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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 this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of The University of British 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 alnifolia, 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 variability and site quality. Output is 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 district 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 All other common and scientific names with authorities are listed in Appendix I. - ii -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. - iii -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 field 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 facilities, and to the B. C. Fish and Wildlife Branch for the provision of equipment. - iv -TABLE OF CONTENTS Page ABSTRACT i ACKNOWLEDGEMENTS iii TABLE OF CONTENTS iv LIST OF TABLES vLIST OF FIGURES vii INTRODUCTION 1 JUSTIFICATION FOR THE STUDY 1 OBJECTIVES 2 METHODS 3 The ApproachThe Variables 4 The System 5 The Components 7 The Functions • • 7 The Analytical Methods 10 THE STUDY AREA 12 ANALYSIS OF PLANT GROWTH 8 COMPONENTS OF TREE GROWTH 1Height GrowthCrown Growth 21 Diameter Growth 6 Volume Growth 7 - v -Page COMPONENTS OF SHRUB GROWTH 27 Crown Diameter Growth 9 Annual Twig Production 35 COMPONENTS OF GRASS AND FORB GROWTH 39 Rate and Pattern of GrowthTotal Grass and Forb Production 44 ANALYSIS OF PLANT COMPETITION 46 Components of Tree Competition 4Components of Shrub Competition 8 Components of Grass and Forb Competition 53 THE MODEL 60 STRUCTUREThe Main Program 61 Simulation of Tree Growth 64 Simulation of Understory Growth 73 CURRENT STATUS OF THE MODEL 86 OUTPUT 8Validation 8 Tree Growth Simulation 89 The Vegetative Community Simulation 9POTENTIAL FOR APPLICATION 115 BIBLIOGRAPHY 117 APPENDIX I 120 APPENDIX II 2 APPENDIX III 123 - vi -LIST OF TABLES Table Page 1. The degree of variability found on seven 1/10-th acre Douglas-fir sample plots 16 2. The degree of variability found within a 1/10-th acre Douglas-fir 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 - vii -LIST OF FIGURES Figure Page 1. The system and its 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 2 7. Relationship between horizontal branch length and total branch length 3 8. Relationship between height to maximum crown width and total tree height 24 9. Relationship between height to base of live crown and maximum crown width 5 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 - viii -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 initiation 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 trees26. 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 trees29. 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 its 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 4 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 6 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 Ill - 1 -GROWTH SIMULATION OF TREES, SHRUBS, GRASSES AND FORBS ON A BIG-GAME WINTER RANGE INTRODUCTION The purpose of the study is to develop a means of predicting the effect of plant community development on ungulate food production. The method used is 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 life, 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 is 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 if more than an extremely superficial and often incomplete assessment of the interactions is 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 critical interactions affecting productivity. The ability 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 distri butions and production for shrubs and (3) mortality and production for grasses and forbs. Knowledge of inter- and intra specific dynamics will 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 initial development and testing of its predictive capability, application was restricted to two plant communities on the Wigwam big-game winter range in the East Kootenay District 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 cally 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 variability 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 is studied individually but in such a manner that it can be integrated into a biologically realistic whole. The achievement of a realistic representation of the system under consideration depends on the attainment of a sufficient degree of: (1) Realism, the ability of the model to duplicate the general form of the real system. (2) Precision, the ability 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 all 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 variability. 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 ally. They include Pseudotsuga menziesii, Amelanchier alnifolia, 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 all species can be accommodated. Competition - The degree of competition is 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 all forbs 1 crown i I annual growth competitive status Figure 1. The system and its levels of organization. - 7 -competitive ability 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 list 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 ability, inherent biological variability, unexplained variability and environmental factors, including soil 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 -if they are to be applied elsewhere. For instance, basal area or age of a forest stand used as a measure of competition are somewhat ambiguous since they only imply, and do not specify, crown closure or degree of crown competition. Despite a considerable volume of literature, it was deemed advisable to derive all necessary functions to ensure that they adequately represen ted (1) the actions and interactions occurring on the particular study area, and (2) a time-course development. The functions derived by Mitchell (1967) for white spruce growth met the requirements of this study and hence were used as a basis for derivation of similar functions for Douglas-fir. Mean height, diameter and surface area (Ferguson, 1968) as well as mean volume were used as measures of shrub growth. Non-random sampling was used to evaluate variability in density of all species (Lyon, 1968) as well as the use of l/10th-meter plots to determine floristic composition of shrubs, grasses and forbs (Daubenmire, 1959). Production of grasses and forbs was determined on both square-yard and l/10th-meter plots. Response of under-story vegetation to the presence of a forest canopy has been reported in numerous studies (Young, McArthur and Hendrick, 1967; Jameson, 1967; Anderson, Loucks and Swain, 1969; and others). In the vast majority of these studies, stand development was expressed as number of stems per unit area, basal area or stand age, rather than as a complete stand description including such factors as crown closure and crown width to diameter ratios. Consequently, the degree of competition exerted by the forest stand is uncertain. The most detailed and applicable study is that of Kemper (1971) conducted on Premier Ridge in the East Kootenay District of British Columbia. - 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, it 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 its 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, it is easily measured and appears to be a fairly 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, it 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 finally forbs. While this is obviously a simplistic approach which ignores such factors as density, age, root competition and phytotoxicity, it was deemed acceptable for the initial 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 fitting. The expected spatial relationship between dependent and independent variables was initially expressed graphically, and then algebraically. Where a single algebraic expression could not be fitted, two or more expressions were used. In these cases the expressions were fitted to pass through common points. Because of the nature of the data, the change from one to another equation is 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 fitting 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 fitted curves allowed close approximation of naturally occurring variability 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  alnifolia 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 its 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 District 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 surficial deposits as glacial tills, lacustrine silts, colluvial 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 idahoensist 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 alnifolia, 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 fires, 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 variability in detail, it would be worthwhile to present a general description of the communities and to show the variability 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 05'W ^^^^= Scale: 1:55,000 Figure 3. Study area showing location and extent of Pseudotsuga-Agropyron and Pseudotsuga-Poa communities. - 15 -The vegetation is 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 soils, interspersed with stands of Douglas-fir. Of the major shrub species, Amelanchier alnifolia, 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 variability found on seven 1/lQ^th acre plots which were measured to provide a basis for determining the predictive accuracy of the model. All values were converted to a per acre basis. The variability 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 variability 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 variability Douglas-fir sample plots. Variable Number of trees per acre 1" + DBH Volume -cu ft per acre 1" + DBH DBH -ins Height -ft Basal area -sq ft Basal area -sq ft 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 variability found within a 1/10-th acre Douglas-fir plot having a density of 500 stems per acre. Variable Values Minimum Average Maximum SD CV % Height -ft 20.0 35.5 61.5 10.13 28.5 DBH -in 2.6 6.3 15.5 2.9 45.4 Basal area -sq ft 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 is coefficient of variation CW is crown width DBH is diameter at breast height - 17 -Table 3. Maximum and minimum densities found for the most commonly occurring shrub species. Species Amelanchier alnifolia  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 in 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 in 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 it appeared to be realistic 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 live crown. Site quality was measured indirectly through its 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 -if Age _< 45 yrs HT = 18.05(SIN(Age(11/50) - II/2) + 1) ft (1) if Age > 45 yrs HT = 1.87 + (0.74066)(Age) ft (2) where: No. of Obs. = 89 R2 = 0.925 SE,, - 5.81 ft E 90 r-Figure 4. Relationship between height and age for dominant Douglas-fir. - 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 - ft 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)(HTAB0,7) ft (3) where: No. of Obs. = 404 R2 = 0.920 SEW = 1.18 ft 10 40 30 40 Height above Branch Base - ft 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, it 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)(BL) - (3.3)((BL/20)3) ft (4) where: No. of Obs. = 65 R2 = 0.896 SE_ = 0.90 ft E Total Branch Length - ft Figure 7. Relationship between horizontal branch length and total branch length. space at points of crown contact, potential crown radius will not be realized. Branch competition is discussed in the Model section. Since simulation of tree crowns was restricted to the visible crown area (the area of that portion of the crown which forms a photographic image when viewed directly from above), it was necessary to define the point of maximum crown width. Prediction of the height of maximum crown width was based - 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 is simulated. if HT < 30 ft HTCWmax = (0.06)(HT) + (0.008)(HT1,9) ft (5) if HT > 30 ft HTCWmax = - 5.5 + (0.425)(HT) ft (6) where: No. Obs. = 94 D2 = 0.828 SE„ = 2.63 ft Figure 8. Relationship between height to maximum crown width (HTCW max) and total tree height. - 25 -Estimation of height to the base of the live crown (HTblc) as a function of height to maximum crown width circumvents the restriction imposed by simulating only the visible crown area. Measurements were made on 50 trees selected from various stocking densities and age classes (Figure 9, Equations 7 and 8). All sample trees were highlined; that is, their lower branches had been killed through browsing by ungulates. Where trees are highlined, HTblc is approximately 7 feet, if HTCWmax £ 10 ft HTblc =0.0 ft (7) if HTCWmax > 10 ft HTblc = - 10 + HTCWmax (8) where: No. of Obs. = 50 ,2 R SET = 0.694 = 9.84 ft o u u CU !> cu M CO m •a •H 50 40 -30 -20 10 -0 10 20 30 40 50 60 Height to Maximum Crown Width - ft Figure 9. Relationship between height to base of live crown and height to maximum crown width. - 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 = (0.165)((CA(HT - 4.5))0,48) - (0.0011)(CA(HT -4.5)) ins (9) where: No. of Obs. = 299 R2 = 0.908 SE„ =1.08 ins 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 alnifolia. 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 fall. 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 circle 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 site. 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 ft (ID Ceanothus if Age £ 40 yrs D if Age > 40 yrs D 2.8(SIN(Age(E/60) - II/5.2) + .5) ft 4.1 + (0.016667)(Age) ft where: No. of Obs. = 96 ,2 R SE_ = 0.127 = 1.30 ft (12) (13) Shepherdia if Age <_ 50 yrs if Age > 50 yrs D = 4.5(SIN(Age(11/70) - II/4) + .6) ft D = 7.17 + (0.0046)(Age) ft where: No. of Obs. = 54 ,2 R SET = 0.438 = 1.287 ft (14) (15) - 30 -Prunus if Age <_ 16 yrs if Age > 16 yrs D = SIN(Age(n/18) - n/2.5) + 1) ft D = 2.0 ft where: No. of Obs. = 100 ,2 R = 0.488 = 0.228 ft (16) (17) Rosa if Age <_ 16 yrs D if Age > 16 yrs D SIN(Age(n/18) - n/2.5) + 1) ft 2.0 ft where: No. of Obs. = 98 v2 R = 0.166 = 0.445 ft (18) (19) Symphoricarpos if Age <_ 18 yrs D if Age > 18 yrs D 0.8(SIN(Age(H/26) - n/6) + 1) ft 1.2 ft where: No. of Obs. = 48 ,2 R SE. = 0.352 = 0.802 ft (20) (21) The prediction of crown diameter was complicated by the fact that the measured age fell short of the time period (100 years) used in the simulation. Stebbins (1951) stated that the lifespan of individual plants sprouting from roots or crowns cannot be estimated because, barring the influence of man, they can only be killed by disease, competition from other plants or by radical changes in habitat. He further stated that in stable plant - 31 -communities seriously diseased plants are rare, so the age of the plant must approach that of the community itself. 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 variability. Figure 12. Crown diameter to age relationship for Amelanchier. Age - yrs Figure 13. Simulated population of Amelanchier. 6 r-20 40 60 80 100 Age - yrs Figure 14. Crown diameter to age relationship for Ceanothus. - 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 Figure 18. Relationship between weight of annual twig production and shrub area. A: Amelanchier B: Ceanothus C: Symphoricarpos - 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 if D < 1.37 WT = 0.4 + (0.6) (D) gms if 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)(D1*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 initiation of spring growth until cessation of growth in the fall. Spring growth, as denoted by the germination of forbs and the obvious presence of new grass, was initiated in the last week of April. The cessation of growth in the fall 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 fall (17 weeks after initiation - 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 initiation 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 first week (May 1), and in treatment 2, at the end of the second week (May 8), etc. The treatments were continued until the end of the 17th week (September 11), at which time growth had ceased. (5) All 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, fitted 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 utilization 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 since Initiation of Spring Growth _L J_ 17 Control Figure 20. Current annual growth of Agropyron by weekly intervals. Weeks since Initiation of Spring Growth Figure 21. Current annual production of forbs by weekly intervals. - 42 -Figure 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 - 43 -is an approximate measure of the productive capacity of the site. 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' if Week _ 9 a = (2.833)(Week1,2) (29) if 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 initiation of spring growth. - 44 -These functions were then applied in the general equation and tested against actual weekly production. Growth was slightly overestimated from week 1 to 9. The relationships shown in equations 29 to 31 were combined and are pre sented in Equations 32 and 33. if Week _ 9 CAG - ((2.833)(Week1,2))TANH((CXO.037 - (0.016)(TANH ((Week)(0.13))))) gms (32) if Week 9 CAG = (38 + (11)TANH((Week - 9)(0.43))TANH((C)(0.037 - (0.016)(TANH((Week)(0.13))))) gms (33) In applying these equations to grass species other than Agropyron, it was assumed that the species differences are expressed only in terms of maximum attainable growth ("a" variable). Consequently,only equations 29 and 30 will require modification for species change. The foregoing relationships were derived from data collected during a single growing season (1970). Modifications of the "a" variable will accommodate variations in annual growth. Total Grass and Forb Production Twenty-four enclosures, each containing 16 square-yard plots, and the 80- by 80-foot enclosure were used to measure total annual growth for Agropyron spicatum, Poa compressa and scabrella, Festuca idahoensis, Stipa  Columbiana, Calamagrostis rubescens and forbs. Forbs were treated as a group rather than as individual species, due to the large number of species represented by relatively few individuals. The 24 enclosures were clipped - 45 -to a height of lh inches prior to initiation of spring growth and then reclipped after cessation of growth in the fall. The clippings were separated into grasses and forbs, oven dried, and weighed. Clippings made on the 80- by 80-foot enclosure fron the 10th to the 17th week, inclusive, were included. The measured values were used to define production levels and variability in production on different sites. - 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 indi viduals and populations subject to inter- and intra-specific competition. Emphasis was placed on the ability 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 criteria 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 is discussed in the Model section. Tree height-growth response to crown competition was not investigated in detail. 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 variability 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 is 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 ability 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 is eliminated if the ratio of the simulated crown area in the presence of competition to the simulated crown area in the absence of com petition is 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 all of the tree growth functions were derived on individuals subject to understory competition, and the model is not structured to allow its 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 -30 L Crown Closure - % Figure 24. Relationship between number of Ceanothus and crown closure of trees. 20 40 60 80 100 Crown Closure - % Figure 25. Relationship between number of Symphoricarpos and crown closure of trees. - 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) if CC < 75% N = 8 - (0.10606)(CC) + (19)((1 - CC/75)2*5) (34) if CC > 75% N = 0.0 (35where: No. of Obs. = 20 N = number of individuals Symphoricarpos if CC < 90% N = 35 - (0.38889) (CC) (36) if CC > 90% N = 0.0 (37where: No. of Obs. = 60 Prunus and Rosa (Theoretical) if CC < 65% N = 7 - (0.1167)(CC) + (9)((1 - CC/65)2*5) (38) If CC > 65% N = 0.0 (39The 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 fit. Points lower than the maximum values were assumed to be the result of low initial 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 initial 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 all 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 floristic 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 Closure - % Figure 27. Relationship between Agropyron production and crown closure of trees. 20 c o •H CM 4-> £ O --3 o -O £ O c u CM 10 h 100 Crown Closure - % Figure 28. Relationship between forb production and crown closure of trees. c o •H tM *J £ o 3 JJ t I U PM 10 5 20 40 60 Crown Closure - % 100 Figure 29. Relationship between combined Calamagrostis, Koeleria and Bromus production and crown closure of trees. - 55 -Agropyron if CC < 85% WT = (0.2353)(85 - CC) + (63.3)((1 - CC)2) gms/m2 (40) if CC > 85% WT = 0.0 gms/m2 (41) where: No. of Obs. = 120 R2 = 0.706 SE^ = 13.39 gms/m2 Koeleria, Calamagrostis and Bromus if CC < 80% WT = (0.05625)(CC) gms/m2 (42) if CC > 80% WT = 0.0 gms/m2 (43) where: No. of Obs. = 120 R2 = 0.50-2 SE„ =1.219 gms/m Forbs if CC < 18.75% WT = 10(SIN(CC(II/28) - n/6) + 1) gms/m2 (44) if CC > 18.75 WT = 0.5 + (18/602,7)((100 - CC)2,52) gms/m2 (45) where: No. of Obs. = 120 R2 = 0.505 2 SE„ = 4.606 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 ft Open | ^ ^ • Border w ! M B Inside V V V \ \ • / R - 0.82 ft 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 initially 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, is 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 -Agropyron if N < 14 WT - (PDN/85)(3 + (0.13334)(15 - N) + (0.0918) ((15 - N)2,5)) gms/yd2 (46) if N > 14 WT - (0.0353)(PDN) gms/yd2 (47) where: No. of Obs. = 10 R2 = 0.898 2 Forbs SE,, = 7.15 gms/yd N = number of Prunus PDN = Agropyron production in absence of Prunus WT = - 12.3 + (3.6) (N) - (0.80752) ((N - 7.5) 1,S) gms/yd2 (48) where: No. of Obs. = 10 R2 = 0.580 2 SE„ = 5.06 gms/yd E N = number of Prunus - 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 is 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), Paille (1970), Arney (1971), Goulding (1972) and others. Botkin, Janak and Wallis (1971) developed the first 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 ability. 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 listing of the program is 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 is 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 is presented in Figure 33. The organization, and hence sequence of calculations and decisions, of the model is based on an assumed hierarchy of competitive ability among trees, shrubs, grasses and forbs. Trees are assumed to have the greatest competitive ability, followed by shrubs and finally grasses and forbs. The hierarchial order is 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 indi vidual plant is 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 -GED 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 its 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 first tree Proceed to next tree Calculate tree height and branch lengths Proceed to next branch Generate first 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 is 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 initialized 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, its species and stem position, and the height at which the unit is 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 is 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 is 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 is accomplished by allowing branches to compete at various heights in the two-dimensional matrix. In the simulation of branch competition, it 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 circle, with radius equal to horizontal branch length, is 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 if 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 all 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 is 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 is assumed to die and is 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 in the form of developmental stand maps showing vertical and cross-sectional projections. Inevitably tree crowns will 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 th ! 10008499J s j 10013418 10013418 10013418 10000118 10000000 10000000 110000111i 10013418 th 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 where: t = tree number th = tree height in hundredths of feet s = stem position b = branch height in hundredths of feet Figure 35. Array coding for two Douglas-fir occupying growing space. - 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 circle having an area equal to the simulated crown area. Calculation of crown length is more complex. In the absence of inter-tree competition, height to maximum crown width is deter mined as a function of total tree height (Equations 5 and 6) and then height to base of live 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 live crown from total tree height. Where crowns are subject to competition for aerial growing space, the height of the longest branch is 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 until the simulation period is exceeded. The information and array coding generated at each calculation interval are retained for incrementation at the next calculation - 72 -************************************************* * B 1 1 1 222B222 1 1 1* * 1 1 1 1 2222222  1 1* *111 22222 11| 1 1 2 2 2 4 4 4 1| * 4444444 * * 4* 444444444 * * 4444B4444* 444444444 * * 4444444* 4 * * 5 5 B 5 5*  5 5 | £ 5 t * £ * * * *. * i. **** 3 3 3 * * 3 B 3* 3 3 3 t * I * * * i **| 1 1 2 2 2 1* *111 22222  1* *1111 2222222  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 is 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) Initial 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 in 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 first sub-plot Proceed to next sub-plot Proceed to next shrub species Take first species Increment age by one calculation interval Take first 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 first location to be occupied Generate next location i No _^-aii ; 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(continued) - 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 is 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 all shrub species, and (4) carryover of Agropyron or Poa in grams per square yard. If tree growth is not simulated, it 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 is used to assign locations. The first 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 "kill" shrubs. In the first method, shrubs are tested for shade tolerance (read as input data); if shade tolerant, they survive in direct shade; if 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 is 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 "killed" until the two are equal. This sequence in mortality is important in that it ensures that shade intolerant shrubs closest to trees die first. 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 is 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 is shade intolerant, the available area is that portion of the plot not shaded by trees or large shrubs; if 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 is 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 circle whose area is 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 is 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) finally readjust production as a function of age and density of small shrub species (Equations 46 to 49). Production in the absence of interspecific competition is 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 initiation 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 initiation 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. - 84 -The adjusted production of grasses and forbs is then readjusted in response to the presence of large and small shrub species. In the case of large shrub species, production is 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 46 to 49). Obviously, the size of the individual shrubs will affect the degree of reduction in productivity. Equations 46 to 48 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 is reduced in direct proportion to the reduction in age as shown in Figure 39. 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 level, output is summarized in terms of: (1) Developmental stand map showing a vertical projection of the shrub stand. (2) Initial 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 its components are necessary for achievement of its full 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 it is necessary to discuss the problems validating the model. Validation The advantage in adopting a systems approach is 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 is correct. Goulding (1972) summed up the validity problem in saying "the problem of validity is that if the real system was known exactly so that the model can be compared, there would have been little point in creating the simulation model." The problem then is one of comparing simulated results against static or average solutions which in themselves represent simple models of the real system and in 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 is 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 itself. 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 sig nificantly different from zero (Cohen and Cyert, 1961). 5) Turing tests (Van Horn, 1968) in which people directly involved in the field 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 validity tests are presented in the remainder of this section. Tree Growth Simulation The principle application of tree growth simulations is 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 site, 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 site. Under these conditions the model adequately duplicates the volume over age curves. Average DBH is adequately duplicated on the medium site for both 7.1" + and 11.1" +, but is underestimated in the 11.1"+ class on the poor site. By increasing the site index, but still remaining within the range for poor site, and decreasing the number of stems, similar volumes can be achieved but with an increase in 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 •rl •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 difficulty 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 in this model for all 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 its 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 -Goulding - 800 trees at 20 years - 300 trees at 20 years Simulated 940 trees at 20 years — 400 trees at 20 years SITE INDEX 90 12500 -4-4 0 20 40 60 80 100 Age - yrs Figure 44. Comparison of Goulding's and my simulated gross cubic foot volume per acre for site index 90. - 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 Goulding1s 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 will require further testing and refinement if it is to be used to generate yield tables. However, it 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 ft 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. Initial sensitivity testing showed that the models were capable of approximating solutions in the absence of trees. As was previously stated, difficulty 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, it 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 fairly 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 in the calculation of productivity, the number of comparisons that could be made is 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 it underestimated production. The response of simulated forb production to changing crown closure exhibits similar trends to those found by Kemper, but was signifi cantly lower. The lower production values probably result from the fact that Kemper's measurements were made on plant communities in secondary grazing succession in 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 it can be used as a management tool for predicting future yields of ungulate food production. Despite the uncertainty as to its predictive accuracy, the understory model can be used to investigate plant interactions and to isolate critical 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 is 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 initial number of Amelanchier was set at 2700 per hectare, representing the upper density found. The most striking feature in the comparison is 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 all 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 initially increases despite a decrease in shrub numbers. The production increase is explained by the fact that although the number of individuals is decreasing, the relative size, and hence productivity, of each individual is increasing. The response of Agropyron to the presence of trees is 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 fifty 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 initial increase in response to increasing crown closure, and decreases when crown closure exceeds 30 percent. In the presence of shrubs, forb production initially 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 is masked by a greater increase due to the presence of Prunus and Symphoricarpos until 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 -Calamagrostis and Koeleria production Forb production Forest crown closure 0 20 40 60 80 100 Time - yrs Figure 49. Comparison of simulated forb and Calamagrostis and Koeleria production response to tree crown closure in the presence and absence of shrubs. - 108 -Forest crown closure appears to be the most critical 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 if he is 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 in 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 is 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. - Ill -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 is essentially confined to the first 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 in 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 justifies 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 if it is to achieve its full 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 feasibility study in using mathematical modelling to simulate plant ecosystem development, to approximate productive capabilities for alternate species or combinations of species, isolate critical functional relationships, assess probable implications of management for wood production on ungulate food production or as a learning tool, the limitations are of little consequence. However, if the model is to be used in management decision making, it will 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 ability to account for large variations in understory production due to annual climatic variations, (3) the ability to allow mortality from causes other than competition,and (4) the development of methods for converting total plant production to utilizable production will be necessary. Following these inclusions, the model would have direct application in: 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. Illos. 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 soils. 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. Paille, G. 1970. Description and prediction of mortality in 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-Hill 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 utilization 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 alnifolia 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 live 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 live 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 APPENDIX III PROGRAM LISTING FOR THE GROWTH SIMULATION OF TREES, SHRUBS, GRASSES AND FORBS ON A BIG-GAME WINTER RANGE MAIN PROGRAM TREE GROWTH SIMULATION TREE GROWTH AND COMPETITION STAND MAPS SUBROUTINE TREE SUBROUTINE XSECT VEGETATIVE COMMUNITY SIMULATION PROGRAM CONTROL AND SPECIFICATIONS « SUBROUTINE AGROP • SUBROUTINE BRANCH • SUBROUTINE REM • SUBROUTINE AREA * SUBROUTINE SGPDN • SUBROUTINE SUM SHRUB GROWTH SHRUB MORTALITY SHRUft AREA SHRUB PRODUCTION GRASS AND FORB PRODUCTION UTILITY PROGRAMS UNIFORM AND RANDOM NUMBER GENERATORS - 124 -C C MAIN PROGRAM C C C SIMULATION OF THE GROWTH AND COMPETITIVE INTERACTIONS OF C . C TREES, SHRUBS AND GRASSES C C ON A BIG-GAME WINTER RANGE IN THE EAST KQOTENAY DISTRICT C C f BRITISH COLUMBIA C C C C DUMMY MAIN PROGRAM TO ALLOW BYPASS OF THE TREE GROWTH SIMULATION C C DIMENSION IARRA(66,66),BL2(96),ACC(4,2i),ATA(4,21),ATG(4,2l),ATF(4 1,21),APQNA(4,2t),AP0NC(4,21),AP0NS(4,21),APDNPR(4,21),APONRO£4,21) 2, APDNSY(4,21) INTEGER*2 JAftRA(66,66),NSET(96),IQQ(96,5),JaQ(96,S),NAGE(50),NNAME 1LC4) ,NNC£OiM(«) ,NNSHEP(4) ,NNPRUN(4) , NNROSE (4) , NNSYMP (4) , JRAND (50) , K 2RANDC50),LRANQ(50),JJRAND(100),KKRAND(100),LLRAND(100), J 3AMEL(20),JCEQN(20),JSHEP(20),JPRUN(20),JROSE(20),JSYMP(20) , I 5CQMC150) ,JCQM(150) , IDE AO 1 (150) , IOE AD2 C150) , IDE AD3 (150) , IDE AD4 (150) 6,LARR1 (66,66) ,LARR2(66,66) , LARR3(66,66) ,LARR4(66,66) , I AREA(153) , ID 7 I AMI(150),IDIAM2C150),IDIAM3(150), IOIAM4£ 150),PER(153),EPER(16), KA eMELC4,21),KCE0N(4,21),*3HEP£4,21),KPKUN(4,21),KR0SE£4,21),K5YMP£4, 921),KCHAR(160),IHT(100,97),ICHAR(99),IBB(50,97),IRAND (97),IXX(97), 1JXX(97),IVOL(97),IDBH(97),ICL(97),IAPER(97),ICW(97), ICB (97),ISA(97 1)»JCHAR(a),IDEAOC97) COMMON IARRA,6L2,ACC,ATA,ATG,ATF,APDNA,APONC,APDNS,ApDNPR,APDNRO,A 1PDNSY,CSUB1,CSU82,CSUB3,CSUB4,RAD,B0RDA,XINA,UTILA,BOROC,XINC,UTIL 2C80KDS, XI N'S,UTILS,AGE,C, CC, TAUT, TAUTS, TAUTT,TAUO,UNOCC, YUNOCCPDN 1,ITHRU,M,ISTRT,IINT.IENO,IYUNOC,IAUTTY,IUNOCC,ILOOP,IX,ISUB,I COUNT 3, IHT, IdB,JARKA,LARR1,LARR2,LARR3,LARR4,IUQ,JUQ, I ARE A , PER, KCHAR, ICO 4M,JCOM,IDEAD1,IDEAD2,IDEAD3,IOEAD4,IDI AM 1,IDIAM2, I DlAM3,ID IAM4,JJR SAND,KKR A NO,LLR AND, ICrtAR, 1RAND, IXX,JXX, I VOL, ID8H, ICL, IAPER, ICW, ICB, 6IBA,IDEAD,NSET,KAMtL,KCEON,KSHEP,KPRUN,KKOSE,KSYMP,NAG£,JRAND,KRAN 7D,LRANO,JAMEL,JCEON,JSMEP,JPRUN,JROSE,JSYMP,EPER,NNAM£L,NNCE0N,NNS 8HEP,NNPRUN,NNROSE,NNSYMP,JCHAR IR 0 B 5 I0UT«6 ITHRUs^ DO 2 Iai,b6 DO 2 J«l,66 lARSAfl,J)»10000000 2 JARRA(I,J)«0 C C READS BRANCH LENGTM-UCCUPANCY DATA DECK C - 125 -DO 3 1*1,96 REA0(IRD,5) BL2CI),NS,(IQQ(I,II),JQO(I,II),II«1,NS) 3 NSET(I)BNS 5 FORMATCFb.4,1313) C C • DELOPT *** DELETE OPTION FOR TREE SUBROUTINE *** C ****** IF DELOPT ,LE, 0 TREE SUB CALLED ****** C READ(IRQ,10) DELOPT 10 FORMAT(12) C C READS STARTING AGE I REAO(lRD,15) ISTRT 15 FORMAT (13) C C READS GROWTH INTERVAL C REAO(I«D,20) IINT 20 FORMAT(13) C C READS UPPER AGE LIMIT C READCIRO,30) IEND 3K FORMAT(I3) IF(OfcLOPT) 1QP,100,40 40 JB0 00 50 IsISTRT,IEND,IINT JBJ*1 50 NA6E(J)«1-1 REA0(IRP,55) IX 5b F0RMATCI5) TINTBIINT NINTsIEND/IINT C C INCREMENTS CROWN CLOSURE IF TREE SUBROUTINE NOT CALLED C CSUBlBjj. CSUB2810, CSUB3B20, CvSUB4s30, GO TO b5 hid CSU8l"C5uBl+40, CSUB2*C3UB2*40, CSUB3SCSUH3+40, C8UB4BCSUH4+40, GO TO b5 62 CSUB18CSU91+40, CSUB2"CSUB2+40. CSUB3«CSuQ3+40. CSUB4*CSU64*40, - 126 -65 M»0 C C CALLS UNDERSTORY ROUTINES C CALL AGROP DO 70 I«i,NlNT n • i c C CALLS UNDERSTORY ROUTINES C /& CALL AGROP IF(C5UB1.LT.10.) GO TO f>0 IFCCSU31.LT,50.) GO TO 62 C MB STAND AGE C ITREE * ITU TREE C IPOS B ITH BRANCH C HABM s HEIGHT TO MAXIMUM CROWN WIDTH C BL • BRANCH LENGTH C HBL • HORIZONTAL BRANCH LENGTH C IOCC » TEST VALUE FOR BRANCH OCCUPANCY C 9B,IbB B HEIGHT TO BRANCH BASE C HT,IHT,HTA,HTS= TREE HEIGHTS C ICW,CWS,CW,ACW » MEASURES OF CROWN WIDTH C IVOL,VOL,VOLS,AVOL • MEASURES OF VOLUME C IDBH,DBHS,DBH,ADBH B MEASURES OF DIAMETER AT BREAST HEIGHT C IBA,BAS,BA,ABA 8 MEASURES OF BASAL AREA C ICL,CLS,CL,ACL a MEASURES OF CROWN LENGTH C IAPER « % CROWN CLOSURE C c XWD«5 I0UT«>6 C C IDELAG ***** OPTION TO DELETE AGROPYRON SUBROUTINE CALL ***** C $SS$S IF IDELAG ,GT. 0 = CALL SUBROUTINE AGRO $$$$$ C READ(IRD,3)IDELAG 3 FORMAT CI2) C C INTEGER TO START GAUSS C READCIRD,10)IX 10 FORMAT(15) C C SI *** READS SITE INDEX *** C READ CIRD,20)SI 20 FORMAT(F5,2) C C ALL TREES INITIALIZED AS BEING ALlVE *** IDEAD *** C NUMTR *** OPTION TO CHANGE NUMBER OF TREES *** - 127 -C READClHD,3&)NUMTR 30 FORMAT(13) C C MATRIX *** OPTION TO ALLOCATE TREE LOCATIONS RANDOMLY *** C RE*D(IRD,3l) MATRIX 31 FORMAT (12) IFCMATRIX.GT.l) GO TO 51 C DO 55 I»1,NUMTR CALL RANDU (IX,IY,YFL) IXX(I)»VFL»«»5, *1, IDEAD(I)s0 5S IX-IY C DO 56 I *» 1 i NUMTR CALL RANDU (IX,IY,YFL) JXX(I)»YFL«fe5.*l. 5b IX»IY 37 ICMK«0 DO 39 NUMTR DO 39 J3 1,HUMTR IF(I.EQ.J) GO TO 39 1'FCIXXCI) ,NE.IXX(J}) GO TO 39 IF(JXXCI3 .NE.JXXCJJ) GO TO 39 LXaJXX (J) 3fl CALL RANUU (JX,IY,YFL) JXX (J)«YFL*65. + 1. iXalY IF(JXXCJ) .fe'Q.LX) GO TO 3fl ICHKal 39 CONTINUE IF(ICH*)59,59,37 51 DO «0 Ial,NUMTR IDEADCI)"0 40 *EAD(IRD,50)IXX(I),JXXCX} 50 FORMAT(213) 59 REAO(IRD,60) ICHAR 60 FORMAT(40A2) C C READS OPTIONS C C C IPRIN *** OPTION TO PRINT OUT STAND MAP *** C ****** IF ,t.E. 1 B NO MAP *** IF ,GT, 1 • MAP ****** C READ CIRD,73)IPRIN 70 FORMAT(12) C C NCOOE *** OPTION TO PRINT IARRA CODE *** » 128 " C ****** IF ,UE, 1 • NO CODE *** IF ,GT, 1 • CODE ****** C «EAD(I«Q,80)NCODE 80 FORMAT (12) C C. NTREE *** OPTION TO PRINT INDIVIDUAL TREE PARAMETERS *** C ****** IF ,LE, i • NO TREES *** IF ,GT. 1 • TREES ****** C READ(IRO,9a)NTREE 90 FORMAT(12) C C ITRFN *** OPTION TO PRINT TREE FUNCTIONS AS GRAPHS *** C ****** IF ,LE, 1 8 MO FUNCTIONS *** IF ,GT. 1 • FUNCTIONS * C REAOURO,220) ITRFN 220 F ORMAT(12) READ(IRO,230)JCHAR 230 FORMAT(2A1) C C LINPR *** OPTION TO DISPLAY VERTICAL XSECT THROUGH STAND *** C ****** IF ,LEt 0 * NO XSECT *** IF ,GE, 1 AND ,LE, 66 XSECT C PRINTED THROUGH LINE a TO VALUE OF LINPR ****** C REAO(IRD,240)L1NPR 240 FORMAT(12) C C GENERATES RANDOM NUMBERS FOR ALLOCATION TO INDIVIDUAL TREES C UMTREaNUMTR VV*.l+.«S*((100,-UMTRE)**6,/100.**6.) AM",5231*.25*C (100,-UMTRE)**6,/100.**6,) C DO 250 IM, NUMTR CALL GAUSSCIX, .2322,AM,V) IF(V,LT,VV) V»VV IF(V.GT.l.l) Vsl.l 250 IRAND(I)•V«ltf00. C DO 310 11*1,19 00 310 JJ=1,19 IHT(11» JJ)»0 310 IB6(IX,JJ)s0 ILO0Pa(ItND-ISTRT)/IINT*l JLCOPsiLOOP-i C C CALCULATES TREE HEIGHTS FOR SPECIFIED AGE INTERVAL C TREE HEIGHTS PLACED IN ARRAY C JB0 c DO 350 I-15TRT,ItNO,IINT - 129 J«J + 1 NAGEU) "1-1 X«I-1 DO 350 K»1,NUMTR RAND1«IRAND(KJ RAND8RAMD1/100K. IF(X-45.5320,330,330 320 HT«RAND*CSI/76.3 * CIS.05* (SIN(X*3.14159/50.-3,14159/2,)•1,)• .7-.038 175*X) GO TQ 3414 330 riT"RANO*(SI/7b.)*Cl.66222+.7044*X) IF(HT.LT..01) HT=,01 340 HT8«HT*100, 350 IHTCJiK)«HT2 C C CALCULATES HEIGHT AT AGE 1 * REPRESENTS LOWEST BRANCH WHORL C DO 360 J»l,l C DO 360 K»i,NUMTR RAND 1•IR AND (K3 RAND'RAND 1/ 1 000 • BBBRAND*1805.*(SIN(3.14159/50,«3.14159/2.) + l.) IF(BB.LT , 1 „) eBol, 360 IBB(J,K)°BB C C PLACES HEIGHTS TO BRANCH BASE FROM AGE INTERVAL 2 TO IMAX IN ARRAY C DO 370 J»2,IL00P L«J-1 C DO 370 KM,NUMTR 370 IBB(JrK)«IhT(LfK) C C PRINTS HEIGHT AND BRANCH BASE ARRAYS FOR TREES 1 TO 9 C WRITE(IOUT,3B0) 380 FQRMAT(M ',5X,'TREE HEIGHTS STOREO IN ARRAY'*/) C wRITE(IOUT,390) 390 FORMAT(3X,* TREE 1 TREE 2 TREE 3 TREE 4 TREE 5 TREE 6 TREE 17 TREE 6 TREE 9') C DO 400 I«l,lLOOP C 400 WRIT£(IOuT,410)(IHT(I,J),J*1,9) 410 F0RMAT(3X,1213) C WRITE(I0Ur,42tf) 420 FORMAT(////,5X,'HEIGHTS TO BRANCH BASE STORED IN ARRAY',/) C - 130 . WRIT£(IOUT,390) c 00 443 I»1,IL0UP C 430 W«ITE(1QUT,410)CIBBC1,J),J«l,9) c . C SETS IARRAU,J) • 10000000 c DO 440 I« 1,6b C DO 440 Jnlfbb 440 IARRA(I,J)sl0000000 450 MB0 C WRlTE(IQUT,45t) 451 PORMAT(/,S.X,'STAND AGE * 0 YRS. ** TREES NOT YET ESTABLISHED') CSUBlBia CSUB2«0 CSU@3*0 CSUB4«0 IFCIOELAG.LE.0) GO TO 460 C GO TO 130 C C CALLS TREE GROWTH ROUTINES C 100 CALL TREE 130 CALL EXIT STOP END C C C SUBROUTINE GAUSS (IX,S,AM,V) C C RANDOM NUMBER GENERATOR FOR NORMAL DISTRIBUTION C A«0.0 DO 50 181,12 CALL RANOUdX, 1 Y, Y) IX • IY 50 A»A«-Y VB(A-6,0)*S+AM RETURN END C C C SUBROUTINE RANDU(I X,IY,YFL) C C RANDOM NUMBER GENERATOR IYBIX*65539 IF CIY)3# 6# 6 IY*IY+2147483fe47+l YFU«IY YFl»YFL*.4656613E"9 RETURN END - 132 -SUBROUTINE TREE C c c STAND GROWTH SIMULATION FOR INTERIOR DOUGLAS-FIR DIMENSION IARRA(bb,bb),BL2(9b),ACC(4,21),ATA(4,21),ATG(4,21),ATF(4 1,21),APDNA(4,21),APDNC(4,21),APDNS(4,21),APONPR(4,21),APQNRO£4,21) 2,APDNSY(4,21) INTEGER*? JARRA(bb,6b),NSET(9b),IOQ(9b,5),JQQ(9b,5),NAGE(50),NNAME 1L(4),NNCE0N(4),NNSM£P(4),NNPRUN(4),NNR0SE£4),NNSYMP£4),JRAND(50),K 2RAND(50),LRAND(50),JJRAND(100),KKRAND(100),LLRAND(100), J 3AMEL(20),JCEQN(20),JSH£P(20),JPRUN(20),JROSE(20) , JSYMP(20) , I 5COM(150),JCOM(150),IDEAD 1(150),IDEAD2(150),IDEAD3£ 150),IDEAD4(150) b,LARRl(bb,b6),LARR2(bb,66),LARR3(b6,bb),LARR4(bb,bb),IAREA (153),10 71 AMI(150),IDIAM2(150),IDIAM3(t50),IDIAM4(150),PER(153),EPER(1b),KA AMEL(a#21),KCE0N(4,21),KSHEP(4,21),KPRUN(4,21),KR0SE(4,21),KSYMP(4, 921),KCHARflb0),IHT(100,97),I CHAR(99),IBB(50,97),IRAND£97),IXX(97), 1JXX(97),I VOL(97),IDBH(97),ICL(97),IAPER£97),ICW(97),ICB£97),IBA(97 1),JCHARC2),IDEADC97) COMMON IARRA,6L2,ACC,ATA,ATG,ATF,APDNA,APDNC,APDNS,APDNPRfAPDNRO,A 1PDNSY,CSUB1,CSUB2,CSUB3,CSU84,RAD,B0RDA,XINA,UTILA,B0RDC,XINC,UTIL 2C, BONDS,X INS,UTIL5,AGE,C,CC,TAUT,TAUTS,TAUTT,TAUO,UNOCC,YUNOCC,PDN 1,ITHRU,M,ISTRT,IINT,IEND,IYUNOC,IAUTTY,IUNOCC,ILQOP,IX,ISUB,ICOUNT 3,IHT,IBB,JARRA,LARR1,LARR2,LARR3,LARR4,IQQ,JQQ,I AREA,PER,KCHAR,ICO 4M, JCOM,IDEAD1,IDEAD2,IDEAD3,IDEAD4,IDIAM1,IDIAM2,IDIAM3,IDIAM4,JJR 5AND,KKRAN0,LLRAND,I CHAR,IRAND,IXX,JXX,IVOL,IOBH,ICL, IAPER,ICw,IC8, bIBA,IDEAD,NSET,KAMEL,KCEON,KSHEP,KPRUN,KROSE,KSYMP,NAGE,JRAND,KRAN 7D,LRAND,JAMEL,JCEDN,JSHEP,JPRUN,JROSE,JSYMP,EPER,NNAMEL,NNCEON,NNS 8MEP,NNPRUN,NNROSE,NNSYMP,JCHAR C c c C c c c c c c c c IA R R A s ARRAY REPRESENTING 1/10 ACRE PLOT JARRA a ARRAY FOR PLOTTING CROWN PROFILES CSU81,,..4 a CROWN CLOSURE OF SUB-PLOTS SUB!,,,,4 a CROWN AREAS FOR 1/40TH ACRE PLOTS HTAS s HEIGHT ABOVE BRANCH CAE • EXPECTED CROWN AREA NUMTR * # OF TREES ICHAR a TREE NUMBERS IXX, JXX 8 I,J TREE LOCATIONS IRAND s TREE GROWTH POTENTIAL CALL AGROP C C C INCREMENTS AGE INTERVAL 4b0 M»M+1 C DO 500 I«l,66 C DO 500 Jel,b6 500 JARRA(I,J)B0 1F(M-ILOOP)510,510,1470 - 133 -510 ITR£E»0 C C STARTS NEW TREE C 520 ITR£E"ITR£E+l L2»l KTMBRa1 IF(ITREE-NUMTR)530,530,790 530 HTlsIHTCM,iTREE) IF(HT1,LE.0,)GO TO 520 C C GOES TO NEXT LOWER BRANCH AND CALCULATES BRANCH LENGTH C DO 760 IBRsl,M IPOSaM+l-IoR 68l«IBBCIPQ5,ITRe£) IF(B81,Lt,0,)GQ TO 520 BBoBBl/100. HT»HT1/100,»BB HTAaHTl/100. HABMa«5.5+,425*HTA IF(HT,GT,0,) GO TO 539 HT =. 1 539 IF(HABM)560,560,540 C C TESTS AND ADJUSTS HEIGHT TO CROWN WIDTH MAX C 543 IF((HTA-MABM)«HTJ550,530,560 550 8L«.98*CHTA-HAbM)**,7 LO TO 570 560 bL*.98«HT**.7 570 haL».9*BL-3.3*CBL**3,/20.**3.) JXaJXX (ITREE) IXalXX CITKEE) C C DESIGNATES POSITION OF TREE BOLE C IARRA(IX,JX)a 97•IHT(M,I TREE)* 100 +10000000 KTHBR»u2 C DO 760 LaKTHBR,96 NSaNSET(L) L2BL C C CROWN GROWTH AND COMPETITION C CROWN GROWTH C DO 760 K«1,NS IFCHBL-BL2CL>)770,580,580 580 I NCR a0 590 INCRalNCR+1 - 134 -GO TO £600,610,620,630,760),INCR 600 JaJX+JQO(L,K) IsIX*IaQCL,K) GO TO 640 610 JBJX-JQQ(L,K) I«IX-IQQCL»K) GO TO 640 620 JsJX+JQQCL,K) I«lX-IflQ(L,K) GO TO 640 630 J»JX-JQO(L,K) I8IX+IQQCL,K) o40 £F(I)670,670,650 650 lP(I-66)b70,&70,660 660 1*1-66 670 IF(J)700,700,660 680 IF(J-66)700,700,690 690 J"J-66 700 IF(I)7i0,7l0,720 710 1*66+1 720 IF(J)730,730,7«0 730 J*66+J C C TEST FOR OCCUPANCY C 740 IOCC*10000000+(IBB £ IPOS,I TREE)* 100) IF ClARRACXfJ)/100-IOCC/100)750,590,590 750 IARRA(I,J)818000000 IARRA£I,J)8lARRA(I,J)•ITREE + IBB£ IPOS,ITREE)*100 GO TO 590 760 CONTINUE 770 GO TO 780 780 CONTINUE C C GOES TO NEXT TREE C GO TO 520 C C PRINTS MATRIX CODES IN I APRA (CROWN COMPETITION) C 790 IF(NCODE-1)880,880,800 C 800 WRITE(IOUT,990)NAGE£M) C WRITE(IOUT,810) 810 FORMAT(2X,'CODES STORED IN IARRA MATHlX-LOCATIONS Ial0 TO 40 1 Jal TO 14*) DO 820 ICaOE«40,50 C 620 WRITECIQUT,830)(IARRA(ICODE,JCODE),JCODE*1,14) 830 FORMAT(2X,1419) - 135 -C WRITE CIQUT,840) 840 FORMATC'l',2X,'LOCATIONS JM5 TO 28') C DO 850 ICOUE«40,50 C 850 WRITECIOUT,830)CIARRA (I CODE,JCODE),JCODE*15,28) C WRITE(IOUT,660) 860 FORMATC'l',2X»'LOCATIONS J s 29 TO 42') C DO 870 ICOOEs40,50 C 870 WRITECIOUT,830) (IARRACI CODE,JCODE),JC0DE*29,42) C 880 yO 890 LL8 1,NUMTR ICw(LL)»0 IVOL(LL)»0 I08H(LL)8# I8A(LL)B0 ICL(LL)»0 lAPER(LL)«0 890 IAREA(LL)ai DO 900 LLM, NUMTR 900 IC8(LL)*9999 ICS (97)o0 DO 983 1^1,66 C C DETERMINES HEIGHT TO CROWN WIDTH MAX C DO 980 J»l,6b NEWaIARRA(I,J)/l00*100 LTREE«IARRA(IPJJ-NEW IF(LTREE)930,930,910 910 IF(£NEW/100-100000) -IC8(LTREE))920,930,930 920 ICBCLTREE)«NEW/100-100000 930 JARRA(I,J)8lARRA(I,J)-NEw NB"JARRA (I,J) IF(NB)960,960,940 940 IF(N6«97)950,960,960 C C CALCULATION OF CROWN AREA C 950 lAREA(NB) • I AREA (NB) «• 1 960 IF(N8)97i4,970,980 . 970 N8898 980 JARRAd, J)BICHAR(NB) C WRITE(IOUT,990)NAGE(M) 990 FORMATCi',2X,'STAND AGE»',2X, 13,//) C 136 -C CALCULATES STAND PARAMETERS C 1000 DO 1100 MMsl,NUMTR HTl'IHTCM,MM) HT*H71/100. 1010 CRAR«IAREA(MM) C C NATURAL MORTALITY C HABMa«5,5+,425*HT IF(HABM)10kll, 1001,1002 1001 HTABBHT GO TO 1003 1002 HTA8«HT-HABM IFCHTAB.LE.0.) HTAB*,1 1003 BL»,98*HTAB*«,7 HBL».9*BL-3.3* CBL**3,/20.**3,) IF(HBL ,LE , 0,) HBLB.1 CAE«3,Hl59»hBL**2. IF ((CRAR/CAE) ,GT. . 1) GO TO 1015 MAGEsM+i IHT(MASE,WM)«IHTCM,MM) IDEAQ (MM)a\ 1015 IF(CRAR*(HT-4,5))1020,1020,1030 1020 D6HS0, GO TO 1043 1030 08M".143*CCRAR*CHT-4,5))**,48 1040 1DBH(MM)BOBH*l0Mf IF (DBH)1050,1050,1063 1050 IBA(MM)"0 GO TO 1070 1P60 IBA(MM)s(D3H/2.)**2,*3,14J 59*100. 1070 ICL(MM)aIHT(M,MM)-ICS (MM) ARElalAREA (MM) ICW(MM)a2,*SQRT (ARE 1/3, 14159) *100, IF (DBH)1080,10K0,1090 1080 V 0 L 8 W, GO TO U00 1090 V0LB-.2,734532+(1 .739410*ALOG (DBH) + J.. !6b033*ALOG (HT)) /2.302585 VOL*10.**VQL 1100 IVQL(MM)aVOL*100, C C PRINTS MAP OF CROWN OCCUPANCY C IF(IPRIN-l)1150,1150,1110 C 1110 WRITEflOUT,1126) 1120 FQRMAT('9',126('*')) C DO 1130 I»i,b6 C - 137 -1130 WRITE CIOUT, 1140) (JARRA (I, J) , J* 1,65) 1140 H0RMAT('9',65A2) C WRITE(I0UT, H20) 1150 HTS"0 DBhS«0 BAS«0 CBSa0 CLS"0 CWS = 0 AREASB3 VOLSa0 APERS«0 IF(NTREE-l)1170,1170,1160 C 1160 WRITECIOUT,1200) 1170 NEWTR»a DO 1220 N&M,NUMTR MORTnlDEADCNb) IF(HORT.GT,0) GO TO 1220 NEWTRsNEWTR+i HTI»IHT(M,NB) HTBMTI/100. 08HI=IDBH (NB) DBHsDBhI/100. BAIelBA(NS) BAsBAl/J 4400. CBIBICB(NB) IFCCBI-9000)1190,1190,1180 1180 CBI30, 1190 CBsClU/lBB. CLBMT-CB CWI«ICW(NB) CWsCWl/10'3. AREABIAREA (NB) APERM00. *AREA/435b, VOuIslVOL(NB) VOLsVOLI/100. rlTS»HTS*HT DBH5BDBHS*QBH BASBBAS+BA CB5»CBS+Cb CLS»CLS+CL CwS«CrtS*CW AREASsAREAS+AREA VOLSBVOLS+VOU c c PRINTS INDIVIDUAL TREE PARAMETERS c IF(NTREE-l) 1240,1240,1210 1200 FORMATC///,IX,' TREE # I J HEIGHT DBH B,A 138 -1. CR.BASE CR,LENGTH C.W, C, AREA C,A. AS X VOLU 2 N E ' , /) C 1210 WRXTEUOUT,1230)NB,XXX(NB),JXX(NB),HTFDBH,BA,CB,CL,CW,AREA,APER, 1VOL 1220 CONTINUE C C CALCULATES STAND AVERAGES C 1230 F0RMAT(3X,3I6,9F11,2) 1240 TREES«NEWTR AHT»HTS/TREES ADBH"0BHS/TREE5 ABABBAS/TREES ACB«CBS/TREE5 ACL»CLS/1REES ACW»CWS/TREES AAREABARSAS/TREES AAPER«AREAS/«356.*100. AVOLBVQLS/TREES C C PRINTS STAND AVERAGES C WRITE(IOUT,1250) 1250 F0RMAT(/////,5X, 'STANO TOTALS',/) C hRITEdOUT, 1260) C 1260 FORMAT(2X,'NUMBER OF TREES HEIGHT DBH 6.A. CR. BAS IE CR. LENGTH CW C. AREA VOLUME *) C WRITE(IOUT,J270)NEWTR,HTS,DBHS,BAS,CBS,CLS,CWS,AREAS,VOLS 1270 FORMAT(7X,I3,5X,7Fll,2,F22,2) LOBTR«NUMTk-NEWTR C WRITE(IOUT, 1280)LOSTR 1280 FORMAT('0',2X,'NUMBER OF TREES HAVING DIED SINCE YEAR 1«',I5) C WRITE (IOUT, 1290) 1290 FORMAT(////,5X,'STAND AVERAGES',//,2X,'NUMBER OF TREES HEIGHT 1 DBH B,A. «T, CWM CR. LENGTH C.W. C, AREA C. 2A, AS X VOLUME',/) C WRITE(IOUT, 1300)NEWTR,AHT,AOBH,AbA,ACB,ACL,ACW,AAREA,AAPER,AVOL 1300 F0RMAT(6X, I3,5X,9Fll,2) C C CALCULATES CROWN AREAS AND CROWN CLOSURES FOR SUBSETS C SUBSETS FORM BASIS FOR EVALUATION OF SHRUB AND GRASS RESPONSE TO C STAND CONDITIONS C C 139 1310 DO 1330 I«l,66 C 00 1320 J*i,66 1320 JARRACI,J)=0 C DO 1330 1=1,66 C DO 1330 J«l,66 NEWslARRACI,J)/100*100 1330 JARRA(I,J)»IARPA(I#J)-NEW SUB1*0 SDB2*0 3U6330 SUB4*0 ISUBS0 1340 ISUBalSUB+1 GO TO (1350,1370,1390,1410),ISUB C C SUBSET # 1 ** 1=1,33/ J=l,33 ** c c 1350 DO 1360 1*1,33 C DO 1360 J»l,33 NBOJAWRA (I ,J) IF(NB.GE.l) SU61«SUB1+1 1360 CONTINUE GO TO 1340 C C SUBSET #2 ** I • 1,33; J • 34,66 ** C C 1370 DO 1380 lal,33 C DO 138a J*34,66 NB»JARRA(I,J) IF(N6,GE.l) SU62BSUB2+1 1380 CONTINUE GO TO 1340 C C SUBSET #3 *# I * 34,66; J • 1,33 ** C 1390 DO 1400 1*34,66 C DO 1400 J=l,33 NQsJARRA(I,J) IF(Nd.GE.i) SUB3BSUB3+1 1400 CONTINUE GO TO 1340 C C SUBSET #4 ** I * 34,66; J a 34,66 *» - 140 -c 1410 DO 1420 1*34,66 C DO 1420 J»34,66 NBiJARRACX,J) IF(NB,GE,1) SUS4*SUB4+1 1420 CONTINUE C8U8l"SUBl/1089t*100, CSUB2aSUB2/1089,*100, csua;jaoU:33/i089, M00, CSU84*3UB4/1089, *100. c WRITECIOUT,1430) 1430 FORMATc////,5X, 'CROWN AREA AND CROWN CLOSURES FOR SUBSETS',///) C WRITE (IOUT,1440) 1440 F0RMATC12X, 'SUB-PLOT 1 - 1*1,33 J* 1,33',2X,'SUB-PLOT 2 - 1*1,33 1J«34,66',2X,'SUB-PLOT 3 - I«34,6b J« 1,33•,2X,'SUB-PLOT 4 - 1*34,66 2 J»34,66',//) C WRITE(IOUT, 1450)SUB 1,SUB2,SUB3,SUB4 1450 FORMAT (IX,'CROWN AREA « ' ,F 15,2,3F29,2,//) C WRITE (IOUT, 1460)CSUB1,CSUB2,CSUB3,CSUB4 1460 FORMAT(IX,'CROWN CLOSURE " ' , F 12 . 2,3F29,2) IF (LINPR.LE.0) GO TO 1463 C CALL XSECT (LINPR) 1463 IF (IDELAG(LE, 0) GO TO 460 C CALL AGROP GO TO 460 1470 IF(ITRFN-l)1490,1490,1480 C 1480 CALL TRFUN 1490 RETURN END - 141 -SUBROUTINE XSECT CLINPR) C C PRINTS VERTICAL X SECTION THROUGH STAND C DIMENSION IARRA(66,66),BL2(96),ACC(4,21),ATA(4,2l),ATG£4,2l) ,ATF£4 1,21),APDNA (4,21),APONC(4,21),APDNS(4,21),APDNPR(4,21),APONRO(4,21) 2,APDNSY(4,21) INTEGE8*£ JARRA (66,66),NSET(96),IQQ(96,5),JQQ(9b,5),NAGE£50),NNAME 1L(4),NNCE0N(4),NNSHEP(4),NNPRUN(4),NNROSE(4),NNSYMP(4),JRANDC50),K 2RAND(50),LRAND(50),JJRAND(100),KKRAND(100),LLRAND(100), J 3AMELC20),JC£ON(20),JSHEP(20),JPRUN(20),JROSE(20),JSYMPC20), I 5COMC150),JCOM(lSa),IDEAD1(150),IDEAD2(150),IDEAD3(150),IDEAD4£ 150) 6,LARR1£66,66),LARR2(66,66),LARR3(66,66),LARR4(66,66),I AREA(153),ID 7 I AMI £150),IDIAM2(150),IDIAM3(150),IDIAM4(150),PER(153),EPER(lb),KA 6MEL(4,21),KCE0N(4,21),KSHEP(4,21),KPRUN(4,21),KROSE(4,21),K5YMP(4, 921),KCHAR( 160),IHT(100,97),ICHAR(99),IBB(50,97),IRAND£97),IXX(97), 1JXX(97),I VOL(97),IDBH(97),ICL(97),IAPER(97),ICW(97),ICB£97),IBA(97 1),JCHAR£2),IDEAD£97) COMMON IARRA,8L2,ACC,ATA,ATG,ATF,APDNA,APDNC,APDNS,APDNPR,APDNRO,A 1PDNSY,CSU81,CSUB2,CSUB3,CSUB4,RAD,B0RDA,X INA,UTILA,BORDC,X INC,UTIL 2CBORDS, XINS,UTILS, AGE, C , CC , TAUT , TAUTS , TAUTT , TAUO , UNOCC , YUNOCCPDN 1,I THRU,M,ISTRT,11 NT,IEND,IYUNOC,IAUTTY,IUNOCC,ILOOP,IX,ISUB,IC0UNT 3,IHT,IBB,JARRA,LARR1,LARR2,LARR3,LARR4,IQQ,JQQ,I AREA,PER,KCHAR,ICO 4M,JCOM,IDEAD1 , ICEAD2,IDEAD3,IDEAD4,ID I AMI,IDIAM2,IDIAM3,IOIAM4,JJR 5AND,KKRANQ,LLRAND,ICHAR,IRAND,IXX,JXX,I VOL,IOBH,ICL,IAPER,ICW,ICB, 6IBA,IDEAD,NSET,KAM£L,KCEON,KSH£P,KPRUN,KROSE,KSYMP,NAGE,JRAND,KRAN 7D,LRAND,JAMEL,JCEON,JSHEP,JPRUN,JROSE,JSYMP,EPER,NNAMEL,NNCEON, NNS 8HEP,NNPRUN,NNROSE,NNSYMP,JCHAR C C C JLOC a LOCATION ON LINE C ILINE a LINE C ISCLE a SCALING FACTOR C NB a CHARACTER TO BE PRINTED C c ICUTab ISCLEaa C 991 DO 992 KCL«1,66 C DO 992 JCLal,66 992 JARRACKCL,JCL)a0 DO 993 JL0C"1,66 ILINEaiARRAUlNPR, JLOC) NaILINE-ILINE/100*100 ILOCa (ILINE + 5000/ 10000* 10000-1 000000k)) / 10000 IFCXLOC.LT.i) ILOCal IF(ISCLE.GT,0) GO TO 995 IFfILQC.GT.66) ISCLEa2 IF(ISCLE-1)994,994,991 - 142 994 JARRACILQC,JLOC)»N GO TO 993 995 IL0CB(IL0C+1)/2 IFCILOC.LT.1) ILQCM JARRACILOC,JLOC)»N 993 CONTINUE C DO 998 J«l,66 C DO 998 1*1,66 996 NBsJARRACI,J) IF(NB)997,997,996 997 NB • 99 998 JARRACI,JJsICHARCNB) C WRITE(I0UT,981)LINPR 981 FQRMAT('1',////,20X,'CROSS-SECTIONAL PROFILE OF STAND - SECTION T 1HR0UGH LINE ',12,///) IFCISCLE.GT.1) GO TO 987 C WRITECI0UT,982) 982 FORMAT(63X, 'VERTICAL SCALE - IFT• « 1 LINE*,//,58X,'HORIZONTAL SC 1 ALE - IFT. B 2 SPACES',///) GO TO 968 C 987 WRITECI0UT,983) 983 FORMATC60X,'VERTICAL SCALE - 2FT, * 1 LINE',//,58X, 'HORIZONTAL SCA 1LE - IFT, » 2 SPACES',///) C 988 WRITECI0UT,964) 964 F0RMATC63X,'LEGEND',//,65X,'NUMBERS REFER TO TREE NUMBER',//,65X,• IB REPRESENTS BOLE POSITION',///,126X,'LINES') C DO 985 I«l,66 K»67-X C 965 WRITECIOUT,966)CJARRA(K,J),JB1,63),K 986 F0RMATC'9',63A2,I2) C WRITE(I0UT,971) 971 FORMATC»9»,131C'*')) RETURN END - 143 -SUBROUTINE AGROP DIMENSION IARRA(66,66),BL2(96),ACC(4,21),ATA(4,21),ATG(4,2l),ATF(4 1,21),APDNA(4,21),APDNC(4,21),APDNS(4,21),APDNPR(4,21),APDNRO(4,21) 2,APDNSYC4,21) INTEGER*2 JARRA(66,66),NSET(96),IOQ(96,5),JQQ(96,5),NAGE(50),NNAME 1L(4),NNCE0N(4),NNSHEP(4),NNPRUN(4),NNR0SE(4),NNSYMP(4),JRANDC50),K 2RAND(50),LRAND(50),JJRAND(100),KKRAND(100),LLRANO(100), J 3AMEK20),JCEON(20),JSHEP(20),JPRUN(20),JROSE(20),JSYMP(20), I 5COMU50),JCOM(150),IDEAD1(150),IDEAD2(150),IDEAD3(150),IDEAD4(150) 6, LARR1(66,66),IARR2(66,66),LARR3(66,66),IARR4(66,66),IAREA(153),ID 71 AMI(150),IDIAM2C150)iIDIAM3(150),IDIAM4(150),PER ( 153),EPER(16),KA 8MEL(4,21),KCE0N(4,21),KSHEP(4,21),KPRUN(4,21),KR0SE(4,21),KSYMP(4, 921),KCHAR(160),IMT(100,97),ICHAR(99),188(50,97),IRAND(97),IXX(97), 1JXX(97),IV0U(97),ID8H(97),ICL(97),IAPER(97),ICW(97),ICB(97),I8A(97 1),JCMAR(2),IDEAD(97) COMMON IARRA,BL2,ACC,ATA,ATG,ATF,APDNA,APDNC,APDNS,APDNPR,APDNRO,A lPDNSY,CSUBi,CSUB2,CSU83,CSUB4,RAD,B0RDA,X INA,UTILA,BORDC,X INC,UTIL 2C,BORDS,X INS,UTILS,AGE,C,CC,TAUT,TAUTS,TAUTT,TAUO,UNOCC,YUNOCC,PDN 1,ITHRU,M,ISTRT,IINT,IEND,IYUN0C,IAUTTY,IUN0CC,IL00P,IX,ISU8,IC0UNT 3,IhT,IBB,JARRA,LARRI,LARR2,LARR3,LARR4,IQQ,JQQ,I AREA,PER,KCMAR,ICO 4M,JCOM,IDEAD 1,IDEAD2,IDEAD3,1DEAD4,ID I AM 1,ID IAM2,IDIAM3,IDIAM4,JJR SAND,KKRAND,LLRAND,ICMAR,IRAND,IXX,JXX,I VOL,IDBH,ICL,IAPER,ICW,ICB, 6IBA,IDEAU,NSET,KAMEL,KCEON,KSHEP,KPRUN,KROSE,KSYMP,NAGE,JRAND,KPAN 7D,LRAND,JAMEL,JCEON,JSHEP,JPRUN,JROSE,JSYMP,EPER,NNAMEL,NNCEON,NNS 8HEP,NNPRUN,NNR0SE,NNSYMP,JCHAR C C C LARR1, , , 4 B SHRUB,GRASS * FORB GROWTH ARRAYS C ITMRU » COUNTER C KCHAR * SHRUB NUMBER C EPER • EXPECTED PERIMETER OF SHRUBS C ID1AM1,,,4 a SHRUB DIAMETER C IDEAD1,,.4 • DEAD SHRUBS C LAMEL,..,LSYMP " VARIABILITY IN SIZE OF SHRUB SPECIES C NNAMEL,•t,NNSYMP * NUMBER OF SHRUBS BY SPECIES / SUB-PLOT C ZERO ARRAYS FOR PRINTING # SHRUBS AND PRODUCTION, AGE, CROWN C CLOSURE C JRAND, ,.,I.LRANO » SHRUB SPECIES GROWTH POTENTIAL C IAREA,AREAS,AAREAS a CROWN AREA MEASUREMENTS C IRDaS IOUT«6 C DO 3 I=l,b6 DO 3 Jal,66 3 JARRA(I,J)30 C IF(ITHRU.GT,0) GO TO 150 IF(M,GT,0) GO TO 150 C READ(IR0,2)EPER - 144 -2 FORMAT (1613) C REA0(IRD,4)KCHAR 4 FORMAT (4flA2) C DO 5 I«i,150 IDIAMl(I)a0 I0IAM2CI)»0 IDIAM3(I)»a IDIAM4(IJ 80 IDEAQ1 CD 30 IDEA02CI)a0 IDEAD3(I)80 5 IDtAD4(I)80 C DO 7 Ial,6fe C UO 7 Jai.fee LARR1(I,J)s0 LARR2 (I,J)80 UARR3 (I,J)80 7 LARR4(I,J)s0 C READ(IRD,10) LAMEL,LCEON,LSHEP,LPRUN,LROSE,LSYMP 10 FORMAT(61b) C READ(IRD,15) I SHRUB,INDISH 15 P0RMAT(2I3) C READ(IRD,20)IDD 20 FORMAT(13) C DO 30 I«l,4 C 30 READ(IRD,40) NMAMELCI),NNCEON(I),NNSHEP(I),NNPRUN(I),NNROSE(I),NNS 1YMP(1) 40 F0RMAT(6I4) C 00 45 Ial , 4 C DO 45 Jal,21 ACC(I,J)a0, ATA(I,J)80, AT6(I#J)«0. ATF(I,J)a0, APDNA(I,J)80, APDNCCI,J)80, APDNS(I,J)80, APDNPRCI,J)a0, APDNRO(I,J)ag, APDN5Y(I,J)80, - 145 KAMELCI,J)"0 «CEQN(I,J)*0 KSHEPC1,J)«0 KPRUNCI, J)B0 KROSECI,Ji«0 4b KSYMPCI»J3«0 C C CALCULATE SHRUB SPECIES GROWTH POTENTIAL C V A M E L a L A H E L VAHEL«VAMEL/10000. vceoNaLceoN VCEON"VCEON/10P00, VSHEP«LSHEP VSHEPsVSHEP/10000. VPRUN«IPKUN VPRUNsyPHUN/10000, VROSE*LROSE VROSEaVROSE/10B00. VSYMPs^SYMP VSYMP»V8YMP/10000, C DO 60 1*1 ,50 CALL GAUSS (iX,VAME!_, 1,0000,V) IFCV,LT,,1) V*.l IF(V.GT.i,b) Vsj.b 60 JRANDCI)«V*1000. C DO 70 1*1,50 CALL GAUSS (IX,VCEON,1,0000,V) IFCV.LT..1) V".l IF(V.GT.l.b) V*1.6 70 KRAND(I)aV*1000, C DO 8a 1*1,50 CALL GAUSS (IX,VSHEP,1,0000,V) IF(V,LT..l) V*.l IF(V.GT.l.b) Val,6 80 LRAND(I)BV*1000, C DO 92 1*1,100 CALL GAUSS (IX,VPRUN,1,0000,V) IF(V,LT,.l) Va.l IF(V.GT.l.b) Val.b 90 JJRANO(I)"V*i000, C DO 100 1*1,100 CALL GAUSS (IX,VKOSE,1,0000,V) IFCV.LT..1)Va.l IFCV.GT.1.6) Val.6 100 KKRAND(I)*V*1000« - 146 C DO 110 1*1, 100 CALL GAUSS (IX,VSYMP, 1 .0000,V) IFCV.LT.,1) V*.l IP(V.GT.1.6) V*1.6 110 LLRAND CI)*V*1000• C C 130 READCJRD,140)PDN 140 FORMAT Cp6 » 2) C 150 WRITECIOUT,160) 160 FORMAT(2X,'NUMBER OF SHRUBS BY SPECIES AT AGE 1' ,//,T24, ' AMEL',T34 1, 'CEQN',T44,'SHEP',T54,'PRUN*,T64,*ROSE',T74,'5YMP',//) C DO 170 1*1,4 C 170 WRITECIOUT, 180)I,NNAMELa),NNCEON(I),NNSHEPCI),NNPRUN(I),NNROSE(I) 1,NNSYMP(I) 180 FORMATC2X,'SUB-PLOT*',12,5X,6110) C C ISUB*0 C C INCREMENTS SUB-SETS C 190 ISijB*ISUB + l IF(ISUB.GT,4) GO TO 4000 NAMEL*NNAMEl. CISUB) NCEONeNNCEON(ISUB) NSHEP*NNSHEP CISUB) NPRUN*NNPRUN CISUB) NROSE*NNROSECISUB) NSYMPaNNSYMP(ISUB) C ITAsNAMEL IFCM,GT,0) GO TO 199 WRITECIOUT,203)ISUB,M GO TO 210 C 199 WRITE(IOUT,200) ISUB,NAGE(M) 200 FORMATC'l',2X»126C'*'),//,5X,'SUB-PLOT •',15,10X,15C»*'),10X,'AGE 1*M5) 210 CONTINUE C DO 220 1*1,66 C DO 220 J*l,66 220 JARRACI,J)*0 IFCITHRU,GT.0) GO TO 430 IFCISUd.GT.1) GO TO 430 - 147 -C C ASSIGNS SHRUB LOCATIONS C 280 00 290 XM,150 CALL RANDU CIX,lY,YFL) IC0M(I)iYFL*65.+l, IXalY CALL RANDU (IX,IY,YFL) JC0M(I)ayFL*65,+l, 290 IX"IY C i00 ICHKSB0 C DO 320 181,150 C DO 320 JB1,150 IF(I.EQ.J) GO TO 320 IF(ICOMtl).NE.ICOM(J)) GO TO 320 IF(JCOMCI).NE.JCOM(J)) GO TO 320 IXL"JCOM(J) 310 CALL RANDU CIX,IY » YFL) JC0M(J)»YFL*65.»1. IXalY IF(JCOM(J).EG.IXL) GO TO 310 ICHKS"1 320 CONTINUE C IFCICHKS.GE.I) GO TO 300 C C SHRUB MORTALITY DUE TO SHADING C AMELANCHIER C CEONOTHUS C SHEPHERD IA C PRUNUS C ROSA C SYMPHORICARPOS C 430 WRITE(I0UT,431) 431 FORMAT£2X,'MORTALITY DUE TO TREE SHRUB COMPETITION',//) IF(lTA,Ea,0) GO TO 481 INUM«0 C DO 480 l8l,ITA K«ICOM(X) L«JCOMCD INUM8INUM+1 C GO TO (435,440,445,450),ISUB 435 IIs(K*l)/2 LARR1£K,L)"151 - 148 -GO TO 455 440 II«CK*l)/2 JJ»CL+l)/2*33 LARR2 CK,L)8151 GO TO 455 445 IIBCK+1}/2+33 JJB(L*1)/2 LARR3CK,U)al51 GO TO 455 450 II=(K + l)/24.33 JJ»(L+l)/2+33 LARR4CK,L)»15i 455 IF (CZARRA CU tJJ)-10000000).EQ.0) GO TO 480 INUMslNUM-1 C GO TO C460,465,470,475),ISUB 460 IDEAD1CI)«1 LARR1CK,L)»0 GO TO 480 465 IDEAD2CI)"1 LARR2 CK,L)B0 GO TO 480 470 IDEAD3(I)al LARR3 CK, L)"0 GO TO 480 475 IDEAD4(I)«1 LARR4 CK,L)a0 480 CONTINUE IKILLAalTA-INUM NAMELaNAMEL-IKILLA WRITECI OUT,2050)ISUB,IK ILLA,NAMEL 2050 F0RMATC2X,'SUB-PLOT «',12,5X,*NO, AMEL. DEAD. »',12,5X, 'NO. AMEL• la*,12) C 481 ITC°50+NCEON IF(ITC.EQ,50) GO TO 545 INUMB0 c DO 540 Is5l,ITC KalCQM(I) LaJCOMCD INUM«INUM+1 C GO TO C485,490,495,500),ISUB 485 IX»(K*l)/2 JJBCL+1)/2 LARR 1 CKiL)a 152 GO TO 510 490 IIa(K*l)/2 JJ«CL*l)/2+33 LARR2CK,L)»152 . 149 -GO TO 510 495 IIB(K*1)/2+33 LAKR3(K,L)*1S2 GO TO 510 500 II«(K+l)/2*33 JJ"(L+l)/2+33 LARR4(K L)S152 510 IF( (IARRAdl, JJ)-10000000) ,EQ.0) GO TO 540 INUM«INUM-1 C GO TO (515,520,525,530),ISUB 515 I0EADI(I)»1 LARR1 (K,L)80 GO TO 540 520 IDEAD2(I)«1 LARR2(K,U)a0 GO TO 540 525 I0EA03CZ}"1 LARR3(K,L)80 GO TO 540 530 l'OEAO«(I)«J LARR4(K,L)a0 540 CONTINUE IKILLCaNCEON-INUM NCEONSNCEON-IKIILC WRITE (IOUT, 20S0) ISUB, IKILLCNCEON 2060 FORMAT(2X, 'SUB-PLOT • ' ,12,5X,'NO, CEON. DEAD "',12,5X,'NO, CEON, • IMS) C 545 ITS»100*NSMEP IF(ITS,EQ,100) GO TO 602 C INUM80 DO 600 Z«iei»ITS MICQM(I) LBJCOM(I) INUMBlNUM+1 C c GO TQ (550,560,565,570),ISUB 550 II-CK+D/2 JJB(L*1)/2 LARR! (K,L)8153 GO TO 575 560 IX"CK*t)/2 JJ»Cl+l)/2*33 LARR2(K,L)B153 GO TO 575 565 IIB(K*1)/2t33 JJB(LM)/2 - 150 -LARR3 (K,L)a 153 GO TO 575 570 XI»(K*l)/2+33 JJs(L + n/2 + 33 L ARR4(K » L)•153 575 IF( (IARRA (II,JJ)-10000000),EQ,0) GO TO 600 INUM"lNUM«l C GO TO (580,565,590,595),ISUB 580 IDEAD1(I)*1 LARR1(K,L)b0 GO TO 600 565 IDEA02CI)"1 l.ARR2(K,L) =0 GO TO 600 590 IDEA03(I.)»1 UARR3(K,L)a0 GO TO 60t) 595 IUEAD4(I)«1 LARR4(K,L)a0 600 CONTINUE C IKILLS=NSH£P-INUM NSHEPsNSHEP-IKILLS C WRITE (IOUT,2070)ISU8,IK ILLS,NSHEP 2070 FORMAT(2X,'SUB-PLOT a ' ,12,5X,'NO, SHEP, DEAD • ' ,12,5X, 'NO• SHEP, i«',i2) 602 GO TO (605,610,615,620),ISUB 605 CCaCSUBi GO TO 625 610 CC«CSUB2 GO TO 625 615 CCaCSUB3 GO TO 625 620 CCaCSUB4 625 CONTINUE C»CC WRITE(I0UT,635) CC 635 FQRMAT(//,10('*'), 5X, 'CROWN CLOSURE a',F6.2,5X,10C ' *')) 670 IF(CC,GT.?4.5) CC*74,5 IF(CC.LE,0) CCB,01 IF(M,EQ,0) GO TO 695 C C DETERMINES NO. OF CEONOTHUS AS A FUNCTION OF CROWN CLOSURE C IF (NAMtL,EQ.0) GO TO 675 MAMELa8,-.10606*CC +19,*((75.-CC)**2.5/75,**2,5)+.5 IF(NAMEL.GT.MAMfcL) NAMELBMAMEL ITAaNAMEL+IKILLA C m 151 * C DETERMINES NO. OK AMELANCHIER AS A FUNCTION OF CROWN CLOSURE C 675 IF CNCEON.EQ.0D CO TO 680 MCE0NB8.-.10606*CC +19.*(£75,-CCJ**2.5/75,**2.5)+,5 IFfNCEON.GT.MCEON) NCEONaMCEQN ITC8NCEON+IKILLC +50 C C DETERMINES NO. OF SHEPHERDIA AS A FUNCTION OF CROWN CLOSURE C 680 IFCNSHEP.EQ.0) GO TO 685 MSHEP»8.-,10606*CC + 19.*C (75.-CC)**2,5/75.**2.5)•.5 IFCNSHEP.GT.MSHEP) NSHEP BMSHEP ITSaNSHEP+IKILLS + 100 C C DETERMINES NO. OF PRUNUS AS A FUNCTION OF CROWN CLOSURE C 685 IF£CC.GT,65.) NPRUN»0 IF(NPRUN.EG.0D GO TO 688 MPRUNB7,-, 1167*CC*9.«((65.-CC)**2./65.**2.)+.5 IF (NPRUN.GT.MPRUN) NPRUN«MPRUN C C C DETERMINES NO, OF ROSES AS A FUNCTION OF CROWN CLOSURE C 688 IFCCC.GT.65.) NROSE"0 IF£NROSE,EQ,0) GO TO 690 MR0SEB7,-.il67*CC+9,*£(b5,-CCD**2./65.**2.)+,5 IF(NROSE.GT.MRCSE) N«OSE*MRCSE C C C DETERMINES NO. OF SYMPHORICARPOS AS A FUNCTION OF CROWN CLOSURE 690 IF(C .GT.90.) NiSYMP«0 IF(NSYMP.EQ.0) GO TO 695 MSYMP»35,-,38889*C+,5 IF(NSYMP.GT.MSYMP) NSYMPeMSYMP C C SETS BORDER, INSIDE AND TOTAL AREA OF AMELANCHIER TO ZERO C 695 BORDA80. XINA«0. UTILA80. C C SETS BORDER, INSIDE AND TOTAL AREA OF CEONOTHUS TO ZERO C BQROC80. XINC80, UTILC80. C C SETS BORDER, INSIDE ANO TOTAL AREA OF SHEPHERDIA TO ZERO C BORDS80, 152 -XI.NS"0, UT1LSB0. C C SETS PRODUCTION OF AMELANCHIER, CEONOTHUS, SHEPHERDIA, PRUNUS, C ROSE AND SYMPHORICARPOS TO ZERO C PDNA"0. PDNCa0, PQN5S0. PDNPR«0, PDNRO*0. PDNSYS0. IFCM.EQ.fl) GO TO 2000 AGEaNAGE £M) XDIAM80, C WRITE (I OUT,699)I SUB,NAMEL,NCEON,NSHEP,NPRUN, NROSE , NSYMP 699 FORMAT(//,5X,'SHRUB #.S SURVIVING IN UNSHADED AREA ' ,//,5X,'SUB-PLO IT a',i5,2X,»* AMtL ••,I5,2Xi'# CEON »',lS,2)(t'# SHEP B',I5,2X,'# P 2RUN 8',I5,2X,'# ROSE B',I5,2X,'# SYMP a',15,///) C c c C IDIAM1(I),,,4 CI) a DIAMETER OF INDIVIDUAL SHRUBS C C C AMELANCHIER CALCULATIONS C NCOUN1a0 c DO 745 1=1, C GO TO (700,705,710,715),ISUB 700 IF(NCOuNl.GE.NAMEL) IDEADl(I)»i IFCIOEAU1 CI) .EQ.l) GO TO 745 GO TO 720 705 IF(NC0UN1,GE.NAMEL) IDEA02(I)»1 IF(I0EAD2(I).EU,1) GO TO 745 GO TO 720 710 IF(NCOUN1.GE.NAMEL) IDEAD3(I)*1 IF(IDEAD3(I).EQ.l) GO TO 745 GO TO 720 715 IF(NCOUNl.GE.NAMEL) IOEA04(I)«l IF(IDEAD4(I).EQ.l) GO TO 745 720 NCOUN1BNCOUN1+1 RANOJBJRANO (I) RANDJ«RANDJ/1000, X2a«l,*30,**i,996 IF(AGE-30,)725,730,730 7 25 XIa-l,*(-1 .* (AGE-30.))**1 ,996 GO TO 735 - 153 730 Xls(AGE-30.)**1.996 735 DlAMaRANDJ* (-1, • , 15* AGE* 1, * £X1 /X2) ) C 60 TO £737,739,741,743),1SUB 737 IDIAM1£1)aDlAM*100, GO TO 745 739 IDIAM2CI)aDlAM*100, GO TO 745 741 IDIAM3CI)8OIAM*100, GO TO 745 743 IDIAM4£I)8DIAM*100, 745 CONTINUE C C CALCULATES DIAMETER OF CEONOTHUS C 755 NCQUN280 C DO 805 1=51,100 C GO TO £760,763,769,772),ISUB 760 IFCNCQUN2.GE.NCE0N) IDEADl£I)»l IF CIDEAD 1(I),EQ,1) GO TO 805 GO TO 775 763 IF(NC0UN2.GE,NCE0N) I0EAD2(I)"1 IF(IDEAD2£I).EQ.l) GO TO 805 GO TO 775 769 IF£NC0UN2,GE,NCE0N) IDEAD3£I)»1 IFCIDEAD3(I),E0,1) GO TO 805 GO TO 775 772 IF(NC0UN2,GE.NCE0N) IDEAD4fI)M IF£IDEAD4£I),EQ,1) GO TO 805 775 NC0UN2»NC0UN2+1 RAND*»KRAND £I«50) RANDK«RANDK/1000, DIAM"RANOK*C5,5*TANH£AGE*,03)) GO TO £780,785,790,795),ISUB 780 IDIAM1(I)»DIAM*100, GO TO 805 785 I0IAM2CI)8OIAM*100, GO TO 805 790 I0IAM3CD 8OIAMH00, GO TO 605 795 IDIAM4CI)8DIAM*100, 805 CONTINUE C C SHEPHERDIA CALCULATIONS C 810 NCOUN3«0 C 00 865 18101,150 GO TO £615,820,825,830),ISUB - 154 * 815 IF£NC0UN3,GE.NSHEP) ZDEAD1 C15) • 1 IFCIDEA01 (I).EQ.l) GO TO 865 GO TO 835 820 IFCNC0UN3.GE.NSHEP) IDEAD2£I)8l 1FCIDEAD2CI).EQ.l) GO TO 865 GO TO 835 625 IFCNC0UN3.GE,NSHEP) IDEAD3CI)* 1 IF(IDEAD3CI).EQ.l) GO TO 865 GO TO 835 830 IFCNC0UN3.GE,NSHEP) IDEAD4(I)»i IF CIDEAD4 (I).EG.1) GO TO 865 835 NCQUN3sNCQUN3+l RANDL»tRANDCI«100) RANOUBRANDL/1000, IFCAGE.LT.28,) DIAM*RANDL*C.16*AGE) IF(AGE,GEt28.) DI AM>R ANDL* C5, +2. 5*T ANH C (AGE-28 , ) * , 033) ) C 645 GO TO (647,849,851,853),ISUB 847 IDIAM1(I)=DIAM*100. GO TO 865 849 IDIAM2(I)=DIAM*100, GO TO 865 851 IDIAM3CI)aDIAM*100. GO TO 865 853 IDIAM4CI)»DIAM*100, 865 CONTINUE C 870 CONTINUE ICOUNTB0 880 ICOUNTsICOUNT+1 C STARTS NEW SHRUB IF(ICQUNT.GT.ITS) GO TO 997 C C CALCULATES SHRUB RADIUS C RADB RADIUS C GO TO £865,690,895,900),ISUB 885 IF(IOEADlCICOUNT).EQ.l) GO TO 880 IFdDlAMl (ICOUNT) ,EQ.0) GO TO 680 RADBIDIAMI(ICOUNT) RADaRAQ/200, IIXBICOM(ICOUNT) JJX»JCOM(ICOUNT) GO TO 905 890 IF(IDEAD2(IC0UNT).EQ.l) GO TO 880 IF(I0IAM2(IC0UNT).EO.0) GO TO 880 RADsIDIAM2(ICOUNT) RADaRAD/200, IIXBICOM(ICOUNT) JJXSJCOM(ICOUNT) GO TO 905 - 155 -895 IFIIUEA03CXC0UNT) ,EQ,1) GO TO 880 IF(IDIAM3(IC0UNT),EQ,0) GO TO 680 HA0-I0IAM3CIC0UNT) RADaRAD/200, IlX»ICQM(ICOUNT) JJXaJCOM(ICOUNT) GO TO 905 900 IF(IDEAD4(IC0UNT),EQ.l) GO TO 680 1F(I0IAM4(IC0UNT).EQ.0) GO TO 880 RAD«IDIAM4(ICOUNT) RADaRAD/200, IlX«ICOM(ICOUNT) JJXaJCOMUCOyNT) 905 CONTINUE IF(ISHRU8,GT ,0) GO TO 995 IFCICOUNT.GT,50,AND.ICOUNT.LE,100) 60 TO 910 IFCICOUNT ,GT,100) GO TO 920 C WRITE(IOUT,906)ICOUNT,RAD,ICOMCI COUNT),JCOM(ICOUNT) 906 FORMAT(2X,'AMEL # a',14,5X,'RADlUS IN FT. a ' ,F8,2,5X,»ILOC a',15,5 IX,»J LOC a',15) GO TO 995 C 910 WRITE(IOUT,915)I COUNT,RAD,ICOM(ICOUNT),JCOM(ICOUNT) 915 FORM AT (2X , 'CEON # a',14 » 5X,'RADlUS IN FT. "< ' , F8 , 2 , 5X , * ILOC a',15,5 IX,»J LOC a',15) GO TO 995 C 920 WRITE(IOUT,925)I COUNT,RAO,I COM(ICOUNT),JCOM(ICOUNT) 925 FORMAT(2X,'SHEP # "',14,5X,'RADlUS IN FT, «',F8,2,5X,'ILOC a',15,5 IX,*J LOC a',15) C C SHRUB GROWTH 995 CALL BRANCH GO TO 880 C 997 DO 998 1=1,153 IAREA(I)sl 998 PER(I)s0 C C SHRUB REMOVAL IF DEAD CALL REM C C SHRUB AREA CALCULATION C CALL AREA (NAMEL,NCE0N,NSHEP,NPRUN,NROSE,NSYMP,PDNS,PDNA,PD 1NC,PUNPR,P0NR0,PDNSY,IN01SH) C C PRODUCTION CALC FOR SHRUBS, GRASSES & FORBS CALL SGPON (NAMEL,NCEON,NSHEP,NPRUN,NROSE,NSYMP,PDNS,PDNA,PD 1NC,PDNPR,PDNR0,PDNSY,INDISH) - 156 -2000 CALL SUM (NAMEL,NCEON,NSHEP,NPRUN,NROSE,NSYMP,PDNS,PONA,PD 1NC,PDNPR,PDNRO,PDNSY,INOISH) IFCISU8.LE.3) GO TO 190 IF(IDD.LE.0) GO TO 3900 C C c PRINTS SHRUB MAPS C C C c c DO 3600 la DO 3600 ja NBaLARRlCI IFCNB.EO.B 3600 JAHRACIfJ) WRITE(IOUT 3700 FORMATC'l* DO 3800 la 3800 WRITECIOUT WRITECIOUT IFCIDD.LE, DO 3601 1-00 3601 Ja NBaLARRSCI IFCNB.EO.0 3601 JARRA(I,J) WRITECIOUT 3701 FORMAT C'1' DO 3601 la 3801 WRITECIOUT WRITE(IOUT OQ 3602 I* DO 3602 Ja NBaLARR3CI IF(NB,EQ.0 3602 JARRA(I,J) WRITECIOUT 3702 FORMATC'l' DO 3802 1= ,66 ,66 J) NBal54 KCHAR(NBJ 37003 2X,'SUB-PLOT # 1', //,2X,'SHRUB MAP',//,1X,130 ( ' * ' ) ) ,66 38503 (JARRA(I,J),J*l,64) 3889) ) GO TO 3900 , 66 ,66 J) NBal54 KCHAR(NB) 3701) 2X,'SUB-PLOT # 2',//,2X,'SHRUB MAP',//,1X,130('*')) ,66 3850) (JARRA(I,J),jai,64) 3889) IF(IDD.LE,2) GO TO 3900 ,66 ,66 J) N8=154 KCHAR(NB) 3702) 2X,'SUB-PLOT # 3',//,2X,'SHRUB MAP',//,1X »130('*')) ,66 157 -C 3802 WRITE(IOUT,3850)(JARRA(I, J),J»1» 64) C WRIT£(I0UT,3889) IF(IDD,LE,3) GO TO 3900 C DO 3603 181,66 DO 3603 J*l,66 NB«LARR4(I,J) IF(NB,£Q.0) NB«154 3603 JARRA(I,J)s»KCHAR(NB) C WRITE(IOUT,3703) 3703 F0RMAT('1',2X,'SUB-PLOT # 4»,//,2X,'SHRUB MAP',//,1X,130('*')) DO 3603 IM,66 C 3803 3850 WRITE(IOUT,3850)(JARRA(I,J),J*l,64) F0RMAT('9*,1X,64A2) C 3889 3900 4000 WRITE(I0UT,3889) FORMATOX, 128('*')) ITHRUalTHRU+i RETURN END * 158 -SUBROUTINE AREA (NAMEL,NCEON,NSHEP,NPRUN,NROSE,NSYMP,PONS,PONA,PD 1NC,PDNPR,PDN«0,PDNSY,INDISH) DIMENSION IARRA(66,66),8L2(96),ACC(4,2l),ATA(4,2i),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),JQQ (96,5),NAGE(50),NNAME 1L(4),NNCE0N(4),NNSHEP(4),NNPRUN(4),NNR0SEC4),NNSYMP(4),JRAND£50),K 2RAND(50),LRAND(50),JJRANDC100),KKRAND(100),UURAND(100), J 3AMEL(20),JCEON(20),JSHEP(20),JPRUN(20),JROSE(20),JSYMP(20), I 5C0M(150),JCOM(150),IDEAD1(150),IDEA02(150),IOEAD3C150),IDEAD4£150) 6,LARR1 (66,66),LARR2(66,66),LARR3(66,66),LARR4(66,663 , 1 AREA(153),10 71 AMI(150),IOIAM2(150),IDIAM3(150),IDIAM4£ 150),PERf153),EPER£ 16),KA 8MEL(4,21),KCE0N(4,21),KSHEP(4,21),KPRUN(4,21),KROSE(4,21),KSYMP(4, 921),KCHARC160),IHT(100,97),ICHAR(99),IBB(50,97),IRAND(97),IXX£97), 1JXX(97),I VOL(97),IDBH(97),ICL(97),IAPER(97),ICW£97),ICB£97),ISA£97 1),JCHAR£2),IDEAD£97) COMMON IARRA,BL2,ACC,ATA,ATG,ATF,APONA,APDNC,APDNS,APDNPR,APDNRO,A 1PDNSY,CSUB1,CSUB2,CSUB3,CSUB4,RAD,80RDA,XINA,UTILA,B0R0C,XINC,UTIL 2C,BORDS,XINS,UTILS,AGE,C,CC,TAUT,TAUTS,TAUTT,TAUO,UNOCC,YUNOCC,PDN 1,ITHRU,M,ISTRT,IINT,IEND,IYUNOC,IAUTTY,IUNOCC,ILOOP,IX,ISUB,ICOUNT 3,IHT,IBB,JARRA,LARR1,LARR2,LARR3,LARR4,IQQ,JQQ,I AREA,PER,KCHAR,ICO 4M,JCOM,IDEAD 1,IDEAD2,IDEAD3,1DEAD4,IDIAMI,IDIAM2,IDIAM3,IDIAM4,JJR 5AND,KKRAND,LLRAN0,ICHAR,IRAND,IXX,JXX,IVOL,IDBH,ICL,IAPER,ICW,ICB, 6I8A,IDEAD,NSET,«AMEL,KCEON,KSHEP,KPRUN,KROSE,KSYMP,NAGE,JRAND,KRAN 7D,LRAND,JAMEL,JCEON,JSHEP,JPRUN,JROSE,JSYMP,EPER,NNAMEL,NNCEON,NNS 8HEP,NNPRUN,NNR0SE,NNSYMP,JCHAR lOUTsb IF £AGE»EG ,0) GO TO 2000 OCCUPATION OF AREA BY SHRUBS DO 1041 1=1,bb 00 1040 J»i,bb Ksj-l XF(K,EQ,0) K«b6 L"I-1 XF(L.EO,0) L«66 GO TO (1000,1010,1020,1030),ISUB 1000 NBaLARRl(I,J) IB«LARR1(I,K) JBaLARRi(L,J) IFfNB.GT.0) I AREA(NB)mlAREA(NB)+1 IF(LARR1(I,J).GT.0.AND.LARR1(I,K),NE,0) GO TO 1003 IF(NB.EO,0) 60 TO 1003 PER(NB)«PER(NB)+l 1003 IFCLARR1(I,J).NE.0.AND.LARR1£I,K),GT,0) GO TO 1006 IF£IB,EQ,0) GO TO 1006 PER£IB)«PER(I8)+1 1006 IF(LARR1(I,J).GT.0.AND.LARR1(L,J).NE.0) GO TO 1009 IF(N8,EQ,0) GO TO 1009 159 -PERCNB)BP£R(NB)<H 1009 IFUARR1 CI, J) .NE.0. AND.LARR1 U, J) .GT.0) GO TO 1040 IFCJB.EQ.0) GO TO 1040 PER(JB)*PER(JB)*1 GO TO 1040 1010 NB«LARR2(X,J) JB»LARR2CL,J) IBs|_ARR2CI,K) IFCNB.GT.0) IAREACNB)"IAREACNB)+1 IFCUARR2CI,J),GT,0. AND ,LARR2CI,*),NE,0) GO TO 1013 IFCNB.EQ.0) GO TO 1013 PERCNB)BPER(NB)+1 1013 IFCLARR2CI,J).NE,0,AND .LARR2CI,K).GT.0) GO TO 1016 XFCia.EQ.0) GO TO 1016 PERCIB)8PER(IB)+1 1016 IFCLARR2CI,J).GT.0.AND,LARR2(L,J),NE.0) GO TO 1019 IF CNB.EQ.0) GO TO 1019 PERCNB)BPERCNB)+1 1019 IFCLARR2CI,J).NE.0.AND,IARR2CL,J),GT.0) GO TO 1040 IFCJB.EQ.0) GO TO 1040 PER(JB)«PER(JB)*t GO TO 1040 1020 NB8UARR3CI,J) JB8LARR3CU,J) IB8LARR3(I,K) IFCNB.GT.0) IAREACNB)8IAREACNB)*1 IFCLARR3CI.J).GT.0,AND,LARR3CI,K).NE.0) GO TO 1023 IFCNB.EO.0) GO TO 1023 PERCNB)BPERCNB)+1 1023 IF£L,ARR3CI,J) .NE.0.AND.LARR3(I,K) .GT.0) GO TO 1026 IFCIB.EO.0) GO TO 1026 PERCIB)8PER(I9)+1 1026 IFCUARR3CI,J).GT.0.AND.LARR3CL,J).NE.0) GO TO 1029 IF(NB.EG,0) GO TO 1029 P£RCNB)8PERCNB)+t 1029 IFCLARR3CI,J).NE,0,AND,LARR3CL,J),GT.0) GO TO 1040 IFCJB.EQ.0) GO TO 1040 PER(JB)BPER (JB) + 1 GO TO 1040 1030 NBB LARR4(I,J) JB*LARR4CL,J) IBaLARR4CI,K) IFCNB.GT.0) IAREA(NB)»IAREA(NB)*1 IFCUARR4CI,J).GT.0,AND,LARR4CI,K).NE.0) GO TO 1033 IFCNB.EQ.0) GO TO 1033 PERCNB)8p£RCNB)*l 1033 IFCUARR4CI,J).NE,0,AND.LARR4CI,K).GT.0) GO TO 1036 IF(IB,EQ,0) GO TO 1036 PER(IB)«PER(IB)*1 1036 IFCLARR4CI,J).GT.0.AND.LARR4(L,J).NE.0) GO TO 1039 IFCNB.EQ.0) GO TO 1039 160 -PER(NB)»PER(NB)*1 1039 IF(LARR4CI,J) , NE.0. AND .L.ARR4 CL, J) .GT.0) GO TO 1040 IFCJB.EQ.0) GO TO 1040 PERCJ8)BPERCJ8)+1 1040 CONTINUE 1041 CONTINUE 2000 RETURN 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 (97), 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 IIX»ICOM(ICQUNT) JJX*JC0M(IC0UNT) GO TO (800,810,820,830),ISUB 800 IF£ICOUNT.LE,50.) L ARR 1 (11X , J JX) •> 151 IF(ICOUNT,GT.50.AND,I COUNT.L£.100) LARR1(11X,JJX)»152 IF(ICOUNT.GT.100) LARRl(IIX,JJX)«153 GO TO 900 810 IF(ICOUNT,LE,50,) LARR2(11 X,JJX)»151 IF(I COUNT,GT,50.AND,I COUNT,LE. 100) LARR2(11X,JJX)•152 IF(ICOUNT.GT,100) LARR2(11 X,JJX)«153 GO TO 900 820 IF(ICOUNT.LE,50.) LARR3(11 X,JJX)•151 IF(I COUNT,GT.50.AND.I COUNT,LE,100) LARR3(11X,JJX)•152 IF £ICOUNT.GT.100) LARR3(I IX,JJX)"153 GO TO 900 830 IF(ICOUNT.LE.50.) LARP4(11X,JJX)•151 IF(I COUNT,GT,50.AND,ICOUNT, LE,100) LARR4(11X,JJX)»152 IF(ICOUNT.GT.100) LARR4 (11 X,JJX)•153 900 DO 1000 L°l,96 NSBNSETCL) DO 1000 M1,NS IF(RAD*2.-BL2(L))996,910,910 C C C C DETERMINES SHRUB SPECIES IIX,JJX * LOCATIONS OCCUPIED * 162 -910 INCR«0 915 INCR»INCR+1 GO TO (920,925,930,935,1000),INCR 920 J«JJX*JQQ(L,K) I"IIXtIQQ(L,K) GO TO 940 925 JajJX-JQQ (L,K) I*IIX-IQQCL,K) GO TO 940 930 J«JJX+JQQ(L,K) IBIIX«IQQCL,K) GO TO 940 935 J«JJX-JQUCL,K) I«IIX*IQQCL,K) 940 IFCI)955,955,945 945 IF(I-66)9S5,955,950 950 1=1-66 955 IF(J)970,970,960 960 IF(J-66)970,970,965 965 JBJ-66 970 IF(I)975,975,960 975 JB66+1 980 IF(J)985,985,990 985 JB66+J 990 GO TO (991,992,993,994),ISUB 991 IF(LARR1(I,J).GT.03 GO TO 915 LARR1 (I, JWCQUNT GO TO 995 992 IF(UARR2(I,J),GT.0) GO TO 915 LARR2(I,J)"ICOUNT GO TO 995 993 IF(LARK3(I,J).GT.0) GO TO 915 LARR3(I,J)BIC0UNT GO TO 995 994 IF(LARR4(I,J).GT.0) GO TO 915 LARR4CI,J)BICOUNT 995 GO TO 915 1000 CONTINUE 996 RETURN END • 163 -SUBROUTINE REM DIMENSION IARRA(66,66),BL2(96),ACC(4,21),ATA(4,2l),ATG(4,2l),ATF(4 1,21),ApDNA(4,2i),APDNCC4,2l),APDNS(4,21),APDNPR(4,21),APDNRO(4,21) 2,APDNSYC4,21) INTEGER*2 JARRA(66,66),NSET(96),IQ0C96,5),JQQ(96,5),NAGE(50),NNAME 1LC4),NNCE0N(4)|NNSHEP(4),NNPRUN(4),NNR0SE(4),NNSYMPC4),JRANO(50),K 2RANDC50),IRAND(50),JJPANDC100),KKRAND(100),LIRANDC100)t J 3AMEL(20),JCEON(20),JSHEP(20),JPRUN(20),JROSE(20),JSYMP(20), I 5C0M (150),JCOM(150),IDEAD1(150),IDEAQ2(150),IDEAD3(150),IDEA04(150) 6,LARR1(66,66),LARR2(66,66),LARR3(66,66),LARR4(66,66),IAREA(153),10 71 AMI(150),IDIAM2(150),IDIAM3(150),IDIAM4(150),PER(153),EPER(16),KA 8MEL(4,21),KCE0N(4,21),KSMEP(4,21),KPRUN(4,21),KROSE(4,21),K5YMP(4, 921),KCHAR(160),IMT(100,97),ICHAR(99),IBB (50,97),IRAND(97),IXX(97), 1JXX(97),I VOL (97),IDBh(97),ICL(97),IAPER(97),ICW(97),ICB(97),IBA(97 1),JCMARC2),I0EAD(97) COMMON IARRA,BL2,ACC,ATA,ATG,ATP,APDNA,APDNC,APDNS,APONPR,APONRO,A 1PDNSY,CSUB1,CSUB2,CSUB3,CSUB4,RAD,B0RDA,XINA,UTILA,B0RDC,XINC,UTIL 2C,BOROS,X INS,UTILS,AGE,C,CC,TAUT,TAUTS,TAUTT,TAUO,UNOCC,YUNOCC,PDN l,IThRU,M,ISTRT,IINT,IEND,IYUN0C,IAUTTY,lUN0CC,IL00P,IX,I5UB,IC0UNT 3,IHT,IBB,JARRA,LARR1,LARR2,LARR3,LARR4,IQQ,JQQ,I AREA,PER,KCHAR,ICO 4M,JCOM,IDEADl,IDEAD2,IDEA03,IDEAD4,IDIAMI,ID IAM2,IDIAM3,IDIAM4,JJR 5AND,KKRAND,LLRAND,ICMAR,IRAND,IXX,JXX,IVOL,IOBH,ICL,IAPER,ICW,ICB, 6IBA,IDEAD,NSET,KAMEL,KCEON,KSHEP,KPRUN,KROSE,KSYMP,NAGE,JRAND,KRAN 7D,LRAN0,JAMEL,JCEON,JSHEP,JPRUN,JROSE,JSYMP,EPER,NNAMEL,NNCE0N,NN8 8HEP,NNPRUN,NNR0SE,NNSYMP,JCHAR C C REMOVES DEAD SHRUBS AND CALCULATES DEGREE OF INTERSHRUB C COMPETITION C 00 60 1»1,66 C DO 59 J8l,66 GO TO (5,10,15,20),ISUB 5 NBeLARRl (I,J) IFCNB.GT.1S0) GO TO 58 IF(IDEADl (No),EQ,1) LARR1 (I,J)»0 GO TO 58 10 NBBLARR2CZ, J) IF(N8.GT.150) GO TO 56 IF£IDEAD2(NB).EQ.l) LARR2(I,J)B0 GO TO 56 15 NB*LARR3CZ,J) 1F(NB.GT,150) GO TO 58 ZF(I0EA03(NB).E0,1) LARR3(I,J)B0 GO TO 58 20 NB«LARR4 (I, J) IF(NB,GT.150) GO TO 56 IF(IDEA04(N5).EQ.1) LARR4(I,J)B0 GO TO 58 58 CONTINUE 59 CONTINUE CONTINUE RETURN END - 165 -SUBROUTINE SGPON (NAMEL, NCEON , NSHEP , NPRUN, NROSE , NSYMP , PONS , PDN A, PD 1NC,PDNPR,PDNRQ,PDNSY,INDI3K) DIMENSION IARRA(66,66),BL2(96),ACC(4,21),ATA(4,2l),ATG(4,2l),ATF(4 1,21), APDNAC4,21),APONC(4,21),APDNS(4,21),APONPR(4,21),APDNRO (4,21) 2,APDNSY(4,21) INTEGER*2 JARRA(66,66),NSET(96),ICQ(96,5),JQQ(96,5),NAGE(50),NNAME 1L(4),NNCE0N(4),NNSHEP(4),NNPRUN(4),NNROSE(4),NNSYMP (4),JRAND (50),K 2RAND(S0),LRAND (50),JJRAND(100),KKRAND(100),LLRAND(100), J 3AMEL(20),JCEONC20),JSHEP(20),JPRUN(20),JROSE(20),JSYMP(20), I 5C0M(150),JCOM(150),IDEADl(150),IDEAD2(150),IDEAD3(150),IDEAD4(150) 6,LARR1 (66,66),LARR2(66,66),LARR3(66,66),LARR4(66,66),I AREA (1 S3),ID 7IAM1(150),ID1AM2(150),IDIAM3(150),IDIAM4(150),PER (tS3),EPER(16),KA 8MEL(4,21),KCE0N(4,21),KSHEP(4,21),KPRUN(4,21),KR0SE(4,21),KSYMP(4, 921),KCMAR(160),IHT(10?,97),I CHAR(99),IBB(50,97),IRAN0(97),IXX(97), 1JXX(97),IV0L(97),ID6MC97),ICL(97),IAPER(97),ICW(97),ICB(97),IBA(97 1),JCHARC2),I0EAD(97) COMMON IARRA,BL2,ACC,ATA,ATG,ATF,APDNA,APONC,APDNS,APDNPR,APDNRO,A IPDNSY,CSUB1,CSU82,CSUB3,CSUB4,RAD,B0RDA,XINA,UTILA,B0RDC,XINC,UTIL 2C,80RD3,XINS,UTILS,AGE,C,CC,TAUT,TAUTS,TAUTT,TAUO,UNOCC,YUNOCC,PDN 1,ITHRU,M,ISTRT,IINT,IEND,IYUN0C,IAUTTY,IUN0CC,IL00P,IX,ISUB,IC0UNT 3,IHT,IBB,JARRA,LARR1,LARR2,LARR3,LARR4,IQQ,JQQ,I AREA,PER,KCHAR,ICO 4M,JCOM,I0£AQi,I0£AD2,IDEAD3,IDEAD4,IDIAMl,IDIAM3fIDIAM3,IDIAM4,JJR 5AND,KKRAND,LLRAND,ICHAR,IRAND,IXX,JXX,IVOL,IDBH,ICL,IAPEH,ICW,ICB, 6 IBA,IDEAO,NSET,KAMEL,KCEON,KSHEP,KPRUN,KROSE,KSYMP,NAGE,JRAND,KRAN 7D,LRAND,JAMEL,JCEON,JSHEP,JPRUN,JROSE,JSYMP,EPER,NNAMEL,NNCEON,NNS 8MEP,NNPRUN,NNROSE,NNSYMP,JCHAR IOUT-6 C C CALCULATES NUMBER AND PRODUCTIVITY OF SHRUBS C C SETS PRODUCTION TO 0, PONAB0„ P D N C 8 0 , PONS 80 « PDNPRS0. PDNRO»0, PDNSY80, IFCAGE.Ett,0) GO TO 1280 DO 1200 IM,150 GO TO (1045,1050,1055,1060),ISUB 1045 DIAM-IDIAM1 (I) IM0RT8I0EAD1 (I) GO TO 1065 1050 0IAM«IDIAM2(I) IM0RTBI0EAQ2(I) GO TO 1065 1055 0lAMsI0IAM3(I) IMCRT8ID£AD3(I) GO TO 1065 1060 DIAMBIDIAM4 (I) IM0RT«IDEA04£I) • 166 -1065 IFCIMORT.EG.l) GO TO 1200 C C CALCULATES BORDER AND INSIDE AREA OF SHRUBS AND PRODUCTION C XlNSa INSIDE AREA C SOROS a BORDER AREA C IF(DIAM,EQ,0) GO TO 1200 RADaOlAM/100. DlAMaRAO RDSaRAO/2, IRADaRAD KBIRAD+1 IF(PER CI).LT.EPER(K)) GO TO 1090 IFCRD8.LT.,82) GO TO 1070 BORDB(RDS*,82)**2.*3,14159-CRDS-,82)**2.*3.14159 XINa(RDS-,82)**2,*3,14159 XFCI.LE.50) XINABXINA+XIN IF(I,GT.50.AND.I,LE.100) XINCBXINC+XIN IFCI.GT.100) XINSaXlNS+XIN GO TO 1075 1070 BORDBCRDS+,82)**2.*3,14159 XIN 80 , C 1075 IFCI.GT.50) GO TO 1076 BORDA*BOROA+BORD XlNAaXINAtXlN X AREA8RDS**2.*3.14159 AMELP»4,1*XAREA GO TO 1130 C 1076 IFCI.GT.100) GO TO 1079 BORDCBBORDC+BORD XINCBXINC+XIN XAREABRDS**2,*3.14159 IF(XAREA.LE.6.) CEONP»60,/6,**1,7*XAREA**1.7 IF(XAR£A,GT,6.) CEONP«8 10 , «1 , 45454* (110.-X ARE A) W00. * (110,-X ARE A) l**2,7/110t**2,7 $ GO TO 1130 C 1079 BORDS8flORDS*BORD XINSBXINS+XIN XAREA>RDS**2.*3.14159 IF CXAREA.LE.3.) SHEPPa25,/3.**2.6*XAREA**2.6 IPCXAREA.GT.3.) SHEPP«250,-250.* C100.-X AREA)**4,1/ 100.**4, 1 GO TO 1130 1090 DIFPBP£R(I) DIFEBEPERCK) DIFBDIFP/DIFE ACTARalAREA (I) ACTARaACT AR/4. IF(EPERCK).NE.4) GO TO 1094 - 167 • B0RD«CRDS+.82)**2t*3,14159 XIN » fci GO TO 1100 1094 IFCRDS.LE..82) GO TO 1095 EXPlNSs(RDS-,82)**2,*3,14159 BORD«DIF*C CRDS+.82)**2.*3,i4l59-EXPIN5) EXPARs3,14159*RDS**2, ACTINSBACTAR*EXPINS/EXPAR 60RDINaDIF*CEXPAR-EXPINS) IFCCBOROIN+ACTINS) .NE.ACTAR) ACTINSBACTAR-BORDIN XINBACTINS IFCXIN.LT.0) XINB0. GO TO 1100 1095 BORDBDIF* CRDS+,82)**2.*3,14159 IF (BORO.EQ.0) XINBACTAR IF(BORO.GT,0) XINB0 1100 AREAalAREA(I) XAREABAREA/4, IFCI.GT.50) GO TO 1105 BORDABaORDA+BORD XINABXINA+XIN AHELPB4.1*XAREA GO TO 1130 1105 IF(I.GT.100) GO TO 1120 BOROCsBOROCtbORD XINCBXINC*XIN IF (X AREA.LE.6.) CEQNP*60,/6,* * 1,7*XAREA**1.7 IF CXAREA•GT,6,) CEONPafl10,.i,45454*(110.-X AREA)-700.•C110.-XAREA) 1**2.7/110,**2.7 1115 GO TO 1130 1120 B0RD8BQ0R0S+B0RD XINS«XIN5*XIN IFCXAREA.LE.3.) 8HEPP«25,/3,**2,6*XAREA**2.6 IF(X AREA,GT,3,) SHEPPa250,-250,*(100.-XAREA)**4,1/100,**401 1130 IF(I,LE,50) PDNABPDNA+AMEUP XF(I.GT,50) GO TO 1140 IFCINDI8H,£Q,0) GO TO 1200 C WRITECIOUT, 1180) I,PER CI),EPER(K),DlAM,X IN,BORD,AMELP,IAREA CI) GO TO 1200 1140 IFCI.GT,50,AND,I,LE,100) PDNCsPDNC+CEONP IFCI.GT.100) 60 TO 1150 IFCINDISH.EQ.0) GO TO 1200 C WRITECIOUT,1180) I,PER CI),EPER(K),DlAM,XIN,BORD,CEQNP,IAREACI) GO TO 1200 1150 IFCI.GT.100) PDNSapDNS+SHEPP IFCINDISH.EQ.0) GO TO 1200 C WRITECIOUT,1180) I,PER CI),EPERCK),DlAM,XIN,BORD,SHEPP,I AREA CI) 1180 FORMAT C2X, ' # *'13,3X,'PERs',15,3x,'EPERB•,15,3X,'01 AM" ' ,Fb,2,3X,* X • 1 b8 " lIN«',Fb,2,3X, •B0RD«SFb,2,3X, •PDN«%F8.2,3X,#AREA"»,I9) 12012) CONTINUE C C C c PDNAsPDNA/25. PDNSBPDNS/25, PDNC««P0NC/2S. WRITECIOUT,1201) PDNA,PDNC,PONS 1201 F0RMATC//#2X,'PDNA a*,F10,4,5X, 'PDNC a',F10.4,5X,'PONS "',F10,4) C XINCA,C,S) • INSIDE AREA FOR LARGE SHRUBS XINABXINA/4, XINC»XINC/4f XINSBXINS/4, C BORO(A,C,S) * BORDER AREA FOR LARGE SHRUBS B0RDA8B0RDA/4. B0RDCB8QRDC/4, BORDSBBORDS/4, C UTILCA,C,S) * AREA UTILIZED CINSIDE • BORDER) FOR LARGE SHRUBS UTILA«BORDA+XlNA UTILC«BOROC*XlNC UTILSBBORDS+XINS C TAUTS a TOTAL AREA OCCUPIED BY CEON, AMEL, AND SHEP TAUTSBUTILA+UTILC+UTILS C TAUTT B AREA IN SHADE TAUTT«1069,*C/100. C TAUT a AREA OCCUPIED BY TREES AND SHRUBS TAUT"TAUTS+TAUTT C TAUO B AREA NOT OCCUPIED BY TREES ANO SHRUBS TAUOB10O9..TAUT IFCTAUO.LT.0) TAUOB0 C IAUTTY * AREA IN SHADE IN SQ. YDS, UNOCC»1089,-TAUT C IUNOCC B OPEN AREA CAREA NOT OCC, BY TREES AND SHRUBS) IN SQ,FT» YUNOCCBUNOCC/9. C IYUNQC B OPEN AREA IN SQ. YDS. IYUNOCBYUNOCC IAUTTYBTAUTT/9, IUNOCCBUNOCC c WRITECIOUT, 1202) TAUTS,TAUTT,TAUT,IYUNOC 1202 FORMAT£///,2X,«TAUTSs*F9,2,3X,'TAUTT" 'F9,2,3X,' TAUT«" ,F9.2,3X,'IYU lNOCa',19) IFCNPRUN.LT,1) GO TO 1225 IPC CNPRUN*IYUNOC),LT,100) JaNPRUN*IYUNOC ITHB0 C DO 1220 I a i, J ITH"ITM*i m 169 * RANOJJaJJRANDCI) RANOJJaRANDJJ/1000. 1FCAGE.GT.20.) GO TO 1212 X2«-1.*(6,**2,14) IFCAGE-6.)1203,1203,1206 1203 Xl«-l,*(<*l,*(AGE»6,))**2,14 GO TO 1209 1206 X18CAGE-6,)**2,14 1209 DPRUN«RANDJJ*C-.2*.17B*AGE+.2*(X1/X2)) GO TO 1215 1212 0PRUN"RANDJJ*2.14 1215 IF(OIAMBUT,ii37) PONPa.04+,6*DPRUN IF CPIAM.GE.I,37) PONPa-8,6 + 7,1*DPRUN 1220 PDNPRsPONPR+PONP PRUNsNPRUN XFCJTH.LT.100) GO TO 1225 bLOCK«100,/PRUN XBLKaYUNQCC/BLOCK PONPReXBLK*PDNPR c 1225 IFCNROSE.LT, 1) GO TO 1240 J«100 IFCCNROSE*IYUNOC),LT,100) J"NROSE*IYUNOC ITH»0 DO 1230 1*1,J ITH»ITH*1 RANDKKaKKRAND(I) RANDKK«RANDKK/1000. DROSE«RANDftK*(2.3*TANH(AGE*.1776)) PDNRa, i + i ,4*DR0SE**1,5 1230 PDNROaPDNRD+PONR RObEeNROSE IP(ITH,LT,100) GO TO 1240 BLOCKai00,/ROSE XBLK«YUNGCC/BLOCK PDNR0BX8LKftPDNR0 1240 IFCNSYMP.LT,1) GO TO 1260 J»100 IPC(NSYMP*IYUNQC) .LT.100) JaNSYMP* IYUNOC ITM80 C DO 1255 I"l,J ITH»ITM+1 RANDLLsLLRAND CI) RANDLLaRANDLL/1000, IF CAGE,LE. 18.) DSYMPapANDLL* C,2*AGE-2,96*AGE**1,4/20,**!,4) IFCAGE.GT.18.) DSYMPaRANDLL*1.05 PDNSha,263*DSYMP*i«l .5 1255 PDNSYaPDNSY+PDNSM SYMPaNSYMP IFCITH,LT.100) GO TO 1260 170 -BL.OCKsl0fc./SYMP XBLKaYUNQCC/tJLOCK PDNSYaXBLK*PDNSY 1258 FO«hATC//»2X, 'PDNRO « • ,F 10 .4,5X, • PONSY » ' ,F10. 4,5X, • PONPR «',P9,4) C 1280 WHlTEdOUT, 1258) PDNRO,PONSY,PDNpR 1260 RETURN END - 171 -SUBROUTINE SUM CNAMEL,NCEON,NSHEP,NPRUN,NROSE,NSYMP,PONS,PDNA,PO 1NCPDNPR, PDNRO, PONSY, INDISH) DIMENSION IARRA(66,66),BL2(96),ACC(4,2l),ATA(4,2l),AT6(4,2l),ATF(4 1,21),APONA (4,21),APDNC(4,21),APDNS(4,21),APDNPR(4,21),APDNRO(4,21) 2,APDNSY(4,21) 1NTEGER*2 JARRA(66, 66),NSET(96),IQQ(96, 5),JQQ(96, 5) , NAGE(50),NNAME 1L(4),NNCE0N(4),NNSHEP(4),NNPRUN(4),NNROSE(4),NNSYMP(4),JRAND(50) ,K 2RAND(50),LRAND(50),JJRAND(100),KKRAND(100),LLRAND(100), J 3AMEL (20),JCEON(20),JSHEP(20),JPRUN(20),JROSE(20),JSYMP(20), I 5C0M(150),JCOM(150),IDEADl(150),IDEAO2(150),IDEAD3(150),IDEAD4(150) 6,LARRt (66,66),LARR2(66,66),LARR3(66,66),LARR4(66,66),IAREA(153),ID 7IAM1 (150),IDIAM2(150),IDIAM3(150),ID IAM4(150),PER(153),EPER(16),KA 8M£L(4,21),KCEON(4,21),KSHEP(4,21),KPRUN(4,21),«ROSE(4,21),KSYMP(4, 921),KCHAR(160),IHT(100,97),I CHAR(99),IBB(50,97),IRAND(97),IXX(97), 1JXX(97),IV0L(97),IDBH(97),ICL(97),IAPER(97),ICW(97),ICB(97),IBA(97 1),JCHARC2),IDEAD(97) COMMON IARRA,8L2,ACC,ATA,ATG,ATF,APONA,APDNC,APDNS,APONPR,APDNRO,A 1PDNSY,CSUB1,CSUB2,CSUB3,CSUB4*RAD,B0R0A,XINA,UTILA,BORDC,X INC,UTIL 2C,80RDS,XINS,UTILS,AGE,C,CC,TAUT,TAUTS,TAUTT,TAUO,UNOCC,YUNOCC,PDN 1,ITHRU,M,ISTRT,I INT,I END,IYUNOC,IAUTTY,IUNOCC,ILOOP,IX,ISUB,ICOUNT 3,IHT,IBB,JARRA,LARR1,LARR2,LARR3,LARR4,IQQ,JQQ,I AREA,PER,KCHAR,ICO 4M,JCOM,IQEADl,I0EA02,IOEA03,IOEAD4,IOIAM1,I0IAM2,IDIAM3,IDIAM4,JJR 5AND,KKRAND,LLRAND,ICHAK,IRAND,IXX,JXX,IVOL,IDBH,ICL,IAPER,ICW,ICB, 6IBA,IDEAD,NSET,KAMEL,KCEON,KSHEP,KPRUN,KROSE,KSYMP#NAGE,JRAND,KRAN 7D,LRAND,JAMEL»JCEON,JSHEP,JPRUN,JROSE,JSYMP,EPER,NNAMEL,NNCE0N,NN3 SHEP,NNPRUN,NNROSE,NNSYMP,JCHAR C C CALCULATES GRASS AND FORB PRODUCTION C CHECKS CROWN CLOSURE OF TREES AND ADJUSTS GRASS PRODUCTION C ADJUSTS GRASS AND FORB PRODUCTION TO SHRUB INSIDE AND BORDER AREA C AND SHRUB NUMBER IOUTsb IF(C.LTQ6S.) PDNAGaPDN/83,3/9,*(27,•,085294*(68T-C)*50,5/68,**6,*( 168,-C)**6,) IF(C,GE,68,AND,C,LE,78,5) PDNAG"PDN/83,3/9,*(26.I16-,3281*C) IF(C,GT,76,5) PDNAGS0, IF (CLE.64.) GRAS8PDN/83.3/9,*(,04S*C) IF(C,GT,64.) GRAS«0. IF (CLE, 16.) F0RB»PDN/e3,3/9,*(2,44.e87*C) IF(C,GT,18, ,AND.C,LT,80.) FORBBPPN/83,3/9.*(,5 +18,/60,**2.7*(80,«C 1)**2.7) IF(C,GE,80.) FORB*0, UBORD*0, UXINa0. UBOR08BORDA*60RDC*BORDS UXINaXINA + XlNC-fXINS A6R0BaPDNAG*uB0RD*l,365/25, GRASBaGRAS*U80RD*l,365/25, F0RB8aF0R8*UBQR0*l,365/25, AGROIapDNAG*UXIN*,081/25. GRASIai5RAS*UXlN*,061/25, - 172 -FORBI•FORB*UXIN*.206/25. AGQ*0. FOO"0. GROB0 AGTO30. FOTQ»0. GR 0 B0« TAaPDNAG*43,56 TG»6RA3*43.56 TFBF0RB*43.56 IFCM.EQ.0) GO TO 2011 IF(CNPRUN+NR0SE*N5YMP),GT.0) GO TO 1270 AGTOBPDNAG*(1089.-TAUTS)/25. FOTO*FOPB*(i0B9,-.TAUTS)/25. GRTOBGRAS* C1089.-TAUTS)/25, GO TO 2000 1270 AGTOBP0NAG*TAUTT/25, FQT0BFQRB*TAUTT/25. GRT0«GRA3*TAUTT/25. IF(NSYMP.EG,0) GO TO 1280 IFCNSYMP AE.14) R£0UCAB(3,*,13334*(15,-NSYMP )•(80,/15.**2.5)* (15 1,-NSYMP )**2,5)/85. IF(NSYMP .GT.14) REDUCAB.0353 RED*1.-REOUCA IF(AGE.LE,25.) REOPERs,04*AGE IF(AGE.GT.25.) REDPER* 1. REDUCA»(1,-(REO*REOPER)) INCFa(3,76+l,02*NSYMP)/3.7 6 AGTQBPQNAG*RE0uXA*TAUTT/25, GRTO«GRAS*REDUCA*TAUTT/25, F0T0aF0RB*TAUTT/25. 1280 NL'MSSHsNPRUN + NROSE + NSYMP IP(NUMSSH.LE.U) REOUCA*(3.+.13334*(l5.-NUMSSH)*£80./15.**2.5)*(l5 1,-NUMSSM)**2,5)/85. IF CNUMSSM.GT,14) REDUCAa,0353 RED*1,-REOuCA IFCAGE.Lt.25.) REOPER*,04*AGE IFCAGE.GT.25.) REDPER B1 . REDUCAaCl,-CRED*REOPER)) iNCFaC3.76*1,02*NUMSSH)/3,76 AGQBPDNAG*TAU0*RE0UCA/25, F00*F0RB*TAU0/25B GR0*GRAS*TAU0*REDUCA/25, 2000 TAsAGO^AGTO+AGROB+AGROI TG*GRO*GRTO+GRASl+GRASB TFBFOO+FOTO^FORBI+FORBB 2011 L"M*1 IFCISUB,NE,l,OR,M.NE,l) GO TO 2015 c DO 2012 JBi,51 C - 173 * C SUMMARY OF PRODUCTION OF SHRUBS,GRASSES AND FORBS C 2012 IHTCJ,97)*0 2015 IFCM.EQ.0) IYUN0CM21 PDNPRoPDNPR/25, PDNR0aPDNR0/25, PDNSYsPONSY/25, IHTCL,97)sNAGECM) ACCCISUB,L)«C ATA(ISUB,L)»TA ATG(ISUB,L)sTG ATF(ISUB,L)aTF KAMEL(ISUB,U*NAMEL APDNAClSU8,L)aPDNA KCE0N(ISU8,L)"NCEON APDNC(ISUB,L)*PDNC K3HEPCISUB,L)BNSHEP APDNS(ISU3,U*PDNS KPRUNCISUB,L)sNPRUN*IYUNOC APDNPR(ISUB,L)BPONPR KROSECISUB,L)"NROSE*IYUNOC APDNRQCISUB,L)aPDNRO KSYMP(ISUB,L) SNSYMP*(C1089-TAUTS)/9.) APDNSYCI3UB,U=PDNSY IPRUN«NPRUN*IYUNOC IROSE«NRQS£*IYUNOC ISYMPaNSYMP*IYUNOC C C PRINT PRODUCTION SUMMARIES C WRITECIOUT,2) 2 FORMAT(2X,T10,'CC',T13,'AGROP PDN%T23,'GRASS PDN *,T34,'FORB PDN', 1T47, '# AMEL',T55,'AMEL PDN',Tb7,'# CE0N',T75,'CEON PDN',T87,'» SHE 2P»,T95,'SHEP PDN') C WRITECI0UT,5)C,TA,TG,TF,NAMEL,PDNA,NCE0N,P0NC,N5HEP,PDNS 5 FORMAT(2X,4Fl0.4,I10,F10,4,110,F10,4,X10,F10,4) C WRITECIOUT,7) 7 FORMAT(2X,T7,'# PRUN ',T15,'PRUN PDN',T27,'# ROSA',T35,'ROSA PDN',T 147,'# SYMP*,T55,'SYMP PDN') C WRITECIOUT,10)IPRUN,PDNPR,IROSE,PDNRO,ISYMP,PDNSY 10 FORMATC2X,I10,F10,4,I10,F10,4,110,Fl0,4) IL00P»CIEND-I8TRT)/IINT +1 IF(ISU8,EQ,4,AND.CM-ILOOP),EQ,0) GO TO 2020 GO TO 3030 2020 IOQa0 C 2022 DO 2027 1=1,4 IF(100.GT,1) GO TO 3000 - 174 -2025 C C WRITECIOUT,2025) I FORMATC'l', 2X i128('*'),//,2X,T56,'SUB-PLOT 12,//,T2,'PARAMETER 1',//,2X, 'AGE') NB 1 J»ll IF(IDO,GT,0) Nsl2 IF(N,EQ,12) J«21 2027 WRITECIOUT,2030) WRITECIOUT,2031) WRITECIOUT,2032) WRITECIOUT,2033) WRITECIOUT,2034) WRITE CIOUT,2035) WRITECIOUT,2036) WRITECIOUT,2037) WRITECIOUT,2038) WRITECIOUT,2039) WRITECIOUT,2040) WRITECIOUT,2041) WRITE CIQUT, 2042) WRITE CIOUT,2043) WRITECIOUT,2044) WRITECIOUT,2045) WRITE CIOUT,2046) (IHTCK,97), (ACC(I,K),K CATACI,K),K CATF CI,K) ,K CATGCI,K) ,K CMMELCI,K) CAPONACI,K) CKCEONCI,K) CAPONC CI,K) CK5HEP(I,K) (APDNSCI,K) CKPRUNCI,K) CAPPNPR CI ,K (KRQSE CI,K) CAPUlMRUCI ,K (KSVMPCI,K) CAPDNSY CI,K KBM,J) BN, J) *N, J) BN, J) BN, J) K 8 N , J ) KBN,J) KBN,J) KBN,J) KBN,J) KBN,J) KBN,J) ,K»N,J) K»N,J) ,K»N,J) KBN,J) ,K*N,J) C C IF CILOOP,LE,10) GO TO 3000 IDQBIDO+I GO TO 2022 2030 FQRMATC2X, 2031 FORMAT(2X, 2032 FORMAT C2X , 2033 FORMAT(2X, 2034 FORMATC2X, 2035 FORMAT(2X, 2036 F0RMATC2X, 2037 FORMAT(2X, 2036 FORMAT(2X, 2039 FORMAT C2X, 2040 FORMAT (2X, 2041 FORMATC2X, 2042 FORMATC2X, 2043 FORMAT(2X » 2044 F0RMATC2X, 2045 FORMAT C2X, 2046 FORMAT C2X, 'AGE', 6X, 'CR, CLOSE ' AGRQP« PDN 'FORB PDN, 'GRASS PDN 'NO, AMELAN 'AMEL, PDN 'NO. CEQN. 'CEON, PDN 'NO, SHEP. 'SHEP, PDN 'NQ, PRUN, 'PRUN, PDN 'NO, ROSE' 'ROSE PDN, 'NO, SYMP. 'SYMP, PON 1110) ', IX, UF10.1) ,', 11F10.3) ,2X,UF10,3) ', IX, UF10.3) ,',11110) ', IX, 11F10.3) ,2X,11110) ',IX,11F10.3) ,2X,11110) ', IX, 11F10.3) ,2X,11110) MX, HF10.3) 3X, 11110) ,2X,11F10.3) ,2X,11110) ', IX, 11F10.3) C C - 175 -3000 RETURN END 

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