model to be constructed would attempt to duplicate, albeit in a simpler manner, the growth and competitive interactions of trees, shrubs, grasses and forbs. JUSTIFICATION FOR THE STUDY Quantitative assessment of the land's capability to produce wood and ungulate food i s essential for the rational solution of forestry-wildlife conflicts and maximization of land productivity. The number and complexity of interactions among individual plants and species necessitates a large and complex bookkeeping system i f more than an extremely superficial and often incomplete assessment of the interactions i s to be made. The primary application of the model would be the assessment of productive capability for wood, shrubs, grasses and forbs under different - 2 - plant community structures and isolation of c r i t i c a l interactions affecting productivity. The a b i l i t y to simulate tree growth alone allows the model to be used for estimations of growth and yield and other related forestry problems. Growth, yield and response to competition under different spacing patterns, stand densities and species composition should be capable of being tested. The model should approximate the development of mixed species plant communities and provide estimates of (1) mortality, height and diameter frequency distributions, crown closure, height to base of live crown, crown width and volumes for trees, (2) mortality, crown diameter frequency d i s t r i - butions and production for shrubs and (3) mortality and production for grasses and forbs. Knowledge of inter- and intra specific dynamics w i l l allow assessment of the implications of management for wood production on ungulate food production, and testing of strategies designed to increase yields of wood, browse, grass and forbs. OBJECTIVES The objectives of the study were to: (1) Quantitatively assess the capability of land to produce wood, browse, grass and forbs. (2) Assess the implications of management for wood production on range carrying capacity for ungulates. (3) Allow formulation and testing of strategies of plant community manipulation designed to increase yields of wood, browse, grass and forb production. - 3 - (4) Determine trade-off functions between wood and ungulate food production. The model would be structured to allow general application through the inclusion of additional growth and competitive functions. However, for i n i t i a l development and testing of i t s predictive capability, application was restricted to two plant communities on the Wigwam big-game winter range in the East Kootenay D i s t r i c t of British Columbia. METHODS The basic structure of the model and the components of tree growth and competition incorporate the approach taken by Mitchell (1967) in the Simulation of the Growth of Even-Aged Stands of White Spruce. Determination of the growth and competitive functions, and construction and programming of the model were performed by the investigator. The model employs empiri- ca l l y derived functions, three dimensional spatial distribution of aerial growing space, and normal random deviates with specified means and standard deviations (henceforth termed "normal random deviates") to express genetic va r i a b i l i t y in situations where relationships are incapable of rigorous solution or data are incomplete. The Approach Definition of the basic processes operating within the system (the vegetative ecosystem of the Wigwam big-game winter range) was approached on the basis of an experimental components analysis (Holling, 1963) which implies that a process can be explained by the action and interaction of a number of - 4 - discrete components. Each process i s studied individually but in such a manner that i t can be integrated into a biologically r e a l i s t i c whole. The achievement of a r e a l i s t i c representation of the system under consideration depends on the attainment of a sufficient degree of: (1) Realism, the ab i l i t y of the model to duplicate the general form of the real system. (2) Precision, the a b i l i t y to predict the time course of the variables. (3) Resolution, the number of attributes of the system represented in the model. The diversity and size of the system precluded detailed examination of a l l components; however, the model adequately represents those aspects regarded as essential. The Variables The current variables used in the model include age, site quality, plant community, species composition, density, competition and inherent biological v a r i a b i l i t y . Such variables as water regimes, root competition and grafting, phytotoxicity and damaging agencies were not investigated due to their complexity. Age - The maximum simulation period is 100 years with a maximum of 20 calculation intervals. Both simulation period and calculation interval are variable within the limits prescribed. Site Quality - Site index of Douglas-fir is used as the integrated expression of environmental factors influencing plant growth. - 5 - Plant Community - The model is capable of handling two plant communities, a Pseudotsuga-Agropyron and a Pseudotsuga-Poa community. Species Composition - Due to the large number of plant species on the study area, only the most commonly occurring species are treated individu- all y . They include Pseudotsuga menziesii, Amelanchier a l n i f o l i a , Ceonothus sanguineus, Shepherdia canadensis, Prunus emarginata, Rosa nutkana, Symphoricarpos albus, Agropyron spicatum, Poa compressa and scabrella, Festuca idahoensis, Calamagrostis rubescens and Koeleria cristata. Forbs were treated as a group rather than as separate species. Density - Variable density of a l l species can be accommodated. Competition - The degree of competition i s indirectly controlled through changes in density. The System For the purpose of the study, the system was defined as the vegetative ecosystem operating on the Wigwam big-game winter range. It was classified into subsystems on the basis of the concept of levels of organization (Odum and Odum, 1959). These include the vegetative ecosystem (System), plant communities (Subsystem 1), populations (Subsystem 2), organisms (Subsystem 3), organ systems (Subsystem 4) and the components or variables that affect the development of the organ systems (Figure 1). The model incorporates the concept that the internal forces moulding the development of the ecosystem are generated by individual organisms, be they trees, grasses, shrubs or forbs; hence the individual plant forms the basis unit of simulation. Emphasis was placed on the growth and WIGWAM BIG-GAME WINTER RANGE SYSTEM Subsystem 1 Subsystem 2 Subsystem 3 Subsystem 4 Components vegetative ecosystem Pseudotsuga-Agropyron community other ecosystems Pseudo tsuga-Po a community trees ^ other Douglas-fir shrubs ^ other Ceanothus grasses forbs other Agropyron 1 branch growth \ crown crown volume growth compet itive status height growth diameter growth competitive status annual twig growth competitive status a l l forbs 1 crown i I annual growth competitive status Figure 1. The system and i t s levels of organization. - 7 - competitive a b i l i t y of the few species which were judged to be dominant, the theory being that these species largely control the community and thereby the occurrence of rarer species (Odum and Odum, 1959). The growth and competitive status of individual plants was expressed through the development of their organ systems, namely, crowns and stems. The components determining crown and stem development were the lowest level of organization intensively investigated. Each level of organization repre- sents the components of the next higher level. The Components Isolation of the components thought to be important features of the system was accomplished by constructing a simplified flow chart of the system (Figure 2). The boxes represent the components investigated. The variables associated with each component are too numerous to l i s t by individual com- ponents. They include such factors as age, species, relative spatial distribution and density, growth rates, crown growth and size, crown closure of trees and shrubs, competitive a b i l i t y , inherent biological v a r i a b i l i t y , unexplained v a r i a b i l i t y and environmental factors, including s o i l and climate. The arrows depict the direction and flow of interactions in the model. The Functions Since the model predicts plant community development, the functions derived must, of necessity, reflect a time-course development, or be directly and easily related to some other variable exhibiting a time-course develop- ment. In addition, the functions should be expressed in unambiguous terms - 8 - __| PLANT COMMUNITY SITE PLANT QUALITY COMMUNITY J PLANT COMMUNITY SUPPRESSION AND DEATH TREE HEIGHT GROWTH CROWN GROWTH DIAMETER AND VOLUME CROWN CLOSURE SUPPRESSION AND DEATH SHRUB SPECIES AND DENSITY CROWN GROWTH SURFACE AREA AND PRODUCTION CROWN CLOSURE OF TREES AND SHRUBS SUPPRESSION, DEATH AND SPECIES CHANGE GRASS AND FORB SPECIES CROWN GROWTH ANNUAL PRODUCTION Figure 2. Components of the system. - 9 - i f t h e y a r e t o be a p p l i e d e l s e w h e r e . F o r i n s t a n c e , b a s a l a r e a o r age o f a f o r e s t s t a n d u s e d as a measu re o f c o m p e t i t i o n a r e somewhat ambiguous s i n c e t h e y o n l y i m p l y , and do n o t s p e c i f y , c rown c l o s u r e o r d e g r e e o f c rown c o m p e t i t i o n . D e s p i t e a c o n s i d e r a b l e vo lume o f l i t e r a t u r e , i t was deemed a d v i s a b l e t o d e r i v e a l l n e c e s s a r y f u n c t i o n s t o e n s u r e t h a t t h e y a d e q u a t e l y r e p r e s e n - t e d (1) t h e a c t i o n s and i n t e r a c t i o n s o c c u r r i n g on t h e p a r t i c u l a r s t u d y a r e a , and (2) a t i m e - c o u r s e d e v e l o p m e n t . The f u n c t i o n s d e r i v e d by M i t c h e l l (1967) f o r w h i t e s p r u c e g row th met t h e r e q u i r e m e n t s o f t h i s s t u d y and h e n c e we re u s e d as a b a s i s f o r d e r i v a t i o n o f s i m i l a r f u n c t i o n s f o r D o u g l a s - f i r . Mean h e i g h t , d i a m e t e r and s u r f a c e a r e a ( F e r g u s o n , 1968) as w e l l as mean vo lume were u s e d as m e a s u r e s o f s h r u b g r o w t h . Non - random s a m p l i n g was u s e d t o e v a l u a t e v a r i a b i l i t y i n d e n s i t y o f a l l s p e c i e s ( L y o n , 1968) as w e l l as t h e u s e o f l / 1 0 t h - m e t e r p l o t s t o d e t e r m i n e f l o r i s t i c c o m p o s i t i o n o f s h r u b s , g r a s s e s and f o r b s ( D a u b e n m i r e , 1 9 5 9 ) . P r o d u c t i o n o f g r a s s e s and f o r b s was d e t e r m i n e d on b o t h s q u a r e - y a r d and l / 1 0 t h - m e t e r p l o t s . R e s p o n s e o f u n d e r - s t o r y v e g e t a t i o n t o t he p r e s e n c e o f a f o r e s t canopy h a s been r e p o r t e d i n numerous s t u d i e s ( Y o u n g , M c A r t h u r and H e n d r i c k , 1 9 6 7 ; J a m e s o n , 1 9 6 7 ; A n d e r s o n , L o u c k s and S w a i n , 1 9 6 9 ; and o t h e r s ) . I n t h e v a s t m a j o r i t y o f t h e s e s t u d i e s , s t a n d d e v e l o p m e n t was e x p r e s s e d as number o f s tems p e r u n i t a r e a , b a s a l a r e a o r s t a n d a g e , r a t h e r t h a n as a c o m p l e t e s t a n d d e s c r i p t i o n i n c l u d i n g s u c h f a c t o r s as c rown c l o s u r e and c rown w i d t h t o d i a m e t e r r a t i o s . C o n s e q u e n t l y , t h e d e g r e e o f c o m p e t i t i o n e x e r t e d b y t h e f o r e s t s t a n d i s u n c e r t a i n . The most d e t a i l e d and a p p l i c a b l e s t u d y i s t h a t o f Kemper (1971) c o n d u c t e d on P r e m i e r R i d g e i n t h e E a s t K o o t e n a y D i s t r i c t o f B r i t i s h C o l u m b i a . - 10 - Kemper (1971) expressed stand development in terms of both age and crown closure and hence his relationships can be applied elsewhere. Competition between individual understory plants have been studied by Donald (1951), Hozumi, Koyama and Kira (1955), Mead (1968) and others, using spatial relationships as a measure of competition. Determination of competitive response between understory plants in this study was based on both plant density and spatial relationships, depending on the size of the individual plants. Density measures were made where the individual plants were small, and spatial relationships were used where the individual plants were large. The Analytical Methods In the analyses, the components were segregated into those deter- mining (1) growth and (2) competitive response. The components of growth should ideally be derived from individuals or populations not subject to competition. In the absence of competition, growth is a direct expression of age, site quality and genetics. In actuality, i t was not always possible to derive the components of growth for individuals or populations completely free from competition. The degree of competition to which an individual was subjected was used to adjust i t s growth rate during simulation. Measurement of competitive stress was based on the availability of aerial growing space and the degree of light interception. While this method does not take root competition into account, and hence has obvious limitations, i t is easily measured and appears to be a f a i r l y good indirect measure of competition. - 11 - If root spread is approximately proportional to crown width, as shown by Smith (1964) for Douglas-fir and other tree species, then crown competition can be used as an approximation of root competition. In considering com- petition, i t was necessary to distinguish between inter- and intra-specific competition. In intra-specific competition, competitive advantage was assumed to be proportional to growth rate. In inter-specific competition, competitive advantage was assigned on the basis of plant height, trees were assumed to have the greatest competitive advantage, followed by shrubs, grasses and f i n a l l y forbs. While this i s obviously a simplistic approach which ignores such factors as density, age, root competition and phytotoxicity, i t was deemed acceptable for the i n i t i a l development of the model. The functional relationships shown throughout this paper were derived empirically except where otherwise shown. Direct descriptive techniques (Jensen, 1964) were used in curve f i t t i n g . The expected spatial relationship between dependent and independent variables was i n i t i a l l y expressed graphically, and then algebraically. Where a single algebraic expression could not be f i t t e d , two or more expressions were used. In these cases the expressions were f i t t e d to pass through common points. Because of the nature of the data, the change from one to another equation i s often quite abrupt. Iterative techniques were used to reduce algebraically introduced curve form bias. Following each iteration the equation was solved for the predicted Y values. Simple linear regressions of the form Y = a + bX where: Y= predicted Y value X= actual Y value were used to select the best f i t t i n g equation. - 12 - In cases where the intensity of association of actual to predicted 2 Y values was low (R less than 0.7), normal random deviates with specified means and standard deviations were generated. Generation of normal random deviates along the f i t t e d curves allowed close approximation of naturally occurring v a r i a b i l i t y and circumvented the problems normally associated with inconclusive relationships. Where plant community structure precluded derivation of relation- ships required for the model, theoretical functions were constructed based on the response of similar species. For example, the response of Amelanchier a l n i f o l i a to increasing crown closure of Douglas-fir could not be determined due to the lack of sufficient areas on which the two species occurred in association. The function derived for Ceonothus sanguineus was applied in i t s place. THE STUDY AREA The study was conducted on the Wigwam big-game winter range located between the Elk and Wigwam rivers (latitude 49° 15' N, longitude 115° 10' W), near Elko in the East Kootenay Di s t r i c t of British Columbia. Climatically, the area corresponds to Kopens' (Trewartha, 1954) Dsk zone. The average total annual precipitation at Elko is 19.6 inches. Geologically, the area is highly diverse. It includes such s u r f i c i a l deposits as glacial t i l l s , lacustrine s i l t s , c o l l u v i a l deposts, talus slopes, outwash gravel terraces and a glacial outwash delta. The range supports significant wintering populations of elk, mule deer and Rocky mountain bighorn sheep. - 13 - The study was centered on two plant communities occurring on the winter range, a Pseudotsuga-Agropyron and a Pseudotsuga-Poa community (Figure 3). The major plant species occurring in the Pseudotsuga-Agropyron community included Pseudotsuga menziesii, Acer glabrum, Shepherdia canadensis, Prunus emarginata, Rosa nutkana, Juniperis horizontalis, Apocyanum androsaemifolium, Agropyron spicatum, Calamagrostis rubescens, Koeleria cristata, Festuca idahoensis t Achillea millefolium, Aster conspicuus, Erigeron spp., Monarda fistulosa and Phlox caespitosa. The major plant species occurring in the Pseudotsuga-Poa community included Pseudotsuga menziesii, Acer glabrum, Populus tremuloides, Amelanchier a l n i f o l i a , Ceanothus sanguineus, Rosa nutkana, Symphoricarpos albus, Berberis repens, Poa compressa and scabrella, Calamagrostis rubescens, Stipa columbiana, Bromus tectorum, Aster conspicuus, Balsamorhiza sagittata, Erigeron spp., Fragaria spp. , and Penstemon spp. As a result of a number of severe forest f i r e s , the last occurring in 1931, the plant communities exhibit a wide diversity in age, plant density, productivity and species composition. While no attempt was made to describe the var i a b i l i t y in d e t a i l , i t would be worthwhile to present a general description of the communities and to show the var i a b i l i t y found on the sample plots. The plant communities on the area are very similar to those described for the Pseudotsuga menziesii zone of McLean (1969) and comparable to those of the lower grassland zone of Tisdale (1947) , the Agropyron spicatum (grassland) associations of Brayshaw (1955, 1965) and the Agropyrion spicati order, alliances Agropyretum spicati and Agropyro (spicati) - Juniperetum scopulorum of Beil (1969). - 14 - Pseudotsuga - Agropyron = Pseudotsuga - Poa 115 0 5 ' W ^ ^ ^ ^ = Scale: 1:55,000 Figure 3. Study area showing location and extent of Pseudotsuga-Agropyron and Pseudotsuga-Poa communities. - 15 - The vegetation i s characterized by large grassland openings, the predominant species being Agropyron spicatum on coarse dry soils and Poa compressa and scabrella on the finer textured wetter s o i l s , interspersed with stands of Douglas-fir. Of the major shrub species, Amelanchier a l n i f o l i a , Prunus emarginata and Shepherdia canadensis occur predominantly in the Agropyron grasslands while Ceanothus sanguineus, Rosa nutkana and Symphoricarpos albus occur in the Poa grasslands. The predominant species occurring beneath Douglas-fir stands include Symphoricarpos albus, Calamagrostis rubescens and Koeleria cristata. Douglas-fir occurs in stands ranging in age from 20 to 130 years, in density from single scattered trees to approximately 2000 stems per acre and in site index (base 100 years) from 50 to 80. Table 1 shows the va r i a b i l i t y found on seven 1/lQ^th acre plots which were measured to provide a basis for determining the predictive accuracy of the model. A l l values were converted to a per acre basis. The v a r i a b i l i t y among individual trees within the plot having a density of 500 trees per acre is shown in Table 2. Measurements of density and productivity in shrub and grass stands were made to evaluate growth capability and the effect of competition and hence can not be used to properly describe the va r i a b i l i t y occurring on the study area. Table 3 shows the approximate variability in density found for the most commonly occurring shrub species. The distribution of shrub species was found to be highly variable, depending on plant association and particular species. The presence of trees appeared to control both the distribution and density of shrubs. In the absence of trees, Amelanchier, Ceanothus, Shepherdia and Symphoricarpos individuals appear to be independent and randomly distributed while Prunus and Rosa appear to occur in clones. - 16 - Table 1. The degree of vari a b i l i t y Douglas-fir sample plots. Variable Number of trees per acre 1" + DBH Volume -cu f t per acre 1" + DBH DBH -ins Height - f t Basal area -sq f t Basal area -sq f t per acre Total age -yrs Crown width/DBH found on seven 1/10-th acre Values Minimum Average Maximum 20 253 500 357 1344 2121 2.4 7.33 16.6 17.0 37.8 68.5 0.031 0.337 1.503 21.9 85.2 124.2 72 92 106 0.978 1.544 2.620 Table 2. The degree of v a r i a b i l i t y found within a 1/10-th acre Douglas- f i r plot having a density of 500 stems per acre. Variable Values Minimum Average Maximum SD CV % Height - f t 20.0 35.5 61.5 10.13 28.5 DBH - i n 2.6 6.3 15.5 2.9 45.4 Basal area -sq f t 0.037 0.26 1.31 0.26 98.3 Volume -cu ft 0.32 4.03 26.4 4.8 119.0 CW/DBH 0.978 1.53 2.37 0.33 21.4 Age -yrs 56 95 111 14.0 14.8 Where: SD is standard deviation CV i s coefficient of variation CW is crown width DBH i s diameter at breast height - 17 - Table 3. Maximum and minimum densities found for the most commonly occurring shrub species. Species Amelanchier a l n i f o l i a Ceanothus sanguineus Shepherdia canadensis Density per 1/40 acre Minimum Maximum 0 0 0 30 42 44 Prunus emarginata Rosa nutkana Symphoricarpos albus Density per sq yd Minimum Maximum 0 0 0 18 16 35 Measurement of grasses and forbs was restricted to the weight of current annual growth and carryover. Again, the variability i n production was high. Table 4 shows,the maximum and minimum weights of current annual growth measured after the cessation of growth in stands not subject to shading by trees or shrubs. Table 4. Variability found in current annual growth for Agropyron, Poa and forbs in the absence of tree and shrub shade. Species Production gms/sq yd Minimum Maximum Agropyron 13.5 66.3 Poa 10.1 72.3 Forbs 0.3 22.4 - 18 - ANALYSIS OF PLANT GROWTH The primary aim i n the plant growth portion of the simulation was to define patterns of growth, variation in growth rates due to genetic and unexplained variation, and growth rate as a function of site quality, age and competition. COMPONENTS OF TREE GROWTH Several tree growth simulation models have been developed, using different approaches (Newnham, 1964; Lee, 1967; Mitchell, 1967; Lin, 1969; Bella, 1970; Arney, 1971). The method adopted was based on Mitchell's (1967) approach because i t appeared to be r e a l i s t i c in a biological sense and also allowed a highly detailed bookkeeping of occurrences in each unit of growing space. The components investigated included site quality, height, crown, diameter and volume growth, height to maximum crown width and height to base of li v e crown. Site quality was measured indirectly through i t s effect on tree growth by determining site index of dominant and codominant Douglas-fir trees (B.C.F.S., Field Pocket Manual). No attempt was made to explain site quality in terms of environmental factors. Height Growth Height-age curves, used here to define the pattern of height growth, were adjusted by site index and normal random deviates drawn from a measured height frequency distribution to give the growth rate of individual simulated trees. This procedure allowed the generation of populations of simulated trees having the same site indices and height frequency distributions as measured stands. - 19 - Height-age curves were derived by conducting stem analyses on five open-grown trees selected as being representative of the maximum attainable growth rate. The average height (HT) at each five year interval (Figure 4) was used to derive the height-age relationship (Equations 1 and 2). The stem analyses were conducted on open-grown trees to remove the effect of competition; however, growth rate can be reduced to allow for the effect of competition during the course of simulation. The five trees used to derive the height-age curve (Equations 1 and 2) had a mean site index of 76 feet at 100 years. To adjust the curve for a different site index, the equations are multiplied by the new site index divided by 76. This procedure adjusts the curve either upward or downward depending on the magnitude of the new site index. The plotted "average" line on the height-age curve (Figure 4) does not exhibit the expected decline in growth rate with advanced age. This discrepancy is probably attributable to the small number of sample trees. Until such time as the number of sample trees is increased, the B. C. Forest Service site index curves (Forestry Handbook for British Columbia, 1971) for interior Douglas-fir will be used in the model. The variability in growth rate of individual trees was determined by constructing a height frequency distribution from two hundred 20-year-old open-grown Douglas-fir trees (Figure 5). Normal random deviates drawn from the distribution were used to adjust the growth rate of individual trees, thereby duplicating the naturally occurring variability. The somewhat skewed distribution probably resulted from browsing damage to the trees in the 2-, 4- and 6-foot height classes. Sections taken through the pith showed that leader damage had occurred over a number of years. - 20 - i f Age _< 45 y r s HT = 1 8 . 0 5 ( S I N ( A g e(11 / 5 0 ) - I I /2) + 1) f t (1 ) i f Age > 45 y r s HT = 1.87 + ( 0 . 7 4 0 6 6 ) ( A g e ) f t (2) w h e r e : N o . o f Obs . = 89 R 2 = 0 . 9 2 5 SE, , - 5 . 8 1 f t E 90 r- F i g u r e 4 . R e l a t i o n s h i p be tween h e i g h t and age f o r dom inan t D o u g l a s - f i r . - 21 - 50 40 * 30 o g Er 20 CD 10 0 2 4 6 8 10 12 14 16 18 20 22 2 4 Height Class - f t Figure 5 . Height frequency distribution for 20-year-old open-grown Douglas-fir. Crown Growth Prediction of crown expansion was based on the relationship derived between branch length (BL) and height above the branch base (HTAB) (See Appendix II for definition of terms). The relationship was obtained by measuring total branch length and tree height above the branch base on 115 trees, both juvenile and mature (Figure 6, Equation 3). Branches were measured at and above the point of maximum crown width. - 22 - BL = (0.98)(HTAB 0 , 7) f t (3) where: No. of Obs. = 404 R2 = 0.920 SE W = 1.18 f t 10 40 30 40 Height above Branch Base - f t 50 60 Figure 6. Relationship between branch length and height above branch base. Crown width was measured as the vertical projection from the edge of the crown. Since branch angle and total branch length determine crown width, i t was necessary to convert total branch length to horizontal branch length (HBL) (Figure 7, Equation 4). Equation 4 represents potential crown radius in the absence of competition, but where branches compete for growing - 23 - HBL = ( 0 . 9 ) ( B L ) - ( 3 . 3 ) ( ( B L / 2 0 ) 3 ) f t (4) w h e r e : N o . o f Obs . = 65 R 2 = 0 . 8 9 6 S E _ = 0 . 9 0 f t E T o t a l B r a n c h L e n g t h - f t F i g u r e 7 . R e l a t i o n s h i p b e t w e e n h o r i z o n t a l b r a n c h l e n g t h and t o t a l b r a n c h l e n g t h . s p a c e a t p o i n t s o f c rown c o n t a c t , p o t e n t i a l c rown r a d i u s w i l l n o t be r e a l i z e d . B r a n c h c o m p e t i t i o n i s d i s c u s s e d i n t h e M o d e l s e c t i o n . S i n c e s i m u l a t i o n o f t r e e c rowns was r e s t r i c t e d t o t h e v i s i b l e c rown a r e a ( t h e a r e a o f t h a t p o r t i o n o f t h e c r o w n w h i c h f o rms a p h o t o g r a p h i c image when v i e w e d d i r e c t l y f r om a b o v e ) , i t was n e c e s s a r y t o d e f i n e t h e p o i n t o f maximum c r o w n w i d t h . P r e d i c t i o n o f t h e h e i g h t o f maximum c rown w i d t h was b a s e d - 24 - on the measurement of total tree height (HT) and height to maximum crown width (HTCW max) on 94 open-grown Douglas-fir (Figure 8 , Equations 5 and 6). Equations 5 and 6 apply only to those trees free from competition. Otherwise, height to maximum crown width i s simulated. i f HT < 30 f t HTCWmax = (0.06)(HT) + ( 0 . 0 0 8 )(HT 1 , 9) f t (5) i f HT > 30 ft HTCWmax = - 5 . 5 + (0.425)(HT) f t (6) where: N o . Obs. = 94 D 2 = 0 . 8 2 8 SE„ = 2 . 6 3 f t Figure 8 . Relationship between height to maximum crown width (HTCW max) and total tree height. - 25 - E s t i m a t i o n o f h e i g h t t o t h e b a s e o f t h e l i v e c rown ( H T b l c ) as a f u n c t i o n o f h e i g h t t o maximum c rown w i d t h c i r c u m v e n t s t h e r e s t r i c t i o n imposed by s i m u l a t i n g o n l y t h e v i s i b l e c rown a r e a . Measu remen ts we re made on 50 t r e e s s e l e c t e d f r om v a r i o u s s t o c k i n g d e n s i t i e s and age c l a s s e s ( F i g u r e 9 , E q u a t i o n s 7 and 8 ) . A l l samp le t r e e s we re h i g h l i n e d ; t h a t i s , t h e i r l o w e r b r a n c h e s had b e e n k i l l e d t h r o u g h b r o w s i n g by u n g u l a t e s . Where t r e e s a r e h i g h l i n e d , H T b l c i s a p p r o x i m a t e l y 7 f e e t , i f HTCWmax £ 10 f t H T b l c = 0 . 0 f t (7) i f HTCWmax > 10 f t H T b l c = - 10 + HTCWmax (8) w h e r e : No . o f O b s . = 50 ,2 R S E T = 0 . 6 9 4 = 9 . 8 4 f t o u u CU !> cu M CO m •a • H 50 40 - 30 - 20 10 - 0 10 20 30 40 50 60 H e i g h t t o Maximum Crown W i d t h - f t F i g u r e 9 . R e l a t i o n s h i p b e t w e e n h e i g h t t o b a s e o f l i v e c rown and h e i g h t t o maximum c rown w i d t h . - 26 - Diameter Growth Prediction of diameter at breast height (DBH) was based on the derived relationship of DBH against tree height minus 4.5 feet (breast height) and crown area (CA) (Figure 10, Equation 9). The relationship DBH = ( 0 . 1 6 5 ) ( ( C A ( H T - 4 . 5 ) ) 0 , 4 8 ) - ( 0 . 0 0 1 1 ) ( C A ( H T - 4 . 5 ) ) i n s (9) where: No. of Obs. = 299 R2 = 0 . 9 0 8 SE„ = 1 . 0 8 i n s Figure 10 . Relationship between diameter at breast height and the product of crown area and tree height minus 4 . 5 feet. - 27 - was derived from open-grown, open, normal and overstocked stands from various age classes. Crown area was calculated from four measures of crown radius taken at right angles. The data were not analyzed by individual stocking or age classes. Volume Growth Volume (V) estimations were based on the application of the simulated tree height and DBH to the B. C. Forest Service volume equations for Interior Douglas-fir (Browne, 1962). No attempt was made to localize the equation, or to estimate effects of dbh limits or decay, waste, and breakage. Log V = -2.734532 + 1.739418Log D + 1.166033 Log H (10) SE for single trees: ± 11.3 per cent L COMPONENTS OF SHRUB GROWTH The components of shrub growth investigated included site quality, height and crown growth and annual twig production. The species examined were Amelanchier a l n i f o l i a . Ceanothus sanguineus. Shepherdia canadensis, Prunus emarginata. Rosa nutkana and Symphoricarpos albus. Preliminary regressions of age and annual twig production against shrub height, volume, surface area and diameter growth indicated that crown diameter growth was the best independent variable. Shrub age was determined by making cross- sections of the stem, or where suckering was prevalent rootstocks, and counting the number of annual rings. Annual twig production was determined by taking the oven-dry weight (24 hrs at 105°C) of the current annual twig growth immediately after leaf f a l l . Shrub height was measured as height to - 28 - the highest part of the general crown profile (Figure 11). The average of Figure 11. Measurement of shrub height. two measures of crown width, taken at right angles, were used to calculate shrub diameter. Volume was calculated as the volume of a hemisphere with a radius equal to the shrub radius. Surface area was calculated as the surface area of a c i r c l e with a diameter equal to the shrub diameter. Large variations in rate of growth and small variations in site quality precluded definition of variations in growth rate due to si t e . Crown Diameter Growth As previously stated, two measures of crown diameter (D) taken at right angles, were made on each shrub and expressed as a function of age. The relationships are presented in Figures 12, 14, 16 and 17, and Equations 11 to 21. Amelanchier D = - 1 + (0.15)(Age) + (1 - Age/30) 1.996 where: No. of Obs. = 64 R2 = 0.471 SE„ = 1.246 f t (ID Ceanothus i f Age £ 40 yrs D i f Age > 40 yrs D 2.8(SIN(Age(E/60) - II/5.2) + .5) f t 4.1 + (0.016667)(Age) f t where: No. of Obs. = 96 ,2 R SE_ = 0.127 = 1.30 f t (12) (13) Shepherdia i f Age <_ 50 yrs i f Age > 50 yrs D = 4.5(SIN(Age(11/70) - II/4) + .6) f t D = 7.17 + (0.0046)(Age) f t where: No. of Obs. = 54 ,2 R SET = 0.438 = 1.287 f t (14) (15) - 30 - P r u n u s i f Age <_ 16 y r s i f Age > 16 y r s D = S IN(Age(n /18) - n/2.5) + 1) f t D = 2 . 0 f t w h e r e : N o . o f O b s . = 100 ,2 R = 0 . 4 8 8 = 0 . 2 2 8 f t (16) (17) R o s a i f Age <_ 16 y r s D i f Age > 16 y r s D SIN(Age(n /18) - n / 2 . 5 ) + 1) f t 2 . 0 f t w h e r e : N o . o f O b s . = 98 v 2 R = 0 . 1 6 6 = 0 . 4 4 5 f t (18) (19) S y m p h o r i c a r p o s i f Age <_ 18 y r s D i f Age > 18 y r s D 0 . 8 ( S I N ( A g e ( H / 2 6 ) - n / 6 ) + 1) f t 1.2 f t w h e r e : N o . o f O b s . = 48 ,2 R S E . = 0 .352 = 0 . 8 0 2 f t (20) (21) The p r e d i c t i o n o f c rown d i a m e t e r was c o m p l i c a t e d b y t h e f a c t t h a t t h e m e a s u r e d age f e l l s h o r t o f t h e t i m e p e r i o d (100 y e a r s ) u s e d i n t h e s i m u l a t i o n . S t e b b i n s (1951) s t a t e d t h a t t h e l i f e s p a n o f i n d i v i d u a l p l a n t s s p r o u t i n g f r o m r o o t s o r c rowns c a n n o t b e e s t i m a t e d b e c a u s e , b a r r i n g t h e i n f l u e n c e o f man , t h e y c a n o n l y b e k i l l e d b y d i s e a s e , c o m p e t i t i o n f r o m o t h e r p l a n t s o r b y r a d i c a l c h a n g e s i n h a b i t a t . He f u r t h e r s t a t e d t h a t i n s t a b l e p l a n t - 31 - communities seriously diseased plants are rare, so the age of the plant must approach that of the community i t s e l f . In the model, those species which exhibited sprouting from crowns or rootstocks, Amelanchier, Ceanothus, Prunus and Rosa, were, in the absence of competition, assumed to have a lifespan exceeding the simulation period. The remaining species, Shepherdia and Symphoricarpos, were replaced when the age of individual plants exceeded the maximum measured age. The application of normal random deviates, as shown in the simulated populations of Amelanchier and Ceanothus (Figures 13 and 15) having the same age distributions as the real populations shown in Figures 12 and 14, allows duplication of the naturally occurring v a r i a b i l i t y . Figure 12. Crown diameter to age relationship for Amelanchier. Age - y r s F i g u r e 1 3 . S i m u l a t e d p o p u l a t i o n o f A m e l a n c h i e r . 6 r- 20 40 60 80 100 Age - y r s F i g u r e 14 . Crown d i a m e t e r t o age r e l a t i o n s h i p f o r C e a n o t h u s . - 33 - 6 h Age - yrs Figure 15. Simulated population of Ceanothus. - 34 - Figure 17. Relationship of shrub diameter to age. A: Symphoricarpo B: Rosa C: Prunus - 35 - Annual Twig Production Prediction of the weight of annual twig production (WT) was based on the relationship between weight of the current year's production of twigs and shrub diameter (D). Shrub diameter was converted to area for Amelanchier, Ceanothus and Shepherdia to simplify modelling procedures. These species occupy and compete for specific volumes of growing space and hence may develop asymmetrical crowns. Weight of leaf production was not investigated, as fallen leaves do not contribute directly to the winter food supply of ungulates. The relationships are presented in Figures 18 and 19, and Equations 22 to 28. Data used to derive these relationships were collected from individuals free from competition. Amelanchier WT = (4.1) (Area) gms (22) where: No. of Obs. = 8 R2 = 0.981 SE^ =9.05 gms Ceanothus WT = 810 - (1.45454)(110 - Area) - (700)((1 - Area/110) 2* 7) (23) gms where: No. of Obs. = 10 R2 = 0.992 SE = 17.17 gms F i g u r e 1 8 . R e l a t i o n s h i p b e t w e e n w e i g h t o f a n n u a l t w i g p r o d u c t i o n and s h r u b a r e a . A : A m e l a n c h i e r B : C e a n o t h u s C : S y m p h o r i c a r p o s - 37 - Figure 19. Relationship between weight of annual twig production and shrub diameter. A: Prunus B: Rosa C: Symphoricarpos - 38 - . 4 . 1 , Shepherdia WT = 250 - (254.92) ((1 - Area/100) x) gms where: No. of Obs. = 10 R2 = 0.580 SE^ = 36.27 gms Prunus Rosa i f D < 1.37 WT = 0.4 + (0.6) (D) gms i f D > 1.37 WT - -8.8 + (7.1)(D) gms where: No. of Obs. = 20 R2 = 0.995 SE„ = 0.221 gms WT = 0.1 + (1.4)(D 1* 5) where: No. of Obs. = 20 IT SE_ 0.527 1.078 gms Symphoricarpos WT = (0.4) (D) gms where: No. of Obs. R2 SE„ 20 0.503 0.119 gms - 39 - COMPONENTS OF GRASS AND FORB GROWTH The components of grass growth investigated include rate and pattern of growth, carryover and total annual growth. Investigation of rate and pattern of growth was restricted to an Agropyron spicatum community. Measure- ments of carryover and annual growth were made on Agropyron spicatum, Poa compressa and scabrella, Festuca idahoensis, Stipa columbiana and Calamagrstis rubescens communities. Rate and Pattern of Growth Measurement of rate and pattern of Agropyron growth was made on an 80- by 80-ft enclosure containing an Agropyron stand free from shrub and tree competition. The experimental procedure was designed to allow the derivation of mathematical relationships describing both the shape and slope of the growth curves from the time of i n i t i a t i o n of spring growth until cessation of growth in the f a l l . Spring growth, as denoted by the germination of forbs and the obvious presence of new grass, was initiated in the last week of Apri l . The cessation of growth in the f a l l occurred in the second week of September, based on the maturation of Agropyron seed heads and a continuous period of 10 weeks of production measurements showing no upward trend. These production measurements were made during the course of the experiment. The procedures used may be summarized as follows: (1) Two hundred and thirty square-yard plots were laid out and their boundaries were strung with haywire. (2) Twenty control plots (2 sets of 10 plots) were not subjected to any treatment until cessation of growth in the f a l l (17 weeks after i n i t i a t i o n - 40 - of spring growth). The plots were then clipped to a height of lh inches and the clippings were separated into carryover and current annual growth. The clippings were then oven-dried and weighed. (3) The remaining 210 plots were clipped to a height of 1% inches prior to the i n i t i a t i o n of spring growth (April 1 to 3, 1970). The clippings (carryover) were oven-dried and weighed. (4) The treatments consisted of clipping and weighing the current annual growth. The plots (10 plots per treatment) in treatment 1 were clipped at the end of the f i r s t week (May 1), and in treatment 2, at the end of the second week (May 8), etc. The treatments were continued u n t i l the end of the 17th week (September 11), at which time growth had ceased. (5) A l l weights represent oven-dried weight (24 hrs at 105°C). (6) A completely randomized design was used in the allocation of control and treatment plots. Figures 20 and 21 show the mean and range in weight of current annual growth by weekly intervals for Agropyron and forbs. The wide variations in current annual growth within treatments for Agropyron can be reduced by plotting current annual growth (CAG) against carryover (C) by weekly intervals (Figure 22). The 17 curves, one for each week, fitt e d to the data have the general form CAG = aTANH(Cb) where "a" represents the maximum attainable growth and "b" represents the shape of the growth curve as a function of carryover. The use of this procedure assumes that carryover, in the absence of ut i l i z a t i o n by ungulates, - 41 - c o o 3 X) o H PH r-l CO 3 C 4-> c CU 3 60 r- 40 - 4! 20 00 J L J L J L J L J _ 3 5 7 9 11 13 15 Weeks s i n c e I n i t i a t i o n o f S p r i n g G r o w t h _L J _ 17 C o n t r o l F i g u r e 2 0 . C u r r e n t a n n u a l g r o w t h o f A g r o p y r o n by w e e k l y i n t e r v a l s . Weeks s i n c e I n i t i a t i o n o f S p r i n g Growth F i g u r e 2 1 . C u r r e n t a n n u a l p r o d u c t i o n o f f o r b s by w e e k l y i n t e r v a l s . - 42 - F i g u r e 2 2 . S e l e c t e d r e l a t i o n s h i p s be tween c u r r e n t a n n u a l g r o w t h and c a r r y - o v e r f o r A g r o p y r o n . A : P r o d u c t i o n f o r weeks 2 , 5 and 10 B : P r o d u c t i o n f o r weeks 16 and 17 and t h e c o n t r o l p l o t s - 43 - is an approximate measure of the productive capacity of the sit e . To simplify calculation and modelling procedures, both the "a" and "b" variables were expressed as a function of their respective week (Figure 23, Equations 29 to 31). variable 'a' i f Week _ 9 a = (2.833)(Week1,2) (29) i f Week 9 a = 38 + (11)TANH((Week - 9) (0.43)) (30) variable 'b' b = 0.037 - (0.016)(TANH((Week)(0.13))) (31) 60 r 40 • H U 20 'a' variable 'b' variable 0.002 • H U at > -J 0.037 2 4 6 8 10 12 14 16 Weeks since Initiation of Spring Growth Figure 23. Plot of the 'a' and 'b' variables from the equation CAG = aTANH(Cb); expressed as a function of weeks since the in i t i a t i o n of spring growth. - 44 - T h e s e f u n c t i o n s w e r e t h e n a p p l i e d i n t h e g e n e r a l e q u a t i o n and t e s t e d a g a i n s t a c t u a l w e e k l y p r o d u c t i o n . Growth was s l i g h t l y o v e r e s t i m a t e d f r o m week 1 t o 9 . The r e l a t i o n s h i p s shown i n e q u a t i o n s 29 t o 31 w e r e comb ined and a r e p r e - s e n t e d i n E q u a t i o n s 32 and 3 3 . i f Week _ 9 CAG - ( ( 2 . 8 3 3 ) ( W e e k 1 , 2 ) ) T A N H ( ( C X O . 0 3 7 - ( 0 . 0 1 6 ) ( T A N H ( ( W e e k ) ( 0 . 1 3 ) ) ) ) ) gms (32) i f Week 9 CAG = (38 + (11)TANH((Week - 9 ) ( 0 . 4 3 ) ) T A N H ( ( C ) ( 0 . 0 3 7 - ( 0 . 0 1 6 ) ( T A N H ( ( W e e k ) ( 0 . 1 3 ) ) ) ) ) gms (33) I n a p p l y i n g t h e s e e q u a t i o n s t o g r a s s s p e c i e s o t h e r t h a n A g r o p y r o n , i t was assumed t h a t t h e s p e c i e s d i f f e r e n c e s a r e e x p r e s s e d o n l y i n t e r m s o f maximum a t t a i n a b l e g r o w t h ( " a " v a r i a b l e ) . C o n s e q u e n t l y , o n l y e q u a t i o n s 29 and 30 w i l l r e q u i r e m o d i f i c a t i o n f o r s p e c i e s c h a n g e . The f o r e g o i n g r e l a t i o n s h i p s we re d e r i v e d f r o m d a t a c o l l e c t e d d u r i n g a s i n g l e g r o w i n g s e a s o n ( 1 9 7 0 ) . M o d i f i c a t i o n s o f t h e " a " v a r i a b l e w i l l accommodate v a r i a t i o n s i n a n n u a l g r o w t h . T o t a l G r a s s and F o r b P r o d u c t i o n T w e n t y - f o u r e n c l o s u r e s , e a c h c o n t a i n i n g 16 s q u a r e - y a r d p l o t s , and t h e 8 0 - by 8 0 - f o o t e n c l o s u r e we re u s e d t o measure t o t a l a n n u a l g r o w t h f o r A g r o p y r o n s p i c a t u m , P o a c o m p r e s s a and s c a b r e l l a , F e s t u c a i d a h o e n s i s , S t i p a Columbiana, C a l a m a g r o s t i s r u b e s c e n s and f o r b s . F o r b s w e r e t r e a t e d as a g roup r a t h e r t h a n as i n d i v i d u a l s p e c i e s , due t o t h e l a r g e number o f s p e c i e s r e p r e s e n t e d b y r e l a t i v e l y few i n d i v i d u a l s . The 24 e n c l o s u r e s w e r e c l i p p e d - 45 - t o a h e i g h t o f lh i n c h e s p r i o r t o i n i t i a t i o n o f s p r i n g g r o w t h a n d t h e n r e c l i p p e d a f t e r c e s s a t i o n o f g r o w t h i n t h e f a l l . The c l i p p i n g s we re s e p a r a t e d i n t o g r a s s e s and f o r b s , o v e n d r i e d , and w e i g h e d . C l i p p i n g s made on t h e 8 0 - b y 8 0 - f o o t e n c l o s u r e f r o n t h e 1 0 t h t o t h e 1 7 t h w e e k , i n c l u s i v e , w e r e i n c l u d e d . The m e a s u r e d v a l u e s we re u s e d t o d e f i n e p r o d u c t i o n l e v e l s and v a r i a b i l i t y i n p r o d u c t i o n on d i f f e r e n t s i t e s . - 46 - ANALYSIS OF PLANT COMPETITION The primary aim of the competition portion of the simulation model was to permit modification of growth potential and survival rates of i n d i - viduals and populations subject to inter- and intra-specific competition. Emphasis was placed on the a b i l i t y to duplicate changes in growth response and survival rather than on understanding the underlying processes. The components of tree, shrub, forb and grass growth derived in the Plant Growth section provide benchmarks for growth potential and survival in the absence of competition. The functions derived in this section serve to modify the above-mentioned components. Components of Tree Competition The components of tree competition investigated include branch competition for aerial growing space, height and diameter growth response to crown competition, and c r i t e r i a for mortality. The effect of competition from shrubs, grasses and forbs was not investigated. Observation of crowns of competing trees indicated that branches of adjacent crowns seldom interlocked in immature and mature stands. Main- tenance of crown integrity is probably due to cessation of apical growth resulting from severe shading or mechanical injury due to wind-induced branch motion (Mitchell, 1967). Crowns of juvenile trees, less subject to both shading and wind-induced motion, exhibit extensive interlocking. Modification of the branch length functions in the presence of crown competition was based on the availability of aerial growing space during simulation. Simulation of actual branch length, and hence crown area, was accomplished by allowing - 47 - branches to compete for growing space in a three-dimensional matrix. The simulation i s discussed in the Model section. Tree height-growth response to crown competition was not investigated in d e t a i l . Four suppressed Douglas-fir were analyzed and their pattern of growth was compared to that of the five open-grown dominants. The shape of the curves was found to be essentially similar, the only difference being in the slope of the curve. Until further investigation, inter-tree competition is assumed to have no effect on rate of height growth, except when crown area becomes so restricted that mortality occurs. Simulating va r i a b i l i t y in rate of height growth was accomplished by applying normal random deviates, sampled from the height frequency distribution described earlier, to the height-age relationship (Figure 4, Equations 1 and 2). Diameter-growth response to crown competition i s implicit in the relationship between DBH, crown area and height (Figure 10, Equation 9). This relationship was derived from sample trees selected as being represen- tative of open-grown individuals and individuals occurring in stands of various densities. The a b i l i t y to duplicate tree mortality during stand development is an essential feature in the model. The removal of trees subjected to insufficient growing space or excessive shading prevents abnormal stand stagnation and allows competing tree crowns to increase in size. In the model, a tree i s eliminated i f the ratio of the simulated crown area in the presence of competition to the simulated crown area in the absence of com- petition i s less than or equal to 0.1, regardless of tree age. The value - 48 - (0.1) was derived by testing the model on stands where the history of natural mortality was known. Mortality due to causes other than crown competition was not included in the model. Removal of understory vegetation has been shown to increase height growth, limb diameter and volume increment of ponderosa pine (Barrett, 1970). Exclusion of the effect of understory vegetation does not seriously affect the tree growth simulation because a l l of the tree growth functions were derived on individuals subject to understory competition, and the model is not structured to allow i t s complete removal. Components of Shrub Competition The components of shrub competition investigated included crown competition between shrubs and the effect of forest crown closure on shrub survival. Shrub response to competition from grasses and forbs was not investigated. Large variations in the rate of height and diameter growth, irregular crown shape and extensive interlocking of crowns precluded direct assessment of the effect of inter-shrub competition on both shrub crown growth and production. General observations indicated that the crowns of species achieving a relatively large size (Amelanchier, Ceanothus and Shepherdia) competed for aerial growing space, while small shrub species (Prunus, Rosa and Symphoricarpos) did not appear to compete for aerial growing space to any extent. The absence of small shrub species in the .immediate proximity of large shrub species, in areas where the two grew in - 49 - association was, for the purpose of modelling, assumed to indicate that crown competition between the two resulted in the mortality of the small shrub species. Modification of the shrub crown diameter to age relationships, in the presence of competition, was based on the availability of aerial growing space during the course of simulation. Distinction was made between what were defined as large shrub species (Amelanchier, Ceanothus and Shepherdia) and small shrub species (Prunus, Rosa and Symphoricarpos). This distinction was necessary because the units of growing space allocated for shrub growth in the simulation (̂  square foot) were too large to accommodate the growth increments of the small shrub species. Allocation of units of growing space of less than \ square feet was impractical because of the associated increase in both calculation time and computer storage require- ments. Investigation of shrub mortality was restricted to the measurement of shrub density as a function of degree of shading, the inference being that tree shade provides a measure of the degree of competition exerted by the forest stand. Ceanothus and Prunus shrub density was measured through a range of crown closures and plotted as a function of crown closure (Figures 24 and 25). Ceanothus density (Equations 34 and 35) was measured on 20 l/40th-acre plots ranging from 0 to 83 percent crown closure, and Symphoricarpos density (Equations 36 and 37) was measured on 60 square-yard plots ranging from 0 to 85 percent crown closure. The lack of associations between Douglas-fir and Amelanchier, Shepherdia, Prunus and Rosa precluded derivation of relationships for these species. The relationship derived - 50 - 3 0 L Crown C l o s u r e - % F i g u r e 2 4 . R e l a t i o n s h i p b e t w e e n number o f C e a n o t h u s and c rown c l o s u r e o f t r e e s . 20 40 60 80 100 Crown C l o s u r e - % F i g u r e 2 5 . R e l a t i o n s h i p be tween number o f S y m p h o r i c a r p o s and c rown c l o s u r e o f t r e e s . - 51 - for Ceanothus (Equations 34 and 35) was applied to Amelanchier and Shepherdia in the simulation model. Theoretical functions were applied to Prunus and Rosa (Figure 26, Equations 38 and 39). The use of the Ceanothus function for Amelanchier and Shepherdia and the theoretical functions for Prunus and Rosa reduces the accuracy of the model. However, they can be replaced with more accurate functions at a later date. 30 0 20 40 60 80 100 Crown Closure - % Figure 26. Theoretical relationship between number of Prunus and Rosa and crown closure of trees. - 52 - Ceanothus (Applied to Amelanchier and Shepherdia) i f CC < 75% N = 8 - (0.10606)(CC) + (19)((1 - CC/75) 2* 5) (34) i f CC > 75% N = 0.0 (35) where: No. of Obs. = 20 N = number of individuals Symphoricarpos i f CC < 90% N = 35 - (0.38889) (CC) (36) i f CC > 90% N = 0.0 (37) where: No. of Obs. = 60 Prunus and Rosa (Theoretical) i f CC < 65% N = 7 - (0.1167)(CC) + (9)((1 - CC/65)2*5) (38) If CC > 65% N = 0.0 (39) The curves for Ceanothus and Symphoricarpos were fitted to pass through the maximum values and consequently regression analyses were not used to determine the goodness of f i t . Points lower than the maximum values were assumed to be the result of low i n i t i a l stocking densities rather than competition. For example, where 8 Ceanothus per l/40th acre were found for crown closures of 12, 24 and 33 percent (Figure 24), the density at 12 and 24 percent crown closure was assumed to reflect low i n i t i a l stocking, while - 53 - the density at 33 percent was assumed to represent the maximum density for that crown closure. Exclusion of the effect of grass and forb competition on shrub production should not seriously affect the accuracy of the simulation as a l l shrubs measured were growing in association with grasses and forbs, and the model is not structured to allow the removal of these plants. Components of Grass and Forb Competition The components of grass and forb competition investigated include response to crown closure, shading by large shrub species, and to changes in density of small shrub species. Competition between grasses and forbs was not investigated. Productivity and species composition for both grasses and forbs was determined on l/40th-acre plots ranging 0 to 85 percent crown closure. On each plot, 40 f l o r i s t i c descriptions (Daubenmire, 1959) and 10 clippings, segregated into Agropyron or Poa, other grasses (Calamagrostis, Koeleria and Bromus), were made on l/10th square-meter sub-plots. The relationships between the oven-dry weight of the clippings and crown closure (CC) are shown in Figures 27, 28 and 29, and Equations 41 to 46. - 54 - e o •H CN 4-1 a 3 eg O 60 20 40 60 Crown C l o s u r e - % F i g u r e 2 7 . R e l a t i o n s h i p b e t w e e n A g r o p y r o n p r o d u c t i o n and c rown c l o s u r e o f t r e e s . 20 c o • H C M 4-> £ O --3 o -O £ O c u CM 10 h 100 Crown C l o s u r e - % F i g u r e 2 8 . R e l a t i o n s h i p b e t w e e n f o r b p r o d u c t i o n and c rown c l o s u r e o f t r e e s . c o • H t M * J £ o 3 JJ t I U PM 10 5 20 40 60 Crown C l o s u r e - % 100 F i g u r e 2 9 . R e l a t i o n s h i p be tween c o m b i n e d C a l a m a g r o s t i s , K o e l e r i a and Bromus p r o d u c t i o n and c rown c l o s u r e o f t r e e s . - 55 - A g r o p y r o n i f CC < 85% WT = ( 0 . 2 3 5 3 ) ( 8 5 - CC) + ( 6 3 . 3 ) ( ( 1 - C C ) 2 ) gms /m 2 (40) i f CC > 85% WT = 0 . 0 g m s / m 2 (41) w h e r e : N o . o f O b s . = 120 R 2 = 0 . 7 0 6 S E ^ = 13 .39 gms /m 2 K o e l e r i a , C a l a m a g r o s t i s and Bromus i f CC < 80% WT = ( 0 . 0 5 6 2 5 ) ( C C ) g m s / m 2 (42) i f CC > 80% WT = 0 . 0 gms /m 2 (43) w h e r e : N o . o f O b s . = 120 R 2 = 0 . 5 0 - 2 SE„ = 1 . 2 1 9 gms/m F o r b s i f CC < 18.75% WT = 10 (S IN (CC( I I / 28 ) - n/6) + 1) gms /m 2 (44) i f CC > 1 8 . 7 5 WT = 0 . 5 + ( 1 8 / 6 0 2 , 7 ) ( ( 1 0 0 - C C ) 2 , 5 2 ) g m s / m 2 (45) w h e r e : N o . o f O b s . = 120 R 2 = 0 . 5 0 5 2 SE„ = 4 . 6 0 6 gms/m - 56 - In determining the response of grasses and forbs to shrubs, distinction was made between large and small shrub species. Competitive response to large shrub species was determined by comparing production in the open, along the border of the shrub and beneath the shrub (Figure 30). ; „ Sphere of Influence 1> • ^ — 1 ! R + 0.82 f t Open | ^ ̂  • Border w ! M B Inside V V V \ \ • / R - 0.82 f t L Radius (R) m Figure 30. Definition of zones of influence for large shrub species. - 57 - Production was measured using a l/10th-meter frame and clipping and weighing grass and forb production. A strip of the shrub, running east-west one-foot wide, was removed prior to clipping. The frame was i n i t i a l l y placed straddling the eastern edge of the shrub, corresponding to the border area, and the vegetation was clipped. The width of the border area, 1.64 feet, equals the length of the l/10th-^neter frame. Successive clips were made to the centre of the shrub and two clips were made on the outside of the shrub. Mean production was calculated for the open, border and inside areas of the shrubs. The values, presented in Table 5, are expressed as a percentage of the pro- duction outside the shrub. Competitive response of grasses and forbs to small shrub-species was determined by expressing production as a function of the number of shrubs per square yard. The plots, located to cover a range in shrub density, were clipped and the clippings separated into grasses and forbs and weighed. The relationship found for Prunus, the only species investigated in the Agropyron community, i s shown in Figure 31 and Equations 46 to 48. Table 5. Comparative productivity of Agropyron, Poa and forbs growing in association with Amelanchier, Ceanothus and Shepherdia. SHRUB SPECIES # of Shrubs Position Production as % of open examined Poa Forbs Amelanchier 10 Open 100 100 Border 68.5 106.3 Inside 13.4 53.9 Poa Forbs Ceanothus 10 Open 100 100 Border 89.5 46.5 Inside 13.7 77.0 Agropyron Forbs Shepherdia 7 Open 100 100 Border 136.5 30.6 Inside 1.8 20.6 - 58 - A g r o p y r o n i f N < 14 WT - ( P D N / 8 5 ) ( 3 + ( 0 . 1 3 3 3 4 ) ( 1 5 - N) + ( 0 . 0 9 1 8 ) ( (15 - N ) 2 , 5 ) ) g m s / y d 2 (46) i f N > 14 WT - ( 0 . 0 3 5 3 ) ( P D N ) g m s / y d 2 (47) w h e r e : N o . o f O b s . = 10 R 2 = 0 . 8 9 8 2 F o r b s SE, , = 7 . 1 5 gms /yd N = number o f P r u n u s PDN = A g r o p y r o n p r o d u c t i o n i n a b s e n c e o f P r u n u s WT = - 1 2 . 3 + ( 3 . 6 ) (N) - ( 0 . 8 0 7 5 2 ) ( (N - 7 . 5 ) 1 , S ) g m s / y d 2 (48) w h e r e : N o . o f O b s . = 10 R 2 = 0 . 5 8 0 2 SE„ = 5 . 0 6 g m s / y d E N = number o f P r u n u s - 59 - • FORBS AGROPYRON 5 10 15 20 2 Number of Prunus per yd Figure 31. Response of Agropyron and forb production to Prunus density. - 60 - THE MODEL Simulation of complex forest ecosystems i s a logical outgrowth of tree growth models. Models of individual tree and stand growth have been developed by Newnham (1964), Lee (1967), Mitchell (1967), Bella (1970), Pail l e (1970), Arney (1971), Goulding (1972) and others. Botkin, Janak and Wallis (1971) developed the f i r s t mixed species, mixed age model. Their model reproduces the major characteristics of competition, secondary succession and changes in vegetation accompanying changes in elevation from a conceptual basis. The model described here attempts to duplicate growth, competition, production and, to a limited degree, secondary succession from an empirical basis. An empirical rather than a conceptual approach was taken in order to achieve a high predictive a b i l i t y . The model simulates growth, competition and production of trees, shrubs, grasses and forbs. Variable inputs include site quality, species composition, density and spatial distribution of individual plants. Output is expressed in terms of wood production, weight of annual twig production of shrubs, current annual growth and carryover of grasses, and current annual growth of forbs. Procedures allowing cultural practices during the course of the simulation have yet to be included. STRUCTURE The computer program written to simulate the growth, competition and production of trees, shrubs, grasses and forbs can conveniently be divided into three sections: the main program, the tree-growth subroutines and the understory (shrubs, grasses and forbs) growth subroutines. A l i s t i n g of the program i s contained in Appendix III. - 61 - The Main Program The main program controls the optional pathways through the tree and understory subroutines (Figure 32). Variable data inputs allow by- passing of either the tree or understory subroutines, thereby allowing (1) simulation of trees alone, (2) shrubs, grasses and forbs in the absence of trees, and (3) the entire plant community. Application of the model to the Pseudotsuga-Poa community is accomplished by substitution of a "POA AND FORB PRODUCTION" subroutine in place of the "AGROPYRON AND FORB PRODUCTION" subroutine. Where shrub, grass and forb growth i s simulated in the absence of trees, crown closure of an actual or hypothetical forest stand can be read in as data. The crown closure can remain constant or be incremented at a pre-specified rate. A simplified flow chart of the main program i s presented in Figure 33. The organization, and hence sequence of calculations and decisions, of the model is based on an assumed hierarchy of competitive a b i l i t y among trees, shrubs, grasses and forbs. Trees are assumed to have the greatest competitive a b i l i t y , followed by shrubs and f i n a l l y grasses and forbs. The hierarchial order i s directly related to the height at which plant crowns compete for, and occupy, aerial growing space. Development of a hierarchial order of computation was necessary because simulated systems are not able to duplicate the simultaneous occurrence of growth found in natural systems. Assessment of the degree of inter-specific competition exerted on an in d i - vidual plant i s accomplished by the transfer of information summaries between the tree and understory-growth subroutines. The transfers, following a definite time sequence, are as follows: - 62 - C START I MAIN PROGRAM 1 1 ±2 ' r NORMAL AND UNIFORM RANDOM NUMBER GENERATOR TREE GROWTH AND COMPETITION 1 I CROWN PROFILES AND CROSS- SECTIONS Trees only Understory only END UNDERSTORY SHRUB GROWTH H SHRUB MORTALITY H SHRUB AREA I SHRUB PRODUCTION H AGROPYRON AND FORB PRODUCTION Trees and Understory combined Figure 32. Flow chart of subroutines showing optional pathways. - 63 - G E D Read input/ data Proceed to tree growth subroutines Proceed to tree growth subroutines * No Proceed to understory growth subroutines Yes r Proceed to understory growth subroutines Figure 33. Simplified flow chart of the main program showing i t s control over optional pathways through the model. - 64 - (1) Computation - Tree height and branch growth, competition for growing space and mortality. Transfer - Locations occupied by branches and percent crown closure to shrub, grass and forb sub-arrays. (2) Computation - Differential mortality, crown diameter growth and competition for growing space of large shrub species. Transfer - Locations occupied by branches and crown closure of trees, and locations occupied by large shrub species to the subroutine responsible for small shrub species growth. (3) Computation - Differential mortality and crown diameter growth for small shrub species. Transfer - Locations occupied by branches and crown closure of trees, locations occupied by large shrub species and area of border and inside zones, and density of small shrub species to the subroutine responsible for grass and forb growth. (4) Computation - Mortality, species change and crown growth of grasses and forbs. Simulation of Tree Growth In the tree growth simulation, growth of the stand is based on the aggregate growth of individual trees occupying a l/10th-acre plot subdivided into square-foot units of growing space (66 x 66). A simplified flow chart of the sequence of calculations and decisions is presented in Figure 34. - 65 - f Start ) ^ Read input dataj Generate tree locations Set calculation interval Take f i r s t tree Proceed to next tree Calculate tree height and branch lengths Proceed to next branch Generate f i r s t branch location to be occupied No Do not occupy (continued) - 66 - Yes Call understory subroutines Increment age by one calculation interval Calculate the following tree and stand parameters Height Crown width Diameter Crown length Volume Crown area Basal area Height to base of live crown No Figure 34. Simplified flow chart of tree-growth subroutines. - 67 - Briefly, trees are assigned to locations within the plot, height and crown radius are incremented, and branches test for and occupy available units of growing space within a three-dimensional matrix. Diameter i s incremented, based on simulated crown area and height. Overtopped trees are removed from the stand, thereby freeing growing space for adjacent trees. Individual tree and stand parameters are calculated for each period. A more detailed discussion of the tree-growth simulation is presented in the remainder of this section. The data requirements include specification of site index at 100 years, number of trees per l/10th acre, mean and variance of a measured height-growth frequency distribution for immature open-grown Douglas-fir, option to read or randomly assign tree locations, simulation period to a maximum of 100 years and number of calculation intervals to a maximum of 20. If a simulation period of 100 years and 20 calculation intervals are specified, the calculation interval is 5 years. Where random tree locations are specified, a uniform random number generator is used to assign locations with the proviso that no two trees occupy the same unit of growing space. The growth rate and height of individual trees is determined by (1) adjusting the slope of the height-age relationship derived for open- grown dominant Douglas-fir (Equations 1 and 2) to give the pre-specified site index, (2) drawing normal random deviates from the height frequency distribution (Figure 5), and (3) solving the relationship for the particular stand age in question. Crown growth of trees is simulated on the l/10th-acre plot which is subdivided into units of growing space referenced by their location in a two-dimensional matrix or array; the third, or vertical dimension, is - 68 - referenced by coded values held in each unit. The array may be visualized as square units of growing space containing a numeric code designating plant occupancy. Prior to computation, the codes are i n i t i a l i z e d at 10000000, signifying that the unit is unoccupied. The code, as illustrated below, is broken down into element nests used to identify the individual plant, i t s species and stem position, and the height at which the unit i s occupied. 10 0000 00 Free element nest Individual plant, species and stem position (99 in this location indicates the location of the tree bole) Height of occupancy in hundredths of feet In the simulation of crown growth, total branch length i s calculated by determining tree height above the branch node and solving the relationship between branch length and height above branch (Equation 3). Total branch length i s then converted to horizontal branch length by solving the relation- ship between horizontal branch length and total branch length (Equation 4). Determination of the actual crown area of individual trees i s accomplished by allowing branches to compete at various heights in the two-dimensional matrix. In the simulation of branch competition, i t is assumed that a unit of growing space can only be occupied by a single tree, and branches of competing trees do not interlock. The sequence in the simulation of branch competition may be summarized as follows: - 69 - (1) Starting from the top of each tree, a c i r c l e , with radius equal to horizontal branch length, i s swept for each branch whorl being considered. The number of branch whorls considered is equal to the number of calculation intervals. (2) Units of growing space are considered to be occupied i f horizontal branch length is greater than the distance from the tree bole to the center of the unit. (3) A previously occupied unit can only be reoccupied at a greater height. (4) When a l l trees have been processed, crown area is determined for individual trees by counting the number of units occupied by each tree. (5) The degree of competition exerted on each tree i s expressed as a function of actual crown area (CAact ) to expected crown area in the absence of competition (CAexp ). If the ratio of CAact to CAexp is less than or equal to 0.1, the tree i s assumed to die and i s removed from the plot. Figure 35 illustrates the coding of two Douglas-fir occupying growing space (refer to Figure 34 for mechanism of branch competition). Codes 10008499 and 10044299 represent the bole position and heights of trees 11 and 18, respectively. Codes 10000118 and 10013418 represent the units occupied by branches originating from nodes at 0.01 and 1.34 feet on tree 18. Code 10000111 represents the units occupied by branches originating from a node at 0.01 feet on tree 11. The array coding can be printed i n the form of developmental stand maps showing vertical and cross-sectional projections. Inevitably tree crowns w i l l attempt to grow beyond the plot confines. Any l - 70 - 10000000 10000000 10000000 10000000 10000000 10000000 10000000 10000000 i b j I 100001111 1 1 1 1 10000118 10000118 10000118 10000000 10000000 r t_ 110000111 t h ! 10008499J s j 10013418 10013418 10013418 10000118 10000000 10000000 110000111 i 10013418 t h 10044299 s t 10013418 b 10000118 10000000 10000000 10000118 10013418 10013418 10013418 10000118 10000000 10000000 10000000 10000118 10000118 10000118 10000000 10000000 10000000 10000000 10000000 10000000 10000000 10000000 10000000 w h e r e : t = t r e e number t h = t r e e h e i g h t i n h u n d r e d t h s o f f e e t s = s t e m p o s i t i o n b = b r a n c h h e i g h t i n h u n d r e d t h s o f f e e t F i g u r e 3 5 . A r r a y c o d i n g f o r two D o u g l a s - f i r o c c u p y i n g g r o w i n g s p a c e . - 71 - portion of a plant crossing the boundary is returned on the opposite side of the plot (Figure 36). This procedure prevents the loss of those portions of plants crossing the boundary and approximates competition from plants growing near the plot periphery. Estimation of crown width, crown length and height to live crown base are derived from the results of the crown-growth simulation. Crown width is determined by calculating the diameter of a ci r c l e having an area equal to the simulated crown area. Calculation of crown length i s more complex. In the absence of inter-tree competition, height to maximum crown width i s deter- mined as a function of total tree height (Equations 5 and 6) and then height to base of l i v e crown is determined as a function of height to maximum crown width (Equations 7 and 8). Crown length is determined by subtracting the height to base of l i v e crown from total tree height. Where crowns are subject to competition for aerial growing space, the height of the longest branch i s taken to represent the point at which crown width is maximum. The calculation sequence follows that for trees not subject to inter-tree competition. Diameter at breast height (DBH) is calculated by solving the relation- ship between DBH, height and crown area (Equation 9). Volume estimation is based on the application of the simulated height and DBH to the B.C. Forest Service volume equation for interior Douglas-fir (Equation 10). Basal area is calculated from the simulated DBH. The sequence of decisions and calculations involved in the simulation of tree growth are repeated at each calculation interval u n t i l the simulation period i s exceeded. The information and array coding generated at each calculation interval are retained for incrementation at the next calculation - 72 - ************************************************* * B 1 1 1 2 2 2 B 2 2 2 1 1 1* * 1 1 1 1 2 2 2 2 2 2 2 1 1 1* * 1 1 1 2 2 2 2 2 1 1 * | 1 1 2 2 2 4 4 4 1 | * 4 4 4 4 4 4 4 * * 4 4 4 4 4 4 4 * * 4 4 4 4 4 4 4 4 4 * * 4 4 4 4 B 4 4 4 4 * * 4 4 4 4 4 4 4 4 4 * * 4 4 4 4 4 4 4 * * 4 4 4 4 4 4 4 * * 5 5 B 5 5 * * 5 5 5 | £  5 t * £ * * * *. * i. * * * * * * * 3 3 3 * * 3 B 3 * * 3 3 3 t * I * * * i * i * * | 1 1 2 2 2 1* * 1 1 1 2 2 2 2 2 1 1* * 1 1 1 1 2 2 2 2 2 2 2 1 1 1* ************************************************************ where: B = bole position 1 = branch locations of tree 1 2 = branch locations of tree 2 etc. Figure 36. Graphical representation of the return of portions of tree crowns crossing the plot boundary. - 73 - interval and, where the understory option is specified, are passed to the understory-growth subroutines. The degree of detail required in the simulation results i s specified by output options supplied as data. At the most detailed level, the following information is summarized at each calculation interval: (1) Internal coding of the tree matrix. (2) Develop stand maps showing vertical and cross-sectional profiles of the stand. (3) Detailed information on each individual tree, including location, height, diameter, basal area, volume, height to crown base and crown width, area and length. (4) Mean tree height, diameter, basal area, volume, height to crown base, and crown width, area and length. ( 5 ) I n i t i a l and current number of trees. (6) Number of trees having died. (7) Crown closure for entire plot. (8) Crown closure for each quarter of the tree plot. At the lowest level of detail, total volume, crown closure, number of trees and mean tree height, diameter, basal area, volume, height to crown base and crown width, area and length are printed. Simulation of Understory Growth In the understory simulation shrub growth is based on the aggregate growth of individuals, grass on the aggregate growth of species and forbs on the aggregate growth of communities. The small size of individual grasses - 74 - and forbs and the great diversity of forb species precluded simulation of individuals. Growth is simulated on a l/10th-acre plot underlying, and receiving information from the l/10th-acre tree array. The understory array is subdivided into h square foot units (132 by 132) partitioned into 4 independent 66 by 66 element sub-arrays (Figure 37); each sub-array is Figure 37. Arrangement of arrays showing relationship between tree and shrub, grass and forb arrays. - 75 - associated with a specific quarter of the tree array. A flow chart showing the sequence of calculations and decisions made during the course of simulation is presented in Figure 38. In general terms, the sequence may be summarized as follows. (1) Input data are read. (2) Locations of large shrub species (Amelanchier, Ceanothus and Shepherdia) are either directly or randomly assigned. (3) Crown closure of the overstory (Douglas-fir stand) is set at zero, specified at a constant level, set at zero and incremented at a pre- specified rate, or passed from the tree-growth simulation. (4) Mortality of large shrub species is determined as a function of direct tree shading, crown closure of the forest stand or both. (5) Crown diameter of large shrub species is incremented and crowns are allowed to compete for aerial growing space. (6) Density of small shrub species (Prunus, Rosa and Symphoricarpos) is determined as a function of crown closure of trees and large shrub species. Crown diameter of individual shrubs is then incremented. (7) Diameter, area and production are calculated for individual shrubs, and mortality by species, total number and production by species and the area occupied by trees, and large and small shrub species are summarized. (8) Production of Agropyron (or Poa), other grasses (Koelaria, Calamagrostis and Bromus) and forbs is calculated i n the absence of both trees and shrubs. (9) Their production is then readjusted as a function of tree shading, location beneath large shrub species (i.e. border and inside areas) and density and age of small shrub species. - 76 - EntAy point ^on. Azcond and and undeAAtoiy togeJh&i ,En&iy point ^on. undeJiAto./iy atone. / and ̂ iA&t pat>6 faoK -tt.ee and ' iLndoAAtoh.u togntkzn. Start ) Read input data/ Generate shrub locations Set calculation interval Take f i r s t sub-plot Proceed to next sub-plot Proceed to next shrub species Take f i r s t species Increment age by one calculation interval Take f i r s t shrub Yes —+- Yes Remove Shrub Count living shrubs by species Proceed to next shrub Yes (continued) - 77 - ± Calculate potential # of shrubs as a function of crown closure of the forest stand Yes Remove that number of shrubs requ ired to reduce actual # to potential Proceed to next shrub i No (continued) - 78 - Generate f i r s t location to be occupied Generate next location i No _ ^ - a i i ; Yes Have .ocations bee! tested? Yes Do not occupy Oc cupy Calculate area not occupied by large shrub species (Amelanchier, Ceanothus, Shepherdia) Calculate density of small shrub species (Prunus, Rosa, Symphoricarpos) as a function of forest crown closure Calculate area available to small shrub species and total number of small shrubs by species Calculate for individual shrubs: Diameter Area Summarize: Mortality by species Total number and production of shrubs by species Inside and border areas of large shrub species by species Total area shaded by trees and large shrub species Total area not shaded by trees or large shrub species T ( c o n t i n u e d ) - 79 - Calculate production for Agropyron, forbs and other grasses (Calamagrostis, Koeleria, Bromus) per unit area for unshaded condition Adjust production per unit area as a function of tree crown closure Readjust production per unit area for border and inside area of large shrub species Readjust production per unit area as a function of small shrub density and age for (1) area in direct tree shade and (2) area not shaded by trees or large shrub species Using precalculated areas of direct tree shade, large shrub species shade and area not shaded by trees or large shrub species, calculate total production for: Agropyron Forbs Other grasses (Calamagrostis, Koeleria, Bromus) Yes Print results Yes Return to tree growth subroutine Stop Figure 38. Simplified flow chart of shrub, grass and forb growth (understory subroutines). - 80 - A more detailed discussion of the simulation i s presented in the remainder of this section. The data requirements for the simulation of the understory develop- ment include specification of (1) the number of large shrub species, (Amelanchier, Ceanothus and Shepherdia), by species per l/40th acre, for each of the four sub-plots, (2) number of small shrub species (Prunus, Rosa and Symphoricarpos), by species per square yard, for each sub-plot, (3) mean and variance of crown diameter frequency distributions for a l l shrub species, and (4) carryover of Agropyron or Poa in grams per square yard. If tree growth is not simulated, i t is necessary to specify the calculation interval, simulation period and the crown closure of the forest stand. As previously stated, crown closure can be specified at zero, a constant value, or set at zero and incremented during the course of simulation. Where large shrub species are assigned specific locations, their locations are read in as data; otherwise, a uniform random number generator i s used to assign locations. The f i r s t step in the understory simulation is to evaluate the influence of the forest stand, whether simulated or specified in terms of crown closure, on shrub mortality. Two methods are used to " k i l l " shrubs. In the f i r s t method, shrubs are tested for shade tolerance (read as input data); i f shade tolerant, they survive i n direct shade; i f shade intolerant, they "die" when directly shaded. Large shrub species are only shaded by trees, while small shrub species may be shaded by trees and large shrub species. Surviving shrubs are then counted by species and the number surviving i s compared to the potential number capable of surviving at the particular crown closure in question (Equations 34 to 39). If the actual number exceeds the potential number, shrubs are randomly " k i l l e d " u n t i l the two are equal. This sequence in mortality is important in that i t ensures that shade intolerant shrubs closest to trees die f i r s t . Shrubs subject to mortality are removed from the plot, thereby freeing aerial growing space. Growth of individual shrubs is expressed in terms of crown diameter which is derived from the relationships between crown diameter and age (Equations 11 to 21) distributions. In simulating crown diameter growth and competition for aerial growing space, distinction i s made between small and large shrub species. Large shrub species compete for designated units of growing space held in the sub-arrays; small shrub species are allocated to those units of growing space not occupied by large shrub species. Crown competition among large shrub species is handled in the same manner as tree crowns except that height of occupancy is not taken into account. The near vertical growth habit of shrub branches and more or less similar heights precludes the necessity of allowing over-topping. Following simulation of crown growth and competition among individuals belonging to the large shrub species, the total number of small shrub species individuals is calculated. The number of individuals is calculated by determining the area available to small shrub species and multiplying this area by the density of surviving individuals. If the species being considered i s shade intolerant, the available area is that portion of the plot not shaded by trees or large shrubs; i f the species is shade tolerant, the area is that portion of the plot not shaded by large shrub species. Crown competition among small shrub species individuals is not simulated - 82 - due to their small size and the tremendously increased computer memory requirements and calculation time which would be necessary (approximately 310,000 additional words of computer memory and up to 29,000,000 additional decisions and calculations - present storage requirement i s 75,000 words). The determination of crown diameter and area of the simulated large shrub species is accomplished by counting the number of units of growing space occupied by each individual, expressing the result in square feet (each unit represents 0.25 square feet), and calculating the diameter of a c i r c l e whose area i s equal to the area of the individual shrub. At the same time, the area occupied by each shrub is segregated into those portions representing the inside and border areas of the shrub (Figure 11). Where the crowns of two or more shrubs are in contact, the border area is expressed as a function of the perimeter of the group, and the remaining area consti- tutes the inside area. For small shrub species, the diameters calculated from the diameter-age relationships (Equations 16 to 21) are not modified. Conversion of shrub diameter (small shrub species) or area (large shrub species) to production is accomplished by substituting the simulated values in Equations 22 to 28. Following calculation of diameter, area and production for individual shrubs, the simulated results are summarized in terms of total number and production of shrubs by species and mortality by species. The calculated values for the border and inside areas of large shrub species, the areas shaded by trees, large shrub species, trees and large shrub species combined and the unshaded area, and the density of small shrub species i s passed to the subroutine responsible for grass and forb growth. - 83 - The sequence of calculations in the determination of grass and forb production is to calculate production (1) in the absence of inter- specific competition, (2) adjust production as a function of forest crown closure (Equations 40 to 45), (3) readjust production for border and inside areas of large shrubs (Table 2) and (4) fi n a l l y readjust production as a function of age and density of small shrub species (Equations 46 to 49). Production in the absence of interspecific competition i s based on the measurement of the previous year's carryover of grass (Agropyron or Poa) which has not been subject to grazing by ungulates. The conversion of carryover to the current year's production is achieved by substituting the value for carryover in Equations 32 and 33 and defining the number of weeks since the i n i t i a t i o n of spring growth. Modification of the equations to accommodate variations in annual growth requires the derivation of cause- effect relationships between climatic influences and annual grass growth. Since these relationships were not investigated, growth is based on the growing season of 1970. The production of forbs is based on the relation- ship between forb weight and weeks since the i n i t i a t i o n of spring growth (Figure 21). The weight of forbs produced refers to the standing crop present at the time of clipping. Adjustment of grass and forb production in response to increasing crown closure of trees is accomplished by solving the relationships between production and crown closure (Equations 40 to 45), calculating the per- centage decrease as compared to production at zero crown closure, and then reducing current annual production by this percentage. - 8 4 - The adjusted production of grasses and forbs is then readjusted i n response to the presence of large and small shrub species. In the case of large shrub species, production i s readjusted as a percentage of production in the open, according to the location beneath the shrub. The correction factors applied are shown in Table 1. Where grasses and forbs are growing in association with small shrub species, production is adjusted as a function of small shrub density (Equations 4 6 to 4 9 ) . Obviously, the size of the individual shrubs w i l l affect the degree of reduction in productivity. Equations 4 6 to 4 8 represent relationships derived in a Prunus community with a mean age of 15 years. For shrub stands of less than 15 years of age, the effect i s reduced i n direct proportion to the reduction in age as shown in Figure 3 9 . The sequence of calculations and decisions described for the growth of shrubs, grasses and forbs is conducted on each of the four sub-plots at each calculation interval until the simulation period is exceeded. The level of output detail required is specified by data statements. At the most detailed le v e l , output i s summarized in terms of: (1) Developmental stand map showing a vertical projection of the shrub stand. (2) I n i t i a l and current number of shrubs by species. ( 3 ) Number of shrubs having died by species. ( 4 ) Cause of mortality (from direct shading or as a function of crown closure of the forest stand). (5) Detailed information on Amelanchier, Ceanothus and Shepherdia including diameter, inside and border areas, total area and production. - 85 - Shrub Age 2.5 years 5 years 7.5 years 10 years 12.5 years 0 5 10 15 20 Number of Prunus per yd' Figure 39. Relationship between Agropyron production and Prunus density by shrub age. (6) Total production by shrub species. (7) Area in tree shade. (8) Area shaded by Amelanchier, Ceanothus and Shepherdia. (9) Area not shaded. (10) Production of grass by species. - 86 - (11) Carryover of grasses. (12) Forb production. At the lowest level of detail, output is in the form of summary tables showing the number of individuals and production by species (Table 6). CURRENT STATUS OF THE MODEL The mathematical model, programmed in Fortran IV on a dual IBM 360/67 at the University of British Columbia, represents a prototype simulator of growth, competition, production and, to a limited degree, secondary succession in a mixed species forest ecosystem. The current version of the model handles 1 tree species (Douglas-fir), 6 shrub species (Amelanchier, Ceanothus, Shepherdia, Prunus, Rosa and Symphoricarpos), and 4 grass species (Agropyron, Poa, Calamagrostis and Koeleria); distinction is not made among forb species. The model is presently being converted for application on a PDP 11/20, with a 48K byte core, at the Pacific Forest Research Centre, of the Canada Depart- ment of the Environment. The model structure provides an adequate bookkeeping system for the actions and interactions that occur during the development of a complex forest ecosystem. However, refinement, expansion and testing of the system and i t s components are necessary for achievement of i t s f u l l potential as a sound accurate predictive tool. OUTPUT The model can be applied as a tree growth, a shrub growth and a grass and forb growth simulator, or as a vegetative community simulator Table 6. Output at lowest level of detail for shrubs, grasses and forbs. Parameter Age 0 10 20 30 40 50 Crown closure - % 0 8 .6 37.0 64. 1 73.9 77.7 Agropyron production - kg/ha 475 223 180 156 10.7 3.6 Forb production - kg/ha 13.8 57 .3 45.0 5. 7 3.1 4.1 Calamagrostis and Koeleria production - kg/ha 0 1 .6 7.2 16. 5 19.1 20.0 No. of Shepherdia per ha 988 889 593 98 0 0 Shepherdia production - kg/ha 0 10 .3 45.2 17. 7 0 0 No. of Prunus per ha 95638 85363 28849 0 0 0 Prunus production - kg/ha 0 82 .0 38.9 0 0 0 - 88 - which allows the inclusion of trees, shrubs, grasses and forbs. It can be used to predict above ground plant production, to determine trade-offs between products and to evaluate the consequence of management decisions. Before presenting examples of the application of the model i t is necessary to discuss the problems validating the model. Validation The advantage in adopting a systems approach i s that a number of functional relationships can be linked in a computer program, thereby allowing interactions among relationships and consequently providing dynamic rather than static or average solutions. While the individual functions may duplicate reality to a high degree, there is no guarantee that the model as a whole i s correct. Goulding (1972) summed up the validity problem in saying "the problem of validity is that i f the real system was known exactly so that the model can be compared, there would have been l i t t l e point in creating the simulation model." The problem then i s one of comparing simulated results against static or average solutions which in themselves represent simple models of the real system and i n turn need not necessarily be valid. Van Horn (1968) defined validation as the process of building an acceptable level of confidence that the inference about a simulated process i s a correct or valid inference of the actual process. This applies to the individual functional relationships, the organization and linkage of the functions and the results of the model i t s e l f . A number of procedures have been proposed for testing the validity of simulation models. These include: - 89 - 1) Testing the model against other models (Forrester, 1968). 2) Empirical testing (Naylor and Finger, 1967). 3) Sensitivity testing (Van Horn, 1968). 4) Regression of simulated series on real series and testing whether the coefficient was significantly different from one and the intercept s i g - nificantly different from zero (Cohen and Cyert, 1961). 5) Turing tests (Van Horn, 1968) in which people directly involved in the f i e l d are asked to distinguish between real and simulated results without prior knowledge as to which were which. Testing of the tree simulation was relatively simple as compared with the vegetative community simulations. The amount of data available for testing the understory simulation results are severely limited, to the extent that only sensitivity testing and some empirical testing could be carried out. Examples of the application of the model and the results of the val i d i t y tests are presented in the remainder of this section. Tree Growth Simulation The principle application of tree growth simulations i s in deter- mining yield predictions for young stands. To date, yield tables, a term applied to presentations of expected yields of forest stands based upon growth inferred by the study of other stands, have been used in the estimation of future yields. For example, in British Columbia, a kind of empirical yield estimation called volume/age curves, of which more than 1000 are available, form the basis of the "Forest Service Method" for - 90 - determining annual allowable cut. Yield at culmination age and rotation age are calculated from the curves which are based on empirical plot data from variously aged natural stands. Localized curves may be necessary to overcome particular differences caused by s i t e , stand density and decay factors (Forestry Handbook for British Columbia, 1971). Validated tree growth simulation models could obviate the necessity for generating local curves as site index and stand density can be varied. The tree growth simulation was tested against the B. C. Forest Service volume/age curves, Goulding's (1972) model, data collected on the study area and by the Turing method. Figures 40 and 41 show a comparison of the simulated results and the B. C. Forest Service volume/age curves for F, F mixtures and Py on medium and poor sites in the Cranbrook, Fernie, Upper Kootenay and Windemere P. S. Y. U.'s. The simulated data are based on specific stand conditions, namely a site index of 80 with 350 stems per acre for the medium site and a site index of 65 with 400 stems per acre for the poor sit e . Under these conditions the model adequately duplicates the volume over age curves. Average DBH i s adequately duplicated on the medium site for both 7.1" + and 11.1" +, but is underestimated in the 11.1"+ class on the poor si t e . By increasing the site index, but s t i l l remaining within the range for poor site, and decreasing the number of stems, similar volumes can be achieved but with an increase i n average DBH. Of six persons questioned, none was able to distinguish between the B. C. Forest Service or simulated data. When asked to make a choice, four guessed correctly but again none was able to give any valid reason for the choice. - 91 - B.C. Forest Service Simulated c o •H 5000 •H •W <U CO o s o 4000 U .5 3000 CU u a cd u p. 2000 1 t-i o > M 1000 Co 1-1 cu 3 DBH Volume DBH Volume MEDIUM SITE DOUGLAS-FIR ^ * r / • 7.1" + 7.1" + 11.1" + 100 Figure 40. Comparison between simulated volume and DBH and B.C. Forest Service volume and DBH taken from V.A.C. 1012, medium site. - 92 - B.C. Forest Service DBH Volume Simulated 14 12 10 CO <u o c •9 8 « m n CU 00 cd n 6 c o • r l •U CU N •4-1 0) 8 4000 U 3 c 3000-CU M o cu 2000 o. <u H a, 1000 oo c0 l - i CU 3 DBH Volume POOR SITE DOUGLAS-FIR 11.1" + .<.-•** 7.1" + 20 : 7.i" + n . i " + 100 Figure 41. Comparison between simulated volume and DBH and B.C. Forest Service volume and DBH taken from V.A.C. 1013, poor site. - 93 - The model was then tested against the growth curves for unthinned stands prepared by Goulding (1972) to show gross volume and mean DBH for site indices 90, 120 and 150 with 300 and 800 trees per acre at age 20. Considerable d i f f i c u l t y was encountered in attempting to duplicate these stand conditions. The model developed allows site index to change during the course of the simulation and stand density is defined at age zero. After numerous runs, conditions approximating those of Goulding were achieved. The results obtained show that the two models, derived independently and using very different approaches, yield similar volumes with differences of up to 250 cubic feet per acre on high sites (Figures 42, 43 and 44). The simulated diameters of Goulding (Figure 45) are considerably lower than those generated i n this model for a l l site classes. This divergence is not con- sidered to be serious as my model tends to underestimate DBH taken from the B. C. Forest Service volume/age curves. The simulation was tested against 6 stands measured on the study area which were not used in the derivation of any of the functional relation- ships. Data collected on the stands included individual tree locations, DBH, crown width, volume and number and location of trees having died since stand establishment. Stumps were used to locate trees which had died. While this method for determining past mortality is subject to under- estimation, the absence of stands with recorded past histories of mortality in the study area necessitated i t s use. Table 7 shows the actual and simulated plot volumes in cubic feet per acre. - 94 - Goulding 800 trees at 20 yrs . " ' 300 trees at 20 yrs 0 20 40 60 80 100 Age - yrs Figure 42. Comparison of Goulding's and my simulated gross cubic foot volume per acre for site index 150. - 95 - Goulding — — - — 800 trees at 20 yrs - - 300 trees at 20 yrs Simulated ••• 680 trees at 20 yrs — — — — — 340 trees at 20 yrs 17500 - Figure 43. Comparison of Goulding's and my simulated gross cubic foot volume per acre for site index 120. - 96 - G o u l d i n g - 800 t r e e s a t 20 y e a r s - 300 t r e e s a t 20 y e a r s S i m u l a t e d 940 t r e e s a t 20 y e a r s — 400 t r e e s a t 20 y e a r s S ITE INDEX 90 12500 - 4-4 0 20 40 60 80 100 Age - y r s F i g u r e 4 4 . C o m p a r i s o n o f G o u l d i n g ' s and my s i m u l a t e d g r o s s c u b i c f o o t vo lume p e r a c r e f o r s i t e i n d e x 9 0 . - 97 - Goulding Simulated 20.0 - 800 trees at 20 yrs . 300 trees at 20 years " 680 trees at 20 years - 340 trees at 20 years 17.5 SITE INDEX 120 CO C PQ Q 01 00 CO u cu 15.0 12.5 10.0 7.5 5.0 2.5 h 0 I i I I I l 0 20 40 60 80 100 Age - yrs Figure 45. Comparison of Goulding 1s and my simulated mean DBH for site index 120. - 98 - Table 7. Comparison of simulated and actual stand volumes measured on the study area. Stand Actual Total Volume 1" + DBH cu ft/acre 1 1710 2 2001 3 1832 4 2131 5 780 6 857 Simulated Total Volume 1" + DBH cu ft/acre 1510 1991 2031 2339 1000 777 Simulated as % of Actual 88.3 99.5 110.9 109.8 128.2 90.7 Stand 2 was also simulated at both 2- and 10-year intervals to ascertain the effect of reducing the calculation interval on both simulation costs and results. Cost was found to be a direct function of the number of calculation intervals; the costs at 2- and 10-year intervals were approximately $43 and $9, respectively. Decreasing the calculation interval from 10 to 2 years had a minor effect on the simulated parameters. Selected stand parameters are shown at 20 year intervals (Table 8). On the basis of these results, the model appears to approximate the real system. Obviously, the model w i l l require further testing and refinement i f i t is to be used to generate yield tables. However, i t is sufficiently accurate to give an approximation of yield for use in the determination of trade-offs between wood and ungulate food production. - 99 - Table 8. Comparison of selected mean tree parameters for calculation intervals of 2 and 10 years. Stand Calculation Average Average Average No. of Trees Age Interval Height DBH Volume per acre yrs yrs ft ins 1" + DBH cu f t 20 2 5.3 0.63 0.007 840 10 5.2 0.59 0.007 830 40 2 14.0 2.6 0.360 770 10 14.8 2.7 0.381 660 60 2 20.6 3.8 1.020 650 10 21.3 3.9 1.076 540 80 2 29.4 5.2 2.451 550 10 30.8 5.6 2.648 450 100 2 38.0 6.5 5.038 450 10 38.9 6.7 4.940 410 The Vegetative Community Simulation The models for shrub growth and grass and forb growth were con- structed after completion of the tree growth model. I n i t i a l sensitivity testing showed that the models were capable of approximating solutions in the absence of trees. As was previously stated, d i f f i c u l t y was encountered in validating the understory simulations due to the lack of data with which to compare the simulated results. Two types of sensitivity tests were undertaken, plant species abundance was varied from absent to the highest densities encountered on the study area and changes were made to the functional relationships and growth rate frequency distributions. - 100 - On the basis of the results obtained in testing the model over a range of plant densities, i t appeared that the model performed adequately except at very low tree and shrub densities. The production of both trees and shrubs appeared to be underestimated and the death of a single individual at these low densities resulted in rather abrupt and marked increases in grass production. Examination of height frequency distribution of naturally occurring, mature, open-grown stands indicated the presence of a dis- proportionate number of faster than average growing individuals, the reason for which is not clear. The normal random deviates generated in the model did not allow for this upward shift in average growth rate at low densities. Therefore, an additional function which increases the mean value and reduces the standard deviation at low densities was added. The addition of this function has apparently solved the problem of growth underestimation. The abrupt and marked increase in grass production following the death of a tree or shrub is a result of the removal of the dead individual from the system, thereby freeing a large amount of growing space. Modification to the system to allow the gradual withdrawal of dead individuals is presently being undertaken. The changes made to the functional relationships and the growth rate frequency distributions showed the system to be f a i r l y stable; small modifications to the functions resulted in small changes in the results and large modifications resulted in large changes in the results. The model was tested against the results obtained by Kemper (1971) on Premier Ridge some 60 miles north of the study area. Unfortunately, due - 101 - to the lack of uniformity i n the calculation of productivity, the number of comparisons that could be made i s limited. Comparison of Kemper's (1971) data for grass production as a function of forest crown closure with that of the simulation shows that the simulated curve describes the data well except at crown closures greater than 70 per cent, where i t underestimated production. The response of simulated forb production to changing crown closure exhibits similar trends to those found by Kemper, but was s i g n i f i - cantly lower. The lower production values probably result from the fact that Kemper's measurements were made on plant communities in secondary grazing succession i n which forb production is greatly increased. Shrub production follows the trends found by Kemper but can't be compared directly because of the different methods of measurement and presentation of results. Insufficient data were collected to allow testing of the model's predictive accuracy for understory production on the study area. On the basis of the small amount of data available, the model appears to duplicate observed production trends. Extensive validity testing of the understory model must be carried out before i t can be used as a management tool for predicting future yields of ungulate food production. Despite the uncertainty as to i t s predictive accuracy, the understory model can be used to investigate plant interactions and to isolate c r i t i c a l relationships affecting productivity. The most interesting and instructive results obtained from the vegetative community simulator are those showing response of shrubs, grasses and forbs to the presence of trees and to competition among one another. Production and density were converted to metric units because this i s the - 102 - usual system used in range studies. Figure 46 shows the response of Amelanchier numbers and production under two tree stands, site index 60 with 2224 and 1112 trees per hectare, respectively, at age zero, as compared to growth in the absence of trees. The i n i t i a l number of Amelanchier was set at 2700 per hectare, representing the upper density found. The most striking feature in the comparison i s the tremendous reduction in number and production when trees are introduced into the system. Clearly, the production of wood and Amelanchier browse are incompatible. Similar relationships were found for a l l shade intolerant shrub species. Figure 47 shows a comparison of the rate of mortality and production of a shade intolerant species, Prunus, and an intermediate shade tolerant species, Symphoricarpos, as a function of changing forest crown closure and time. Both species show a decrease in numbers as crown closure increases, the rate of decrease being greatest in the shade intolerant species. In both cases production shows a lag effect; that is,production i n i t i a l l y increases despite a decrease in shrub numbers. The production increase i s explained by the fact that although the number of individuals i s decreasing, the relative size, and hence productivity, of each individual is increasing. The response of Agropyron to the presence of trees i s essentially similar to that of shade intolerant shrubs. Figure 48 shows the response of Agropyron production under the same conditions used to determine Amelanchier response to tree shade. Production was set at 475 kilograms per hectare which represents good production on the study area. Again production shows - 103 - Agropyron Number no trees 1112 trees per ha 2224 trees per ha Production cd M CD Ox 00 ^5 G O •H +J U 3 -a o u P. •H O I 300 200 100 3000 2000 1000 100 Time - yrs J 1 : 18 52 64 76 84 Tree Crown Closure - % at 1112 trees per ha i I i i i 0 40 80 90 96 99 Tree Crown Closure - % at 2224 trees per ha Figure 46. Simulated effect of tree crown closure on Amelanchier numbers and production. - 104 - Production 0 20 40 60 80 100 Time - yrs Figure 47. Simulated shrub mortality and production response to changing crown closure for a shade intolerant and an intermediate shade tolerant species. A: Prunus B: Symphoricarpos - 105 - — — trees absent - - — - 1112 trees per ha 2224 trees per ha Figure 48. Comparison of simulated Agropyron production for site index 60 with 2224, 1112 and zero trees per hectare. - 106 - a very rapid decrease as tree crown closure increases. A change in crown closure from 0 to 10 per cent causes a f i f t y per cent reduction in pro- duction. The production response of forbs and Calamagrostis and Koeleria to changing crown closure as affected by the presence and absence of shrubs, in this case Shepherdia, Prunus and Symphoricarpos, is shown in Figure 49. The production curves are a product of a number of complex interactions. Production of Calamagrostis and Koeleria increases in response to increasing crown closure both in the presence and absence of shrubs. However, the presence of shrubs depresses the rate of increase. In the absence of shrubs, forb production shows an i n i t i a l increase in response to increasing crown closure, and decreases when crown closure exceeds 30 percent. In the presence of shrubs, forb production i n i t i a l l y shows a faster and more pronounced increase, followed by a more rapid and pronounced decrease. The shift from a pronounced increase to a pronounced decrease in production results from the opposing effect of Shepherdia, Prunus and Symphoricarpos on forb production and differing mortality rates for the shrubs. Shepherdia results in a decrease in forb production, while Prunus and Symphoricarpos increase pro- duction. The decrease in forb production resulting from the presence of Shepherdia i s masked by a greater increase due to the presence of Prunus and Symphoricarpos unt i l age 20. At age 20, or crown closure of approximately 12 percent, mortality of Prunus and Symphoricarpos reduces their compensatory effect, and forb production shows a net decrease due to the effect of the surviving Shepherdia. - 107 - C a l a m a g r o s t i s and K o e l e r i a p r o d u c t i o n F o r b p r o d u c t i o n F o r e s t c rown c l o s u r e 0 20 40 60 80 100 T ime - y r s F i g u r e 4 9 . C o m p a r i s o n o f s i m u l a t e d f o r b and C a l a m a g r o s t i s and K o e l e r i a p r o d u c t i o n r e s p o n s e t o t r e e c rown c l o s u r e i n t h e p r e s e n c e and a b s e n c e o f s h r u b s . - 108 - Forest crown closure appears to be the most c r i t i c a l factor determining understory production. Therefore, the ungulate manager, faced with the problem of providing browse and grazing, must be able to predict future tree crown closures i f he i s to manage the resource. The tree growth model can provide this information. Figure 50 illustrates the effect of site index and stand density, the two most important factors affecting crown closure, on the rate of crown closure for three stand densities, 2224, 988 and 247 trees per hectare at year zero, and two site indices, 80 and 60. Tree locations were randomly assigned. Determination of trade-off functions between production of wood and Agropyron demonstrates even more clearly the degree of incompatibility between the two products (Figure 51). Agropyron production was specified at 475 kilograms per acre and the tree stands were assigned a site index of 60 with 2224 and 741 trees per hectare at age zero. Wood production was con- verted to cubic meters per hectare for the comparison. Under both stand conditions Agropyron production was decreased by approximately 55 per cent before any volume increment occurred. Reduction of stand density from 2224 to 741 trees per hectare resulted in a short term net increase i n Agropyron production at the cost of a loss of 111 cubic meters of wood per hectare. The response of Agropyron to the presence of Amelanchier, and other shrub species, is similar to that of trees in that there is a reduction in production, but this loss i s compensated by the production of browse (Figure 52). Agropyron production was specified at 475 kilograms per hectare and Amelanchier density at 2700 individuals per hectare. The trade-off function shows a straight line almost one-to-one conversion with a slight loss in production in the change from Agropyron to Amelanchier. crown closure. - 110 - 160 r cd u <u CO c o •H +J o 3 -a o M PM T3 O •s 140 120 100 80 60 40 20 0 SITE INDEX 60 2224 trees per ha 741 trees per Via J 100 200 300 400 500 Agropyron Production - kg per ha Figure 51. Trade-off between wood and Agropyron production. - I l l - Combined Agropyron and Amelanchier production Trade-off CO • G U <U P* 60 c o •H 4J O tJ o u CM 60 CO 3 I U CU •H 43 O 500 400 300 200 100 100 200 300 Agropyron Production 400 500 kg per ha Figure 52. Trade-off between Agropyron production and annual twig production of Amelanchier. - 112 - The discussion of the simulation results gives a brief insight into the complexity of interactions handled by the model and the form of output. The model appears capable of predicting the production of trees, shrubs, grasses and forbs in complex plant communities with a reasonable degree of accuracy, allows isolation of the effect and response of individual plant species and provides a basis for determining production trade-offs among different plant species and hence providing a management tool for the optimization of land productivity for specified management goals. It would seem worth while to give a brief example of how the model could be applied on the study area to evaluate the consequence of reducing the density of Douglas-fir stands on the production of wood and ungulate food. Amelanchier, Agropyron and forb production are compared under two Douglas-fir densities, 2224 and 247 trees per hectare at year zero with a site index of 60. Amelanchier production was calculated for 2700 individuals per hectare and Agropyron for a mean production of 40 grams per square meter. Table 9 shows the comparative productions. At 2224 trees per hectare, wood production reaches 8,000 cubic feet per hectare, while the production of Amelanchier, Agropyron and forbs i s essentially confined to the f i r s t 30 years. Amelanchier production reaches a maximum of 25 kg/ha at 20 years and then declines rapidly to zero at 32 years; Agropyron production reaches a maximum of 210 kg/ha at 10 years and declines to zero at 36 years,and forb production reaches a maximum of 55 kg/ha at 10 years and declines gradually to 10 kg/ha at 100 years. Reduction of stand density to 247 stems per hectare reduces wood production by approximately 70 per cent to 62.3 cubic meters per hectare but results in very significant increases i n the Table 9. Comparative productivities of wood, Amelanchier, Agropyron and forbs for two Douglas-fir stands with 2224 and .247 stems per acre and site index 60. SITE INDEX 60 2224 trees per ha 247 trees per ha Age Wood cu ft/ha Amel. kg/ha Agrop. kg/ha Forbs kg/ha Wood cu ft/ha Amel kg/h Agrop. a kg/ha Forbs kg/ha 0 0 0 0 0 0 0 0 0 10 0 12 210 55 0 11 400 40 20 0 25 60 25 0 25 390 45 30 250 3 10 12 8 31 375 50 40 1200 0 0 10 125 37 340 55 50 2500 0 0 10 250 38 310 60 60 3500 0 0 10 820 39 280 59 70 5000 0 0 10 1250 39 250 58 80 6300 0 0 10 1750 40 230 55 90 7500 0 0 10 2000 40 215 52 100 8000 0 0 10 2200 41 200 50 - 114 - production of Amelanchier, Agropyron and forbs. Amelanchier production increases steadily to a maximum of 41 kg/ha at 100 years; Agropyron pro- duction reaches a maximum of 400 kg/ha at 10 years and then declines to 200 kg/ha at 100 years,and forb production reaches a maximum of 60 kg/ha at 50 years and then declines to 50 kg/ha at 100 years. In the absence of trees.Amelanchier production would have reached 380 kg/ha, Agropyron 475 kg/ha and forbs 42 kg/ha. whether the increase in ungulate food pro- duction j u s t i f i e s the associated reduction in wood production is beyond the scope of this study. - 115 - POTENTIAL FOR APPLICATION At the present stage of development, the model has a number of limitations that should be overcome i f i t is to achieve i t s f u l l potential as a research, educational or management tool. The limitations may be segregated into (1) system or (2) component oriented restraints. The system oriented limitations result from system design and are relatively easily overcome. They include: (1) Inability to allow natural regeneration or cultural practices during the course of simulation. (2) Simulation plot must be square. (3) Definite upper limit on number of species and individuals within each species. (4) Excessive amounts of information generated. The component oriented limitations are of a more serious nature than the system restraints, depending on the purpose of the study. As a f e a s i b i l i t y study in using mathematical modelling to simulate plant ecosystem development, to approximate productive capabilities for alternate species or combinations of species, isolate c r i t i c a l functional relationships, assess probable implications of management for wood production on ungulate food production or as a learning tool, the limitations are of l i t t l e consequence. However, i f the model is to be used in management decision making, i t w i l l be necessary to (1) improve and elaborate the functional relationships, (2) derive additional relationships,and (3) undertake further validity testing. Additional information required would include (1) a more precise - 116 - definition of site quality, (2) the a b i l i t y to account for large variations in understory production due to annual climatic variations, (3) the a b i l i t y to allow mortality from causes other than competition,and (4) the development of methods for converting total plant production to utilizable production w i l l be necessary. Following these inclusions, the model would have direct application i n : 1) Determining production capabilities for alternate species or combinations of species. 2) Testing various combinations of species to determine the best combination in terms of ungulate food production. 3) Predicting food availability through the winter. 4) Predicting plant succession and the duration and amount of food produced by individual species and combinations of species. 5) Deriving trade-off functions between wood and ungulate food production. 6) Prediction of wood yield. - 117 - BIBLIOGRAPHY A. R.D.A. 1967. Maps compiled for the British Columbia Agro-Climatology Committee, A.R.D.A. Dept. of Geography, University of British Columbia. Anderson, R. C , Loucks, 0. L. and A. M. Swain. 1969. Herbaceous response to canopy cover, light intensity and throughfall precipitation in coniferous forests. Ecology 50(2): 255-263. Arney, J. D. 1972. Computer simulation of Douglas-fir tree and stand growth. Ph.D. Thesis. School of Forestry. Oregon State University. 77 pp. B. C. Forest Service. 1969. Cranbrook, Fernie, Upper Kootenay and Windemere P.S.Y.U.'s. Volume/age and D.B.H./age curves 7.1"+ and 11.1"+ D.B.H. for F, F mixtures and Py - TG 1-6, 8, 32. Medium and Poor sites. V.A.C.s 1012 and 1013. . Field Pocket Manual. Forest Surveys and Inventory Division. 83 pp. Barrett, J. W. 1970. Ponderosa pine saplings respond to control of spacing and understory vegetation. U.S.D.A., Forest Service, Res. Paper 106. 16 pp. Beil, C. E. 1969. Plant associations of the Cariboo-aspen-lodgepole pine- Douglas-fir parkland zone. Ph.D. Thesis. U.B.C. Dept. of Botany. 342 pp. Bella, I. E. 1969. Simulation of growth, yield and management of aspen. Ph.D. Thesis. Faculty of Forestry, University of British Columbia. 190 pp. Botkin, D. B., Janak, J. F. and J. R. Wallis. 1971. Some ecological consequences of a computer model of forest growth. IBM Research. RC3493 (# 15799). Yorktown Heights, New York. 44 pp. Brayshaw, T. C. 1955. An ecological classification of the ponderosa pine stands in the southeastern interior of British Columbia. Ph.D. Thesis. Dept. of Botany and Biology, U.B.C. 240 pp. . 1965. The dry forest of southern British Columbia. The Ecology of Western North America. 1: 65-75. Browne, J. E. 1962. Standard cubic-foot volume tables for the commercial tree species of British Columbia. B. C. Forest Service, Surveys and Inventory Division. A. Sutton, Queen's Printer, 107 pp. Cohen, K. J., and R. M. Cyert. 1961. Computer models in dynamic economics. Quart. Jour. Econ. LXXV: 112-127. Daubenmire, R. 1943. Vegetation zonation of the Rocky mountains. Botan. Rev. 9: 325-393. - 118 - Daubenmire, R. 1959. A canopy cover method of vegetation analysis. North- west Science, 33(1): 43-64. Donald, C. M. 1951. Competition among pasture plants. I. Intra-specific competition among annual pasture plants. Australian Jour. Agric. Res. I l l o s . 2(4): 355-375. Ferguson, R. B. Survival and growth of young bitterbrush browsed by deer. Jour. Wildlife Mgm., 32(4): 769-772. Forestry Handbook for British Columbia. 3rd. Edition 1971. Forest Club, U.B.C. 815 pp. Forrester, J. W. 1960. Industrial dynamics. Cambridge, MIT Press. 464 pp. Goulding, C. J. 1972. Simulation techniques for a stochastic model of the growth of Douglas-fir. Ph.D. Thesis. U.B.C. Faculty of Forestry. 234 pp. Holling, C. S. 1963. An experimental component analysis of population processes. Mem. Ent. Soc. Can. 32: 22-32. Hozumi, K., Koyama, H. and T. Kira. 1955. Intraspecific competition among higher plants. IV. A preliminary account of the interaction between adjacent individuals. J. Inst. Polytech. Osaka Cy University., Ser. D, 6: 121-130. Jameson, D. A. 1967. The relationship of tree overstory and herbaceous understory vegetation. J. Range Mgm. 20(4): 247-250. Jensen, C. E. 1964. Algebraic descriptions of forms in space. Columbus, Central States Forest Experimental Station. 75 pp. Kemper, J. B. 1971. Secondary autogenic succession in the southern Rocky mountain trench. M.Sc. Thesis. Department of Plant Science, University of British Columbia. 139 pp. Lee, Yam (Jim). 1967. Stand models for lodgepole pine and limits of their application. Ph.D. Thesis. Faculty of Forestry, University of British Columbia. 332 pp. Lin, Jim. 1969. Growing space index and stand simulation of young western hemlock in Oregon. Ph.D. Thesis. School of Forestry, Duke University. 182 pp. Lyon, L. J. 1968. An evaluation of density sampling methods in a shrub community. Jour. Range Mgm. 21(1): 16-20. _. 1968. Estimation of twig production of serviceberry from crown volumes. Jour. Wildlife Mgm., 32(1): 115-119. - 119 - McLean, A. 1969. Plant communities of the Similkameen Valley, British Columbia and their relationships to so i l s . Ph.D. Thesis. Washington State Univ., Pullman, Wash. 133 pp. McLean, A. and W. D. Holland. 1958. Vegetation zones and their relation to the soils and climate of the upper Columbia valley. Can. Jour. Plant. Sci., 38: 328-345. Mead, R. 1968. Measurement of competition between individual plants in a population. J. Ecology, 56(1): 35-45. Mitchell, K. J. 1967. Simulation and growth of even-aged stands of white spruce. Ph.D. Thesis, Yale University, 124 pp. Naylor, T. H., and J. M. Finger. 1967. Verification of computer simulation models. Man. Sci. 10(1): 105-114. Newnham, R. M. 1964. The development of a stand model for Douglas-fir. Ph.D. Thesis. Faculty of Forestry, University of British Columbia. 201 pp. Odum, E. P. and H. T. Odum. 1959. Fundamentals of Ecology. W. B. Saunders Company, Philadelphia and London, pp 546. Opie, J. E. 1968. Predictability of individual tree growth using various definitions of competing basal area. Forest Science 14(3): 314-323. Pa i l l e , G. 1970. Description and prediction of mortality i n some coastal Douglas-fir stands. Ph.D. Thesis. U.B.C. Faculty of Forestry. 300 pp. Smith, J. H. G. 1964. Root spread can be estimated from crown width of Douglas-fir, lodgepole pine and other British Columbia tree species. For. Chron. 40(4): 456-473. Stebbins, G. L. 1951. Variation and evolution in plants. Columbia University Press. N.Y. 643 pp. Tisdale, E. W. 1947. The grasslands of the Southern interior of British Columbia. Ecology 28: 346-382. Trewartha, G. T. 1954. An introduction to climate. 3rd Edition McGraw- H i l l Book Company, Inc. N. Y. 402 pp. Van Horn, R. 1968. Validation. In "The design of computer simulation experiments." pp. 232-251. Ed. T. H. Naylor. Durham, N. C. Duke Univ. Press. Young, J. A., McArthur, J. A. B. and D. W. Hendrick. 1967. Forage ut i l i z a t i o n in a mixed-coniferous forest of northeastern Oregon. J. Forestry 65: 391-393. - 120 - APPENDIX I. COMMON AND SCIENTIFIC NAMES PLANTS Douglas-fir Serviceberry Buckbrush Buffalo berry Cherry Rose Snowberry Wheatgrass Bluegrass Fescue Reedgrass Junegrass Brome grass Trembling aspen Douglas maple Juniper Mahonia Needlegrass Yarrow Pseudotsuga menziesii (Mirb.) Franco Amelanchier a l n i f o l i a Nutt. Ceanothus sanguineus Pursh. Shepherdia canadensis Nutt. Prunus emarginata (Dougl.) Rosa nutkana Presl. Symphoricarpos albus (L.) Blake Agropyron spicatum (Pursh) Scribn. and Smith Poa compressa L. Poa scabrella (Churb.) Benth. ex Vasey. Festuca Idahoensis Elmer Calamagrostis rubescens Buckl. Koeleria cristata Pers. Bromus tectorum L. Populus tremuloides Michx. Acer glabrum Torr. var. douglasii (Hook.) Dipp. Juniperus horizontalis Moench. Berberis repens Lindl. Stipa columbiana Macoun. Achillea millefolium L. Hitchcock, C. L., Cronquist, A., Ownby, M. and J. W. Thompson. 1969. Vascular plants of the Pacific Northwest. University of Washington Press. Seattle and London. 5 Vols. - 121 - Large purple aster Pasture wormwood Spring sunflower Beardtongue Tuffted phlox Aster conspicuus Lindl. Artemesia frigida Willd. Balsamorhiza sagittata (Pursh.) Nutt, Monarda fistulosa L. Penstemon spp. Phlox caespitosa Nutt. UNGULATES Elk Mule deer Rocky mountain big-horn sheep Cervus canadensis nelsoni, Bailey Odocoileus hemionus hemionus (Rafinsque) Ovis canadensis canadensis Shaw McTaggart Cowan, I. and C. J. Guiget. 1965. The mammals of British Columbia, A. Sutton, Queen's Printer (B. C. Provincial Museum, Hand- book No. 9). - 122 - APPENDIX II where: a - tree height (HT) b - crown radius (CR) c - height to l i v e crown base (HTblc) d - maximum crown width (CWmax) e - horizontal branch length (HBL) f - branch length (BL) g - height above branch base (HTAB) h - height to maximum crown width (HTCWmax) i - length of liv e crown j - point of maximum crown width - 123 - C C C C C c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c A P P E N D I X I I I P R O G R A M L I S T I N G F O R T H E G R O W T H S I M U L A T I O N O F T R E E S , S H R U B S , G R A S S E S A N D F O R B S O N A B I G - G A M E W I N T E R R A N G E M A I N P R O G R A M T R E E G R O W T H S I M U L A T I O N T R E E G R O W T H A N D C O M P E T I T I O N S T A N D M A P S S U B R O U T I N E T R E E S U B R O U T I N E X S E C T V E G E T A T I V E C O M M U N I T Y S I M U L A T I O N P R O G R A M C O N T R O L A N D S P E C I F I C A T I O N S « S U B R O U T I N E A G R O P • S U B R O U T I N E B R A N C H • S U B R O U T I N E R E M • S U B R O U T I N E A R E A * S U B R O U T I N E S G P D N • S U B R O U T I N E S U M S H R U B G R O W T H S H R U B M O R T A L I T Y S H R U f t A R E A S H R U B P R O D U C T I O N G R A S S A N D F O R B P R O D U C T I O N U T I L I T Y P R O G R A M S U N I F O R M A N D R A N D O M N U M B E R G E N E R A T O R S - 1 2 4 - C C M A I N P R O G R A M C C C S I M U L A T I O N O F T H E G R O W T H A N D C O M P E T I T I V E I N T E R A C T I O N S O F C . C T R E E S , S H R U B S A N D G R A S S E S C C O N A B I G - G A M E W I N T E R R A N G E I N T H E E A S T K Q O T E N A Y D I S T R I C T C C O f B R I T I S H C O L U M B I A C C C C D U M M Y M A I N P R O G R A M T O A L L O W B Y P A S S O F T H E T R E E G R O W T H S I M U L A T I O N C C D I M E N S I O N I A R R A ( 6 6 , 6 6 ) , B L 2 ( 9 6 ) , A C C ( 4 , 2 i ) , A T A ( 4 , 2 1 ) , A T G ( 4 , 2 l ) , A T F ( 4 1 , 2 1 ) , A P Q N A ( 4 , 2 t ) , A P 0 N C ( 4 , 2 1 ) , A P 0 N S ( 4 , 2 1 ) , A P D N P R ( 4 , 2 1 ) , A P O N R O £ 4 , 2 1 ) 2 , A P D N S Y ( 4 , 2 1 ) I N T E G E R * 2 J A f t R A ( 6 6 , 6 6 ) , N S E T ( 9 6 ) , I Q Q ( 9 6 , 5 ) , J a Q ( 9 6 , S ) , N A G E ( 5 0 ) , N N A M E 1 L C 4 ) ,NNC £ O i M ( « ) , N N S H E P ( 4 ) , N N P R U N ( 4 ) , N N R O S E ( 4 ) , N N S Y M P ( 4 ) , J R A N D ( 5 0 ) , K 2 R A N D C 5 0 ) , L R A N Q ( 5 0 ) , J J R A N D ( 1 0 0 ) , K K R A N D ( 1 0 0 ) , L L R A N D ( 1 0 0 ) , J 3 A M E L ( 2 0 ) , J C E Q N ( 2 0 ) , J S H E P ( 2 0 ) , J P R U N ( 2 0 ) , J R O S E ( 2 0 ) , J S Y M P ( 2 0 ) , I 5 C Q M C 1 5 0 ) , J C Q M ( 1 5 0 ) , I D E A O 1 ( 1 5 0 ) , I O E A D 2 C 1 5 0 ) , I D E A D 3 ( 1 5 0 ) , I D E A D 4 ( 1 5 0 ) 6 , L A R R 1 ( 6 6 , 6 6 ) , L A R R 2 ( 6 6 , 6 6 ) , L A R R 3 ( 6 6 , 6 6 ) , L A R R 4 ( 6 6 , 6 6 ) , I A R E A ( 1 5 3 ) , I D 7 I A M I ( 1 5 0 ) , I D I A M 2 C 1 5 0 ) , I D I A M 3 ( 1 5 0 ) , I O I A M 4 £ 1 5 0 ) , P E R ( 1 5 3 ) , E P E R ( 1 6 ) , K A e M E L C 4 , 2 1 ) , K C E 0 N ( 4 , 2 1 ) , * 3 H E P £ 4 , 2 1 ) , K P K U N ( 4 , 2 1 ) , K R 0 S E £ 4 , 2 1 ) , K 5 Y M P £ 4 , 9 2 1 ) , K C H A R ( 1 6 0 ) , I H T ( 1 0 0 , 9 7 ) , I C H A R ( 9 9 ) , I B B ( 5 0 , 9 7 ) , I R A N D ( 9 7 ) , I X X ( 9 7 ) , 1 J X X ( 9 7 ) , I V O L ( 9 7 ) , I D B H ( 9 7 ) , I C L ( 9 7 ) , I A P E R ( 9 7 ) , I C W ( 9 7 ) , I C B ( 9 7 ) , I S A ( 9 7 1 ) » J C H A R ( a ) , I D E A O C 9 7 ) C O M M O N I A R R A , 6 L 2 , A C C , A T A , A T G , A T F , A P D N A , A P O N C , A P D N S , A p D N P R , A P D N R O , A 1 P D N S Y , C S U B 1 , C S U 8 2 , C S U B 3 , C S U B 4 , R A D , B 0 R D A , X I N A , U T I L A , B O R O C , X I N C , U T I L 2 C 8 0 K D S , X I N ' S , U T I L S , A G E , C , C C , T A U T , T A U T S , T A U T T , T A U O , U N O C C , Y U N O C C P D N 1 , I T H R U , M , I S T R T , I I N T . I E N O , I Y U N O C , I A U T T Y , I U N O C C , I L O O P , I X , I S U B , I C O U N T 3 , I H T , I d B , J A R K A , L A R R 1 , L A R R 2 , L A R R 3 , L A R R 4 , I U Q , J U Q , I A R E A , P E R , K C H A R , I C O 4 M , J C O M , I D E A D 1 , I D E A D 2 , I D E A D 3 , I O E A D 4 , I D I AM 1 , I D I A M 2 , I D l A M 3 , I D I A M 4 , J J R S A N D , K K R A N O , L L R A N D , I C r t A R , 1 R A N D , I X X , J X X , I V O L , I D 8 H , I C L , I A P E R , I C W , I C B , 6 I B A , I D E A D , N S E T , K A M t L , K C E O N , K S H E P , K P R U N , K K O S E , K S Y M P , N A G £ , J R A N D , K R A N 7 D , L R A N O , J A M E L , J C E O N , J S M E P , J P R U N , J R O S E , J S Y M P , E P E R , N N A M £ L , N N C E 0 N , N N S 8 H E P , N N P R U N , N N R O S E , N N S Y M P , J C H A R I R 0 B 5 I 0 U T « 6 I T H R U s ^ D O 2 I a i , b 6 D O 2 J « l , 6 6 l A R S A f l , J ) » 1 0 0 0 0 0 0 0 2 J A R R A ( I , J ) « 0 C C R E A D S B R A N C H L E N G T M - U C C U P A N C Y D A T A D E C K C - 1 2 5 - DO 3 1 * 1 , 9 6 R E A 0 ( I R D , 5 ) B L 2 C I ) , N S , ( I Q Q ( I , I I ) , J Q O ( I , I I ) , I I « 1 , N S ) 3 N S E T ( I ) B N S 5 F O R M A T C F b . 4 , 1 3 1 3 ) C C • D E L O P T *** DELETE O P T I O N F O R T R E E S U B R O U T I N E *** C * * * * * * I F D E L O P T , L E , 0 T R E E S U B C A L L E D * * * * * * C R E A D ( I R Q , 1 0 ) D E L O P T 10 F O R M A T ( 1 2 ) C C R E A D S S T A R T I N G AGE I R E A O ( l R D , 1 5 ) I S T R T 1 5 F O R M A T ( 1 3 ) C C R E A D S G R O W T H I N T E R V A L C R E A O ( I « D , 2 0 ) I I N T 2 0 FORMAT(13) C C R E A D S UPPER A G E L I M I T C R E A D C I R O , 3 0 ) IEND 3 K F O R M A T ( I 3 ) I F ( O f c L O P T ) 1 Q P , 1 0 0 , 4 0 4 0 J B 0 0 0 5 0 I s I S T R T , I E N D , I I N T J B J * 1 5 0 N A 6 E ( J ) « 1 - 1 R E A 0 ( I R P , 5 5 ) I X 5 b F 0 R M A T C I 5 ) T I N T B I I N T N I N T s I E N D / I I N T C C I N C R E M E N T S C R O W N C L O S U R E I F T R E E S U B R O U T I N E N O T C A L L E D C C S U B l B j j . C S U B 2 8 1 0 , C S U B 3 B 2 0 , C v S U B 4 s 3 0 , G O T O b 5 hid C S U 8 l " C 5 u B l + 4 0 , CSUB2*C3UB2*40, C S U B 3 S C S U H 3 + 4 0 , C 8 U B 4 B C S U H 4 + 4 0 , G O T O b 5 6 2 C S U B 1 8 C S U 9 1 + 4 0 , CSUB2"CSUB2+40. C S U B 3 « C S u Q 3 + 4 0 . CSUB4*CSU64*40, - 1 2 6 - 6 5 M » 0 C C C A L L S U N D E R S T O R Y R O U T I N E S C C A L L A G R O P D O 7 0 I « i , N l N T n • i c C C A L L S U N D E R S T O R Y R O U T I N E S C /& C A L L A G R O P I F ( C 5 U B 1 . L T . 1 0 . ) G O T O f>0 I F C C S U 3 1 . L T , 5 0 . ) G O T O 6 2 C M B S T A N D A G E C I T R E E * I T U T R E E C I P O S B I T H B R A N C H C H A B M s H E I G H T T O M A X I M U M C R O W N W I D T H C B L • B R A N C H L E N G T H C H B L • H O R I Z O N T A L B R A N C H L E N G T H C I O C C » T E S T V A L U E F O R B R A N C H O C C U P A N C Y C 9 B , I b B B H E I G H T T O B R A N C H B A S E C H T , I H T , H T A , H T S = T R E E H E I G H T S C I C W , C W S , C W , A C W » M E A S U R E S O F C R O W N W I D T H C I V O L , V O L , V O L S , A V O L • M E A S U R E S O F V O L U M E C I D B H , D B H S , D B H , A D B H B M E A S U R E S O F D I A M E T E R A T B R E A S T H E I G H T C I B A , B A S , B A , A B A 8 M E A S U R E S O F B A S A L A R E A C I C L , C L S , C L , A C L a M E A S U R E S O F C R O W N L E N G T H C I A P E R « % C R O W N C L O S U R E C c X W D « 5 I 0 U T « > 6 C C I D E L A G ***** O P T I O N T O D E L E T E A G R O P Y R O N S U B R O U T I N E C A L L ***** C $ S S $ S I F I D E L A G , G T . 0 = C A L L S U B R O U T I N E A G R O $ $ $ $ $ C R E A D ( I R D , 3 ) I D E L A G 3 F O R M A T C I 2 ) C C I N T E G E R T O S T A R T G A U S S C R E A D C I R D , 1 0 ) I X 1 0 F O R M A T ( 1 5 ) C C S I *** R E A D S S I T E I N D E X *** C R E A D C I R D , 2 0 ) S I 2 0 F O R M A T ( F 5 , 2 ) C C A L L T R E E S I N I T I A L I Z E D A S B E I N G A L l V E *** I D E A D *** C N U M T R *** O P T I O N T O C H A N G E N U M B E R O F T R E E S *** - 1 2 7 - C R E A D C l H D , 3 & ) N U M T R 3 0 F O R M A T ( 1 3 ) C C M A T R I X *** O P T I O N T O A L L O C A T E T R E E L O C A T I O N S R A N D O M L Y *** C R E * D ( I R D , 3 l ) M A T R I X 3 1 F O R M A T ( 1 2 ) I F C M A T R I X . G T . l ) G O T O 5 1 C DO 5 5 I » 1 , N U M T R C A L L R A N D U ( I X , I Y , Y F L ) I X X ( I ) » V F L » « » 5 , * 1 , I D E A D ( I ) s 0 5 S I X - I Y C D O 5 6 I *» 1 i N U M T R C A L L R A N D U ( I X , I Y , Y F L ) J X X ( I ) » Y F L « f e 5 . * l . 5 b I X » I Y 3 7 I C M K « 0 D O 3 9 N U M T R DO 3 9 J 3 1 , H U M T R I F ( I . E Q . J ) G O T O 3 9 1 ' F C I X X C I ) , N E . I X X ( J } ) G O T O 3 9 I F ( J X X C I 3 . N E . J X X C J J ) G O T O 3 9 L X a J X X ( J ) 3 f l C A L L R A N U U ( J X , I Y , Y F L ) J X X ( J ) « Y F L * 6 5 . + 1 . i X a l Y I F ( J X X C J ) . f e ' Q . L X ) G O T O 3 f l I C H K a l 3 9 C O N T I N U E I F ( I C H * ) 5 9 , 5 9 , 3 7 5 1 D O « 0 I a l , N U M T R I D E A D C I ) " 0 4 0 * E A D ( I R D , 5 0 ) I X X ( I ) , J X X C X } 5 0 F O R M A T ( 2 1 3 ) 5 9 R E A O ( I R D , 6 0 ) I C H A R 6 0 F O R M A T ( 4 0 A 2 ) C C R E A D S O P T I O N S C C C I P R I N *** O P T I O N T O P R I N T O U T S T A N D M A P *** C ****** I F , t . E . 1 B N O M A P *** I F , G T , 1 • M A P ****** C R E A D C I R D , 7 3 ) I P R I N 7 0 F O R M A T ( 1 2 ) C C N C O O E *** O P T I O N T O P R I N T I A R R A C O D E *** » 1 2 8 " C ****** I F , U E , 1 • NO C O D E *** I F , G T , 1 • C O D E ****** C « E A D ( I « Q , 8 0 ) N C O D E 8 0 F O R M A T ( 1 2 ) C C . N T R E E *** O P T I O N T O P R I N T I N D I V I D U A L T R E E P A R A M E T E R S *** C ****** I F , L E , i • N O T R E E S *** I F , G T . 1 • T R E E S ****** C R E A D ( I R O , 9 a ) N T R E E 9 0 F O R M A T ( 1 2 ) C C I T R F N *** O P T I O N T O P R I N T T R E E F U N C T I O N S A S G R A P H S *** C ****** I F , L E , 1 8 MO F U N C T I O N S *** I F , G T . 1 • F U N C T I O N S * C R E A O U R O , 2 2 0 ) I T R F N 2 2 0 F O R M A T ( 1 2 ) R E A D ( I R O , 2 3 0 ) J C H A R 2 3 0 F O R M A T ( 2 A 1 ) C C L I N P R *** O P T I O N T O D I S P L A Y V E R T I C A L X S E C T T H R O U G H S T A N D *** C ****** I F , L E t 0 * NO X S E C T *** I F , G E , 1 A N D , L E , 6 6 X S E C T C P R I N T E D T H R O U G H L I N E a T O V A L U E O F L I N P R ****** C R E A O ( I R D , 2 4 0 ) L 1 N P R 2 4 0 F O R M A T ( 1 2 ) C C G E N E R A T E S R A N D O M N U M B E R S F O R A L L O C A T I O N T O I N D I V I D U A L T R E E S C U M T R E a N U M T R V V * . l + . « S * ( ( 1 0 0 , - U M T R E ) * * 6 , / 1 0 0 . * * 6 . ) A M " , 5 2 3 1 * . 2 5 * C ( 1 0 0 , - U M T R E ) * * 6 , / 1 0 0 . * * 6 , ) C DO 2 5 0 I M , N U M T R C A L L G A U S S C I X , . 2 3 2 2 , A M , V ) I F ( V , L T , V V ) V » V V I F ( V . G T . l . l ) V s l . l 2 5 0 I R A N D ( I ) • V « l t f 0 0 . C D O 3 1 0 1 1 * 1 , 1 9 0 0 3 1 0 J J = 1 , 1 9 I H T ( 1 1 » J J ) » 0 3 1 0 I B 6 ( I X , J J ) s 0 I L O 0 P a ( I t N D - I S T R T ) / I I N T * l J L C O P s i L O O P - i C C C A L C U L A T E S T R E E H E I G H T S F O R S P E C I F I E D A G E I N T E R V A L C T R E E H E I G H T S P L A C E D I N A R R A Y C JB0 c D O 3 5 0 I - 1 5 T R T , I t N O , I I N T - 129 J«J + 1 N A G E U ) " 1 - 1 X « I - 1 DO 3 5 0 K»1,NUMTR R A N D 1 « I R A N D ( K J R A N D 8 R A M D 1 / 1 0 0 K . I F ( X - 4 5 . 5 3 2 0 , 3 3 0 , 3 3 0 3 2 0 H T « R A N D * C S I / 7 6 . 3 * C I S . 0 5 * ( S I N ( X * 3 . 1 4 1 5 9 / 5 0 . - 3 , 1 4 1 5 9 / 2 , ) • 1 , ) • .7-.038 1 7 5 * X ) GO TQ 3414 3 3 0 riT"RANO*(SI/7b.)*Cl.66222+.7044*X) I F ( H T . L T . . 0 1 ) HT=,01 3 4 0 H T 8 « H T * 1 0 0 , 3 5 0 IHTCJiK)«HT2 C C C A L C U L A T E S HEIGHT AT AGE 1 * R E P R E S E N T S LOWEST BRANCH WHORL C DO 3 6 0 J»l,l C DO 3 6 0 K»i,NUMTR RAND 1 • I R AND (K3 RAND'RAND 1/ 1 000 • B B B R A N D * 1 8 0 5 . * ( S I N ( 3 . 1 4 1 5 9 / 5 0 , « 3 . 1 4 1 5 9 / 2 . ) + l . ) I F ( B B . L T , 1 „) e B o l , 3 6 0 I B B ( J , K ) ° B B C C P L A C E S H E I G H T S TO BRANCH BASE FROM AGE I N T E R V A L 2 TO IMAX I N ARRAY C DO 370 J » 2 , I L 0 0 P L«J-1 C DO 3 7 0 K M , N U M T R 3 7 0 I B B ( J r K ) « I h T ( L f K ) C C P R I N T S HEIGHT AND BRANCH BASE ARRAYS FOR T R E E S 1 TO 9 C W R I T E ( I O U T , 3 B 0 ) 3 8 0 F Q R M A T ( M ' , 5 X , ' T R E E H E I G H T S STOREO I N A R R A Y ' * / ) C w R I T E ( I O U T , 3 9 0 ) 3 9 0 F O R M A T ( 3 X , * TREE 1 T R E E 2 TREE 3 TREE 4 TREE 5 TREE 6 T R E E 17 TREE 6 TREE 9') C DO 4 0 0 I « l , l L O O P C 4 0 0 W R I T £ ( I O u T , 4 1 0 ) ( I H T ( I , J ) , J * 1 , 9 ) 4 1 0 F 0 R M A T ( 3 X , 1 2 1 3 ) C WRITE(I0Ur,42tf) 4 2 0 F O R M A T ( / / / / , 5 X , ' H E I G H T S TO BRANCH B A S E STORED I N A R R A Y ' , / ) C - 130 . W R I T £ ( I O U T , 3 9 0 ) c 0 0 4 4 3 I » 1 , I L 0 U P C 4 3 0 W « I T E ( 1 Q U T , 4 1 0 ) C I B B C 1 , J ) , J « l , 9 ) c . C S E T S I A R R A U , J ) • 1 0 0 0 0 0 0 0 c D O 4 4 0 I « 1 , 6 b C D O 4 4 0 J n l f b b 4 4 0 I A R R A ( I , J ) s l 0 0 0 0 0 0 0 4 5 0 M B 0 C W R l T E ( I Q U T , 4 5 t ) 4 5 1 P O R M A T ( / , S . X , ' S T A N D A G E * 0 Y R S . ** T R E E S N O T Y E T E S T A B L I S H E D ' ) C S U B l B i a C S U B 2 « 0 C S U @ 3 * 0 C S U B 4 « 0 I F C I O E L A G . L E . 0 ) G O T O 4 6 0 C G O T O 1 3 0 C C C A L L S T R E E G R O W T H R O U T I N E S C 1 0 0 C A L L T R E E 1 3 0 C A L L E X I T S T O P E N D C C C S U B R O U T I N E G A U S S ( I X , S , A M , V ) C C R A N D O M N U M B E R G E N E R A T O R F O R N O R M A L D I S T R I B U T I O N C A « 0 . 0 D O 5 0 1 8 1 , 1 2 C A L L R A N O U d X , 1 Y , Y ) I X • I Y 5 0 A » A « - Y V B ( A - 6 , 0 ) * S + A M R E T U R N E N D C C C S U B R O U T I N E R A N D U ( I X , I Y , Y F L ) C C R A N D O M N U M B E R G E N E R A T O R I Y B I X * 6 5 5 3 9 I F C I Y ) 3 # 6# 6 I Y * I Y + 2 1 4 7 4 8 3 f e 4 7 + l Y F U « I Y Y F l » Y F L * . 4 6 5 6 6 1 3 E " 9 R E T U R N END - 1 3 2 - S U B R O U T I N E T R E E C c c S T A N D G R O W T H S I M U L A T I O N F O R I N T E R I O R D O U G L A S - F I R D I M E N S I O N I A R R A ( b b , b b ) , B L 2 ( 9 b ) , A C C ( 4 , 2 1 ) , A T A ( 4 , 2 1 ) , A T G ( 4 , 2 1 ) , A T F ( 4 1 , 2 1 ) , A P D N A ( 4 , 2 1 ) , A P D N C ( 4 , 2 1 ) , A P D N S ( 4 , 2 1 ) , A P O N P R ( 4 , 2 1 ) , A P Q N R O £ 4 , 2 1 ) 2 , A P D N S Y ( 4 , 2 1 ) I N T E G E R * ? J A R R A ( b b , 6 b ) , N S E T ( 9 b ) , I O Q ( 9 b , 5 ) , J Q Q ( 9 b , 5 ) , N A G E ( 5 0 ) , N N A M E 1 L ( 4 ) , N N C E 0 N ( 4 ) , N N S M £ P ( 4 ) , N N P R U N ( 4 ) , N N R 0 S E £ 4 ) , N N S Y M P £ 4 ) , J R A N D ( 5 0 ) , K 2 R A N D ( 5 0 ) , L R A N D ( 5 0 ) , J J R A N D ( 1 0 0 ) , K K R A N D ( 1 0 0 ) , L L R A N D ( 1 0 0 ) , J 3 A M E L ( 2 0 ) , J C E Q N ( 2 0 ) , J S H £ P ( 2 0 ) , J P R U N ( 2 0 ) , J R O S E ( 2 0 ) , J S Y M P ( 2 0 ) , I 5 C O M ( 1 5 0 ) , J C O M ( 1 5 0 ) , I D E A D 1 ( 1 5 0 ) , I D E A D 2 ( 1 5 0 ) , I D E A D 3 £ 1 5 0 ) , I D E A D 4 ( 1 5 0 ) b , L A R R l ( b b , b 6 ) , L A R R 2 ( b b , 6 6 ) , L A R R 3 ( b 6 , b b ) , L A R R 4 ( b b , b b ) , I A R E A ( 1 5 3 ) , 1 0 7 1 A M I ( 1 5 0 ) , I D I A M 2 ( 1 5 0 ) , I D I A M 3 ( t 5 0 ) , I D I A M 4 ( 1 5 0 ) , P E R ( 1 5 3 ) , E P E R ( 1 b ) , K A A M E L ( a # 2 1 ) , K C E 0 N ( 4 , 2 1 ) , K S H E P ( 4 , 2 1 ) , K P R U N ( 4 , 2 1 ) , K R 0 S E ( 4 , 2 1 ) , K S Y M P ( 4 , 9 2 1 ) , K C H A R f l b 0 ) , I H T ( 1 0 0 , 9 7 ) , I C H A R ( 9 9 ) , I B B ( 5 0 , 9 7 ) , I R A N D £ 9 7 ) , I X X ( 9 7 ) , 1 J X X ( 9 7 ) , I V O L ( 9 7 ) , I D B H ( 9 7 ) , I C L ( 9 7 ) , I A P E R £ 9 7 ) , I C W ( 9 7 ) , I C B £ 9 7 ) , I B A ( 9 7 1 ) , J C H A R C 2 ) , I D E A D C 9 7 ) C O M M O N I A R R A , 6 L 2 , A C C , A T A , A T G , A T F , A P D N A , A P D N C , A P D N S , A P D N P R f A P D N R O , A 1 P D N S Y , C S U B 1 , C S U B 2 , C S U B 3 , C S U 8 4 , R A D , B 0 R D A , X I N A , U T I L A , B 0 R D C , X I N C , U T I L 2 C , B O N D S , X I N S , U T I L 5 , A G E , C , C C , T A U T , T A U T S , T A U T T , T A U O , U N O C C , Y U N O C C , P D N 1 , I T H R U , M , I S T R T , I I N T , I E N D , I Y U N O C , I A U T T Y , I U N O C C , I L Q O P , I X , I S U B , I C O U N T 3 , I H T , I B B , J A R R A , L A R R 1 , L A R R 2 , L A R R 3 , L A R R 4 , I Q Q , J Q Q , I A R E A , P E R , K C H A R , I C O 4 M , J C O M , I D E A D 1 , I D E A D 2 , I D E A D 3 , I D E A D 4 , I D I A M 1 , I D I A M 2 , I D I A M 3 , I D I A M 4 , J J R 5 A N D , K K R A N 0 , L L R A N D , I C H A R , I R A N D , I X X , J X X , I V O L , I O B H , I C L , I A P E R , I C w , I C 8 , b I B A , I D E A D , N S E T , K A M E L , K C E O N , K S H E P , K P R U N , K R O S E , K S Y M P , N A G E , J R A N D , K R A N 7 D , L R A N D , J A M E L , J C E D N , J S H E P , J P R U N , J R O S E , J S Y M P , E P E R , N N A M E L , N N C E O N , N N S 8 M E P , N N P R U N , N N R O S E , N N S Y M P , J C H A R C c c C c c c c c c c c I A R R A s A R R A Y R E P R E S E N T I N G 1 / 1 0 A C R E P L O T J A R R A a A R R A Y F O R P L O T T I N G C R O W N P R O F I L E S C S U 8 1 , , . . 4 a C R O W N C L O S U R E O F S U B - P L O T S S U B ! , , , , 4 a C R O W N A R E A S F O R 1 / 4 0 T H A C R E P L O T S H T A S s H E I G H T A B O V E B R A N C H C A E • E X P E C T E D C R O W N A R E A N U M T R * # O F T R E E S I C H A R a T R E E N U M B E R S I X X , J X X 8 I , J T R E E L O C A T I O N S I R A N D s T R E E G R O W T H P O T E N T I A L C A L L A G R O P C C C I N C R E M E N T S A G E I N T E R V A L 4 b 0 M»M+1 C D O 5 0 0 I « l , 6 6 C DO 5 0 0 J e l , b 6 5 0 0 J A R R A ( I , J ) B 0 1 F ( M - I L O O P ) 5 1 0 , 5 1 0 , 1 4 7 0 - 1 3 3 - 5 1 0 I T R £ E » 0 C C S T A R T S N E W T R E E C 5 2 0 I T R £ E " I T R £ E + l L 2 » l K T M B R a 1 I F ( I T R E E - N U M T R ) 5 3 0 , 5 3 0 , 7 9 0 5 3 0 H T l s I H T C M , i T R E E ) I F ( H T 1 , L E . 0 , ) G O T O 5 2 0 C C G O E S T O N E X T L O W E R B R A N C H A N D C A L C U L A T E S B R A N C H L E N G T H C D O 7 6 0 I B R s l , M I P O S a M + l - I o R 6 8 l « I B B C I P Q 5 , I T R e £ ) I F ( B 8 1 , L t , 0 , ) G Q T O 5 2 0 B B o B B l / 1 0 0 . H T » H T 1 / 1 0 0 , » B B H T A a H T l / 1 0 0 . H A B M a « 5 . 5 + , 4 2 5 * H T A I F ( H T , G T , 0 , ) G O T O 5 3 9 H T = . 1 5 3 9 I F ( H A B M ) 5 6 0 , 5 6 0 , 5 4 0 C C T E S T S A N D A D J U S T S H E I G H T T O C R O W N W I D T H M A X C 5 4 3 I F ( ( H T A - M A B M ) « H T J 5 5 0 , 5 3 0 , 5 6 0 5 5 0 8 L « . 9 8 * C H T A - H A b M ) * * , 7 L O T O 5 7 0 5 6 0 b L * . 9 8 « H T * * . 7 5 7 0 h a L » . 9 * B L - 3 . 3 * C B L * * 3 , / 2 0 . * * 3 . ) J X a J X X ( I T R E E ) I X a l X X C I T K E E ) C C D E S I G N A T E S P O S I T I O N O F T R E E B O L E C I A R R A ( I X , J X ) a 9 7 • I H T ( M , I T R E E ) * 1 0 0 + 1 0 0 0 0 0 0 0 K T H B R » u 2 C D O 7 6 0 L a K T H B R , 9 6 N S a N S E T ( L ) L 2 B L C C C R O W N G R O W T H A N D C O M P E T I T I O N C C R O W N G R O W T H C D O 7 6 0 K « 1 , N S I F C H B L - B L 2 C L > ) 7 7 0 , 5 8 0 , 5 8 0 5 8 0 I N C R a 0 5 9 0 I N C R a l N C R + 1 - 1 3 4 - G O T O £ 6 0 0 , 6 1 0 , 6 2 0 , 6 3 0 , 7 6 0 ) , I N C R 6 0 0 J a J X + J Q O ( L , K ) I s I X * I a Q C L , K ) G O T O 6 4 0 6 1 0 J B J X - J Q Q ( L , K ) I « I X - I Q Q C L » K ) G O T O 6 4 0 6 2 0 J s J X + J Q Q C L , K ) I « l X - I f l Q ( L , K ) G O TO 6 4 0 6 3 0 J » J X - J Q O ( L , K ) I 8 I X + I Q Q C L , K ) o 4 0 £ F ( I ) 6 7 0 , 6 7 0 , 6 5 0 6 5 0 l P ( I - 6 6 ) b 7 0 , & 7 0 , 6 6 0 6 6 0 1 * 1 - 6 6 6 7 0 I F ( J ) 7 0 0 , 7 0 0 , 6 6 0 6 8 0 I F ( J - 6 6 ) 7 0 0 , 7 0 0 , 6 9 0 6 9 0 J " J - 6 6 7 0 0 I F ( I ) 7 i 0 , 7 l 0 , 7 2 0 7 1 0 1 * 6 6 + 1 7 2 0 I F ( J ) 7 3 0 , 7 3 0 , 7 « 0 7 3 0 J * 6 6 + J C C T E S T F O R O C C U P A N C Y C 7 4 0 I O C C * 1 0 0 0 0 0 0 0 + ( I B B £ I P O S , I T R E E ) * 1 0 0 ) I F C l A R R A C X f J ) / 1 0 0 - I O C C / 1 0 0 ) 7 5 0 , 5 9 0 , 5 9 0 7 5 0 I A R R A ( I , J ) 8 1 8 0 0 0 0 0 0 I A R R A £ I , J ) 8 l A R R A ( I , J ) • I T R E E + I B B £ I P O S , I T R E E ) * 1 0 0 G O T O 5 9 0 7 6 0 C O N T I N U E 7 7 0 G O T O 7 8 0 7 8 0 C O N T I N U E C C G O E S T O N E X T T R E E C G O T O 5 2 0 C C P R I N T S M A T R I X C O D E S I N I A P R A ( C R O W N C O M P E T I T I O N ) C 7 9 0 I F ( N C O D E - 1 ) 8 8 0 , 8 8 0 , 8 0 0 C 8 0 0 W R I T E ( I O U T , 9 9 0 ) N A G E £ M ) C W R I T E ( I O U T , 8 1 0 ) 8 1 0 F O R M A T ( 2 X , ' C O D E S S T O R E D I N I A R R A M A T H l X - L O C A T I O N S I a l 0 T O 4 0 1 J a l T O 1 4 * ) D O 8 2 0 I C a O E « 4 0 , 5 0 C 6 2 0 W R I T E C I Q U T , 8 3 0 ) ( I A R R A ( I C O D E , J C O D E ) , J C O D E * 1 , 1 4 ) 8 3 0 F O R M A T ( 2 X , 1 4 1 9 ) - 1 3 5 - C W R I T E C I Q U T , 8 4 0 ) 8 4 0 F O R M A T C ' l ' , 2 X , ' L O C A T I O N S J M 5 T O 2 8 ' ) C DO 8 5 0 I C O U E « 4 0 , 5 0 C 8 5 0 W R I T E C I O U T , 8 3 0 ) C I A R R A ( I C O D E , J C O D E ) , J C O D E * 1 5 , 2 8 ) C W R I T E ( I O U T , 6 6 0 ) 8 6 0 F O R M A T C ' l ' , 2 X » ' L O C A T I O N S J s 2 9 T O 4 2 ' ) C D O 8 7 0 I C O O E s 4 0 , 5 0 C 8 7 0 W R I T E C I O U T , 8 3 0 ) ( I A R R A C I C O D E , J C O D E ) , J C 0 D E * 2 9 , 4 2 ) C 8 8 0 y O 8 9 0 L L 8 1 , N U M T R I C w ( L L ) » 0 I V O L ( L L ) » 0 I 0 8 H ( L L ) 8 # I 8 A ( L L ) B 0 I C L ( L L ) » 0 l A P E R ( L L ) « 0 8 9 0 I A R E A ( L L ) a i DO 900 L L M , N U M T R 9 0 0 I C 8 ( L L ) * 9 9 9 9 I C S (97)o0 D O 9 8 3 1 ^ 1 , 6 6 C C D E T E R M I N E S H E I G H T T O CROWN W I D T H M A X C DO 9 8 0 J » l , 6 b N E W a I A R R A ( I , J ) / l 0 0 * 1 0 0 L T R E E « I A R R A ( I P J J - N E W I F ( L T R E E ) 9 3 0 , 9 3 0 , 9 1 0 9 1 0 I F ( £ N E W / 1 0 0 - 1 0 0 0 0 0 ) - I C 8 ( L T R E E ) ) 9 2 0 , 9 3 0 , 9 3 0 9 2 0 I C B C L T R E E ) « N E W / 1 0 0 - 1 0 0 0 0 0 9 3 0 J A R R A ( I , J ) 8 l A R R A ( I , J ) - N E w N B " J A R R A ( I , J ) I F ( N B ) 9 6 0 , 9 6 0 , 9 4 0 9 4 0 I F ( N 6 « 9 7 ) 9 5 0 , 9 6 0 , 9 6 0 C C C A L C U L A T I O N O F C R O W N A R E A C 9 5 0 l A R E A ( N B ) • I A R E A ( N B ) «• 1 9 6 0 I F ( N 8 ) 9 7 i 4 , 9 7 0 , 9 8 0 . 9 7 0 N8898 9 8 0 J A R R A d , J ) B I C H A R ( N B ) C W R I T E ( I O U T , 9 9 0 ) N A G E ( M ) 9 9 0 F O R M A T C i ' , 2 X , ' S T A N D A G E » ' , 2 X , 1 3 , / / ) C 1 3 6 - C C A L C U L A T E S S T A N D P A R A M E T E R S C 1 0 0 0 D O 1 1 0 0 M M s l , N U M T R H T l ' I H T C M , M M ) H T * H 7 1 / 1 0 0 . 1 0 1 0 C R A R « I A R E A ( M M ) C C N A T U R A L M O R T A L I T Y C H A B M a « 5 , 5 + , 4 2 5 * H T I F ( H A B M ) 1 0 k l l , 1 0 0 1 , 1 0 0 2 1 0 0 1 H T A B B H T G O T O 1 0 0 3 1 0 0 2 H T A 8 « H T - H A B M I F C H T A B . L E . 0 . ) H T A B * , 1 1 0 0 3 B L » , 9 8 * H T A B * « , 7 H B L » . 9 * B L - 3 . 3 * C B L * * 3 , / 2 0 . * * 3 , ) I F ( H B L , L E , 0,) H B L B . 1 C A E « 3 , H l 5 9 » h B L * * 2 . I F ( ( C R A R / C A E ) , G T . . 1 ) G O T O 1 0 1 5 M A G E s M + i I H T ( M A S E , W M ) « I H T C M , M M ) I D E A Q (MM)a\ 1 0 1 5 I F ( C R A R * ( H T - 4 , 5 ) ) 1 0 2 0 , 1 0 2 0 , 1 0 3 0 1 0 2 0 D6HS0, G O TO 1 0 4 3 1 0 3 0 0 8 M " . 1 4 3 * C C R A R * C H T - 4 , 5 ) ) * * , 4 8 1 0 4 0 1 D B H ( M M ) B O B H * l 0 M f I F ( D B H ) 1 0 5 0 , 1 0 5 0 , 1 0 6 3 1 0 5 0 I B A ( M M ) " 0 G O T O 1 0 7 0 1 P 6 0 I B A ( M M ) s ( D 3 H / 2 . ) * * 2 , * 3 , 1 4 J 5 9 * 1 0 0 . 1 0 7 0 I C L ( M M ) a I H T ( M , M M ) - I C S ( M M ) A R E l a l A R E A (MM) I C W ( M M ) a 2 , * S Q R T ( A R E 1 / 3 , 1 4 1 5 9 ) * 1 0 0 , I F ( D B H ) 1 0 8 0 , 1 0 K 0 , 1 0 9 0 1 0 8 0 V 0 L 8 W, G O TO U00 1 0 9 0 V 0 L B - . 2 , 7 3 4 5 3 2 + ( 1 . 7 3 9 4 1 0 * A L O G ( D B H ) + J.. ! 6 b 0 3 3 * A L O G ( H T ) ) / 2 . 3 0 2 5 8 5 V O L * 1 0 . * * V Q L 1 1 0 0 I V Q L ( M M ) a V O L * 1 0 0 , C C P R I N T S M A P O F C R O W N O C C U P A N C Y C I F ( I P R I N - l ) 1 1 5 0 , 1 1 5 0 , 1 1 1 0 C 1 1 1 0 W R I T E f l O U T , 1 1 2 6 ) 1 1 2 0 F Q R M A T ( ' 9 ' , 1 2 6 ( ' * ' ) ) C D O 1 1 3 0 I » i , b 6 C - 1 3 7 - 1 1 3 0 W R I T E C I O U T , 1 1 4 0 ) ( J A R R A ( I , J ) , J * 1 , 6 5 ) 1 1 4 0 H 0 R M A T ( ' 9 ' , 6 5 A 2 ) C W R I T E ( I 0 U T , H 2 0 ) 1 1 5 0 H T S " 0 D B h S « 0 B A S « 0 C B S a 0 C L S " 0 C W S = 0 A R E A S B 3 V O L S a 0 A P E R S « 0 I F ( N T R E E - l ) 1 1 7 0 , 1 1 7 0 , 1 1 6 0 C 1 1 6 0 W R I T E C I O U T , 1 2 0 0 ) 1 1 7 0 N E W T R » a D O 1 2 2 0 N & M , N U M T R M O R T n l D E A D C N b ) I F ( H O R T . G T , 0 ) G O T O 1 2 2 0 N E W T R s N E W T R + i H T I » I H T ( M , N B ) H T B M T I / 1 0 0 . 0 8 H I = I D B H ( N B ) D B H s D B h I / 1 0 0 . B A I e l B A ( N S ) B A s B A l / J 4 4 0 0 . C B I B I C B ( N B ) I F C C B I - 9 0 0 0 ) 1 1 9 0 , 1 1 9 0 , 1 1 8 0 1 1 8 0 C B I 3 0 , 1 1 9 0 C B s C l U / l B B . C L B M T - C B C W I « I C W ( N B ) C W s C W l / 1 0 ' 3 . A R E A B I A R E A ( N B ) A P E R M 0 0 . * A R E A / 4 3 5 b , V O u I s l V O L ( N B ) V O L s V O L I / 1 0 0 . r l T S » H T S * H T D B H 5 B D B H S * Q B H B A S B B A S + B A CB5»CBS+Cb C L S » C L S + C L CwS«CrtS*CW A R E A S s A R E A S + A R E A V O L S B V O L S + V O U c c P R I N T S I N D I V I D U A L T R E E P A R A M E T E R S c I F ( N T R E E - l ) 1 2 4 0 , 1 2 4 0 , 1 2 1 0 1 2 0 0 F O R M A T C / / / , I X , ' T R E E # I J H E I G H T D B H B , A 1 3 8 - 1 . C R . B A S E C R , L E N G T H C.W, C , A R E A C , A . AS X V O L U 2 N E ' , / ) C 1 2 1 0 W R X T E U O U T , 1 2 3 0 ) N B , X X X ( N B ) , J X X ( N B ) , H T F D B H , B A , C B , C L , C W , A R E A , A P E R , 1 V O L 1 2 2 0 C O N T I N U E C C C A L C U L A T E S S T A N D A V E R A G E S C 1 2 3 0 F 0 R M A T ( 3 X , 3 I 6 , 9 F 1 1 , 2 ) 1 2 4 0 T R E E S « N E W T R A H T » H T S / T R E E S A D B H " 0 B H S / T R E E 5 A B A B B A S / T R E E S A C B « C B S / T R E E 5 A C L » C L S / 1 R E E S A C W » C W S / T R E E S A A R E A B A R S A S / T R E E S A A P E R « A R E A S / « 3 5 6 . * 1 0 0 . A V O L B V Q L S / T R E E S C C P R I N T S S T A N D A V E R A G E S C W R I T E ( I O U T , 1 2 5 0 ) 1 2 5 0 F 0 R M A T ( / / / / / , 5 X , ' S T A N O T O T A L S ' , / ) C h R I T E d O U T , 1 2 6 0 ) C 1 2 6 0 F O R M A T ( 2 X , ' N U M B E R O F T R E E S H E I G H T DBH 6 . A . C R . B A S I E C R . L E N G T H CW C . A R E A V O L U M E * ) C W R I T E ( I O U T , J 2 7 0 ) N E W T R , H T S , D B H S , B A S , C B S , C L S , C W S , A R E A S , V O L S 1 2 7 0 F O R M A T ( 7 X , I 3 , 5 X , 7 F l l , 2 , F 2 2 , 2 ) L O B T R « N U M T k - N E W T R C W R I T E ( I O U T , 1 2 8 0 ) L O S T R 1 2 8 0 F O R M A T ( ' 0 ' , 2 X , ' N U M B E R O F T R E E S H A V I N G D I E D S I N C E Y E A R 1 « ' , I 5 ) C W R I T E ( I O U T , 1 2 9 0 ) 1 2 9 0 F O R M A T ( / / / / , 5 X , ' S T A N D A V E R A G E S ' , / / , 2 X , ' N U M B E R O F T R E E S H E I G H T 1 D B H B , A . « T , CWM C R . L E N G T H C.W. C , A R E A C . 2 A , A S X V O L U M E ' , / ) C W R I T E ( I O U T , 1 3 0 0 ) N E W T R , A H T , A O B H , A b A , A C B , A C L , A C W , A A R E A , A A P E R , A V O L 1 3 0 0 F 0 R M A T ( 6 X , I 3 , 5 X , 9 F l l , 2 ) C C C A L C U L A T E S C R O W N A R E A S A N D C R O W N C L O S U R E S F O R S U B S E T S C S U B S E T S F O R M B A S I S F O R E V A L U A T I O N O F S H R U B A N D G R A S S R E S P O N S E T O C S T A N D C O N D I T I O N S C C 139 1 3 1 0 D O 1 3 3 0 I « l , 6 6 C 0 0 1 3 2 0 J * i , 6 6 1 3 2 0 J A R R A C I , J ) = 0 C D O 1 3 3 0 1 = 1 , 6 6 C D O 1 3 3 0 J « l , 6 6 N E W s l A R R A C I , J ) / 1 0 0 * 1 0 0 1 3 3 0 J A R R A ( I , J ) » I A R P A ( I # J ) - N E W S U B 1 * 0 S D B 2 * 0 3 U 6 3 3 0 S U B 4 * 0 I S U B S 0 1 3 4 0 I S U B a l S U B + 1 G O T O ( 1 3 5 0 , 1 3 7 0 , 1 3 9 0 , 1 4 1 0 ) , I S U B C C S U B S E T # 1 ** 1 = 1 , 3 3 / J = l , 3 3 ** c c 1 3 5 0 D O 1 3 6 0 1 * 1 , 3 3 C D O 1 3 6 0 J » l , 3 3 NBOJAWRA ( I , J ) I F ( N B . G E . l ) S U 6 1 « S U B 1 + 1 1 3 6 0 C O N T I N U E G O T O 1 3 4 0 C C S U B S E T # 2 ** I • 1 , 3 3 ; J • 3 4 , 6 6 ** C C 1 3 7 0 D O 1 3 8 0 l a l , 3 3 C D O 1 3 8 a J * 3 4 , 6 6 N B » J A R R A ( I , J ) I F ( N 6 , G E . l ) S U 6 2 B S U B 2 + 1 1 3 8 0 C O N T I N U E G O T O 1 3 4 0 C C S U B S E T # 3 *# I * 3 4 , 6 6 ; J • 1 , 3 3 ** C 1 3 9 0 D O 1 4 0 0 1 * 3 4 , 6 6 C D O 1 4 0 0 J = l , 3 3 N Q s J A R R A ( I , J ) I F ( N d . G E . i ) S U B 3 B S U B 3 + 1 1 4 0 0 C O N T I N U E G O T O 1 3 4 0 C C S U B S E T # 4 ** I * 3 4 , 6 6 ; J a 3 4 , 6 6 * » - 140 - c 1 4 1 0 DO 1 4 2 0 1 * 3 4 , 6 6 C DO 1 4 2 0 J » 3 4 , 6 6 N B i J A R R A C X , J ) I F ( N B , G E , 1 ) S U S 4 * S U B 4 + 1 1 4 2 0 CONTINUE C 8 U 8 l " S U B l / 1 0 8 9 t * 1 0 0 , C S U B 2 a S U B 2 / 1 0 8 9 , * 1 0 0 , csua;jaoU:33/i089, M 0 0 , C S U 8 4 * 3 U B 4 / 1 0 8 9 , * 1 0 0 . c W R I T E C I O U T , 1 4 3 0 ) 1 4 3 0 F O R M A T c / / / / , 5 X , 'CROWN AREA AND CROWN CLOS U R E S FOR S U B S E T S ' , / / / ) C WRITE ( I O U T , 1 4 4 0 ) 1 4 4 0 F 0 R M A T C 1 2 X , 'SUB-PLOT 1 - 1 * 1 , 3 3 J * 1 , 3 3 ' , 2 X , ' S U B - P L O T 2 - 1 * 1 , 3 3 1 J « 3 4 , 6 6 ' , 2 X , ' S U B - P L O T 3 - I«34,6b J« 1 , 3 3 • , 2 X , ' S U B - P L O T 4 - 1 * 3 4 , 6 6 2 J » 3 4 , 6 6 ' , / / ) C W R I T E ( I O U T , 1 4 5 0 ) S U B 1 , S U B 2 , S U B 3 , S U B 4 1 4 5 0 FORMAT (IX,'CROWN AREA « ' , F 1 5 , 2 , 3 F 2 9 , 2 , / / ) C WRITE ( I O U T , 1 4 6 0 ) C S U B 1 , C S U B 2 , C S U B 3 , C S U B 4 1 4 6 0 FORMAT(IX,'CROWN CLOSURE " ' , F 12 . 2 , 3 F 2 9 , 2 ) I F ( L I N P R . L E . 0 ) GO TO 1 4 6 3 C C A L L XSECT ( L I N P R ) 1 4 6 3 I F ( I D E L A G ( L E , 0) GO TO 4 6 0 C C A L L AGROP GO TO 4 6 0 1 4 7 0 I F ( I T R F N - l ) 1 4 9 0 , 1 4 9 0 , 1 4 8 0 C 1 4 8 0 C A L L TRFUN 1 4 9 0 RETURN END - 1 4 1 - S U B R O U T I N E X S E C T C L I N P R ) C C P R I N T S V E R T I C A L X S E C T I O N T H R O U G H S T A N D C D I M E N S I O N I A R R A ( 6 6 , 6 6 ) , B L 2 ( 9 6 ) , A C C ( 4 , 2 1 ) , A T A ( 4 , 2 l ) , A T G £ 4 , 2 l ) , A T F £ 4 1 , 2 1 ) , A P D N A ( 4 , 2 1 ) , A P O N C ( 4 , 2 1 ) , A P D N S ( 4 , 2 1 ) , A P D N P R ( 4 , 2 1 ) , A P O N R O ( 4 , 2 1 ) 2 , A P D N S Y ( 4 , 2 1 ) I N T E G E 8 * £ J A R R A ( 6 6 , 6 6 ) , N S E T ( 9 6 ) , I Q Q ( 9 6 , 5 ) , J Q Q ( 9 b , 5 ) , N A G E £ 5 0 ) , N N A M E 1 L ( 4 ) , N N C E 0 N ( 4 ) , N N S H E P ( 4 ) , N N P R U N ( 4 ) , N N R O S E ( 4 ) , N N S Y M P ( 4 ) , J R A N D C 5 0 ) , K 2 R A N D ( 5 0 ) , L R A N D ( 5 0 ) , J J R A N D ( 1 0 0 ) , K K R A N D ( 1 0 0 ) , L L R A N D ( 1 0 0 ) , J 3 A M E L C 2 0 ) , J C £ O N ( 2 0 ) , J S H E P ( 2 0 ) , J P R U N ( 2 0 ) , J R O S E ( 2 0 ) , J S Y M P C 2 0 ) , I 5 C O M C 1 5 0 ) , J C O M ( l S a ) , I D E A D 1 ( 1 5 0 ) , I D E A D 2 ( 1 5 0 ) , I D E A D 3 ( 1 5 0 ) , I D E A D 4 £ 1 5 0 ) 6 , L A R R 1 £ 6 6 , 6 6 ) , L A R R 2 ( 6 6 , 6 6 ) , L A R R 3 ( 6 6 , 6 6 ) , L A R R 4 ( 6 6 , 6 6 ) , I A R E A ( 1 5 3 ) , I D 7 I A M I £ 1 5 0 ) , I D I A M 2 ( 1 5 0 ) , I D I A M 3 ( 1 5 0 ) , I D I A M 4 ( 1 5 0 ) , P E R ( 1 5 3 ) , E P E R ( l b ) , K A 6 M E L ( 4 , 2 1 ) , K C E 0 N ( 4 , 2 1 ) , K S H E P ( 4 , 2 1 ) , K P R U N ( 4 , 2 1 ) , K R O S E ( 4 , 2 1 ) , K 5 Y M P ( 4 , 9 2 1 ) , K C H A R ( 1 6 0 ) , I H T ( 1 0 0 , 9 7 ) , I C H A R ( 9 9 ) , I B B ( 5 0 , 9 7 ) , I R A N D £ 9 7 ) , I X X ( 9 7 ) , 1 J X X ( 9 7 ) , I V O L ( 9 7 ) , I D B H ( 9 7 ) , I C L ( 9 7 ) , I A P E R ( 9 7 ) , I C W ( 9 7 ) , I C B £ 9 7 ) , I B A ( 9 7 1 ) , J C H A R £ 2 ) , I D E A D £ 9 7 ) COMMON I A R R A , 8 L 2 , A C C , A T A , A T G , A T F , A P D N A , A P D N C , A P D N S , A P D N P R , A P D N R O , A 1 P D N S Y , C S U 8 1 , C S U B 2 , C S U B 3 , C S U B 4 , R A D , B 0 R D A , X I N A , U T I L A , B O R D C , X I N C , U T I L 2 C B O R D S , X I N S , U T I L S , A G E , C , C C , T A U T , T A U T S , T A U T T , T A U O , U N O C C , Y U N O C C P D N 1 , I T H R U , M , I S T R T , 1 1 N T , I E N D , I Y U N O C , I A U T T Y , I U N O C C , I L O O P , I X , I S U B , I C 0 U N T 3 , I H T , I B B , J A R R A , L A R R 1 , L A R R 2 , L A R R 3 , L A R R 4 , I Q Q , J Q Q , I A R E A , P E R , K C H A R , I C O 4 M , J C O M , I D E A D 1 , I C E A D 2 , I D E A D 3 , I D E A D 4 , I D I A M I , I D I A M 2 , I D I A M 3 , I O I A M 4 , J J R 5 A N D , K K R A N Q , L L R A N D , I C H A R , I R A N D , I X X , J X X , I V O L , I O B H , I C L , I A P E R , I C W , I C B , 6 I B A , I D E A D , N S E T , K A M £ L , K C E O N , K S H £ P , K P R U N , K R O S E , K S Y M P , N A G E , J R A N D , K R A N 7 D , L R A N D , J A M E L , J C E O N , J S H E P , J P R U N , J R O S E , J S Y M P , E P E R , N N A M E L , N N C E O N , N N S 8 H E P , N N P R U N , N N R O S E , N N S Y M P , J C H A R C C C J L O C a L O C A T I O N O N L I N E C I L I N E a L I N E C I S C L E a S C A L I N G F A C T O R C NB a C H A R A C T E R T O B E P R I N T E D C c I C U T a b I S C L E a a C 9 9 1 DO 9 9 2 K C L « 1 , 6 6 C D O 9 9 2 J C L a l , 6 6 9 9 2 J A R R A C K C L , J C L ) a 0 D O 9 9 3 J L 0 C " 1 , 6 6 I L I N E a i A R R A U l N P R , J L O C ) N a I L I N E - I L I N E / 1 0 0 * 1 0 0 I L O C a ( I L I N E + 5 0 0 0 / 1 0 0 0 0 * 1 0 0 0 0 - 1 0 0 0 0 0 0 k ) ) / 1 0 0 0 0 I F C X L O C . L T . i ) I L O C a l I F ( I S C L E . G T , 0 ) GO T O 9 9 5 I F f I L Q C . G T . 6 6 ) I S C L E a 2 I F ( I S C L E - 1 ) 9 9 4 , 9 9 4 , 9 9 1 - 1 4 2 9 9 4 J A R R A C I L Q C , J L O C ) » N G O T O 9 9 3 9 9 5 I L 0 C B ( I L 0 C + 1 ) / 2 I F C I L O C . L T . 1 ) I L Q C M J A R R A C I L O C , J L O C ) » N 9 9 3 C O N T I N U E C D O 9 9 8 J « l , 6 6 C D O 9 9 8 1 * 1 , 6 6 9 9 6 N B s J A R R A C I , J ) I F ( N B ) 9 9 7 , 9 9 7 , 9 9 6 9 9 7 N B • 9 9 9 9 8 J A R R A C I , J J s I C H A R C N B ) C W R I T E ( I 0 U T , 9 8 1 ) L I N P R 9 8 1 F Q R M A T ( ' 1 ' , / / / / , 2 0 X , ' C R O S S - S E C T I O N A L P R O F I L E O F S T A N D - S E C T I O N T 1 H R 0 U G H L I N E ' , 1 2 , / / / ) I F C I S C L E . G T . 1 ) G O T O 9 8 7 C W R I T E C I 0 U T , 9 8 2 ) 9 8 2 F O R M A T ( 6 3 X , ' V E R T I C A L S C A L E - I F T • « 1 L I N E * , / / , 5 8 X , ' H O R I Z O N T A L S C 1 A L E - I F T . B 2 S P A C E S ' , / / / ) G O T O 9 6 8 C 9 8 7 W R I T E C I 0 U T , 9 8 3 ) 9 8 3 F O R M A T C 6 0 X , ' V E R T I C A L S C A L E - 2 F T , * 1 L I N E ' , / / , 5 8 X , ' H O R I Z O N T A L S C A 1 L E - I F T , » 2 S P A C E S ' , / / / ) C 9 8 8 W R I T E C I 0 U T , 9 6 4 ) 9 6 4 F 0 R M A T C 6 3 X , ' L E G E N D ' , / / , 6 5 X , ' N U M B E R S R E F E R T O T R E E N U M B E R ' , / / , 6 5 X , • I B R E P R E S E N T S B O L E P O S I T I O N ' , / / / , 1 2 6 X , ' L I N E S ' ) C D O 9 8 5 I « l , 6 6 K » 6 7 - X C 9 6 5 W R I T E C I O U T , 9 6 6 ) C J A R R A ( K , J ) , J B 1 , 6 3 ) , K 9 8 6 F 0 R M A T C ' 9 ' , 6 3 A 2 , I 2 ) C W R I T E ( I 0 U T , 9 7 1 ) 9 7 1 F O R M A T C » 9 » , 1 3 1 C ' * ' ) ) R E T U R N E N D - 1 4 3 - S U B R O U T I N E A G R O P D I M E N S I O N I A R R A ( 6 6 , 6 6 ) , B L 2 ( 9 6 ) , A C C ( 4 , 2 1 ) , A T A ( 4 , 2 1 ) , A T G ( 4 , 2 l ) , A T F ( 4 1 , 2 1 ) , A P D N A ( 4 , 2 1 ) , A P D N C ( 4 , 2 1 ) , A P D N S ( 4 , 2 1 ) , A P D N P R ( 4 , 2 1 ) , A P D N R O ( 4 , 2 1 ) 2 , A P D N S Y C 4 , 2 1 ) I N T E G E R * 2 J A R R A ( 6 6 , 6 6 ) , N S E T ( 9 6 ) , I O Q ( 9 6 , 5 ) , J Q Q ( 9 6 , 5 ) , N A G E ( 5 0 ) , N N A M E 1 L ( 4 ) , N N C E 0 N ( 4 ) , N N S H E P ( 4 ) , N N P R U N ( 4 ) , N N R 0 S E ( 4 ) , N N S Y M P ( 4 ) , J R A N D C 5 0 ) , K 2 R A N D ( 5 0 ) , L R A N D ( 5 0 ) , J J R A N D ( 1 0 0 ) , K K R A N D ( 1 0 0 ) , L L R A N O ( 1 0 0 ) , J 3 A M E K 2 0 ) , J C E O N ( 2 0 ) , J S H E P ( 2 0 ) , J P R U N ( 2 0 ) , J R O S E ( 2 0 ) , J S Y M P ( 2 0 ) , I 5 C O M U 5 0 ) , J C O M ( 1 5 0 ) , I D E A D 1 ( 1 5 0 ) , I D E A D 2 ( 1 5 0 ) , I D E A D 3 ( 1 5 0 ) , I D E A D 4 ( 1 5 0 ) 6 , L A R R 1 ( 6 6 , 6 6 ) , I A R R 2 ( 6 6 , 6 6 ) , L A R R 3 ( 6 6 , 6 6 ) , I A R R 4 ( 6 6 , 6 6 ) , I A R E A ( 1 5 3 ) , I D 7 1 A M I ( 1 5 0 ) , I D I A M 2 C 1 5 0 ) i I D I A M 3 ( 1 5 0 ) , I D I A M 4 ( 1 5 0 ) , P E R ( 1 5 3 ) , E P E R ( 1 6 ) , K A 8 M E L ( 4 , 2 1 ) , K C E 0 N ( 4 , 2 1 ) , K S H E P ( 4 , 2 1 ) , K P R U N ( 4 , 2 1 ) , K R 0 S E ( 4 , 2 1 ) , K S Y M P ( 4 , 9 2 1 ) , K C H A R ( 1 6 0 ) , I M T ( 1 0 0 , 9 7 ) , I C H A R ( 9 9 ) , 1 8 8 ( 5 0 , 9 7 ) , I R A N D ( 9 7 ) , I X X ( 9 7 ) , 1 J X X ( 9 7 ) , I V 0 U ( 9 7 ) , I D 8 H ( 9 7 ) , I C L ( 9 7 ) , I A P E R ( 9 7 ) , I C W ( 9 7 ) , I C B ( 9 7 ) , I 8 A ( 9 7 1 ) , J C M A R ( 2 ) , I D E A D ( 9 7 ) C O M M O N I A R R A , B L 2 , A C C , A T A , A T G , A T F , A P D N A , A P D N C , A P D N S , A P D N P R , A P D N R O , A l P D N S Y , C S U B i , C S U B 2 , C S U 8 3 , C S U B 4 , R A D , B 0 R D A , X I N A , U T I L A , B O R D C , X I N C , U T I L 2 C , B O R D S , X I N S , U T I L S , A G E , C , C C , T A U T , T A U T S , T A U T T , T A U O , U N O C C , Y U N O C C , P D N 1 , I T H R U , M , I S T R T , I I N T , I E N D , I Y U N 0 C , I A U T T Y , I U N 0 C C , I L 0 0 P , I X , I S U 8 , I C 0 U N T 3 , I h T , I B B , J A R R A , L A R R I , L A R R 2 , L A R R 3 , L A R R 4 , I Q Q , J Q Q , I A R E A , P E R , K C M A R , I C O 4 M , J C O M , I D E A D 1 , I D E A D 2 , I D E A D 3 , 1 D E A D 4 , I D I AM 1 , I D I A M 2 , I D I A M 3 , I D I A M 4 , J J R S A N D , K K R A N D , L L R A N D , I C M A R , I R A N D , I X X , J X X , I V O L , I D B H , I C L , I A P E R , I C W , I C B , 6 I B A , I D E A U , N S E T , K A M E L , K C E O N , K S H E P , K P R U N , K R O S E , K S Y M P , N A G E , J R A N D , K P A N 7 D , L R A N D , J A M E L , J C E O N , J S H E P , J P R U N , J R O S E , J S Y M P , E P E R , N N A M E L , N N C E O N , N N S 8 H E P , N N P R U N , N N R 0 S E , N N S Y M P , J C H A R C C C L A R R 1 , , , 4 B S H R U B , G R A S S * F O R B G R O W T H A R R A Y S C I T M R U » C O U N T E R C K C H A R * S H R U B N U M B E R C E P E R • E X P E C T E D P E R I M E T E R O F S H R U B S C I D 1 A M 1 , , , 4 a S H R U B D I A M E T E R C I D E A D 1 , , . 4 • D E A D S H R U B S C L A M E L , . . , L S Y M P " V A R I A B I L I T Y I N S I Z E O F S H R U B S P E C I E S C N N A M E L , • t , N N S Y M P * N U M B E R O F S H R U B S B Y S P E C I E S / S U B - P L O T C Z E R O A R R A Y S F O R P R I N T I N G # S H R U B S A N D P R O D U C T I O N , A G E , C R O W N C C L O S U R E C J R A N D , , . , I . L R A N O » S H R U B S P E C I E S G R O W T H P O T E N T I A L C I A R E A , A R E A S , A A R E A S a C R O W N A R E A M E A S U R E M E N T S C I R D a S I O U T « 6 C D O 3 I = l , b 6 D O 3 J a l , 6 6 3 J A R R A ( I , J ) 3 0 C I F ( I T H R U . G T , 0 ) G O T O 1 5 0 I F ( M , G T , 0 ) GO TO 1 5 0 C R E A D ( I R 0 , 2 ) E P E R - 1 4 4 - 2 F O R M A T ( 1 6 1 3 ) C R E A 0 ( I R D , 4 ) K C H A R 4 F O R M A T ( 4 f lA2) C DO 5 I « i , 1 5 0 I D I A M l ( I ) a 0 I 0 I A M 2 C I ) » 0 I D I A M 3 ( I ) » a I D I A M 4 ( I J 80 I D E A Q 1 CD 3 0 I D E A 0 2 C I ) a 0 I D E A D 3 ( I ) 8 0 5 I D t A D 4 ( I ) 8 0 C D O 7 I a l , 6 f e C U O 7 J a i . f e e L A R R 1 ( I , J ) s 0 L A R R 2 ( I , J ) 8 0 U A R R 3 ( I , J ) 8 0 7 L A R R 4 ( I , J ) s 0 C R E A D ( I R D , 1 0 ) L A M E L , L C E O N , L S H E P , L P R U N , L R O S E , L S Y M P 1 0 F O R M A T ( 6 1 b ) C R E A D ( I R D , 1 5 ) I S H R U B , I N D I S H 1 5 P 0 R M A T ( 2 I 3 ) C R E A D ( I R D , 2 0 ) I D D 2 0 F O R M A T ( 1 3 ) C D O 3 0 I « l , 4 C 3 0 R E A D ( I R D , 4 0 ) N M A M E L C I ) , N N C E O N ( I ) , N N S H E P ( I ) , N N P R U N ( I ) , N N R O S E ( I ) , N N S 1 Y M P ( 1 ) 4 0 F 0 R M A T ( 6 I 4 ) C 0 0 4 5 I a l , 4 C D O 4 5 J a l , 2 1 A C C ( I , J ) a 0 , A T A ( I , J ) 8 0 , A T 6 ( I # J ) « 0 . A T F ( I , J ) a 0 , A P D N A ( I , J ) 8 0 , A P D N C C I , J ) 8 0 , A P D N S ( I , J ) 8 0 , A P D N P R C I , J ) a 0 , A P D N R O ( I , J ) a g , A P D N 5 Y ( I , J ) 8 0 , - 1 4 5 K A M E L C I , J ) " 0 « C E Q N ( I , J ) * 0 K S H E P C 1 , J ) « 0 K P R U N C I , J ) B 0 K R O S E C I , J i « 0 4 b K S Y M P C I » J 3 « 0 C C C A L C U L A T E S H R U B S P E C I E S G R O W T H P O T E N T I A L C V A M E L a L A H E L V A H E L « V A M E L / 1 0 0 0 0 . v c e o N a L c e o N V C E O N " V C E O N / 1 0 P 0 0 , V S H E P « L S H E P V S H E P s V S H E P / 1 0 0 0 0 . V P R U N « I P K U N V P R U N s y P H U N / 1 0 0 0 0 , V R O S E * L R O S E V R O S E a V R O S E / 1 0 B 0 0 . V S Y M P s ^ S Y M P V S Y M P » V 8 Y M P / 1 0 0 0 0 , C DO 60 1 * 1 ,50 C A L L G A U S S ( i X , V A M E ! _ , 1 , 0 0 0 0 , V ) I F C V , L T , , 1 ) V * . l I F ( V . G T . i , b ) V s j . b 6 0 J R A N D C I ) « V * 1 0 0 0 . C D O 7 0 1 * 1 , 5 0 C A L L G A U S S ( I X , V C E O N , 1 , 0 0 0 0 , V ) I F C V . L T . . 1 ) V " . l I F ( V . G T . l . b ) V * 1 . 6 7 0 K R A N D ( I ) a V * 1 0 0 0 , C D O 8 a 1 * 1 , 5 0 C A L L G A U S S ( I X , V S H E P , 1 , 0 0 0 0 , V ) I F ( V , L T . . l ) V * . l I F ( V . G T . l . b ) V a l , 6 8 0 L R A N D ( I ) B V * 1 0 0 0 , C DO 9 2 1 * 1 , 1 0 0 C A L L G A U S S ( I X , V P R U N , 1 , 0 0 0 0 , V ) I F ( V , L T , . l ) V a . l I F ( V . G T . l . b ) V a l . b 9 0 J J R A N O ( I ) " V * i 0 0 0 , C DO 1 0 0 1 * 1 , 1 0 0 C A L L G A U S S ( I X , V K O S E , 1 , 0 0 0 0 , V ) I F C V . L T . . 1 ) V a . l I F C V . G T . 1 . 6 ) V a l . 6 1 0 0 K K R A N D ( I ) * V * 1 0 0 0 « - 146 C D O 1 1 0 1 * 1 , 1 0 0 C A L L G A U S S ( I X , V S Y M P , 1 . 0 0 0 0 , V ) I F C V . L T . , 1 ) V * . l I P ( V . G T . 1 . 6 ) V * 1 . 6 1 1 0 L L R A N D C I ) * V * 1 0 0 0 • C C 1 3 0 R E A D C J R D , 1 4 0 ) P D N 1 4 0 F O R M A T C p 6 » 2 ) C 1 5 0 W R I T E C I O U T , 1 6 0 ) 1 6 0 F O R M A T ( 2 X , ' N U M B E R O F S H R U B S B Y S P E C I E S A T A G E 1 ' , / / , T 2 4 , ' A M E L ' , T 3 4 1 , ' C E Q N ' , T 4 4 , ' S H E P ' , T 5 4 , ' P R U N * , T 6 4 , * R O S E ' , T 7 4 , ' 5 Y M P ' , / / ) C D O 1 7 0 1 * 1 , 4 C 1 7 0 W R I T E C I O U T , 1 8 0 ) I , N N A M E L a ) , N N C E O N ( I ) , N N S H E P C I ) , N N P R U N ( I ) , N N R O S E ( I ) 1 , N N S Y M P ( I ) 1 8 0 F O R M A T C 2 X , ' S U B - P L O T * ' , 1 2 , 5 X , 6 1 1 0 ) C C I S U B * 0 C C I N C R E M E N T S S U B - S E T S C 1 9 0 I S i j B * I S U B + l I F ( I S U B . G T , 4 ) G O T O 4 0 0 0 N A M E L * N N A M E l . C I S U B ) N C E O N e N N C E O N ( I S U B ) N S H E P * N N S H E P C I S U B ) N P R U N * N N P R U N C I S U B ) N R O S E * N N R O S E C I S U B ) N S Y M P a N N S Y M P ( I S U B ) C I T A s N A M E L I F C M , G T , 0 ) G O T O 1 9 9 W R I T E C I O U T , 2 0 3 ) I S U B , M G O T O 2 1 0 C 1 9 9 W R I T E ( I O U T , 2 0 0 ) I S U B , N A G E ( M ) 2 0 0 F O R M A T C ' l ' , 2 X » 1 2 6 C ' * ' ) , / / , 5 X , ' S U B - P L O T • ' , 1 5 , 1 0 X , 1 5 C » * ' ) , 1 0 X , ' A G E 1 * M 5 ) 2 1 0 C O N T I N U E C DO 2 2 0 1 * 1 , 6 6 C D O 2 2 0 J * l , 6 6 2 2 0 J A R R A C I , J ) * 0 I F C I T H R U , G T . 0 ) G O T O 4 3 0 I F C I S U d . G T . 1 ) G O T O 4 3 0 - 1 4 7 - C C A S S I G N S S H R U B L O C A T I O N S C 2 8 0 0 0 2 9 0 X M , 1 5 0 C A L L R A N D U C I X , l Y , Y F L ) I C 0 M ( I ) i Y F L * 6 5 . + l , I X a l Y C A L L R A N D U ( I X , I Y , Y F L ) J C 0 M ( I ) a y F L * 6 5 , + l , 2 9 0 I X " I Y C i 0 0 I C H K S B 0 C D O 3 2 0 1 8 1 , 1 5 0 C D O 3 2 0 J B 1 , 1 5 0 I F ( I . E Q . J ) G O T O 3 2 0 I F ( I C O M t l ) . N E . I C O M ( J ) ) G O T O 3 2 0 I F ( J C O M C I ) . N E . J C O M ( J ) ) G O T O 3 2 0 I X L " J C O M ( J ) 3 1 0 C A L L R A N D U C I X , I Y » Y F L ) J C 0 M ( J ) » Y F L * 6 5 . » 1 . I X a l Y I F ( J C O M ( J ) . E G . I X L ) G O T O 3 1 0 I C H K S " 1 3 2 0 C O N T I N U E C I F C I C H K S . G E . I ) G O T O 3 0 0 C C S H R U B M O R T A L I T Y D U E T O S H A D I N G C A M E L A N C H I E R C C E O N O T H U S C S H E P H E R D I A C P R U N U S C R O S A C S Y M P H O R I C A R P O S C 4 3 0 W R I T E ( I 0 U T , 4 3 1 ) 4 3 1 F O R M A T £ 2 X , ' M O R T A L I T Y D U E T O T R E E S H R U B C O M P E T I T I O N ' , / / ) I F ( l T A , E a , 0 ) G O T O 4 8 1 I N U M « 0 C D O 4 8 0 l 8 l , I T A K « I C O M ( X ) L « J C O M C D I N U M 8 I N U M + 1 C G O T O ( 4 3 5 , 4 4 0 , 4 4 5 , 4 5 0 ) , I S U B 4 3 5 I I s ( K * l ) / 2 L A R R 1 £ K , L ) " 1 5 1 - 1 4 8 - G O T O 4 5 5 4 4 0 I I « C K * l ) / 2 J J » C L + l ) / 2 * 3 3 L A R R 2 C K , L ) 8 1 5 1 G O T O 4 5 5 4 4 5 I I B C K + 1 } / 2 + 3 3 J J B ( L * 1 ) / 2 L A R R 3 C K , U ) a l 5 1 G O T O 4 5 5 4 5 0 I I = ( K + l ) / 2 4 . 3 3 J J » ( L + l ) / 2 + 3 3 L A R R 4 C K , L ) » 1 5 i 4 5 5 I F ( C Z A R R A C U t J J ) - 1 0 0 0 0 0 0 0 ) . E Q . 0 ) G O T O 4 8 0 I N U M s l N U M - 1 C G O T O C 4 6 0 , 4 6 5 , 4 7 0 , 4 7 5 ) , I S U B 4 6 0 I D E A D 1 C I ) « 1 L A R R 1 C K , L ) » 0 G O T O 4 8 0 4 6 5 I D E A D 2 C I ) " 1 L A R R 2 C K , L ) B 0 G O T O 4 8 0 4 7 0 I D E A D 3 ( I ) a l L A R R 3 C K , L ) " 0 G O T O 4 8 0 4 7 5 I D E A D 4 ( I ) « 1 L A R R 4 C K , L ) a 0 4 8 0 C O N T I N U E I K I L L A a l T A - I N U M N A M E L a N A M E L - I K I L L A WRITECI O U T , 2 0 5 0 ) I S U B , I K I L L A , N A M E L 2 0 5 0 F 0 R M A T C 2 X , ' S U B - P L O T « ' , 1 2 , 5 X , * N O , A M E L . D E A D . » ' , 1 2 , 5 X , ' N O . A M E L • l a * , 1 2 ) C 4 8 1 I T C ° 5 0 + N C E O N I F ( I T C . E Q , 5 0 ) G O T O 5 4 5 I N U M B 0 c D O 5 4 0 I s 5 l , I T C K a l C Q M ( I ) L a J C O M C D I N U M « I N U M + 1 C G O T O C 4 8 5 , 4 9 0 , 4 9 5 , 5 0 0 ) , I S U B 4 8 5 I X » ( K * l ) / 2 J J B C L + 1 ) / 2 L A R R 1 C K i L ) a 1 5 2 G O T O 5 1 0 4 9 0 I I a ( K * l ) / 2 J J « C L * l ) / 2 + 3 3 L A R R 2 C K , L ) » 1 5 2 . 1 4 9 - G O T O 5 1 0 4 9 5 I I B ( K * 1 ) / 2 + 3 3 L A K R 3 ( K , L ) * 1 S 2 G O T O 5 1 0 5 0 0 I I « ( K + l ) / 2 * 3 3 J J " ( L + l ) / 2 + 3 3 L A R R 4 ( K L ) S 1 5 2 5 1 0 I F ( ( I A R R A d l , J J ) - 1 0 0 0 0 0 0 0 ) , E Q . 0 ) G O T O 5 4 0 I N U M « I N U M - 1 C G O T O ( 5 1 5 , 5 2 0 , 5 2 5 , 5 3 0 ) , I S U B 5 1 5 I 0 E A D I ( I ) » 1 L A R R 1 ( K , L ) 8 0 G O T O 5 4 0 5 2 0 I D E A D 2 ( I ) « 1 L A R R 2 ( K , U ) a 0 G O T O 5 4 0 5 2 5 I 0 E A 0 3 C Z } " 1 L A R R 3 ( K , L ) 8 0 G O T O 5 4 0 5 3 0 l ' O E A O « ( I ) « J L A R R 4 ( K , L ) a 0 5 4 0 C O N T I N U E I K I L L C a N C E O N - I N U M N C E O N S N C E O N - I K I I L C W R I T E ( I O U T , 2 0 S 0 ) I S U B , I K I L L C N C E O N 2 0 6 0 F O R M A T ( 2 X , ' S U B - P L O T • ' , 1 2 , 5 X , ' N O , C E O N . D E A D " ' , 1 2 , 5 X , ' N O , C E O N , • I M S ) C 5 4 5 I T S » 1 0 0 * N S M E P I F ( I T S , E Q , 1 0 0 ) G O T O 6 0 2 C INUM80 DO 6 0 0 Z « i e i » I T S M I C Q M ( I ) L B J C O M ( I ) I N U M B l N U M + 1 C c G O T Q ( 5 5 0 , 5 6 0 , 5 6 5 , 5 7 0 ) , I S U B 5 5 0 I I - C K + D / 2 J J B ( L * 1 ) / 2 L A R R ! ( K , L ) 8 1 5 3 G O T O 5 7 5 5 6 0 I X " C K * t ) / 2 J J » C l + l ) / 2 * 3 3 L A R R 2 ( K , L ) B 1 5 3 G O T O 5 7 5 5 6 5 I I B ( K * 1 ) / 2 t 3 3 J J B ( L M ) / 2 - 150 - L A R R 3 ( K , L ) a 1 5 3 GO T O 5 7 5 5 7 0 X I » ( K * l ) / 2 + 3 3 J J s ( L + n / 2 + 3 3 L A R R 4 ( K » L ) • 1 5 3 5 7 5 I F ( ( I A R R A ( I I , J J ) - 1 0 0 0 0 0 0 0 ) , E Q , 0 ) GO TO 6 0 0 I N U M " l N U M « l C G O T O ( 5 8 0 , 5 6 5 , 5 9 0 , 5 9 5 ) , I S U B 5 8 0 I D E A D 1 ( I ) * 1 L A R R 1 ( K , L ) b 0 G O T O 6 0 0 5 6 5 I D E A 0 2 C I ) " 1 l . A R R 2 ( K , L ) = 0 G O TO 6 0 0 5 9 0 I D E A 0 3 ( I . ) » 1 U A R R 3 ( K , L ) a 0 G O TO 6 0 t ) 5 9 5 I U E A D 4 ( I ) « 1 L A R R 4 ( K , L ) a 0 6 0 0 C O N T I N U E C I K I L L S = N S H £ P - I N U M N S H E P s N S H E P - I K I L L S C W R I T E ( I O U T , 2 0 7 0 ) I S U 8 , I K I L L S , N S H E P 2 0 7 0 F O R M A T ( 2 X , ' S U B - P L O T a ' , 1 2 , 5 X , ' N O , S H E P , D E A D • ' , 1 2 , 5 X , ' N O • S H E P , i « ' , i 2 ) 6 0 2 GO T O ( 6 0 5 , 6 1 0 , 6 1 5 , 6 2 0 ) , I S U B 6 0 5 C C a C S U B i G O T O 6 2 5 6 1 0 C C « C S U B 2 G O T O 6 2 5 6 1 5 C C a C S U B 3 G O T O 6 2 5 6 2 0 C C a C S U B 4 6 2 5 C O N T I N U E C » C C W R I T E ( I 0 U T , 6 3 5 ) C C 6 3 5 F Q R M A T ( / / , 1 0 ( ' * ' ) , 5 X , ' C R O W N C L O S U R E a ' , F 6 . 2 , 5 X , 1 0 C ' * ' ) ) 6 7 0 I F ( C C , G T . ? 4 . 5 ) C C * 7 4 , 5 I F ( C C . L E , 0 ) C C B , 0 1 I F ( M , E Q , 0 ) GO TO 6 9 5 C C D E T E R M I N E S N O . O F C E O N O T H U S A S A F U N C T I O N O F C R O W N C L O S U R E C I F ( N A M t L , E Q . 0 ) G O T O 6 7 5 M A M E L a 8 , - . 1 0 6 0 6 * C C + 1 9 , * ( ( 7 5 . - C C ) * * 2 . 5 / 7 5 , * * 2 , 5 ) + . 5 I F ( N A M E L . G T . M A M f c L ) N A M E L B M A M E L I T A a N A M E L + I K I L L A C m 1 5 1 * C D E T E R M I N E S N O . O K A M E L A N C H I E R A S A F U N C T I O N O F C R O W N C L O S U R E C 6 7 5 I F C N C E O N . E Q . 0 D C O T O 6 8 0 M C E 0 N B 8 . - . 1 0 6 0 6 * C C + 1 9 . * ( £ 7 5 , - C C J * * 2 . 5 / 7 5 , * * 2 . 5 ) + , 5 I F f N C E O N . G T . M C E O N ) N C E O N a M C E Q N I T C 8 N C E O N + I K I L L C + 5 0 C C D E T E R M I N E S N O . O F S H E P H E R D I A A S A F U N C T I O N O F C R O W N C L O S U R E C 6 8 0 I F C N S H E P . E Q . 0 ) G O T O 6 8 5 M S H E P » 8 . - , 1 0 6 0 6 * C C + 1 9 . * C ( 7 5 . - C C ) * * 2 , 5 / 7 5 . * * 2 . 5 ) • . 5 I F C N S H E P . G T . M S H E P ) N S H E P B M S H E P I T S a N S H E P + I K I L L S + 1 0 0 C C D E T E R M I N E S N O . O F P R U N U S A S A F U N C T I O N O F C R O W N C L O S U R E C 6 8 5 I F £ C C . G T , 6 5 . ) N P R U N » 0 I F ( N P R U N . E G . 0 D G O T O 6 8 8 M P R U N B 7 , - , 1 1 6 7 * C C * 9 . « ( ( 6 5 . - C C ) * * 2 . / 6 5 . * * 2 . ) + . 5 I F ( N P R U N . G T . M P R U N ) N P R U N « M P R U N C C C D E T E R M I N E S N O , O F R O S E S A S A F U N C T I O N O F C R O W N C L O S U R E C 6 8 8 I F C C C . G T . 6 5 . ) N R O S E " 0 I F £ N R O S E , E Q , 0 ) G O T O 6 9 0 M R 0 S E B 7 , - . i l 6 7 * C C + 9 , * £ ( b 5 , - C C D * * 2 . / 6 5 . * * 2 . ) + , 5 I F ( N R O S E . G T . M R C S E ) N « O S E * M R C S E C C C D E T E R M I N E S NO. O F S Y M P H O R I C A R P O S A S A F U N C T I O N O F C R O W N C L O S U R E 6 9 0 I F ( C . G T . 9 0 . ) N i S Y M P « 0 I F ( N S Y M P . E Q . 0 ) GO T O 6 9 5 M S Y M P » 3 5 , - , 3 8 8 8 9 * C + , 5 I F ( N S Y M P . G T . M S Y M P ) N S Y M P e M S Y M P C C S E T S B O R D E R , I N S I D E A N D T O T A L A R E A O F A M E L A N C H I E R TO Z E R O C 6 9 5 B O R D A 8 0 . X I N A « 0 . U T I L A 8 0 . C C S E T S B O R D E R , I N S I D E A N D T O T A L A R E A O F C E O N O T H U S T O Z E R O C BQROC80. XINC80, U T I L C 8 0 . C C S E T S B O R D E R , I N S I D E A N O T O T A L A R E A O F S H E P H E R D I A TO Z E R O C BORDS80, 1 5 2 - X I . N S " 0 , U T 1 L S B 0 . C C S E T S P R O D U C T I O N OF A M E L A N C H I E R , C E O N O T H U S , S H E P H E R D I A , P R U N U S , C R O S E A N D S Y M P H O R I C A R P O S T O Z E R O C P D N A " 0 . P D N C a 0 , P Q N 5 S 0 . P D N P R « 0 , P D N R O * 0 . P D N S Y S 0 . I F C M . E Q . f l ) G O T O 2 0 0 0 A G E a N A G E £ M ) X D I A M 8 0 , C W R I T E ( I O U T , 6 9 9 ) I S U B , N A M E L , N C E O N , N S H E P , N P R U N , N R O S E , N S Y M P 6 9 9 F O R M A T ( / / , 5 X , ' S H R U B # . S S U R V I V I N G I N U N S H A D E D A R E A ' , / / , 5 X , ' S U B - P L O I T a ' , i 5 , 2 X , » * A M t L ••,I5,2Xi'# C E O N »',lS,2)(t'# S H E P B ' , I 5 , 2 X , ' # P 2 R U N 8 ' , I 5 , 2 X , ' # R O S E B ' , I 5 , 2 X , ' # S Y M P a ' , 1 5 , / / / ) C c c C I D I A M 1 ( I ) , , , 4 C I ) a D I A M E T E R O F I N D I V I D U A L S H R U B S C C C A M E L A N C H I E R C A L C U L A T I O N S C N C O U N 1 a 0 c DO 7 4 5 1 = 1 , C GO TO ( 7 0 0 , 7 0 5 , 7 1 0 , 7 1 5 ) , I S U B 7 0 0 I F ( N C O u N l . G E . N A M E L ) I D E A D l ( I ) » i I F C I O E A U 1 C I ) . E Q . l ) G O T O 7 4 5 G O T O 7 2 0 7 0 5 I F ( N C 0 U N 1 , G E . N A M E L ) I D E A 0 2 ( I ) » 1 I F ( I 0 E A D 2 ( I ) . E U , 1 ) G O T O 7 4 5 G O T O 7 2 0 7 1 0 I F ( N C O U N 1 . G E . N A M E L ) I D E A D 3 ( I ) * 1 I F ( I D E A D 3 ( I ) . E Q . l ) G O T O 7 4 5 G O T O 7 2 0 7 1 5 I F ( N C O U N l . G E . N A M E L ) I O E A 0 4 ( I ) « l I F ( I D E A D 4 ( I ) . E Q . l ) G O T O 7 4 5 7 2 0 N C O U N 1 B N C O U N 1 + 1 R A N O J B J R A N O ( I ) R A N D J « R A N D J / 1 0 0 0 , X 2 a « l , * 3 0 , * * i , 9 9 6 I F ( A G E - 3 0 , ) 7 2 5 , 7 3 0 , 7 3 0 7 2 5 X I a - l , * ( - 1 .* ( A G E - 3 0 . ) ) * * 1 , 9 9 6 G O T O 7 3 5 - 1 5 3 7 3 0 X l s ( A G E - 3 0 . ) * * 1 . 9 9 6 7 3 5 D l A M a R A N D J * ( - 1 , • , 1 5 * A G E * 1 , * £ X 1 / X 2 ) ) C 6 0 T O £ 7 3 7 , 7 3 9 , 7 4 1 , 7 4 3 ) , 1 S U B 7 3 7 I D I A M 1 £ 1 ) a D l A M * 1 0 0 , G O T O 7 4 5 7 3 9 I D I A M 2 C I ) a D l A M * 1 0 0 , G O T O 7 4 5 7 4 1 I D I A M 3 C I ) 8 O I A M * 1 0 0 , G O T O 7 4 5 7 4 3 I D I A M 4 £ I ) 8 D I A M * 1 0 0 , 7 4 5 C O N T I N U E C C C A L C U L A T E S D I A M E T E R O F C E O N O T H U S C 7 5 5 N C Q U N 2 8 0 C D O 8 0 5 1 = 5 1 , 1 0 0 C G O T O £ 7 6 0 , 7 6 3 , 7 6 9 , 7 7 2 ) , I S U B 7 6 0 I F C N C Q U N 2 . G E . N C E 0 N ) I D E A D l £ I ) » l I F C I D E A D 1 ( I ) , E Q , 1 ) G O T O 8 0 5 G O T O 7 7 5 7 6 3 I F ( N C 0 U N 2 . G E , N C E 0 N ) I 0 E A D 2 ( I ) " 1 I F ( I D E A D 2 £ I ) . E Q . l ) G O T O 8 0 5 G O T O 7 7 5 7 6 9 I F £ N C 0 U N 2 , G E , N C E 0 N ) I D E A D 3 £ I ) » 1 I F C I D E A D 3 ( I ) , E 0 , 1 ) G O T O 8 0 5 G O T O 7 7 5 7 7 2 I F ( N C 0 U N 2 , G E . N C E 0 N ) I D E A D 4 f I ) M I F £ I D E A D 4 £ I ) , E Q , 1 ) G O T O 8 0 5 7 7 5 N C 0 U N 2 » N C 0 U N 2 + 1 R A N D * » K R A N D £ I « 5 0 ) R A N D K « R A N D K / 1 0 0 0 , D I A M " R A N O K * C 5 , 5 * T A N H £ A G E * , 0 3 ) ) G O T O £ 7 8 0 , 7 8 5 , 7 9 0 , 7 9 5 ) , I S U B 7 8 0 I D I A M 1 ( I ) » D I A M * 1 0 0 , G O T O 8 0 5 7 8 5 I 0 I A M 2 C I ) 8 O I A M * 1 0 0 , G O T O 8 0 5 7 9 0 I 0 I A M 3 C D 8 O I A M H 0 0 , G O T O 6 0 5 7 9 5 I D I A M 4 C I ) 8 D I A M * 1 0 0 , 8 0 5 C O N T I N U E C C S H E P H E R D I A C A L C U L A T I O N S C 8 1 0 N C O U N 3 « 0 C 0 0 8 6 5 1 8 1 0 1 , 1 5 0 G O T O £ 6 1 5 , 8 2 0 , 8 2 5 , 8 3 0 ) , I S U B - 1 5 4 * 8 1 5 I F £ N C 0 U N 3 , G E . N S H E P ) Z D E A D 1 C15) • 1 I F C I D E A 0 1 ( I ) . E Q . l ) G O T O 8 6 5 G O T O 8 3 5 8 2 0 I F C N C 0 U N 3 . G E . N S H E P ) I D E A D 2 £ I ) 8 l 1 F C I D E A D 2 C I ) . E Q . l ) G O T O 8 6 5 G O T O 8 3 5 6 2 5 I F C N C 0 U N 3 . G E , N S H E P ) I D E A D 3 C I ) * 1 I F ( I D E A D 3 C I ) . E Q . l ) G O T O 8 6 5 G O T O 8 3 5 8 3 0 I F C N C 0 U N 3 . G E , N S H E P ) I D E A D 4 ( I ) » i I F C I D E A D 4 ( I ) . E G . 1 ) G O T O 8 6 5 8 3 5 N C Q U N 3 s N C Q U N 3 + l R A N D L » t R A N D C I « 1 0 0 ) R A N O U B R A N D L / 1 0 0 0 , I F C A G E . L T . 2 8 , ) D I A M * R A N D L * C . 1 6 * A G E ) I F ( A G E , G E t 2 8 . ) D I A M > R A N D L * C 5 , + 2 . 5 * T A N H C ( A G E - 2 8 , ) * , 0 3 3 ) ) C 6 4 5 G O T O ( 6 4 7 , 8 4 9 , 8 5 1 , 8 5 3 ) , I S U B 8 4 7 I D I A M 1 ( I ) = D I A M * 1 0 0 . G O T O 8 6 5 8 4 9 I D I A M 2 ( I ) = D I A M * 1 0 0 , G O T O 8 6 5 8 5 1 I D I A M 3 C I ) a D I A M * 1 0 0 . G O T O 8 6 5 8 5 3 I D I A M 4 C I ) » D I A M * 1 0 0 , 8 6 5 C O N T I N U E C 8 7 0 C O N T I N U E I C O U N T B 0 8 8 0 I C O U N T s I C O U N T + 1 C S T A R T S N E W S H R U B I F ( I C Q U N T . G T . I T S ) G O T O 9 9 7 C C C A L C U L A T E S S H R U B R A D I U S C R A D B R A D I U S C G O T O £ 8 6 5 , 6 9 0 , 8 9 5 , 9 0 0 ) , I S U B 8 8 5 I F ( I O E A D l C I C O U N T ) . E Q . l ) G O T O 8 8 0 I F d D l A M l ( I C O U N T ) , E Q . 0 ) G O T O 6 8 0 R A D B I D I A M I ( I C O U N T ) R A D a R A Q / 2 0 0 , I I X B I C O M ( I C O U N T ) J J X » J C O M ( I C O U N T ) G O T O 9 0 5 8 9 0 I F ( I D E A D 2 ( I C 0 U N T ) . E Q . l ) GO T O 8 8 0 I F ( I 0 I A M 2 ( I C 0 U N T ) . E O . 0 ) G O T O 8 8 0 R A D s I D I A M 2 ( I C O U N T ) R A D a R A D / 2 0 0 , I I X B I C O M ( I C O U N T ) J J X S J C O M ( I C O U N T ) G O T O 9 0 5 - 1 5 5 - 8 9 5 I F I I U E A 0 3 C X C 0 U N T ) , E Q , 1 ) G O T O 8 8 0 I F ( I D I A M 3 ( I C 0 U N T ) , E Q , 0 ) G O T O 6 8 0 H A 0 - I 0 I A M 3 C I C 0 U N T ) R A D a R A D / 2 0 0 , I l X » I C Q M ( I C O U N T ) J J X a J C O M ( I C O U N T ) G O T O 9 0 5 9 0 0 I F ( I D E A D 4 ( I C 0 U N T ) , E Q . l ) G O T O 6 8 0 1 F ( I 0 I A M 4 ( I C 0 U N T ) . E Q . 0 ) G O T O 8 8 0 R A D « I D I A M 4 ( I C O U N T ) R A D a R A D / 2 0 0 , I l X « I C O M ( I C O U N T ) J J X a J C O M U C O y N T ) 9 0 5 C O N T I N U E I F ( I S H R U 8 , G T , 0 ) G O T O 9 9 5 I F C I C O U N T . G T , 5 0 , A N D . I C O U N T . L E , 1 0 0 ) 6 0 T O 9 1 0 I F C I C O U N T , G T , 1 0 0 ) G O T O 9 2 0 C W R I T E ( I O U T , 9 0 6 ) I C O U N T , R A D , I C O M C I C O U N T ) , J C O M ( I C O U N T ) 9 0 6 F O R M A T ( 2 X , ' A M E L # a ' , 1 4 , 5 X , ' R A D l U S I N F T . a ' , F 8 , 2 , 5 X , » I L O C a ' , 1 5 , 5 I X , » J L O C a ' , 1 5 ) G O T O 9 9 5 C 9 1 0 W R I T E ( I O U T , 9 1 5 ) I C O U N T , R A D , I C O M ( I C O U N T ) , J C O M ( I C O U N T ) 9 1 5 F O R M A T ( 2 X , ' C E O N # a ' , 1 4 » 5 X , ' R A D l U S I N F T . "< ' , F 8 , 2 , 5 X , * I L O C a ' , 1 5 , 5 I X , » J L O C a ' , 1 5 ) G O T O 9 9 5 C 9 2 0 W R I T E ( I O U T , 9 2 5 ) I C O U N T , R A O , I C O M ( I C O U N T ) , J C O M ( I C O U N T ) 9 2 5 F O R M A T ( 2 X , ' S H E P # " ' , 1 4 , 5 X , ' R A D l U S I N F T , « ' , F 8 , 2 , 5 X , ' I L O C a',15,5 I X , * J L O C a ' , 1 5 ) C C S H R U B G R O W T H 9 9 5 C A L L B R A N C H G O T O 8 8 0 C 9 9 7 DO 9 9 8 1 = 1 , 1 5 3 I A R E A ( I ) s l 9 9 8 P E R ( I ) s 0 C C S H R U B R E M O V A L I F D E A D C A L L R E M C C S H R U B A R E A C A L C U L A T I O N C C A L L A R E A ( N A M E L , N C E 0 N , N S H E P , N P R U N , N R O S E , N S Y M P , P D N S , P D N A , P D 1 N C , P U N P R , P 0 N R 0 , P D N S Y , I N 0 1 S H ) C C P R O D U C T I O N C A L C F O R S H R U B S , G R A S S E S & F O R B S C A L L S G P O N ( N A M E L , N C E O N , N S H E P , N P R U N , N R O S E , N S Y M P , P D N S , P D N A , P D 1 N C , P D N P R , P D N R 0 , P D N S Y , I N D I S H ) - 1 5 6 - 2 0 0 0 C A L L S U M ( N A M E L , N C E O N , N S H E P , N P R U N , N R O S E , N S Y M P , P D N S , P O N A , P D 1 N C , P D N P R , P D N R O , P D N S Y , I N O I S H ) I F C I S U 8 . L E . 3 ) G O T O 1 9 0 I F ( I D D . L E . 0 ) G O T O 3 9 0 0 C C c P R I N T S S H R U B M A P S C C C c c D O 3 6 0 0 l a D O 3 6 0 0 j a N B a L A R R l C I I F C N B . E O . B 3 6 0 0 J A H R A C I f J ) W R I T E ( I O U T 3 7 0 0 F O R M A T C ' l * D O 3 8 0 0 l a 3 8 0 0 W R I T E C I O U T W R I T E C I O U T I F C I D D . L E , D O 3 6 0 1 1- 00 3 6 0 1 J a N B a L A R R S C I I F C N B . E O . 0 3 6 0 1 J A R R A ( I , J ) W R I T E C I O U T 3 7 0 1 F O R M A T C ' 1 ' D O 3 6 0 1 l a 3 8 0 1 W R I T E C I O U T W R I T E ( I O U T O Q 3 6 0 2 I * D O 3 6 0 2 J a N B a L A R R 3 C I I F ( N B , E Q . 0 3 6 0 2 J A R R A ( I , J ) W R I T E C I O U T 3 7 0 2 F O R M A T C ' l ' D O 3 8 0 2 1 = , 6 6 , 6 6 J ) N B a l 5 4 K C H A R ( N B J 3 7 0 0 3 2 X , ' S U B - P L O T # 1 ' , / / , 2 X , ' S H R U B M A P ' , / / , 1 X , 1 3 0 ( ' * ' ) ) , 6 6 3 8 5 0 3 ( J A R R A ( I , J ) , J * l , 6 4 ) 3 8 8 9 ) ) G O T O 3 9 0 0 , 6 6 , 6 6 J ) N B a l 5 4 K C H A R ( N B ) 3 7 0 1 ) 2 X , ' S U B - P L O T # 2 ' , / / , 2 X , ' S H R U B M A P ' , / / , 1 X , 1 3 0 ( ' * ' ) ) , 6 6 3 8 5 0 ) ( J A R R A ( I , J ) , j a i , 6 4 ) 3 8 8 9 ) I F ( I D D . L E , 2 ) G O T O 3 9 0 0 , 6 6 , 6 6 J ) N 8 = 1 5 4 K C H A R ( N B ) 3 7 0 2 ) 2 X , ' S U B - P L O T # 3 ' , / / , 2 X , ' S H R U B M A P ' , / / , 1 X » 1 3 0 ( ' * ' ) ) , 6 6 1 5 7 - C 3 8 0 2 W R I T E ( I O U T , 3 8 5 0 ) ( J A R R A ( I , J ) , J » 1 » 6 4 ) C W R I T £ ( I 0 U T , 3 8 8 9 ) I F ( I D D , L E , 3 ) G O T O 3 9 0 0 C D O 3 6 0 3 1 8 1 , 6 6 D O 3 6 0 3 J * l , 6 6 N B « L A R R 4 ( I , J ) I F ( N B , £ Q . 0 ) N B « 1 5 4 3 6 0 3 J A R R A ( I , J ) s » K C H A R ( N B ) C W R I T E ( I O U T , 3 7 0 3 ) 3 7 0 3 F 0 R M A T ( ' 1 ' , 2 X , ' S U B - P L O T # 4 » , / / , 2 X , ' S H R U B M A P ' , / / , 1 X , 1 3 0 ( ' * ' ) ) D O 3 6 0 3 I M , 6 6 C 3 8 0 3 3 8 5 0 W R I T E ( I O U T , 3 8 5 0 ) ( J A R R A ( I , J ) , J * l , 6 4 ) F 0 R M A T ( ' 9 * , 1 X , 6 4 A 2 ) C 3 8 8 9 3 9 0 0 4 0 0 0 W R I T E ( I 0 U T , 3 8 8 9 ) F O R M A T O X , 1 2 8 ( ' * ' ) ) I T H R U a l T H R U + i R E T U R N E N D * 1 5 8 - S U B R O U T I N E A R E A ( N A M E L , N C E O N , N S H E P , N P R U N , N R O S E , N S Y M P , P O N S , P O N A , P D 1 N C , P D N P R , P D N « 0 , P D N S Y , I N D I S H ) D I M E N S I O N I A R R A ( 6 6 , 6 6 ) , 8 L 2 ( 9 6 ) , A C C ( 4 , 2 l ) , A T A ( 4 , 2 i ) , A T G ( 4 , 2 l ) , A T F ( 4 1 , 2 1 ) , A P D N A ( 4 , 2 1 ) , A P D N C ( 4 , 2 1 ) , A P D N S ( 4 , 2 1 ) , A P D N P R ( 4 , 2 1 ) , A P D N R O ( 4 , 2 1 ) 2 , A P D N S Y ( 4 , 2 1 ) I N T E G E R * 2 J A R R A ( 6 6 , 6 6 ) , N S E T ( 9 6 ) , I Q Q ( 9 6 , 5 ) , J Q Q ( 9 6 , 5 ) , N A G E ( 5 0 ) , N N A M E 1 L ( 4 ) , N N C E 0 N ( 4 ) , N N S H E P ( 4 ) , N N P R U N ( 4 ) , N N R 0 S E C 4 ) , N N S Y M P ( 4 ) , J R A N D £ 5 0 ) , K 2 R A N D ( 5 0 ) , L R A N D ( 5 0 ) , J J R A N D C 1 0 0 ) , K K R A N D ( 1 0 0 ) , U U R A N D ( 1 0 0 ) , J 3 A M E L ( 2 0 ) , J C E O N ( 2 0 ) , J S H E P ( 2 0 ) , J P R U N ( 2 0 ) , J R O S E ( 2 0 ) , J S Y M P ( 2 0 ) , I 5 C 0 M ( 1 5 0 ) , J C O M ( 1 5 0 ) , I D E A D 1 ( 1 5 0 ) , I D E A 0 2 ( 1 5 0 ) , I O E A D 3 C 1 5 0 ) , I D E A D 4 £ 1 5 0 ) 6 , L A R R 1 ( 6 6 , 6 6 ) , L A R R 2 ( 6 6 , 6 6 ) , L A R R 3 ( 6 6 , 6 6 ) , L A R R 4 ( 6 6 , 6 6 3 , 1 A R E A ( 1 5 3 ) , 1 0 7 1 A M I ( 1 5 0 ) , I O I A M 2 ( 1 5 0 ) , I D I A M 3 ( 1 5 0 ) , I D I A M 4 £ 1 5 0 ) , P E R f 1 5 3 ) , E P E R £ 1 6 ) , K A 8 M E L ( 4 , 2 1 ) , K C E 0 N ( 4 , 2 1 ) , K S H E P ( 4 , 2 1 ) , K P R U N ( 4 , 2 1 ) , K R O S E ( 4 , 2 1 ) , K S Y M P ( 4 , 9 2 1 ) , K C H A R C 1 6 0 ) , I H T ( 1 0 0 , 9 7 ) , I C H A R ( 9 9 ) , I B B ( 5 0 , 9 7 ) , I R A N D ( 9 7 ) , I X X £ 9 7 ) , 1 J X X ( 9 7 ) , I V O L ( 9 7 ) , I D B H ( 9 7 ) , I C L ( 9 7 ) , I A P E R ( 9 7 ) , I C W £ 9 7 ) , I C B £ 9 7 ) , I S A £ 9 7 1 ) , J C H A R £ 2 ) , I D E A D £ 9 7 ) C O M M O N I A R R A , B L 2 , A C C , A T A , A T G , A T F , A P O N A , A P D N C , A P D N S , A P D N P R , A P D N R O , A 1 P D N S Y , C S U B 1 , C S U B 2 , C S U B 3 , C S U B 4 , R A D , 8 0 R D A , X I N A , U T I L A , B 0 R 0 C , X I N C , U T I L 2 C , B O R D S , X I N S , U T I L S , A G E , C , C C , T A U T , T A U T S , T A U T T , T A U O , U N O C C , Y U N O C C , P D N 1 , I T H R U , M , I S T R T , I I N T , I E N D , I Y U N O C , I A U T T Y , I U N O C C , I L O O P , I X , I S U B , I C O U N T 3 , I H T , I B B , J A R R A , L A R R 1 , L A R R 2 , L A R R 3 , L A R R 4 , I Q Q , J Q Q , I A R E A , P E R , K C H A R , I C O 4 M , J C O M , I D E A D 1 , I D E A D 2 , I D E A D 3 , 1 D E A D 4 , I D I A M I , I D I A M 2 , I D I A M 3 , I D I A M 4 , J J R 5 A N D , K K R A N D , L L R A N 0 , I C H A R , I R A N D , I X X , J X X , I V O L , I D B H , I C L , I A P E R , I C W , I C B , 6 I 8 A , I D E A D , N S E T , « A M E L , K C E O N , K S H E P , K P R U N , K R O S E , K S Y M P , N A G E , J R A N D , K R A N 7 D , L R A N D , J A M E L , J C E O N , J S H E P , J P R U N , J R O S E , J S Y M P , E P E R , N N A M E L , N N C E O N , N N S 8 H E P , N N P R U N , N N R 0 S E , N N S Y M P , J C H A R l O U T s b I F £ A G E » E G ,0) G O T O 2 0 0 0 O C C U P A T I O N O F A R E A B Y S H R U B S DO 1 0 4 1 1 = 1 , b b 0 0 1 0 4 0 J » i , b b K s j - l X F ( K , E Q , 0 ) K « b 6 L " I - 1 X F ( L . E O , 0 ) L « 6 6 G O T O ( 1 0 0 0 , 1 0 1 0 , 1 0 2 0 , 1 0 3 0 ) , I S U B 1 0 0 0 N B a L A R R l ( I , J ) I B « L A R R 1 ( I , K ) J B a L A R R i ( L , J ) I F f N B . G T . 0 ) I A R E A ( N B ) m l A R E A ( N B ) + 1 I F ( L A R R 1 ( I , J ) . G T . 0 . A N D . L A R R 1 ( I , K ) , N E , 0 ) G O T O 1 0 0 3 I F ( N B . E O , 0 ) 6 0 T O 1 0 0 3 P E R ( N B ) « P E R ( N B ) + l 1 0 0 3 I F C L A R R 1 ( I , J ) . N E . 0 . A N D . L A R R 1 £ I , K ) , G T , 0 ) G O T O 1 0 0 6 I F £ I B , E Q , 0 ) G O T O 1 0 0 6 P E R £ I B ) « P E R ( I 8 ) + 1 1 0 0 6 I F ( L A R R 1 ( I , J ) . G T . 0 . A N D . L A R R 1 ( L , J ) . N E . 0 ) G O T O 1 0 0 9 I F ( N 8 , E Q , 0 ) G O T O 1 0 0 9 1 5 9 - P E R C N B ) B P £ R ( N B ) < H 1 0 0 9 I F U A R R 1 C I , J ) . N E . 0 . A N D . L A R R 1 U , J ) . G T . 0 ) G O T O 1 0 4 0 I F C J B . E Q . 0 ) G O T O 1 0 4 0 P E R ( J B ) * P E R ( J B ) * 1 G O T O 1 0 4 0 1 0 1 0 N B « L A R R 2 ( X , J ) J B » L A R R 2 C L , J ) I B s | _ A R R 2 C I , K ) I F C N B . G T . 0 ) I A R E A C N B ) " I A R E A C N B ) + 1 I F C U A R R 2 C I , J ) , G T , 0 . A N D , L A R R 2 C I , * ) , N E , 0 ) G O T O 1 0 1 3 I F C N B . E Q . 0 ) G O T O 1 0 1 3 P E R C N B ) B P E R ( N B ) + 1 1 0 1 3 I F C L A R R 2 C I , J ) . N E , 0 , A N D . L A R R 2 C I , K ) . G T . 0 ) G O T O 1 0 1 6 X F C i a . E Q . 0 ) G O T O 1 0 1 6 P E R C I B ) 8 P E R ( I B ) + 1 1 0 1 6 I F C L A R R 2 C I , J ) . G T . 0 . A N D , L A R R 2 ( L , J ) , N E . 0 ) G O T O 1 0 1 9 I F C N B . E Q . 0 ) G O T O 1 0 1 9 P E R C N B ) B P E R C N B ) + 1 1 0 1 9 I F C L A R R 2 C I , J ) . N E . 0 . A N D , I A R R 2 C L , J ) , G T . 0 ) G O T O 1 0 4 0 I F C J B . E Q . 0 ) G O T O 1 0 4 0 P E R ( J B ) « P E R ( J B ) * t G O T O 1 0 4 0 1 0 2 0 N B 8 U A R R 3 C I , J ) J B 8 L A R R 3 C U , J ) I B 8 L A R R 3 ( I , K ) I F C N B . G T . 0 ) I A R E A C N B ) 8 I A R E A C N B ) * 1 I F C L A R R 3 C I . J ) . G T . 0 , A N D , L A R R 3 C I , K ) . N E . 0 ) G O T O 1 0 2 3 I F C N B . E O . 0 ) G O T O 1 0 2 3 P E R C N B ) B P E R C N B ) + 1 1 0 2 3 I F £ L , A R R 3 C I , J ) . N E . 0 . A N D . L A R R 3 ( I , K ) . G T . 0 ) G O T O 1 0 2 6 I F C I B . E O . 0 ) G O T O 1 0 2 6 P E R C I B ) 8 P E R ( I 9 ) + 1 1 0 2 6 I F C U A R R 3 C I , J ) . G T . 0 . A N D . L A R R 3 C L , J ) . N E . 0 ) G O T O 1 0 2 9 I F ( N B . E G , 0 ) G O T O 1 0 2 9 P £ R C N B ) 8 P E R C N B ) + t 1 0 2 9 I F C L A R R 3 C I , J ) . N E , 0 , A N D , L A R R 3 C L , J ) , G T . 0 ) G O T O 1 0 4 0 I F C J B . E Q . 0 ) G O T O 1 0 4 0 P E R ( J B ) B P E R ( J B ) + 1 G O T O 1 0 4 0 1 0 3 0 N BB L A R R 4 ( I , J ) J B * L A R R 4 C L , J ) I B a L A R R 4 C I , K ) I F C N B . G T . 0 ) I A R E A ( N B ) » I A R E A ( N B ) * 1 I F C U A R R 4 C I , J ) . G T . 0 , A N D , L A R R 4 C I , K ) . N E . 0 ) G O T O 1 0 3 3 I F C N B . E Q . 0 ) G O T O 1 0 3 3 P E R C N B ) 8 p £ R C N B ) * l 1 0 3 3 I F C U A R R 4 C I , J ) . N E , 0 , A N D . L A R R 4 C I , K ) . G T . 0 ) G O T O 1 0 3 6 I F ( I B , E Q , 0 ) G O T O 1 0 3 6 P E R ( I B ) « P E R ( I B ) * 1 1 0 3 6 I F C L A R R 4 C I , J ) . G T . 0 . A N D . L A R R 4 ( L , J ) . N E . 0 ) G O T O 1 0 3 9 I F C N B . E Q . 0 ) G O T O 1 0 3 9 160 - P E R ( N B ) » P E R ( N B ) * 1 1 0 3 9 I F ( L A R R 4 C I , J ) , N E . 0 . A N D . L . A R R 4 C L , J ) . G T . 0 ) G O T O 1 0 4 0 I F C J B . E Q . 0 ) G O T O 1 0 4 0 P E R C J 8 ) B P E R C J 8 ) + 1 1 0 4 0 C O N T I N U E 1 0 4 1 C O N T I N U E 2 0 0 0 R E T U R N END - 161 - SUBROUTINE BRANCH DIMENSION IARRA(66,66),BL2(96),ACC(4,2i),ATA(4,2l),ATG£4,2l),ATF(4 1,21) ,APDNA (4,21) ,APDNC(4, 21) , APDNS £4,21) ,APDNPR (4,21) ,APDNRO (4,21) 2,APDNSY£4,21) INTEGER*2 JARRA(66,66),NSET£96),IQQ(96,5),J0Q(96,5),NAGE(50),NNAME 1L(4),NNC£0N(4),NNSHEP(4),NNPRUN(4),NNR0SE(4),NNSYMP(4),JRAND£50),K 2RAND(50),LRANO(50),JJRAND(100),KKRAND(100),LLRAND(100), J 3AMEU(20),JCEON(20),JSHEP£20),JPPUN(20),JROSE(20),JSYMPC20), I 5COMU50),JCOM(150),IDEAD 1 (150),IOEAD2(150),I0EAD3£ 150),IDEAD4£ 150) 6, LARR1 £66,66) .I.ARR2 £66,66) ,LARR3 £66,66) ,LARR4 £66,66) , I AREA £153) , ID 71 AMI(150),IDIAM2C150),IDIAM3(150),IDIAM4(150),PER(153),EPER£ 16),KA 8M£|.(4,21) ,KCEON (4,21) ,KSHEP (4,21) ,KPRUN £4,21) ,KROSE £4,21) ,KSYMP £4, 921),KCHAR(160),IHT(100,97),I CHAR(99),IBB(50,97),IRAND (97),IXX ( 9 7 ) , 1JXX(97),IV0L(97),IDBH(97),ICL£97),IAPER£97),ICWC97),ICB(97),IBA(97 1),JCHAR(2),IDEAD(97) COMMON IARRA,Bu2,ACC,ATA,ATG,ATP,APDNA,APDNC,APDNS,APDNPR,APDNRO,A 1PDNSY,CSUB1,CSUB2,CSUB3,CSUB4,RAD,B0RDA,XINA,UTILA,B0RDC,XINC,UTIL 2C,BORDS,XINS,UTILS,AGE,C,CC,TAUT,TAUTS,TAUTT,TAUO,UNOCC,YUNOCC,PDN 1,ITHRU,M,ISTRT,I1NT,I£ND,IYUN0C,IAUTTY,IUN0CC,IL00P,IX,ISUB,IC0UNT 3,IHT,138,JARRA,LARR1,LARR2,LARR3,LARR4,IQQ,JQQ,I AREA,PER,KCHAR,I CO 4M,JC0M,lDEADl,IDEA02,I0EAD3,ID£AD4,IDIAMi,IDlAM2,IDlAM3,IDIAM4,JJR 5AND,KKRAN0,ULRAND,ICHAR,IRAND,IXX,JXX,I VOL,IDBH,ICL,IAPER,ICW,ICB, 6 IBA,I DEAD,NS£T,KAMEL,KCEON,KSHEP,KPRUN,KROSE,KSYMP,NAGE,JRAND,KRAN 7D,LRAN0,JAMEL,JCEON,JSHEP,JPRUN,JROSE,JSYMP,EPER,NNAMEL,NNCEON,NNS 8HEP,NNPRUN,NNR0SE,NNSYMP,JCHAR I I X » I C O M ( I C Q U N T ) J J X * J C 0 M ( I C 0 U N T ) GO TO ( 8 0 0 , 8 1 0 , 8 2 0 , 8 3 0 ) , I S U B 8 0 0 I F £ I C O U N T . L E , 5 0 . ) L ARR 1 ( 1 1 X , J J X ) •> 1 5 1 I F ( I C O U N T , G T . 5 0 . A N D , I C O U N T . L £ . 1 0 0 ) L A R R 1 ( 1 1 X , J J X ) » 1 5 2 I F ( I C O U N T . G T . 1 0 0 ) L A R R l ( I I X , J J X ) « 1 5 3 GO TO 9 0 0 8 1 0 I F ( I C O U N T , L E , 5 0 , ) L A R R 2 ( 1 1 X , J J X ) » 1 5 1 I F ( I C O U N T , G T , 5 0 . A N D , I C O U N T , L E . 1 0 0 ) L A R R 2 ( 1 1 X , J J X ) • 1 5 2 I F ( I C O U N T . G T , 1 0 0 ) L A R R 2 ( 1 1 X , J J X ) « 1 5 3 GO TO 9 0 0 8 2 0 I F ( I C O U N T . L E , 5 0 . ) L A R R 3 ( 1 1 X , J J X ) • 1 5 1 I F ( I C O U N T , G T . 5 0 . A N D . I C O U N T , L E , 1 0 0 ) L A R R 3 ( 1 1 X , J J X ) • 1 5 2 I F £ I C O U N T . G T . 1 0 0 ) L A R R 3 ( I I X , J J X ) " 1 5 3 GO TO 9 0 0 8 3 0 I F ( I C O U N T . L E . 5 0 . ) L A R P 4 ( 1 1 X , J J X ) • 1 5 1 I F ( I C O U N T , G T , 5 0 . A N D , I C O U N T , L E , 1 0 0 ) L A R R 4 ( 1 1 X , J J X ) » 1 5 2 I F ( I C O U N T . G T . 1 0 0 ) L A R R 4 ( 1 1 X , J J X ) • 1 5 3 9 0 0 DO 1 0 0 0 L°l,96 N S B N S E T C L ) DO 1 0 0 0 M 1 , N S I F ( R A D * 2 . - B L 2 ( L ) ) 9 9 6 , 9 1 0 , 9 1 0 C C C C DETERMINES SHRUB SPECIES IIX,JJX * LOCATIONS OCCUPIED * 1 6 2 - 9 1 0 I N C R « 0 9 1 5 I N C R » I N C R + 1 G O T O ( 9 2 0 , 9 2 5 , 9 3 0 , 9 3 5 , 1 0 0 0 ) , I N C R 9 2 0 J « J J X * J Q Q ( L , K ) I " I I X t I Q Q ( L , K ) G O T O 9 4 0 9 2 5 J a j J X - J Q Q ( L , K ) I * I I X - I Q Q C L , K ) G O T O 9 4 0 9 3 0 J « J J X + J Q Q ( L , K ) I B I I X « I Q Q C L , K ) G O TO 9 4 0 9 3 5 J « J J X - J Q U C L , K ) I « I I X * I Q Q C L , K ) 9 4 0 I F C I ) 9 5 5 , 9 5 5 , 9 4 5 9 4 5 I F ( I - 6 6 ) 9 S 5 , 9 5 5 , 9 5 0 9 5 0 1 = 1 - 6 6 9 5 5 I F ( J ) 9 7 0 , 9 7 0 , 9 6 0 9 6 0 I F ( J - 6 6 ) 9 7 0 , 9 7 0 , 9 6 5 9 6 5 J B J - 6 6 9 7 0 I F ( I ) 9 7 5 , 9 7 5 , 9 6 0 9 7 5 J B 6 6 + 1 9 8 0 I F ( J ) 9 8 5 , 9 8 5 , 9 9 0 9 8 5 J B 6 6 + J 9 9 0 G O T O ( 9 9 1 , 9 9 2 , 9 9 3 , 9 9 4 ) , I S U B 9 9 1 I F ( L A R R 1 ( I , J ) . G T . 0 3 GO T O 9 1 5 L A R R 1 ( I , J W C Q U N T G O T O 9 9 5 9 9 2 I F ( U A R R 2 ( I , J ) , G T . 0 ) G O T O 9 1 5 L A R R 2 ( I , J ) " I C O U N T G O T O 9 9 5 9 9 3 I F ( L A R K 3 ( I , J ) . G T . 0 ) GO T O 9 1 5 L A R R 3 ( I , J ) B I C 0 U N T G O T O 9 9 5 9 9 4 I F ( L A R R 4 ( I , J ) . G T . 0 ) GO T O 9 1 5 L A R R 4 C I , J ) B I C O U N T 9 9 5 G O T O 9 1 5 1 0 0 0 C O N T I N U E 9 9 6 R E T U R N E N D • 1 6 3 - S U B R O U T I N E R E M D I M E N S I O N I A R R A ( 6 6 , 6 6 ) , B L 2 ( 9 6 ) , A C C ( 4 , 2 1 ) , A T A ( 4 , 2 l ) , A T G ( 4 , 2 l ) , A T F ( 4 1 , 2 1 ) , A p D N A ( 4 , 2 i ) , A P D N C C 4 , 2 l ) , A P D N S ( 4 , 2 1 ) , A P D N P R ( 4 , 2 1 ) , A P D N R O ( 4 , 2 1 ) 2 , A P D N S Y C 4 , 2 1 ) I N T E G E R * 2 J A R R A ( 6 6 , 6 6 ) , N S E T ( 9 6 ) , I Q 0 C 9 6 , 5 ) , J Q Q ( 9 6 , 5 ) , N A G E ( 5 0 ) , N N A M E 1 L C 4 ) , N N C E 0 N ( 4 ) | N N S H E P ( 4 ) , N N P R U N ( 4 ) , N N R 0 S E ( 4 ) , N N S Y M P C 4 ) , J R A N O ( 5 0 ) , K 2 R A N D C 5 0 ) , I R A N D ( 5 0 ) , J J P A N D C 1 0 0 ) , K K R A N D ( 1 0 0 ) , L I R A N D C 1 0 0 ) t J 3 A M E L ( 2 0 ) , J C E O N ( 2 0 ) , J S H E P ( 2 0 ) , J P R U N ( 2 0 ) , J R O S E ( 2 0 ) , J S Y M P ( 2 0 ) , I 5 C 0 M ( 1 5 0 ) , J C O M ( 1 5 0 ) , I D E A D 1 ( 1 5 0 ) , I D E A Q 2 ( 1 5 0 ) , I D E A D 3 ( 1 5 0 ) , I D E A 0 4 ( 1 5 0 ) 6 , L A R R 1 ( 6 6 , 6 6 ) , L A R R 2 ( 6 6 , 6 6 ) , L A R R 3 ( 6 6 , 6 6 ) , L A R R 4 ( 6 6 , 6 6 ) , I A R E A ( 1 5 3 ) , 1 0 7 1 A M I ( 1 5 0 ) , I D I A M 2 ( 1 5 0 ) , I D I A M 3 ( 1 5 0 ) , I D I A M 4 ( 1 5 0 ) , P E R ( 1 5 3 ) , E P E R ( 1 6 ) , K A 8 M E L ( 4 , 2 1 ) , K C E 0 N ( 4 , 2 1 ) , K S M E P ( 4 , 2 1 ) , K P R U N ( 4 , 2 1 ) , K R O S E ( 4 , 2 1 ) , K 5 Y M P ( 4 , 9 2 1 ) , K C H A R ( 1 6 0 ) , I M T ( 1 0 0 , 9 7 ) , I C H A R ( 9 9 ) , I B B ( 5 0 , 9 7 ) , I R A N D ( 9 7 ) , I X X ( 9 7 ) , 1 J X X ( 9 7 ) , I V O L ( 9 7 ) , I D B h ( 9 7 ) , I C L ( 9 7 ) , I A P E R ( 9 7 ) , I C W ( 9 7 ) , I C B ( 9 7 ) , I B A ( 9 7 1 ) , J C M A R C 2 ) , I 0 E A D ( 9 7 ) C O M M O N I A R R A , B L 2 , A C C , A T A , A T G , A T P , A P D N A , A P D N C , A P D N S , A P O N P R , A P O N R O , A 1 P D N S Y , C S U B 1 , C S U B 2 , C S U B 3 , C S U B 4 , R A D , B 0 R D A , X I N A , U T I L A , B 0 R D C , X I N C , U T I L 2 C , B O R O S , X I N S , U T I L S , A G E , C , C C , T A U T , T A U T S , T A U T T , T A U O , U N O C C , Y U N O C C , P D N l , I T h R U , M , I S T R T , I I N T , I E N D , I Y U N 0 C , I A U T T Y , l U N 0 C C , I L 0 0 P , I X , I 5 U B , I C 0 U N T 3 , I H T , I B B , J A R R A , L A R R 1 , L A R R 2 , L A R R 3 , L A R R 4 , I Q Q , J Q Q , I A R E A , P E R , K C H A R , I C O 4 M , J C O M , I D E A D l , I D E A D 2 , I D E A 0 3 , I D E A D 4 , I D I A M I , I D I A M 2 , I D I A M 3 , I D I A M 4 , J J R 5 A N D , K K R A N D , L L R A N D , I C M A R , I R A N D , I X X , J X X , I V O L , I O B H , I C L , I A P E R , I C W , I C B , 6 I B A , I D E A D , N S E T , K A M E L , K C E O N , K S H E P , K P R U N , K R O S E , K S Y M P , N A G E , J R A N D , K R A N 7 D , L R A N 0 , J A M E L , J C E O N , J S H E P , J P R U N , J R O S E , J S Y M P , E P E R , N N A M E L , N N C E 0 N , N N 8 8 H E P , N N P R U N , N N R 0 S E , N N S Y M P , J C H A R C C R E M O V E S D E A D S H R U B S A N D C A L C U L A T E S D E G R E E O F I N T E R S H R U B C C O M P E T I T I O N C 0 0 6 0 1 » 1 , 6 6 C D O 5 9 J 8 l , 6 6 G O T O ( 5 , 1 0 , 1 5 , 2 0 ) , I S U B 5 N B e L A R R l ( I , J ) I F C N B . G T . 1 S 0 ) G O T O 5 8 I F ( I D E A D l ( N o ) , E Q , 1 ) L A R R 1 ( I , J ) » 0 G O T O 5 8 1 0 N B B L A R R 2 C Z , J ) I F ( N 8 . G T . 1 5 0 ) G O T O 5 6 I F £ I D E A D 2 ( N B ) . E Q . l ) L A R R 2 ( I , J ) B 0 G O T O 5 6 1 5 N B * L A R R 3 C Z , J ) 1 F ( N B . G T , 1 5 0 ) G O T O 5 8 Z F ( I 0 E A 0 3 ( N B ) . E 0 , 1 ) L A R R 3 ( I , J ) B 0 G O T O 5 8 2 0 N B « L A R R 4 ( I , J ) I F ( N B , G T . 1 5 0 ) G O T O 5 6 I F ( I D E A 0 4 ( N 5 ) . E Q . 1 ) L A R R 4 ( I , J ) B 0 G O T O 5 8 5 8 C O N T I N U E 5 9 C O N T I N U E CONTINUE RETURN END - 1 6 5 - S U B R O U T I N E S G P O N ( N A M E L , N C E O N , N S H E P , N P R U N , N R O S E , N S Y M P , P O N S , P D N A , P D 1 N C , P D N P R , P D N R Q , P D N S Y , I N D I 3 K ) D I M E N S I O N I A R R A ( 6 6 , 6 6 ) , B L 2 ( 9 6 ) , A C C ( 4 , 2 1 ) , A T A ( 4 , 2 l ) , A T G ( 4 , 2 l ) , A T F ( 4 1 , 2 1 ) , A P D N A C 4 , 2 1 ) , A P O N C ( 4 , 2 1 ) , A P D N S ( 4 , 2 1 ) , A P O N P R ( 4 , 2 1 ) , A P D N R O ( 4 , 2 1 ) 2 , A P D N S Y ( 4 , 2 1 ) I N T E G E R * 2 J A R R A ( 6 6 , 6 6 ) , N S E T ( 9 6 ) , I C Q ( 9 6 , 5 ) , J Q Q ( 9 6 , 5 ) , N A G E ( 5 0 ) , N N A M E 1 L ( 4 ) , N N C E 0 N ( 4 ) , N N S H E P ( 4 ) , N N P R U N ( 4 ) , N N R O S E ( 4 ) , N N S Y M P ( 4 ) , J R A N D ( 5 0 ) , K 2 R A N D ( S 0 ) , L R A N D ( 5 0 ) , J J R A N D ( 1 0 0 ) , K K R A N D ( 1 0 0 ) , L L R A N D ( 1 0 0 ) , J 3 A M E L ( 2 0 ) , J C E O N C 2 0 ) , J S H E P ( 2 0 ) , J P R U N ( 2 0 ) , J R O S E ( 2 0 ) , J S Y M P ( 2 0 ) , I 5 C 0 M ( 1 5 0 ) , J C O M ( 1 5 0 ) , I D E A D l ( 1 5 0 ) , I D E A D 2 ( 1 5 0 ) , I D E A D 3 ( 1 5 0 ) , I D E A D 4 ( 1 5 0 ) 6 , L A R R 1 ( 6 6 , 6 6 ) , L A R R 2 ( 6 6 , 6 6 ) , L A R R 3 ( 6 6 , 6 6 ) , L A R R 4 ( 6 6 , 6 6 ) , I A R E A ( 1 S 3 ) , I D 7 I A M 1 ( 1 5 0 ) , I D 1 A M 2 ( 1 5 0 ) , I D I A M 3 ( 1 5 0 ) , I D I A M 4 ( 1 5 0 ) , P E R ( t S 3 ) , E P E R ( 1 6 ) , K A 8 M E L ( 4 , 2 1 ) , K C E 0 N ( 4 , 2 1 ) , K S H E P ( 4 , 2 1 ) , K P R U N ( 4 , 2 1 ) , K R 0 S E ( 4 , 2 1 ) , K S Y M P ( 4 , 9 2 1 ) , K C M A R ( 1 6 0 ) , I H T ( 1 0 ? , 9 7 ) , I C H A R ( 9 9 ) , I B B ( 5 0 , 9 7 ) , I R A N 0 ( 9 7 ) , I X X ( 9 7 ) , 1 J X X ( 9 7 ) , I V 0 L ( 9 7 ) , I D 6 M C 9 7 ) , I C L ( 9 7 ) , I A P E R ( 9 7 ) , I C W ( 9 7 ) , I C B ( 9 7 ) , I B A ( 9 7 1 ) , J C H A R C 2 ) , I 0 E A D ( 9 7 ) C O M M O N I A R R A , B L 2 , A C C , A T A , A T G , A T F , A P D N A , A P O N C , A P D N S , A P D N P R , A P D N R O , A I P D N S Y , C S U B 1 , C S U 8 2 , C S U B 3 , C S U B 4 , R A D , B 0 R D A , X I N A , U T I L A , B 0 R D C , X I N C , U T I L 2 C , 8 0 R D 3 , X I N S , U T I L S , A G E , C , C C , T A U T , T A U T S , T A U T T , T A U O , U N O C C , Y U N O C C , P D N 1 , I T H R U , M , I S T R T , I I N T , I E N D , I Y U N 0 C , I A U T T Y , I U N 0 C C , I L 0 0 P , I X , I S U B , I C 0 U N T 3 , I H T , I B B , J A R R A , L A R R 1 , L A R R 2 , L A R R 3 , L A R R 4 , I Q Q , J Q Q , I A R E A , P E R , K C H A R , I C O 4 M , J C O M , I 0 £ A Q i , I 0 £ A D 2 , I D E A D 3 , I D E A D 4 , I D I A M l , I D I A M 3 f I D I A M 3 , I D I A M 4 , J J R 5 A N D , K K R A N D , L L R A N D , I C H A R , I R A N D , I X X , J X X , I V O L , I D B H , I C L , I A P E H , I C W , I C B , 6 I B A , I D E A O , N S E T , K A M E L , K C E O N , K S H E P , K P R U N , K R O S E , K S Y M P , N A G E , J R A N D , K R A N 7 D , L R A N D , J A M E L , J C E O N , J S H E P , J P R U N , J R O S E , J S Y M P , E P E R , N N A M E L , N N C E O N , N N S 8 M E P , N N P R U N , N N R O S E , N N S Y M P , J C H A R I O U T - 6 C C C A L C U L A T E S N U M B E R A N D P R O D U C T I V I T Y O F S H R U B S C C S E T S P R O D U C T I O N T O 0 , P O N A B 0 „ P D N C 8 0 , P O N S 8 0 « P D N P R S 0 . P D N R O » 0 , P D N S Y 8 0 , I F C A G E . E t t , 0 ) G O TO 1 2 8 0 DO 1 2 0 0 I M , 1 5 0 G O T O ( 1 0 4 5 , 1 0 5 0 , 1 0 5 5 , 1 0 6 0 ) , I S U B 1 0 4 5 D I A M - I D I A M 1 ( I ) I M 0 R T 8 I 0 E A D 1 ( I ) G O T O 1 0 6 5 1 0 5 0 0 I A M « I D I A M 2 ( I ) I M 0 R T B I 0 E A Q 2 ( I ) GO T O 1 0 6 5 1 0 5 5 0 l A M s I 0 I A M 3 ( I ) I M C R T 8 I D £ A D 3 ( I ) G O TO 1 0 6 5 1 0 6 0 D I A M B I D I A M 4 ( I ) I M 0 R T « I D E A 0 4 £ I ) • 1 6 6 - 1 0 6 5 I F C I M O R T . E G . l ) GO TO 1 2 0 0 C C C A L C U L A T E S B O R D E R A N D I N S I D E A R E A O F S H R U B S A N D P R O D U C T I O N C X l N S a I N S I D E A R E A C S O R O S a B O R D E R A R E A C I F ( D I A M , E Q , 0 ) GO TO 1 2 0 0 R A D a O l A M / 1 0 0 . D l A M a R A O R D S a R A O / 2 , I R A D a R A D K B I R A D + 1 I F ( P E R C I ) . L T . E P E R ( K ) ) GO TO 1 0 9 0 I F C R D 8 . L T . , 8 2 ) GO TO 1 0 7 0 B O R D B ( R D S * , 8 2 ) * * 2 . * 3 , 1 4 1 5 9 - C R D S - , 8 2 ) * * 2 . * 3 . 1 4 1 5 9 X I N a ( R D S - , 8 2 ) * * 2 , * 3 , 1 4 1 5 9 X F C I . L E . 5 0 ) X I N A B X I N A + X I N I F ( I , G T . 5 0 . A N D . I , L E . 1 0 0 ) X I N C B X I N C + X I N I F C I . G T . 1 0 0 ) X I N S a X l N S + X I N GO TO 1 0 7 5 1 0 7 0 B O R D B C R D S + , 8 2 ) * * 2 . * 3 , 1 4 1 5 9 X I N 8 0 , C 1 0 7 5 I F C I . G T . 5 0 ) G O TO 1 0 7 6 B O R D A * B O R O A + B O R D X l N A a X I N A t X l N X A R E A 8 R D S * * 2 . * 3 . 1 4 1 5 9 A M E L P » 4 , 1 * X A R E A GO TO 1 1 3 0 C 1 0 7 6 I F C I . G T . 1 0 0 ) GO TO 1 0 7 9 B O R D C B B O R D C + B O R D X I N C B X I N C + X I N X A R E A B R D S * * 2 , * 3 . 1 4 1 5 9 I F ( X A R E A . L E . 6 . ) C E O N P » 6 0 , / 6 , * * 1 , 7 * X A R E A * * 1 . 7 I F ( X A R £ A , G T , 6 . ) C E O N P « 8 1 0 , « 1 , 4 5 4 5 4 * ( 1 1 0 . - X A R E A ) W 0 0 . * ( 1 1 0 , - X A R E A ) l * * 2 , 7 / 1 1 0 t * * 2 , 7 $ GO TO 1 1 3 0 C 1 0 7 9 B O R D S 8 f l O R D S * B O R D X I N S B X I N S + X I N X A R E A > R D S * * 2 . * 3 . 1 4 1 5 9 I F C X A R E A . L E . 3 . ) S H E P P a 2 5 , / 3 . * * 2 . 6 * X A R E A * * 2 . 6 I P C X A R E A . G T . 3 . ) S H E P P « 2 5 0 , - 2 5 0 . * C 1 0 0 . - X A R E A ) * * 4 , 1 / 1 0 0 . * * 4 , 1 GO TO 1 1 3 0 1 0 9 0 D I F P B P £ R ( I ) D I F E B E P E R C K ) D I F B D I F P / D I F E A C T A R a l A R E A ( I ) A C T A R a A C T A R / 4 . I F ( E P E R C K ) . N E . 4 ) GO TO 1 0 9 4 - 1 6 7 • B 0 R D « C R D S + . 8 2 ) * * 2 t * 3 , 1 4 1 5 9 X I N » fci G O T O 1 1 0 0 1 0 9 4 I F C R D S . L E . . 8 2 ) G O T O 1 0 9 5 E X P l N S s ( R D S - , 8 2 ) * * 2 , * 3 , 1 4 1 5 9 B O R D « D I F * C C R D S + . 8 2 ) * * 2 . * 3 , i 4 l 5 9 - E X P I N 5 ) E X P A R s 3 , 1 4 1 5 9 * R D S * * 2 , A C T I N S B A C T A R * E X P I N S / E X P A R 6 0 R D I N a D I F * C E X P A R - E X P I N S ) I F C C B O R O I N + A C T I N S ) . N E . A C T A R ) A C T I N S B A C T A R - B O R D I N X I N B A C T I N S I F C X I N . L T . 0 ) X I N B 0 . G O T O 1 1 0 0 1 0 9 5 B O R D B D I F * C R D S + , 8 2 ) * * 2 . * 3 , 1 4 1 5 9 I F ( B O R O . E Q . 0 ) X I N B A C T A R I F ( B O R O . G T , 0 ) X I N B 0 1 1 0 0 A R E A a l A R E A ( I ) X A R E A B A R E A / 4 , I F C I . G T . 5 0 ) G O T O 1 1 0 5 B O R D A B a O R D A + B O R D X I N A B X I N A + X I N A H E L P B 4 . 1 * X A R E A G O T O 1 1 3 0 1 1 0 5 I F ( I . G T . 1 0 0 ) G O T O 1 1 2 0 B O R O C s B O R O C t b O R D X I N C B X I N C * X I N I F ( X A R E A . L E . 6 . ) C E Q N P * 6 0 , / 6 , * * 1 , 7 * X A R E A * * 1 . 7 I F C X A R E A • G T , 6 , ) C E O N P a f l 1 0 , . i , 4 5 4 5 4 * ( 1 1 0 . - X A R E A ) - 7 0 0 . • C 1 1 0 . - X A R E A ) 1 * * 2 . 7 / 1 1 0 , * * 2 . 7 1 1 1 5 G O T O 1 1 3 0 1 1 2 0 B 0 R D 8 B Q 0 R 0 S + B 0 R D X I N S « X I N 5 * X I N I F C X A R E A . L E . 3 . ) 8 H E P P « 2 5 , / 3 , * * 2 , 6 * X A R E A * * 2 . 6 I F ( X A R E A , G T , 3 , ) S H E P P a 2 5 0 , - 2 5 0 , * ( 1 0 0 . - X A R E A ) * * 4 , 1 / 1 0 0 , * * 4 0 1 1 1 3 0 I F ( I , L E , 5 0 ) P D N A B P D N A + A M E U P X F ( I . G T , 5 0 ) G O T O 1 1 4 0 I F C I N D I 8 H , £ Q , 0 ) G O T O 1 2 0 0 C W R I T E C I O U T , 1 1 8 0 ) I , P E R C I ) , E P E R ( K ) , D l A M , X I N , B O R D , A M E L P , I A R E A C I ) G O T O 1 2 0 0 1 1 4 0 I F C I . G T , 5 0 , A N D , I , L E , 1 0 0 ) P D N C s P D N C + C E O N P I F C I . G T . 1 0 0 ) 6 0 T O 1 1 5 0 I F C I N D I S H . E Q . 0 ) G O T O 1 2 0 0 C W R I T E C I O U T , 1 1 8 0 ) I , P E R C I ) , E P E R ( K ) , D l A M , X I N , B O R D , C E Q N P , I A R E A C I ) GO TO 1 2 0 0 1 1 5 0 I F C I . G T . 1 0 0 ) P D N S a p D N S + S H E P P I F C I N D I S H . E Q . 0 ) G O T O 1 2 0 0 C W R I T E C I O U T , 1 1 8 0 ) I , P E R C I ) , E P E R C K ) , D l A M , X I N , B O R D , S H E P P , I A R E A C I ) 1 1 8 0 F O R M A T C 2 X , ' # * ' 1 3 , 3 X , ' P E R s ' , 1 5 , 3 x , ' E P E R B • , 1 5 , 3 X , ' 0 1 A M " ' , F b , 2 , 3 X , * X • 1 b 8 " l I N « ' , F b , 2 , 3 X , • B 0 R D « S F b , 2 , 3 X , • P D N « % F 8 . 2 , 3 X , # A R E A " » , I 9 ) 12012) C O N T I N U E C C C c P D N A s P D N A / 2 5 . P D N S B P D N S / 2 5 , P D N C « « P 0 N C / 2 S . W R I T E C I O U T , 1 2 0 1 ) P D N A , P D N C , P O N S 1 2 0 1 F 0 R M A T C / / # 2 X , ' P D N A a * , F 1 0 , 4 , 5 X , ' P D N C a ' , F 1 0 . 4 , 5 X , ' P O N S " ' , F 1 0 , 4 ) C X I N C A , C , S ) • I N S I D E A R E A F O R L A R G E S H R U B S X I N A B X I N A / 4 , X I N C » X I N C / 4 f X I N S B X I N S / 4 , C B O R O ( A , C , S ) * B O R D E R A R E A F O R L A R G E S H R U B S B 0 R D A 8 B 0 R D A / 4 . B 0 R D C B 8 Q R D C / 4 , B O R D S B B O R D S / 4 , C U T I L C A , C , S ) * A R E A U T I L I Z E D C I N S I D E • B O R D E R ) F O R L A R G E S H R U B S U T I L A « B O R D A + X l N A U T I L C « B O R O C * X l N C U T I L S B B O R D S + X I N S C T A U T S a T O T A L A R E A O C C U P I E D B Y C E O N , A M E L , A N D S H E P T A U T S B U T I L A + U T I L C + U T I L S C T A U T T B A R E A I N S H A D E T A U T T « 1 0 6 9 , * C / 1 0 0 . C T A U T a A R E A O C C U P I E D BY T R E E S A N D S H R U B S T A U T " T A U T S + T A U T T C T A U O B A R E A N O T O C C U P I E D B Y T R E E S A N O S H R U B S T A U O B 1 0 O 9 . . T A U T I F C T A U O . L T . 0 ) T A U O B 0 C I A U T T Y * A R E A I N S H A D E I N S Q . Y D S , U N O C C » 1 0 8 9 , - T A U T C I U N O C C B O P E N A R E A C A R E A N O T O C C , B Y T R E E S A N D S H R U B S ) I N S Q , F T » Y U N O C C B U N O C C / 9 . C I Y U N Q C B O P E N A R E A I N S Q . Y D S . I Y U N O C B Y U N O C C I A U T T Y B T A U T T / 9 , I U N O C C B U N O C C c W R I T E C I O U T , 1 2 0 2 ) T A U T S , T A U T T , T A U T , I Y U N O C 1 2 0 2 F O R M A T £ / / / , 2 X , « T A U T S s * F 9 , 2 , 3 X , ' T A U T T " ' F 9 , 2 , 3 X , ' T A U T « " , F 9 . 2 , 3 X , ' I Y U l N O C a ' , 1 9 ) I F C N P R U N . L T , 1 ) G O T O 1 2 2 5 I P C C N P R U N * I Y U N O C ) , L T , 1 0 0 ) J a N P R U N * I Y U N O C I T H B 0 C D O 1 2 2 0 I a i , J I T H " I T M * i m 1 6 9 * R A N O J J a J J R A N D C I ) R A N O J J a R A N D J J / 1 0 0 0 . 1 F C A G E . G T . 2 0 . ) G O T O 1 2 1 2 X 2 « - 1 . * ( 6 , * * 2 , 1 4 ) I F C A G E - 6 . ) 1 2 0 3 , 1 2 0 3 , 1 2 0 6 1 2 0 3 X l « - l , * ( < * l , * ( A G E » 6 , ) ) * * 2 , 1 4 G O T O 1 2 0 9 1 2 0 6 X 1 8 C A G E - 6 , ) * * 2 , 1 4 1 2 0 9 D P R U N « R A N D J J * C - . 2 * . 1 7 B * A G E + . 2 * ( X 1 / X 2 ) ) G O T O 1 2 1 5 1 2 1 2 0 P R U N " R A N D J J * 2 . 1 4 1 2 1 5 I F ( O I A M B U T , i i 3 7 ) P O N P a . 0 4 + , 6 * D P R U N I F C P I A M . G E . I , 3 7 ) P O N P a - 8 , 6 + 7 , 1 * D P R U N 1 2 2 0 P D N P R s P O N P R + P O N P P R U N s N P R U N X F C J T H . L T . 1 0 0 ) G O T O 1 2 2 5 b L O C K « 1 0 0 , / P R U N X B L K a Y U N Q C C / B L O C K P O N P R e X B L K * P D N P R c 1 2 2 5 I F C N R O S E . L T , 1 ) G O T O 1 2 4 0 J « 1 0 0 I F C C N R O S E * I Y U N O C ) , L T , 1 0 0 ) J " N R O S E * I Y U N O C I T H » 0 D O 1 2 3 0 1 * 1 , J I T H » I T H * 1 R A N D K K a K K R A N D ( I ) R A N D K K « R A N D K K / 1 0 0 0 . D R O S E « R A N D f t K * ( 2 . 3 * T A N H ( A G E * . 1 7 7 6 ) ) P D N R a , i + i , 4 * D R 0 S E * * 1 , 5 1 2 3 0 P D N R O a P D N R D + P O N R R O b E e N R O S E I P ( I T H , L T , 1 0 0 ) G O T O 1 2 4 0 B L O C K a i 0 0 , / R O S E X B L K « Y U N G C C / B L O C K P D N R 0 B X 8 L K f t P D N R 0 1 2 4 0 I F C N S Y M P . L T , 1 ) G O T O 1 2 6 0 J » 1 0 0 I P C ( N S Y M P * I Y U N Q C ) . L T . 1 0 0 ) J a N S Y M P * I Y U N O C I T M 8 0 C D O 1 2 5 5 I " l , J I T H » I T M + 1 R A N D L L s L L R A N D C I ) R A N D L L a R A N D L L / 1 0 0 0 , I F C A G E , L E . 1 8 . ) D S Y M P a p A N D L L * C , 2 * A G E - 2 , 9 6 * A G E * * 1 , 4 / 2 0 , * * ! , 4 ) I F C A G E . G T . 1 8 . ) D S Y M P a R A N D L L * 1 . 0 5 P D N S h a , 2 6 3 * D S Y M P * i « l . 5 1 2 5 5 P D N S Y a P D N S Y + P D N S M S Y M P a N S Y M P I F C I T H , L T . 1 0 0 ) G O T O 1 2 6 0 1 7 0 - B L . O C K s l 0 f c . / S Y M P X B L K a Y U N Q C C / t J L O C K P D N S Y a X B L K * P D N S Y 1 2 5 8 F O « h A T C / / » 2 X , ' P D N R O « • , F 1 0 . 4 , 5 X , • P O N S Y » ' , F 1 0 . 4 , 5 X , • P O N P R « ' , P 9 , 4 ) C 1 2 8 0 W H l T E d O U T , 1 2 5 8 ) P D N R O , P O N S Y , P D N p R 1 2 6 0 R E T U R N E N D - 1 7 1 - S U B R O U T I N E S U M C N A M E L , N C E O N , N S H E P , N P R U N , N R O S E , N S Y M P , P O N S , P D N A , P O 1 N C P D N P R , P D N R O , P O N S Y , I N D I S H ) D I M E N S I O N I A R R A ( 6 6 , 6 6 ) , B L 2 ( 9 6 ) , A C C ( 4 , 2 l ) , A T A ( 4 , 2 l ) , A T 6 ( 4 , 2 l ) , A T F ( 4 1 , 2 1 ) , A P O N A ( 4 , 2 1 ) , A P D N C ( 4 , 2 1 ) , A P D N S ( 4 , 2 1 ) , A P D N P R ( 4 , 2 1 ) , A P D N R O ( 4 , 2 1 ) 2 , A P D N S Y ( 4 , 2 1 ) 1 N T E G E R * 2 J A R R A ( 6 6 , 6 6 ) , N S E T ( 9 6 ) , I Q Q ( 9 6 , 5 ) , J Q Q ( 9 6 , 5 ) , N A G E ( 5 0 ) , N N A M E 1 L ( 4 ) , N N C E 0 N ( 4 ) , N N S H E P ( 4 ) , N N P R U N ( 4 ) , N N R O S E ( 4 ) , N N S Y M P ( 4 ) , J R A N D ( 5 0 ) ,K 2 R A N D ( 5 0 ) , L R A N D ( 5 0 ) , J J R A N D ( 1 0 0 ) , K K R A N D ( 1 0 0 ) , L L R A N D ( 1 0 0 ) , J 3 A M E L ( 2 0 ) , J C E O N ( 2 0 ) , J S H E P ( 2 0 ) , J P R U N ( 2 0 ) , J R O S E ( 2 0 ) , J S Y M P ( 2 0 ) , I 5 C 0 M ( 1 5 0 ) , J C O M ( 1 5 0 ) , I D E A D l ( 1 5 0 ) , I D E A O 2 ( 1 5 0 ) , I D E A D 3 ( 1 5 0 ) , I D E A D 4 ( 1 5 0 ) 6 , L A R R t ( 6 6 , 6 6 ) , L A R R 2 ( 6 6 , 6 6 ) , L A R R 3 ( 6 6 , 6 6 ) , L A R R 4 ( 6 6 , 6 6 ) , I A R E A ( 1 5 3 ) , I D 7 I A M 1 ( 1 5 0 ) , I D I A M 2 ( 1 5 0 ) , I D I A M 3 ( 1 5 0 ) , I D I A M 4 ( 1 5 0 ) , P E R ( 1 5 3 ) , E P E R ( 1 6 ) , K A 8 M £ L ( 4 , 2 1 ) , K C E O N ( 4 , 2 1 ) , K S H E P ( 4 , 2 1 ) , K P R U N ( 4 , 2 1 ) , « R O S E ( 4 , 2 1 ) , K S Y M P ( 4 , 9 2 1 ) , K C H A R ( 1 6 0 ) , I H T ( 1 0 0 , 9 7 ) , I C H A R ( 9 9 ) , I B B ( 5 0 , 9 7 ) , I R A N D ( 9 7 ) , I X X ( 9 7 ) , 1 J X X ( 9 7 ) , I V 0 L ( 9 7 ) , I D B H ( 9 7 ) , I C L ( 9 7 ) , I A P E R ( 9 7 ) , I C W ( 9 7 ) , I C B ( 9 7 ) , I B A ( 9 7 1 ) , J C H A R C 2 ) , I D E A D ( 9 7 ) C O M M O N I A R R A , 8 L 2 , A C C , A T A , A T G , A T F , A P O N A , A P D N C , A P D N S , A P O N P R , A P D N R O , A 1 P D N S Y , C S U B 1 , C S U B 2 , C S U B 3 , C S U B 4 * R A D , B 0 R 0 A , X I N A , U T I L A , B O R D C , X I N C , U T I L 2 C , 8 0 R D S , X I N S , U T I L S , A G E , C , C C , T A U T , T A U T S , T A U T T , T A U O , U N O C C , Y U N O C C , P D N 1 , I T H R U , M , I S T R T , I I N T , I E N D , I Y U N O C , I A U T T Y , I U N O C C , I L O O P , I X , I S U B , I C O U N T 3 , I H T , I B B , J A R R A , L A R R 1 , L A R R 2 , L A R R 3 , L A R R 4 , I Q Q , J Q Q , I A R E A , P E R , K C H A R , I C O 4 M , J C O M , I Q E A D l , I 0 E A 0 2 , I O E A 0 3 , I O E A D 4 , I O I A M 1 , I 0 I A M 2 , I D I A M 3 , I D I A M 4 , J J R 5 A N D , K K R A N D , L L R A N D , I C H A K , I R A N D , I X X , J X X , I V O L , I D B H , I C L , I A P E R , I C W , I C B , 6 I B A , I D E A D , N S E T , K A M E L , K C E O N , K S H E P , K P R U N , K R O S E , K S Y M P # N A G E , J R A N D , K R A N 7 D , L R A N D , J A M E L » J C E O N , J S H E P , J P R U N , J R O S E , J S Y M P , E P E R , N N A M E L , N N C E 0 N , N N 3 S H E P , N N P R U N , N N R O S E , N N S Y M P , J C H A R C C C A L C U L A T E S G R A S S A N D F O R B P R O D U C T I O N C C H E C K S C R O W N C L O S U R E O F T R E E S A N D A D J U S T S G R A S S P R O D U C T I O N C A D J U S T S G R A S S A N D F O R B P R O D U C T I O N T O S H R U B I N S I D E A N D B O R D E R A R E A C A N D S H R U B N U M B E R I O U T s b I F ( C . L T Q 6 S . ) P D N A G a P D N / 8 3 , 3 / 9 , * ( 2 7 , • , 0 8 5 2 9 4 * ( 6 8 T - C ) * 5 0 , 5 / 6 8 , * * 6 , * ( 1 6 8 , - C ) * * 6 , ) I F ( C , G E , 6 8 , A N D , C , L E , 7 8 , 5 ) P D N A G " P D N / 8 3 , 3 / 9 , * ( 2 6 . I 1 6 - , 3 2 8 1 * C ) I F ( C , G T , 7 6 , 5 ) P D N A G S 0 , I F ( C L E . 6 4 . ) G R A S 8 P D N / 8 3 . 3 / 9 , * ( , 0 4 S * C ) I F ( C , G T , 6 4 . ) G R A S « 0 . I F ( C L E , 1 6 . ) F 0 R B » P D N / e 3 , 3 / 9 , * ( 2 , 4 4 . e 8 7 * C ) I F ( C , G T , 1 8 , , A N D . C , L T , 8 0 . ) F O R B B P P N / 8 3 , 3 / 9 . * ( , 5 + 1 8 , / 6 0 , * * 2 . 7 * ( 8 0 , « C 1 ) * * 2 . 7 ) I F ( C , G E , 8 0 . ) F O R B * 0 , U B O R D * 0 , U X I N a 0 . U B O R 0 8 B O R D A * 6 0 R D C * B O R D S U X I N a X I N A + X l N C - f X I N S A 6 R 0 B a P D N A G * u B 0 R D * l , 3 6 5 / 2 5 , G R A S B a G R A S * U 8 0 R D * l , 3 6 5 / 2 5 , F 0 R B 8 a F 0 R 8 * U B Q R 0 * l , 3 6 5 / 2 5 , A G R O I a p D N A G * U X I N * , 0 8 1 / 2 5 . G R A S I a i 5 R A S * U X l N * , 0 6 1 / 2 5 , - 1 7 2 - FORBI•FORB*UXIN*.206/25. A G Q * 0 . F O O " 0 . G R O B 0 A G T O 3 0 . F O T Q » 0 . G R 0 B 0 « T A a P D N A G * 4 3 , 5 6 T G » 6 R A 3 * 4 3 . 5 6 T F B F 0 R B * 4 3 . 5 6 I F C M . E Q . 0 ) G O T O 2 0 1 1 I F ( C N P R U N + N R 0 S E * N 5 Y M P ) , G T . 0 ) G O TO 1 2 7 0 A G T O B P D N A G * ( 1 0 8 9 . - T A U T S ) / 2 5 . FOTO*FOPB*(i0B9,-.TAUTS)/25. G R T O B G R A S * C 1 0 8 9 . - T A U T S ) / 2 5 , G O TO 2 0 0 0 1 2 7 0 A G T O B P 0 N A G * T A U T T / 2 5 , F Q T 0 B F Q R B * T A U T T / 2 5 . G R T 0 « G R A 3 * T A U T T / 2 5 . I F ( N S Y M P . E G , 0 ) G O T O 1 2 8 0 I F C N S Y M P A E . 1 4 ) R £ 0 U C A B ( 3 , * , 1 3 3 3 4 * ( 1 5 , - N S Y M P ) • ( 8 0 , / 1 5 . * * 2 . 5 ) * ( 1 5 1 , - N S Y M P ) * * 2 , 5 ) / 8 5 . I F ( N S Y M P . G T . 1 4 ) R E D U C A B . 0 3 5 3 R E D * 1 . - R E O U C A I F ( A G E . L E , 2 5 . ) R E O P E R s , 0 4 * A G E I F ( A G E . G T . 2 5 . ) R E D P E R * 1 . R E D U C A » ( 1 , - ( R E O * R E O P E R ) ) I N C F a ( 3 , 7 6 + l , 0 2 * N S Y M P ) / 3 . 7 6 A G T Q B P Q N A G * R E 0 u X A * T A U T T / 2 5 , G R T O « G R A S * R E D U C A * T A U T T / 2 5 , F 0 T 0 a F 0 R B * T A U T T / 2 5 . 1 2 8 0 N L ' M S S H s N P R U N + N R O S E + N S Y M P I P ( N U M S S H . L E . U ) R E O U C A * ( 3 . + . 1 3 3 3 4 * ( l 5 . - N U M S S H ) * £ 8 0 . / 1 5 . * * 2 . 5 ) * ( l 5 1 , - N U M S S M ) * * 2 , 5 ) / 8 5 . I F C N U M S S M . G T , 1 4 ) R E D U C A a , 0 3 5 3 RED*1,-REOuCA I F C A G E . L t . 2 5 . ) R E O P E R * , 0 4 * A G E I F C A G E . G T . 2 5 . ) R E D P E R B 1 . R E D U C A a C l , - C R E D * R E O P E R ) ) i N C F a C 3 . 7 6 * 1 , 0 2 * N U M S S H ) / 3 , 7 6 A G Q B P D N A G * T A U 0 * R E 0 U C A / 2 5 , F 0 0 * F 0 R B * T A U 0 / 2 5 B G R 0 * G R A S * T A U 0 * R E D U C A / 2 5 , 2 0 0 0 T A s A G O ^ A G T O + A G R O B + A G R O I T G * G R O * G R T O + G R A S l + G R A S B T F B F O O + F O T O ^ F O R B I + F O R B B 2 0 1 1 L " M * 1 I F C I S U B , N E , l , O R , M . N E , l ) G O T O 2 0 1 5 c DO 2 0 1 2 J B i , 5 1 C - 1 7 3 * C S U M M A R Y O F P R O D U C T I O N O F S H R U B S , G R A S S E S A N D F O R B S C 2 0 1 2 I H T C J , 9 7 ) * 0 2 0 1 5 I F C M . E Q . 0 ) I Y U N 0 C M 2 1 P D N P R o P D N P R / 2 5 , P D N R 0 a P D N R 0 / 2 5 , P D N S Y s P O N S Y / 2 5 , I H T C L , 9 7 ) s N A G E C M ) A C C C I S U B , L ) « C A T A ( I S U B , L ) » T A A T G ( I S U B , L ) s T G A T F ( I S U B , L ) a T F K A M E L ( I S U B , U * N A M E L A P D N A C l S U 8 , L ) a P D N A K C E 0 N ( I S U 8 , L ) " N C E O N A P D N C ( I S U B , L ) * P D N C K 3 H E P C I S U B , L ) B N S H E P A P D N S ( I S U 3 , U * P D N S K P R U N C I S U B , L ) s N P R U N * I Y U N O C A P D N P R ( I S U B , L ) B P O N P R K R O S E C I S U B , L ) " N R O S E * I Y U N O C A P D N R Q C I S U B , L ) a P D N R O K S Y M P ( I S U B , L ) S N S Y M P * ( C 1 0 8 9 - T A U T S ) / 9 . ) A P D N S Y C I 3 U B , U = P D N S Y I P R U N « N P R U N * I Y U N O C I R O S E « N R Q S £ * I Y U N O C I S Y M P a N S Y M P * I Y U N O C C C P R I N T P R O D U C T I O N S U M M A R I E S C W R I T E C I O U T , 2 ) 2 F O R M A T ( 2 X , T 1 0 , ' C C ' , T 1 3 , ' A G R O P P D N % T 2 3 , ' G R A S S PDN * , T 3 4 , ' F O R B P D N ' , 1 T 4 7 , '# A M E L ' , T 5 5 , ' A M E L P D N ' , T b 7 , ' # C E 0 N ' , T 7 5 , ' C E O N P D N ' , T 8 7 , ' » S H E 2 P » , T 9 5 , ' S H E P P D N ' ) C W R I T E C I 0 U T , 5 ) C , T A , T G , T F , N A M E L , P D N A , N C E 0 N , P 0 N C , N 5 H E P , P D N S 5 F O R M A T ( 2 X , 4 F l 0 . 4 , I 1 0 , F 1 0 , 4 , 1 1 0 , F 1 0 , 4 , X 1 0 , F 1 0 , 4 ) C W R I T E C I O U T , 7 ) 7 F O R M A T ( 2 X , T 7 , ' # P R U N ' , T 1 5 , ' P R U N P D N ' , T 2 7 , ' # R O S A ' , T 3 5 , ' R O S A P D N ' , T 1 4 7 , ' # S Y M P * , T 5 5 , ' S Y M P P D N ' ) C W R I T E C I O U T , 1 0 ) I P R U N , P D N P R , I R O S E , P D N R O , I S Y M P , P D N S Y 1 0 F O R M A T C 2 X , I 1 0 , F 1 0 , 4 , I 1 0 , F 1 0 , 4 , 1 1 0 , F l 0 , 4 ) I L 0 0 P » C I E N D - I 8 T R T ) / I I N T +1 I F ( I S U 8 , E Q , 4 , A N D . C M - I L O O P ) , E Q , 0 ) G O T O 2 0 2 0 GO T O 3 0 3 0 2 0 2 0 I O Q a 0 C 2 0 2 2 DO 2 0 2 7 1 = 1 , 4 I F ( 1 0 0 . G T , 1 ) GO T O 3 0 0 0 - 1 7 4 - 2 0 2 5 C C W R I T E C I O U T , 2 0 2 5 ) I F O R M A T C ' l ' , 2 X i 1 2 8 ( ' * ' ) , / / , 2 X , T 5 6 , ' S U B - P L O T 1 2 , / / , T 2 , ' P A R A M E T E R 1 ' , / / , 2 X , ' A G E ' ) NB 1 J » l l I F ( I D O , G T , 0 ) N s l 2 I F ( N , E Q , 1 2 ) J « 2 1 2 0 2 7 W R I T E C I O U T , 2 0 3 0 ) W R I T E C I O U T , 2 0 3 1 ) W R I T E C I O U T , 2 0 3 2 ) W R I T E C I O U T , 2 0 3 3 ) W R I T E C I O U T , 2 0 3 4 ) W R I T E C I O U T , 2 0 3 5 ) W R I T E C I O U T , 2 0 3 6 ) W R I T E C I O U T , 2 0 3 7 ) W R I T E C I O U T , 2 0 3 8 ) W R I T E C I O U T , 2 0 3 9 ) W R I T E C I O U T , 2 0 4 0 ) W R I T E C I O U T , 2 0 4 1 ) W R I T E C I Q U T , 2 0 4 2 ) W R I T E C I O U T , 2 0 4 3 ) W R I T E C I O U T , 2 0 4 4 ) W R I T E C I O U T , 2 0 4 5 ) W R I T E C I O U T , 2 0 4 6 ) ( I H T C K , 9 7 ) , ( A C C ( I , K ) , K C A T A C I , K ) , K C A T F C I , K ) ,K C A T G C I , K ) ,K C M M E L C I , K ) C A P O N A C I , K ) C K C E O N C I , K ) C A P O N C C I , K ) C K 5 H E P ( I , K ) ( A P D N S C I , K ) C K P R U N C I , K ) C A P P N P R C I ,K ( K R Q S E C I , K ) C A P U l M R U C I ,K ( K S V M P C I , K ) C A P D N S Y C I , K K B M , J ) BN, J ) *N, J ) BN, J ) BN, J ) K 8 N , J ) K B N , J ) K B N , J ) K B N , J ) K B N , J ) K B N , J ) K B N , J ) , K » N , J ) K » N , J ) , K » N , J ) K B N , J ) , K * N , J ) C C I F C I L O O P , L E , 1 0 ) GO TO 3 0 0 0 I D Q B I D O + I GO TO 2 0 2 2 2 0 3 0 F Q R M A T C 2 X , 2 0 3 1 F O R M A T ( 2 X , 2 0 3 2 F O R M A T C 2 X , 2 0 3 3 F O R M A T ( 2 X , 2 0 3 4 F O R M A T C 2 X , 2 0 3 5 F O R M A T ( 2 X , 2 0 3 6 F 0 R M A T C 2 X , 2 0 3 7 F O R M A T ( 2 X , 2 0 3 6 F O R M A T ( 2 X , 2 0 3 9 F O R M A T C 2 X , 2 0 4 0 F O R M A T ( 2 X , 2 0 4 1 F O R M A T C 2 X , 2 0 4 2 F O R M A T C 2 X , 2 0 4 3 F O R M A T ( 2 X » 2 0 4 4 F 0 R M A T C 2 X , 2 0 4 5 F O R M A T C 2 X , 2 0 4 6 F O R M A T C 2 X , ' A G E ' , 6 X , 'CR, C L O S E ' A G R Q P « PDN ' F O R B P D N , ' G R A S S P D N 'NO, A M E L A N ' A M E L , PDN 'NO. C E Q N . ' C E O N , P D N 'NO, S H E P . ' S H E P , P D N 'NQ, P R U N , ' P R U N , P D N 'NO, R O S E ' ' R O S E P D N , 'NO, S Y M P . ' S Y M P , P O N 1 1 1 0 ) ', I X , U F 1 0 . 1 ) ,', 1 1 F 1 0 . 3 ) , 2 X , U F 1 0 , 3 ) ', I X , U F 1 0 . 3 ) , ' , 1 1 1 1 0 ) ', I X , 1 1 F 1 0 . 3 ) , 2 X , 1 1 1 1 0 ) ' , I X , 1 1 F 1 0 . 3 ) , 2 X , 1 1 1 1 0 ) ', I X , 1 1 F 1 0 . 3 ) , 2 X , 1 1 1 1 0 ) M X , H F 1 0 . 3 ) 3 X , 1 1 1 1 0 ) , 2 X , 1 1 F 1 0 . 3 ) , 2 X , 1 1 1 1 0 ) ', I X , 1 1 F 1 0 . 3 ) C C - 17 5 - 3 0 0 0 RETURN END

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