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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  i n the department of Zoology  We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA JULY, 1973  In p r e s e n t i n g  t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r  an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e  and  study.  I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying o f t h i s t h e s i s f o r s c h o l a r l y purposes may by h i s r e p r e s e n t a t i v e s .  be granted by  the Head of my  I t i s understood t h a t copying or p u b l i c a t i o n  o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be written  Department or  permission.  Department of The U n i v e r s i t y o f B r i t i s h Columbia Vancouver 8, Canada  allowed without  my  - i ABSTRACT Plant growth, production, competition and, to a limited degree, secondary succession have been simulated for a mixed species forest ecosystem operating on a big-game winter range. on empirically derived relationships.  The simulation was based  The major plant species i n v e s t i -  gated included Pseudotsuga menziesii (Mirb.) Franco (Douglas-fir)"'", Amelanchier a l n i f o l i a , Ceanothus sanguineus, Shepherdia  canadensis,  Prunus v i r g i n i a n a , Rosa nutkana, Symphoricarpos albus, Agropyron Poa compressa and s c a b r e l l a , Calamagrostis  spicatum,  rubescens and Koeleria c r i s t a t a .  D i s t i n c t i o n was not made among forb species. The simulation model predicts plant community development and production by species f o r a maximum period of 100 years following establishment, with up to 20 c a l c u l a t i o n i n t e r v a l s . the basic simulation u n i t .  Individual plants form  Variable data inputs include simulation period,  c a l c u l a t i o n i n t e r v a l , species composition, density, inherent b i o l o g i c a l v a r i a b i l i t y and s i t e q u a l i t y .  Output i s expressed i n 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 i n the East Kootenay d i s t r i c t of B r i t i s h Columbia, the model provides a quantitative comparison of the land's c a p a b i l i t y to produce wood, browse, grasses and forbs.  I t also provides a basis f o r the solution of f o r e s t r y - w i l d l i f e  A l l other common and s c i e n t i f i c names with authorities are l i s t e d i n Appendix I.  - i i c o n f l i c t s , such as assessment of the implications of management for wood production on ungulate food production, and formulation and testing of strategies designed to increase y i e l d s of wood, browse, grass and forbs.  - i i iACKNOWLEDGEMENTS The author g r a t e f u l l y acknowledges h i s indebtedness to the faculty and s t a f f of the Departments of Zoology, Forestry and Agriculture and the Institute of Animal Resource Ecology of the University of B r i t i s h Columbia, e s p e c i a l l y Dr. C. J . Walters, Dr. C. S. H o l l i n g , Dr. H. C. Nordan, Dr. F. L. Bunnell, Dr. J . H. G. Smith, Dr. V. C. Brink, and Dr. J . F. Bendell.  Their  h e l p f u l advice and guidance are greatly appreciated. Very special thanks are extended to Dr. P. J . Bandy, of the B. C. Fish and W i l d l i f e Branch, for his u n f a i l i n g support, guidance and enthusiasm as project supervisor, to Mr. K. M. Magar, Mr. F. Heywood, and Mr. J . Inkster f o r their invaluable assistance i n programming, and to Mr. J . F. Dronzek of the Canadian Forestry Service for f i e l d assistance. Assistance and equipment i n establishment  of the c l i m a t o l o g i c a l  network was provided by Mr. J . R. Marshall, B. C. Department of Agriculture, Agroclimatology  Sector, Canada Land  Inventory.  The author i s g r a t e f u l to the Canadian Forestry Service for educational leave to undertake graduate studies, f i n a n c i a l assistance while attending u n i v e r s i t y , and use of department f a c i l i t i e s , and to the B. C. Fish and W i l d l i f e Branch for the provision of equipment.  - iv -  TABLE OF CONTENTS Page ABSTRACT  i  ACKNOWLEDGEMENTS  i i i  TABLE OF CONTENTS  iv  LIST OF TABLES  vi  LIST OF FIGURES  v i i  INTRODUCTION  1  JUSTIFICATION FOR THE STUDY  1  OBJECTIVES  2  METHODS  3  The Approach  3  The Variables  4  The System  5  The Components  7  The Functions The A n a l y t i c a l Methods THE STUDY AREA ANALYSIS OF PLANT GROWTH COMPONENTS OF TREE GROWTH  • •  7 10 12 18 18  Height Growth  18  Crown Growth  21  Diameter Growth  26  Volume Growth  27  - v-  Page COMPONENTS OF SHRUB GROWTH  27  Crown Diameter Growth  29  Annual Twig Production  35  COMPONENTS OF GRASS AND FORB GROWTH  39  Rate and Pattern of Growth  39  Total Grass and Forb Production  44  ANALYSIS OF PLANT COMPETITION  46  Components of Tree Competition  46  Components of Shrub Competition  48  Components of Grass and Forb Competition  53  THE MODEL STRUCTURE  60 60  The Main Program  61  Simulation of Tree Growth  64  Simulation of Understory Growth  73  CURRENT STATUS OF THE MODEL  86  OUTPUT  86  Validation  88  Tree Growth Simulation  89  The Vegetative Community Simulation  99  POTENTIAL FOR APPLICATION  115  BIBLIOGRAPHY  117  APPENDIX I  120  APPENDIX II  122  APPENDIX I I I  123  - vi -  LIST OF TABLES Table 1. 2. 3.  4.  5.  Page  The degree of v a r i a b i l i t y found on seven 1/10-th acre Douglas-fir sample plots  16  The degree of v a r i a b i l i t y found within a 1/10-th acre Douglasf i r plot having a density of 500 stems per acre  16  Maximum and minimum densities found for the most commonly occurring shrub species  17  V a r i a b i l i t y found i n current annual growth for Agropyron, Poa and forbs i n the absence of tree and shrub shade  17  Comparative productivity of Agropyron, Poa and forbs growing i n association with Amelanchier, Ceanothus and Shepherdia.  . . .  6.  Output at lowest l e v e l of d e t a i l for shrubs, grasses and forbs. .  7.  Comparison the study Comparison intervals  8. 9.  of simulated and actual stand volumes measured on area of selected mean tree parameters for c a l c u l a t i o n of 2 and 10 years  Comparative p r o d u c t i v i t i e s of wood, Amelanchier, Agropyron and forbs for two Douglas-fir stands with 2224 and 247 stems per acre and s i t e index 60  57 87  98 99  113  - vii -  LIST OF FIGURES Figure  Page  1.  The system and i t s l e v e l s of organization  6  2.  Components of the system  8  3.  Study area showing the location and extent of the PseudotsugaAgropyron and Pseudotsuga-Poa  communities  4.  Relationship between height and age for dominant Douglas-fir  5.  Height frequency d i s t r i b u t i o n for 20-year-old open-grown Douglas-fir Relationship between branch length and height above branch base  6. 7. 8. 9. 10.  14 .  20  21 22  Relationship between horizontal branch length and t o t a l branch length  23  Relationship between height to maximum crown width and t o t a l tree height  24  Relationship between height to base of l i v e crown and maximum crown width  25  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 Relationship between weight of annual twig production and shrub area. A: Amelanchier B: Ceanothus C: Shepherdia  18.  34 36  - viii Figure 19.  Page  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 i n t e r v a l s .  . . .  41  21. 22.  Current annual production of forbs by weekly i n t e r v a l s . . . . Selected relationships between current annual growth and carryover for Agropyron. A: Production for weeks 2, 5 and 10 B: Production for weeks 16 and 17 and the control p l o t s . . . .  41  23.  24. 25. 26. 27. 28. 29.  42  Plot of the 'a' and 'b' variables from the equation GAG = a x TANH (Co x b) expressed as a function of weeks since the i n i t i a t i o n of spring growth. .  43  Relationship between the number of Ceanothus and crown closure of trees  50  Relationship between the number of Symphoricarpos and crown closure of trees  50  Theoretical r e l a t i o n s h i p between number of Prunus and Rosa and crown closure of trees  51  Relationship between Agropyron production and crown closure of trees  54  Relationship between forb production and crown closure of trees  54  Relationship between combined Calamagrostis, Bromus production  Koeleria and  and crown closure of trees  54  30.  D e f i n i t i o n of zones of influence for large shrub species. . . .  56  31.  Response of Agropyron and forb production  32.  Flow chart of subroutines  33. 34.  Simplified flow chart of main program showing i t s c o n t r o l over optional pathways through the model Simplified flow chart of tree growth subroutines  35.  Array coding f o r two Douglas-fir trees occupying growing space. . 70  to Prunus density. .  showing optional pathways  . 59 62  63 65  - ix Figure 36. 37.  38.  39. 40. 41. 42. 43. 44. 45. 46. 47.  48. 49.  50.  Page  Graphic representation of the return of portions of tree crowns crossing the plot boundary  72  Arrangement of arrays showing the relationship between tree, shrub and grass and forb arrays  74  Simplified flowchart of shrub, grass and forb growth (understory subroutines)  76  Relationship between Agropyron production and Prunus density by shrub age  85  Comparison between simulated volume and DBH and B.C. Forest Service volume and DBH taken from V.A.C. 1012, medium s i t e .  .  91  Comparison between simulated volume and DBH and B.C. Forest Service volume and DBH taken from V.A.C. 1013, low s i t e . . . .  92  Comparison of Goulding's and my simulated gross cubic foot volume per acre for s i t e index 150  94  Comparison of Goulding's and my simulated gross cubic foot volume per acre for s i t e index 120  95  Comparison of Goulding's and my simulated gross cubic foot volume per acre for s i t e index 90  96  Comparison of Goulding's and my simulated mean DBH index 120  97  for s i t e  Simulated e f f e c t of tree crown closure on Amelanchier and production  number 103  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  Comparison of simulated Agropyron production f o r s i t e index 60 with 2224, 1112 and zero trees per acre  105  Comparison of simulated forb and Calamagrostis and K o e l e r i a production response to tree crown closure i n the presence and absence of shrubs  107  E f f e c t of forest stand density and s i t e index on forest crown closure  109  -  X  -  Figure 51.  Trade-off between wood and Agropyron production  52.  Trade-off between Agropyron production and annual twig production of Amelanchier  Page 110  Ill  -  1  -  GROWTH SIMULATION OF TREES, SHRUBS, GRASSES AND FORBS ON A BIG-GAME WINTER RANGE  INTRODUCTION The purpose of the study i s to develop a means of predicting the e f f e c t of plant community development on ungulate food production. used i s computer simulation of plant growth and competition.  The method  Abstract mathe-  matical representation of the system i n a computer allows (1) incorporation of an otherwise p r o h i b i t i v e number of i n t e r - r e l a t i o n s h i p s , (2) manipulation and study not f e a s i b l e i n real l i f e , and (3) representation of years of plant community development i n seconds. The simulation model to be constructed would attempt to duplicate, a l b e i t i n a simpler manner, the growth and competitive  interactions of trees,  shrubs, grasses and forbs.  JUSTIFICATION FOR THE STUDY Quantitative assessment of the land's c a p a b i l i t y to produce wood and ungulate food i s e s s e n t i a l f o r the r a t i o n a l solution of f o r e s t r y - w i l d l i f e c o n f l i c t s and maximization of land productivity.  The number and complexity  of interactions among i n d i v i d u a l plants and species necessitates a large and complex bookkeeping system i f more than an extremely s u p e r f i c i a l and often incomplete assessment of the interactions i s to be made. The primary a p p l i c a t i o n of the model would be the assessment of productive c a p a b i l i t y for wood, shrubs, grasses and forbs under different  - 2 -  plant community structures and i s o l a t i o n of c r i t i c a l interactions affecting productivity.  The a b i l i t y to simulate tree growth alone allows the model  to be used f o r estimations of growth and y i e l d and other related forestry problems. Growth, y i e l d 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) m o r t a l i t y , height and diameter frequency d i s t r i b u t i o n s , crown closure, height to base of l i v e crown, crown width and volumes f o r trees, (2) m o r t a l i t y , crown diameter frequency  distri-  butions and production for shrubs and (3) mortality and production f o r grasses and forbs.  Knowledge of i n t e r - and i n t r a s p e c i f i c dynamics w i l l  allow assessment of the implications of management f o r wood production on ungulate food production, and testing of strategies designed to increase y i e l d s of wood, browse, grass and forbs.  OBJECTIVES The objectives of the study were t o : (1)  Quantitatively assess the c a p a b i l i t y of land to produce wood,  browse, grass and forbs. (2)  Assess the implications of management f o r wood production on  range carrying capacity f o r ungulates. (3)  Allow formulation and testing of strategies of plant community  manipulation designed to increase y i e l d s 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 a p p l i c a t i o n through the i n c l u s i o n of additional growth and competitive functions.  However, f o r  i n i t i a l development and testing of i t s p r e d i c t i v e c a p a b i l i t y , a p p l i c a t i o n was r e s t r i c t e d to two plant communities on the Wigwam big-game winter range i n the East Kootenay D i s t r i c t of B r i t i s h Columbia.  METHODS The basic structure of the model and the components of tree growth and competition incorporate the approach taken by M i t c h e l l (1967) i n 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 i n v e s t i g a t o r . The model employs empiric a l l y derived functions, three dimensional  s p a t i a l d i s t r i b u t i o n of a e r i a l  growing space, and normal random deviates with specified means and standard deviations (henceforth termed "normal random deviates") to express genetic v a r i a b i l i t y i n situations where relationships are incapable of rigorous solution or data are  incomplete.  The Approach D e f i n i t i o n 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 i n t e r a c t i o n of a number of  - 4 d i s c r e t e components.  Each process i s studied i n d i v i d u a l l y but i n such a  manner that i t can be integrated into a b i o l o g i c a l l y r e a l i s t i c whole. The achievement of a r e a l i s t i c representation of the system under consideration depends on the attainment of a s u f f i c i e n t degree o f : (1)  Realism, the a b i l i t y of the model to duplicate the general  form of the r e a l system. (2)  P r e c i s i o n , the a b i l i t y to predict the time course of the  variables. (3)  Resolution, the number of a t t r i b u t e s of the system  represented  i n the model. The d i v e r s i t y and size of the system precluded d e t a i l e d examination of a l l components; however, the model adequately represents  those aspects regarded  as e s s e n t i a l .  The  Variables  The current variables used i n the model include age, s i t e q u a l i t y , plant community, species composition, density, competition biological variability.  and inherent  Such variables as water regimes, root  competition  and g r a f t i n g , phytotoxicity and damaging agencies were not investigated due to their complexity. Age  - The maximum simulation period i s 100 years with a maximum of 20 c a l c u l a t i o n i n t e r v a l s . Both simulation period and c a l c u l a t i o n i n t e r v a l are variable within the l i m i t s prescribed.  Site Quality - S i t e index of Douglas-fir i s used as the integrated of environmental factors influencing plant growth.  expression  - 5 Plant Community - The model i s 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 i n d i v i d u ally.  They include Pseudotsuga menziesii, Amelanchier a l n i f o l i a ,  Ceonothus sanguineus, Shepherdia canadensis, Prunus emarginata, Rosa nutkana, Symphoricarpos albus, Agropyron spicatum, Poa compressa and s c a b r e l l a , Festuca idahoensis, Calamagrostis rubescens and Koeleria cristata.  Forbs were treated as a group rather than as separate species.  Density - Variable density of a l l species can be accommodated. Competition - The degree of competition i s i n d i r e c t l y controlled through changes i n 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 c l a s s i f i e d  into subsystems on the basis of the concept of levels of organization (Odum and Odum, 1959). plant communities  These include the vegetative ecosystem (System),  (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 i n t e r n a l forces moulding the development of the ecosystem are generated by i n d i v i d u a l organisms, be they trees, grasses, shrubs or forbs; hence the i n d i v i d u a l plant forms the basis unit of simulation.  Emphasis was placed on the growth and  WIGWAM BIG-GAME WINTER RANGE  vegetative ecosystem  SYSTEM  Pseudo tsuga-Po a community  Pseudotsuga-Agropyron community  Subsystem 1  Subsystem 2  shrubs  trees  \  Subsystem 4  Components  grasses  ^ other Ceanothus  ^ other Douglas-fir  Subsystem 3  other ecosystems  other Agropyron  crown  crown  diameter growth competitive status volume growth compet i t i v e status  Figure 1.  The system and i t s levels of organization.  1  all forbs  1  crown  annual growth  height growth  branch growth  forbs  annual twig growth competitive status  competitive status  i  I  - 7 competitive  a b i l i t y of the few species which were judged to be dominant, the  theory being that these species l a r g e l y control the community and thereby the occurrence of rarer species  (Odum and Odum, 1959).  The growth and competitive status of i n d i v i d u a l plants was expressed through the development of t h e i r organ systems, namely, crowns and stems. The components determining  crown and stem development were the lowest l e v e l  of organization i n t e n s i v e l y investigated.  Each l e v e l of organization repre-  sents the components of the next higher l e v e l .  The Components I s o l a t i o n of the components thought to be important features of the system was accomplished by constructing a s i m p l i f i e d flow chart of the system (Figure 2).  The boxes represent the components investigated.  The variables  associated with each component are too numerous to l i s t by i n d i v i d u a l components.  They include such factors as age, species, r e l a t i v e s p a t i a l  d i s t r i b u t i o n and density, growth rates, crown growth and s i z e , crown closure of trees and shrubs, competitive a b i l i t y , inherent b i o l o g i c a l v a r i a b i l i t y , unexplained  v a r i a b i l i t y and environmental factors, including s o i l and climate.  The arrows depict the d i r e c t i o n and flow of interactions i n the model.  The  Functions  Since the model predicts plant community development, the functions derived must, of necessity, r e f l e c t a time-course development, or be d i r e c t l y and e a s i l y related to some other variable exhibiting a time-course development.  In addition, the functions should be expressed i n unambiguous terms  - 8-  SUPPRESSION AND DEATH  __| PLANT COMMUNITY TREE HEIGHT GROWTH  CROWN GROWTH  DIAMETER AND VOLUME CROWN CLOSURE SUPPRESSION AND DEATH  SITE QUALITY  PLANT COMMUNITY  SHRUB SPECIES AND DENSITY  CROWN GROWTH  SURFACE AREA AND PRODUCTION CROWN CLOSURE OF TREES AND SHRUBS  SUPPRESSION, DEATH AND SPECIES CHANGE  J PLANT COMMUNITY  GRASS AND FORB SPECIES ANNUAL PRODUCTION  Figure 2.  Components of the system.  CROWN GROWTH  -  if  they  9  -  a r e t o be a p p l i e d e l s e w h e r e .  a forest  s t a n d used as a measure of  they only  imply,  and do n o t  For instance, b a s a l area or competition  specify,  age  of  a r e somewhat a m b i g u o u s  crown c l o s u r e o r degree o f  since  crown  competition. D e s p i t e a c o n s i d e r a b l e volume of to derive ted  (1)  and (2) for  all  the  necessary functions  a time-course development.  used as a b a s i s f o r height,  derivation  evaluate v a r i a b i l i t y use of  The f u n c t i o n s  requirements of s i m i l a r  growth.  in density  l/10th-meter plots  g r a s s e s and f o r b s  shrub  of  of  vegetation  numerous s t u d i e s  to  all  this  functions  species floristic  1959).  the presence o f  a forest  including  for  Douglas-fir.  as w e l l  ( L y o n , 1968)  Consequently, uncertain.  as w e l l  T h e most d e t a i l e d  c o n d u c t e d on P r e m i e r R i d g e i n  as  Response of  1967; Jameson, In  was  under-  is  of  stems p e r  forest  unit  description  stand  t h a t o f Kemper  the East Kootenay D i s t r i c t  in  1967;  the v a s t m a j o r i t y  e x e r t e d by the  and a p p l i c a b l e s t u d y  the  g r a s s e s and f o r b s  t h a n as a c o m p l e t e s t a n d  competition  to  shrubs,  as crown c l o s u r e and crown w i d t h t o d i a m e t e r  the degree of  Mean  a s mean v o l u m e  composition of  s t a n d d e v e l o p m e n t was e x p r e s s e d as number o f  such f a c t o r s  (1967)  canopy has been r e p o r t e d  (Young, M c A r t h u r and H e n d r i c k ,  area, b a s a l area or stand age, rather  area,  s t u d y and hence were  Production of  A n d e r s o n , L o u c k s and S w a i n , 1 9 6 9 ; and o t h e r s ) . these s t u d i e s ,  study  d e r i v e d by M i t c h e l l  d e t e r m i n e d on b o t h s q u a r e - y a r d and l / 1 0 t h - m e t e r p l o t s . story  represen-  N o n - r a n d o m s a m p l i n g was u s e d  to determine  (Daubenmire,  was deemed a d v i s a b l e  o c c u r r i n g on the p a r t i c u l a r  d i a m e t e r and s u r f a c e a r e a ( F e r g u s o n , 1968)  were used as measures o f  it  to ensure that they adequately  a c t i o n s and i n t e r a c t i o n s  w h i t e s p r u c e g r o w t h met t h e  literature,  of B r i t i s h  ratios. is (1971) Columbia.  - 10 Kemper (1971) expressed stand development i n terms of both age and crown closure and hence h i s relationships can be applied elsewhere.  Competition  between i n d i v i d u a l understory plants have been studied by Donald (1951), Hozumi, Koyama and K i r a (1955), Mead (1968) and others, using s p a t i a l relationships as a measure of competition.  Determination of competitive  response between understory plants i n this study was based on both plant density and s p a t i a l relationships, depending on the size of the i n d i v i d u a l plants.  Density measures were made where the i n d i v i d u a l plants were small,  and s p a t i a l r e l a t i o n s h i p s were used where the i n d i v i d u a l plants were large.  The A n a l y t i c a l Methods In the analyses, the components were segregated i n t o those determining (1) growth and (2) competitive response.  The components of growth  should i d e a l l y be derived from individuals or populations not subject to competition.  In the absence of competition, growth i s a d i r e c t expression  of age, s i t e quality and genetics.  In a c t u a l i t y , i t was not always possible  to derive the components of growth f o r individuals or populations free from competition.  completely  The degree of competition to which an i n d i v i d u a l was  subjected was used to adjust i t s growth rate during simulation.  Measurement  of competitive stress was based on the a v a i l a b i l i t y of a e r i a l growing space and the degree of l i g h t interception. While t h i s method does not take root competition into account, and hence has obvious l i m i t a t i o n s , i t i s e a s i l y measured and appears to be a f a i r l y good i n d i r e c t measure of competition.  - 11 If root spread i s approximately proportional to crown width, as shown by Smith (1964) f o r Douglas-fir and other tree species, then crown competition can be used as an approximation of root competition.  In considering com-  p e t i t i o n , i t was necessary to d i s t i n g u i s h between i n t e r - and i n t r a - s p e c i f i c competition.  In i n t r a - s p e c i f i c competition, competitive advantage was  assumed to be proportional to growth rate. competitive advantage was  In i n t e r - s p e c i f i c competition,  assigned on the basis of plant height, trees  were assumed to have the greatest competitive advantage, followed by shrubs, grasses and f i n a l l y forbs.  While this i s obviously a s i m p l i s t i c approach  which ignores such factors as density, age, root competition and phytotoxicity, i t was deemed acceptable for the i n i t i a l development of the model. The functional relationships shown throughout derived empirically except where otherwise shown.  this paper were  Direct descriptive  techniques (Jensen, 1964) were used i n curve f i t t i n g .  The expected  relationship between dependent and independent variables was expressed graphically, and then a l g e b r a i c a l l y .  spatial  initially  Where a single algebraic  expression could not be f i t t e d , two or more expressions were used.  In  these cases the expressions were f i t t e d to pass through common points. Because of the nature of the data, the change from one to another i s often quite abrupt.  I t e r a t i v e techniques were used to reduce a l g e b r a i c a l l y  introduced curve form b i a s .  Following each i t e r a t i o n the equation  solved for the predicted Y values. Y = a + bX  equation  where:  Simple l i n e a r regressions of the form Y= predicted Y value X= actual Y value  were used to select the best f i t t i n g  was  equation.  - 12 In cases where the i n t e n s i t y of association of actual to predicted 2 Y values was  low  (R  means and standard  l e s s than 0.7), normal random deviates with s p e c i f i e d deviations were generated.  Generation of normal random  deviates along the f i t t e d curves allowed close approximation of n a t u r a l l y occurring v a r i a b i l i t y and circumvented the problems normally associated with inconclusive r e l a t i o n s h i p s . Where plant community structure precluded derivation of r e l a t i o n ships required f o r the model, t h e o r e t i c a l functions were constructed based on the response of s i m i l a r species.  For example, the response of Amelanchier  a l n i f o l i a to increasing crown closure of Douglas-fir could not be determined due to the lack of s u f f i c i e n t areas on which the two species occurred i n association.  The function derived for Ceonothus sanguineus was  applied i n  i t s place. THE  STUDY AREA The study was  conducted on the Wigwam big-game winter range located  between the Elk and Wigwam r i v e r s ( l a t i t u d e 49°  15' N, longitude 115°  10'  W),  near Elko i n the East Kootenay D i s t r i c t of B r i t i s h Columbia. C l i m a t i c a l l y , the area corresponds to Kopens' (Trewartha, 1954) zone.  The average t o t a l annual p r e c i p i t a t i o n at Elko i s 19.6 Geologically, the area i s highly diverse.  Dsk  inches.  It includes such s u r f i c i a l  deposits as g l a c i a l t i l l s , l a c u s t r i n e s i l t s , c o l l u v i a l deposts, talus slopes, outwash gravel terraces and a g l a c i a l outwash d e l t a . The range supports s i g n i f i c a n t wintering populations deer and Rocky mountain bighorn sheep.  of elk, mule  - 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 i n the Pseudotsuga-Agropyron  community included Pseudotsuga menziesii, Acer glabrum, Shepherdia canadensis, Prunus emarginata, Rosa nutkana, Juniperis h o r i z o n t a l i s , Apocyanum androsaemifolium, Agropyron spicatum, Calamagrostis rubescens, Koeleria c r i s t a t a , Festuca idahoensis  t  A c h i l l e a m i l l e f o l i u m , Aster  conspicuus, Erigeron spp., Monarda f i s t u l o s a and Phlox caespitosa. major plant species occurring i n the Pseudotsuga-Poa  The  community included  Pseudotsuga menziesii, Acer glabrum, Populus tremuloides, Amelanchier a l n i f o l i a , Ceanothus sanguineus, Rosa nutkana, Symphoricarpos albus, Berberis repens, Poa compressa and s c a b r e l l a , Calamagrostis rubescens, Stipa columbiana, Bromus tectorum, Aster conspicuus, Balsamorhiza s a g i t t a t a , Erigeron spp., Fragaria spp. , and Penstemon spp. As a result of a number of severe forest f i r e s , the l a s t occurring i n 1931, the plant communities exhibit a wide d i v e r s i t y i n age, plant density, productivity and species composition. While no attempt was made to describe the v a r i a b i l i t y i n d e t a i l , i t would be worthwhile to present a general description of the communities and to show the v a r i a b i l i t y found on the sample p l o t s . The plant communities on the area are very s i m i l a r 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 s p i c a t i order, a l l i a n c e s Agropyretum s p i c a t i and Agropyro (spicati) - Juniperetum scopulorum of B e i l (1969).  -  14  -  Pseudotsuga - Agropyron 115  05'W  = Pseudotsuga - Poa  ^^^^=  Scale: 1:55,000  Figure 3.  Study area showing location and extent of Pseudotsuga-Agropyron and Pseudotsuga-Poa  communities.  - 15 -  The vegetation i s characterized by large grassland openings, the predominant species being Agropyron spicatum on coarse dry s o i l s and  Poa  compressa and s c a b r e l l a on the f i n e r textured wetter s o i l s , interspersed with stands of Douglas-fir. Of the major shrub species, Amelanchier  alnifolia,  Prunus emarginata and Shepherdia canadensis occur predominantly i n the Agropyron grasslands while Ceanothus sanguineus, Rosa nutkana and Symphoricarpos albus occur i n the Poa grasslands.  The predominant species  occurring beneath Douglas-fir stands include Symphoricarpos albus, Calamagrostis rubescens and Koeleria c r i s t a t a . Douglas-fir occurs i n stands ranging i n age from 20 to 130 years, i n density from single scattered trees to approximately 2000 stems per acre and i n s i t e index (base 100 years) from 50 to 80.  Table 1 shows the  v a r i a b i l i t y found on seven 1/lQ^th acre plots which were measured to provide a basis for determining the p r e d i c t i v e accuracy of the model. were converted to a per acre basis.  A l l values  The v a r i a b i l i t y among i n d i v i d u a l trees  within the plot having a density of 500 trees per acre i s shown i n Table 2. Measurements of density and productivity i n shrub and grass stands were made to evaluate growth c a p a b i l i t y and the e f f e c t of competition and hence can not be used to properly describe the v a r i a b i l i t y occurring on the study area.  Table 3 shows the approximate v a r i a b i l i t y i n density found f o r  the most commonly occurring shrub species. was  The d i s t r i b u t i o n of shrub species  found to be highly v a r i a b l e , depending on plant association and p a r t i c u l a r  species.  The presence of trees appeared to control both the d i s t r i b u t i o n  and density of shrubs.  In the absence of trees, Amelanchier,  Ceanothus,  Shepherdia and Symphoricarpos individuals appear to be independent  and  randomly d i s t r i b u t e d while Prunus and Rosa appear to occur i n clones.  - 16 -  The degree of v a r i a b i l i t y found on seven 1/10-th acre  Table 1.  Douglas-fir sample p l o t s . Values  Variable Minimum Number of trees per acre 1" + DBH  Average  20  Volume -cu f t per acre 1" + DBH  357  DBH -ins  253  500  1344  2121  2.4  Height - f t  7.33  17.0  Basal area -sq f t  Maximum  16.6  37.8  0.031  68.5  0.337  1.503  Basal area -sq f t per acre  21.9  85.2  124.2  Total age -yrs  72  92  106  Crown width/DBH  Table 2.  0.978  1.544  2.620  The degree of v a r i a b i l i t y found within a 1/10-th acre Douglasf i r plot having a density of 500 stems per acre.  Variable  Values Minimum  Height - f t  20.0  Average 35.5  DBH - i n  2.6  6.3  Basal area -sq f t  0.037  0.26  Volume -cu f t  0.32  4.03  CW/DBH  0.978  1.53  Age -yrs  56  95 Where:  SD  CV %  61.5  10.13  28.5  15.5  2.9  45.4  0.26  98.3  Maximum  1.31 26.4 2.37 111  4.8 0.33 14.0  119.0 21.4 14.8  SD i s standard deviation CV i s c o e f f i c i e n t of v a r i a t i o n CW i s crown width DBH i s diameter at breast height  - 17 Table 3. Maximum and minimum densities found f o r the most commonly occurring shrub species.  Species  Density per 1/40 acre Minimum Maximum  Amelanchier a l n i f o l i a  0  30  Ceanothus sanguineus  0  42  Shepherdia canadensis  0  44  Density per sq yd Minimum Maximum 0  18  Rosa nutkana  0  16  Symphoricarpos albus  0  35  Prunus  emarginata  Measurement of grasses and forbs was r e s t r i c t e d  to the weight of  current annual growth and carryover. Again, the v a r i a b i l i t y i n production was high.  Table 4 shows,the maximum and minimum weights of current annual  growth measured after the cessation of growth i n stands not subject to shading by trees or shrubs.  Table 4.  V a r i a b i l i t y found i n current annual growth f o r Agropyron, Poa and forbs i n the absence of tree and shrub shade. Species  Production gms/sq yd Minimum  Maximum  Agropyron  13.5  66.3  Poa  10.1  72.3  0.3  22.4  Forbs  - 18 ANALYSIS OF PLANT GROWTH The primary aim i n the plant growth portion of the simulation was to define patterns of growth, v a r i a t i o n i n growth rates due to genetic and unexplained v a r i a t i o n , and growth rate as a function of s i t e q u a l i t y , age and  competition.  COMPONENTS OF TREE GROWTH Several tree growth simulation models have been developed,  using  d i f f e r e n t approaches (Newnham, 1964; Lee, 1967; M i t c h e l l , 1967; L i n , 1969; B e l l a , 1970; Arney, 1971).  The method adopted was based on M i t c h e l l ' s  (1967) approach because i t appeared to be r e a l i s t i c i n a b i o l o g i c a l sense and also allowed a highly detailed bookkeeping of occurrences of growing space.  i n each unit  The components investigated included s i t e q u a l i t y , height,  crown, diameter and volume growth, height to maximum crown width and height to base of l i v e crown. Site quality was measured i n d i r e c t l y through i t s e f f e c t on tree growth by determining  s i t e index of dominant and codominant Douglas-fir  trees (B.C.F.S., F i e l d Pocket Manual). quality i n terms of environmental  No attempt was made to explain s i t e  factors.  Height Growth Height-age curves, used here to define the pattern of height growth, were adjusted by s i t e index and normal random deviates drawn from a measured height frequency d i s t r i b u t i o n to give the growth rate of i n d i v i d u a l simulated trees.  This procedure allowed the generation of populations of simulated  trees having the same s i t e indices and height frequency d i s t r i b u t i o n s 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 w i l l 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.  -  if  A g e _< 45  20  -  yrs  HT = 1 8 . 0 5 ( S I N ( A g e ( 1 1 / 5 0 ) - II/2) if  A g e > 45  + 1)  ft  (1)  yrs  HT = 1 . 8 7 + ( 0 . 7 4 0 6 6 ) ( A g e ) where:  ft No. of R  2  SE,, E  (2) O b s . = 89 =  0.925  -  5.81  ft  90 r-  Figure 4.  R e l a t i o n s h i p between h e i g h t  and age f o r  dominant  Douglas-fir.  - 21 -  50  40  *  o  30  g Er  20  CD  10 0 2  4  6  8  10  12  14  16  18  20  22  24  Height Class - f t Figure 5 .  Height frequency d i s t r i b u t i o n f o r 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 f o r d e f i n i t i o n of terms).  The relationship was obtained by  measuring t o t a l branch length and tree height above the branch base on 115 trees, both juvenile and mature (Figure 6, Equation 3). measured at and above the point of maximum crown width.  Branches were  - 22 -  BL = (0.98)(HTAB )  ft  0,7  where:  No. of Obs. = 404 R  = 0.920  2  SE  10  (3)  = 1.18 f t  W  40  30  40  50  60  Height above Branch Base - f t Figure 6.  Relationship between branch length and height above branch base. Crown width was measured as the v e r t i c a l projection from the edge  of the crown.  Since branch angle and t o t a l branch length determine crown  width, i t was necessary to convert t o t a l branch length to horizontal branch length (HBL) (Figure 7, Equation 4).  Equation 4 represents potential crown  radius i n the absence of competition, but where branches compete f o r growing  - 23 -  HBL = ( 0 . 9 ) ( B L )  -  (3.3)((BL/20) )  ft  3  where:  No. of R  O b s . = 65 = 0.896  2  SE_ E  = 0.90  T o t a l Branch Length F i g u r e 7.  (4)  ft  ft  R e l a t i o n s h i p between h o r i z o n t a l b r a n c h l e n g t h and t o t a l  branch  length.  space at p o i n t s  of  Branch competition  crown c o n t a c t , is discussed in  S i n c e s i m u l a t i o n of area  (the  a r e a of  potential  tree  that portion  of  crown r a d i u s w i l l  n o t be r e a l i z e d .  the Model s e c t i o n . c r o w n s was r e s t r i c t e d  the v i s i b l e  crown  the crown which forms a p h o t o g r a p h i c  image  when v i e w e d d i r e c t l y  from a b o v e ) , i t  maximum c r o w n w i d t h .  P r e d i c t i o n of  was n e c e s s a r y t o the height  to  d e f i n e the p o i n t  of  o f maximum c r o w n w i d t h was b a s e d  - 24 on the measurement of t o t a l tree height (HT) and height to maximum crown width (HTCW max) on 9 4 open-grown Douglas-fir (Figure 8 , Equations 6).  Equations  5 and  5 and 6 apply only to those trees free from competition.  Otherwise, height to maximum crown width i s simulated. i f HT < 30 f t HTCWmax = ( 0 . 0 6 ) ( H T ) + ( 0 . 0 0 8 ) ( H T  1 , 9  )  ft  (5)  i f HT > 30 f t HTCWmax = - 5 . 5 + ( 0 . 4 2 5 ) ( H T ) where:  (6)  N o . Obs. = 9 4 D  2  SE„  Figure 8 .  ft  = 0.828  = 2.63ft  Relationship between height to maximum crown width (HTCW max) and t o t a l tree height.  - 25 E s t i m a t i o n of function  of  height  by s i m u l a t i n g o n l y trees  height  to  the base of  the l i v e  crown  t o maximum c r o w n w i d t h c i r c u m v e n t s the v i s i b l e  crown a r e a .  the  (HTblc)  restriction  All  b r a n c h e s had been k i l l e d highlined, if  HTblc i s  HTCWmax £  sample t r e e s were h i g h l i n e d ;  10  HTCWmax > 10 HTblc = -  7  is,  (Figure their  Where t r e e s  9,  lower are  feet,  ft  HTblc = 0 . 0 if  that  through b r o w s i n g by u n g u l a t e s .  approximately  imposed  M e a s u r e m e n t s w e r e made o n 5 0  s e l e c t e d f r o m v a r i o u s s t o c k i n g d e n s i t i e s and age c l a s s e s  E q u a t i o n s 7 and 8 ) .  as a  ft  (7)  ft 10 + HTCWmax where:  (8)  No. o f  O b s . = 50  ,2 R SE  =  0.694  = 9.84  T  ft  50 o u u  40  -  30  -  CU  !>  cu M  CO  20  m  10  -  •a •H  0  10  Height Figure 9.  20  width.  40  50  t o Maximum Crown W i d t h -  R e l a t i o n s h i p between h e i g h t maximum c r o w n  30  to base of  live  60 ft  crown and h e i g h t  to  - 26 Diameter Growth Prediction of diameter at breast height (DBH) was based on the derived relationship of DBH against tree height minus 4.5 feet (breast height) and crown area (CA) (Figure 10, Equation 9). The relationship DBH = ( 0 . 1 6 5 ) ( ( C A ( H T -  4.5))  where:  0 , 4 8  -  (0.0011)(CA(HT - 4 . 5 ) )  ins  (9)  No. of Obs. = 299 R  2  SE„  Figure 1 0 .  )  = 0.908 =1.08  ins  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 r i g h t angles.  The data were not analyzed by i n d i v i d u a l stocking or  age classes.  Volume Growth Volume (V) estimations were based on the a p p l i c a t i o n 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 l o c a l i z e the equation,  or to estimate effects of dbh l i m i t s or decay, waste, and breakage.  Log V = -2.734532 + 1.739418Log D + 1.166033 Log H SE  L  (10)  for single trees: ± 11.3 per cent  COMPONENTS OF SHRUB GROWTH The components of shrub growth investigated included s i t e q u a l i t y , height and crown growth and annual twig production.  The species examined  were Amelanchier a l n i f o l i a . Ceanothus sanguineus. Shepherdia Prunus emarginata. Rosa nutkana and Symphoricarpos albus.  canadensis,  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 v a r i a b l e . Shrub age was determined  by making cross-  sections of the stem, or where suckering was prevalent rootstocks, and counting the number of annual rings. by taking  Annual twig production was determined  the oven-dry weight (24 hrs at 105°C) of the current annual twig  growth immediately  a f t e r leaf f a l l .  Shrub height was measured as height to  - 28 the highest part of the general crown p r o f i l e (Figure 11).  Figure 11.  The average of  Measurement of shrub height.  two measures of crown width, taken at right angles, were used to calculate shrub diameter.  Volume was calculated as the volume of a hemisphere with a  radius equal to the shrub radius.  Surface area was calculated as the surface  area of a c i r c l e with a diameter equal to the shrub diameter. Large variations i n rate of growth and small variations i n s i t e q u a l i t y precluded d e f i n i t i o n of variations i n growth rate due to s i t e .  Crown Diameter Growth As previously stated, two measures of crown diameter (D) taken at r i g h t angles, were made on each shrub and expressed as a function of age. The relationships are presented i n Figures 12, 14, 16 and 17, and Equations 11 to 21. Amelanchier D = - 1 + (0.15)(Age) + (1 - Age/30) where:  1.996  (ID  No. of Obs.  =  64  R  =  0.471  =  1.246 f t  2  SE„  Ceanothus i f Age £ 40 y r s  D  2.8(SIN(Age(E/60) - II/5.2) + .5)  i f Age > 40 yrs  D  4.1 + (0.016667)(Age) where:  ft  ft  (12) (13)  No. of Obs.  =  96  ,2 R  =  0.127  SE_  =  1.30 f t  Shepherdia i f Age <_ 50 y r s  D = 4.5(SIN(Age(11/70) - II/4) + .6)  i f Age > 50 yrs  D = 7.17 + (0.0046)(Age) where:  ft  ft  (15)  No. of Obs.  =  54  ,2 R  =  0.438  SE  =  1.287 f t  T  (14)  -  30  -  Prunus if  A g e <_ 16 y r s  D = SIN(Age(n/18) -  if  A g e > 16 y r s  D = 2.0  n/2.5) +  1)  (16)  ft  (17)  ft where:  No. of  Obs.  ,2 R  =  100  =  0.488  =  0.228  ft  Rosa if  A g e <_ 16 y r s  D  S I N ( A g e ( n / 1 8 ) - n / 2 . 5 ) + 1)  if  A g e > 16 y r s  D  2.0  (18)  ft  (19)  ft where:  No. of Obs. R v  2  =  98  =  0.166  =  0.445  ft  Symphoricarpos if  A g e <_ 18 y r s  D  0.8(SIN(Age(H/26)  if  Age > 18 y r s  D  1.2  + 1)  (20)  ft  (21)  ft where:  The p r e d i c t i o n o f  - n/6)  No. of Obs.  =  48  ,2 R  =  0.352  SE.  =  0.802  c r o w n d i a m e t e r was c o m p l i c a t e d b y t h e f a c t  age f e l l  s h o r t of the time p e r i o d  Stebbins  (1951)  (100 y e a r s ) u s e d i n t h e  s t a t e d t h a t the l i f e s p a n of  ft  t h a t the measured  simulation.  individual plants  sprouting  from r o o t s o r crowns cannot be e s t i m a t e d b e c a u s e , b a r r i n g the i n f l u e n c e man, they can o n l y be k i l l e d by d i s e a s e , by r a d i c a l changes i n h a b i t a t .  competition from other p l a n t s  He f u r t h e r  stated that  in stable  plant  of or  - 31 communities seriously diseased plants are rare, so the age of the plant must approach that of the community i t s e l f .  In the model, those species which  exhibited sprouting from crowns or rootstocks, Amelanchier, Ceanothus, Prunus and Rosa, were, i n the absence of competition, exceeding the simulation period.  assumed to have a l i f e s p a n  The remaining species, Shepherdia and  Symphoricarpos, were replaced when the age of i n d i v i d u a l plants exceeded the maximum measured age.  The application of normal random deviates, as  shown i n the simulated populations of Amelanchier and Ceanothus  (Figures 13  and 15) having the same age d i s t r i b u t i o n s as the real populations shown i n Figures 12 and 14, allows duplication of the n a t u r a l l y occurring v a r i a b i l i t y .  Figure 1 2 . Crown diameter to age r e l a t i o n s h i p for Amelanchier.  Age -  Figure  13.  Simulated population  6  of  Amelanchier.  r-  20  40  60 Age -  Figure  14.  yrs  Crown d i a m e t e r  to  80  yrs  age r e l a t i o n s h i p  for  Ceanothus.  100  - 33 -  6  h  Age - yrs Figure 15.  Simulated population of Ceanothus.  - 34 -  Figure 17.  Relationship of shrub diameter to age. B: Rosa  C: Prunus  A: Symphoricarpo  - 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 s p e c i f i c volumes of growing space and hence may develop asymmetrical  crowns.  Weight of l e a f production was not investigated,  as f a l l e n leaves do not contribute d i r e c t l y to the winter food supply of ungulates.  The relationships are presented i n 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 R  2  SE^  = 0.981 =9.05  gms  Ceanothus WT = 810 - (1.45454)(110 - Area) - (700)((1 - Area/110) * ) 2  7  gms where:  No. of Obs. = 10 R  2  SE  =  0.992  = 17.17  gms  (23)  Figure  18.  R e l a t i o n s h i p between weight shrub a r e a .  A: Amelanchier  of  annual twig production  B: Ceanothus  C:  and  Symphoricarpos  - 37 -  Figure 19.  Relationship between weight of annual twig production and shrub diameter.  A:  Prunus  B: Rosa  C: Symphoricarpos  - 38 Shepherdia .4.1,  WT = 250 - (254.92) ((1 - A r e a / 1 0 0 ) ) x  where:  gms  No. of Obs.  =  10  R  2  =  0.580  SE^  =  36.27 gms  No. of Obs.  = 20  R  2  = 0.995  SE„  = 0.221  No. of Obs.  = 20  Prunus i f D < 1.37 WT = 0.4 + (0.6) (D)  gms  i f D > 1.37 WT - -8.8 + (7.1)(D)  gms where:  gms  Rosa WT = 0.1 + (1.4)(D * ) 1  5  where:  IT  0.527  SE_  1.078 gms  No. of Obs.  20  R  0.503  Symphoricarpos WT = (0.4) (D)  gms where:  2  SE„  0.119 gms  - 39 COMPONENTS OF GRASS AND FORB GROWTH The components of grass growth investigated include rate and pattern of growth, carryover and t o t a l annual growth.  Investigation of rate and  pattern of growth was r e s t r i c t e d to an Agropyron spicatum community.  Measure-  ments of carryover and annual growth were made on Agropyron spicatum, Poa compressa and s c a b r e l l a , Festuca idahoensis, Stipa columbiana and Calamagrstis rubescens communities.  Rate and Pattern of Growth Measurement of rate and pattern of Agropyron growth was made on an 80- by 80-ft enclosure containing an Agropyron stand free from shrub and tree competition.  The experimental procedure was designed to allow the derivation  of mathematical relationships describing both the shape and slope of the growth curves from the time of i n i t i a t i o n of spring growth u n t i l cessation of growth i n the f a l l .  Spring growth, as denoted by the germination of forbs  and the obvious presence of new grass, was i n i t i a t e d i n the l a s t week of A p r i l . The cessation of growth i n the f a l l occurred i n 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. measurements were made during the course of the experiment.  These production The procedures  used may be summarized as follows: (1)  Two hundred and t h i r t y square-yard plots were l a i d out and their  boundaries were strung with haywire. (2)  Twenty control plots (2 sets of 10 plots) were not subjected to  any treatment u n t i l cessation of growth i n the f a l l  (17 weeks a f t e r i n i t i a t i o n  - 40 -  of spring growth).  The plots were then clipped to a height of lh inches  and the clippings were separated into carryover and current annual growth. The clippings were then oven-dried and weighed. (3)  The remaining 210 plots were clipped to a height of 1% inches  p r i o r to the i n i t i a t i o n of spring growth (April 1 to 3, 1970).  The clippings  (carryover) were oven-dried and weighed. (4) annual growth.  The treatments consisted of c l i p p i n g and weighing the current The plots (10 plots per treatment) i n treatment 1 were  clipped at the end of the f i r s t week (May 1), and i n treatment 2, at the end of the second week (May 8), etc. of the 17th week (September  The treatments were continued u n t i l the end  11), at which time growth had ceased.  (5)  A l l weights represent oven-dried weight (24 hrs at 105°C).  (6)  A completely randomized design was used i n the a l l o c a t i o n of  control and treatment p l o t s . Figures 20 and 21 show the mean and range i n weight of current annual growth by weekly i n t e r v a l s f o r Agropyron and forbs.  The wide  variations i n current annual growth within treatments f o r Agropyron can be reduced by  p l o t t i n g current annual growth (CAG) against carryover (C) by  weekly i n t e r v a l s (Figure 22).  The 17 curves, one for each week, f i t t e d to  the data have the general form CAG = aTANH(Cb) where "a" represents the maximum attainable growth and "b" represents the shape of the growth curve as a function of carryover. The use of this procedure assumes that carryover, i n the absence of u t i l i z a t i o n by ungulates,  -  41  -  60 r-  c o o  3  X)  40  -  o H  PH  r-l CO  3 C  4!  20  4-> c CU  3 J  00 3  5  L  J  L  7  J  9  Weeks s i n c e I n i t i a t i o n o f Figure 20.  Current  Current  J  11  13  Spring  L  annual production  of  forbs  Spring  J_  _L  15  17  Growth  a n n u a l growth o f A g r o p y r o n by weekly  Weeks s i n c e I n i t i a t i o n o f Figure 21.  L  intervals.  Growth  by w e e k l y  intervals.  J_  Control  -  Figure 22.  Selected relationships over for B:  Agropyron.  Production  42  -  between c u r r e n t  A: Production  for  a n n u a l growth and weeks 2 ,  f o r w e e k s 16 a n d 17 a n d t h e  5 a n d 10  control  plots  carry-  - 43 i s an approximate measure of the productive capacity of the s i t e . simplify c a l c u l a t i o n and modelling  To  procedures, both the "a" and "b" variables  were expressed as a function of their respective week (Figure 23, Equations 29 to 31). v a r i a b l e 'a' i f Week _ 9 a = (2.833)(Week )  (29)  1,2  i f Week  9  a = 38 + (11)TANH((Week - 9) (0.43))  (30)  v a r i a b l e 'b' b = 0.037 - (0.016)(TANH((Week)(0.13)))  (31) 'a' variable  60 r 'b' v a r i a b l e  40 0.002  •H  U  20 •H  U at >  -J 0.037 2  4  6  8  10  12  14  16  Weeks since I n i t i a t i o n 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 i n i t i a t i o n of spring growth.  -  These f u n c t i o n s  -  were then a p p l i e d i n  a c t u a l weekly production. 9.  44  The r e l a t i o n s h i p s  the  general equation  G r o w t h was s l i g h t l y  shown i n e q u a t i o n s  29 t o  and t e s t e d  overestimated  against  f r o m week 1 t o  31 w e r e c o m b i n e d a n d a r e  pre-  s e n t e d i n E q u a t i o n s 32 a n d 3 3 .  if  Week _ 9 CAG -  ((2.833)(Week  1 , 2  ))TANH((CXO.037 -  ((Week)(0.13))))) if  Week  (11)TANH((Week -  it  was  applying  maximum a t t a i n a b l e  ("a"  variable).  modification  for  Total  Grass and Forb Twenty-four  the  8 0 - by 8 0 - f o o t  i n annual  (33)  than  are expressed only  Agropyron,  i n terms  Consequently,only equations  were d e r i v e d from d a t a  29  Modifications  of  collected  the " a " v a r i a b l e  growth.  Production e n c l o s u r e s , each c o n t a i n i n g  16 s q u a r e - y a r d p l o t s , a n d  e n c l o s u r e were used t o measure t o t a l a n n u a l growth  A g r o p y r o n s p i c a t u m , P o a c o m p r e s s a and s c a b r e l l a , F e s t u c a i d a h o e n s i s , Columbiana, C a l a m a g r o s t i s r u b e s c e n s a n d f o r b s .  Forbs were t r e a t e d  group  t h e l a r g e number o f  rather  of  s p e c i e s change.  during a s i n g l e growing season (1970). accommodate v a r i a t i o n s  gms  grass species other  species differences  growth  require  9)(0.43))TANH((C)(0.037  to  The f o r e g o i n g r e l a t i o n s h i p s  will  (32)  (0.016)(TANH((Week)(0.13)))))  these equations  assumed t h a t t h e  a n d 30 w i l l  gms  9  CAG = (38 +  In  (0.016)(TANH  t h a n as i n d i v i d u a l  r e p r e s e n t e d by r e l a t i v e l y  species,  due t o  few i n d i v i d u a l s .  The 24 e n c l o s u r e s w e r e  for Stipa  as a species clipped  - 45 to  a height  of  reclipped after separated into made o n t h e  lh i n c h e s p r i o r cessation of  8 0 - by 8 0 - f o o t  levels  i n i t i a t i o n of  growth i n the  g r a s s e s and f o r b s ,  i n c l u s i v e , were i n c l u d e d . production  to  s p r i n g growth and  fall.  oven d r i e d ,  enclosure f r o n the  The c l i p p i n g s  and w e i g h e d . 10th  to  the  in production  were  Clippings 17th  The m e a s u r e d v a l u e s w e r e u s e d t o  and v a r i a b i l i t y  then  on d i f f e r e n t  week,  define sites.  - 46 ANALYSIS OF PLANT COMPETITION The primary aim of the competition portion of the simulation model was  to permit modification of growth p o t e n t i a l and s u r v i v a l rates of i n d i -  viduals and populations subject to i n t e r - and i n t r a - s p e c i f i c Emphasis was  competition.  placed on the a b i l i t y to duplicate changes i n growth response  and s u r v i v a l rather than on understanding the underlying processes.  The  components of tree, shrub, forb and grass growth derived i n the Plant Growth section provide benchmarks for growth p o t e n t i a l and s u r v i v a l i n the absence of competition.  The functions derived i n this section serve to modify the  above-mentioned components.  Components of Tree Competition The components of tree competition competition  investigated include branch  for a e r i a l growing space, height and diameter growth response  to crown competition, and c r i t e r i a for mortality. from shrubs, grasses and forbs was Observation of adjacent tenance  The effect of  competition  not investigated.  of crowns of competing trees indicated that branches  crowns seldom interlocked i n immature and mature stands.  Main-  of crown i n t e g r i t y i s probably due to cessation of a p i c a l growth  r e s u l t i n g from severe shading or mechanical injury due to wind-induced branch motion ( M i t c h e l l , 1967).  Crowns of j u v e n i l e trees, less subject to both  shading and wind-induced motion, exhibit extensive i n t e r l o c k i n g . Modification of the branch length functions i n the presence of crown competition was based on the a v a i l a b i l i t y of a e r i a l growing space during simulation. actual branch length, and hence crown area, was  Simulation of  accomplished by allowing  - 47 branches to compete for growing space i n a three-dimensional matrix.  The  simulation i s discussed i n the Model section. Tree height-growth in detail.  response to crown competition was not investigated  Four suppressed Douglas-fir were analyzed and their pattern of  growth was compared to that of the f i v e open-grown dominants.  The shape of  the curves was found to be e s s e n t i a l l y s i m i l a r , the only difference being i n the slope of the curve.  U n t i l further investigation, i n t e r - t r e e competition  i s assumed to have no effect on rate of height growth, except when crown area becomes so r e s t r i c t e d that mortality occurs. of height growth was accomplished  Simulating v a r i a b i l i t y i n rate  by applying normal random deviates, sampled  from the height frequency d i s t r i b u t i o n described e a r l i e r , to the height-age relationship (Figure 4, Equations 1 and 2). Diameter-growth response to crown competition i s i m p l i c i t i n the relationship between DBH, crown area and height (Figure 10, Equation 9). This relationship was derived from sample trees selected as being represent a t i v e of open-grown individuals and individuals occurring i n stands of various d e n s i t i e s . The a b i l i t y to duplicate tree mortality during stand development i s an essential feature i n the model.  The removal of trees subjected to  i n s u f f i c i e n t growing space or excessive shading prevents abnormal stand stagnation and allows competing tree crowns to increase i n s i z e .  In the  model, a tree i s eliminated i f the r a t i o of the simulated crown area i n the presence of competition to the simulated crown area i n the absence of comp e t i t i o n i s less than or equal to 0.1, regardless of tree age. The value  - 48 -  (0.1) was derived by testing the model on stands where the history of natural mortality was known.  M o r t a l i t y due to causes other than crown competition  was not included i n 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 e f f e c t of understory vegetation does not seriously a f f e c t the tree growth simulation because a l l of the tree growth functions were derived on individuals subject to understory competition, and the model i s not structured to allow i t s complete removal.  Components of Shrub Competition The components of shrub competition investigated included crown competition between shrubs and the effect of forest crown closure on shrub survival.  Shrub response to competition from grasses and forbs was  not  investigated. Large v a r i a t i o n s i n the rate of height and diameter growth, i r r e g u l a r crown shape and extensive interlocking of crowns precluded d i r e c t assessment of the e f f e c t of inter-shrub competition on both shrub crown growth and production.  General observations indicated that the crowns of  species achieving a r e l a t i v e l y large size (Amelanchier,  Ceanothus and  Shepherdia) competed for a e r i a l growing space, while small shrub species (Prunus, Rosa and Symphoricarpos) did not appear to compete for a e r i a l growing space to any extent.  The absence of small shrub species i n the  .immediate proximity of large shrub species, i n areas where the two grew i n  - 49 association was, f o r the purpose of modelling, assumed to indicate that crown competition between the two resulted i n the mortality of the small shrub species. Modification of the shrub crown diameter to age relationships, i n the presence of competition, was based on the a v a i l a b i l i t y of a e r i a l growing space during the course of simulation.  D i s t i n c t i o n was made between  what were defined as large shrub species (Amelanchier, Ceanothus and Shepherdia) and small shrub species (Prunus, Rosa and Symphoricarpos).  This  d i s t i n c t i o n was necessary because the units of growing space allocated for shrub growth i n the simulation (^ square foot) were too large to accommodate the growth increments of the small shrub species.  A l l o c a t i o n of units of  growing space of less than \ square feet was impractical because of the associated increase i n both c a l c u l a t i o n time and computer storage requirements. Investigation of shrub mortality was r e s t r i c t e d 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  -  30  50  -  L  Crown C l o s u r e - % Figure  24.  Relationship  b e t w e e n number o f  20  40  Ceanothus and crown c l o s u r e o f  60  80  trees.  100  Crown C l o s u r e - %  Figure 25.  Relationship of  trees.  between number o f  Symphoricarpos  and crown  closure  - 51 for Ceanothus (Equations 34 and 35) was applied to Amelanchier and Shepherdia i n the simulation model.  Theoretical functions were applied to Prunus and  Rosa (Figure 26, Equations 38 and 39).  The use of the Ceanothus function f o r  Amelanchier and Shepherdia and the t h e o r e t i c a l functions f o r Prunus and Rosa reduces the accuracy  of the model.  However, they can be replaced with more  accurate functions at a l a t e r date.  30  0  20  40  60  80  100  Crown Closure - %  Figure 26.  Theoretical r e l a t i o n s h i p between number of Prunus and Rosa and crown closure of trees.  - 52 Ceanothus (Applied to Amelanchier and Shepherdia) i f CC < 75% N = 8 - (0.10606)(CC) + (19)((1 - CC/75) * ) 2  (34)  5  i f CC > 75% N = 0.0  (35) where:  No. of Obs. = 20 N  = number of individuals  Symphoricarpos i f CC < 90% N = 35 - (0.38889) (CC)  (36)  i f CC > 90% N = 0.0  (37) where:  No. of Obs. = 60  Prunus and Rosa (Theoretical) i f CC < 65% N = 7 - (0.1167)(CC) + (9)((1 - CC/65) * ) 2  5  (38)  I f CC > 65% N = 0.0  (39)  The curves for Ceanothus and Symphoricarpos were f i t t e d to pass through  the maximum values and consequently regression analyses were not  used to determine the goodness of f i t .  Points lower than the maximum values  were assumed to be the result of low i n i t i a l stocking densities rather than competition.  For example, where 8 Ceanothus per l/40th acre were found for  crown closures of 12, 24 and 33 percent 24 percent  (Figure 24), the density at 12 and  crown closure was assumed to r e f l e c t low i n i t i a l stocking, while  - 53 -  the density at 33 percent was assumed to represent the maximum density f o r that crown closure. Exclusion of the effect of grass and forb competition on shrub production should not seriously a f f e c t the accuracy of the simulation as a l l shrubs measured were growing i n association with grasses and forbs, and the model i s 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 i n density of small shrub species.  Competition between grasses and forbs  was not investigated. Productivity and species composition f o r both grasses and forbs was determined on l/40th-acre plots ranging 0 to 85 percent crown closure. On each p l o t , 40 f l o r i s t i c descriptions (Daubenmire, 1959) and 10 clippings, segregated into Agropyron or Poa, other grasses (Calamagrostis, Koeleria and Bromus), were made on l/10th square-meter  sub-plots.  The relationships  between the oven-dry weight of the clippings and crown closure (CC) are shown i n Figures 27, 28 and 29, and Equations 41 to 46.  -  e o  •H  4-1  3 O  CN  54  -  a  eg 60  20  40  60  Crown C l o s u r e - % F i g u r e 27.  Relationship trees.  between Agropyron p r o d u c t i o n  and crown c l o s u r e  of  20  c o •H 4->  O 3 -O O u  CM  £  -o £ c  10  h  CM  100 Crown C l o s u r e - % Figure 28.  between  forb production  and crown c l o s u r e of  trees.  60  100  10  c o •H * J  Relationship  t M  £  o  t3 I  JJ  5  U  PM  20  40  Crown C l o s u r e - % Figure 29.  Relationship production  b e t w e e n c o m b i n e d C a l a m a g r o s t i s , K o e l e r i a a n d Bromus  and crown c l o s u r e  of  trees.  -  55  -  Agropyron if  CC < 85% WT = ( 0 . 2 3 5 3 ) ( 8 5  if  -  CC) +  (63.3)((1 -  gms/m  (41) No. of  =  120  2  =  0.706  SE^  =  13.39  R  Obs.  gms/m  2  C a l a m a g r o s t i s a n d Bromus CC < 80% WT = ( 0 . 0 5 6 2 5 ) ( C C )  if  (40)  2  2  where:  if  gms/m  2  CC > 85% WT = 0 . 0  Koeleria,  CC) )  gms/m  (42)  2  CC > 80% WT =  0.0  gms/m  (43)  2  where:  No. of R  Obs.  2  SE„  =  120  =  0.50-  =1.219  2 gms/m  Forbs if  CC < 1 8 . 7 5 % WT = 1 0 ( S I N ( C C ( I I / 2 8 )  if  CC >  -  + 1)  n/6)  gms/m  (44)  2  18.75  WT = 0 . 5 +  (18/60  2 , 7  )((100  -  where:  CC)  2 , 5 2  )  gms/m  (45)  2  No. of Obs.  =  120  R  =  0.505  =  4.606  2  SE„  2 gms/m  - 56 -  In determining the response of grasses and forbs to shrubs, d i s t i n c t i o n was made between large and small shrub species.  Competitive  response to large shrub species was determined by comparing production i n the open, along the border of the shrub and beneath the shrub (Figure 30).  ; „ •  ^  —  !  Sphere of Influence  1>  1  R + 0.82 f t  Open ^ ^  |  •  w  Border V V V  !M •  L m  Figure 30.  B  /  Inside  \ \  R - 0.82 f t  Radius (R)  D e f i n i t i o n of zones of influence f o r large shrub species.  - 57 Production was measured using a l/10th-meter frame and c l i p p i n g and weighing grass and forb production.  A s t r i p of the shrub, running east-west one-foot  wide, was removed p r i o r to c l i p p i n g .  The frame was i n i t i a l l y placed straddling  the eastern edge of the shrub, corresponding to the border area, and the vegetation was clipped.  The width of the border area, 1.64 feet, equals the  length of the l/10th-^neter frame.  Successive c l i p s were made to the centre  of the shrub and two c l i p s 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 i n Table 5, are expressed as a percentage of the production 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 p l o t s , located to cover a range  i n shrub density, were clipped and the clippings separated into grasses and forbs and weighed.  The relationship found for Prunus, the only species  investigated i n the Agropyron community, i s shown i n Figure 31 and Equations 46 to 48. Table 5. Comparative productivity of Agropyron, Poa and forbs growing i n association with Amelanchier, Ceanothus and Shepherdia. SHRUB SPECIES  # of Shrubs examined  Position  Amelanchier  10  Open Border Inside  Ceanothus  10  Open Border Inside  Shepherdia  7  Open Border Inside  Production as % of open Poa 100 68.5 13.4  Forbs 100 106.3 53.9  Poa 100 89.5 13.7  Forbs 100 46.5 77.0  Agropyron 100 136.5 1.8  Forbs 100 30.6 20.6  -  58  -  Agropyron if  N < 14 WT -  (PDN/85)(3 + ((15  if  - N)  (0.13334)(15 2 , 5  ))  - N) +  gms/yd  (0.0918) (46)  2  N > 14 WT -  (0.0353)(PDN)  gms/yd  (47)  2  where:  No. of  =  10  2  =  0.898  SE,,  =  7.15  N  = number o f  PDN  = Agropyron production  R  Obs.  gms/yd  2  Prunus  absence of  Prunus  )  2  Forbs WT = -  12.3 +  ( 3 . 6 ) (N)  -  (0.80752) ((N -  where:  No. of  7.5)  gms/yd  =  10  2  =  0.580  SE„ E  =  5.06  N  =  number o f  R  Obs.  1 , S  gms/yd  (48)  2  Prunus  in  - 59 -  •  FORBS  AGROPYRON 5  10  15  20  2 Number of Prunus per yd Figure 31.  Response of Agropyron and forb production to Prunus density.  - 60 -  THE MODEL Simulation of complex forest ecosystems i s a l o g i c a l outgrowth of tree growth models.  Models of individual tree and stand growth have been  developed by Newnham (1964), Lee (1967), M i t c h e l l (1967), B e l l a (1970), P a i l l e (1970), Arney (1971), Goulding Wallis (1971) developed model reproduces  (1972) and others.  Botkin, Janak and  the f i r s t mixed species, mixed age model.  Their  the major c h a r a c t e r i s t i c s of competition, secondary  succession and changes i n vegetation accompanying changes i n elevation from a conceptual b a s i s .  The model described here attempts to duplicate growth,  competition, production and, to a l i m i t e d degree, secondary succession from an empirical basis.  An empirical rather than a conceptual approach was taken  i n order to achieve a high p r e d i c t i v e a b i l i t y . The model simulates growth, competition and production of trees, shrubs, grasses and forbs.  Variable inputs include s i t e q u a l i t y , species  composition, density and s p a t i a l d i s t r i b u t i o n of i n d i v i d u a l plants.  Output  i s expressed i n 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 c u l t u r a l 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: and the understory  the main program, the tree-growth  subroutines  (shrubs, grasses and forbs) growth subroutines.  of the program i s contained i n Appendix I I I .  A listing  - 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 i n the absence of trees, and (3) the entire plant community. Pseudotsuga-Poa community i s accomplished  Application of the model to the  by substitution of a "POA AND  FORB PRODUCTION" subroutine i n place of the "AGROPYRON AND FORB PRODUCTION" subroutine.  Where shrub, grass and forb growth i s simulated i n the absence  of trees, crown closure of an actual or hypothetical forest stand can be read i n as data.  The crown closure can remain constant or be incremented  at a p r e - s p e c i f i e d rate.  A s i m p l i f i e d flow chart of the main program i s  presented i n Figure 33. The organization, and hence sequence of c a l c u l a t i o n s and decisions, of the model i s based on an assumed hierarchy of competitive a b i l i t y among trees, shrubs, grasses and forbs.  Trees are assumed to have the greatest  competitive a b i l i t y , followed by shrubs and f i n a l l y grasses and forbs. The h i e r a r c h i a l order i s d i r e c t l y related to the height at which plant crowns compete f o r , and occupy, a e r i a l growing space.  Development of a h i e r a r c h i a l  order of computation was necessary because simulated systems are not able to duplicate the simultaneous  occurrence of growth found i n natural systems.  Assessment of the degree of i n t e r - s p e c i f i c competition exerted on an i n d i v i d u a l plant i s accomplished  by the transfer of information summaries  between the tree and understory-growth subroutines. a d e f i n i t e time sequence, are as follows:  The t r a n s f e r s , following  - 62 -  C  START  I  END  MAIN PROGRAM  1  1  NORMAL AND UNIFORM  r  ±2 '  RANDOM NUMBER GENERATOR  TREE GROWTH AND COMPETITION  UNDERSTORY  I  1  CROWN PROFILES AND CROSSSECTIONS  SHRUB GROWTH  H  SHRUB  MORTALITY  H  SHRUB AREA  I  SHRUB  PRODUCTION  H  AGROPYRON AND FORB Trees only  PRODUCTION  Understory only Trees and Understory combined  Figure 32.  Flow chart of subroutines showing optional pathways.  - 63 -  G E D Read input/ data  Proceed to tree growth subroutines Proceed to tree growth subroutines *  No  Proceed to understory growth subroutines  Yes r  Proceed to understory growth subroutines  Figure 33.  Simplified flow chart of the main program showing i t s control over optional pathways through the model.  - 64 (1)  Computation - Tree height and branch growth, competition for growing space and m o r t a l i t y . Transfer - Locations occupied by branches and percent crown closure to shrub, grass and forb sub-arrays.  (2)  Computation - D i f f e r e n t i a l m o r t a l i t y , 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 - D i f f e r e n t i a l 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 - M o r t a l i t y , species change and crown growth of grasses and forbs.  Simulation of Tree Growth In the tree growth simulation, growth of the stand i s based on the aggregate growth of i n d i v i d u a l trees occupying a l/10th-acre plot subdivided into square-foot units of growing space (66 x 66).  A s i m p l i f i e d flow chart  of the sequence of calculations and decisions i s presented i n Figure 34.  - 65 -  f ^  Start  Read input  )  dataj  Generate tree locations Set c a l c u l a t i o n interval Take f i r s t  tree  Proceed to next tree Calculate tree height and branch lengths Proceed to next branch  No  Generate f i r s t branch location to be occupied  Do not occupy (continued)  - 66 -  Yes  C a l l understory subroutines  Increment age by one calculation interval  Calculate the following tree and stand parameters Height Diameter Volume Basal area  Crown width Crown length Crown area Height to base of l i v e crown  No  Figure 34.  Simplified flow chart of tree-growth  subroutines.  - 67 B r i e f l y , trees are assigned to locations within the p l o t , height and crown radius are incremented, and branches test for and occupy available units of growing space within a three-dimensional  matrix.  based on simulated crown area and height.  Diameter i s incremented,  Overtopped trees are removed  from the stand, thereby freeing growing space for adjacent trees. tree and stand parameters are calculated for each period. discussion of the tree-growth simulation i s presented  Individual  A more d e t a i l e d  i n the remainder of  this section. The data requirements include s p e c i f i c a t i o n of s i t e index at  100  years, number of trees per l/10th acre, mean and variance of a measured height-growth frequency d i s t r i b u t i o n 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 c a l c u l a t i o n i n t e r v a l s to a maximum of 20. If a simulation period of 100 years and 20 c a l c u l a t i o n i n t e r v a l s are s p e c i f i e d , the c a l c u l a t i o n i n t e r v a l i s 5 years. s p e c i f i e d , a uniform  Where random tree locations are  random number generator  i s used to assign locations  with the proviso that no two trees occupy the same unit of growing space. The growth rate and height of i n d i v i d u a l trees i s determined by (1) adjusting the slope of the height-age relationship derived for opengrown dominant Douglas-fir (Equations 1 and 2) to give the pre-specified s i t e index, (2) drawing normal random deviates from the height frequency d i s t r i b u t i o n (Figure 5), and  (3) solving the r e l a t i o n s h i p for the p a r t i c u l a r  stand age i n question. Crown growth of trees i s simulated  on the l/10th-acre plot which  i s subdivided into units of growing space referenced by their l o c a t i o n i n a two-dimensional matrix or array; the t h i r d , or v e r t i c a l dimension, i s  - 68 referenced by coded values held i n each unit.  The array may be v i s u a l i z e d  as square units of growing space containing a numeric code designating plant occupancy.  P r i o r to computation, the codes are i n i t i a l i z e d at 10000000,  s i g n i f y i n g that the unit i s unoccupied.  The code, as i l l u s t r a t e d below, i s  broken down into element nests used to i d e n t i f y the i n d i v i d u a l plant, i t s species and stem p o s i t i o n , and the height at which the unit i s occupied.  10  0000  00  Free element nest  Individual plant, species and stem p o s i t i o n (99 i n this location indicates the location of the tree bole) Height of occupancy i n hundredths of feet  In the simulation of crown growth, t o t a l branch length i s calculated by determining tree height above the  branch node and solving the relationship  between branch length and height above branch (Equation 3).  Total branch  length i s then converted to horizontal branch length by solving the r e l a t i o n ship between horizontal branch length and t o t a l branch length (Equation 4). Determination of the actual crown area of i n d i v i d u a l trees i s accomplished by allowing branches to compete at various heights i n the two-dimensional matrix. In the simulation of branch competition, i t i s assumed that a u n i t of growing space can only be occupied by a single tree, and branches of competing do not i n t e r l o c k .  trees  The sequence i n the simulation of branch competition may  be summarized as follows:  - 69 (1)  Starting from the top of each tree, a c i r c l e , with radius equal  to horizontal branch length, i s swept for each branch whorl being considered. The number of branch whorls considered i s equal to the number of c a l c u l a t i o n intervals. (2)  Units of growing space are considered to be occupied i f  horizontal branch length i s greater than the distance from the tree bole to the center of the u n i t . (3)  A previously occupied unit can only be reoccupied at a greater  (4)  When a l l trees have been processed, crown area i s determined  height.  for i n d i v i d u a l trees by counting the number of units occupied by each tree. (5)  The degree of competition exerted on each tree i s expressed  as a function of actual crown area (CAact ) to expected  crown area i n the  absence of competition (CAexp ) . I f the ratio of CAact to CAexp i s less than or equal to 0.1, the tree i s assumed to die and i s removed from the plot. Figure 35 i l l u s t r a t e s 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 p o s i t i o n and heights of trees 11 and 18, respectively.  Codes 10000118 and 10013418 represent the units occupied by  branches originating from nodes at 0.01 and 1.34 feet on tree 18. Code 10000111 represents the units occupied by branches originating from a node at 0.01 feet on tree 11. The array coding can be printed i n the form of developmental  stand maps showing v e r t i c a l and cross-sectional projections.  Inevitably tree crowns w i l l attempt to grow beyond the plot confines. Any l  -  10000000  10000000  r  t_ 110000111  10000000  70  -  10000000  10000000  10000000  10000000  10000000  10000118  10000118  10000118  10000000  10000000  th ! 10008499J 10013418 s j  10013418  10013418  10000118  10000000  10013418  th 10044299 s  t 10013418  b 10000118  10000000  i  b  j  I 100001111 1 1 1 1  10000000 110000111i  10000000  10000118  10013418  10013418  10013418  10000118  10000000  10000000  10000000  10000118  10000118  10000118  10000000  10000000  10000000  10000000  10000000  10000000  10000000  10000000  10000000  where: t = t r e e number  th = tree height  s = stem p o s i t i o n  Figure 35.  Array  i n hundredths of  feet  b = branch height i n hundredths of  coding for  two D o u g l a s - f i r  occupying growing  space.  feet  - 71 portion of a plant crossing the boundary i s 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 l i v e crown base are derived from the results of the crown-growth simulation.  Crown width  i s determined by calculating the diameter of a c i r c l e having an area equal to the simulated crown area.  Calculation of crown length i s more complex. In  the absence of i n t e r - t r e e competition, height to maximum crown width i s determined as a function of t o t a l tree height (Equations 5 and 6) and then height to base of l i v e crown i s determined as a function of height to maximum crown width (Equations 7 and 8).  Crown length i s determined by subtracting the  height to base of l i v e crown from t o t a l tree height.  Where crowns are subject  to competition for a e r i a l growing space, the height of the longest branch i s taken to represent the point at which crown width i s maximum.  The c a l c u l a t i o n  sequence follows that f o r trees not subject to i n t e r - t r e e competition. Diameter at breast height (DBH) i s calculated by solving the r e l a t i o n ship between DBH, height and crown area (Equation 9).  Volume estimation i s  based on the a p p l i c a t i o n of the simulated height and DBH to the B.C. Forest Service volume equation for i n t e r i o r Douglas-fir (Equation 10).  Basal area i s  calculated from the simulated DBH. The sequence of decisions and c a l c u l a t i o n s involved i n the simulation of tree growth are repeated at each c a l c u l a t i o n i n t e r v a l u n t i l the simulation period i s exceeded.  The information and array coding generated at each  c a l c u l a t i o n i n t e r v a l are retained for incrementation at the next c a l c u l a t i o n  - 72 -  ************************************************* * B 1 1 1 2 2 2 B 2 2 2 * 1 1 1 1 2 2 2 2 2 2 2 * 1 1 1 2 2 2 2 2 | 1 1 2 2 2 4  4  4  1 1 1* 1 1 1* 1 1 * 1|  * * *  4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4  *  4 4 4 4 B 4 4 4 4  *  * * * * *  4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 B 5 5 5 5 5  * * * * |  £  * * *  t  5  * * * * * * * * *  £ * *. i. * * * *  3 3 3 3  *  3  B 3  3 3  * * * * *  * t  I * i i *  1 1 2 2 2 1* * 1 1 1 2 2 2 2 2 1 1* * 1 1 1 1 2 2 2 2 2 2 2 1 1 1* ************************************************************ where: |  B = bole p o s i t i o n 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 i n t e r v a l and, where the understory  option i s s p e c i f i e d , are passed to the  understory-growth subroutines. The degree of d e t a i l required i n the simulation results i s s p e c i f i e d by output options supplied as data.  At the most detailed l e v e l , the following  information i s summarized at each c a l c u l a t i o n i n t e r v a l : (1)  Internal coding of the tree matrix.  (2)  Develop stand maps showing v e r t i c a l and cross-sectional  p r o f i l e s of the stand. (3)  Detailed information on each i n d i v i d u a l tree, including  l o c a t i o n , height, diameter, basal area, volume, height to crown base and crown width, area and length. (4)  Mean tree height, diameter, basal area, volume, height to  crown base, and crown width, area and length. (5)  I n i t i a l and current number of trees.  (6)  Number of trees having died.  (7)  Crown closure for e n t i r e p l o t .  (8)  Crown closure for each quarter of the tree p l o t .  At the lowest l e v e l of d e t a i l , t o t a l 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 i s based on the aggregate  growth of i n d i v i d u a l s , grass on the aggregate growth of species and forbs on the aggregate growth of communities.  The small size of i n d i v i d u a l grasses  - 74 and forbs and the great d i v e r s i t y of forb species precluded simulation of individuals.  Growth i s simulated on a l/10th-acre plot underlying, and  receiving information from the l/10th-acre tree array.  The understory array  i s subdivided into h square foot units (132 by 132) p a r t i t i o n e d into 4 independent 66 by 66 element sub-arrays  Figure 37.  (Figure 37); each sub-array i s  Arrangement of arrays showing r e l a t i o n s h i p between tree and shrub, grass and forb arrays.  - 75 associated with a s p e c i f i c quarter of the tree array.  A flow chart showing  the sequence of calculations and decisions made during the course of simulation i s presented i n 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 d i r e c t l y or randomly (3)  Crown closure of the overstory  assigned. (Douglas-fir stand) i s set at  zero, s p e c i f i e d at a constant l e v e l , set at zero and incremented at a pres p e c i f i e d rate, or passed from the tree-growth simulation. (4)  M o r t a l i t y of large shrub species i s determined as a function of  d i r e c t tree shading, crown closure of the forest stand or both. (5)  Crown diameter of large shrub species i s incremented and crowns  are allowed to compete for a e r i a l growing space. (6) i s determined  Density of small shrub species (Prunus, Rosa and Symphoricarpos) as  a function of crown closure of trees and large shrub species.  Crown diameter of i n d i v i d u a l shrubs i s then incremented. (7)  Diameter, area and production are calculated for i n d i v i d u a l  shrubs, and mortality by species, t o t a l 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 i s calculated i n the absence of both trees and shrubs. (9)  Their production  i s then readjusted as a function of tree shading,  l o c a t i o n beneath large shrub species ( i . e . border and inside areas) and and age of small shrub species.  density  - 76 -  ,En&iy point ^on. undeJiAto./iy atone. / and ^iA&t pat>6 faoK -tt.ee and ' iLndoAAtoh.u togntkzn. EntAy  point  ^on. Azcond and  and undeAAtoiy  togeJh&i  )  Start  Read input data/ Generate shrub locations  Set c a l c u l a t i o n i n t e r v a l  Take f i r s t sub-plot Increment age by one calculation interval  Proceed to next sub-plot Take f i r s t species Proceed to next shrub species Take f i r s t  shrub  Yes —+-  Yes Remove Shrub Count l i v i n g 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 i r e d to reduce actual # to p o t e n t i a l  Proceed to next shrub No  i  (continued)  - 78 -  Generate f i r s t l o c a t i o n to be occupied Generate next location i  No  Yes  Have _ ^ - a i i ;.ocations bee! tested?  Oc cupy  Yes Do not occupy  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 t o t a l number of small shrubs by species Calculate f o r i n d i v i d u a l Diameter  shrubs:  Area Summarize:  Mortality by species Total number and production of shrubs by species Inside and border areas of large shrub species by species Total area shaded by trees and large shrub species Total area not shaded by trees or large shrub species T ( c o n t i n u e d )  - 79 -  Calculate production f o r Agropyron, forbs and other grasses (Calamagrostis, K o e l e r i a , Bromus) per unit area for unshaded condition Adjust production per unit area as a function of tree crown closure  Readjust production per unit area f o r border and inside area of large shrub species Readjust production per unit area as a function of small shrub density and age f o r (1) area i n d i r e c t tree shade and (2) area not shaded by trees or large shrub species Using precalculated areas of d i r e c t tree shade, large shrub species shade and area not shaded by trees or large shrub species, calculate t o t a l production f o r : Agropyron Forbs Other grasses (Calamagrostis, K o e l e r i a , 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 d e t a i l e d discussion of the simulation i s presented i n the remainder of this section. The data requirements f o r the simulation of the understory  develop-  ment include s p e c i f i c a t i o n of (1) the number of large shrub species, (Amelanchier,  Ceanothus and Shepherdia),  by species per l/40th acre, f o r  each of the four sub-plots, (2) number of small shrub species (Prunus, Rosa and Symphoricarpos), by species per square yard, f o r each sub-plot, (3) mean and variance of crown diameter frequency d i s t r i b u t i o n s for a l l shrub species, and (4) carryover of Agropyron or Poa i n grams per square yard.  I f tree growth i s not simulated, i t i s necessary  to specify the  c a l c u l a t i o n i n t e r v a l , simulation period and the crown closure of the forest stand.  As previously stated, crown closure can be s p e c i f i e d at zero, a  constant value, or set at zero and incremented during the course of simulation. Where large shrub species are assigned s p e c i f i c l o c a t i o n s , t h e i r locations are read i n as data; otherwise, a uniform random number generator  i s used  to assign l o c a t i o n s . The f i r s t step i n the understory  simulation i s to evaluate the  influence of the forest stand, whether simulated or specified i n terms of crown closure, on shrub mortality.  Two methods are used to " k i l l "  shrubs.  In the f i r s t method, shrubs are tested f o r shade tolerance (read as input data); i f shade tolerant, they survive i n d i r e c t shade; i f shade i n t o l e r a n t , they " d i e " when d i r e c t l y shaded.  Large shrub species are only shaded by  trees, while small shrub species may be shaded by trees and large shrub species.  Surviving shrubs are then counted by species and the number  surviving i s compared to the p o t e n t i a l number capable of surviving at the  p a r t i c u l a r crown closure i n question  (Equations  34 to 39).  I f the actual  number exceeds the p o t e n t i a l number, shrubs are randomly " k i l l e d " u n t i l two are equal.  the  This sequence i n mortality i s important i n that i t ensures  that shade intolerant shrubs closest to trees die f i r s t .  Shrubs subject to  mortality are removed from the p l o t , thereby freeing a e r i a l growing space. Growth of i n d i v i d u a l shrubs i s expressed i n terms of crown diameter which i s derived from the relationships between crown diameter and (Equations  11 to 21)  and competition  age  d i s t r i b u t i o n s . In simulating crown diameter growth  for a e r i a l growing space, d i s t i n c t i o n i s made between  small and large shrub species.  Large shrub species compete for  units of growing space held i n the sub-arrays;  designated  small shrub species are  allocated to those units of growing space not occupied by large shrub species.  Crown competition  among large shrub species i s handled i n the  same manner as tree crowns except that height of occupancy i s not taken into account.  The near v e r t i c a l growth habit of shrub branches and more  or l e s s s i m i l a r heights precludes  the necessity of allowing  Following simulation of crown growth and competition belonging  over-topping.  among individuals  to the large shrub species, the t o t a l number of small shrub  species i n d i v i d u a l s i s calculated.  The number of i n d i v i d u a l s i s calculated  by determining the area available to small shrub species and multiplying t h i s area by the density of surviving i n d i v i d u a l s . considered  I f the species  being  i s shade i n t o l e r a n t , the available area i s that portion of the  p l o t not shaded by trees or large shrubs; i f the species i s shade tolerant, the area i s that portion of the plot not shaded by large shrub species. Crown competition  among small shrub species individuals i s not  simulated  - 82 due to t h e i r small size and the tremendously increased computer memory requirements  and c a l c u l a t i o n time which would be necessary  (approximately  310,000 additional words of computer memory and up to 29,000,000 additional decisions and calculations - present storage requirement  i s 75,000 words).  The determination of crown diameter and area of the simulated large shrub species i s accomplished by counting the number of units of growing space occupied by each i n d i v i d u a l , expressing the result i n square feet (each u n i t represents 0.25 square f e e t ) , and calculating the diameter of a c i r c l e whose area i s equal to the area of the i n d i v i d u a l shrub.  At the same  time, the area occupied by each shrub i s segregated into those portions representing the inside and border areas of the shrub  (Figure 11). Where  the crowns of two or more shrubs are i n contact, the border area i s expressed as a function of the perimeter of the group, and the remaining area c o n s t i 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 i s accomplished  by substituting the simulated  values i n Equations 22 to 28. Following c a l c u l a t i o n of diameter, area and production f o r individual shrubs, the simulated results are summarized i n terms of t o t a l number and production of shrubs by species and mortality by species.  The calculated  values f o r the border and inside areas of large shrub species, the areas shaded by trees, large shrub species, trees and large shrub species combined and the unshaded area, and the density of small shrub species i s passed to the subroutine responsible f o r grass and forb growth.  - 83 The sequence of calculations i n the determination of grass and forb production i s to calculate production (1) i n the absence of i n t e r s p e c i f i c 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) f i n a l l y readjust production as a  function of age and density of small shrub species (Equations 46 to 49). Production i n the absence of i n t e r s p e c i f i c competition i s based on the measurement of the previous year's carryover of grass (Agropyron or Poa) which has not been subject to grazing by ungulates.  The conversion of  carryover to the current year's production i s achieved by substituting the value f o r carryover i n Equations 32 and 33 and defining the number of weeks since the i n i t i a t i o n of spring growth.  Modification of the equations to  accommodate variations i n annual growth requires the derivation of causee f f e c t relationships between c l i m a t i c influences and annual grass growth. Since these relationships were not investigated, growth i s based on the growing season of 1970.  The production of forbs i s based on the r e l a t i o n -  ship between forb weight and weeks since the i n i t i a t i o n of spring growth (Figure 21).  The weight of forbs produced refers to the standing crop  present at the time of c l i p p i n g . Adjustment of grass and forb production i n response to increasing crown closure of trees i s accomplished  by solving the relationships between  production and crown closure (Equations 40 to 45), calculating the percentage 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 i s then readjusted i n response to the presence of large and small shrub species.  In the case of  large shrub species, production i s readjusted as a percentage of production i n the open, according to the l o c a t i o n beneath the shrub. factors applied are shown i n Table 1.  The correction  Where grasses and forbs are growing  i n association with small shrub species, production i s adjusted as a function of small shrub density (Equations 4 6 to 4 9 ) . Obviously, the size of the i n d i v i d u a l shrubs w i l l a f f e c t the degree of reduction i n p r o d u c t i v i t y . Equations 4 6 to 4 8 represent relationships derived i n a Prunus community with a mean age of 15 years.  For shrub stands of less than 15 years of  age, the e f f e c t i s reduced i n d i r e c t proportion to the reduction i n age as shown i n Figure 3 9 . The sequence of calculations and decisions described f o r the growth of shrubs, grasses and forbs i s conducted on each of the four sub-plots at each c a l c u l a t i o n i n t e r v a l u n t i l the simulation period i s exceeded. of output d e t a i l required i s s p e c i f i e d by data statements.  The l e v e l  At the most  detailed l e v e l , output i s summarized i n terms of: (1)  Developmental stand map  showing a v e r t i c a l projection of the  shrub stand. (2)  I n i t i a l and current number of shrubs by species.  (3)  Number of shrubs having died by species.  (4)  Cause of mortality (from d i r e c t shading or as a function of  crown closure of the forest stand). (5)  Detailed information on Amelanchier, Ceanothus and  including diameter,  Shepherdia  inside and border areas, t o t a l 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 i n 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 l e v e l of d e t a i l , output i s i n 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 i n Fortran IV on a dual IBM 360/67 at the University of B r i t i s h Columbia, represents a prototype simulator of growth, competition, production and, to a limited degree, secondary succession i n a mixed species forest ecosystem.  The current version of the model  handles 1 tree species (Douglas-fir), 6 shrub species (Amelanchier, Shepherdia, Prunus, Rosa and Symphoricarpos), and 4 grass species Poa, Calamagrostis  Ceanothus, (Agropyron,  and K o e l e r i a ) ; d i s t i n c t i o n i s not made among forb species.  The model i s presently being converted for application on a PDP 11/20, with a 48K byte core, at the P a c i f i c Forest Research Centre, of the Canada Department of the Environment. The model structure provides an adequate bookkeeping system for the actions and interactions that occur during the development of a complex forest ecosystem.  However, refinement, expansion  and testing of the system  and i t s components are necessary for achievement of i t s f u l l p o t e n t i a l as a sound accurate p r e d i c t i v e t o o l .  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 l e v e l of d e t a i l for shrubs, grasses and forbs.  Parameter  Age 0  Crown closure - % Agropyron production - kg/ha Forb production - kg/ha Calamagrostis and Koeleria production - kg/ha No. of Shepherdia per ha Shepherdia production - kg/ha No. of Prunus per ha Prunus production - kg/ha  0 475  10  8 .6 223  20  30  37.0  64. 1  180  156  40  50  73.9  77.7  10.7  3.6  13.8  57 .3  45.0  5. 7  3.1  4.1  0  1 .6  7.2  16. 5  19.1  20.0  98  0  0  17.7  0  0  0  0  0  0  0  0  988 0 95638 0  889 10 .3 85363 82 .0  593 45.2 28849 38.9  - 88 which allows the i n c l u s i o n of trees, shrubs, grasses and forbs. used to predict above ground plant production,  I t can be  to determine trade-offs  between products and to evaluate the consequence of management decisions. Before presenting examples of the application of the model i t i s necessary to discuss the problems v a l i d a t i n g the model.  Validation The advantage i n adopting a systems approach i s that a number of functional relationships can be linked i n a computer program, thereby allowing interactions among relationships and consequently providing dynamic rather than s t a t i c or average solutions.  While the i n d i v i d u a l functions may  duplicate r e a l i t y to a high degree, there i s no guarantee that the model as a whole i s correct.  Goulding (1972) summed up the v a l i d i t y problem i n  saying "the problem of v a l i d i t y i s that i f the real system was known exactly so that the model can be compared, there would have been l i t t l e point i n creating the simulation model."  The problem then i s one of comparing  simulated  r e s u l t s against s t a t i c or average solutions which i n themselves  represent  simple models of the real system and i n turn need not necessarily  be v a l i d . Van Horn (1968) defined v a l i d a t i o n as the process of building an acceptable l e v e l of confidence  that the inference about a simulated process  i s a correct or v a l i d inference of the actual process.  This applies to the  i n d i v i d u a l functional relationships, the organization and linkage of the functions and the r e s u l t s of the model i t s e l f .  A number of procedures have  been proposed for testing the v a l i d i t y of simulation models.  These include:  - 89 -  1)  Testing  the model against other models (Forrester, 1968).  2)  Empirical  3)  S e n s i t i v i t y testing (Van Horn, 1968).  4)  Regression of simulated series on r e a l series and testing whether the  testing (Naylor and  c o e f f i c i e n t was  Finger, 1967).  s i g n i f i c a n t l y different from one  and  the intercept s i g -  n i f i c a n t l y d i f f e r e n t from zero (Cohen and Cyert, 1961). 5)  Turing tests (Van Horn, 1968)  i n which people d i r e c t l y involved  f i e l d are asked to distinguish between r e a l and  i n the  simulated results without  p r i o r knowledge as to which were which. Testing  of the tree simulation  was  with the vegetative community simulations.  r e l a t i v e l y simple as compared The amount of data available for  testing the understory simulation  results are severely l i m i t e d , to the extent  that only s e n s i t i v i t y testing and  some empirical  testing could be carried  out. Examples of the application of the model and  the results of  the  v a l i d i t y tests are presented i n the remainder of this section.  Tree Growth Simulation The p r i n c i p l e application of tree growth simulations i s i n determining y i e l d predictions  for young stands.  To date, y i e l d tables, a term  applied to presentations of expected y i e l d s of forest stands based upon growth i n f e r r e d by the study of other stands, have been used i n the estimation of future y i e l d s .  For example, i n B r i t i s h Columbia, a kind  of empirical y i e l d estimation c a l l e d volume/age curves, of which more than 1000  are available, form the basis of the "Forest Service Method" for  - 90 determining annual allowable cut.  Y i e l d at culmination age and r o t a t i o n  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 p a r t i c u l a r differences caused by s i t e , stand density and decay factors (Forestry Handbook for B r i t i s h Columbia, 1971).  Validated tree  growth simulation models could obviate the necessity for generating l o c a l curves as s i t e index and stand density can be varied. The tree growth simulation was Service volume/age curves, Goulding's  tested against the B. C. Forest  (1972) model, data c o l l e c t e d 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 s i t e s i n the Cranbrook, Fernie, Upper Kootenay and Windemere P. S. Y. U.'s.  The simulated data are based on s p e c i f i c stand  conditions, namely a s i t e index of 80 with 350 stems per acre for the medium s i t e and a s i t e 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  i s adequately duplicated on the medium s i t e  for both 7.1" + and 11.1" +, but i s underestimated the poor s i t e .  i n the 11.1"+ class on  By increasing the s i t e index, but s t i l l remaining within  the range f o r poor s i t e , and decreasing the number of stems, similar volumes can be achieved but with an increase i n average  DBH.  Of s i x persons questioned, none was able to d i s t i n g u i s h between the B. C. Forest Service or simulated data. four guessed correctly but again none was the choice.  When asked to make a choice,  able to give any v a l i d reason for  - 91 B.C. Forest Service  DBH Volume  Simulated DBH Volume MEDIUM SITE DOUGLAS-FIR ^ *  7.1" + c o •H 5000 •H •W  r/  <U CO  o 4000  •  s o U  7.1" +  .5 3000 CU  u a  cd  u p. 2000  11.1"  1  t-i  o > M  Co 1-1  1000  cu  3  100  Figure 40.  Comparison between simulated volume and DBH and B.C. Forest Service volume and DBH taken from V.A.C. 1012, medium s i t e .  +  - 92 -  B.C. Forest Service DBH Volume Simulated  DBH Volume POOR SITE DOUGLAS-FIR  14  11.1" +  12 c o  10 CO  <u o c  .<.-•** 7.1" +  •rl •U CU N  •4-1  0)  •9 « m n  8  8 4000 U  CU  00  cd  n  6  3 c  CU  3000-  M o cu 2000 o. <u  :  7.i" +  H n.i" +  a, 1000 oo c0  l-i CU  3  20  Figure 41.  100  Comparison between simulated volume and DBH and B.C. Forest Service volume and DBH taken from V.A.C. 1013, poor s i t e .  - 93 The model was then tested against the growth curves for unthinned stands prepared by Goulding (1972) to show gross volume and mean DBH f o r s i t e indices 90, 120 and 150 with 300 and 800 trees per acre at age 20. Considerable d i f f i c u l t y was encountered i n attempting to duplicate these stand conditions.  The model developed allows s i t e index to change during  the course of the simulation and stand density i s defined at age zero. A f t e r numerous runs, conditions approximating those of Goulding were achieved. The results obtained show that the two models, derived independently and using very d i f f e r e n t approaches, y i e l d similar volumes with differences of up to 250 cubic feet per acre on high s i t e s (Figures 42, 43 and 44).  The  simulated diameters of Goulding (Figure 45) are considerably lower than those generated i n this model f o r a l l s i t e classes.  This divergence i s 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 i n the derivation of any of the functional r e l a t i o n ships. DBH,  Data collected on the stands included i n d i v i d u a l tree locations,  crown width, volume and number and l o c a t i o n of trees having died since  stand establishment.  Stumps were used to locate trees which had died.  While t h i s method for determining past mortality i s subject to underestimation, the absence of stands with recorded past h i s t o r i e s of mortality i n the study area necessitated i t s use.  Table 7 shows the actual and  simulated plot volumes i n cubic feet per acre.  - 94 -  Goulding 800 trees at 20 yrs .  0  " ' 300 trees at 20 yrs  20  40  60  80  100  Age - yrs Figure 42.  Comparison of Goulding's and my simulated gross cubic foot volume per acre f o r s i t e index 150.  - 95 -  Goulding — — - — - Simulated ••• — — — — —  17500  Figure 43.  800 trees at 20 yrs 300 trees at 20 yrs 680 trees at 20 yrs 340 trees at 20 yrs  -  Comparison of Goulding's and my simulated volume per acre f o r s i t e index 120.  gross cubic foot  -  96  -  Goulding -  800 t r e e s  at  20  years  300 t r e e s  at  20  years  940 t r e e s  at  20  years  400 t r e e s  at  20  years  Simulated —  S I T E I N D E X 90 12500  -  4-4  0  20  40 Age -  Figure 44.  Comparison of  Goulding's  volume per a c r e f o r  site  60  100  yrs  and my s i m u l a t e d index  80  90.  gross cubic  foot  - 97 Goulding  - 800 trees at 20 yrs . 300 trees at 20 years  Simulated " 680 trees at 20 years  20.0  - 340 trees at 20 years  17.5  SITE INDEX 120  15.0  CO  C  12.5  PQ Q  01  00  CO  10.0  u  cu  7.5  5.0  2.5 h  0 I 0  i 20  I 40  I 60  I 80  l 100  Age - y r s Figure 45.  Comparison of Goulding s and my simulated mean DBH f o r 1  s i t e index 120.  - 98 -  Table 7.  Comparison of simulated and actual stand volumes measured on the study area.  Stand  Actual Total Volume 1" + DBH cu f t / a c r e  Simulated Total Volume 1" + DBH cu ft/acre  Simulated as % of Actual  1  1710  1510  88.3  2  2001  1991  99.5  3  1832  2031  110.9  4  2131  2339  109.8  5  780  1000  128.2  6  857  777  90.7  Stand 2 was also simulated at both 2- and 10-year i n t e r v a l s to ascertain the e f f e c t of reducing the calculation i n t e r v a l on both simulation costs and r e s u l t s .  Cost was  found to be a d i r e c t function of the number  of c a l c u l a t i o n i n t e r v a l s ; the costs at 2- and 10-year i n t e r v a l s were approximately  $43 and $9, respectively.  Decreasing the c a l c u l a t i o n i n t e r v a l  from 10 to 2 years had a minor e f f e c t on the simulated parameters.  Selected  stand parameters are shown at 20 year intervals (Table 8). On the basis of these r e s u l t s , the model appears to approximate the real system.  Obviously, the model w i l l require further testing and  refinement i f i t i s to be used to generate y i e l d tables.  However, i t i s  s u f f i c i e n t l y accurate to give an approximation of y i e l d f o r use i n the determination of trade-offs between wood and ungulate food production.  - 99 Table 8.  Stand Age yrs  Comparison of selected mean tree parameters i n t e r v a l s of 2 and 10 years.  Calculation Interval yrs  Average Volume 1" + DBH cu f t  for calculation  Average Height ft  Average DBH ins  No. of Trees per acre  0.63 0.59  0.007 0.007  840 830  20  2 10  5.3 5.2  40  2 10  14.0 14.8  2.6 2.7  0.360 0.381  770 660  60  2 10  20.6 21.3  3.8 3.9  1.020 1.076  650 540  80  2 10  29.4 30.8  5.2 5.6  2.451 2.648  550 450  100  2 10  38.0 38.9  6.5 6.7  5.038 4.940  450 410  The Vegetative Community Simulation The models for shrub growth and grass and forb growth were constructed after completion of the tree growth model.  I n i t i a l sensitivity  testing showed that the models were capable of approximating solutions i n the absence of trees.  As was previously stated, d i f f i c u l t y was  encountered  i n v a l i d a t i n g the understory simulations due to the lack of data with which to compare the simulated r e s u l t s . Two  types of s e n s i t i v i t y 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 d i s t r i b u t i o n s .  - 100  -  On the basis of the r e s u l t s obtained i n testing the model over a range of plant d e n s i t i e s , i t appeared that the model performed adequately except at very low tree and shrub d e n s i t i e s . and  The production of both trees  shrubs appeared to be underestimated and the death of a single i n d i v i d u a l  at these low densities resulted i n rather abrupt and marked increases grass production.  in  Examination of height frequency d i s t r i b u t i o n of naturally  occurring, mature, open-grown stands indicated the presence of a d i s proportionate number of faster than average growing i n d i v i d u a l s , the reason for which i s not c l e a r .  The normal random deviates generated i n the model  did not allow for t h i s upward s h i f t i n average growth rate at low Therefore, an additional function which increases the standard deviation at low densities was function has apparently solved abrupt and marked increase  densities.  the mean value and  added.  reduces  The addition of this  the problem of growth underestimation.  i n grass production following  The  the death of a tree  or shrub i s a result of the removal of the dead i n d i v i d u a l from the system, thereby freeing a large amount of growing space.  Modification  to the system  to allow the gradual withdrawal of dead individuals i s presently  being  undertaken. The  changes made to the functional relationships and  the growth  rate frequency d i s t r i b u t i o n s showed the system to be f a i r l y stable; small modifications  to the functions resulted i n small changes i n the r e s u l t s and  large modifications  resulted i n large changes i n the r e s u l t s .  The model was  tested against  the r e s u l t s obtained by Kemper (1971)  on Premier Ridge some 60 miles north of the study area.  Unfortunately,  due  - 101 to the lack of uniformity i n the c a l c u l a t i o n of productivity, the number of comparisons that could be made i s l i m i t e d .  Comparison of Kemper's (1971)  data for grass production as a function of forest crown closure with that of  the simulation shows that the simulated curve describes the data well  except at crown closures greater than 70 per cent, where i t underestimated production.  The response of simulated forb production to changing crown  closure exhibits similar trends to those found by Kemper, but was cantly lower.  signifi-  The lower production values probably r e s u l t from the fact that  Kemper's measurements were made on plant communities i n secondary grazing succession i n which forb production i s greatly increased.  Shrub production  follows the trends found by Kemper but can't be compared d i r e c t l y because of the d i f f e r e n t methods of measurement and presentation of r e s u l t s . I n s u f f i c i e n t data were collected to allow testing of the model's p r e d i c t i v e 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 v a l i d i t y testing of the understory model must be carried out before i t can be used as a management tool for predicting future y i e l d s of ungulate food production.  Despite the uncertainty as to i t s predictive  accuracy, the understory model can be used to investigate plant interactions and to i s o l a t e c r i t i c a l relationships a f f e c t i n g productivity. The most interesting and i n s t r u c t i v e 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 t h i s i s the  - 102 -  usual system used i n range studies. Figure 46 shows the response of Amelanchier numbers and production under two tree stands, s i t e index 60 with 2224 and 1112 trees per hectare, respectively, at age zero, as compared to growth i n the absence of trees. The i n i t i a l number of Amelanchier was set at 2700 per hectare, representing the upper density found.  The most s t r i k i n g feature i n the comparison i s  the tremendous reduction i n number and production when trees are introduced into the system.  Clearly, the production of wood and Amelanchier browse  are incompatible. shrub species.  Similar relationships were found f o r a l l shade intolerant  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 i n numbers as crown closure  increases, the rate of decrease being greatest i n the shade intolerant species.  In both cases production shows a lag e f f e c t ; that is,production  i n i t i a l l y increases despite a decrease i n shrub numbers.  The production  increase i s explained by the fact that although the number of individuals i s decreasing, the r e l a t i v e s i z e , and hence p r o d u c t i v i t y , of each i n d i v i d u a l i s increasing. The response of Agropyron to the presence of trees i s e s s e n t i a l l y s i m i l a r 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  1112 trees per ha  no trees  2224 trees per ha  Number Production  300  3000  200  2000  100  1000  cd M CD Ox 00 ^5  G O •H +J  U  3 -a o u  P.  •H O  I 100 18  Time - yrs J 1 : 52 64  76  84  Tree Crown Closure - % at 1112 trees per ha i  0  I  i  i  i  40  80  90  96  99  Tree Crown Closure - % at 2224 trees per ha Figure 46.  Simulated e f f e c t 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 f o r 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 f o r s i t e index 60 with 2224, 1112 and zero trees per hectare.  - 106 a very rapid decrease as tree crown closure increases.  A change i n crown  closure from 0 to 10 per cent causes a f i f t y per cent reduction i n production. The production response of forbs and Calamagrostis and Koeleria to  changing crown closure as affected by the presence and absence of shrubs,  i n this case Shepherdia, Prunus and Symphoricarpos,  i s shown i n Figure 49.  The production curves are a product of a number of complex interactions. Production of Calamagrostis and Koeleria increases i n response to increasing crown closure both i n the presence and absence of shrubs. presence of shrubs depresses the rate of increase.  However, the  In the absence of shrubs,  forb production shows an i n i t i a l increase i n response to increasing crown closure, and decreases when crown closure exceeds 30 percent. of shrubs, forb production i n i t i a l l y  shows a faster and more pronounced  increase, followed by a more rapid and pronounced a pronounced  decrease.  The s h i f t from  increase to a pronounced decrease i n production results from the  opposing effect of Shepherdia, Prunus and Symphoricarpos and d i f f e r i n g mortality rates for the shrubs.  on forb production  Shepherdia r e s u l t s i n a  decrease i n forb production, while Prunus and Symphoricarpos duction.  In the presence  increase pro-  The decrease i n forb production resulting from the presence of  Shepherdia i s masked by a greater increase due to the presence of Prunus and Symphoricarpos  u n t i l age 20.  At age 20, or crown closure of approximately  12 percent, mortality of Prunus and Symphoricarpos  reduces t h e i r compensatory  e f f e c t , and forb production shows a net decrease due to the effect of the surviving Shepherdia.  -  107  -  Calamagrostis Forb  20  crown  40  Comparison of production  simulated  response to  and a b s e n c e o f  shrubs.  closure  60  Time Figure 49.  production  production  Forest  0  and K o e l e r i a  80  100  yrs  f o r b and C a l a m a g r o s t i s and t r e e crown c l o s u r e i n  the  Koeleria  presence  - 108 Forest crown closure appears to be the most c r i t i c a l factor determining understory production.  Therefore, the ungulate manager, faced  with the problem of providing browse and grazing, must be able to predict future tree crown closures i f he i s to manage the resource. model can provide this information.  The tree growth  Figure 50 i l l u s t r a t e s the effect of  s i t e 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 s i t e indices, 80 and  60.  Tree locations were randomly assigned. Determination and  of trade-off functions between production of wood  Agropyron demonstrates even more c l e a r l y the degree of incompatibility  between the two products  (Figure 51).  Agropyron production was  s p e c i f i e d at  475 kilograms per acre and the tree stands were assigned a s i t e index of 60 with 2224 and 741 trees per hectare at age zero.  Wood production was  verted to cubic meters per hectare for the comparison.  con-  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 i n a short term net increase i n Agropyron production at the cost of a loss of 111 cubic meters of wood per hectare. The response of Agropyron to the presence of Amelanchier,  and other  shrub species, i s s i m i l a r to that of trees i n that there i s a reduction i n production, but t h i s loss i s compensated by the production of browse (Figure 52).  Agropyron production was  hectare and Amelanchier  specified at 475 kilograms per  density at 2700 individuals per hectare.  The  trade-off function shows a straight l i n e almost one-to-one conversion with a s l i g h t loss i n production i n the change from Agropyron to  Amelanchier.  crown closure.  - 110 -  160  r  SITE INDEX 60 140  2224 trees per ha  120 cd  741 trees per Via  u  <u CO  100  c o  •H +J  o 3 -a o  80  M PM  T3 O  •s  60  40  20  0  J  100  200  300  400  Agropyron Production - kg per ha Figure 51.  Trade-off between wood and Agropyron production.  500  - Ill  -  Combined Agropyron and Amelanchier production Trade-off  CO •G  U  500  <U P* 60  c o  400  •H 4J O  tJ  o u  300  CM 60  CO  3  I  200  U  CU •H 43 O  100  100  200  300  Agropyron Production Figure 52.  400 kg per ha  Trade-off between Agropyron production and annual twig production of Amelanchier.  500  - 112 The discussion of the simulation results gives a b r i e f 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 i n complex plant communities with a reasonable degree of accuracy, allows i s o l a t i o n of the e f f e c t and response of i n d i v i d u a l plant species and provides a basis f o r determining production trade-offs among d i f f e r e n t plant species and hence providing a management tool f o r the optimization of land productivity f o r specified management goals. It would seem worth while to give a b r i e f 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 s i t e index of 60. Amelanchier  production was calculated f o r 2700 individuals  per hectare and Agropyron f o r 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, years.  Agropyron and forbs i s e s s e n t i a l l y confined to the f i r s t 30  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 i n very s i g n i f i c a n t increases i n the  Table 9.  Comparative p r o d u c t i v i t i e s of wood, Amelanchier, Agropyron and forbs for two Douglas-fir stands with 2224 and .247 stems per acre and s i t e index 60. SITE INDEX 60 2224 trees per ha  Age  Wood cu ft/ha  247 trees per ha  Amel. kg/ha  Agrop. kg/ha  Forbs kg/ha  Wood cu ft/ha  Amel kg/h a  Agrop. 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 s t e a d i l y to a maximum of 41 kg/ha at 100 years; Agropyron production 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 i n ungulate food pro-  duction j u s t i f i e s the associated reduction i n wood production i s beyond the scope of this study.  - 115  -  POTENTIAL FOR APPLICATION At the present stage of development, the model has a number of l i m i t a t i o n s that should be overcome i f i t i s to achieve i t s f u l l p o t e n t i a l as a research, educational or management t o o l .  The l i m i t a t i o n s may  be  segregated into (1) system or (2) component oriented r e s t r a i n t s . The system oriented l i m i t a t i o n s r e s u l t from system design and r e l a t i v e l y e a s i l y overcome. (1)  are  They include:  I n a b i l i t y to allow natural regeneration  or c u l t u r a l practices  during the course of simulation. (2)  Simulation p l o t must be square.  (3)  D e f i n i t e upper l i m i t on number of species and i n d i v i d u a l s  within each species. (4)  Excessive amounts of information generated.  The component oriented l i m i t a t i o n s are of a more serious nature than the system r e s t r a i n t s , depending on the purpose of the study. f e a s i b i l i t y study i n using mathematical modelling  As a  to simulate plant ecosystem  development, to approximate productive c a p a b i l i t i e s for alternate species or combinations of species, i s o l a t e c r i t i c a l functional r e l a t i o n s h i p s , assess probable implications of management for wood production on ungulate food production or as a learning t o o l , the l i m i t a t i o n s are of l i t t l e consequence. However, i f the model i s to be used i n management decision making, i t w i l l be necessary to (1) improve and elaborate the functional r e l a t i o n s h i p s , (2) derive additional relationships,and (3) undertake further v a l i d i t y testing.  Additional information required would include (1) a more precise  - 116 d e f i n i t i o n of s i t e q u a l i t y ,  -  (2) the a b i l i t y to account for large v a r i a t i o n s  i n understory production due to annual c l i m a t i c v a r i a t i o n s , to allow mortality from causes other than competition,and  (3) the a b i l i t y  (4) the development  of methods for converting t o t a l plant production to u t i l i z a b l e production w i l l be  necessary. Following these inclusions, the model would have d i r e c t a p p l i c a t i o n  in: 1)  Determining  production c a p a b i l i t i e s for alternate species or  combinations of species. 2) combination  Testing various combinations of species to determine the best i n terms of ungulate food production.  3)  Predicting food a v a i l a b i l i t y through the winter.  4)  Predicting plant succession and the duration and amount of  food produced by i n d i v i d u a l species and combinations of species. 5)  Deriving trade-off functions between wood and ungulate  production. 6)  Prediction of wood y i e l d .  food  - 117 BIBLIOGRAPHY A. R.D.A.  1967. Maps compiled for the B r i t i s h Columbia Agro-Climatology Committee, A.R.D.A. Dept. of Geography, University of B r i t i s h Columbia.  Anderson, R. C , Loucks, 0. L. and A. M. Swain. 1969. Herbaceous response to canopy cover, l i g h t i n t e n s i t y and throughfall p r e c i p i t a t i o n i n 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. f o r F, F mixtures and Py - TG 1-6, 8, 32. Medium and Poor s i t e s . V.A.C.s 1012 and 1013. Division.  . F i e l d Pocket Manual. 83 pp.  Forest Surveys and Inventory  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. B e i l , C. E. 1969. Plant associations of the Cariboo-aspen-lodgepole pineDouglas-fir parkland zone. Ph.D. Thesis. U.B.C. Dept. of Botany. 342 pp. B e l l a , I. E. 1969. Simulation of growth, y i e l d and management of aspen. Ph.D. Thesis. Faculty of Forestry, University of B r i t i s h Columbia. 190 pp. Botkin, D. B., Janak, J . F. and J . R. W a l l i s . 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 c l a s s i f i c a t i o n of the ponderosa pine stands i n the southeastern i n t e r i o r of B r i t i s h Columbia. Ph.D. Thesis. Dept. of Botany and Biology, U.B.C. 240 pp. . 1965. The dry forest of southern B r i t i s h Columbia. Ecology of Western North America. 1: 65-75.  The  Browne, J . E. 1962. Standard cubic-foot volume tables f o r the commercial tree species of B r i t i s h Columbia. B. C. Forest Service, Surveys and Inventory D i v i s i o n . A. Sutton, Queen's P r i n t e r , 107 pp. Cohen, K. J . , and R. M. Cyert. 1961. Computer models i n dynamic economics. Quart. Jour. Econ. LXXV: 112-127. Daubenmire, R. 1943. Vegetation zonation of the Rocky mountains. Rev. 9: 325-393.  Botan.  - 118 -  Daubenmire, R. 1959. A canopy cover method of vegetation analysis. west Science, 33(1): 43-64.  North-  Donald, C. M. 1951. Competition among pasture plants. I. I n t r a - s p e c i f i c competition among annual pasture plants. Australian Jour. Agric. Res. I l l o s . 2(4): 355-375. Ferguson, R. B. Survival and growth of young bitterbrush browsed by deer. Jour. W i l d l i f e Mgm., 32(4): 769-772. Forestry Handbook for B r i t i s h Columbia. U.B.C. 815 pp. Forrester, J . W.  1960.  3rd. E d i t i o n  I n d u s t r i a l dynamics.  1971.  Forest Club,  Cambridge, MIT Press.  464  pp.  Goulding, C. J . 1972. Simulation techniques f o r a stochastic model of the growth of Douglas-fir. Ph.D. Thesis. U.B.C. Faculty of Forestry. 234 pp. H o l l i n g , C. S. 1963. An experimental component analysis of population processes. Mem. Ent. Soc. Can. 32: 22-32. Hozumi, K., Koyama, H. and T. K i r a . 1955. I n t r a s p e c i f i c competition among higher plants. IV. A preliminary account of the i n t e r a c t i o n between adjacent i n d i v i d u a l s . 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 i n space. Central States Forest Experimental Station. 75 pp.  Columbus,  Kemper, J . B. 1971. Secondary autogenic succession i n the southern Rocky mountain trench. M.Sc. Thesis. Department of Plant Science, University of B r i t i s h Columbia. 139 pp. Lee, Yam  (Jim). 1967. Stand models f o r lodgepole pine and l i m i t s of t h e i r application. Ph.D. Thesis. Faculty of Forestry, University of B r i t i s h Columbia. 332 pp.  L i n , Jim.  1969. Growing space index and stand simulation of young western hemlock i n Oregon. Ph.D. Thesis. School of Forestry, Duke University. 182 pp.  Lyon, L. J . 1968. An evaluation of density sampling methods i n a shrub community. Jour. Range Mgm. 21(1): 16-20. _. 1968. Estimation of twig production of serviceberry from crown volumes. Jour. W i l d l i f e Mgm., 32(1): 115-119.  - 119 McLean, A. 1969. Plant communities of the Similkameen Valley, B r i t i s h Columbia and t h e i r relationships to s o i l s . Ph.D. Thesis. Washington State Univ., Pullman, Wash. 133 pp. McLean, A. and W. D. Holland. 1958. Vegetation zones and t h e i r r e l a t i o n to the s o i l s and climate of the upper Columbia v a l l e y . Can. Jour. Plant. S c i . , 38: 328-345. Mead, R.  1968. Measurement of competition between i n d i v i d u a l plants i n a population. J . Ecology, 56(1): 35-45.  M i t c h e l l , 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. V e r i f i c a t i o n of computer simulation models. Man. S c i . 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 B r i t i s h Columbia. 201 pp. Odum, E. P. and H. T. Odum. 1959. Fundamentals of Ecology. Company, Philadelphia and London, pp 546.  W. B. Saunders  Opie, J . E. 1968. P r e d i c t a b i l i t y of i n d i v i d u a l tree growth using various d e f i n i t i o n s of competing basal area. Forest Science 14(3): 314-323. P a i l l e , G. 1970. Description and prediction of mortality i n some coastal Douglas-fir stands. Ph.D. Thesis. U.B.C. Faculty of Forestry. 300 pp. Smith, J . H. G. 1964. Root spread can be estimated from crown width of Douglas-fir, lodgepole pine and other B r i t i s h Columbia tree species. For. Chron. 40(4): 456-473. Stebbins, G. L. 1951. Variation and evolution i n plants. University Press. N.Y. 643 pp.  Columbia  T i s d a l e , E. W. 1947. The grasslands of the Southern i n t e r i o r of B r i t i s h Columbia. Ecology 28: 346-382. Trewartha, G. T. 1954. An introduction to climate. H i l l Book Company, Inc. N. Y. 402 pp.  3rd E d i t i o n McGraw-  Van Horn, R. 1968. V a l i d a t i o n . 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. i n a mixed-coniferous forest of northeastern 65: 391-393.  1967. Forage u t i l i z a t i o n Oregon. J . Forestry  - 120 APPENDIX I.  COMMON AND  SCIENTIFIC NAMES  PLANTS Douglas-fir  Pseudotsuga menziesii (Mirb.) Franco  Serviceberry  Amelanchier a l n i f o l i a Nutt.  Buckbrush  Ceanothus sanguineus Pursh.  Buffalo berry  Shepherdia canadensis Nutt.  Cherry  Prunus emarginata (Dougl.)  Rose  Rosa nutkana P r e s l .  Snowberry  Symphoricarpos albus (L.) Blake  Wheatgrass  Agropyron spicatum (Pursh) Scribn. and Smith  Bluegrass  Poa compressa L. Poa s c a b r e l l a (Churb.) Benth. ex Vasey.  Fescue Festuca Idahoensis Elmer Reedgrass Calamagrostis rubescens Buckl. Junegrass Koeleria c r i s t a t a Pers. Brome grass Bromus tectorum L. Trembling aspen Populus tremuloides Michx. Douglas maple Acer glabrum  Torr. var. douglasii (Hook.) Dipp.  Juniper Juniperus h o r i z o n t a l i s Moench. Mahonia Berberis repens L i n d l . Needlegrass Stipa columbiana Macoun. Yarrow A c h i l l e a millefolium L.  Hitchcock, C. L., Cronquist, A., Ownby, M. and J . W. Thompson. 1969. Vascular plants of the P a c i f i c Northwest. University of Washington Press. Seattle and London. 5 Vols.  - 121 -  Large purple aster  Aster conspicuus L i n d l .  Pasture wormwood  Artemesia f r i g i d a  Spring  Balsamorhiza  sunflower  Willd.  s a g i t t a t a (Pursh.) Nutt,  Monarda f i s t u l o s a L. Beardtongue  Penstemon spp.  Tuffted phlox  Phlox caespitosa  Nutt.  UNGULATES Elk  Cervus canadensis nelsoni, Bailey  Mule deer  Odocoileus hemionus hemionus (Rafinsque)  Rocky mountain big-horn sheep  Ovis canadensis canadensis Shaw  McTaggart Cowan, I. and C. J . Guiget. 1965. The mammals of B r i t i s h Columbia, A. Sutton, Queen's P r i n t e r (B. C. P r o v i n c i a l Museum, Handbook No. 9).  - 122 -  APPENDIX I I  where: a - tree height (HT)  f - branch length (BL)  b - crown radius (CR)  g - height above branch base (HTAB)  c - height to l i v e crown base (HTblc)  h - height to maximum crown width  d - maximum crown width (CWmax) e - h o r i z o n t a l branch length (HBL)  (HTCWmax) i - length of l i v e crown j - point of maximum crown width  - 123 C C C C C  c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c  APPENDIX  PROGRAM  I I I  LISTING  FOR  THE GROWTH TREES, ON  MAIN  TREE  SHRUBS, A  SIMULATION GRASSES  BIG-GAME  OF  AND  WINTER  FORBS RANGE  PROGRAM  GROWTH  SIMULATION  TREE GROWTH STAND MAPS  VEGETATIVE  AND  COMMUNITY  SUBROUTINE SUBROUTINE  COMPETITION  SIMULATION  PROGRAM C O N T R O L AND S P E C I F I C A T I O N S SHRUB GROWTH SHRUB MORTALITY SHRUft AREA SHRUB PRODUCTION G R A S S AND F O R B PRODUCTION  UTILITY  « • • • * •  SUBROUTINE SUBROUTINE SUBROUTINE SUBROUTINE SUBROUTINE SUBROUTINE  PROGRAMS UNIFORM  TREE XSECT  AND  RANDOM  NUMBER  GENERATORS  AGROP BRANCH REM AREA SGPDN SUM  -  C C C C C C . C C C C C C C C C C C  124  MAIN  SIMULATION  OF  ON  A  BIG-GAME  WINTER  MAIN  PROGRAM  TO  AND  SHRUBS RANGE  Of  DUMMY  PROGRAM  T H E GROWTH TREES,  -  COMPETITIVE AND  ALLOW  EAST  C C C  KQOTENAY  DISTRICT  COLUMBIA  BYPASS  OF  THE TREE  GROWTH  SIMULATION  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, A P D N S Y ( 4 , 2 1 ) INTEGER*2 JAftRA(66,66),NSET(96),IQQ(96,5),JaQ(96,S),NAGE(50),NNAME 1 L C 4 ) ,NNC£OiM(«) , N N S H E P ( 4 ) , N N P R U N ( 4 ) , N N R O S E ( 4 ) ,N N S Y M P ( 4 ) , J R A N D ( 5 0 ) , K 2RANDC50),LRANQ(50),JJRAND(100),KKRAND(100),LLRAND(100), J 3AMEL(20),JCEQN(20),JSHEP(20),JPRUN(20),JROSE(20),JSYMP(20) , I 5 C Q M C 1 5 0 ) , J C Q M ( 1 5 0 ) , I D E AO 1 ( 1 5 0 ) , I O E A D 2 C 1 5 0 ) , I D E A D 3 ( 1 5 0 ) , I D E A D 4 ( 1 5 0 ) 6 , L A R R 1 ( 6 6 , 6 6 ) , L A R R 2 ( 6 6 , 6 6 ) ,L A R R 3 ( 6 6 , 6 6 ) , L A R R 4 ( 6 6 , 6 6 ) ,IA R E A ( 1 5 3 ) ,I D 7 IA M I ( 1 5 0 ) , I D I A M 2 C 1 5 0 ) , I D I A M 3 ( 1 5 0 ) , I O I A M 4 £ 1 5 0 ) , P E R ( 1 5 3 ) , E P E R ( 1 6 ) , 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 2 C 8 0 K D S , X IN ' S , U T I L S , A G E , C , C C ,TAUT, T A U T S , T A U T T , T A U O , U N O C C , Y U N O C C P D N 1 , I T H R U , M , I S T R T , I I N T . I E N O , I Y U N O C , I A U T T Y , I U N O C C , I L O O P , I X , I S U B , I COUNT 3, I H T , I d B , J A R K A , L A R R 1 , L A R R 2 , L A R R 3 , L A R R 4 , I U Q , J U Q , IA R EA ,PER, KCHAR, I C O 4M,JCOM,IDEAD1,IDEAD2,IDEAD3,IOEAD4,IDI AM 1 , I D I A M 2 , I D l A M 3 , I D I A M 4 , J J R SAND,KKR ANO,LLR AND, ICrtAR, 1RAND, I X X , J X X , IVOL, I D 8 H , I C L , I A P E R , ICW, I C B , 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 5 I0UT«6 ITHRUs^ DO 2 Iai,b6 DO 2 J « l , 6 6 lARSAfl,J)»10000000 JARRA(I,J)«0 B  2  OF  GRASSES  IN THE  BRITISH  INTERACTIONS  READS  BRANCH  LENGTM-UCCUPANCY  DATA  DECK  -  3  C  5  C • C  C  10  C C I  C C  C C  DO 3 1 * 1 , 9 6 REA0(IRD,5) BL2CI),NS,(IQQ(I,II),JQO(I,II),II«1,NS) NSET(I)BNS FORMATCFb.4,1313) DELOPT ******  20  C  3K 40  50 5b  DELETE O P T I O N F O R T R E E S U B R O U T I N E DELOPT ,LE, 0 TREE SUB CALLED  AGE  REAO(lRD,15) FORMAT (13)  ISTRT  READS  INTERVAL  GROWTH  REAO(I«D,20) FORMAT(13) UPPER  *** ******  DELOPT  STARTING  READS  C  *** I F  READ(IRQ,10) FORMAT(12) READS  15  125-  IINT  AGE LIMIT  READCIRO,30) IEND FORMAT(I3) IF(OfcLOPT) 1QP,100,40 J B 0 00 5 0 I s I S T R T , I E N D , I I N T JBJ*1 NA6E(J)«1-1 REA0(IRP,55) IX F0RMATCI5) TINTBIINT  NINTsIEND/IINT  C C  INCREMENTS  C  CROWN  CSUBlBjj. CSUB2 10, CSUB3B20, CvSUB4s30, GO T O b 5 8  hid  CSU8l"C5uBl+40,  CSUB2*C3UB2*40, CSUB3SCSUH3+40,  C8UB4BCSUH4+40, 62  GO T O b 5 CSUB18CSU91+40, CSUB2"CSUB2+40.  CSUB3«CSuQ3+40.  CSUB4*CSU64*40,  CLOSURE  I F TREE  SUBROUTINE  NOT CALLED  -  65 C C C  126 -  M » 0 CALLS  UNDERSTORY  ROUTINES  CALL AGROP DO 7 0 I « i , N l N T  n•i  c C C  CALLS /&  C C C C C C C C C C C C C C C C  UNDERSTORY  ROUTINES  CALL AGROP I F ( C 5 U B 1 . L T . 1 0 . ) G O T O f>0 I F C C S U 3 1 . L T , 5 0 . ) GO T O 6 2 M B STAND AGE ITREE * I T U TREE IPOS B I T H BRANCH HABM s H E I G H T TO MAXIMUM CROWN WIDTH BL • BRANCH LENGTH HBL • HORIZONTAL BRANCH LENGTH IOCC » TEST VALUE FOR BRANCH OCCUPANCY 9 B , I b B B HEIGHT TO BRANCH BASE HT,IHT,HTA,HTS= TREE HEIGHTS ICW,CWS,CW,ACW » MEASURES OF CROWN WIDTH IVOL,VOL,VOLS,AVOL • MEASURES OF VOLUME IDBH,DBHS,DBH,ADBH B MEASURES OF DIAMETER IBA,BAS,BA,ABA 8 MEASURES OF BASAL AREA I C L , C L S , C L , A C L a MEASURES O F CROWN LENGTH I A P E R « % CROWN CLOSURE  AT BREAST  HEIGHT  c XWD«5  I0UT«>6 C C C C  IDELAG $SS$S  AGROPYRON SUBROUTINE CALL SUBROUTINE AGRO $$$$$  READ(IRD,3)IDELAG FORMAT CI2)  3 C C C  INTEGER  10 C C C  TO START  GAUSS  READCIRD,10)IX FORMAT(15) S I  20 C C C  ***** OPTION TO D E L E T E I F IDELAG ,GT. 0 = CALL  ***  READS  SITE  INDEX  ***  READ C I R D , 2 0 ) S I FORMAT(F5,2) A L L TREES INITIALIZED AS BEING ALlVE *** I D E A D *** NUMTR *** OPTION TO CHANGE NUMBER OF T R E E S ***  *****  -  127 -  C 30 C C C  READClHD,3&)NUMTR FORMAT(13) MATRIX  31  ***  OPTION  TO ALLOCATE  TREE  LOCATIONS  RANDOMLY  ***  RE*D(IRD,3l) MATRIX FORMAT (12) IFCMATRIX.GT.l) GO T O 5 1  C  5S  DO 5 5 I»1,NUMTR CALL RANDU (IX,IY,YFL) IXX(I)»VFL»«»5, * 1 , IDEAD(I)s0 IX-IY  C  5b 37  3fl  39 51 40 50 59 60 C C C C C C C  READS  IPRIN ******  70 C C  D O 5 6 I *» 1 i N U M T R CALL RANDU (IX,IY,YFL) JXX(I)»YFL«fe5.*l. IX»IY ICMK«0 DO 3 9 NUMTR DO 3 9 J 3 1 , H U M T R I F ( I . E Q . J ) GO TO 3 9 1'FCIXXCI) ,NE.IXX(J}) GO TO 3 9 I F ( J X X C I 3 . N E . J X X C J J ) GO T O 3 9 LXaJXX (J) CALL RANUU (JX,IY,YFL) JXX ( J ) « Y F L * 6 5 . +1. iXalY I F ( J X X C J ) .fe'Q.LX) G O T O 3 f l ICHKal CONTINUE IF(ICH*)59,59,37 DO « 0 I a l , N U M T R IDEADCI)"0 *EAD(IRD,50)IXX(I),JXXCX} FORMAT(213) REAO(IRD,60) ICHAR FORMAT(40A2) OPTIONS  *** OPTION TO PRINT I F ,t.E. 1 B NO M A P  OUT STAND MAP *** I F ,GT, 1  READ CIRD,73)IPRIN FORMAT(12) NCOOE  ***  OPTION  TO PRINT  IARRA  CODE  ***  *** • MAP  ******  »  C C  ******  I F ,UE, 1  •  128 "  NO C O D E  ***  I F ,GT, 1  •  CODE  ******  «EAD(I«Q,80)NCODE  80 C C. C C  FORMAT (12) NTREE ******  90 C C C C  230 C C C C C  TO PRINT I N D I V I D U A L TREE PARAMETERS *** • NO T R E E S *** I F ,GT. 1 • TREES ******  READ(IRO,9a)NTREE FORMAT(12) ITRFN ******  220  *** OPTION I F ,LE, i  *** OPTION I F ,LE, 1  8  TO PRINT TREE FUNCTIONS AS GRAPHS MO F U N C T I O N S *** I F ,GT. 1 •  REAOURO,220) ITRFN F ORMAT(12) READ(IRO,230)JCHAR FORMAT(2A1) LINPR *** OPTION TO DISPLAY VERTICAL XSECT THROUGH STAND *** ****** I F , L E 0 * NO X S E C T *** I F , G E , 1 A N D , L E , 6 6 X S E C T PRINTED THROUGH L I N E a TO VALUE OF LINPR ****** t  240 C C C  REAO(IRD,240)L1NPR FORMAT(12) GENERATES  RANDOM  NUMBERS  FOR ALLOCATION  TO INDIVIDUAL  UMTREaNUMTR VV*.l+.«S*((100,-UMTRE)**6,/100.**6.) AM",5231*.25*C (100,-UMTRE)**6,/100.**6,) C  250  DO 2 5 0 I M , N U M T R CALL GAUSSCIX, .2322,AM,V) IF(V,LT,VV) V»VV IF(V.GT.l.l) V s l . l IRAND(I)•V«ltf00.  C  310  C C C C  c  *** FUNCTIONS  DO 3 1 0 1 1 * 1 , 1 9 00 3 1 0 J J = 1 , 1 9 IHT(11» JJ)»0 IB6(IX,JJ)s0 ILO0Pa(ItND-ISTRT)/IINT*l JLCOPsiLOOP-i CALCULATES TREE HEIGHTS FOR S P E C I F I E D AGE TREE HEIGHTS PLACED I N ARRAY  JB0 DO  350  I-15TRT,ItNO,IINT  INTERVAL  TREES  *  - 129  J«J + 1 N A G E U ) "1-1  X«I-1  DO 3 5 0 K » 1 , N U M T R RAND1«IRAND(KJ RAND8RAMD1/100K.  320 330 340 C C C  350  360  370  B A S E FROM A G E I N T E R V A L 2 TO  IMAX  IN  ARRAY  TREE  6  TREE  DO 3 7 0 K M , N U M T R IBB(JrK)«IhT(L K) f  P R I N T S H E I G H T AND B R A N C H 380  C  WRITE(IOUT,3B0) FQRMAT(M  ',5X,'TREE  wRITE(IOUT,390) FORMAT(3X,* TREE 1 17 T R E E 6 T R E E 9')  BASE ARRAYS F O R TREES 1 T O 9  H E I G H T S STOREO TREE  2  IN  TREE 3  ARRAY'*/)  TREE 4  TREE 5  DO 4 0 0 I « l , l L O O P 400  410  C C  WHORL  DO 370 J » 2 , I L 0 0 P L«J-1  390  C  R E P R E S E N T S LOWEST B R A N C H  DO 3 6 0 K » i , N U M T R RAND 1 • I R AND ( K 3 R A N D ' R A N D 1/ 1 000 • BBBRAND*1805.*(SIN(3.14159/50,«3.14159/2.) + l . ) I F ( B B . L T , 1 „) e B o l , IBB(J,K)°BB P L A C E S H E I G H T S TO B R A N C H  C  C  AT A G E 1 *  DO 3 6 0 J » l , l  C  C C C  IHTCJiK)«HT2  CALCULATES HEIGHT  C  C C  IF(X-45.5320,330,330 H T « R A N D * C S I / 7 6 . 3 * C I S . 0 5 * ( S I N ( X * 3 . 1 4 1 5 9 / 5 0 . - 3 , 1 4 1 5 9 / 2 , ) • 1 , ) • .7-.038 175*X) GO TQ 3414 riT"RANO*(SI/7b.)*Cl.66222+.7044*X) I F ( H T . L T . . 0 1 ) HT=,01 HT8«HT*100,  420  WRIT£(IOuT,410)(IHT(I,J),J*1,9) F0RMAT(3X,1213)  WRITE(I0Ur,42tf) FORMAT(////,5X,'HEIGHTS  TO  BRANCH  BASE STORED  IN  ARRAY',/)  - 130 .  WRIT£(IOUT,390)  c  00  443  I»1,IL0UP  C 430  c. C  W « I T E ( 1 Q U T , 4 1 0 ) C I B B C 1 , J ) , J « l , 9 ) SETS  c  DO  I A R R A U , J )  440  •  10000000  I«1,6b  C DO 4 4 0 J n l b b IARRA(I,J)sl0000000 f  440 450  MB0  C 451  WRlTE(IQUT,45t) PORMAT(/,S.X,'STAND CSUBlBia CSUB2«0 CSU@3*0 CSUB4«0 IFCIOELAG.LE.0)  AGE  GO  TO  *  0  YRS.  **  TREES  NOT  460  C GO C C C  TO  CALLS 100 130  CALL CALL STOP END  130 TREE  GROWTH  ROUTINES  TREE EXIT  C C C SUBROUTINE C C C  RANDOM  50  GAUSS  NUMBER  (IX,S,AM,V)  GENERATOR  FOR  A«0.0 DO 5 0 181,12 C A L L R A N O U d X , 1 Y, Y) IX •IY A»A«-Y VB(A-6,0)*S+AM RETURN END  C C C SUBROUTINE C C  RANDOM  RANDU(I  NUMBER  X,IY,YFL)  GENERATOR  NORMAL  DISTRIBUTION  YET  ESTABLISHED')  IYBIX*65539 I F C I Y ) 3 # 6# 6 IY*IY+2147483fe47+l YFU«IY YFl»YFL*.4656613E"9 RETURN  END  -  SUBROUTINE  132 -  TREE  C  c c  STAND  GROWTH  SIMULATION  FOR INTERIOR  DOUGLAS-FIR  DIMENSION I A R R A ( b b , b b ) , B L 2 ( 9 b ) , A C C ( 4 , 2 1 ) , A T A ( 4 , 2 1 ) , A T G ( 4 , 2 1 ) , A T F ( 4 1,21),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 3 A M E L ( 2 0 ) , J C E Q N ( 2 0 ) , J S H £ P ( 2 0 ) , J P R U N ( 2 0 ) , J R O S E ( 2 0 ) ,J S Y M P ( 2 0 ) , I 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 A M I ( 1 5 0 ) , I D I A M 2 ( 1 5 0 ) , I D I A M 3 ( t 5 0 ) , I D I A M 4 ( 1 5 0 ) , P E R ( 1 5 3 ) , E P E R ( 1 b ) , K A 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, J C O M , I D E A D 1 , I D E A D 2 , I D E A D 3 , I D E A D 4 , I D I A M 1 , I D I A M 2 , I D I A M 3 , I D I A M 4 , J J R 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  IA RR A s ARRAY R E P R E S E N T I N G 1 / 1 0 ACRE PLOT JARRA a ARRAY F O R P L O T T I N G CROWN P R O F I L E S C S U 8 1 , , . . 4 a CROWN C L O S U R E OF S U B - P L O T S S U B ! , , , , 4 a CROWN A R E A S F O R 1 / 4 0 T H A C R E PLOTS HTAS s HEIGHT ABOVE BRANCH C A E • E X P E C T E D CROWN AREA NUMTR * # OF T R E E S ICHAR a TREE NUMBERS I X X , J X X 8 I , JT R E E LOCATIONS IRAND s TREE GROWTH P O T E N T I A L CALL AGROP  C C C  INCREMENTS  C  4b0  AGE  INTERVAL  M»M+1  C DO  500  I«l,66  DO  500  J e l , b 6  C 500  JARRA(I,J)B0 1F(M-ILOOP)510,510,1470  -  510 C C C  ITR£E»0 STARTS  520  530 C C C  133 -  NEW  TREE  ITR£E"ITR£E+l L2»l KTMBRa1 IF(ITREE-NUMTR)530,530,790 HTlsIHTCM,iTREE) IF(HT1,LE.0,)GO TO 5 2 0 GOES  TO  NEXT  LOWER  BRANCH  AND  CALCULATES  BRANCH  DO 7 6 0 I B R s l , M IPOSaM+l-IoR  68l«IBBCIPQ5,ITRe£)  539 C C C  I F ( B 8 1 , L t , 0 , ) G Q TO 5 2 0 BBoBBl/100. HT»HT1/100,»BB HTAaHTl/100. HABMa«5.5+,425*HTA IF(HT,GT,0,) GO TO 5 3 9 HT = . 1 IF(HABM)560,560,540 TESTS  543 550 560 570  C C C  AND  ADJUSTS  HEIGHT  TO  POSITION  IARRA(IX,JX)a  OF  TREE  MAX  KTHBR»u2 DO 7 6 0 L a K T H B R , 9 6 NSaNSET(L) L2BL  CROWN  BOLE  9 7 • I H T ( M , I T R E E ) * 100 + 1 0 0 0 0 0 0 0  C  580 590  WIDTH  IF((HTA-MABM)«HTJ550,530,560 8L«.98*CHTA-HAbM)**,7 LO TO 5 7 0 bL*.98«HT**.7 haL».9*BL-3.3*CBL**3,/20.**3.) JXaJXX (ITREE) IXalXX CITKEE) DESIGNATES  C C C C  CROWN  GROWTH AND C O M P E T I T I O N CROWN GROWTH  DO 7 6 0 K « 1 , N S IFCHBL-BL2CL>)770,580,580 INCR a 0 INCRalNCR+1  LENGTH  -  600  GO T O £600,610,620,630,760),INCR JaJX+JQO(L,K)  IsIX*IaQCL,K)  GO 610  620  630 o40 650 660 670 680 690 700 710 720 730  TO 6 4 0  JBJX-JQQ(L,K)  I«IX-IQQCL»K) GO TO 6 4 0 JsJX+JQQCL,K) I«lX-IflQ(L,K) GO T O 6 4 0 J»JX-JQO(L,K) I8IX+IQQCL,K) £F(I)670,670,650 lP(I-66)b70,&70,660 1*1-66 IF(J)700,700,660 IF(J-66)700,700,690 J"J-66 I F ( I ) 7 i 0 , 7 l 0 , 7 2 0 1*66+1 IF(J)730,730,7«0 J*66+J  C C C  TEST 740 750  760 770 780 C C C  FOR  OCCUPANCY  IOCC*10000000+(IBB £IPOS,I T R E E ) * 100) IF ClARRACXfJ)/100-IOCC/100)750,590,590 IARRA(I,J)818000000 I A R R A £ I , J ) 8 l A R R A ( I , J ) • I T R E E +IBB£ IPOS,ITREE)*100 GO T O 5 9 0 CONTINUE GO T O 7 8 0 CONTINUE GOES GO  C C C  134 -  TO NEXT  TREE  TO 5 2 0  PRINTS  MATRIX  CODES  I N IAPRA  790  IF(NCODE-1)880,880,800  800  WRITE(IOUT,990)NAGE£M)  (CROWN  COMPETITION)  C C 810  WRITE(IOUT,810) FORMAT(2X,'CODES 1 J a l TO 1 4 * )  DO  STORED  IN IARRA  MATHlX-LOCATIONS  8 2 0 ICaOE«40,50  C 620 830  WRITECIQUT,830)(IARRA(ICODE,JCODE),JCODE*1,14) FORMAT(2X,1419)  Ial0  TO 40  -  135 -  C  840  WRITE C I Q U T , 8 4 0 ) FORMATC'l',2X,'LOCATIONS  J M 5 TO 2 8 ' )  C  DO  850  ICOUE«40,50  C 850  WRITECIOUT,830)CIARRA  (I CODE,JCODE),JCODE*15,28)  860  WRITE(IOUT,660) FORMATC'l',2X»'LOCATIONS  C  J  s  29 TO 4 2 ' )  C  DO  8 7 0  ICOOEs40,50  C  870  WRITECIOUT,830)  880  yO 890 L L ICw(LL)»0 IVOL(LL)»0 I08H(LL) #  (IARRACI  CODE,JCODE),JC0DE*29,42)  C 8  1,NUMTR  8  I8A(LL)B0  890 900  ICL(LL)»0 lAPER(LL)«0 IAREA(LL)ai DO 900 L L M , N U M T R IC8(LL)*9999  I C S (97)o0 DO C C C  9 8 3  1^1,66  DETERMINES  HEIGHT  T O CROWN  WIDTH  MAX  DO 9 8 0 J » l , 6 b NEW IARRA(I,J)/l00*100 a  LTREE«IARRA(IPJJ-NEW  910 920 930  IF(LTREE)930,930,910 IF(£NEW/100-100000) -IC8(LTREE))920,930,930 ICBCLTREE)«NEW/100-100000 JARRA(I,J)8lARRA(I,J)-NEw NB"JARRA ( I , J )  940  IF(NB)960,960,940 IF(N6«97)950,960,960  C  C  CALCULATION  O F CROWN  AREA  C  950 960 970 980  l A R E A ( N B ) • I A R E A ( N B ) «• 1 IF(N8)97i4,970,980 . N8898 J A R R A d , J)BICHAR(NB)  990  WRITE(IOUT,990)NAGE(M) FORMATCi',2X,'STAND AGE»',2X,  C  C  13,//)  136  C C 1000  1010 C C C  CALCULATES  STAND  -  PARAMETERS  DO 1 1 0 0 M M s l , N U M T R HTl'IHTCM,MM) HT*H71/100. CRAR«IAREA(MM) NATURAL  MORTALITY  HABMa«5,5+,425*HT IF(HABM)10kll, 1001  1002 1003  1001,1002  HTABBHT  GO T O 1 0 0 3 HTA8«HT-HABM IFCHTAB.LE.0.) HTAB*,1 BL»,98*HTAB*«,7 HBL».9*BL-3.3* CBL**3,/20.**3,) I F ( H B L , L E , 0,)  HBLB.1  C A E « 3 , H l 5 9 » h B L * * 2 . I F ( ( C R A R / C A E ) , G T ..1) GO T O MAGEsM+i  1015  1020  IHT(MASE,WM)«IHTCM,MM) I D E A Q (MM)a\ IF(CRAR*(HT-4,5))1020,1020,1030  D6HS0, GO  1030  1040 1050 1P60 1070  1080 1090 1100 C C C  TO  1 0 4 3  08M".143*CCRAR*CHT-4,5))**,48  1DBH(MM)BOBH*l0M IF (DBH)1050,1050,1063 IBA(MM)"0 GO T O 1 0 7 0 IBA(MM)s(D3H/2.)**2,*3,14J 59*100. I C L ( M M ) a I H T ( M , M M ) - I C S (MM) A R E l a l A R E A (MM) ICW(MM)a2,*SQRT (ARE 1/3, 14159) * 1 0 0 , IF (DBH)1080,10K0,1090 V 0 L W, GO TO U00 V 0 L B - . 2 , 7 3 4 5 3 2 + ( 1 . 7 3 9 4 1 0 * A L O G ( D B H ) + J.. ! 6 b 0 3 3 * A L O G VOL*10.**VQL IVQL(MM)aVOL*100, f  8  PRINTS  MAP O F CROWN  OCCUPANCY  IF(IPRIN-l)1150,1150,1110 C 1110 1120 C  WRITEflOUT,1126) FQRMAT('9',126('*')) DO  C  1 0 1 5  1 1 3 0 I»i,b6  (HT)) /2.302585  -  1130 1140  137 -  W R I T E C I O U T , 1 1 4 0 ) ( J A R R A ( I , J ) ,J * 1 , 6 5 ) H0RMAT('9',65A2)  C 1150  C  1160  1170  WRITE(I0UT, H 2 0 ) HTS"0 DBhS«0 BAS«0 CBSa0 CLS"0 CWS = 0 AREASB3 VOLSa0 APERS«0 IF(NTREE-l)1170,1170,1160 WRITECIOUT,1200)  NEWTR»a  DO 1 2 2 0 N & M , N U M T R MORTnlDEADCNb) I F ( H O R T . G T , 0 ) GO T O1 2 2 0 NEWTRsNEWTR+i  HTI»IHT(M,NB)  HTBMTI/100. 0 8 H I = I D B H (NB) DBHsDBhI/100. BAIelBA(NS) BAsBAl/J 4400. CBIBICB(NB)  IFCCBI-9000)1190,1190,1180 1180  1190  CBI30,  CBsClU/lBB. CLBMT-CB CWI«ICW(NB)  CWsCWl/10'3. AREABIAREA  A P E R M 0 0 .  (NB)  *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  c 1200  INDIVIDUAL  TREE  PARAMETERS  IF(NTREE-l) 1240,1240,1210 FORMATC///,IX,' TREE #  I  J  HEIGHT  DBH  B,A  138  1. CR.BASE 2 NE ', /)  -  C.W,  CR,LENGTH  C,  AREA  C , A . AS  X  VOLU  C  1210 1220  WRXTEUOUT,1230)NB,XXX(NB),JXX(NB),HT DBH,BA,CB,CL,CW,AREA,APER, 1VOL CONTINUE F  C  C  CALCULATES  STAND  AVERAGES  C  1230 1240  F0RMAT(3X,3I6,9F11,2) 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  1250  WRITE(IOUT,1250) F 0 R M A T ( / / / / / , 5 X , 'STANO  TOTALS',/)  C  h R I T E d O U T , 1260) C  1260  FORMAT(2X,'NUMBER IE CR. LENGTH  OF  TREES CW  C.  HEIGHT AREA  DBH  6.A. C R . BAS V O L U M E *)  C  1270  WRITE(IOUT,J270)NEWTR,HTS,DBHS,BAS,CBS,CLS,CWS,AREAS,VOLS FORMAT(7X,I3,5X,7Fll,2,F22,2) LOBTR«NUMTk-NEWTR  C  1280  WRITE(IOUT, 1280)LOSTR FORMAT('0',2X,'NUMBER  OF TREES  HAVING  DIED  SINCE  YEAR  1«',I5)  C  1290  WRITE (IOUT, 1 2 9 0 ) FORMAT(////,5X,'STAND AVERAGES',//,2X,'NUMBER 1 DBH B,A. « T , CWM C R . L E N G T H 2A, AS X VOLUME',/)  OF T R E E S C.W.  C,  HEIGHT AREA C.  C  1300  WRITE(IOUT, 1300)NEWTR,AHT,AOBH,AbA,ACB,ACL,ACW,AAREA,AAPER,AVOL F0RMAT(6X, I 3 , 5 X , 9 F l l , 2 )  C  C C C C C  C A L C U L A T E S CROWN A R E A S AND CROWN C L O S U R E S F O R S U B S E T S S U B S E T S FORM B A S I S FOR E V A L U A T I O N OF SHRUB AND GRASS R E S P O N S E STAND CONDITIONS  TO  139  1310  DO  1330 I«l,66  C  1320  00 1 3 2 0 J * i , 6 6 JARRACI,J)=0  C  DO  1330 1=1,66  C  1330  DO 1 3 3 0 J « l , 6 6 NEWslARRACI,J)/100*100 J A R R A ( I , J ) » I A R P A ( I # J ) - N E W  SUB1*0  1340  SDB2*0 3U6330 SUB4*0 ISUBS0 ISUBalSUB+1 GO T O ( 1 3 5 0 , 1 3 7 0 , 1 3 9 0 , 1 4 1 0 ) , I S U B  C  C  SUBSET  1350  DO  1360  DO  1360 J»l,33  c c  #  1  **  1=1,33/  J=l,33  **  1*1,33  C NBOJAWRA ( I , J )  1360  IF(NB.GE.l) CONTINUE GO T O 1 3 4 0  SU61«SUB1+1  C  C  SUBSET  #2  **  I  •  1,33;  J  •  34,66  **  C C  1370  DO  1380  l a l , 3 3  DO  138a  J*34,66  C  NB»JARRA(I,J)  1380  IF(N6,GE.l) CONTINUE GO T O 1 3 4 0  SU62BSUB2+1  C  C  SUBSET  # 3  *#  I  * 34,66;  J  •  1,33  J  a  34,66  **  C  1390  DO  1400  1*34,66  C  1400  DO 1 4 0 0 J = l , 3 3 NQsJARRA(I,J) IF(Nd.GE.i) SUB3BSUB3+1 CONTINUE GO T O 1 3 4 0  C  C  SUBSET  # 4  **  I  *  34,66;  *»  - 140 -  c  1410 C  1420  DO 1 4 2 0 1 * 3 4 , 6 6 DO 1 4 2 0 J » 3 4 , 6 6 NBiJARRACX,J) I F ( N B , G E , 1 ) SUS4*SUB4+1 CONTINUE C8U8l"SUBl/1089 *100, CSUB2aSUB2/1089,*100, csua;jaoU:33/i089, M 0 0 , CSU84*3UB4/1089, * 1 0 0 . t  c 1430 C  WRITECIOUT,1430) F O R M A T c / / / / , 5 X , 'CROWN AREA AND CROWN C L O S U R E S FOR S U B S E T S ' , / / / )  WRITE ( I O U T , 1 4 4 0 ) 1440 F0RMATC12X, 'SUB-PLOT 1 - 1*1,33 J * 1,33',2X,'SUB-PLOT 2 - 1*1,33 1 J « 3 4 , 6 6 ' , 2 X , ' S U B - P L O T 3 - I « 3 4 , 6 b J« 1 , 3 3 • , 2 X , ' S U B - P L O T 4 - 1 * 3 4 , 6 6 2 J»34,66',//) C WRITE(IOUT, 1450)SUB 1,SUB2,SUB3,SUB4 1 4 5 0 FORMAT ( I X , ' C R O W N AREA « ' , F 1 5 , 2 , 3 F 2 9 , 2 , / / ) C WRITE ( I O U T , 1 4 6 0 ) C S U B 1 , C S U B 2 , C S U B 3 , C S U B 4 1 4 6 0 F O R M A T ( I X , ' C R O W N C L O S U R E " ' , F 12 . 2 , 3 F 2 9 , 2 ) I F ( L I N P R . L E . 0 ) GO TO 1 4 6 3 C CALL XSECT ( L I N P R ) 1 4 6 3 I F ( I D E L A G L E , 0 ) GO TO 4 6 0 C C A L L AGROP GO TO 4 6 0 1470 IF(ITRFN-l)1490,1490,1480 C 1480 CALL TRFUN 1490 RETURN END (  -  SUBROUTINE C C C  PRINTS  XSECT  VERTICAL  141  -  CLINPR) X  SECTION  THROUGH  STAND  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 I A R R A , 8 L 2 , A C C , A T A , A T G , A T F , A P D N A , A P D N C , A P D N S , A P D N P R , A P D N R O , A 1PDNSY,CSU81,CSUB2,CSUB3,CSUB4,RAD,B0RDA,X INA,UTILA,BORDC,X INC,UTIL 2 C B O R D S , X I N S , U T I L S , A G E , C , CC , T A U T , T A U T S , T A U T T , T A U O , U N O C C , Y U N O C C P D N 1,I THRU,M,ISTRT,11 N T , I E N D , I Y U N O C , I A U T T Y , I U N O C C , I L O O P , I X , I S U B , I C 0 U N T 3,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 7 D , L R A N D , J A M E L , J C E O N , J S H E P , J P R U N , J R O S E , J S Y M P , E P E R , N N A M E L , N N C E O N , NNS 8HEP,NNPRUN,NNROSE,NNSYMP,JCHAR C C  C C C C  JLOC a L O C A T I O N ON LINE ILINE a LINE ISCLE a SCALING FACTOR NB a C H A R A C T E R TO BE PRINTED  C  c ICUTab  ISCLEaa C  991  DO  992  KCL«1,66  C DO  992  992 JCLal,66 JARRACKCL,JCL)a0 DO 9 9 3 JL0C"1,66 I L I N E a i A R R A U l N P R ,  JLOC)  NaILINE-ILINE/100*100 I L O C a ( I L I N E +5000/ 10000* 1 0 0 0 0 - 1 000000k)) / 1 0 0 0 0 IFCXLOC.LT.i) ILOCal IF(ISCLE.GT,0)  GO  TO  IFfILQC.GT.66) ISCLEa2 IF(ISCLE-1)994,994,991  995  -  994 995  142  JARRACILQC,JLOC)»N GO T O 993 IL0CB(IL0C+1)/2  IFCILOC.LT.1) I L Q C M JARRACILOC,JLOC)»N 993  CONTINUE  C DO  998  J«l,66  C 996 997 998  DO 9 9 8 1*1,66 NBsJARRACI,J) IF(NB)997,997,996 NB • 9 9 JARRACI,JJsICHARCNB)  C  981  WRITE(I0UT,981)LINPR FQRMAT('1',////,20X,'CROSS-SECTIONAL 1HR0UGH L I N E ',12,///) I F C I S C L E . G T . 1 ) GO T O 987  PROFILE  OF  STAND  -  SECTION  T  C 982  WRITECI0UT,982) FORMAT(63X, 'VERTICAL SCALE 1ALE - I F T . B 2 SPACES',///) GO T O 968  IFT•  «  1  LINE*,//,58X,'HORIZONTAL  SC  C 987 983  WRITECI0UT,983) FORMATC60X,'VERTICAL SCALE 1LE - I F T , » 2 SPACES',///)  988 964  WRITECI0UT,964) F0RMATC63X,'LEGEND',//,65X,'NUMBERS R E F E R TO T R E E IB R E P R E S E N T S BOLE P O S I T I O N ' , / / / , 1 2 6 X , ' L I N E S ' )  -  2FT,  *  1  LINE',//,58X,'HORIZONTAL  SCA  C  C DO 9 8 5 K»67-X  I«l,66  C 965 986  WRITECIOUT,966)CJARRA(K,J),JB1,63),K F0RMATC'9',63A2,I2)  C 971  WRITE(I0UT,971) FORMATC»9»,131C'*')) RETURN END  NUMBER',//,65X,•  -  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, L A R R 1 ( 6 6 , 6 6 ) , I A R R 2 ( 6 6 , 6 6 ) , L A R R 3 ( 6 6 , 6 6 ) , I A R R 4 ( 6 6 , 6 6 ) , I A R E A ( 1 5 3 ) , I D 71 A M I ( 1 5 0 ) , I D I A M 2 C 1 5 0 ) i I D I A M 3 ( 1 5 0 ) , I D I A M 4 ( 1 5 0 ) , P E R ( 1 5 3 ) , E P E R ( 1 6 ) , K A 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 4 M , J C O M , I D E A D 1 , I D E A D 2 , I D E A D 3 , 1 D E A D 4 , I D I AM 1 , I D I A M 2 , I D I A M 3 , I D I A M 4 , J J R 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 C C C C C C C C C C C C  L A R R 1 , , ,4 B SHRUB,GRASS * FORB GROWTH ARRAYS ITMRU » COUNTER KCHAR * SHRUB NUMBER EPER • E X P E C T E D P E R I M E T E R OF SHRUBS ID1AM1,,,4 a SHRUB DIAMETER I D E A D 1 , , . 4 • DEAD SHRUBS LAMEL,..,LSYMP " VARIABILITY I N S I Z E OF SHRUB SPECIES NNAMEL,•t,NNSYMP * N U M B E R OF S H R U B S BY S P E C I E S / S U B - P L O T Z E R O A R R A Y S F O R P R I N T I N G # S H R U B S AND P R O D U C T I O N , A G E , CROWN CLOSURE JRAND, ,.,I.LRANO » SHRUB S P E C I E S GROWTH P O T E N T I A L I A R E A , A R E A S , A A R E A S a CROWN A R E A MEASUREMENTS IRDaS IOUT«6  C  3  DO 3 I=l,b6 DO 3 J a l , 6 6 JARRA(I,J)30  C I F ( I T H R U . G T , 0 ) GO T O I F ( M , G T , 0 ) GO TO 1 5 0 C READ(IR0,2)EPER  150  -  2  FORMAT (1613)  4  REA0(IRD,4)KCHAR F O R M A T (4flA2)  144  -  C  C  DO 5 I « i , 1 5 0 IDIAMl(I)a0 I0IAM2CI)»0 IDIAM3(I)»a  5  I D I A M 4 ( I J 80 I D E A Q 1 CD 30 IDEA02CI)a0 IDEAD3(I)80 IDtAD4(I)80  C  DO  7  Ial,6fe  C  7  UO 7 J a i . f e e LARR1(I,J)s0 LARR2 (I,J)80 UARR3 ( I , J ) 8 0 L A R R 4 ( I , J ) s 0  10  READ(IRD,10) FORMAT(61b)  15  READ(IRD,15) P0RMAT(2I3)  20  READ(IRD,20)IDD FORMAT(13)  C  C  LAMEL,LCEON,LSHEP,LPRUN,LROSE,LSYMP  I SHRUB,INDISH  C  C  DO  30  I«l,4  C  30 40  READ(IRD,40) 1YMP(1) F0RMAT(6I4)  C  00  45  Ial ,  4  C  DO 4 5 Jal,21 ACC(I,J)a0, ATA(I,J)80, AT6(I#J)«0. A T F ( I , J ) a 0 , APDNA(I,J)80, APDNCCI,J)80, APDNS(I,J)80, APDNPRCI,J)a0, APDNRO(I,J)ag, APDN5Y(I,J)80,  NMAMELCI),NNCEON(I),NNSHEP(I),NNPRUN(I),NNROSE(I),NNS  -  145  KAMELCI,J)"0 «CEQN(I,J)*0 KSHEPC1,J)«0 KPRUNCI,  4b C C C  J)B0  KROSECI,Ji«0 KSYMPCI»J3«0 CALCULATE  SHRUB  SPECIES  GROWTH  VAM EL L AHE L VAHEL«VAMEL/10000. a  vceoNaLceoN  VCEON"VCEON/10P00, VSHEP«LSHEP VSHEPsVSHEP/10000.  VPRUN«IPKUN VPRUNsyPHUN/10000, VROSE*LROSE VROSEaVROSE/10B00. VSYMPs^SYMP VSYMP»V8YMP/10000,  C  60  D O 6 0 1 * 1 ,50 CALL GAUSS (iX,VAME!_, IFCV,LT,,1) V * . l IF(V.GT.i,b) Vsj.b JRANDCI)«V*1000.  70  DO 7 0 1*1,50 CALL GAUSS (IX,VCEON,1,0000,V) IFCV.LT..1) V " . l IF(V.GT.l.b) V*1.6 KRAND(I)aV*1000,  1,0000,V)  C  C  C  DO  8a  1*1,50  80  CALL GAUSS (IX,VSHEP,1,0000,V) I F ( V , L T . . l ) V * . l IF(V.GT.l.b) Val,6 LRAND(I)BV*1000,  90  DO 9 2 1*1,100 CALL GAUSS (IX,VPRUN,1,0000,V) I F ( V , L T , . l ) V a . l IF(V.GT.l.b) Val.b J J R A N O ( I ) " V * i 0 0 0 ,  100  DO 100 1*1,100 CALL GAUSS (IX,VKOSE,1,0000,V) IFCV.LT..1)Va.l IFCV.GT.1.6) Val.6 KKRAND(I)*V*1000«  C  POTENTIAL  - 146  C  110  DO 1 1 0 1 * 1 , 1 0 0 CALL GAUSS (IX,VSYMP,1 .0000,V) IFCV.LT.,1) V * . l IP(V.GT.1.6) V*1.6 LLRAND CI)*V*1000•  130 140  READCJRD,140)PDN FORMAT C 6 » 2)  C C p  C 150 160  WRITECIOUT,160) F O R M A T ( 2 X , ' N U M B E R OF S H R U B S BY S P E C I E S AT AGE 1' , / / , T 2 4 , ' A M E L ' , T 3 4 1, ' C E Q N ' , T 4 4 , ' S H E P ' , T 5 4 , ' P R U N * , T 6 4 , * R O S E ' , T 7 4 , ' 5 Y M P ' , / / )  C DO  170  1*1,4  C 170 180  WRITECIOUT, 180)I,NNAMELa),NNCEON(I),NNSHEPCI),NNPRUN(I),NNROSE(I) 1,NNSYMP(I) FORMATC2X,'SUB-PLOT*',12,5X,6110)  C C ISUB*0 C C C  INCREMENTS 190  SUB-SETS  ISijB*ISUB +l IF(ISUB.GT,4) GO T O NAMEL*NNAMEl. CISUB) NCEONeNNCEON(ISUB) NSHEP*NNSHEP CISUB) NPRUN*NNPRUN CISUB) NROSE*NNROSECISUB) NSYMPaNNSYMP(ISUB)  4000  C ITAsNAMEL I F C M , G T , 0 ) GO T O 199 WRITECIOUT,203)ISUB,M GO TO 210 C 199 200 210  WRITE(IOUT,200) ISUB,NAGE(M) FORMATC'l',2X»126C'*'),//,5X,'SUB-PLOT 1 * M 5 ) CONTINUE  C DO  220  1*1,66  C 220  DO 2 2 0 J * l , 6 6 JARRACI,J)*0 I F C I T H R U , G T . 0 ) GO TO 430 I F C I S U d . G T . 1 ) GO TO 430  •',15,10X,15C»*'),10X,'AGE  C C C  ASSIGNS 280  290  SHRUB  -  147  GO GO  TO TO  -  LOCATIONS  00 290 X M , 1 5 0 CALL RANDU CIX,lY,YFL) I C 0 M ( I ) i Y F L * 6 5 . + l , IXalY CALL RANDU (IX,IY,YFL) J C 0 M ( I ) a y F L * 6 5 , + l , IX"IY  C i00  ICHKSB0  C DO  320  181,150  C  310  320  DO 3 2 0 J B 1 , 1 5 0 I F ( I . E Q . J ) GO T O 3 2 0 IF(ICOMtl).NE.ICOM(J)) IF(JCOMCI).NE.JCOM(J)) IXL"JCOM(J) C A L L R A N D U C I X , I Y »Y F L ) JC0M(J)»YFL*65.»1. IXalY IF(JCOM(J).EG.IXL) ICHKS"1 CONTINUE  GO  TO  320 320  310  C IFCICHKS.GE.I) C C C C C C C C C  SHRUB MORTALITY AMELANCHIER CEONOTHUS SHEPHERD IA PRUNUS ROSA SYMPHORICARPOS 430 431  GO  TO  DUE  300 TO  SHADING  WRITE(I0UT,431) FORMAT£2X,'MORTALITY DUE I F ( l T A , E a , 0 ) GO TO 4 8 1 INUM«0  TO  C DO 4 8 0 l 8 l , I T A K«ICOM(X) L « J C O M C D INUM8INUM+1 C 435  GO T O (435,440,445,450),ISUB I I s ( K * l ) / 2 LARR1£K,L)"151  TREE  SHRUB C O M P E T I T I O N ' , / / )  -  440  148  -  GO TO 455 II«CK*l)/2 JJ»CL+l)/2*33 LARR2 CK,L) 151 GO TO 455 IIBCK+1}/2+33 JJB(L*1)/2 LARR3CK,U)al51 GO TO 455 II=(K + l)/24.33 JJ»(L+l)/2+33 LARR4CK,L)»15i IF (CZARRA C U tJJ)-10000000).EQ.0) INUMslNUM-1 8  445  450  455  GO  TO  480  C 460  465  GO T O C460,465,470,475),ISUB IDEAD1CI)«1 LARR1CK,L)»0 GO T O 480 IDEAD2CI)"1 LARR2 CK,L) 0 GO T O 480 IDEAD3(I)al L A R R 3 CK, L ) " 0 GO TO 480 IDEAD4(I)«1 LARR4 CK,L)a0 CONTINUE IKILLAalTA-INUM NAMELaNAMEL-IKILLA WRITECI O U T , 2 0 5 0 ) I S U B , I K ILLA,NAMEL 0 F0RMATC2X,'SUB-PLOT «',12,5X,*NO, la*,12) B  470  475 480  205 C  481  c  ITC°50+NCEON IF(ITC.EQ,50) INUMB0  GO  TO  545  DO 5 4 0 I s 5 l , I T C KalCQM(I) LaJCOMCD INUM«INUM+1 C  485  GO T O C485,490,495,500),ISUB IX»(K*l)/2 JJBCL+1)/2  490  LARR 1 C K i L ) a 152 GO T O 510 I I a ( K * l ) / 2 JJ«CL*l)/2+33 LARR2CK,L)»152  AMEL.  DEAD.  » ' , 1 2 , 5 X , 'NO.  AMEL•  .  GO 495  500  149  -  TO 510 IIB(K*1)/2+33  LAKR3(K,L)*1S2 GO T O 510 II«(K+l)/2*33 JJ"(L+l)/2+33 LARR4(K L ) 1 5 2 IF( ( I A R R A d l , JJ)-10000000) INUM«INUM-1 S  510  ,EQ.0)  GO  TO  540  C GO 515  520  TO  (515,520,525,530),ISUB  I0EADI(I)»1 LARR1 (K,L)80 GO T O 540 IDEAD2(I)«1 LARR2(K,U)a0 GO T O 540  525  I0EA03CZ}"1 LARR3(K,L)80 GO T O 540 530 l'OEAO«(I)«J LARR4(K,L) 0 540 CONTINUE IKILLCaNCEON-INUM NCEONSNCEON-IKIILC WRITE (IOUT, 20S0) ISUB, IKILLCNCEON 2060 FORMAT(2X, 'SUB-PLOT • ',12,5X,'NO, I M S ) a  C 545  ITS»100*NSMEP IF(ITS,EQ,100)  GO  TO  602  C  INUM80 DO 6 0 0  Z«iei»ITS  M I C Q M ( I ) LBJCOM(I) INUMBlNUM+1 C  c 550  560  565  GO TQ (550,560,565,570),ISUB I I - C K + D / 2 JJB(L*1)/2 LARR! (K,L)8153 GO T O 575 IX"CK*t)/2 JJ»Cl+l)/2*33 LARR2(K,L)B153 GO TO 575 IIB(K*1)/2t33 J J B ( L M ) / 2  CEON.  DEAD  "',12,5X,'NO,  CEON,  •  - 150 -  570  575  LARR3 (K,L)a 153 GO TO 5 7 5 XI»(K*l)/2+33 J J s ( L +n / 2 +33 L ARR4(K » L)•153 I F (( I A R R A ( I I , J J ) - 1 0 0 0 0 0 0 0 ) , E Q , 0 ) INUM"lNUM«l  GO  TO  600  C 580  GO T O (580,565,590,595),ISUB IDEAD1(I)*1 LARR1(K,L) 0 b  565  590  GO T O 6 0 0 IDEA02CI)"1 l . A R R 2 ( K , L ) =0 G O TO 6 0 0 IDEA03(I.)»1 UARR3(K,L) 0 GO TO 6 0 t ) IUEAD4(I)«1 LARR4(K,L)a0 CONTINUE a  595 600 C  IKILLS=NSH£P-INUM NSHEPsNSHEP-IKILLS C WRITE ( I O U T , 2 0 7 0 ) I S U 8 , I K  2070 602 605 610 615 620 625  635 670  C C C  ILLS,NSHEP  FORMAT(2X,'SUB-PLOT a ',12,5X,'NO, S H E P , D E A D • ' , 1 2 , 5 X , 'NO• i«',i2) GO T O (605,610,615,620),ISUB CCaCSUBi GO T O 6 2 5 CC«CSUB2 GO T O 6 2 5 CCaCSUB3 GO T O 6 2 5 CCaCSUB4 CONTINUE C»CC WRITE(I0UT,635) CC F Q R M A T ( / / , 1 0 ( ' * ' ) , 5 X , 'CROWN C L O S U R E a',F6.2,5X,10C '* ' ) ) IF(CC,GT.?4.5) CC*74,5 IF(CC.LE,0) CCB,01 IF(M,EQ,0) GO TO 6 9 5 DETERMINES  NO.  OF  CEONOTHUS  AS  A  FUNCTION  OF  CROWN  I F ( N A M t L , E Q . 0 ) GO TO 6 7 5 MAMELa8,-.10606*CC +19,*((75.-CC)**2.5/75,**2,5)+.5 IF(NAMEL.GT.MAMfcL) NAMEL MAMEL ITAaNAMEL+IKILLA B  C  CLOSURE  SHEP,  m 151*  C C  DETERMINES 675  N O . OK A M E L A N C H I E R  DETERMINES 680  C C C  C C C C  C C C 690  C C C  NO. OF SHEPHERDIA  AS A FUNCTION  O F CROWN  CLOSURE  NO. OF PRUNUS  AS A FUNCTION  O F CROWN  CLOSURE  NO, OF ROSES  AS A FUNCTION  O F CROWN  CLOSURE  IFCCC.GT.65.) NROSE"0 IF£NROSE,EQ,0) GO T O 6 9 0 MR0SEB7,-.il67*CC+9,*£(b5,-CCD**2./65.**2.)+,5 IF(NROSE.GT.MRCSE) N«OSE*MRCSE  D E T E R M I N E S NO. O F S Y M P H O R I C A R P O S I F ( C.GT.90.) NiSYMP«0 I F ( N S Y M P . E Q . 0 ) GO T O 6 9 5 MSYMP»35,-,38889*C+,5 IF(NSYMP.GT.MSYMP) NSYMPeMSYMP SETS  695  +50  IF£CC.GT,65.) NPRUN»0 IF(NPRUN.EG.0D GO T O 6 8 8 MPRUNB7,-, 1 1 6 7 * C C * 9 . « ( ( 6 5 . - C C ) * * 2 . / 6 5 . * * 2 . ) + . 5 IF (NPRUN.GT.MPRUN) NPRUN«MPRUN  DETERMINES 688  CLOSURE  I F C N S H E P . E Q . 0 ) GO T O 6 8 5 M S H E P » 8 . - , 1 0 6 0 6 * C C +19.*C ( 7 5 . - C C ) * * 2 , 5 / 7 5 . * * 2 . 5 ) • . 5 I F C N S H E P . G T . M S H E P ) N S H E P BMSHEP ITSaNSHEP+IKILLS + 100 DETERMINES  685  O F CROWN  I FCNCEON.EQ.0D CO TO 6 8 0 MCE0NB8.-.10606*CC + 1 9 . * ( £ 7 5 , - C C J * * 2 . 5 / 7 5 , * * 2 . 5 ) + , 5 IFfNCEON.GT.MCEON) NCEONaMCEQN ITC8NCEON+IKILLC  C C C  AS A FUNCTION  BORDER,  AS A FUNCTION  O F CROWN  INSIDE  AND TOTAL  AREA  OF AMELANCHIER  INSIDE  AND TOTAL  AREA  OF C E O N O T H U S  INSIDE  ANO TOTAL  AREA  OF S H E P H E R D I A  TO  ZERO  BORDA80. XINA«0. UTILA80.  C C C  SETS  BORDER,  TO  ZERO  BQROC80. XINC80, UTILC80.  C C  SETS  BORDER,  C  BORDS80,  TO  CLOSURE  ZERO  152  -  XI.NS"0, UT1LS 0. B  C C C C  SETS  PRODUCTION OF A M E L A N C H I E R , ROSE AND SYMPHORICARPOS TO  PDNA"0. PDNCa0, PQN5S0. PDNPR«0, PDNRO*0. PDNSYS0. IFCM.EQ.fl) GO TO AGEaNAGE £M) XDIAM80,  CEONOTHUS, ZERO  SHEPHERDIA,  PRUNUS,  2000  C 699  WRITE (IOUT,699)I SUB,NAMEL,NCEON,NSHEP,NPRUN, NROSE , NSYMP FORMAT(//,5X,'SHRUB #.S S U R V I V I N G I N UNSHADED AREA ' , / / , 5 X , ' S U B - P L O IT a',i5,2X,»* AMtL C E O N »',lS,2)(t'# SHEP B',I5,2X,'# P 2RUN 8',I5,2X,'# ROSE B',I5,2X,'# SYMP a',15,///)  ••,I5,2Xi'#  C  c c C C C C C  I D I A M 1 ( I ) , , , 4 CI)  AMELANCHIER  a DIAMETER  OF INDIVIDUAL  CALCULATIONS  NCOUN1a0  c  7 4 5  DO  1=1,  C 700  705  710  715 720  GO T O ( 7 0 0 , 7 0 5 , 7 1 0 , 7 1 5 ) , I S U B IF(NCOuNl.GE.NAMEL) IDEADl(I)»i I F C I O E A U 1 CI) . E Q . l ) GO TO7 4 5 GO T O 7 2 0 IF(NC0UN1,GE.NAMEL) IDEA02(I)»1 I F ( I 0 E A D 2 ( I ) . E U , 1 ) GO TO 7 4 5 GO T O 7 2 0 IF(NCOUN1.GE.NAMEL) IDEAD3(I)*1 I F ( I D E A D 3 ( I ) . E Q . l ) GO TO7 4 5 GO T O 7 2 0 IF(NCOUNl.GE.NAMEL) IOEA04(I)«l I F ( I D E A D 4 ( I ) . E Q . l ) GO T O 7 4 5 NCOUN1BNCOUN1+1 RANOJBJRANO ( I )  7 25  RA X2 IF X I GO  N a ( a  DJ«RANDJ/1000, «l,*30,**i,996 AGE-30,)725,730,730 - l , * ( - 1 .* ( A G E - 3 0 . ) ) * * 1 , 9 9 6 TO7 3 5  SHRUBS  -  153  730 735  Xls(AGE-30.)**1.996 D l A M a R A N D J * ( - 1 , • , 1 5 * A G E * 1, * £ X 1 / X 2 ) )  737  60 TO £737,739,741,743),1SUB IDIAM1£1)aDlAM*100,  C  739 741 743 745 C C C  GO T O 745 IDIAM2CI)aDlAM*100, GO TO 745 IDIAM3CI)8OIAM*100, GO TO 745 IDIAM4£I)8DIAM*100, CONTINUE CALCULATES  755  DIAMETER  OF  CEONOTHUS  NCQUN280  C DO  805  1=51,100  C 760  763  769  772 775  780 785 790 795 805 C C C  GO T O £760,763,769,772),ISUB IFCNCQUN2.GE.NCE0N) IDEADl£I)»l I F C I D E A D 1 ( I ) , E Q , 1 ) GO T O 805 GO T O 775 IF(NC0UN2.GE,NCE0N) I0EAD2(I)"1 IF(IDEAD2£I).EQ.l) GO T O 805 GO TO 775 IF£NC0UN2,GE,NCE0N) IDEAD3£I)»1 IFCIDEAD3(I),E0,1) GO T O 805 GO TO 775 IF(NC0UN2,GE.NCE0N) I D E A D 4 f I ) M IF£IDEAD4£I),EQ,1) GO T O 805 NC0UN2»NC0UN2+1 RAND*»KRAND £I«50) RANDK«RANDK/1000, DIAM"RANOK*C5,5*TANH£AGE*,03)) GO TO £780,785,790,795),ISUB IDIAM1(I)»DIAM*100, GO T O 805 I0IAM2CI)8OIAM*100, GO T O 805 I 0 I A M 3 C D 8OIAMH00, GO TO 605 IDIAM4CI)8DIAM*100, CONTINUE SHEPHERDIA  810  CALCULATIONS  NCOUN3«0  C 00 GO  865 TO  18101,150 £615,820,825,830),ISUB  -  815  820  625  830 835  IF£NC0UN3,GE.NSH IFCIDEA01 (I).EQ. GO T O 8 3 5 IFCNC0UN3.GE.NSH 1FCIDEAD2CI).EQ.  154 *  EP) Z D E A D 1 C15) • 1 l ) GO TO 8 6 5 EP) IDEAD2£I)8l l ) GO TO 8 6 5  GO T O 8 3 5 IFCNC0UN3.GE,NSHE IF(IDEAD3CI).EQ.l GO T O 8 3 5 IFCNC0UN3.GE,NSHE IF CIDEAD4 (I).EG.1 NCQUN3sNCQUN3+l  P) IDEAD3CI)* 1 ) GO T O 8 6 5 P) IDEAD4(I)»i ) GO T O 8 6 5  RANDL»tRANDCI«100) RANOUBRANDL/1000, IFCAGE.LT.28,) DIAM*RANDL*C.16*AGE) I F ( A G E , G E 2 8 . ) D I AM>R A N D L * C 5 , + 2 .5 * T A N H C ( A G E - 2 8 ,) * ,0 3 3 ) ) t  C  645 847 849 851 853 865  GO TO (647,849,851,853),ISUB IDIAM1(I)=DIAM*100. GO T O 8 6 5 IDIAM2(I)=DIAM*100, GO T O 8 6 5 IDIAM3CI)aDIAM*100. GO T O 8 6 5 IDIAM4CI)»DIAM*100, CONTINUE  C 870  880 C  CONTINUE  ICOUNTB0 ICOUNTsICOUNT+1 S T A R T S NEW S H R U B IF(ICQUNT.GT.ITS)  GO  TO 997  C  C C C  C A L C U L A T E S SHRUB RADB RADIUS  885  RADIUS  GO T O £865,690,895,900),ISUB I F ( I O E A D l C I C O U N T ) . E Q . l ) GO T O 8 8 0 I F d D l A M l ( I C O U N T ) ,EQ.0) GO TO 6 8 0 RADBIDIAMI(ICOUNT) RADaRAQ/200, IIXBICOM(ICOUNT) JJX»JCOM(ICOUNT)  890  GO T O 9 0 5 IF(IDEAD2(IC0UNT).EQ.l) IF(I0IAM2(IC0UNT).EO.0) RADsIDIAM2(ICOUNT) RADaRAD/200, IIXBICOM(ICOUNT) JJXSJCOM(ICOUNT)  GO  TO 9 0 5  GO GO  TO 8 8 0 TO 8 8 0  -  155  895  I F I I U E A 0 3 C X C 0 U N T ) ,EQ,1) IF(IDIAM3(IC0UNT),EQ,0) HA0-I0IAM3CIC0UNT) RADaRAD/200, IlX»ICQM(ICOUNT) JJXaJCOM(ICOUNT) GO TO 905  900  I F ( I D E A D 4 ( I C 0 U N T ) , E Q . l ) GO T O 680 1 F ( I 0 I A M 4 ( I C 0 U N T ) . E Q . 0 ) GO T O 880 RAD«IDIAM4(ICOUNT) RADaRAD/200, IlX«ICOM(ICOUNT) JJXaJCOMUCOyNT) CONTINUE I F ( I S H R U 8 , G T , 0 ) GO T O 995 IFCICOUNT.GT,50,AND.ICOUNT.LE,100) IFCICOUNT , G T , 1 0 0 ) GO T O 920  905  GO GO  TO TO  -  880 680  60  TO  910  C 906  WRITE(IOUT,906)ICOUNT,RAD,ICOMCI COUNT),JCOM(ICOUNT) FORMAT(2X,'AMEL # a',14,5X,'RADlUS IN F T . a ' , F 8 , 2 , 5 X , » I L O C IX,»J LOC a',15) GO T O 995  a',15,5  C 910 915  WRITE(IOUT,915)I COUNT,RAD,ICOM(ICOUNT),JCOM(ICOUNT) F O R M A T ( 2 X , ' C E O N # a ' , 1 4 » 5 X , ' R A D l U S I N F T . "< ' , F 8 , 2 , 5 X , * I L O C IX,»J LOC a',15) GO T O 995  920 925  W R I T E ( I O U T , 9 2 5 ) ICOUNT,RAO,I COM(ICOUNT),JCOM(ICOUNT) FORMAT(2X,'SHEP # "',14,5X,'RADlUS IN F T , « ' , F 8 , 2 , 5 X , ' I L O C I X , * J LOC a',15)  a',15,5  C  C C 995  a',15,5  SHRUB GROWTH CALL BRANCH GO T O 880  C 997 998 C C C C C  DO 9 9 8 1=1,153 IAREA(I)sl PER(I)s0 SHRUB REMOVAL CALL REM SHRUB  AREA  IF  DEAD  CALCULATION  CALL AREA (NAMEL,NCE0N,NSHEP,NPRUN,NROSE,NSYMP,PDNS,PDNA,PD 1NC,PUNPR,P0NR0,PDNSY,IN01SH) C C  PRODUCTION C A L C FOR SHRUBS, GRASSES & FORBS CALL SGPON (NAMEL,NCEON,NSHEP,NPRUN,NROSE,NSYMP,PDNS,PDNA,PD 1NC,PDNPR,PDNR0,PDNSY,INDISH)  -  2000  156  -  C A L L SUM (NAMEL,NCEON,NSHEP,NPRUN,NROSE,NSYMP,PDNS,PONA,PD 1NC,PDNPR,PDNRO,PDNSY,INOISH) IFCISU8.LE.3) GO T O 190 I F ( I D D . L E . 0 ) GO T O 3900  C C  PRINTS  c  3600  3700  MAPS  DO 3 6 0 0 l a DO 3 6 0 0 j a NBaLARRlCI IFCNB.EO.B JAHRACIfJ)  ,66 ,66 J) NBal54 KCHAR(NBJ  WRITE(IOUT  37003  FORMATC'l* DO  3800  SHRUB  3800  l a  WRITECIOUT WRITECIOUT IFCIDD.LE, DO  2X,'SUB-PLOT  38503  3701  WRITECIOUT 3701) FORMAT C'1' DO  3601  l a  C 3801 C  WRITECIOUT  MAP',//,1X,130 ('* ') )  (JARRA(I,J),J*l,64)  3889) ) GO T O , 66 ,66 J) NBal54  3601  C  1', / / , 2 X , ' S H R U B  ,66  3601 13601 Ja NBaLARRSCI IFCNB.EO.0 JARRA(I,J)  00  #  3900  KCHAR(NB)  2X,'SUB-PLOT  #  2',//,2X,'SHRUB  MAP',//,1X,130('*'))  ,66  3850) (JARRA(I,J),jai,64) WRITE(IOUT I F ( I D D . L E , 2 ) GO T O 3900 3889) OQ 3 6 0 2 I * , 6 6  c c 3602  3702  DO 3 6 0 2 J a NBaLARR3CI IF(NB,EQ.0 JARRA(I,J)  ,66 J) N8=154 KCHAR(NB)  WRITECIOUT FORMATC'l' 3702) DO 3 8 0 2 1= 2 X , ' S U B - P L O T ,66  #  3',//,2X,'SHRUB  MAP',//,1X  »130('*'))  157  C C  3802  C C  WRITE(IOUT,3850)(JARRA(I, J),J»1» WRIT£(I0UT,3889) IF(IDD,LE,3) GO T O  C  3603  -  64)  3900  DO 3 6 0 3 181,66 DO 3 6 0 3 J * l , 6 6 NB«LARR4(I,J) IF(NB,£Q.0) NB«154 JARRA(I,J)s»KCHAR(NB)  3703  WRITE(IOUT,3703) F0RMAT('1',2X,'SUB-PLOT DO 3 6 0 3 I M , 6 6  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  #  4»,//,2X,'SHRUB  MAP',//,1X,130('*'))  *  158  -  SUBROUTINE AREA (NAMEL,NCEON,NSHEP,NPRUN,NROSE,NSYMP,PONS,PONA,PD 1NC,PDNPR,PDN«0,PDNSY,INDISH) DIMENSION I A R R A ( 6 6 , 6 6 ) , 8 L 2 ( 9 6 ) , A C C ( 4 , 2 l ) , A T A ( 4 , 2 i ) , A T G ( 4 , 2 l ) , A T F ( 4 1,21),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 A M I ( 1 5 0 ) , I O I A M 2 ( 1 5 0 ) , I D I A M 3 ( 1 5 0 ) , I D I A M 4 £ 1 5 0 ) , P E R f 1 5 3 ) , E P E R £ 1 6 ) , K A 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 I F £ A G E » E G ,0) OCCUPATION DO  1000  1041  1006  OF  TO  AREA  2000 BY  SHRUBS  1=1,bb  00 1040 J»i,bb K s j - l XF(K,EQ,0) K«b6 L"I-1 XF(L.EO,0) L«66 GO T O (1000,1010,1020,1030),ISUB 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)  IF(NB.EO,0) 1003  GO  60  TO  PER(NB)«PER(NB)+l IFCLARR1(I,J).NE.0.AND.LARR1£I,K),GT,0) I F £ I B , E Q , 0 ) GO TO 1006 PER£IB)«PER(I8)+1 IF(LARR1(I,J).GT.0.AND.LARR1(L,J).NE.0)  IF(N8,EQ,0)  GO  TO  GO  TO  1003  GO  TO  1006  GO  TO  1009  1003  1009  159  -  PERCNB)BP£R(NB)<H  1009  1010  I F U A R R 1 CI,J) .NE.0. AND.LARR1 U ,J) .GT.0) I F C J B . E Q . 0 ) GO T O 1 0 4 0 PER(JB)*PER(JB)*1 GO T O 1 0 4 0 NB«LARR2(X,J) JB»LARR2CL,J) IBs|_ARR2CI,K) IFCNB.GT.0) IAREACNB)"IAREACNB)+1 I F C U A R R 2 C I , J ) , G T , 0 . AND, L A R R 2 C I , * ) , N E , 0 ) I F C N B . E Q . 0 ) GO TO 1 0 1 3  GO TO1 0 4 0  GO T O 1 0 1 3  PERCNB)BPER(NB)+1  1013  IFCLARR2CI,J).NE,0,AND .LARR2CI,K).GT.0)  XFCia.EQ.0) 1016  GO T O  GO T O 1 0 1 6  1016  PERCIB)8PER(IB)+1 IFCLARR2CI,J).GT.0.AND,LARR2(L,J),NE.0) I F CNB.EQ.0) GO TO1 0 1 9  GO  TO1 0 1 9  PERCNB)BPERCNB)+1  1019  1020  IFCLARR2CI,J).NE.0.AND,IARR2CL,J),GT.0) I F C J B . E Q . 0 ) GO T O 1 0 4 0 PER(JB)«PER(JB)*t GO T O 1 0 4 0 NB8UARR3CI,J) JB8LARR3CU,J) IB8LARR3(I,K) IFCNB.GT.0) IAREACNB)8IAREACNB)*1 IFCLARR3CI.J).GT.0,AND,LARR3CI,K).NE.0) IFCNB.EO.0) GO T O 1 0 2 3  GO TO 1 0 4 0  GO TO1 0 2 3  PERCNB)BPERCNB)+1  1023  1026  1029  1030  1033  1036  IF£L,ARR3CI,J) .NE.0.AND.LARR3(I,K) .GT.0) IFCIB.EO.0) GO TO1 0 2 6 PERCIB)8PER(I9)+1 IFCUARR3CI,J).GT.0.AND.LARR3CL,J).NE.0) I F ( N B . E G , 0 ) GO T O1 0 2 9 P£RCNB)8PERCNB)+t IFCLARR3CI,J).NE,0,AND,LARR3CL,J),GT.0) I F C J B . E Q . 0 ) GO TO1 0 4 0 PER(JB)BPER (JB)+ 1 GO T O 1 0 4 0 NBB L A R R 4 ( I , J ) JB*LARR4CL,J) IBaLARR4CI,K) IFCNB.GT.0) IAREA(NB)»IAREA(NB)*1 IFCUARR4CI,J).GT.0,AND,LARR4CI,K).NE.0) IFCNB.EQ.0) GO TO 1 0 3 3 PERCNB)8p£RCNB)*l IFCUARR4CI,J).NE,0,AND.LARR4CI,K).GT.0) I F ( I B , E Q , 0 ) GO TO 1 0 3 6 PER(IB)«PER(IB)*1 IFCLARR4CI,J).GT.0.AND.LARR4(L,J).NE.0) IFCNB.EQ.0) GO T O 1 0 3 9  GO  TO1 0 2 6  GO  TO1 0 2 9  GO  TO1 0 4 0  GO  TO1 0 3 3  GO  TO1 0 3 6  GO  TO1 0 3 9  160 -  1039  1040 1041 2000  PER(NB)»PER(NB)*1 I F ( L A R R 4 C I , J ) , N E . 0 . AND .L.ARR4 C L , J ) . G T . 0 ) IFCJB.EQ.0) GO T O 1040 PERCJ8)BPERCJ8)+1 CONTINUE CONTINUE RETURN  END  GO  TO  1040  - 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, 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 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 £ 921),KCHAR(160),IHT(100,97),I CHAR(99),IBB(50,97),IRAND (97),IXX ( 9 7 ) , 1JXX(97),IV0L(97),IDBH(97),ICL£97),IAPER£97),ICWC97),ICB(97),IBA(97 1),JCHAR(2),IDEAD(97) COMMON IARRA,Bu2,ACC,ATA,ATG,ATP,APDNA,APDNC,APDNS,APDNPR,APDNRO,A 1PDNSY,CSUB1,CSUB2,CSUB3,CSUB4,RAD,B0RDA,XINA,UTILA,B0RDC,XINC,UTIL 2C,BORDS,XINS,UTILS,AGE,C,CC,TAUT,TAUTS,TAUTT,TAUO,UNOCC,YUNOCC,PDN 1,ITHRU,M,ISTRT,I1NT,I£ND,IYUN0C,IAUTTY,IUN0CC,IL00P,IX,ISUB,IC0UNT 3,IHT,138,JARRA,LARR1,LARR2,LARR3,LARR4,IQQ,JQQ,I AREA,PER,KCHAR,I CO 4M,JC0M,lDEADl,IDEA02,I0EAD3,ID£AD4,IDIAMi,IDlAM2,IDlAM3,IDIAM4,JJR 5AND,KKRAN0,ULRAND,ICHAR,IRAND,IXX,JXX,I VOL,IDBH,ICL,IAPER,ICW,ICB, 6 IBA,I DEAD,NS£T,KAMEL,KCEON,KSHEP,KPRUN,KROSE,KSYMP,NAGE,JRAND,KRAN 7D,LRAN0,JAMEL,JCEON,JSHEP,JPRUN,JROSE,JSYMP,EPER,NNAMEL,NNCEON,NNS 8HEP,NNPRUN,NNR0SE,NNSYMP,JCHAR C C C  DETERMINES SHRUB SPECIES IIX,JJX * LOCATIONS OCCUPIED  C IIX»ICOM(ICQUNT) JJX*JC0M(IC0UNT) GO 800  TO  (800,810,820,830),ISUB  IF£ICOUNT.LE,50.)  L A R R 1 ( 1 1 X , J J X ) •> 1 5 1  IF(ICOUNT,GT.50.AND,I COUNT.L£.100)  IF(ICOUNT.GT.100) GO 810  TO  900  IF(ICOUNT,LE,50,)  LARR2(11  X,JJX)»151  I F ( I COUNT,GT,50.AND,I COUNT,LE. 100) IF(ICOUNT.GT,100) GO 820  TO  X,JJX)«153  LARR3(11  X,JJX)•151  900  IF(ICOUNT.LE,50.) IF £ICOUNT.GT.100) GO  TO  LARR3(I  900  IF(ICOUNT.LE.50.) IF(ICOUNT.GT.100)  DO  LARP4(11X,JJX)•151  1 0 0 0 L°l,96 1000  LARR4(11X,JJX)»152  LARR4 (11 X , J J X ) • 1 5 3  NSBNSETCL) DO  LARR3(11X,JJX)•152  IX,JJX)"153  I F ( I COUNT,GT,50.AND,ICOUNT, LE,100)  900  LARR2(11X,JJX)•152  LARR2(11  I F ( I COUNT,GT.50.AND.I COUNT,LE,100)  830  LARR1(11X,JJX)»152  LARRl(IIX,JJX)«153  M 1 , N S  IF(RAD*2.-BL2(L))996,910,910  *  910 915  925  930  935 940 945 950 955 960 965 970 975 980 985  990 991  992  993  994 995 1000 996  -  INCR«0 INCR»INCR+1 GO  920  162  TO  (920,925,930,935,1000),INCR  J«JJX*JQQ(L,K) I"IIXtIQQ(L,K) GO TO 9 4 0 JajJX-JQQ(L,K) I*IIX-IQQCL,K) GO T O 9 4 0 J«JJX+JQQ(L,K) IBIIX«IQQCL,K) G O TO 940 J«JJX-JQUCL,K) I«IIX*IQQCL,K) IFCI)955,955,945 IF(I-66)9S5,955,950 1=1-66 IF(J)970,970,960 IF(J-66)970,970,965 JBJ-66 IF(I)975,975,960 JB66+1 IF(J)985,985,990 JB66+J  GO TO (991,992,993,994 IF(LARR1(I,J).GT.03 GO LARR1 (I, J W C Q U N T GO T O 9 9 5 IF(UARR2(I,J),GT.0) GO LARR2(I,J)"ICOUNT GO T O 9 9 5 IF(LARK3(I,J).GT.0) GO LARR3(I,J)BIC0UNT GO T O 9 9 5 I F ( L A R R 4 ( I , J ) . G T . 0 ) GO LARR4CI,J)BICOUNT GO TO 9 1 5 CONTINUE RETURN END  ),ISUB TO 9 1 5  TO  915  TO  915  TO  915  •  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 ( 1 5 0 ) , J C O M ( 1 5 0 ) , I D E A D 1 ( 1 5 0 ) , I D E A Q 2 ( 1 5 0 ) , I D E A D 3 ( 1 5 0 ) , I D E A 0 4 ( 1 5 0 ) 6,LARR1(66,66),LARR2(66,66),LARR3(66,66),LARR4(66,66),IAREA(153),10 71 A M I ( 1 5 0 ) , I D I A M 2 ( 1 5 0 ) , I D I A M 3 ( 1 5 0 ) , I D I A M 4 ( 1 5 0 ) , P E R ( 1 5 3 ) , E P E R ( 1 6 ) , K A 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), 1 J X X ( 9 7 ) , I VOL ( 9 7 ) , I D B h ( 9 7 ) , I C L ( 9 7 ) , I A P E R ( 9 7 ) , I C W ( 9 7 ) , I C B ( 9 7 ) , I B A ( 9 7 1),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 C  REMOVES DEAD SHRUBS COMPETITION  AND  CALCULATES  C  00  60  1»1,66  DO  59  J 8 l , 6 6  C  5  10  15  20  58 59  GO T O (5,10,15,20),ISUB NBeLARRl (I,J) I F C N B . G T . 1 S 0 ) GO TO 58 I F ( I D E A D l (No),EQ,1) LARR1 ( I , J ) » 0 GO T O 58 NBBLARR2CZ, J) I F ( N 8 . G T . 1 5 0 ) GO TO 56 IF£IDEAD2(NB).EQ.l) LARR2(I,J)B0 GO T O 56 NB*LARR3CZ,J) 1 F ( N B . G T , 1 5 0 ) GO T O 58 ZF(I0EA03(NB).E0,1) LARR3(I,J)B0 GO T O 58 NB«LARR4 (I, J) I F ( N B , G T . 1 5 0 ) GO T O 56 IF(IDEA04(N5).EQ.1) LARR4(I,J)B0 GO TO 58 CONTINUE CONTINUE  DEGREE  OF  INTERSHRUB  CONTINUE RETURN END  -  165-  SUBROUTINE SGPON ( N A M E L , N C E O N ,N S H E P ,N P R U N , N R O S E ,NSYMP ,P O N S ,PDN A, P D 1NC,PDNPR,PDNRQ,PDNSY,INDI3K) DIMENSION I A R R A ( 6 6 , 6 6 ) , B L 2 ( 9 6 ) , A C C ( 4 , 2 1 ) , A T A ( 4 , 2 l ) , A T G ( 4 , 2 l ) , A T F ( 4 1,21), 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 , L A R R 1 ( 6 6 , 6 6 ) , L A R R 2 ( 6 6 , 6 6 ) , L A R R 3 ( 6 6 , 6 6 ) , L A R R 4 ( 6 6 , 6 6 ) , I AREA (1 S 3 ) , I D 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,IDIAM3 IDIAM3,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 f  IOUT-6 C C C C  CALCULATES SETS  NUMBER  PRODUCTION  AND P R O D U C T I V I T Y  TO 0,  PONAB0„  P DNC 0, P O N S 80 « PDNPRS0. PDNRO»0, PDNSY 0, I F C A G E . E t t , 0 ) GO TO 1 2 8 0 DO 1 2 0 0 I M , 1 5 0 GO T O (1045,1050,1055,1060),ISUB DIAM-IDIAM1 (I) 8  8  1045  IM0RT I0EAD1 GO T O 1 0 6 5 0IAM«IDIAM2( IM0RT I0EAQ2( GO TO 1065 0lAMsI0IAM3( 8  1050  B  1055  (I) I) I) I)  IMCRT8ID£AD3(I)  GO 1060  TO  1 0 6 5  DIAMBIDIAM4  (I)  IM0RT«IDEA04£I)  OF  SHRUBS  •  1065 C C  IFCIMORT.EG.l) CALCULATES  C C C  XlNSa SOROS  1070  GO  BORDER  166 -  TO 1 2 0 0 AND  INSIDE  AREA  OF  SHRUBS  AND  PRODUCTION  I N S I D E AREA a BORDER AREA  IF(DIAM,EQ,0) GO TO 1 2 0 0 RADaOlAM/100. DlAMaRAO RDSaRAO/2, IRADaRAD KBIRAD+1 IF(PER CI).LT.EPER(K)) GO T O 1 0 9 0 I F C R D 8 . L T . , 8 2 ) GO TO 1 0 7 0 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 1 0 7 5 BORDBCRDS+,82)**2.*3,14159 XIN 0 , 8  C 1075  I F C I . G T . 5 0 ) GO TO 1 0 7 6 BORDA*BOROA+BORD XlNAaXINAtXlN X AREA8RDS**2.*3.14159 AMELP»4,1*XAREA GO TO 1 1 3 0  C 1076  I F C I . G T . 1 0 0 ) GO TO 1 0 7 9 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 ,4 5 4 5 4 * ( 1 1 0 . - X ARE A) W 0 0 . * ( 1 1 0 , - X ARE A) l**2,7/110 **2,7 GO TO 1 1 3 0 t  $ C 1079  1090  BORDS8flORDS*BORD XINSBXINS+XIN XAREA>RDS**2.*3.14159 IF CXAREA.LE.3.) SHEPPa25,/3.**2.6*XAREA**2.6 IPCXAREA.GT.3.) S H E P P « 2 5 0 , - 2 5 0 . * C 1 0 0 . - X A R E A ) * * 4 , 1 /1 0 0 . * * 4 , 1 GO TO 1 1 3 0 DIFPBP£R(I) DIFEBEPERCK) DIFBDIFP/DIFE ACTARalAREA (I) ACTARaACT AR/4. I F ( E P E R C K ) . N E . 4 ) GO TO 1 0 9 4  -  167 •  B 0 R D « C R D S + . 8 2 ) * * 2 * 3 , 1 4 1 5 9 X I N » fci GO T O 1 1 0 0 I F C R D S . L E . . 8 2 ) GO TO 1 0 9 5 EXPlNSs(RDS-,82)**2,*3,14159 BORD«DIF*C CRDS+.82)**2.*3,i4l59-EXPIN5) EXPARs3,14159*RDS**2, t  1094  ACTINSBACTAR*EXPINS/EXPAR  60RDINaDIF*CEXPAR-EXPINS) IFCCBOROIN+ACTINS) .NE.ACTAR)  ACTINSBACTAR-BORDIN  XINBACTINS  1095  1100  IFCXIN.LT.0) XINB0. GO T O 1 1 0 0 BORDBDIF* C R D S + , 8 2 ) * * 2 . * 3 , 1 4 1 5 9 IF (BORO.EQ.0) XINBACTAR IF(BORO.GT,0) XINB0 AREAalAREA(I) XAREABAREA/4, IFCI.GT.50)  GO  TO  BORDABaORDA+BORD  1105  XINABXINA+XIN  1105  AHELPB4.1*XAREA GO T O 1 1 3 0 I F ( I . G T . 1 0 0 ) GO T O 1 1 2 0 BOROCsBOROCtbORD XINCBXINC*XIN  I F ( XA R E A . L E . 6 . ) C E Q N P * 6 0 , / 6 , * * 1 , 7 * X A R E A * * 1 . 7 IF CXAREA•GT,6,) CEONPafl10,.i,45454*(110.-X AREA)-700.•C110.-XAREA) 1**2.7/110,**2.7 1 1 1 5 GO TO 1 1 3 0 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,**4 1 1130 I F ( I , L E , 5 0 ) PDNABPDNA+AMEUP X F ( I . G T , 5 0 ) GO T O 1 1 4 0 IFCINDI8H,£Q,0) GO T O 1 2 0 0 0  C  1140  WRITECIOUT, 1180) I,PER C I ) , E P E R ( K ) , D l A M , X IN,BORD,AMELP,IAREA CI) GO T O 1 2 0 0 IFCI.GT,50,AND,I,LE,100) PDNCsPDNC+CEONP IFCI.GT.100) 60 TO 1 1 5 0 IFCINDISH.EQ.0) GO TO 1 2 0 0  C  WRITECIOUT,1180) I,PER CI),EPER(K),DlAM,XIN,BORD,CEQNP,IAREACI) TO 1 2 0 0 IFCI.GT.100) PDNSapDNS+SHEPP IFCINDISH.EQ.0) GO T O 1 2 0 0  GO  1150 C  1180  WRITECIOUT,1180) I,PER CI),EPERCK),DlAM,XIN,BORD,SHEPP,I AREA CI) F O R M A T C2X, '# * ' 1 3 , 3 X , ' P E R s ' , 1 5 , 3 x , ' E P E R B • , 1 5 , 3 X , ' 0 1 AM" ', F b , 2 , 3 X , * X  •  1b8  lIN«',Fb,2,3X, • B 0 R D « S F b , 2 , 3 X , 12012) C O N T I N U E  "  • P D N « % F 8 . 2 , 3 X ,  #  A R E A " » , I 9 )  C C C  c  1201 C  PDNAsPDNA/25. PDNSBPDNS/25, PDNC««P0NC/2S. WRITECIOUT,1201) PDNA,PDNC,PONS F0RMATC//#2X,'PDNA a * , F 1 0 , 4 , 5 X , 'PDNC a ' , F 1 0 . 4 , 5 X , ' P O N S "',F10,4) XINCA,C,S) • I N S I D E AREA FOR LARGE SHRUBS XINABXINA/4, XINC»XINC/4 XINSBXINS/4, BORO(A,C,S) * BORDER AREA FOR L A R G E SHRUBS B0RDA8B0RDA/4. B0RDCB8QRDC/4, BORDSBBORDS/4, UTILCA,C,S) * AREA U T I L I Z E D C I N S I D E • BORDER) FOR L A R G E SHRUBS UTILA«BORDA+XlNA UTILC«BOROC*XlNC UTILSBBORDS+XINS TAUTS a T O T A L A R E A O C C U P I E D BY C E O N , AMEL, AND SHEP TAUTSBUTILA+UTILC+UTILS TAUTT B AREA IN SHADE TAUTT«1069,*C/100. TAUT a A R E A O C C U P I E D BY T R E E S A N D SHRUBS TAUT"TAUTS+TAUTT TAUO B A R E A NOT O C C U P I E D BY T R E E S ANO SHRUBS TAUOB10O9..TAUT IFCTAUO.LT.0) TAUOB0 IAUTTY * AREA IN SHADE I N SQ. YDS, UNOCC»1089,-TAUT IUNOCC B OPEN AREA C A R E A NOT O C C , BY T R E E S AND S H R U B S ) IN SQ,FT» YUNOCCBUNOCC/9. IYUNQC B OPEN AREA I N SQ. YDS. IYUNOCBYUNOCC IAUTTYBTAUTT/9, IUNOCCBUNOCC f  C  C  C C C C  C C C  c 1202  WRITECIOUT, 1202) TAUTS,TAUTT,TAUT,IYUNOC F O R M A T £ / / / , 2 X , « T A U T S s * F 9 , 2 , 3 X , ' T A U T T " ' F 9 , 2 , 3 X , 'T A U T « " , F 9 . 2 , 3 X , ' I Y U lNOCa',19) I F C N P R U N . L T , 1 ) GO T O 1225 IPC CNPRUN*IYUNOC),LT,100) ITHB0  C DO  1220  I a i, J  ITH"ITM*i  JaNPRUN*IYUNOC  m 169  1203 1206 1209 1212 1215 1220  c 1225  1230  1240  *  RANOJJaJJRANDCI) RANOJJaRANDJJ/1000. 1 F C A G E . G T . 2 0 . ) GO TO 1212 X2«-1.*(6,**2,14) IFCAGE-6.)1203,1203,1206 Xl«-l,*(<*l,*(AGE»6,))**2,14 GO TO 1209 X18CAGE-6,)**2,14 DPRUN«RANDJJ*C-.2*.17B*AGE+.2*(X1/X2)) GO TO 1215 0PRUN"RANDJJ*2.14 IF(OIAM UT,i 37) PONPa.04+,6*DPRUN IF CPIAM.GE.I,37) PONPa-8,6 + 7,1*DPRUN PDNPRsPONPR+PONP PRUNsNPRUN X F C J T H . L T . 1 0 0 ) GO T O 1225 bLOCK«100,/PRUN XBLKaYUNQCC/BLOCK PONPReXBLK*PDNPR B  i  I F C N R O S E . L T , 1) GO TO 1240 J«100 IFCCNROSE*IYUNOC),LT,100) J"NROSE*IYUNOC ITH»0 DO 1 2 3 0 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 PDNROaPDNRD+PONR RObEeNROSE IP(ITH,LT,100) GO T O 1240 BLOCKai00,/ROSE XBLK«YUNGCC/BLOCK PDNR0BX8LKftPDNR0 I F C N S Y M P . L T , 1 ) GO TO 1260 J»100 IPC(NSYMP*IYUNQC) .LT.100) JaNSYMP* IYUNOC ITM80  C  1255  DO 1 2 5 5 I " l , J ITH»ITM+1 RANDLLsLLRAND CI) RANDLLaRANDLL/1000, IF C A G E , L E . 18.) DSYMPapANDLL* C , 2 * A G E - 2 , 9 6 * A G E * * 1 , 4 / 2 0 , * * ! , 4 ) IFCAGE.GT.18.) DSYMPaRANDLL*1.05 P D N S h a , 2 6 3 * D S Y M P * i « l .5 PDNSYaPDNSY+PDNSM SYMPaNSYMP IFCITH,LT.100) GO TO 1260  170  1258  BL.OCKsl0fc./SYMP XBLKaYUNQCC/tJLOCK PDNSYaXBLK*PDNSY F O « h A T C / / » 2 X , 'PDNRO  -  « • , F 10 . 4 , 5 X , •P O N S Y  C 1280 1260  W H l T E d O U T ,1258) RETURN END  PDNRO,PONSY,PDNpR  » ' , F 1 0 . 4 , 5 X , •P O N P R  «',P9,4)  -  171  -  S U B R O U T I N E SUM CNAMEL,NCEON,NSHEP,NPRUN,NROSE,NSYMP,PONS,PDNA,PO 1 N C P D N P R , PDNRO, PONSY, INDISH) DIMENSION I A R R A ( 6 6 , 6 6 ) , B L 2 ( 9 6 ) , A C C ( 4 , 2 l ) , A T A ( 4 , 2 l ) , A T 6 ( 4 , 2 l ) , A T F ( 4 1,21),APONA (4,21),APDNC(4,21),APDNS(4,21),APDNPR(4,21),APDNRO(4,21) 2,APDNSY(4,21) 1 N T E G E R * 2 J A R R A ( 6 6 ,6 6 ) , N S E T ( 9 6 ) , I Q Q ( 9 6 , 5 ) , J Q Q ( 9 6 , 5 ) , N A G E ( 5 0 ) , N N A M E 1 L ( 4 ) , N N C E 0 N ( 4 ) , N N S H E P ( 4 ) , N N P R U N ( 4 ) , N N R O S E ( 4 ) , N N S Y M P ( 4 ) , J R A N D ( 5 0 ) ,K 2RAND(50),LRAND(50),JJRAND(100),KKRAND(100),LLRAND(100), J 3AMEL ( 2 0 ) , J C E O N ( 2 0 ) , J S H E P ( 2 0 ) , J P R U N ( 2 0 ) , J R O S E ( 2 0 ) , J S Y M P ( 2 0 ) , I 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 ( 1 5 0 ) , I D I A M 2 ( 1 5 0 ) , I D I A M 3 ( 1 5 0 ) , I D I A M 4 ( 1 5 0 ) , P E R ( 1 5 3 ) , E P E R ( 1 6 ) , K A 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 C C C  CALCULATES GRASS AND FORB PRODUCTION C H E C K S CROWN C L O S U R E OF T R E E S AND A D J U S T S GRASS PRODUCTION A D J U S T S GRASS AND FORB P R O D U C T I O N TO SHRUB I N S I D E AND BORDER AREA AND SHRUB NUMBER IOUTsb IF(C.LT 6S.) PDNAGaPDN/83,3/9,*(27,•,085294*(68 -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 ( C L E . 6 4 . ) GRAS8PDN/83.3/9,*(,04S*C) IF(C,GT,64.) GRAS«0. Q  IF ( C L E , 16.)  T  F0RB»PDN/e3,3/9,*(2,44. 87*C)  IF(C,GT,18, ,AND.C,LT,80.) 1)**2.7) IF(C,GE,80.) FORB*0, UBORD*0, UXINa0.  e  FORBBPPN/83,3/9.*(,5 +18,/60,**2.7*(80,«C  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,  -  1 7 2-  FORBI•FORB*UXIN*.206/25. AGQ*0. FOO"0. GRO 0 B  AGTO30.  FOTQ»0. GR 0 0 « TAaPDNAG*43,56 TG»6RA3*43.56 TF F0RB*43.56 I F C M . E Q . 0 ) GO TO 2 0 1 1 IF(CNPRUN+NR0SE*N5YMP),GT.0) AGTOBPDNAG*(1089.-TAUTS)/25. B  B  GO TO1 2 7 0  FOTO*FOPB*(i0B9,-.TAUTS)/25.  GRTOBGRAS* C 1 0 8 9 . - T A U T S ) / 2 5 , GO  TO  1270  2000  AGTO P0NAG*TAUTT/25, FQT0 FQRB*TAUTT/25. GRT0«GRA3*TAUTT/25. I F ( N S Y M P . E G , 0 ) GO T O 1 2 8 0 IFCNSYMP A E . 1 4 ) R£0UCA (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 I F ( A G E . G T . 2 5 . ) REDPER* 1. REDUCA»(1,-(REO*REOPER)) INCFa(3,76+l,02*NSYMP)/3.7 6 AGTQ PQNAG*RE0uXA*TAUTT/25, GRTO«GRAS*REDUCA*TAUTT/25, F0T0aF0RB*TAUTT/25. 1 2 8 0 NL'MSSHsNPRUN +N R O S E + N S Y M P 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 B  B  B  B  RED*1,-REOuCA  IFCAGE.Lt.25.) REOPER*,04*AGE IFCAGE.GT.25.) REDPER 1. REDUCAaCl,-CRED*REOPER)) iNCFaC3.76*1,02*NUMSSH)/3,76 B  AGQBPDNAG*TAU0*RE0UCA/25,  F00*F0RB*TAU0/25 GR0*GRAS*TAU0*REDUCA/25, TAsAGO^AGTO+AGROB+AGROI TG*GRO*GRTO+GRASl+GRASB B  2000  TFBFOO+FOTO^FORBI+FORBB  c  2011 L"M*1 IFCISUB,NE,l,OR,M.NE,l)  C  DO  2 0 1 2 J i , 5 1 B  GO TO  2 0 1 5  -  C C  SUMMARY 2012 2015  OF  PRODUCTION  OF  173  *  SHRUBS,GRASSES  AND  FORBS  IHTCJ,97)*0 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) PDNA 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) PDNRO KSYMP(ISUB,L) SNSYMP*(C1089-TAUTS)/9.) APDNSYCI3UB,U=PDNSY IPRUN«NPRUN*IYUNOC IROSE«NRQS£*IYUNOC ISYMPaNSYMP*IYUNOC a  a  C C  PRINT  PRODUCTION  SUMMARIES  C 2  WRITECIOUT,2) FORMAT(2X,T10,'CC',T13,'AGROP PDN%T23,'GRASS PDN * , T 3 4 , ' F O R B PDN', 1 T 4 7 , '# A M E L ' , T 5 5 , ' A M E L PDN',Tb7,'# CE0N',T75,'CEON PDN',T87,'» SHE 2P»,T95,'SHEP PDN')  C 5  WRITECI0UT,5)C,TA,TG,TF,NAMEL,PDNA,NCE0N,P0NC,N5HEP,PDNS FORMAT(2X,4Fl0.4,I10,F10,4,110,F10,4,X10,F10,4)  C 7  WRITECIOUT,7) FORMAT(2X,T7,'# PRUN ',T15,'PRUN 147,'# SYMP*,T55,'SYMP PDN')  PDN',T27,'#  ROSA',T35,'ROSA  C 10  2020  WRITECIOUT,10)IPRUN,PDNPR,IROSE,PDNRO,ISYMP,PDNSY FORMATC2X,I10,F10,4,I10,F10,4,110,Fl0,4) IL00P»CIEND-I8TRT)/IINT +1 I F ( I S U 8 , E Q , 4 , A N D . C M - I L O O P ) , E Q , 0 ) GO T O 2 0 2 0 GO T O 3 0 3 0 IOQa0  C 2022  DO 2 0 2 7 1 = 1 , 4 IF(100.GT,1) GO  TO  3000  PDN',T  -  2025  C C  2027  174  -  WRITECIOUT,2025) I F O R M A T C ' l ' , 2Xi 1 2 8 ( ' * ' ) , / / , 2 X , T 5 6 , ' S U B - P L O T 1',//,2X, 'AGE') NB 1 J»ll IF(IDO,GT,0) Nsl2 IF(N,EQ,12)J « 2 1 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)  ( I H T C K , 9 7 ) , KBM,J) ( A C C ( I , K ) , K BN, J ) C A T A C I , K ) , K *N, J ) C A T F C I , K ) ,K BN, J ) C A T G C I , K ) ,K BN, J ) CMMELCI,K) K N ,J ) CAPONACI,K) KBN,J) CKCEONCI,K) KBN,J) CAPONC CI,K) KBN,J) CK5HEP(I,K) KBN,J) (APDNSCI,K) KBN,J) CKPRUNCI,K) KBN,J) C A P P N P R C I ,K , K » N , J ) (KRQSE CI,K) K»N,J) C A P U l M R U C I ,K , K » N , J ) (KSVMPCI,K) KBN,J) CAPDNSY CI,K ,K*N,J)  IF CILOOP,LE,10)  GO TO  8  3000  IDQBIDO+I  GO  TO  2022  C C 2030 2031 2032 2033 2034 2035 2036 2037 2036 2039 2040 2041 2042 2043 2044 2045 2046 C C  F Q R M A T C 2 X , 'AGE', 6 X , 1 1 1 0 ) F O R M A T ( 2 X , ' C R , C L O S E ', I X , U F 1 0 . 1 ) P D N ,', 1 1 F 1 0 . 3 ) F O R M A T C2X , ' AGRQP« PDN, , 2 X , U F 1 0 , 3 ) F O R M A T ( 2 X , 'FORB F O R M A T C 2 X , ' G R A S S P D N ', I X , U F 1 0 . 3 ) AMELAN , ' , 1 1 1 1 0 ) F O R M A T ( 2 X , 'NO, F 0 R M A T C 2 X , ' A M E L , P D N ', I X , 1 1 F 1 0 . 3 ) CEQN. , 2 X , 1 1 1 1 0 ) F O R M A T ( 2 X , 'NO. F O R M A T ( 2 X , 'CEON, PDN ' , I X , 1 1 F 1 0 . 3 ) F O R M A T C 2 X , 'NO, SHEP. , 2 X , 1 1 1 1 0 ) F O R M A T ( 2 X , ' S H E P , P D N ', I X , 1 1 F 1 0 . 3 ) PRUN, , 2 X , 1 1 1 1 0 ) F O R M A T C 2 X , 'NQ, PDN M X , H F 1 0 . 3 ) F O R M A T C 2 X , 'PRUN, ROSE' 3X, 11110) F O R M A T ( 2 X » 'NO, F 0 R M A T C 2 X , 'ROSE PDN, , 2 X , 1 1 F 1 0 . 3 ) SYMP. , 2 X , 1 1 1 1 0 ) F O R M A T C 2 X , 'NO, ' S Y M P , P O N ', I X , 1 1 F 1 0 . 3 ) FORMAT C2X,  12,//,T2,'PARAMETER  - 175 -  3000 RETURN END  

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