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Order and organization in lodgepole pine forests of West-Central British Columbia Brulisauer, Alfred Robert 1994

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ORDER AND ORGANIZATION IN LODGEPOLE PINE FORESTS OF WEST-CENTRAL BRITISH COLUMBIA  by ALFRED ROBERT BRULISAUER dipl. Ingenieur-Agronome The Swiss Federal Institute of Technology, 1978  Zurich  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES (Department of Botany)  We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA March 1994 ©  Alfred Robert Brulisauer,  1994  _  _____  thesis in partial fulfilment of the requirements for degree at the University of British Columbia, I agree that the Library freely available for reference and study. I further agree that permission copying of this thesis for scholarly purposes may be granted by the In presenting this  department  or  by  his  or  her  representatives.  It  is  understood  that  an advanced shall make it for extensive head of my copying  or  t my written publication of this thesis for financial gain shall not be allowed withou permission.  (Signature)  Department of The University of British Columbia Vancouver, Canada  Date  DE-6 (2)88)  ti c cj-  I&  99 L.f  ABSTRACT  Trends of temporal development were documented for lodgepole pine-dominated forest communities recovering after fire disturbance in the interior of British Columbia. Order and organization within these communities, considered to be key indicators of the recovery process,  were quantified by means of equal frequency ellipses in  multivariate space and angular comparisons between eigenvectors. Estimates of ecological order were also based on more traditional methods such as Shannon diversity and spatial heterogeneity. Observed trends were evaluated in light of recent attempts to interpret  development  energetic  dynamics  in  in  the  living  non-equilibrium  world  as  systems.  resulting Of  from  particular  interest were phenomenological similarities between successional and organismic development as predicted from an interpretation of succession as a developmental process. In addition, implications of the  results  to  questions  of  diversity and  stability  and  their  mutual relationship in ecological systems were also explored. Similarities organismic  development  (Weber et al. communities  were  1989,  evaluated according to  Salthe 1991)  appeared  to  .  follow  between  successional  four phenomenological  and rules  Succession in the investigated similar  trends  as  found  in  organismic development in terms of energetic efficiency, structural complexity, speed and course of development and system stability. The undivided data (xeric and mesic stands combined) suggested a steady decrease in diversity up to a penultimate phase with a ii  subsequent increase as climax was approached. Eccentricity of the equal  frequency  redundant  system  ellipses,  interpreted  configurations,  to  be  followed  a  an  indicator  similar  of  pattern,  thereby behaving in agreement with expectations from Prigogine’s minimum dissipation principle multiple Order,  pathways  quantified  in  exchange  based  on  predicting for  higher  species  relatively stable during succession.  a  system  to  energetic  data,  was  sacrifice  efficiency.  found  to  remain  Organizational dynamics were  most pronounced at the onset of succession and slowed down with increasing stand age. Stability and resilience were found to be lower on sites of poor environmental conditions than on mesic sites. No relationship, however,  of  stability  or  resilience  with  diversity  could  be  established as levels of diversity in both mesic and xeric sites were similar. Lower redundancy on xeric sites was interpreted as an indicator for lower stability,  leading to higher sensitivity to  environmental fluctuations during the process of recovery. It was development  found that processes were  reasonably  in successional  similar  except  and organismic for  sites  in  unproductive locations. This was interpreted to be a result of the lower degree of integration of such sites. Thus, communities  appeared  to  exhibit  patterns  the investigated  similar  to  organismic  development if autogenic processes were able to proceed relatively undisturbed.  iii  TABLE OF CONTENTS  PAGE  ABSTRACT TABLE OF CONTENTS  .  LIST OF TABLES LIST OF FIGURES  .  ACKNOWLEDGEMENTS DEDICATION  INTRODUCTION CHAPTER 1.  SUCCESSION  -  .  .  .  .  .  .  .  .  .  A THERM0DYNAIvIIC INTERPRETATION  1.1. Traditional concepts 1.2. A thermodynamic interpretation 1.2.1. Conceptual background 1.2.2. Application of thermodynamic principles to successional development 1.2.3. Consequences of the thermodynamic concept for community theory 1.2.4. Development and information CHAPTER 2. 2.1. 2.2. 2.3. 2.4.  2.5.  .  .  ORDER AND ORGANIZATION IN COMMUNITY DEVELOPMENT Order Organization Quantifications Diversity and stability 2.4.1. Diversity 2.4.2. Stability 2.4.3. The interplay of stability and diversity Research objectives  jj iv Vi  viii  Xi  xii 1 4 4 7 7  11 12 19 22 22 25 26 28 28 31 35 38  CHAPTER 3.  THE STUDY AREA  39  CHAPTER 4.  DATA COLLECTION  43  4.1. 4.2.  Selection of study sites Vegetational and environmental variables 4.2.1. Ground cover vegetation 4.2.2. Tree layer 4.2.3. Environmental variables .  .  .  .  CHAPTER 5. 5.1.  QUANTIFYING ORDER AND ORGANIZATION IN FOREST SUCCESSION Space-time substitution iv  .  .  .  .  43  44  44 44 45 47 47  5.1.1. 5.1.2.  Separating habitat and age effect Division of sites into mesic and xeric variants 5.2. Potential problems in quantifying organization 5.3. Proposed solution quantifying “organizational change” instead of “degree of organization” 5.4. Analytical methods 5.4.1. Equal frequency ellipse statistics 5.4.1.1. Area of the equal frequency ellipse 5.4.1.2. Eccentricity of the equal frequency ellipse 5.4.1.3. Orientation of the equal frequency ellipse angle theta 5.4.2. Angular comparisons between eigenvectors .  49 50 52  -  .  -  CHAPTER 6. 6.1.  RESULTS  53 54 56 58 58 61 63 65  Successional changes in observed randomness 65 6.1.1. Estimates of variance the spread of the observations 66 6.1.1.1. Ground cover 67 6.1.1.1.1. All strata combined 67 6.1.1.1.2. Separate strata 71 6.1.1.1.3. Variability of ground cover assessed by Shannon diversity and spatial heterogeneity 75 6.1.1.2. Structure of the tree layer 80 6.1.1.2.1. Tree diameter structure 84 6.1.2. Redundancy variable intercorrelation 85 6.1.2.1. Ground cover 87 6.1.2.1.1. All strata combined 87 6.1.2.1.2. Separate strata 90 6.1.2.2. Structure of the tree layer 92 Organizational change 94 6.2.1. Ground cover 94 6.2.1.1. All strata combined 94 6.2.1.2. Separate strata 98 6.2.2. Structure of the tree layer 102 -  .  .  .  .  •  .  •  .  .  .  •  .  .  -  6.2.  .  .  .  .  CHAPTER 7. 7.1. 7.2. 7.3.  DISCUSSION  106  Order and organization Order Organization  . .  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H(D  .3  CD rn rr  0)  fr Q) 0—  N)  w  H  —H-o)p OCDF P1 C) 1CCUrtH,  CDmli  -3lico (DP)Q  —  •  tflH-I-hO  ‘tJ ‘<D) Ii 0  u0 0H-CD-  ‘CDOCD  H’zIQ<  N)  (f  H  ACKNOWLEDGEMENTS  While this thesis explores analogies between successional and  organismic  development  one  might  also  speculate  about  similarities between the development of a thesis and patterns observed in the living world  (which of course is not implying  that an academic environment does not belong to the world of the living). rules  The development of this thesis followed thermodynamic  in  principle:  both  in  the  first  stages  time  (if  not  seemed unlimited, as the product matured constraints  resources) on  while  time  ultimately,  and  resources  became  more  notable  may have helped to increase efficiency.  which,  Drs.  Gary  Bradfield and Jack Maze have accompanied me on this journey as supervisors.  Not  only  were  inspiration and encouragement everything else  they  an  invaluable  in good and rough times,  of  above  it was their friendship that made my time in  graduate school a worthwhile experience. thank Dr.  source  Wilfred Schofield and Dr.  I would also like to  Robert DeWreede for their  friendly advice while serving on my committee. Jerry Poulin and Pat Goddard,  our hosts in the Chezacut logging camp during two  field seasons, made life much easier for us by their incessant help  and  Logging  generosity. Enterprises  Arnold Ltd.  Bremner  are  and  his  gratefully  crew  of  Clusko  acknowledged  for  permission to use their facilities in Chezacut. Lastly I would like  to  thank my wife Ulrike who not only helped collecting  field data but. facilitated the completion of this thesis by all kinds of priceless support. xi  This thesis is dedicated to the loving memory of my father Alfred F. Brulisauer  xii  INTRODUCTION  “It is necessary to study not only parts and processes in isolation but also to solve the decisive problems found in the organization and order unifying them, resulting from dynamic interaction of parts, and making the behaviour of parts different when studied in isolation or within the whole.” (L. v. Bertalanffy)  Most  ecologists  would  agree  that  terrestrial  plant  succession results from the manifold interactions between the various biotic and abiotic constituents of a system as a new site is colonized or a previously occupied one recovers from disturbance. theory of  Some  controversy  succession  exists,  should be  sought  properties of individual species 1974,  however, at  the  whether  level  of  a  the  (Drury and Nisbet 1973, Horn  1975, Pickett 1976, Connell and Slatyer 1977, Noble and  Slatyer 1980, Huston and Smith 1987) approach  seeking  explanations  in  or rather in a holistic systems-level  properties  (Margalef 1968, Odum 1969, Schneider 1988, Weber et al. 1989) The  recovery  of  vegetation  after  it  has  undergone  disturbance has many parallels with features observed in the phylogeny and ontogeny of living organisms,  such as the trend  towards  and  features concept  increasing that  led Clements  of plant  criticized  by  complexity,  (1916)  communities.  Gleason  diversity  (1926)  to propose  This  concept,  and  Ramensky  stability  -  an organismic however, (1926),  first enjoys  little popularity among modern ecologists. Whittaker (1975, p. 1  362)  concluded  that  system,  and  control  “since  as  a  consequent  on  evolution  community  inherited  no  community  the  whole,  genetic  community of  the  has  no  message  evolution  species  that  central for  is  the  largely  make  up  the  community.” The thrust of this study was to take a second look at this  controversy,  initiated  by  the  suspicion  that  the  parallels between succession, evolution and ontogeny are not purely  accidental  principle.  but  Recent  are  expressions  efforts  to  apply  thermodynamics to biological systems and  Wiley  1986,  Wicken  1987)  of  an  underlying  non-equilibrium  (Prigogine 1980, Brooks  have  contributed  insights  suggesting that analogies between developmental patterns of organismic growth and of ecological succession are indeed non trivial and can be interpreted as the result of patterns of energy  flow.  An  interpretation  from  a  thermodynamic  perspective would place the phenomenon of succession in the larger context of systems development in general, and thereby make  its  investigation  worthwhile  beyond  its  strict  application to plant ecology alone. Wicken (1987) regarded the study of succession to be of particular interest because it “provides a tractable microcosm for evolution”. So far this recent discussion has been preoccupied mainly with  providing  reinterpretation evolution,  the of  theoretical  developmental  foundation  patterns  as  ontogeny and ecosystem development. 2  for  observed  a in  The present  an  was  study  ecological  attempt  system as  to  apply  theory  the  found in the  to  a  simple  lodgepole pine-dominated  forests of the Interior of British Columbia and to quantify such patterns of development in the context of the recovery process  after  external  development  of  progression  towards  disturbance  living  systems  states  of  by  is  fire.  Since  characterized  higher  by  organization  the a and  complexity, the quantification presented here concentrated on capturing  key  the  organization  -  features  of  development  order  -  and  in an ecological context.  The main objectives of this study thereby were fourfold: 1)  to  introduce  dynamics  of  some  quantitative  successional  tools  development;  2)  to to  capture  the  evaluate  the  phenomenological similarities between organismic and ecosystem development;  3)  to  interpret  the  observed patterns  from a  thermodynamic perspective; and 4) to explore the consequences of  the  results  as  applied  to  stability.  3  the  problem  of  ecosystem  CHAPTER 1 SUCCESSION  1.1.  -  A THERMODYNAMIC INTERPRETATION  Traditional concepts  Odum  (1969),  in  Clementsian  succession as a process  of  tradition,  described  ecosystem development with many  parallels to the development of organisms. He illustrated this similarity  by  claiming  that  succession  was  “reasonably  directional”, “community-controlled”, i.e. self-directed, and “in a  culminated  stabilized ecosystem”.  In Odum’s view the  strategies of succession and evolution follow the same end to  “increased  gain  physical  control  environment  in  of,  the  or  homeostasis  sense  of  with,  achieving  -  the  maximum  protection from perturbations.” Odum’s list of “trends to be expected in the development of ecosystems” presents twenty f our attributes that distinguish immature from mature systems, independent (Table 1)  .  of  the particular composition of  the  community  The foundation of Odum’s concept rests on  energetic considerations, building on Lotka’s law of “maximum energy”  biological  in  systems  driving force of succession  (Lotka  1922).  (and evolution)  Thereby  the  is the selective  advantage of systems with higher energy output than potential competitors. output  is  “Under the appropriate conditions, maximum power  the  criterion  for  the  survival  systems, both living and non-living” 4  of many kinds  of  (Odum and Pinkerton 1955,  Ecosystem Attributes  1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.  Gross production/ community respiration (P/R ratio) Gross production/ standing crop biomass (P/B ratio) Biomass supported/unit energy flow (B/E ratio) Net community production Food chains Total organic matter Inorganic nutrients Species diversityvariety component Species diversityequitability component Biochemical diversity Stratification and spatial heterogeneity (pattern diversity) Niche specialization Size of organism Life cycles Mineral cycles Nutrient exchange rate, between organisms and environment Role of detritus in nutrient regeneration Growth form  19. Production 20. Internal symbiosis 21. Nutrient conservation 22. Stability (resistance to external perturb.) 23. Entropy 24. Information Table 1.  Developmental Stages  Mature Stages  >1 or <1  approaches 1  High  Low  Low  High  High Linear, mostly grazing Small Extrabiotic  Low Web-like, detritus Large Intrabiotic  Low  High  Low Low Poorly organized  High High Well organized  Broad Small Short, Open Rapid  Narrow Large Long, complex Closed Slow  simple  Unimportant  Important  For rapid growth, (r-selection) Quantity Undeveloped Poor Poor  For feedback control, (K- selection) Quality Developed Good Good  High Low  Low High  Trends to be expected in the development of ecosystems (from Odum (1969).  5  p. 332). Thus, Odum applies a holistic approach to succession with “ecoenergetics” as its unifying principle and the system as a reacting,  interacting whole.  Conversely, theories in a more reductionist tradition see not  succession explained  by  as  “community-controlled”  species-level  processes  but  sufficiently  as  differential  such  strategies of exploiting resources, e.g. the dominance of r selected species early in the ones  in  concluded  later that  stages. “a  Drury  complete  succession versus and  Nisbet  theory of  (1973,  succession  K-selected p.  362)  should be  sought at the organismic, physiological or cellular level, and not  in emergent properties of populations or communities”;  most of the phenomena of succession could be “understood as resulting from the differential growth, differential survival and perhaps  differential dispersal of  species”.  Similarly,  Pickett (1976, p. 112) held that succession was “basically the replacement of species in order of decreasing opportunism” and as  such  “due  strategies”.  to  the  Horn  interaction of  (1974,  1975)  different  evolutionary  used such differential  life  history attributes to model forest succession as a Markovian process, species, were  based  on  the  probabilities  of  replacement  of  and concluded that several properties of succession  “direct  statistical  replacement process  consequences  of  a  plant-by-plant  and have no uniquely biological basis”  (Horn 1975, p. 209)  6  1.2. A thermodynamic interpretation  Conceptual background  1.2.1.  Recent attempts to apply non-equilibrium thermodynamics to  living  systems  Wicken 1987)  (Prigogine  1980,  Brooks  and Wiley 1986,  produced some results that may have  important  consequences for successional theory and may be able to bridge the rift between reductionist and holistic approaches. Biological  systems  can  be  viewed  as  thermodynamic  entities that survive as a result of processing matter and energy.  According to  entropy  of  closed  the  systems  second  law of  invariably  thermodynamics  increases  over  the time  leading ultimately to an equilibrium state of maximal entropy where  the  parts  of  the  system are  arranged  in a  state  maximum randomness. Quite contrary to closed systems,  of  living  systems are not moving towards such an equilibrium of maximum randomness, but rather tend to develop an increasing level of organization and complexity during the course of ontogeny and phylogeny.  This  thermodynamics systems are  apparent  violation  can  be  explained  “open,  i.  e.  by  of the  the  second  fact  that  law  of  living  constantly exchanging energy with  the environment. The entropy within the system is lowered at the expense of the surroundings; the overall entropy increases although system.  there  is  a  local  decrease  As living systems grow, 7  of  entropy within  the  their absolute entropy may  still increase over time, but their relative entropy, measured as the fraction of the number of actually occupied the number of develop  available states  (Landsberg 1984,  (Hreai)  will decrease  (Hmax)  to  as they  Brooks and Wiley 1986).  Prigogine (1955) realized that living systems share this and other features with dissipative structures.  Dissipative  structures,  (structures  forming  on  the  convection systems  hurricanes  e.g.  due  to are  that  equilibrium  surface  by  of  strong able  or  Benard  fluids  certain  temperature  to  exchanging  maintain energy  cells as  a  result  gradient), themselves  with  the  of  are  open  away  from  outside  world.  Within a discrete range of energy input such systems tend to towards  develop  increasing  organization,  a  feature  termed  I!self_organizationu. Such systems are further characterized by increasing  internal  (Morowitz systems,  1968)  cycling  Ulanowicz  .  of  energy  the  (1986),  as  they  analyzing  identified cycling as a key feature  model  mature flow  in developing  systems; under certain conditions increased cycling would lead to an increase of total systems throughput as well as raising the level of organization and complexity. The persisting flow of  energy  will  prevent  such  systems  from  reaching  thermodynamic equilibrium; instead the system will eventually settle  down  in  a  state  of  least  dissipation,  investing  a  maximum amount of the inflow in internal structure building (Prigogine 1980). The  concept  of  “dissipative 8  structures”  provides  a  framework for an explanation of the essential properties of developmental processes in the living world,  attributes such  as the directional tendencies towards increasing organization and complexity, larger body size and increasing specialization and diversity in ontogeny and evolution. Higher organization and complexity are achieved by minimizing dissipation. This is realized by internal cycling of the available energy leading to an increasingly finer network of functional interactions accompanied  by  increasing  specialization  and  coherence.  Similarly, the tendency of organisms to become larger as they develop can be interpreted as an energy conserving strategy as large organisms require less energy to maintain themselves per unit biomass than small ones. The actions of the minimum dissipation law also affect the stability of a system. energy,  energetic  elimination important  of  Apart  efficiency  redundant  consequences  can  system  on  the  from increased cycling of also  be  gained  configurations.  systems  resistance  from  the  This  has  against  external disturbance since such redundant configurations are thought to be important in maintaining homeostasis in the face of  disturbance  external  (Odum 1953) “external occurs,  .  meaning  approached.  flow pathways  Concurrently with this decrease in resistance or  stability”  development  through compensatory  an  that  slows Thus,  down  increase in  the  and  with  a  in  absence state  increasing 9  “internal  of age  of  stability”  disturbance,  equilibrium and  is  declining  redundancy,  the  disturbance  while  internally. system  system becomes more vulnerable to external time  same  becoming  more  stable  These two properties define the senescence of a  (Weber et al.  Thus,  the  at  1989)  dissipative  characterized  by  systems  increasingly  in  their  efficient  within a constrained energy economy.  mature use  phase  are  of  resources  Conversely,  under the  relatively unconstrained circumstances of its early phase of development, an open system displays the tendency to maximize the  total  expansion, efficient recognized  system  flow  rather than fashion. by  throughput,  Lotka  those  to use  This  “maximum  (1922,  resulting resources  in  system  the most  energy principle”, holds  148)  p.  in  that  first  “natural  selection will so operate as to increase the total mass of the organic system, and to increase the total energy flux through the system so long as there is present an unutilized residue of matter and available energy”. Prigogine’s tendencies,  and Lotka’s  each  principles  prevailing  at  a  are  countervailing  different  stage  of  development. The mutual interaction between the two is still relatively  unexplored.  According  cooperative tension of focus  resources  into  to  Wicken  (1987)  the  the two will favour strategies that the  stabilizing the web of  system,  energetic  while  at  the  same  interconnections.  time  Thereby  dissipation will decrease and biomass/throughput ratios will be  increased.  In  his  analyses 10  of  model  flow  networks,  Ulanowicz  (1980), showed that the system will seek an optimal  configuration  at  a  point  of  compromise  between  total  throughput and internal organization.  1.2.2.  Application  of  thermodynamic  principles  to  successional development  principles  The  of  “minimum  dissipation”  and  “maximum  energy” provide an explanation for essential properties of the development of organisms and evolution. Similar tendencies are apparent (1969)  in successional processes of  list  twenty-four  by  the  above  summarized in Odum’s  attributes  successional stages (Table 1) explained  as  of  early  and mature  Most of these properties can be  .  discussed  trade-off  between  system  expansion in early stages and energy efficiency in the mature phase.  This  decreasing (Table 1, invest  shift  ratio  is  of  item 2),  gross  clearly  illustrated  by  the  production/standing crop biomass  a result of the tendency of the system to  increasing  in  most  internal  quantitative growth. Ulanowicz  organization  (1986)  rather  showed that,  than  for model  flow networks, many of the attributes of mature systems (Table 1,  items  2,  increased  3,  7,  amounts  15, of  16,  17,  energy  20)  are  can  cycled  be and  produced  when  stored.  The  observed shift from r- towards K-selected species  (Drury and  Nisbet 1973, Pickett 1976, Noble and Slatyer 1980) is a result of  the  same  strategy.  In  an 11  unstable  environment  where  competition is low and energy abundant it is advantageous to invest  the  in  conversely,  a  production stable  of  early-maturing  situation  approaching  progeny; ecological  saturation with limited available energy per individual will lead to a preference of K-selected individuals. From a thermodynamic perspective a reply to (1976,  p.  statement that  112)  Pickett’s  “succession can be understood  solely in terms of the interaction of evolutionary strategies without climax”  reference  to  a  deterministic  progression  toward  would be that both evolutionary strategies and the  deterministic  drive  underlying causes,  toward  viz.  climax  follow  from  Lotka’s “maximum power”  the  same  law and the  “minimum dissipation” principle. Thus evolutionary strategies can be viewed as means whereby controlling thermodynamic laws are expressed in microstates making up the macrostate which is the ecosystem.  1.2.3.  Consequences  of  the  thermodynamic  concept  for  community theory  It  is  obvious  from  the  above  that  a  thermodynamic  interpretation of succession is a holistic one. The principal agent driving succession is identified as an overall energetic strategy of the  system,  a unifying principle directing the  processes manifest on the level of populations and species. Although analogies of succession with organismic processes are 12  considered  difficult  ecologists,  to  accept  by  many  of  today’s  plant  the thermodynamic scenario provides a plausible  explanation for the undeniable similarities of the process of succession with evolution and ontogeny, such as directionality towards  increasing  efficiency,  organizational  stability  and  size.  complexity, The  principles thereby are Lotka’s law of Prigogine’s principle of expansion  the  of  organization and  and  complexity.  close neighbourhood to  common  the  organizing  “maximum energy”  “minimum dissipation”,  system  energetic  driving  it  Such a view Clementsian  causing the  towards is  and  higher  ostensibly in  “superorganism”  and  will have to stand up to Gleasonian objections as well as to Darwininan theory. The Clementsian concept communities boundaries together.  were  strongly clusters  and  view  This  attacked by Gleason  (Clements 1916) integrated  of  species  held that plant  units  with  tightly  sharp  associating  was  simultaneously  but  independently  (1926)  and Ramensky  (1926)  based on the  in species abundance  and presence  observation that changes  occurred so gradually that a division of the vegetation into distinct associations was not justified. Clements’ organismic view was further rejected on the grounds that a community had no  continuity by descent  control  system  community  as  or  a  “individualistic”  an  whole  reflecting  inherited  concept  in  genetic  1947,  (Cain  its 13  lack of  its  message  Whittaker  most  extreme  a  central for  1975).  the This  formulation  would  that  imply  “consequence  of  responses  the  of  ’ 1 environment  the the  spatial  distribution  individual,  species  to  of  relatively  the  gradients  plants  is  a  uncoordinated  in  the  physical  (Simberloff 1980, summarizing the work of Curtis  and McIntosh 1951, Such a radical  Curtis 1955,  stand,  1959, Whittaker 1956,  however,  1967)  is rarely taken as there  is  generally little doubt that the distribution and abundance of the species of  a community result not only from individual  responses to the abiotic environment but also from plant-toplant  interactions.  Such interactions  for light,  water and nutrients,  parasitic  relationships,  experimental 1960,  McCormick Grace  and  and descriptive 1960,  Goss  1972,  Thurston  Connell  Whetzel  Turkington  have  and  1981,  Aarssen  interactions  may  evolutionary  timescale.  interactions  may be  affect  explored  studies 1969,  Eis  Silander  and  1970, 1980,  community Whereas  structure  Harper  (1982)  take  place  to  a  host  Paine  that even  of  De Wit  Sharitz  Antonovics  documented  (1984)  by  (Tansley 1917,  Lubchenco  restricted  neighbouring plants, Eis  allelopathy, mutualistic and been  1972,  including competition  and 1984,  1982). biotic an  on  argued  that  only between  found that entire networks of  (1970)  trees and living stumps were connected by intraspecific root grafting,  a result that led him to recommend a “modification  of the generally accepted concept that individual plants are discrete physiological units” In  light  of  this  (p.29).  evidence 14  it  appears  justified  to  conclude  that  plant  organization. community  communities  Therefore,  properties  (productivity,  stability,  are  etc.)  have  to  the  at  respiration,  likely  some  be  degree  level  biomass,  of  of the  diversity,  influenced  by  these  interactions. Furthermore, it is instructive to note that even though the  thrust  of  the  1947  articles  by Cain,  Egler and  Mason in Ecological Monographs (which led to a breakthrough of the “individualistic” concept) was directed primarily against the  concept  of  communities  as  discrete  entities  taxonomic grouping of these in associations, that  community had  a  beyond  an  assembly  (1917,  p.  473)  no  of  reality  unrelated objects.  himself wrote  “...  occupied competition restricts it proportions”; community]  and  consists  itself  in  Egler  (1947,  of  group  a  and  the  no one claimed was  nothing  fact,  Gleason  or  In  as soon as the ground is [the species] 388)  p. of  to its proper  noted:  species  “...  reacting  [the  among  themselves and with all their environmental factors, so as to attain a ‘degree of integration’  and organization”.  It has to be added that the Clements-Gleason conflict was concerned mainly with plant-plant interactions which obviously comprise only a fraction of the total community interactions. As Ulanowicz  (1986, p.  152)  has noted,  “organization is seen  to exist over the total ensemble of transfers, and. likely place search  -  to  discover  it  is  where  Gleason  .  .  the least  confined his  among the members of the same trophic level”.  Wicken  (1987)  discussed 15  the  holistic  approach  of  thermodynamic  community interpretation in light  evolutionary  concepts.  Whereas  in  of  current  neo-Darwinian  theory  natural selection, resulting in the survival of the fittest, is found to be the driving force of evolution, a thermodynamic interpretation goes one step further and identifies “fitness” as the ability to optimize patterns of thermodynamic flow, be it by maximizing energy flux in unconstrained situations or by increasing principle  its acts  efficient on  all  use  as  a  system  levels  of  a  biological  matures.  This  hierarchy;  individuals, populations and communities are all selected for their ability to maximize and efficiently use energy flow. System configurations of higher organization and complexity are  thereby  at  a  competitive  advantage  over  lower  order  configurations; the higher their organization and complexity, the  more  efficiently  systems  operating.  are  In  WIcken’s  interpretation this advantage constitutes the driving force of developmental  processes,  evolution or  succession.  holds  that  selection  be  it  While  acts  the  on  current  only  on  level  of  ontogeny,  evolutionary theory  individuals  but  not  on  ecosystems as a whole, a thermodynamic approach cannot accept a treatment of that  the  individual units in isolation as  intricate  interactions  among  the  it appears  members  of  a  community will necessarily influence the individual strategies of maximizing and conserving energy flow.  Individuals in an  ecosystem are particularly tied together through the cycling of resources. While each individual “is in business for itself 16  exploiting energy sources for survival and reproduction, it is the  ecosystemic  cycle  to which they  these niches available” Selection  thus  contribute  (Wicken 1987, p.  acts  136)  hierarchically,  parameters determining the  that makes  with higher-level  adaptive possibilities  of  lower  orders. Adaptive strategies are passed on in a top-down way because  ecosystems  have  a  higher  level  of  autonomy  than  populations or individuals. Ecosystems are constrained only by abiotic  constituents  (temperature,  water,  light  etc.),  but  populations and individuals are additionally constrained by their functional relationships with other biotic elements of the system. Levels  of  autonomy  are  best  illustrated by  Polanyi’s  (1969) example of a literary composition: the highest level of autonomy belongs to the text as a whole; the rules of the text determine  the  choice  of  the  sentences;  according to the rules of the sentence; strung  together  according  to  the  words  are  chosen  finally letters are  rules  of  the  words.  Accordingly, constraints on units in an ecosystem increase the lower their location in the hierarchy. Evidence  of  top-down  hierarchical  relationships  in  ecosystems is given by the fact that community properties such as biomass, predictable  respiration etc. patterns;  behaviour of units predictable.  This  (e.g.  at  behave according to relatively  lower  levels  in  the  hierarchy  individual plants) will become less  compares  to 17  the  microstate/macrostate  distinction in entropic  systems  specific  of  configuration  the  (Layzer 1975). community  is  Whereas the one  of  many  alternatives and difficult if not impossible to predict, among such alternatives  the  collective  community properties will  remain relatively stable. While the clerks of a bank come and go the character and purpose of the bank remains unchanged. Thus,  a  thermodynamic  interpretation  of  succession  appears to support the holistic tradition in ecology, although not  in  sense  the  of  Clements’  difference between Clements  superorganism  and thermodynamic  the  -  main  theory being  that ecological systems are not understood to be essentially similar to organisms, but that development on all levels can be understood as patterns of energy flow. The ability  strength to  of  the  thermodynamic  integrate  the  findings  tradition as well.  lies  in  its  the  individualistic  (1973)  observed shift  of  Drury and Nisbet’s  view  from r- to K-selected species has its place in the theory as well  as  Gleason’s  composition.  The  selected  ones  tendency  towards  system;  thus,  (1926)  replacement  can be  of  interpreted  increasing  long  spend a minimal  gradual  living  amount  of  changes  r-selected as  a  community  species  by  K-  consequence  of  the  efficiency  of  the  large body size  that  energetic  species of  of  energy for reproduction will  be  favoured in the mature phase of succession. From a Clementsian perspective it was assumed that plant communities  ought  to  have  sharp 18  boundaries  if  organismic  analogies  were  interpretation  to does  be  correct.  not  Although  claim  that  a  thermodynamic  ecosystems  operate  according to an organismic paradigm, there are common threads with Clements, above all the claim that an ecosystem operates as an integrated whole. It appears now that a gradual spatial change in composition of the elements of a system, for example in response to an underlying environmental gradient, does not necessarily disjoin the interaction between these elements. Thus even if a gradual shift in composition occurs it does not necessarily follow that the system will cease to operate as an integrated unit. Sharp boundaries between different types of natural communities would seem to be no crucial requirement for  communities  to  operate  according  to  thermodynamic  principles.  1.2.4. Development and information  An alternative application of developmental  processes  relies  informational considerations argued  that  Prigogine’s  thermodynamic  less  on  energetic  theory to than  (Brooks and Wiley 1986).  theory  requires  modification  on  It is when  applied to living systems. While hurricanes and Benard cells are ephemeral phenomena that vanish once the energy field that created them ceases to exist,  living organisms are able to  preserve their state of organization by means of the genetic system as the carrier of organizational information. In order 19  to account for this fundamental difference, Brooks and Wiley, following Gatlin (1972), expanded, or rather generalized the second law of thermodynamics to the concept of information. By this view, living systems develop and evolve as a consequence of  the operation of  the  second law in the genetic  While proponents of the “energetic camp” p.  claim  390)  that  transformation”,  “information  Brooks et al.  (Weber et al.  remains  (1989,  system.  tied  energy  maintain that  414)  p.  to  1989,  “biological energy and biological information probably became decoupled  partly  early  in  the  development  of  life.”  A  consequence of this view is that the traditional emphasis of Darwinian  theory  selection  in  on  the  evolution  organism  is  as  the  maintained.  primary  Whereas  unit  of  in Wicken’s  scenario evolution of the species follows the needs of the ecosystem as a whole by means of selection of flow patterns, Brooks  et  hierarchy  al.  (1989,  merely  p.  maintain that  420)  “explains  the  dimensions  the of  ecological the  playing  field, while the genealogical hierarchy gives the rules of the game  being  played”.  In  both  camps  it  is  agreed  that  evolutionary processes operate on all levels and all scales and  it  appears  that  the  differences  of  the  two dissenting  opinions are primarily a matter of emphasis rather than of fundamental disagreement. In  this  energetic  introduction  approach  because  I  have the  relied focus  of  primarily this  on  an  study  is  ecological and explanations are sought for the phenomenon of 20  ecological succession. An ecosystem does not possess an agent whereby historical information is preserved and passed on into the future.  Informational considerations therefore have not  been pursued in detail in providing a theoretical framework for the following analysis.  21  CHAPTER 2 ORDER AND ORGANIZATION IN COUNITY DEVELOPMENT  A  thermodynamic  developmental workings thesis  of  was  process  with  explore  to  of  interprets  of  order  communities.  the  evidence  succession and  succession  essential  ontogeny and evolution.  interpretation changes  view  by  to  similarities objective  One in  support  quantifying  organization within  the  of  be  to of  a  the this  such an  successional investigated  The key feature of a developmental process is  certainly its progression towards increasing complexity and organization. In ecology quantifications of such concepts have been restricted to model systems (e.g. May 1972, 1973) but to my knowledge have rarely been attempted with real data. Before presenting such a quantification for a recovery sequence of lodgepole  pine-dominated  Columbia,  systems  in  west-central  British  a clarification of the terms as used in this study  appears necessary.  2.1. Order  “Order’ pattern  and  is  essentially  involves  concerned  predictability  with  structure  associated  with  or the  spatial or temporal arrangement of the elements of the system. In  a  system  equiprobable  of  low  chance  of  order  all  being 22  elements  encountered  will at  a  have  an  particular  location or time. concept  of  1 Thus  entropy  order has  in  a close affinity to the  thermodynamics  as  well  as  to  “uncertainty”, an analogous term common in information theory. Order in the context of thermodynamics has been defined as representing the proportion by which a system deviates from the equilibrium state of maximal randomness (Landsberg 1984), expressed as (1  -  symbolizing the total of  Hreai/Hmax)i with  potentially available states or maximal entropy of the system, and Hreat  being  the  actual  amount  of  states  occupied.  This  formula defines order as a relative quantity arising from the relationship  of  the  potential  complexity  (randomness  or  and Hreaii the observed or actual randomness of the  entropy) system.  in  ‘reaL’  statistical  terms,  relates  to  the  variation  found within a data set; the larger the error associated with the  estimate  measurement,  of  parameter,  a  the  lower  its  the higher its uncertainty and,  precision if  of  remains  constant, the lower the order of the described system will be. Order also corresponds to the ecology, which  concept of  diversity in  as measured for example by the Shannon-Weaver index  expresses  the  uncertainty  attached  to  the  specific  identity of a randomly selected individual (Pielou 1966). With increasing diversity uncertainty will increase and, given will stay constant, Order periodicity,  its order will decrease.  generally as  is  associated  illustrated 23  by  the  with  pattern  precise  and  geometric  arrangement of an inorganic crystal. Order thus is generated wherever the elements of a system are arranged in a highly predictable involved,  fashion.  e.g.  Where different  the different  types of  elements are  letters of an alphabet,  order  depends not only on the probability of each element but also on the conditional probabilities between these elements. Thus, the  coefficient  regression  of  determination  of  ) 2 (r  (Phillips et al.  the  correlation  determinant  of  the  (1  -  I RI )  IRI being is  -  also  the higher the r 2  respectively  the  -  or  I RI ) for  -  1973),  matrix  expression of the order of a system; term  correlation  which corresponds to the quantity (1  -  a multivariate situation  the  a  -  better  an or the  predictability among the elements of the system. This fact also illustrates the relationship between order and  the  concept  Redundancy or level  of  of  redundancy  in  information density is  predictability between the  Redundancy is present,  for example,  information an  theory.  expression of  elements  of  a  the  system.  in the transmission of a  text, where it would be sufficient to get the message across by using only one symbol but two symbols usually co-occur. The occurrence of these two symbols will be highly correlated and one  of  them  is  considered  Landsberg’s  (1984)  formula  redundancy  (1949)  for  to  be  formula for order as  proposed  are identical.  24  redundant. (1 by  -  In  Hreai/Hmax)  Shannon  fact,  and the  and Weaver  Redundancy meaning will  in  this  decrease  classical  the  information  uncertainty about  an  theoretical outcome.  A  highly redundant code will be of high predictability. The term “redundancy”, however, has an alternative meaning. In ecology, “redundancy”  has  been  used  to  describe  the  presence  of  multiple pathways in a system (Odum 1953, Ulanowicz 1986). As multiple pathways will open up alternative channels of energy flow,  flow  patterns  will  become  less  predictable  with  increasing redundancy. Thus, the presence of such functional redundancy will increase one’s uncertainty about an outcome quite  the  redundancy.  opposite  effect  of  the  information  In the subsequent quantifications,  -  theoretical  redundancy is  used in its latter meaning.  2.2. Organization  Whereas order involves structure or pattern, organization is more concerned with the functional relationships occurring between the parts of a system. An assembly of parts is said to be organized when they behave in a coherent manner in order to carry  out  a  certain  activity.  Thus,  organization  is  the  characteristic feature that distinguishes a system from a mere collection of independent parts. This implies that the interactions in a system are non random;  in  “choices”,  man-made  systems  one  would  speak  of  informed  for example as reflected by the wiring diagram of 25  a computer. Each informed choice is a force acting against the randomness of the state of a system gone  arranging  into  the  -  the more information has  elements  the  further  such  an  arrangement would be removed from maximal randomness (Hmax)  It  appears  is  therefore  that  the  non-randomness  a  of  system  affected not only by its order but also by its organization.  2 .3.  Quantifications  Various  different  techniques  have  been  proposed  to  quantify order and organization. Layzer (1975) stated that in the realms of thermodynamics the  sum  content  of  the  (I)  of  actual a  system was  entropy at equilibrium  Ht  Brooks information  +  and  I  entropy  =  always  and  the  constant,  information equal  to  its  (Hmax):  constant  Wiley  (Hrea[)  =  (1986),  H.  equating  organization  with  (I), proposed the use of this formula as a means  to quantify the amount or level of organization.  The use of  this  concept  formula  rests  on  the  assumption  that  the  of  entropy and the second law of thermodynamics in general can be expanded and applied to information statistics  (Weber at al.  1989) Banerjee et al.  (1990)  proposed a method of calculating 26  order  organization  and  Layzer’s  (1975)  They  variance/covariance  used matrix  (1984) the  to  systems  based  on  formula for order and  determinant  estimate  the  of  actual  the  entropy  of the system. The maximal entropy (H) at equilibrium suggested  was  multivariate  and Landsberg’s  organization.  (Hreai)  in  to  be  equal  to  variance/covariance matrix where equal zero,  the all  determinant  off-diagonal  of  a  elements  indicating complete independence of all elements  of the system from each other. As a graphic representation of these concepts they also argued that the amount of dispersion of data points in multivariate space was an expression of the order  of  a  system,  whereas  the  shape  of  the  dispersion  reflected the structure of the variable interrelationships, i.e. the organization. As the dispersion of points fluctuated, so  did  Hmax  as  -  the  shape  of  that  dispersion  of  points  changed, so did Hreai There is a crucial point though: any one Hreat  does  not  imply  dispersion.  Hreai  microstates  of  a  may which  specific be are  shape  viewed all  as  of a  the  points  in  macrostate,  specific  dispersions  a  the in  multivariate space that have the same Hreat• A simpler approach was presented by Denbigh (1975). The degree or amount of organization,  termed “integrality”,  was  suggested to be a monotonically increasing function of the number of different elements of a system and of the number of useful connections facilitating its function. Rather  than  concentrating 27  on  the  mere  number  of  connections,  Ulanowicz  proposed  (1986)  to  quantify  “ascendency”, a quantity expressing both the size of a system as  well  as  its  degree  of  organization.  Ascendency  is  calculated based on the amount of transfer of matter or energy among the parts of the system. (1986),  the  calculates  approach  is  based  Similar to Brooks and Wiley on  information  theory  and  “ascendency” as the amount of mutual information  present between the nodes of a flow network.  2.4. Diversity and stability  A discussion of order and organization is not complete without the treatment of diversity and stability since there appears  to  be  a  certain  overlap  between  the  two  sets  of  concepts. Diversity and stability are often discussed together and  there  has  been  much  speculation  and  investigation  on  whether the two are linked by a cause-and-effect relationship. One of the objectives of this thesis was to explore what a quantification of the dynamics of order and organization would be able to contribute to this discussion.  2.4.1. Diversity  As mentioned above,  “order” shares a certain conceptual  similarity with “diversity”.  The higher the diversity of a  community, the lower is the predictability of the identity of 28  a randomly selected individual,  hence the lower the order  -  conversely, the higher the predictability of such an outcome, the higher the order and the lower the diversity. series  A  of  different  indices  have  been  proposed  to  measure the various aspects of diversity (see Greig-Smith 1983 for review)  .  The three main components of diversity include  species-richness, species-evenness or equitability and spatial heterogeneity or pattern diversity (Odum 1969, Odum  Pielou 1975).  (1969) predicted all three components of diversity  to be low at the onset of succession and to increase as the system matures;  others postulated a decline of diversity in  the climax after a peak in intermediate stages (Margalef 1968, Horn 1974). Auclair and Goff  examining a variety of  (1971),  deciduous and coniferous forests, found diversity on sites of favourable environmental conditions generally to be highest at intermediate  stages  reflecting  the  overlap  of  pioneer  and  climax species; the subsequent decline was attributed to the exclusion of the shade-intolerant groups in later stages. On xeric  sites,  increase  however,  with  time.  diversity In  was  studies  of  found  to  old-field  continually succession  (Nicholson and Monk 1974, Inouye et. al 1987) species richness and within-field heterogeneity in  species  composition were  found to continually increase with field age. (1987, decline stages  p.  24)  conceded,  however,  Inouye et al.  that “given enough time” a  in species richness could possibly follow in later if  fire  were  excluded, 29  because  old-fields  in  the  absence of fire would develop a pronounced shrub layer and a large component of the herbaceous vegetation would thereby be lost. Connell different  suggested that levels of diversity among  (1978)  communities could be  explained as  resulting from  different frequencies of disturbance. His “intermediate disturbance hypothesis” holds that highest species diversity is  maintained  at  intermediate  levels  of  disturbance.  If  intervals between disturbances are short, a community will be unable to transcend the pioneer stage with its typically low diversity; conversely, very long,  if intervals between disturbances are  competitive exclusion will reduce diversity to a  level lower than in intermediate stages. A thermodynamic explanation of the behaviour of diversity in  the  course  of  of  “least  principle  systems  development  dissipation”.  As  follows the  resources will become increasingly limited.  from  system  the  matures  The tendency of  the system to utilize the resources most efficiently (minimum dissipation),  will  lead  to  increasingly  finer  niche  partitioning of the habitat with the result of an increasing species  diversity.  At  the  same  time  energy  cycling  will  increase and cause increased mutual sustenance. The decline of diversity as the system approaches climax can be explained as the  strategy  redundancy,  to  i.e.  maximize  efficiency  at  the  expense  of  by sacrificing those species that are not  essential in efficient mutual sustenance but rather contribute 30  to maintaining a multiplicity of pathways (Ulanowicz 1980).  2.4.2.  Stability  Whereas  diversity  overlaps  conceptually  with  order,  organization, or more precisely the change thereof, relates to the  stability of  a  system  the higher  -  the  ability of  a  system to avoid organizational change when disturbed, the more stable it is. This ability is often also termed “resistance”, a subcategory of stability describes  “how  equilibrium  fast  the  following  “Internal stability”,  as opposed to “resilience” which  -  variables  return  perturbation”  1984,  (P1mm  on the other hand,  towards p.  their 322).  would describe the  internal tendencies of a system towards change (Salthe 1991), as  illustrated,  for example,  by the  absence or  slowing of  species turnover in mature successional stages. Odum  (1969)  predicted  perturbations to be highest Conversely, Weber et al.  resistance  in mature  to  external  successional  stages.  (1989) maintained that resistance to  external perturbation gradually decreased with age. Experimental evidence is rare and controversial. 1-Turd et al. two  (1971) experimentally tested resistance to perturbation of old-fields  of  different  age  by  adding  inorganic  fertilizer. They found the older one to be both more stable and  more  diverse  than  the  younger 31  one,  but  only  at  the  producer level, whereas diversity and stability decreased on the level of herbivores and carnivores with increasing age. Predictions  concerning  stability  from a  thermodynamic  viewpoint concentrate on the behaviour of multiple pathways of matter or energy in maturing systems. pathways  considered  are  to  be  important  homeostasis in the face of disturbance 1955).  Since  components  a  system the  and  is  defined  Multiple or redundant  by  in  maintaining  (Odum 1953, the  identity  interactions between them,  McArthur of  and some  its of  these interactions are concerned with the exchange of matter and energy,  it  interrupted  the  follows that if this exchange is impeded or makeup  of  the  system  will  be  altered.  Redundant pathways are channels of energy or matter that will maintain  the  flow  and  characteristics of the function.  Thermodynamic  thereby  preserve  the  original  system when other pathways cease to theory would predict  efficiency to  increase as the system matures, which can be achieved either by  increased  multiple  cycling  pathways  and/or  by  (Ulanowicz  sacrificing  1986).  Thus  a  redundant  or  thermodynamic  interpretation appears to support the view that as redundant pathways are eliminated a system will become more sensitive to disturbance as it matures. It is clear from the above that the idea of flow pathways is primarily concerned with the exchange of matter or energy between different trophic levels, and in order to test these ideas, ideally patterns of flow pathways should be documented 32  for a successional sequence in an ecological system. Although in this thesis data are available only for species composition and abundance on the producer level for different points in successional time, conclusions regarding system stability may still be possible based on a quantification of the redundancy in the  present  data  structure.  This  approach rests  on the  assumption that the degree of redundant system configurations (multiple pathways) the  would be reflected by the redundancy of  structure  data  as  quantified,  for  example  by  equal  frequency ellipses in multivariate space (see section 5.4.1) If  it  is  further  assumed  that  changes  in  the  correlation  structure of the species data will reflect an organizational change  the  of  whole  it  system,  can be  assumed with equal  justification that a change in redundancy of this one trophic reflect  level will  changes  in redundancy of  the  system as  whole. The  “resilience”  aspect  of  community  stability  is  concerned with speed and course of recovery from disturbance and describes the processes by which a system recovers from perturbation and regains theory  such  an  its  equilibrium.  equilibrium  state  has  In successional been  addressed  traditionally as “climax”, a concept subject to considerable controversy.  Whittaker  “steady-state population,  of  with  community the  p.153)  (1953,  defined  productivity,  dynamic  balance  of  climax  structure its  as  a  and  populations  determined in relation to its site”. In support of the climax 33  concept, Grime (1979, p.154) describes secondary succession to be characterized by the  “progressive decline in the rate of  floristic change”. This declining rate of autogenic change in maturing successional systems has been referred to as increase in “internal stability” Conversely, conceding  (Weber et al.  Connell  that  such  an  and  1989)  Slatyer  equilibrium  (1977,  may  be  1135),  p.  possible  in  communities where species replacement occurred in a strictly vegetative  fashion,  claim  to  have  “found  no  example  of  a  community of sexually reproducing individuals in which it has been demonstrated that  the average  species composition has  reached a steady-state equilibrium. Until this is demonstrated we conclude that,  in general,  succession never stops.”  It should perhaps be noted here that “internal stability” (Weber  et  al.  1989)  is  not  to  be  confounded  with  the  “resistance” aspect of stability. Internal stability refers to the autogenic changes such as species turnover and population fluctuations Resistance,  that on the  occur  in  the  other hand,  absence  refers  of the  to  system to cope with external perturbation. stability  is  believed  to  increase  as  decline by others  ability of  a  Whereas internal  the  resistance is thought to increase by some  disturbance.  system  matures,  (Odum 1969)  (Ulanowicz 1986, Weber et al.  and to  1989)  The analytical methods of this study were used to explore the dynamics of recovery and to what extent a steady state is approached by the system as it recovers from disturbance. 34  2.4.3.  The interplay of diversity and stability  Multiple pathways have been interpreted to be buffers of a system against disturbance. McArthur (1955, p.534) proposed as  a  measure  of  community  stability  “the  amount  of  choice  which the energy has in following the paths up through a food web”.  From this idea it would follow that the chances of a  system to become more stable increase with its complexity, conclusion years (e.g.  that  has  dominated  ecological  thought  for  a  many  (Elton 1958). Mathematical explorations of the problem May  suggesting  1972, that  later  1973) it  was  testing McArthur’s  not  argument  undermined generally  this  true.  proposition Pimm  with simulated data  (1979),  found  that  stability could either increase or decrease with increasing complexity,  depending  on  which  trophic  level  increased  in  complexity. Stability increased with increasing complexity of the producer level,  but declined when higher trophic levels  became more complex. To my knowledge only two field studies have attempted to document the connection between diversity and stability for the producer level. McNaughton  (1978),  Both are  in support of  Pimm’s results.  applying May’s mathematical models to an  ecological system, quantified plant community organization in East  African  grasslands.  He 35  made  the  (rather  sweeping)  assumption  that  positive  associations  between neighbouring  species reflected facilitation and negative ones were evidence for competition. From May’s model it followed that stability might  increase with diversity if  interaction strength  effect of species j’s density on a change in species i) connectance  (the and  (the fraction of all possible pairs of species  which interact directly) declined as more species were added. Both interaction strength and connectance richness increased which,  declined as species  for the producer level,  appears to  support the traditional proposition that more diverse systems are more stable. The other study  (Frank and McNaughton 1991)  came to a  similar conclusion, finding that in grasslands of Yellowstone National Park,  stability, measured as the resistance against  drought-induced change in plant species composition, increased with diversity. Pimm support  (1979)  and the two cited field studies appear to  conclusion  the  that  increasing  complexity  on  the  producer level (the level this thesis is exclusively concerned with) will lead to higher system stability. Ulanowicz should be  (1986)  regarded as  environment  a  proportion of  system  suggested that diversity and stability a  cybernetic  would  be  forced  multiple pathways  developing  high  environment  would  diversity. allow  couple. to  36  maintain  (high redundancy),  Conversely,  more  In an unstable  efficient  a  more  a  high  thereby benign  organization  (low  dissipation) accompanied by lower diversity; however, related to its low redundancy, such a system would be more fragile and displaced  equilibrium more  from  easily  than  one  developed  under harsh external conditions. Thus, the system would settle in  a  point  compromise  of  organization,  the  between  equilibrium point  redundancy being  and  optimal  dictated by  the  amount of stress imposed on the system by the environment. Whereas  the  cited  studies  are  efforts  to  explore  the  relationship of stability Ci. e. resistance) and diversity in plant communities, no work to my knowledge has quantitatively related the resilience (i. e. the rate of recovery), of plant communities to their diversity or complexity. Thus a further goal of this study was to explore how the state of order of the  recovering  system is  related to the  system recovers from disturbance.  37  rate  at which the  2.5. Research objectives  Specific research objectives of this thesis included:  1.  To  quantify  “order”  and  “organization”  by  multivariate techniques in a recovery sequence of lodgepole pine-dominated forest communities.  2.  To  evaluate  a  thermodynamic  interpretation  of  succession for the community under investigation in light of  this  quantitative analysis of order and  organization. As such an interpretation claims to provide an explanation for developmental processes in general,  phenomenological  similarities between  patterns of successional and organismic development were also explored.  3.  To investigate the relationship of diversity with different aspects of stability,  namely resistance  and resilience of the system, based on the results obtained  by  “organization”  a  quantification the  as  disturbance.  38  system  of  “order” recovers  and from  CHAPTER 3 THE STUDY AREA  The data for this thesis were collected in 1991 and 1992 in  lodgepole  pine-dominated  forest  communities  of  the  Chilcotin River headwaters, west-central British Columbia. The relatively  high  frequency  of  forest  fires  has  produced  a  landscape composed of a mosaic of forest stands of different ages. Heinselmann  (1981)  cited fire frequencies of ca.  every  50 years for a comparable community type in Eastern British before  Columbia  the  arrival  of  European  settlers  whereas  present fire frequency is reported to be ca. 200 years. These stands offer ideal objects for the study of temporal dynamics related  to  their  relative  structural  and  compositional  simplicity as well as for the availability and accessibility of different age classes and site conditions within the same community type. The study area lies in the Interior Plateau physiographic region of British Columbia  (Fig.  country of  rolling  mostly  flat  between  or  gently  1000  and  consisting of lava flow,  1500  1).  m.  Its central part  terrain with The  geologic  is a  elevations underlay,  is covered in most parts by glacial  drift with very little bedrock exposed. Within this area the Itcha  and  volcanoes, ca.  Ilgachuz Mountains,  formed by dome-shaped shield  rise above the study sites,  reaching a height of  2400 m (Holland 1976). The study area falls within a very 39  ‘-  .  Ci) Ct  Q  H,  H  I  P  C)  o  •  H  H  Ci)  <  H,  0  P.)  ‘-ci  5  c-ICD  H  3 3 i pJ  P) 3  5 CD  CD  Ct  Ct CD çi  P.)  HCt  Cl)  -  CD CD  1-4  C)  •  o  Cl)  H,  0  S  1-  o  H,  CD  Ct  H-  w  w  H  H-  Ci)  c-IJ H-  Ct  p H H  H,  H-  )  P.) H  -)  Is) -J  H,  CD  ‘-Q  hI P  CD  <  P.)  H  P.)  H-  Ci)  P.)  CD  5  P.) t‘<  q p i  (1  p  H  HCt  o  Ct  ()  P.)  Ci)  Ct  1-4  0  ‘-CI  CD  hI  Ct  (1  p.)  CD °  H-  H0)  Ct  Ci)  p.  CD  —  -  0  P.)  0 hI  °  CD  Ct tY  0  Ct  Ci) Ct  Ct hI H-  P.)  CD CD  1-4  C)  CD Ci) Ct  H  0 0  Cl)  CD  0  H-  --  —  ‘.71  Ct  P.)  CD 1  H  -  hI CD p.)  0 P.) 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H,  Q  Cli ( CD  CD  CD  H0  Ct  I-  CD  <  Cli  CD  Cr  CD  H-  in ‘ZI CD  Cl)  Hi  -C)  H-  Cr  CD  Cr  CU U)  CD  CU  ft  CD  Cr  0 I-ti  CD  U) -  p,  U)  CD  H-  Mi  H-  Cl  0  CD  0  ,  Cl  it  i CD  H-  rr  CD  C)  CD CD  S  CI)  3’  Cr  t  0  U)  CU  H-  Cl  H-  P Cl CD U) Cr  CD  Mi  CD  it Cl)  0  Q  (l  CT)  ) 1  5  U)  CD  c-r  CD  Cr  U) H-Cl)  i CD  CD  CD  C) CD  k<  P  d  0  H,  Cr  CD  H-  IrJ  U)  0  U)  H  Cl)  H-  P  CU  o  H  i  o  d  CD  Cl  i0  H-  C) C) Cl) U)  o  S  I-h Hi  Cr  I-  0  CD  i  U) H-  CD CD U)  it  Cr  P CD Cli U) Cr  Cr  CU  Hi  CD  CD  CD  C)  H  CU  U)  II  CD CU  <  -  i-  CD  .<  CU  i—i  CD CD  ft  CD  Cr  ‘  0  CD  t  CD  HCr  Cl  CU H:i  8  o  U)  r  U) HCr CT)  O\°  C)  P  ‘D (3l I  oi  o\o  Ui  I  —  ii  -  o\0  -i Ui  I  P  U,  II  \O  0  I  O  II  i  o\0  Cr1  CD 0  CD  CU  CD  CD  L\)  •  )  I  CD  CU  CF  H-  CD  H-  Cr CD  I H-CU  Cr 1 CD CD  (.Q  Cr H-  8  a  H-  ii  ft CD  Cl CD  U)  CU  II  o\0  Ui  a  II  P  CD U)  U)  Cl) U)  I  CD  o  U) H-  (Q  H-  0  P  0  CD  ft  i  CD  HCr 3 H  Hi  Cl  Cl)  Cfl CD  Ii  Hi  Hi  0  HCD  CD  P  Cl)  H  l-  CD  <  0  C)  Cr  Cli it CD Cl  S  H-  CD U)  H-  U)  CD i  C)  P  0 P Cli HP 0 PU) k< CD  HU)  <  CU  Cr  H  Cl  CU  Cr  CU  -i  C)  CU  U)  CD  0 d  ‘-<  )-  y  CF  C) CD i  I-  CD  d  Cl  -  it  CD C)  U)  Cli  Cr  CD CU  P  Cli  Cl)  hj  CD  H-  U,  Cr  Cl)  C)  I—’  0  k<  HC) Cl) P P  it  Cli  Cr  U)  <  CD  I-  CD  5  C>  Ui  <  j  CD  iCU  Cl) Cl  5  U)  Cli  U) CT) C) Cr U)  pi  CF  c  c-t  Ct  CD  CD  ;;-  Cl  CD  -  CT)  o  j  p  CD  3  ft  CU  C)  H-  Cl  CD  l-  CD  d  -  Cl  P Cl) C) CD  CD  CD  U)  Cl)  S  p p CD H  Cl)  ‘-d Cli  CD  ft  U) H-  C)  Cl)  CD  -  0 i  CD  O  P  U]  H  CD  Cr  H-  Cl  C) 0  CU  Cl  cj  I-  CD  ‘<  I—’  Cli  U) 1:5  CD  ft  Cl  Cl)  Cl) ft H  CD  CD  CD  Cr j  Hi  0  CD  ft  CD  C)  CD  CU  H  i ft Cl)  CD  0 j  <  HII  CD  ç.  Cl)  p  Cli  i  0  H-  it  CU  Ct  CD  CD 1C  HCl) 1J P CD < (DID P Cli  j  Cl  Cli  0  Cl) Ct H-  t  CD  CD  <  F  CD  0  C)  Cl  0  Q  P  Tree density was estimated by the point-centred quarter method (Cottam and Curtis 1956) older than 10 years  .  Distance to the nearest tree  (age of young individuals of  lodgepole  pine can be easily determined by counting branch whorls on the main stem) was recorded in each of 4 quadrants centred on the 30 sample points used for estimating percent cover of ground and shrub vegetation. Percentage of overstorey canopy cover was determined by counting  the  number  of  points  under  the  canopy  at  1-rn  intervals along the three transect lines. Crown height was estimated by means of an Abney level and recorded for 12 trees per site on four systematically chosen points on each transect.  4.2.3. Environmental variables  Preliminary  inspections  of  site  conditions  and  the  associated plant cover suggested that floristic differences were influenced primarily by differences in the moisture and temperature regime which inspired the choice of environmental variables  sampled.  Light  regime  could  be  inferred  from  variables sampled of the tree layer, such as stand density and percent canopy cover. On two systematically chosen points on each transect, two soil samples of 50 cm depth were taken (n=6 per site) coarse  soil  fragments  (particles 45  >2  mm:  gravel,  .  Percent cobbles,  stones)  was  determined  by  measuring  the  volume  of  coarse  particles in proportion to the total soil volume. Aspect level.  and slope were measured with compass  Potential direct solar radiation  and Abney  (cal/cm / 2 day)  for a  midsummer day (June 22) was calculated for each site based on values for slope steepness, aspect and latitude  (Buffo et al.  1972) Position  on  the  slope  (top,  upper,  mid-slope,  lower,  bottom) was recorded for each site. Elevation on each site was determined Clusko 11  by  means  River”,  of  topographical  1:50,000,  Dept.  Resources)  46  of  maps  93  c/9  Mines  and  (sheet  Energy,  CHAPTER 5 QUANTIFYING ORDER AND ORGANIZATION IN FOREST SUCCESSION  5.1.  Space-time substitution  Forest succession generally does not occur within timescales convenient for human examination; typical life-spans of ecologists and, more importantly of research projects, are too short to document vegetational change of a recovery sequence within the same stand.  The next best solution is to compare  stands of different age that occur under similar environmental conditions;  thus,  a  sequence  in  time  is  substituted  by  a  sequence in space and conclusions on successional dynamics are inferred from the latter. Such an approach of course suffers from the shortcoming that site conditions among such stands will at best be similar but hardly ever identical. To justify substitution  space-time  environmental  it  will  have  conditions among stands of  to  be  shown  that  different age are  essentially similar. In  addition  similarity  it  to  the  should be  requirement  shown  that  of  environmental  vegetational  variation  resulting from historical factors, such as fire intensity and availability  of  propagules,  is  unimportant.  Therefore,  order to be able to assess such historical variation, within  the  same  identical age,  age  class  preferably  should  not  sites be  i.e. not originating after the same fire. 47  in  of  Space-time substitution was considered to be valid for the selected stands of this study for the following reasons:  1.  The geographical distribution of the sites was confined to  a  relatively  small  range.  within a circle of ca. elevation  covered  assumption  of  not  The  sites  25 km diameter; more  similar  than  climatic  Ca.  were  located  differences in 170  m.  conditions  Thus for  an all  selected sites seems valid. 2.  Within the study area only sites from upland locations were selected;  no sites from valley bottoms or ravines  were chosen. 3.  Species  composition of  the tree layer among sites was  very similar if not identical.  On most sites lodgepole  pine was the sole tree species; only on some of the more mesic sites were occasional individuals of spruce found. 4.  Although the combination of site factors (slope, aspect, percentage of coarse soil fragments) each site, cover  beta diversity  between  sites  of  was different for  (gradient length) the  same  age  for ground  class  was  low  (section 5.4.). 5.  Before quantifying order and organization an effort was made to take environmental variation into consideration by a)  separating habitat and age effect  from the data  (section 5.1.1.), and b) dividing the data into mesic and xeric variants  (section 5.1.2.) 48  Every  6.  age  different  class fires  included -  thus  stands  that  allowing  originated  an  assessment  from of  unexplained variation resulting from historical factors.  5.1.1.  Separating habitat and age effect  Before quantifying order and organization an effort was made to remove environmental variation from the data in order to  variation  retain  purpose,  reflecting  age  effect  alone.  For  this  the total variation of all 62 sites was partitioned  into the variation caused by the environmental factors and the variation reflecting stand age by a procedure recommended by Johnson  (1981) Regressing the vegetational variables with stand age  1)  yielded the residual variation from which age effect had been removed;  Johnson  labelled  these  residuals  as  “habitat  To obtain the variation resulting from age,  two PCA’s  variation”. 2)  were performed: one on the raw data and one on the residuals obtained in step 1). The scores for each site obtained by the PCA on the residuals were then subtracted from the site scores obtained by the PCA on the raw data. upon  which  subsequent  It is these final scores  characterization  of  order  and  organization for was based. This rather indirect approach was necessitated by age not 49  0  ft H0  H-  C) CD Cl  3  C) 0  CD Fl  P1  ft  ,-  CD  H 0  H H  CD  CD  P1  I-I CD  P1  H  P1  Cl)  P1  Cl  -  ci ‘<  H  Cl CD i Cl)  CT) CD  fit-  Ci)  Hft CD  HC)  f-I  >< CD  Q  CD  ,  o  C)  i-  Q  d  o  —  J CD  ci :CD  U)  P1  H  CD H  U)  P1  CD  H  l CD CD  (—I  CD  ft  Hi  0  i-i  ci  U)  CD  ci  CD  3  CD Cl)  Hft  U)  HC)  f-I  X CT)  Cl  91 3  H-  CD Ci)  0 Mi  CD  H-  f-I CD  <  H  (.Q  H3  f-I Cl  C) C) 0  P1  P1 Cl CD  CD  CD  o  H-i  0  U)  C) ft H0  Cl)  f-i  f-I  C) 0  -  0  ft H-  C) H 1 (I) Cl) HHi HC)  <  ft H-  P1  CD  Ii hI C) ft H-  CD  L_L  U)  CD  ft  H-  Cl  C)  Mi H-  H-  Cl)  U)  P1  H  C)  < CD  ft H-  CD C)  CD CD  Fl  1  P1  HU)  Cl  HU) ft  O  ft  CD  I-I  CD  H, Mi  H-  Cl  (-I-  C))  CD  H i CD  Mi  Fd 0 Cl)  ft  i  H  C) 0  0 ft C)Mi  CD H‘-Q  3  C) ‘-1 O  ‘< U) HU)  H  P1  P1  H-  Fl  H-  Cl  Hi  0  CD  C1  0 ft  H Hi  Cl  Hi  U)  Cl)  Mi  0  CD 3 C) CD  Cl  H3 C) H-  0  C)  1  3  0  ft H-  1  Cl  1  I-I  Cl  p,  ft  CD  U)  U)  ft  CD  -‘  Hi I-  IU) CD  0 P1  C)  CD  0  H  Cl)  H CD U)  P1 b  h’ H-  pj  <  H  ci P1  CD  i  I-I 0  H-  <  CD 3  CD  ft  IQ  H-  3  Cl  0  f-  Cl  o  U) CD  p  3  H  Cl  Hi  0  Cl) U)  3  ft H-  C) Cl)  HMi H-  Cl)  P1  H  C)  CD  <  ft H  CD C)  ‘--  CD  ci  ft  H-  O\O  ‘-  Mi  3 C) CD  Cl CD  H3 C) H-  C)  C)  P3  i  CD  ft  Cl) Hi tQ  Cl  f-I 0  ft  U)  H-  Mi  P1  H  X  CD Cl)  P1  ft  (  Cl)  P1  f-I  H CD Cl)  Cl)  CD  Cl  HO < U) H-  3 C’  CD  d 0  0  p1 H  H-  i  I-I H-  b  C) CD Cl  Cl  HCl)  Cl)  f-I  CD  1  Cl) H  P1  ft  P1  Cl  Cl  i  P1  H-  U)  CD  S  0  0  H-  <  H-  Cl  0  H-  Cl  C)  0  H-  Cl  H-  Cl  b  k<  0  )  Q  ft  C-F  3 Cl)  H-  5  H-  ‘I  HU) C)  Cl  Cl  CD Cl) (-F CD  0  U) U) HMi HC) P1 ft H-  C) H  CD  Cl)  -  Cl  U) HMi HCD  U)  C) H 91  0  CD  CD  U)  CD  H-  Cl  i-  0  P1 C) C)  Cl  I  HCD  0  CD  C) P-  CD  Ti  H-  0  HH  c-I-  ft 0  H-  U)  U) Hci CD  H  p1  P1  ft  tT  0 3 S CD  f-I  H-  <  i  CD  f-I  H  5  ,  I-I  -Q  0  c-f-  H-  CT)  H-  Cl  CD  cF  U)  ‘-Q CD  U)  Cl  Mi HCD H  CD  ft  H  <  P1  CD  U)  b  0  CD  <  CD C) ft H-  C)gCD  ‘-1  3  CD  ft 91  Cl)  Cl)  U)  Hft CD  CD  J  H  ft  P1  ‘-I H-  <  P1  ft  P1  Hf-l  ft Hi1QH,  CD  CD  ‘—3  CD  Ti CD  H  CD C)  (-F  CD Cl  H  f-I  U) C)  Cl  CD  0  91  CD  ft  0  C)  P1  0  f-I  P1  CD  P1 ft H  I-I  H ft CD  P1  U)  (F  P1  H  f-I  P1  HC)  f_I  CD  Cl  P1  HC)  CD U)  S  0  ft  H  ft CD U)  H-  U)  0 Mi  H 0  Cl)  H-  1:1 H  H  U,  -  CD U)  C) H-  ‘—‘  f-I  -  Mi  Ti CD  P1 H  <1  CD  S  P1  U)  CD  ::5-  c-f-  Mi  <  H0 i  U)  U)  CD  f-I  ‘-I  I-I 0  Hi  U)  CD  Ti  H  )  ft CD  HC)  Cl  I-h  U) CD  H-  I-  CD  f-I CD  Cl)  pj  CD  Ti U)  C) P1  CD  b H CD  P1  Ti  C)  Cl)  (  3  H-  b CD  T (.Q  H-  P1  U) HU)  H  P1  CD  P1  P1  U)  U)ft  U)  C) H P1  (.Q CD  P1  S  CD  c-f-  0  CD  U)  H H  91  H  Cl  H  Ti  CD  I-I CD  U) Ti  ft  -  U)  U) CD  U)  91  H  C)  CD  P1  J’  0 Ti H Cl  on mesic  sites;  (Figs.  and 4)  3  characterized by dominance  of  .  Xer±c  fruticose  sites were lichens  further  (Cladonia,  Cladina spp., Stereocaulon spp.) whereas on mesic sites ground cover was dominated primarily by the feather mosses Pleurozium splendens  Ilylocomium  and  schreberi  and  foliose  the  lichen  Pelt igera aphthosa. Calculations for order and organization performed on the separate mesic and xeric variants of course were based on the i. e. not treated by the technique of Johnson  original data,  (1981) as described in section 5.1.1., because this technique, if successful, would also remove differences between mesic and xeric variants.  b)  a) 15000  100  -  80  N  100QQ  \  .._x sooo  f’%j4 /  o-  17  //•  40-  20 0  1  2  I  I  I  I  .3  4.  5  6  1  WE GLJ.SS  Fig.  3.  2  .3 A  4  oL.ss  5  6  Temporal development of a) tree density and b) canopy cover. Separate mesic (M) and xeric (X) sites.  51  b)  a)  60  20  1  I  I  60 16  /  1/ /1 / ,•“  10  4.  /1  //  20  /1  0  1/  ‘I  ii  10  I I 0  2  a •A  4  6  6  4  1  5  6  cuss  Temporal development of a) crown height and b) /ha) for living trees. Separate mesic 2 basal area (m (M) and xeric (X) sites.  Fig. 4.  5.2.  0-  -  1  Potential problems in quantifying organization  While  it  is  theoretically  possible  to  calculate  the  degree of organization of a system based on the interaction pattern of its constituent elements,  (Denbigh 1975, Ulanowicz  1986), in natural communities one is faced with the more basic problem of identifying such interactions. Greig-Smith  (1986)  identified  heterogeneity  of  the  habitat to be the principal difficulty in assessing degree of organization in plant communities. habitat  In a completely uniform  it would be possible to assign any deviation of  52  a  random  distribution  of  heterogeneous habitat,  the  species  however,  to  interaction.  In  a  it is difficult to separate  non-random patterns resulting from interaction from those that reflect heterogeneity of the habitat. Thus, in a heterogeneous habitat,  positive  a  necessarily simply be  result  association from  caused by a  a  of  two  beneficial  species  does  not  but  may  interaction  similarity in their response  to the  physical environment.  5.3.  Proposed solution  -  quantifying “organizational change”  instead of “degree of organization”  The approach taken by this thesis attempts to circumvent the  above  resulting species  mentioned from  habitat  interactions  difficulty  of  separating  heterogeneity by  from  quantifying  those  not  a  patterns caused by  “degree  of  organization” for a particular community-type but the change thereof  between  time  intervals.  In  the  ideal  case  where  changes are quantified between different time intervals within the  same  habitat,  heterogeneity  reflecting  habitat  can  be  assumed to be stable and the between-time-interval variation can be relegated entirely to organizational change. less than ideal situation,  as in this study,  development  based  is  monitored  on  stands  In the  where temporal from  different  locations in so-called space-time substitution, an effort can be made to approximate ideal conditions by removing habitat 53  influence from the data structure and separating the data into environmental variants  (see section 5.1.)  5.4. Analytical methods  Data analysis in this thesis focused on quantitatively describing the temporal dynamics of order and organization as the system recovers from disturbance.  To quantify levels of  order in each age class and the organizational changes between these  temporal  emphasizing  stages a multivariate approach was  variable  intercorrelations  as  applied, means  a  of  expressing these dynamics. The use of multivariate techniques was  considered  to  be  essential  in  capturing  order  and  organization because both concepts describe qualities of the system as a whole which cannot be assessed by a fragmentation of the system into the separate individual variables. Multivariate analysis was based primarily on principal component analysis  (PCA).  Although reciprocal averaging and  detrended correspondence analysis have been shown to produce less distortion of long environmental gradients than PCA so called “horseshoe” or “arch” effect 1987)  -  (Gauch 1982,  -  the  Minchin  the use of PCA appears to be justified for the data  set of this study, sites were  since the environmental conditions on all  relatively  similar  except  for  gradient between mesic and xeric sites.  a  Gauch  short  moisture  (1982)  stated  that for data sets with gradient lengths of less than two or 54  three “half-changes”, PCA, assuming a linear response of the species to underlying gradients, may be superior to uni-modal methods  as  such  correspondence  reciprocal  analysis.  The  averaging unit  or  detrended  “half-change”  expression of gradient length or beta-diversity, the  is  an  defined as  “distance along an environmental gradient necessary to  reduce sample similarity to one-half that of zero-distance” (Whittaker 1960,  48).  p.  Gradient length was calculated for  all sites and was found to be highest on sites of age class 4 (151-200 yrs.)  with an average gradient length of  .940 half-  changes. methods  The change  were  structure  of  based  among  this  on  study  the  to  quantify organizational  assumption  variables  reflects  that  the  the  correlation  organization  of  a  system; thus, an assessment of organizational change is based on changing variable intercorrelations Maze  et  al.  abundance  1986,  and  other  evaluate organization, these  variables  For  1987).  a  vegetational  (Scagel et al.  plant  community  variables  are  1984,  species used  to  whereas the changing correlations of  between  time  intervals  will  reflect  the  organizational change of the community as it moves between different successional stages. All program  calculations SYSTAT  were  (Wilkinson  performed 1990).  using  Equal  the  frequency  computer ellipse  statistics were calculated by a program written by Rob Scagel.  55  5.4.1. Equal frequency ellipse statistics  The degree of order and organizational change, based on the  investigation  associated  of  change  variable  of  these  intercorrelations  relationships  in  and  time  the were  illustrated by the calculation and graphic display of equal frequency ellipses in multivariate space. Equal frequency ellipses are two-dimensional extensions of  the  one-dimensional  standard  deviation.  The  standard  deviation is a measure of the spread of the observations. bivariate  space  the  standard  deviation  distributed  observations  takes  the  form  describing  the  containing  the  region  for of  an  In  normally ellipse  percentage  of  observations specified by the probability level. Location,  size and shape of the equal frequency ellipse  depend on several different parameters; the coordinates of the bivariate  mean  will  determine  the  centre  of  the  ellipse  whereas the standard deviations of both variables and their covariances will  determine  the  shape  and the  size of  this  region. The size of the ellipse will of course also depend on the probability level associated with it. The orientation of the ellipse is determined by the slope of the principal axis fitted through the data points. The angle between the original and the major axis of the ellipse is commonly designated as “theta”. 56  Principal  component analysis is a convenient technique  used to obtain the location of the major and minor axes of the ellipse. of  ) 2 A 11  The two e±genvalues  variation  in the  respectively,  by  direction of  appropriate  representing the amount  the major and minor axis  calculation  (Jolicoeur  and  Mosimann 1960), will yield the coordinates of the extremities of  the  axes  A’,B  (A,  and B’)  the  -  determine the shape of the ellipse frequency  ellipse  these  points  four points  (Fig.  are  5)  given  .  needed to  For a 95%-equal  by  the  following  vector equations:  Major axis:  , 1 (X  ) 2 X  =  ) ±  Minor axis:  , X 1 (X ) 2  =  !2)  ±  5.99  *  , ) 11 (U 12 U  5.99 A 2  *  , 21 (TJ  22 U )  The centroid of the ellipse is given by 5 and X . U 2 11 and 12 symbolize the first two eigenvector elements of the first U PCA axis,  while , 21 U  22 symbolize the same elements for the U  second one. Eigenvector elements represent the cosines of the angles by which the principal axes are rotated in relation to the original axes; associated  with  orientation of axes.  thus the first element of the eigenvector  the the  major major  axis  axis  ) 11 (U  in  will  also  relation to  yield  the  the  original  The value of 5.99 is the chi-square value at the 95%-  level with two degrees of freedom. An  equal  eccentricity,  frequency ellipse  is  and  Each  orientation. 57  described by of  these  its  area,  properties  ())  U]  CD  ci  H’  0  Ci CD  H  <  CD  -  ci  H CD  H  cv  U)  ci J’ CD  pi i-  H  H-  C)  CD  CD  ci  ci II CD  CD  C)  ci  CD  12  cv  C)  H’  CD CD  CD  CD  C)  P)  ci  HU)  12  CD  rt Y’  CD  H’ 0  CD  CD  -  (1  12  CD  H  H  H-  d U) CD  H-  H  H  CD  II  CD  o  C) H  CD  —  u-i  M  ,  -  I  -  H-  cv  CD  ci  M  Q  ci J’  H CD  CD  -t-  H  cv  CD $2  H-  12  C) H-  H’  ci  CD  ci  CD  CD  CD  CD  C)  cv  ci  HU)  CD  ci  H H’  cv  k<  CD  H’ 0  P  CD H’  U)  P)  12  cv  H  ‘  ‘  cv  U)  F-I  -  U)  < CD  pi  I-  0  Hi  5  J  cv  ci  H-  H-  ri-  CD  CD C)  12  cv  H’  ci  H CD  j  0  H-  ‘  ci H-  cv  H-  U) CD  H-  H H  CD  CD  CD  H’  H  CD  cv  H’  0  H’<  CD  CD  H’  0  H-CD  CD U) U]  d tI  >c  CD  CD  (I)  H H-  H  CD  ‘<  CD  CD  H’  H  cv  CD  CD  Ct  0  Hç1  C)  j-.  ci  C)  C) CD  M  H  •  Ui  X  1  H  CD  H’  Q  5  CD  U)  H’ 0  -  d U) CD  H-  C)  <  CD  Ci  CD  H’  H  Ci 1  CD  CD  ci  H’  cv  CD  I-i  CD  Pi  H  CD  CD  CD  rt  Cl) t-  H CD HO H  ‘<  ci J CD  CD  U) ci  H’  o  CD  12  0  CD  ci  0  d  CD  U)  cv  12  ci CD  d  ci CD  H-  b’ CD  )-j  CD  0  CD  ci  cv  cv  CD  P1  CD  0  CD H’  CD  CD  cv  CD  < CD  H-  12  U)  CD U)  i—’  ci 3’ CD  U)  CD j ci  S  i-. CD  CD P1  CD 12  rt  cv  CD  d  CD  H’  C) HU) H 0  CD  I-  ‘ti  CD  ci  H-  CD  i  0  H-  ci  Hb’  ICD Pi  U)  d  CD  j H  S  cv  U)  CD  ci  H’  CD  cv  ci  H H CD  5  U)  -  (I)  CD  pi U)  CD  Hci  12  ci CD  cv  H-  C)  U)  cv  H-  CD  CD  ci  12  i  H-  CD  CD  ci  ci 12 CD 12Q H’  1j 12 P-H-CD H U) ‘d H ci CD I-’ Pi  H HO H  cv  ICD  P.  Cr  CD  CD  HU)  0  H-  H  d 0 Cfl  CD  Ct 3’  Mi  0  H-  o  U)  ><  CD  pi  H-  ci  l  *  cv  H-  *  -.  H-  Pi <  ‘1  0  LJ  5  H’  o  ci  12 Ci C)  0  ci  Pi  0-’  ci CD  H  cv  H C)  cv  C)  HU)  CD  H H-  H  CD  ci  H’  0  CD  U  CD  U) CD  CD H H H-  C)  CD  CD  H’  H  CD  CD  0 H  CD  H  H  •  Ui  •  5  cv)-  U)  i  cv  g  1  H-  H  CD  ci  cv  S  0  C H’  CD  ci  ci  CD  HH, H’ CD  12  cv  U)  CD  <  0  C)  p1  H’  o  ci U)  iR Cl P1 ci  -  .  IH  CD  12  U) ci  U)  ci  H’  ci  N  cv  :i H-  P1  I-  0  t-  12 CD  I-  0  eccentricity. This value reflects the bivariate correlation  -  a strong linear correlation would yield a very narrow equal  frequency ellipse whereas no correlation at all would result in a circular shape of the bivariate distribution. Therefore eccentricity is the  indicating variables  (1)  closely related to the strength  of  2 of a regression, r  association  between  the  two  and (2).  4 3.  VAPJABLE( 1) Fig.  S.  Ellipse with foci F and F’. Orientation ellipse is defined by angle theta.  59  of  the  Thus eccentricity, like area, relates to the order of the system. The stronger the linear association of the variables the more orderly the system will be. In a system of perfectly correlated variables, where all variation is accounted for by a linear relationship between the variables, the shape of the ellipse will approach a straight line. Thereby the area of the ellipse will approach zero, a reflection of a state of maximal order. Although aspects  of  eccentricity  order,  the  and  area  information  parameters is not identical  -  both  express  conveyed  by  certain the  two  nor need the two follow parallel  trends, e.g. in a series of ellipses drawn at different stages of  development  variables  of  (i.e.  a  system.  high  High  correlation  eccentricity)  is  not  between  two  necessarily  associated with high precision of repeated measurements (small area),  nor  do  highly  similar  repeated observations  (small  area) always indicate a high correlation between the variables (high eccentricity); although, everything else being equal an increase in correlation would lead to a smaller sample error. As mentioned earlier only  on  the  probability  (section 2.1.), of  each  element  order depends not but  also  on  the  conditional probability between different types of elements. Eccentricity is an expression of order due to such conditional probabilities between different types of elements  -  a property  known as “redundancy” in information theory. In an ecological context,  “redundancy” has been used to describe the presence 60  of alternative flow pathways  (Odum 1953,  Ulanowicz 1986),  a  property that will be reflected in the correlation structure of a system. For my purposes I will use the term in the latter meaning and assume that eccentricity is an expression of such functional redundancy inherent in a system. To avoid confusion it should perhaps be mentioned here again that redundancy in its strict information theoretical application will increase the predictability about an outcome, whereas in its ecological meaning redundancy will decrease predictability. Although  redundancy,  representing  conditional  probability, expresses an aspect of order, it appears to also carry information relating to the organization of the system. As discussed earlier (section 2.4.), a system may develop high redundancy in situations of external stress  -  a reaction that  appears to relate to the organization of the system but can also  reflect  its  order  thereby  suggesting  that  order  organization are not altogether independent concepts but,  and at  least in certain situations, may be interrelated.  5.4.1.3.  Orientation of the equal frequency ellipse  -  angle  “theta”  The orientation equal  frequency  organization.  (angle theta)  ellipse  of the major axis of the  quantifies  a  different  aspect  of  Conceptually similar to the slope of a linear  regression, it indicates the amount of change observed in the 61  direction of variable(2) upon a change on variable(l). Whereas eccentricity  reflects  a  quantity  (strength)  of  variable  intercorrelation, angle theta rather describes a qualitative aspect of the relationship between two variables. The amount of  change  in the orientation of  assessment  of  this  the  qualitative  ellipse will yield an  change  of  organization  occurring in a system in time or space. At  this  point  equal  frequency  described for bivariate data sets.  ellipses  have  been  Their application can be  extended to multivariate data by reducing the variables of the original matrix to a smaller number of principal components. Equal frequency ellipses can then be drawn around the scores for each combination of two components.  Ellipses  in three-  dimensional or higher order space are also possible if the equal frequency space of three or more axes is of interest. Equal  frequency  ellipses  are  a  convenient  way  to  illustrate differences between groups within a data set. For this analysis ellipses around the scores of the first two PCA axes were drawn to portray the changes occurring between six age  classes  in  a  temporal  sequence  of  successional  development. Equal frequency ellipse statistics were applied to the two main components of the vegetation, viz, ground cover and tree layer. Ground cover was investigated as a whole as well as divided into four strata bryophytes)  in  order  to  (forbs/grasses, shrubs,  investigate 62  the  behaviour  lichens, of  the  w  I-  CO  p  -  -  i  Cl) ft  CD  CD  ft  H-  l  0  H-  ft U)  0  Co  C)  H  CD H  5 Cl)  H-  ‘tI  CO  CD  HO  CD  C) Cl-  CD CD Cl)  I-j  2 CD IQ  i i.c  P1  CD  ft  i  0  Cl  N  H-  o  CD  (.Q  Cl)  Ct H-  JJ  C)  H  C)  ) I—’  C)  C)  H Cli ft  CD  CD  i  C  Cl)  H  0  CO  ft  Cl)  l-C H  b ‘-<  CD  Hi  CD  S  CD  CO CO CD CO  Cl)  Cl)  tj CD  -  :;  CD  lH-  0  CD  ft  -  ft  ci  Cl)  CD CO  tziH-J Cl) I—’ II HCO CD H-  C)  ‘ti C)  CO  I-’  o  CD  CD  CD HlQ  Cl)  ‘<  CO CD Cl  CO  Cl)  Cl)  0  pj H Cl)  P1 CO  CDHft HCD ) ft HHo I-h CD j H1 0 CD Ii 0 CD H CD ft l-i CD Cl) CD ft IH0 I-i HCD 5 HCO CD 0  j  ft 1  CO  CD  <  CT)  H-  P) b H CD  CD H-  ))  CO  0  CD  CD  H-  CD  CD CD  CD  CI)  0  C  H Cl)  M  U’  C)  •  —  Cl)  ci  CD  U,  o  H  CD  -  0  CD  C) CO  H  H  CD  P Cl)  H  ft CD  i-  d P  CO CD  —  C) ft CO  Cl)  CD  ft  H H H  CD Cl)  CO  C)  H-  Cl)  CU  Ci)  o  CO CD  C)  CD Cl) I-’-  S  0  H,  CD  Cl)  ft I-  CD  CD Cl)  °  CD  CO  CD  CD  0 1 CO  ft H-  J  H  H C)  C)  CD  C)  0  Cl)  -  ft  H-  C)  Ci C) Cl-  5  CD  CO ft  -  1<  CO Hft  CD  Cl  CD  Cl)  H  CD CD  ft t-  CD  -  ft  I-h  CU  l-’ ) H  II  5 CD ft CD  P1  ft  H-  Cl)  C)  Cl)  0  H  H Cl) ft  C)  H  C) P)  CD  ft  0  H  CO CD Cl  CD  CD  Cl)  HCD  CD  CO  ft  Cl)  CU  CD  ft  I-h  0  H  C  Cl)  CU C)  CD  H-  -  C) CU  5  i-j CU  -  CT)  ft  1<  0 d  <  II  lj  CO  HC)  H  -  b’ CO  I-h  Cl)  0  -  Cl)  ft  CO ft  CD  C)  e  CD  CO  CO  HCD  CT)  < CD t  Q  o  $1  -.  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Successional changes in observed randomness  In  the  concerned  preceding  with  chapters  structure  or  “order”  was  pattern.  (Hreai)  defined  Landsberg  to  be  (1984)  described the state of order of a system as arising from the relationship  of  available states  two  factors:  (Hmax)  and the actual or observed randomness  of the system (Hreat)  .  the  amount  of  potentially  As a first step in an assessment of the  state of order of the investigated systems the calculations presented in this section will explore this actual randomness (Hreai)i  or degree of predictability within the configurations  of these communities. The relationship of these results with a theoretical state of total randomness  (H)  and with order  will be discussed and interpreted in the next chapter. Predictability  or  the  state  of  randomness  system can be captured from two angles:  (1)  HreaL  in  a  the variance, as  reflected by the spread of the observations and quantified in univariate  statistics  by  the  standard  deviation  or,  in  a  bivariate situation, by the area of equal frequency ellipses; and  (2)  by  conditional  probabilities  found  within  the  configuration of the system. Conditional probabilities refer to the degree of variable intercorrelations and relate to the concept  of  redundancy  in  information 65  theory.  Results  and  discussion are presented for both of these two aspects.  6.1.1. Estimates of variance  The  state  communities was  of  the spread of the observations  -  randomness  within  the  assessed by the variance or  investigated spread of  the  transect scores obtained by principal component analysis. PCA was applied in order to reduce the original large amount of variables to a manageable smaller number. new variables,  the PCA axes,  These transformed  represented a robust summary of  the original configuration and provided the raw material for the subsequent analysis. Each of the total of 185 transects was represented by one value or “score” on each PCA axis. Transect scores on PCA axes 1 and 2 were then plotted for each age class these  separately and around the data points in each of  these  two-dimensional  ellipses was drawn. estimate  for  the  graphs  a  95-equal  frequency  The size of these ellipses provided an  variance  or  state  of  randomness  in  the  system. Areas of the ellipse were calculated for: a)  ground cover data including 64 species of herbs, grasses, shrubs, bryophytes and lichens  b)  (see Appendix I); and  the structure of the tree layer including measurements of tree  density,  canopy  cover,  crown  height  and  tree  diameter. Variation in ground cover composition was also assessed based on Shannon diversity and spatial heterogeneity. 66  Results are displayed for the combined mesic and xeric sites where environmental differences between the sites had been  removed by the  Combined data supposed between  to the  displayed  thus be  technique represent  unconfounded  sampled  for  sites.  separate  described  in  section  the  age effect  by  environmental  Additionally,  mesic  and xeric  alone  and are  differences  results sites  S.1.1.  in  are  also  order  to  demonstrate how successional patterns differ in a different environmental setting.  6.1.1.1. Ground Cover 6.1.1.1.1. All Strata Combined  The cover  areas  species  of  95%-equal  (mesic  and  frequency  xeric  data  ellipses combined)  for  ground  showed  a  continuous monotonic increase from age class 1 to 5, followed by slight decline in age class 6  67  (Table 2; Figs.  6 and 7).  AGE CLASS 1  AGE CLASS 2  2  AGE CLASS 3  2  2  N  0  0  C) 0  C)  —I  -2  -2  -1  0  1  -2  2  —1  2  0  -1  PCA AXIS I  1  -2  2  AGE CLASS 5  I  2  AGE CLASS 6  N  0  0  2  ,  —l  2  0  2  N  6.  -1  PCA AXIS I  2  Fig.  2  ‘CA AXIS I  AGE CLASS 4  PCA AXIS 1  C  N  0  -2  —I  a  —i  o POAAXIS 1  i  -2  —1  0 POA AXIS 1  95%-equal frequency ellipses around PCA scores of transects on axes 1 and 2 for ground cover species, combined data.  68  (b)  (a)  10  I  / I  Ga  / / I / /  I  D  a LfJ4  .-..k  /  ia  I  ‘ii  / “N Y .  p  I I  Gi  I  Go  1  2  3  4  5  6  I  I  I  I  2  3  4  5  7.  Area of the 95%-equal frequency ellipse around PCA scores of transects on axes 1 and 2 for ground (a) Combined data, habitat effect cover species. (X) and xeric (M) Separate mesic (b) removed. sites.  AREA  AGE CLASS  1 2 3 4 5 6  Table 2.  6  A GLASS  AGE CLASS  Fig.  /  Combined Data  Mesic  Xeric  .158 .265 .368 .473 .584 .431  .585 3.499 3.804 2.696 6.014 9.874  1.983 3.799 3.917 3.653 1.252 2.864  Area of the 95%-equal frequency ellipse around PCA scores of transects on axes 1 and 2 for ground cover species.  69  The  increase in area of the ellipse with successional  time reflects an increase  in disparity among the transects  within each age class, where transect disparity is determined by  compositional  transect  points  predictability  dissimilarity. therefore of  is  the  Increasing  an  spread  expression  species  of  of  the  decreasing  configuration.  Species  composition and abundance will become less predictable with increasing number of  species  (species richness)  and with a  more even distribution of the individual plants in a sample among the species present  (equitability). Thus, when applied  to species data, the area of the equal frequency ellipse is an expression  of  species  diversity,  a  traditional  concept  ecology for which a host of indices have been proposed the  Shannon-Weaver  attached  to  the  index  that  specific  expresses  identity  of  a  the  in  (e.g.  uncertainty  randomly  selected  individual; Pielou 1966) The steady increase and subsequent decline of the area of the ellipse for the combined transects of this study is in agreement  with  Margalef (1968) and Johnson  theoretical ,  Horn (1974)  (1988)  initial  stages  penultimate  phase,  the  ,  expectations  as  outlined  by  Pickett (1976), Ulanowicz (1986)  which predicted diversity to increase in succession, and  then  to  reach  to  decline  a  maximum as  in  the  climax  is  approached. For  the  separate mesic  and xeric  variants  (Fig.  7b),  ellipse areas were reasonably similar up to age class 4. 70  In  Cl  0)  CD  V  CD  0)  -  0)  CD  U) 0)  Cl)  —...  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H-  CD (Q H-  CD  CV  CV  P1  HCQ  J CD  CF  ICl)  pi  ‘-j CD  ‘-  p1  ‘ p Cl) Cl) CD  Cl)  Hi  CV  CV  Pi  -  0  Cl)  Pi  k<  Cl) HCV  CD  <  H-  tj  -  P1 H-  P1  3 CD  CD 0 I—’ H-  CD  0 ‘ CD P1 Cl)  II  ‘-Ci  0)  PJ Hi ft CD  Cl)  CD  H HC)  ‘CD ) 0)  3 CD  1  CV tCD  CV  Cl)  i-  pi  Q  CV  Cl)  Cl) CD  C) 1i Cl) Pi  H-  3  CD  CV  p  Pi j  Cl)  CD  Cl)  CD  0 I-  CD  CV  m  Hi HI-  CD P1  Cl) H3 (C  Hi  0  CD  H-CD  I—’ F-’ ‘<  CD  CD  p  0  Cl)  Cl)  CD  ‘<  0  k<  ty  J 3  Cl)  b  J’ I-  i  0 CD 0) CD H0  Cl) Ii 0  Cl) CD  ‘-Ci  H-  CD H I—’  CD  CV  0 Hi  ICD P1  p1  CD  CV  -  Cl)  Pi Cl) Cl) CD  IQ  Y Cl)  V  0  Hi  0  -  -  ‘•‘J H  -  W  CD  H  Pi  -3  Cl)  ‘-Ci  0  I-  CD  0 CV  CD  CV  CF  H  Cl)  CD  ILl)  0)  P1  Cl)  Hi C  Hi  0  CF  II P1 Cl)  CV  0  0  Cl)  C  Ii  0  ‘-Ci H-  Cl)  o  0  CV  Cl) P1 F-’ Cl)  Cl)  P1  P1  Cl)  o  P1 i H-  CD  CV  Hi  o  Cl)  CD  CF  Hi  o  o  HCl)  P1  ‘-Ci  •  H-  CD  CV  j  ‘-Ci  C  I-Q l-  P1  j-  Hi  o  o  CV  Cl)  CD  0 H-  CD  Cl) ‘-Ci  P1 Cl) Cl)  0 0  ‘-  IX  P1  <  H-  CD  Hi  P1 i Cl) CD  CiCD 0  ‘-Ci  0  IQ  CD  H-  Cl)  CD  H-  CD  H-  0 0  Hi CD  0  C  H CD  I-  0  H P1  S H-  Hi CD  H H-  H P1 I-  S H-  1 CI’  c  CD  Cl)  rV  ‘—<  0 0  H-  0  H P1  CV  p1  ‘-Ci i—’  I—’ p1  0  P1 Cl)  -  l-’  Hi  0  Cl)Cl) HH-  CD  CD iCD  CV  .  Cl) —  N  H-  Q i  H  0  0  ‘<  ‘I—’  CD PJ  -  i-,  H-  0 0 CD  Cl)  Hi  stages of succession.  A  division  of  the  sites  into  mesic  and  xeric  variants for this part of the analysis was not attempted in order to avoid an inappropriate reduction of the data base: after the division of the original matrix into separate strata a  further  appear  to  division  of  considerably  the  data  decrease  into  two  the  hygrotopes  reliability  of  would the  results.  AGE CLASS  AREA Forbs/Grasses  Shrubs  Lichens  Bryophytes  1 2 3  1.411 .549 .330  .081 .067 .114  .000 .043 .033  .034 .052 .095  5 6  .824 2.405  .287 .426  .029 .013  .090 .124  4  Table 3.  .410  .461  .035  .106  Area of the 95-equal frequency ellipse around PCA scores of transects on axis 1 and 2 for ground cover species, separate strata.  73  FORBS/GRASSES  SHRUBS  j:____________  1.6  0.5  AGE CLASS  AGE GLASS  LICHENS  BRYOPHYTES  0.05  0.16  AGE CLASS  Fig.  8.  AGE CLASS  Area of the 95%-equal frequency ellipse around PCA scores of transects on axis 1 and 2 for ground cover species, separate strata.  74  6.1.1.1.3.  Variability  of  ground  cover  assessed  by  Shannon diversity and spatial heterogeneity  As an alternative to assessing the state of randomness by quantifying areas of equal frequency ellipses,  variation in  species  the  composition  diversity index.  was  also  calculated  by  Shannon  Shannon diversity is a measure derived from  information theory and calculates predictability based on the number  categories  of  proportion of  (e.g.  individual  species)  elements  in  (e.g.  a  system  and  individual  the  plants)  belonging to each category.  Shannon diversity will increase  with  species  increasing  numbers  of  increasingly even spread of them  the  (species  richness)  individual organisms  and  among  (equitability). Both Shannon diversity and the size of equal frequency  ellipses within  provide  the  ellipses  as  a  system. used  in  measure How  of  are  this  variation  they  thesis  or predictability  related? reflect  Equal the  frequency  disparity  in  species composition and abundance among the transects within each age  class.  With increasing disparity among transects,  equal frequency ellipses will also increase. The information conveyed by the ellipses appears to be related closely and directly comparable to Shannon diversity. Similar to Shannon diversity, disparity among transects, and hence ellipse size, is likely to increase with increasing number of species and an increasingly even spread of the individual plants among these. 75  The logic  is simple:  with more choices being available the  probability of two transects being identical will decrease. A different aspect of variation found within the species configuration of a community can be captured by calculations of  “pattern diversity”  or  “spatial  heterogeneity”.  Whereas  Shannon diversity is concerned with the number of species and the distribution of the individual plants among them, pattern diversity takes the spatial arrangement of the species within the community into account. With decreasing similarity between individual community,  sampling spatial  units  (e.g.  quadrats)  within  the  heterogeneity or pattern diversity will  increase. Whereas Shannon diversity quantifies variation based on  the  identity of  the  heterogeneity  spatial  distribution  within  the  individual is  elements  concerned  system.  The  with two  of  the the  measures  system, spatial are  not  totally independent, as with increasing species richness and equitability spatial heterogeneity is likely to increase as well. Spatial heterogeneity was assessed following Inouye et al.  (1987)  based on Czenakowski’s similarity index,  known as “percent similarity”  commonly  (Greig-Smith 1983). The method  provides an estimate for spatial heterogeneity by comparing species  composition  of  two  sampling  units  (quadrats)  in  different locations. Percent similarity was calculated by the following formula:  76  Percent similarity (PS)  whereby min(x . x 1 ) 2  =  200  D  *  1 min(x , 1 (x  p  was  represents the smaller one of the values Percent similarity  calculated between all pairs of  transect.  With  p  ) 2 x  +  for species p in the two units compared. (PS)  ,  10  quadrats  per  quadrats  transect  this  in each  led  to  45  comparisons per transect from which an average value for each transect  was  calculated as  obtained. (100  diversity and different  variability  spatial the  in is  heterogeneity  was  then  PS).  -  frequency  Equal  Spatial  ellipses  on the  one  heterogeneity on  level  of  assessed.  hierarchy  Whereas  the for  equal  hand and Shannon other hand are which  frequency  community ellipses  assess the among-transect variability,  Shannon diversity and  spatial  with  heterogeneity  are  concerned  within-transect  variability. To provide a comparison to the results obtained by equal frequency ellipses,  successional trends of Shannon diversity  and spatial heterogeneity for ground cover species, both for combined and separate mesic and xeric sites are displayed in Figs.  9 and 10.  77  b)  a)  3.5  35  so  .  j25  ‘Ii  /  20  1  2  I  I  I  I  3  4  6  6  2.0  I  1  8  5  AGE CLASS  AGE GLASS  Fig.  4  3  2  (a) Shannon diversity for ground cover species. and xeric (X) mesic (M) Separate Combined data. (b) sites.  9  b)  a)  100  100  :  t_.  •  80  I  I  I  I  I  3  4  6  6  :  S  \\/1\  / I  2  3  I  I  I  4  5  6  AGE GL6  Fig.  10  cover. ground (a) for heterogeneity Spatial Combined data. (b) Separate mesic (M) and xeric (X) sites.  V  78  A comparison of the results obtained by calculating area of  frequency ellipses  equal  Shannon diversity (Fig.  9)  for ground cover  (Fig.  7)  and  reveals some resemblances as well  as some differences between the curves. Shannon diversity for the combined data increases sharply from age class 1 to 2 and remains relatively constant in later stages. Conversely, equal frequency ellipses show a steady increase up to age class 5, followed by a slight decline. The most conspicuous difference between the two methods,  however,  is the behaviour of mesic  and xeric variants in later stages. Equal frequency ellipses for mesic sites suddenly expand in later stages of succession, whereas no increase was found in the same stages for Shannon diversity.  mentioned  As  previously,  the  division  of  the  transects into xeric and mesic variants implies a reduction of the sample size from the combined to the divided data. mesic  variant  observations  in  (n  =  age 6)  class  6  is  particularly  low  The in  which may cause the associated ellipse  size to be inflated. striking  Quite  is  the  similarity  of  the  curves  for  Shannon diversity and spatial heterogeneity (Figs. 9 and 10). Although  the  two  formulas  used  have  little  in  common,  variability based on species composition appears to be closely related  to  the  variability  in  spatial  species. Similar to Shannon diversity, is  likely to  arrangement  of  the  spatial heterogeneity  increase with increasing species richness and  equitability because of a reduced probability of two sampling 79  units being identical. In all three methods, equal frequency ellipses, Shannon diversity and spatial heterogeneity, variability based on the species composition and abundance increased with increasing species richness and equitability. richness  and  equitability  are  Since increasing species  two  important  aspects  of  increasing diversity, all three methods represent measures of ecological diversity within a community.  6.1.1.2. Structure of the tree layer  After a slight initial increase,  the area of the equal  frequency ellipse for data points of the tree layer dropped considerably between age class 2 and 3 and remained on a low level during all  subsequent stages of succession  (Table 4,  Figs. 11 and 12). Measurements of the tree layer included the four structural variables, tree density, crown height, percent canopy cover, considerable  and tree diameter. decrease  in  The curve thus suggests a  structural  diversity of  the  tree  layer in course of succession. Structural diversity on mesic sites decreased continually suggesting that such stands become increasingly uniform with increasing age. On xeric sites the trend  is  less  pronounced  and  suggests  that  poor  growing  conditions in these locations may interfere with this tendency towards lower structural diversity. The high values for ellipse size on mesic sites of age 80  classes 1 and 2 reflect primarily the large variation in tree density on young sites. confirmation,  Although no data are available for  observations in the field suggested that tree  density on young sites recovering from disturbance by fire may be influenced by the age of the previous stand.  If the burnt  stand had been an immature one, only a small number of seeds would  be  available  to  produce  the  post-fire  generation;  conversely, if the previous stand had been a mature one, ripe would be  cones  abundant  and  generation would be high.  seedling  density  in  the  next  With increasing age tree density  tends to become more similar among initially divergent stands owing to increased self-thinning on high-density stands. The values  large  of  age  contrast class  1  between may  xeric  reflect  the  and  mesic  larger  sites  in  spectrum of  densities encountered on mesic sites; drought-like conditions on xeric sites are generally unfavourable for seedling growth and initial stand densities tend to be considerably lower than those of mesic sites.  Moreover,  even if the previous  stand  supplied a large crop of ripe cones, seedling density on xeric sites  will  still  be  lower  because  mortality.  81  of  higher  seedling  AREA  AGE CLASS Combined Data .090 .108 .028 .036 .030 .033  1 2 3 4 5 6  Mesic  Xeric  25.573 6.885 2.867 4.009 2.362 2.168  4.368 15.354 2.741 6.335 2.308 1.435  Area of the 95%-equal frequency ellipse around PCA scores of transects on axes 1 and 2 for structural variables of the tree layer.  Table 4.  (b)  (a) w  0.15  I  -I---  I  I  I  D  2 o.io  [a  Ix  U-J  ‘NI I I I I!  oo5  ‘C)  0)  w  z  w  I I. U. 0  I  0.00  1  2  3  4  6  6  11.  1’  Xi i 1  AGE GS  Fig.  10  Il .4.  2  3  4  5  6  AGE CLASS  Area of the 95%-equal frequency ellipse around PCA scores of transects on axes 1 and 2 for structural variables of the tree layer. (a) Combined data. (b) Separate mesic (M) and xeric (X) sites.  82  AGE CLASS 1  AGE CLASS 2  AGE CLASS 3  4  4—  4—  3  3  3  2  2  0  0  2 C.1  -1  —1  —1  -2  -2  -2  -3  -3  -3  -4  -4  —4  -3  -4  -3  -2  PCA AYJS 1  3 2 el  2  -i  -2 -3 -4  :t  —4  -3  -2  -,  0  1  PCA MS 1  Fig.  12.  0  1  2  3  1  —4  -4  -3  -2  2  3  AGE CLASS 5  m  4  3  3  0  1  -1  -2 -3 4  -4  —4  -3  -2  -,  0  1  PCA A4S 1  0  1  2  3  4  I  AGE CLASS 6  4  2 oj  -1  Po. cs  PCA ftXG 1  AGE CLASS 4 4  -1  2  3  4  -  -  -  2  4  PCA ,4)$ 1  95%-equal frequency ellipses around PCA scores of transects on axis 1 and 2 for structural variables of the tree layer, combined data.  83  OD ls  Hit  0  it  H-  Cl)  CD  Cl)  :•  ‘3  rt <  CD Cl)  P.)  CD  it  <  H  H-  H  HP.) b H-  U I  HP.) 1J H-  J F  0  ‘  C)  k<  CD Fl P.) h C)  H-  H  ‘<  C)  CL)  CD  CD .Q li P H  S  •  j  Hi 0  CD  -<  P.)  Cl)  ‘-  CD Ci) Mi  0  it  CD C)  Fl P.)  Cl)  < CD H  H-  CD Fl  I  it  H CD  3  H-  it  CD  H-  it  0  CD  Cl)  P.)  Fl CD  P.)  CD Fl  HH-, H  Cl  HC?  it  ‘zj  Fl 0  P.) H  I-  it  C)  )-,  Cl)  CD  ICD  3  Cl)  CD  t-  CD C) it  P.)  Cl)  0 3  Cl  P.) Cl) CD  Cl)  it I-  I  0  0  it H-  P.)  H  P.) H C)  C)  CD  -.  Cl)  P.)  CD  ‘•d  i P.)  P.) Q  ‘t5 p.)  0  Fl CE)  C5  CD  it  H-  0  (.Q  S  P.)  CD Cl  CD  Cl)  CD  CD  5p.)W H HCD it P.)  Cl) <  Fl  0  ‘.<  0 Fl  C) it  H-  pi P  ct I  0 i  c  Ci)  3  H-  Cl  H-  Hi  CD  it  it  C)  H-  it Fl P.)  0  it  Cl)  P.)  Cl)  Cl)  -  W  H  (Q  H-  CD  H  H b  H H-  CD  CD Fl CD  C1  CD  CD H-  P.)  H  0)  Z  CD  CD  CD  3  CD  Mi  Mi  H-  pj  1  0) it Pi  it  H-  Cl)  P.)  Fl CD  C)  H-  Hit  H ‘<  P.)  C) 0  CD Cl  Cl)  CD P.)  i-  it ‘-<  Cl) H-  Fl  CD  <  H-  Cl  H  P.)  ‘<  0  CD  P.)  CD  o  HCD Cl  Fl  CD  CD  Cl)  ii CD  CD  Cl) Cl)  H Pi  I-  CD it CD  H)  HP.) S CD it  CD  j  0  0) CD çL  U  b H)  CD  Cl) 3  C)  .)  CD  Fl CD  5 CD  C)  H-  Cl)  H-  P.) it  Cn  i  p.)  c  it  0  Cl  P.) (j) CD  .<  it  Cl) H-  Fl  CD  <  H-  Cl  P.) H  Fl  C) it  Cl)  •  H-  H p.)  Ui  •  L3  Hi  0  Cl) CD Cl)  J Cl)  P.) H  P.) it CD 1  C)  CD  I  CD  it Jct  i Cl)  Z it 0  H-  5-f., HCD  Cl) H-  pi TI)  C) H  C)  TI) CD  P.)  CD Fl  Cl)  it  Fl CD 5 CD  Ti)  c”  Cl)  CD it CD Fl  HP.)  k<  0 Fl it  ‘j  CD  it  CD  H-  Cl  CD  it  CD  H  p.)  H-  ..A  CD  CD  CD  it  H-  H  H  HP b  I-  <  p.  çt I  C)  CD P.)  CD  j  0  C? CD  H-  Cl)  i  j  H-  Hit  CD  Z-  C?  0  Cl  CD  02  pi  H-  0)  it  TI)  CD  Cl)  0)  P.)  Cl  ••  CD C!)  P.)  Fl  < .) H  CD  P.)  CD  P.)  0  Cl  CD  0)  P.)  J  Cl  N CD  H-  (I)  C)  CD (l)  it  CD C)  l)  P) 3  t-  it  it CD  CD  H-  CD  CD  -  i.<  H-  CD  CD H-CD Ti) Cl  F-3  0  C) p 3 0 ‘d  P.) C)  CD  it  CD  Cl)  P.) Cl) Cl) CD  Cs)  H0  Fl CD  ‘zj  CD  F-I  Fl CD  C)  H-  Fl CD  CD  Mi  H-  pj  0)  HCD H  ‘<  Cl  P.)  Cl) it  CD  0)  Fl CD  it  3 CD  it  F-h  0  CD  Fl  C)  Cl) it Fl  CD  CD  H-  CD  0  pJ Cl) Cl)  it  CT) Fl  <  H .)  CD CD  it  CD  it  Hit  ‘<  HH H  H-  p  P.)  CD  Q Hi  it  CD  S  TI) C!)  0)  Cl)  P.)  CD  Fl  C)  CD it  it CD  CD  5  Cl HP.)  CD  ‘-3 Fl Cl)  H  -  IJ  -  H  -  H  b)  a)  3  3  /  /  >-  >-  1  X.:/  /  /  VI  /  1.  / / /  I;’ a)  I  1  /  I  I  (  0  1  3  2  4  5  ,  1  6  2  13.  4  6  6  AGE GLASS  ASE CLASS  Fig.  3  Structural diversity of the tree layer based on diameter structure of living trees. a) Combined data. b) Separate rnesic (M) and xeric (X) sites.  6.1.2. Eccentricity of equal frequency ellipses  -  an expression of redundancy  Eccentricity of an equal frequency ellipse reflects the degree of correlation between two independent variables. eccentricity, high  High  represented by a narrow ellipse, will indicate  correlation  or  redundancy  configuration. 85  to  be  present  in  the  Redundancy  in  community  organization  relates  to  the  presence of alternative energy pathways within an ecological system (Odum 1971, Ulanowicz 1986). Although in this thesis no measurements relating to energy flow between the constituent elements of the community were made and ellipses were drawn based on species data and structural  attributes alone,  shape  allow  these  of  relating  to  ellipses  redundant  eccentricity rests  may  still  pathways.  on two  Such  an  assumptions:  some  the  inference  interpretation of that  1)  changes  in  organization of the community as a whole will be reflected by the correlation structure within one trophic level, that  redundant  correlations underlying  pathways  in  the  would  species  assumptions  of  be  reflected  configuration.  the  present  and 2)  by  high  Since  the  interpretation  of  eccentricity remain untested, the following results are to be regarded as a tentative exploration of the matter. Principal  component  axes  represent  summary  a  of  the  species configuration and high redundancy,  according to the  above  high  assumptions  between  the  would  axes.  be  This  reflected  by  may,  first  at  correlation sight,  seem  contradictory, as PCA axes are, by definition, uncorrelated. In the analysis of this study species data were subject to PCA for all age classes combined  (185 transects)  .  The ellipses,  however, were drawn around the scores obtained by this PCA for each  class  separately.  Whereas  the  condition  of  uncorrelatedness of the PCA axes holds for the data set as a 86  whole,  the  condition  matrix,  e.g.  does  not  apply  for  segments  of  the  system  was  for individual age classes.  Redundancy  as  an  aspect  randomness  in  a  captured by the eccentricity of 95%-equal frequency ellipses around PCA scores of transects on axis 1 and 2 for:  ground cover data  a)  grasses, the  b)  including  of  tree  the  measurements of tree density,  6.1.2.1.  species  of  herbs,  shrubs, bryophytes and lichens;  structure  height,  64  layer  including  canopy cover,  crown  and tree diameter.  Ground Cover  6.1.2.1.1. All Strata Combined  After  an  initially  stable  ellipses around PCA scores  phase,  eccentricity  of  the  for ground cover increased to a  maximum in age class 4 and declined slightly in later stages (Table 5, variants  Fig.  14a). Eccentricity values for mesic and xeric  fluctuated more  than the  combined data.  Mesic and  xeric patterns were almost parallel up to age class 4  (151-200  yrs.)  but towards the mature stages of age class 5  (200-300  yrs.)  and 6  (>300 yrs.)  eccentricity on mesic sites declined  whereas it increased on xeric sites (Fig. 14b) class 6  .  Except for age  (>300 yrs.), values for mesic sites were consistently  higher than for xeric ones,  suggesting a higher presence of 87  multiple pathways on mesic sites.  As multiple pathways are  important in maintaining system stability it can be concluded that  ground  cover  disturbance. mesic  sites  expression  The in of  on  xeric  decline  of  sites  is  more  eccentricity  the  mature phase  may be  the  tendency  the  of  for  vulnerable combined  interpreted as  system  to  to and an  sacrifice  redundancy in exchange for increased energetic efficiency, a tendency expected from dissipative structures as they approach maturity. Such a trade-off, however, will result in increased vulnerability to external disturbance. In contrast, redundancy on xeric sites increased considerably from age class S to 6. As  redundancy is expected to  rise after a system has been  perturbed this could be a result of minor disturbances in this late stage of  succession.  The nature of such a disturbance  will be discussed in the next chapter.  88  (b)  (a) I  too  I  I  1.00  I  05 )-  I.  0.95  0.90  0.90 >I—  os  Q  0.8O  LLI  I—  oss  z  0.75  0.70  0.70  \  \ \ \  M/  1  0 0.80  0.75  I  I  3  2  4  5  / I  14.  $  1  V 2  3  4  6  6  AGE GLASS  ECCENTRI CITY  Combined Data  Table 5.  ‘—I  Eccentricity of the 95%-equal frequency ellipse around PCA scores of transects on axes 1 and 2 for Combined data, (b) species. cover (a) ground sites. Separate mesic (M) and xeric (X)  AGE CLASS  1 2 3 4 5 6  I...--.  I ‘1 ‘ I ‘ I i ‘I  AGE GLASS  Fig.  .)ç  I  ‘ ‘  1  6  ‘  %_  \_—  \,(  ‘  1  “  Mesic  Xeric  .952 .876 .994 .925 .952 .919  .905 .691 .855 .728 .815 .950  .902 .866 .939 .983 .976 .961  Eccentricity of the 95%-equal frequency ellipse around PCA scores of transects on axes 1 and 2 for ground cover species.  89  6.1.2.1.2. Separate Strata  Calculations of eccentricity for individual ground cover strata  (forbs/grasses,  shrubs,  lichens, bryophytes)  produced  contrasting results between forbs/grasses on the one hand and lichens  bryophytes  and  on  the  other  (Fig.  15,  Table  6).  Eccentricity for lichens and bryophytes increased to a peak in age class 4 and declined in later stages; forbs/grasses showed the opposite trend by decreasing to a minimum in age class 5, followed by an increase towards age class 6. Thus,  comparing  these results with values for ground cover as a whole (section it appears that the overall trend of decline in  6.1.1.1.1.), redundancy  in  later  successional  stages  primarily by lichens and bryophytes.  is  brought  In a previous  about  section  it has been noted and discussed that the area of  (6.1.1.1.2.)  the ellipse for forbs/grasses follows a different pattern than for the other strata; this distinct behaviour is also apparent in trends early  of  stages,  eccentricity. experience  a  Forbs/grasses, comeback as  most abundant  the  stands  in  open up  towards the end of succession. It is therefore not surprising that redundancy of the forb/grass layer increases again in the very last stage. Conversely, lichens and bryophytes appear to follow the  overall  tendency of  redundancy with increasing age. the  shrub  layer  defy  an  the  system to  decrease  its  The erratic fluctuations of  immediate  explanation;  they  may  reflect the relatively impoverished shrub flora consisting of 90  only seven shrub species.  1.0  B.--—  —  —  — _.- —  —  -4  —.-  0.8 /  >I—  I  0 0.6 cc  /  \  I \ I ‘I  I—  0 0.4  \ ,,S  113  02  0.0  1  2  3  4  5  8  AGE GLASS Fig.  15.  Eccentricity of the 95%-equal frequency ellipse around PCA scores of transects on axis 1 and 2 for strata; separate species, cover ground lichens (L), shrubs (S), (F), forbs/grasses bryophytes (B).  ECCENTRICITY  AGE CLASS  Forbs/Grasses 1 2 3 4 5 6 Table 6.  .789 .872 .850 .773 .712 .894  Shrubs .854 .753 .325 .766 .961 .861  Lichens  .788 .878 .910 .844 .767  Bryophytes .950 .856 .934 .961 .945 .915  Eccentricity of the 95%-equal frequency ellipse around PCA scores of transects on axis 1 and 2 for ground cover species, separate strata. 91  Structure of the Tree Layer  6.1.2.2.  Whereas  for  the  eccentricities  combined transects  structural variables of  the  tree  for  layer appeared to undergo  little change in course of succession, a conspicuous contrast between (Fig. and  sites  16, high  of  mesic  and of  locations  xeric  was  evident  Table 7). Mesic sites maintained relatively stable values  throughout  all  eccentricity  classes;  age  values for xeric stands were lower and also fluctuated more.  (b)  (a)  GO  0.6  Ge  0.4  G4  .  I \ix V  02  GO  1  2  .3  4  5  I  6  16.  3  4  5  6  AGE OLS  AGE CLASS  Fig.  2  Eccentricity of the 95-equal frequency ellipse around PCA scores of transects on axes 1 and 2 for structural variables of the tree layer. (a) Combined data. (b) Separate mesic (M) and xeric (X) transects.  92  AGE CLASS  ECCENTRICITY Combined Data  Mesic  Xeric  .789 .872 .850 .773 .712 .894  .843 .873 .939 .926 .898 .923  .757 .707 .628 .392 .747 .899  1 2 3 4 5 6 Table 7.  All  Eccentricity of the 95-equal frequency ellipse around PCA scores of transects on axes 1 and 2 for structural variables of the tree layer.  four original  structural variables  (tree diameter,  canopy cover, crown height and tree density) capture a certain dimension of tree growth. With lodgepole pine as the only tree species  on  consequence species.  most of  the  stands,  stand  structure  characteristic  Measurements,  thus,  growth  primarily  is of  a  direct  this  single  reflect  growth  and  development of lodgepole pine in the study area rather than redundancy or multiplicity of pathways of the system. The high and  stable  eccentricities  on  mesic  intercorrelations between variables,  sites  reflecting  high  can then be interpreted  as an expression of balanced growth of this species in all the four dimensions measured. Lower eccentricity values for xeric sites reflect lower variable  intercorrelations.  This  higher  amount  variation in such locations may be caused by the  of  extra  increased  susceptibility of such systems to environmental fluctuations. 93  6.2. Organizational Change  Organizational  change  between  phases  of  successional  development was quantified based on two related methods,  a)  the change between adjacent age classes in orientation (angle theta)  of equal frequency ellipses around PCA scores,  and b)  the angle between eigenvectors of adjacent age classes.  The  methods are related because both are based on the comparison of  eigenvector  elements  reflecting  change  in  variable  intercorrelation and are therefore expected to yield similar results. might  In light of the expected similarity of results,  wonder  why  methods  both  were  applied  to  one  document  organizational change, instead of only one. With increasingly complex data transformation,  (the calculation of angle theta  involves a second PCA performed on the transect scores of each age  class previously obtained by a  first  PCA)  the  results  become increasingly remote from the original data. It appeared therefore  desirable  verify  to  the  results  obtained  by  orientation of the ellipses by utilizing a second technique.  6.2.1. Ground Cover 6.2.1.1. All Strata Combined  The  results  organizational  of  change  the in  two  ground 94  methods cover  for  data  quantifying  were  in  close  agreement  (Tables 8 and 9). Overall trends  successional change  development  between  age  class  showed 1  and  a  drastic  2,  for  divided  the  organizational  followed  decreasing changes over age classes 2 -6 Results  (combined data) in  data  by  (Figs. show  a  gradually  17a,  l8a)  conspicuous  difference between mesic and xeric data (Tables 8 and 9, Figs. 17b and 18b)  .  Mesic sites basically follow the same trends as  the combined data  -  a sharp organizational change between age  class 1 and 2 followed by moderate ones in later stages. xeric  sites,  stages,  however,  after  levelling off  in  On  intermediate  changes in theta take a sharp increase again towards  the end of succession. Both  change  of  theta  and  angles  between  eigenvectors  suggest a decrease in the rate of organizational change with time for the combined and mesic data, whereas on xeric sites the dynamics of organization appear not to stop. A possible cause  for  this  difference  in  behaviour may  be  the  higher  vulnerability of xeric sites to external disturbance, minor offset  changes a  in  delicate  environmental balance.  conditions  Thereby  an  may  extra  be  where  able  to  element  of  variation to indicators of organizational change is added and the  recovery  process  is  prevented  approaching equilibrium.  95  from  slowing  down  and  (b)  (a)  300  300  -  D  200  200  C)  /  Ui I  Ui I  if:  AGE GLASS  Fig.  AGE OLASS  change between adjacent age classes in orientation (angle theta) of the 95%---equal frequency ellipse around PCA scores of transects on axes 1 and 2 for ground cover data, all strata. (a) Combined data. (b) Separate mesic (M) and xeric (X) sites.  17.  (b)  (a) 250  ‘  ‘  ‘  250  i  .  . .  00 g 2  20O  150  150  .= °-  AGE G1.ASS  18.  )5i  /44//  ////‘  11:  Fig.  •  Angle between eigenvectors (PCA axis 1 and 2) of adjacent age classes for ground cover data, all Separate mesic (M) strata. (a) Combined data. (b) and xeric (X) sites. 96  The results for the combined and mesic data thus indicate a gradual decrease in species turnover as succession proceeds. This  behaviour  is  expected  from  a  classical  viewpoint  of  succession theory which would predict succession to end with a community “in which the species perpetuate themselves” and where “species composition should remain the same over a long period of time”  (Mueller-Dombois and Ellenberg 1974, p. 397).  This behaviour is also in agreement with a general tendency observed in developmental patterns, namely a “gradual increase in internal stability toward change”  -  or a decrease in internal tendencies  (Saithe 1991, p. 87). In the case of continuous  minor external disturbances, however, such internal stability is difficult to achieve and successional processes may never approach equilibrium.  SITE GROUP AGE CLASS COMPARI SON Combined Data 1/2 2/3 3/4 4/5 5/6  Table 8.  75.6 16.9 9.8 9.5 1.2  Change (angle around ground  Mesic  Xeric  93.2 6.0 6.7 11.2 2.6  83.6 0.1 5.0 77.7 83.8  between adjacent age classes in orientation theta) of the 95%-equal frequency ellipse PCA scores of transects on axes 1 and 2 for cover data, all strata. 97  0)  X CD  H-  CD  j  Cl  CD  I-Q  d H  P1 H-  CD d  CD  Cl  H-  P1  Cl Cl)  H  Cl)  Cl)  CD tCl)  CD  Cl  P1 Cl  H  CD  CD  Cl  P1  13 1  Ii 1  0  P1  Cl  13  CD  P1  CD  <  -  CD  H H-  P1  j  P1  Cl)  H-  P1  (1  H C)  CD (I)  H  pi  ‘—3  .  CD  13  0  H-  Q  1  CD  H-  b  0 0  CD  Cl  H-  H Cl  <.  H Cl  .  13  H CD  0 H-  H-  CL)  Cl) P1  ®  P1 Cl P1  Cl) Cl  P1 13  -  Cl  w  Ui (  w  0 CD  i-  j  IQ  0 Cl  C!) Cl h  P1  H-  p CD  N P1  Cl) CD  -  H  CD  <  H CD  H1h H (Cl h CD  CD I Cl P1 H3  UiHP1 Cl) 0  _n  0 M  Cl)  0  CD i ClCD Cl)  0  Cl  H  C) CD Cl)  Q ft  P1  Cl  ‘d  P1  Cl  P1  CD Fj  Q  0  0  CD  P1  P1 Cl)  0 0  0  II  Cl)  13  ft  H  H-  Ci)  it  Cl  Cl)  d ‘d  H  0  ®  Cl  Cl  P1  .  CD  P1  ()  HN  P1  (-Q  0 II  H0  C?  H-  Cl  8  CD  j  Cl  -  I-h  0  Cl)  ®  Cl  LJ  CD  (1)  f  C?  Cl  Cl) Cl  <1 Cl)  H  P1  CD  I CD  —  Cl)  d  b  Cl)  13  H H0  -  ® Ui  CJ  P1  fr  ‘-Q  Cl)  I-h 0 1  —  Ui Cl h P1  I-h  13  P1 Cl H-  P1  d  Cl) CD  H  P1  H1  <  H-  H-  ft  H-  P1  :i  (Cl  0  0  0 CD H Cl P1 b H H-OClUi  0 0  CD  Cl  CT)  Cl)  P1  H CD  0  0  p1  Cl  Cl  U)  ®  P1 Cl  P1  CD  t’J  Cl  P1 HO HI—h  Cl  iP1 P113  H  Cl)  QH  P1  0t1  Ui  0  0 I-hCl  Ui Ui® CD Cl)  u(D CD  Cl®  P1CD  ClC)(D  Cl I1LJ(-Q PIPJH  -  H (Cl  H  OWW0U1  uiuiwj W0JQ  O0I1HH  oJ’-J1u,o  J(y-w  HW  OOHJO  -...  OU1WM  _-. -..  H Cl) C’,  P10  H  Cl)>< HCD hi H  P1  Cl)  H-  P10  H-  Cl)  H®  Cl)X  xH  P1  P1  MCl  WPI  H-ti  CD  P1  H H  Cl)  H-  Plfl  z  0U)  H  IQ  00  C)  ‘-UI  ci  0  0  ‘-3 Li  Cl) I-I  11,  19 and 20).  Figs.  Both ways of computation revealed the  same order of the strata in overall magnitude of change, with f orbs and grasses taking the lead, followed by lichens, shrubs and bryophytes. A conspicuous change between age class 1 and 2  in  bryophyte  the  layer,  followed by very minor  changes  during later successional stages is captured equally by the two techniques. Similar to the dynamics of area (section 6.1.1.1.2.) and eccentricity  (section 6.1.2.1.2.)  forb/grasses again differ  from the other strata by increased activity in the last time interval the  (age class 5-6)  enhanced  .  This activity most likely reflects  opportunities  for  early  colonizers  when  the  stands open up as the tree layer reaches its upper age limit in the mature stages. dynamic  component  organizational stand  age.  The  of  Thereby forbs/grasses become the most the  system;  in  all  other  strata  changes gradually slow down with increasing most  lethargic  strata  are  the  shrubs  and  bryophytes which exhibit only minor organizational changes, particularly in intermediate and late successional stages.  99  200-  I  I  Lii > -J  Lu  150  7  -  100-  /  /  /  /  fr_  j-i —4 —  —  —  I— Li  —-  0 Lu 0 z  50  4:  0 0-  1  2  3  4  6  5  AGE CLASS Fig.  19.  Change between adjacent age classes in orientation (angle theta) of the 95%-equal frequency ellipse around PCA scores of axes 1 and 2 for ground cover data, separate strata; forbs/grasses (F), shrubs (S), lichens (L), bryophytes (B).  AGE CLASS COMPARISON  LIFE FORM STRATA Forbs/Grasses  Shrubs  Lichens  31.1 34.1 18.5 11.1 32.3  29.1 8.8 22.6 14.0 9.3  67.8 21.5 25.4 13.9 13.0  1/2 2/3 3/4 4/5 5/6 Table 10.  Change (angle around ground  Bryophytes 58.3 1.3 1.2 1.9 1.6  between adjacent age classes in orientation theta) of the 95%-equal frequency ellipse PCA scores of transects on axes 1 and 2 for cover data, separate strata. 100  n  -j D  300  I  I  -  0  /L  0)  P0  1_  /  7,-  200  6’  uJ w w z  Ui Ui  ,—  /  -d  ,‘/ / /•... ‘1/ tl  100-  ,‘/  I Ui  —  /  AS  —  •.G  1/  cn  1’  I”,  Ui  ‘I  II  z 0-  1  I  I  I  I  I  2  3  4  5  6  AGE CLASS Fig.  20.  Angle between eigenvectors (PCA axis 1 and 2) of data, cover ground for classes age adjacent separate strata; forbs/grasses (F), shrubs (5), lichens (L), bryophytes (B).  LIFE FORM STRATA  AGE CLASS COMPARISON Forbs/Grasses axisl axis2 1/2 2/3 3/4 4/5 5/6  61.0 54.9 39.4 60.8 40.6  72.7 76.2 25.4 46.3 46.1  Shrubs axisi axis2 50.3 42.9 53.0 25.1 31.2  78.4 43.6 40.8 31.7 39.4  Lichens axisi axis2 89.8 42.4 34.9 32.5 26.0  89.7 53.2 62.3 72.1 37.8  Bryophytes axisl axis2 86.7 9.5 15.5 5.6 16.6  85.5 32.5 36.2 21.6 17.1  Table 11. Angle between eigenvectors (PCA axis 1 and 2) of cover data, for ground classes age adjacent separate strata. 101  6.2.2.  Structure of the Tree Layer  The  tree  organizational  layer  (angle  theta)  to  undergo  change during succession  21 and 22)  Figs.  appears  .  very  little  12  and 13,  (Tables  Differences in orientation of the ellipse  rarely  exceeded  and  100,  eigenvectors mostly stayed below 45°.  angles  between  It should be emphasized  that the absolute magnitude of the angles are not comparable between the two methods. Whereas for comparisons of theta an angle of 20° reflects a considerable difference between two stages,  angles between eigenvectors up to 20° are considered  to represent “fundamentally similar vectors” p.  (Pimentel 1979,  87) Since both methods estimate organizational change based  on changing variable intercorrelation, angles  imply  that  the  structural variables of density,  correlation  structure  the tree layer  crown height and diameter)  the relatively small of  the  four  (canopy cover,  tree  remains fairly constant  through time. This does not mean that no changes occur in the tree layer through time,  but that the changes are not of an  organizational nature which would involve changing variable intercorrelations. In other words, the temporal changes occur harmoniously in all measured dimensions. One reason for this is certainly the monospecific composition of these forests; in mesic and xeric locations the harsh climatic conditions allow for no other species than lodgepole pine in the study area. As 102  outlined  in  section  6.1.2.2.  measurements  on  the  four  variables reflect temporal variation within this species only. The most important variation observed on a developing species of course is due to growth. If such growth occurs harmoniously in all dimensions measured, correlation structure in time will be  stable,  and,  by definition,  no organizational  change is  observed. Whereas suggested  the  small  results changes  indicated  in  the  by  early  the  angle  stages,  the  theta changes  indicated by comparisons of eigenvectors are slightly larger at  the  beginning  particularly (Table 13, In  for  Fig.  and the  again  combined  at  the  data  end  and  of  succession,  the  xeric  variant  tree  layer  remains  22)  conclusion  it  appears  that  the  relatively unaffected by organizational changes in time. The organizational changes that do occur are most conspicuous on xeric sites towards the end of succession. This  confirms the  observed trends of the ground cover data and may again reflect the  previously  discussed  increased  sites to environmental fluctuations.  103  vulnerability  of  xeric  (b)  (a) 100  i  I  I  100  I  80  g60  60  ASE GLASS  A GLASS  Fig.  Change between adjacent age classes in orientation (angle theta) of the 95%-confidence ellipse around PCA scores of axes 1 and 2 for structural variables of the tree layer. (a) Combined data. (b) Separate mesic (M) and xeric (X) sites.  21.  (b)  (a) 250  .  ,  260  i  200 g  ,  ,  .  15o,  /  100  /  ieo  ‘A  /1  A GLftS6  Fig.  22.  1ng1e between eigenvectors (PCA axis 1 and 2) of adjacent age classes for structural variables of the tree layer (a) Combined data. (b) (b) Separate mesic (M) and xeric (X) sites.  104  U,  F-’ C  LJ  CD  U)  hM  00  U)  H  H- P  I-  HJ.  I-)  rr  cc-)  rt  U)  rt  C)  CD  (12<  U)CD CD  I—’CD pi H  j  PJ(p CD ‘-<CD CD  CD rt(D  rto) CD I-CD CD  CD  w  H  CD  H  HI  U,W  (flL’)  M  W  OUU1ODW  ww OHQ  c’-)  U)  H-  ><O  H(D tJH  w,<  >< H  J  HU)  Q  U) JH-  U)X HCD  ‘WwJ  H-  Pi <  ‘  rt  (1)  ‘d  0  0  HI Li  I—CD  OHrt rtF—1) H-rt dH UU)Q  CD  U)oi  I-jCD  HQ H  h  CD  MFU)  ‘-<CD CDU)  -1-  CDCDCD  Içti O 0 CD  rt  l-h  Ø0)  U)Q-CD CD 0 ç  H U)EJ L,3J  P)CD <1  YCDCD  pi  H-1Q PJ i H1  <  H t’J  CD  I-’  P)  I—’  H’ (12(1) 0I:1)  p  i-’j  00  HH-  --  uQ x0  U1MW cx,OWU,w  HWU1U1 U]U1U1MW  o:’o1U,  U,’r.wJH  FW 1 WJW  o’DD  H w’-Qwoo-  OTIOOU  owo  OU1WL’)  U1WL’JH  0  C)  cI)(I) 0C1  Ic)  XL1I  00  0  0  Hi LXI  Cl) I-’  CHAPTER 7 DISCUSSION  The question whether ecological succession is a process essentially similar to the processes observed in evolution and of  ontogeny  living  organisms  has  plagued  the  minds  of  ecologists for the better part of this century. While during the  few  last  “organismic”  decades  most  ecologists  concepts of succession,  have  discarded  recent applications of  non-equilibrium thermodynamics to living systems have again emphasized the similarity of the processes Wicken 1987, thesis  Schneider 1988)  was  to  interpretations apply  to  the  explore of  One of the objectives of this  .  whether  succession  recovery  (Ulanowicz 1986,  as  and  a  sequence  process  of  what  to of  extent  development  lodgepole-pine  forests  documented here. Whereas exhibit  non-living  systems,  increasing randomness,  when  left  to  themselves,  ultimately leading towards a  state of equilibrium where randomness is at a maximum, living systems,  in  apparent  violation  of  the  second  law  of  thermodynamics, appear able to counter this tendency of decay. If  ecological  succession  is  indeed  comparable  to  the  development of living organisms, it will have to be shown that the  most  striking  attribute  of  developing  organisms,  this  ability not only to resist increase of randomness but even to lower it,  is equally present in developing ecosystems. 106  7.1. Order and Organization  Order  and  interchangeable  organization, fashion,  represent  non-randomness. The first one, with  structure  function.  or  although  form,  two distinct  order,  the  often  used  in  aspects of  is concerned primarily  latter,  organization,  with  Both order and organization appear to increase as  organisms  develop.  ontogeny,  involves  Organization, the  whether  development  of  in  phylogeny  or  increasingly complex  networks of interaction between the constituent components of living systems.  In this case,  the increase in non-randomness  is one of functional relationships, comparable for example to the non-randomness inherent in a wiring diagram of a computer. Order, on the other hand, is concerned with structure or pattern; structure is generated by an orderly arrangement of elements in space or time and involves predictability. Mature organisms ones;  a  in most seed  of  cases an  oak  are more tree  comparison to its adult form.  is  structured than structurally  immature  simple  As the systems develop,  in  non-  randomness increases, reflecting an increase in structure. One might argue that a simple structure like an acorn would be a more predictable and therefore more orderly entity than a full grown tree. This apparent contradiction leads to an important point: order of a system is a relative quantity. To determine the state of order of a system two factors must be considered: structure and complexity. 107  Structure can be defined as the constraints imposed on the elements of the system that produces the pattern. The more an assembly of elements is structured, the more these elements are  constrained  in  their  freedom  of  arrangement.  With  increasing determination of arrangement of its elements, the system will become more predictable. The other factor determining the state of order is the complexity of  the  I  system.  will  define  complexity  in the  context of order as arising from the combination of the number of categories in a system distribution  of  the  (e.g.  individual  categories.  If  functional  relationships,  the  species)  concept  of  and the number and  elements  complexity  the  number  among is  and  those  expanded strength  to of  connections between the elements of a system would also have to be included in the definition. Two aspects of complexity can be distinguished: actual or real  complexity  (Hreat)  and  potential  complexity  (Hmax)  Potential complexity is a measure of system size and refers to a theoretical state of equilibrium where no constraints apply, where no non-random structure is imposed, and the arrangement of elements is completely random. Potential complexity can be quantified as the number of potentially available states,  a  quantity comparable to thermodynamic entropy at equilibrium. Real or actual complexity, actual randomness of  on the other hand,  the system,  owing to operation of constraints. 108  refers to the  a quantity lower than Hmax  As  system  a  available  expands,  states,  will  the  Hmaxi  increase  predictions more difficult  number  as  well,  of  potentially  which  will  make  unless this increase in  -  is  offset by a simultaneous increase of the constraints. Thus, it is quite possible that, although the constraints imposed on a large system are more restrictive than those of a smaller one, the state of predictability within the smaller system will be higher because of the lower number of potentially available states. relative  The  state  of  quantity,  order  taking  of  in  a  system,  therefore,  consideration  both  is  a  potential  complexity as well as the constraints imposed on it, where the constraints are given by the difference between  and HreaL  Thus order, as introduced in Chapter two, can be expressed in the form of a proportion as representing  the  fraction  (1 of  Hreai/Hmax)  -  (Landsberg 1984),  totally available  states  the  system is unable to access because of the constraints. A hypothetical graph proposed by Brooks et al. illustrate  the  relationship  between  developing system is shown in Fig.  Hreai  23.  and  (1989) to in  Hmax  a  As the system grows  both Hmax and Hreai will increase. The critical point is that Hmax is  increasing  increase  in  resolves  the  faster  order  (1  apparent  than Hreai -  which  Hreai/Hmax)  violation  .  by  leads  The  same  living  to  an  absolute  argument systems  of  also the  second law of thermodynamics by showing how entropy and order can both increase at the same time.  109  Hmax  Order  H  real  Time  Fig.  The relationship between maximum randomness or potential complexity Hmax and observed randomness HreaL of a developing system over time (after Brooks et al. 1989)  23.  The (1989)  above graph was to  illustrate  originally used by Brooks  the  behaviour  developing systems, whereby the quantity  of  et  organization -  Hreati  al. in  according  to Layzer (1975), was interpreted to represent organization or information. The similarity of Landberg’s (1984) definition of 110  order  Layzer’s  and  affinity  of  the  interchangeably.  two In  of  (1975)  organization  concepts  this  thesis  which an  distinguish clearly between the two  -  reflects  are  attempt  often was  the used  made  to  order relating to non-  randomness based on structure or form,  and organization to  functional relationships. It is obvious that form and function in a living organism are not entirely independent, but it is also obvious that form in nature can rarely be sufficiently explained by function. The wealth of beauty and playfulness in nature has so far resisted (in my opinion,  successfully)  all  utilitarian attempts of reducing its variety of forms to some hidden ultimate causes and purposes.  7.1.1. Order  One of the goals of this thesis was assess  the  change  during  state of order of recovery  to quantitatively  an ecological  after  disturbance.  system and its Because  of  the  immense complexity of such systems an appraisal of the state of order of an ecosystem as a whole is obviously an impossible task. With the enormous multitude of sources influencing the state of order in an ecosystem,  an assessment of ecological  order  confined  must,  by  necessity,  be  to  some  selected  component of the total system. In this thesis observed randomness and its change during the process of recovery after disturbance were assessed based 111  on ground cover data (species composition and abundance)  and  structural attributes of the tree layer  For  age  each  class,  the  variation  (section 6.1.).  associated  with  the  system  configuration was quantified by the size of equal frequency ellipses  around  transect  scores  obtained  by  principal  component analysis. Such scores represent the coordinates of the transects on the respective PCA axes and provide a summary of the system configuration.  With increasing spread of the  scores the size of the ellipse will increase, increase  variation  in  decreasing  or  indicating an  predictability.  Alternatively, variation of ground cover composition was also assessed by  Shannon’s  diversity  index  and  calculations  of  spatial heterogeneity. 110w  are  such  measures  of  ecological  variation  to  be  interpreted in terms of order? As outlined before, order in a developing  system  may  increase  while  at  the  time  same  predictability may decrease. Such a situation typically occurs in  the  course  of  development  as  the  rise  of  structure  is  accompanied by an increase in the number of totally available states (Hmax)i as previously illustrated by the model of Brooks et al. as  (Fig. 23). The size of equal frequency ellipses as well  Shannon  estimate  diversity  spatial  predictability  of  configuration potentially  and  but  contain  available  heterogeneity provide  associated  no  information  states.  comparable to the quantity Hreati 112  Estimates  with  the  relating of  an  system to  the  variation  are  providing a measure of the  actual  state of randomness  state of order,  in the system.  To establish the  such measures of variation will have to be  related to the potential complexity of the system  maxh  One possible approach is to calculate Hmax based on the formula for “informational entropy”, a formula previously used to calculate Shannon diversity:  H  =  p  -  *  log p , 1  where p represents the probability of an individual to belong to  the  i-th  realized when  category. a  According  this  to  randomly selected  formula  individual  has  Hmax  an  is  equal  chance to belong to any of the specified categories and will be of the value log n, n symbolizing the number of categories. Such Hmax values obviously depend exclusively on the number of categories in the system but take no account of the number of elements of the system. Using Shannon diversity as a representation of Hreai and calculating Hmax according to order,  as  assessed  by  the above  Landsberg’s  outlined procedure,  formula,  will  not  be  influenced by the number of species in the system but rather by  the  evenness  of  the  distribution of  individuals plants  among the species, a property known as equitability. The  following  simple  illustration  shows  that  such  a  definition of order is indeed appropriate and that it is the equitability  rather than the number of categories or elements  that determines the degree of structure of a system. Consider 113  two blocks, one with nine cells (three columns and three rows) with sixteen cells  and one  (four columns,  cells represent the categories, represented by black dots.  four rows).  Thefl  the individual elements are  In both blocks the black dots are  arranged in the same fashion, forming a diagonal line from the bottom  left  corner  to  the  top  right  hand one.  Thus,  both  blocks are identical in structure or order but not in number of elements or categories. Landsberg’s formula will yield an equal value for order in both cases regardless of the number of categories or elements as shown by the calculations below.  :  a)  -  9 categories 75 elements 3*25/75*].cg 25/75 Hreat = = log 9 Oräer = (1 Hreat/Hx) = 1/2 -  =  log 3  -  b) 16 categories 40 elements Hreai = log = log 16 Hma Orã.er = 1/2  A different concept of ecological order was proposed by Pineda et al. as  the  (1988). They defined ecological order  “correspondence  between 114  species  and  (p.  289)  environmental  characteristics”. Similarly, Phipps  gave a definition  (1981)  of ecological order not based on purely spatial configurations of the species but rather  “on the correlative variation of  vegetation and other distinct features”.  By this definition  order increases as the correlation between a set of external predictor variables and the  configuration of the  community  increases. Whereas in the previously discussed methods order was  an  expression  community  alone,  variables,  internal  the  environmental  of  definition  between  one,  species  regardless  this  probabilities  the  of  two  variables.  any  is  and  The  external  based  different  species,  configuration  an  of  conditional variables,  external  difference  the  explanatory  on  sets  of  one,  between  an the  the  two  definitions appears to be comparable to the difference between the two different techniques of ordination, based on methods of either indirect or direct gradient analysis Ecological order, according to Pineda et al.  (Gauch 1982).  (1988) and Phipps  (1981), will be influenced to a large degree by the choice of the  predictor  configuration conditional  variables, alone.  Thus,  probabilities  information about  the  rather  than  calculations may  skill,  in  many  by of  order  cases  persistence,  the  and  system based  provide luck  of  on  more the  ecologist of measuring the appropriate variables controlling the system than about the system itself. Further, as discussed in more  detail  pattern  is  in  hardly  Chapter ever  1,  it  appears  determined 115  by  a  that  a  set  of  community external  H H a-,  CD  CD  c-F  N  0  0 HCD  CD  CD  Ct  CD  CD  a  Ct  HMi  CD  ci)  ..  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I  I  1  3  6  PGA AXIS I  Overlap of equal frequency ellipses around PCA scores of transects on axes 1 and 2 ground cover species in mesic and xeric sites: a) age class 1 (1-50 yrs.) ; b) age class 4 (151-200 yrs.)  It appears ecological  -1  now that there  order.  Order  in  is no single definition for  this  thesis  was  defined  as  a  probabilistic concept, arising from the relationship of actual and potential complexity in a system;  with increasing order  the relative predictability increases. It is obvious that from  117  such a definition, the state of order in a system will depend on the categories of the system chosen for an assessment of probabilities. Such categories, of course, do not always have to be species; estimates of ecological order can be based with justification  equal  on  any  selection  of  quantifiable  categories describing a particular aspect of the system. Thus, it is conceivable that order involving predictability of one set of attributes  (e.g.  species composition)  whereas order based on a different  time,  vegetation  (e.g.  structure)  may  may increase in  set of attributes  decrease.  Moreover,  contradictory trends may even be found for one and the same variable depending on the level of hierarchy where variability is assessed. This was found in calculations for the structure of  the  tree  variability  layer  (section  decreased  6.1.2.1.)  while  where  among-transect  within-transect  variability  increased with increasing stand age. Thus, where order is assessed for systems of the immense complexity of ecosystems, no single definition of the state of order may exist as every such assessment will be confined to a selected subset of attributes of the whole system. How, then, do these various concepts of ecological order compare  to  trends  observed  in  organismic  development?  Ecological order obviously strongly depends on the properties used to assess such trends. In this thesis community variation was  measured  based  on  species  composition  and  structural  attributes of the tree layer. All three methods of assessing 118  H  F-’  U,  -  xJ  U) Cl) CD Cl)  Cu  C) 1 H  CD  P)  F-’ F—’  Cu  Ct  o  0  ft  ft pi  Cl)  CD  k<  CD  C) Ct  CD  <  H  CD Ct  Cl)  H0  CI-  I-i P)  CD  H-i H  C) H-  CD  Cr  Cl)  CT)  CD  H-  S  CF  i 0  1:1  CI)  0  -0  H  -  CD  Cr  H-  CI-  Hi  0  CD Cl)  CD CD h  H-  H F-’ F-’  rt  Ct  H-  S S  C) 0  CD  ft :-  0  j’  Ct  H  Ct  P)  H-  CD  -  —  a)  H ‘o  -  CD  ci, U)  CI)  t-  Cr  ‘-  i-  H-  0  C-) ‘•ij;  p  CD  Cu C)  )  0  I—h  0  I-i  0—  H  0  CD H  CI) H-  S  F CD  CD  t-  0  CD n  Ct  m r  in  Cl)  —  U)  U)  HC)  Cl)  H CD  I-h  0  CD  U)  C)  CD  Ct  CD  II  H-  0  CD  85  CD  S 0  HH F-’  CD  I-  0  b  Cr CD  CD  H-i  -< U)  CD  rt  CD  k<  ‘i  H-  0  Cl)  Cl) Cl)  Cr  t Cl)  ‘j  H-  H-  d  CD H 0  CD  CI)  Ct  Cu  H-  CD  I-  0  0  rr  CD  Ct  CD C)  < ‘d  CD  H-  5  CD  J• HHP) U) HCt  Cu  CD  CD  CD  F-’  Cr  Cl)  S d  <  Cl)  0  C)  U)  H0  CD  CD  Ct  HU)  I  i-  i CD  0  H-  Cl) CD  C)  Cu  F—’  5  ‘<  Cl)  Cl)  CD  C)  CD  i  0  Ci) H-  F-’  C) 0 :i  CI)  H-  CI)  )  U)  CF  Cu  CD  0 W  0  çt  CD  CI)  CD  l-  CD  J’  HI  Ct  Cu  Ct  CD  H’  0 i C)  C)  ()  CF  1  CD  Cr  ‘tl  5  CD  CF  ‘<  Ct  H-  F-’  H-  b  Ct p  F-’C)  Q  CD  ‘z5  H-  P)  C)  CD  CD  CF  Cr  CD  Ct  H-  ‘-  CD  Cl  0  CD  C1  CD  H-  ‘<  H-  H-  U)  C1 CD  Cu  1J  -  U)  CD CI) Cl) CD  I-’  CD  i,  5  CD  Ct  Cl)  Cl) ‘<  Z  CD  CD  U)  H-  CD  II  C) i  CD  <  H-  CD  H  C)  CD  U)  i  H  CD  C) h CD Cu U)  H-  CD  Ct  5  U)  Cr  b’ CD  CD ‘<  Cl)  ii  I-  d  CD  k<  Cl) Hft  I-  CD  H <  H-  CD  Cu U)  CD  0  H  Cl)  U)  H  0  U)  CD  -  -  H0  Cl)  C) C) CD  U)  0 r-t  8  CD  H-  i-<  HHCr  CD  CD CI)  CI)  I  0  CD  Cu U)  CD  I-  H-  CF  U)  C)  CD  .Q  Hi  :i  Cu  CI)  Cl  CD  CF  U)  IQ CD  U)  CD H Ct  CD  0  CD  Ct  CD  CI) H  H  CI)  CF  C!)  Cl  CI)  CF  Cl) H  CD  H  Cl  0  CI)  H-  H H  CD CI)  CI)  U)  CD  H  CD  CD H  S  CI)  0  H-  Ct  U) H  S  0  C) 0  CD Cl)  CD C)  U)  H  H0  Ct  H  CI)  b)  a) _-1Qo  _.100  80  8O  60  I  40  40.  60  g  i—20  _....! x  .  2  1  3  . 1  8  5  4  AX GLASS  Fig.  3  2  A  4  5  6  GLASS  Percent order for ground cover data, based on Shannon diversity, a) Combined data. b) Separate mesic (M) and xeric (X) sites.  25.  The second argument relates to the nature of the elements (i.  e.  the species)  randomness  of  the  that are used in assessing the state of system.  therefore,  entities;  Species  are  highly  structured  an increase in species diversity will  lead to an increase in structural diversity of the system. Structural  complexity  is  certainly not  equivalent  to  high  randomness, but rather its opposite, which would lead to the conclusion that increasing diversity in a living system, or, in  more  fashionable  terminology,  increasing  biodiversity,  represents an increase in order. Thus, ecosystems recovering from disturbance appear to be similar to developing organisms in terms of increasing structural complexity.  120  7.1.2. Organization  Ecological organization,  in contrast to order,  is less  concerned with structure or patterns than with the functional relationships between the elements of the system. Every change in  organization  will  reflected  be  by  a  change  in  the  correlation structure of the participating elements. Following this  rationale,  change  organization  in  between  different  stages of development was quantified based on the changing correlation structure for the species-by-transect matrix. In  Chapter  1,  based  on  energetic  considerations,  directional processes as observed in ontogeny, evolution and succession  were  interpreted  to  be  driven  by  the  same  underlying principles, i.e. to result from the dynamic tension between Lotka’s maximum energy law and Prigogine’s minimum dissipation principle. From the viewpoint of organization, if such analogies are to be valid, it will have to be documented that natural communities are cohesive entities that possess a certain  degree  of  autonomy.  As  outlined  in  Chapter  1,  interactions between the constituent species of a community have  been  trophic  sufficiently  levels,  documented,  justifying  the  both  within  conclusion  and  that  among  natural  communities are indeed more than a mere assembly of unrelated objects. organisms  There are,  however,  and ecosystems,  undeniable differences between  and the question remains whether  these differences preclude an interpretation of successional 121  and organismic development as arising from the same underlying causes. The main difference between organismic and successional development is certainly the higher flexibility of ecosystems responding  in  to  plasticity  allows  influences  within  external  signals.  organisms a  to  certain  Although  respond  range,  to  phenotypic  environmental  such modifications  are  relatively minor in comparison to the dominating genotypic constraints.  Conversely,  the  system  configuration  of  an  ecosystem appears to be much less internally controlled than that  an organism.  of  An example  for the  relatively loose  constraints of the communities of this study is given by the considerable  often  differences  between mesic and xeric variants variants,  for  example,  exhibit  in  organizational  (Fig.  17b,  considerable  change from age class 4  (151-200 yrs.) to 5  both  tree  ground  cover  and  18b,  layer,  change  21b). Xeric  organizational  (201-300 yrs.)  whereas  mesic  follow a relatively smooth course of action,  in  variants  comparable to  trajectories of organismic development. This higher flexibility in response of ecosystems appears to  be  a  result  of  their  comparison to organisms.  lower  degree  of  integration  in  Evidence for this lower degree of  integration, for example, is given also by the fact that local disturbances  often  result  in  a  pattern  of  different  successional stages within an ecosystem. An organism, on the other  hand,  will  always  respond 122  as  a  whole  to  local  disturbances. organisms,  The  for  process  example,  of  will  wound always  healing tend  to  in  healthy  recreate  the  original form. This ability of integration is crucial to the survival  of  an  organism  and  its  loss,  as  in  the  case  of  malignant growth, may ultimately lead to its death. In forested ecosystems, mosaics of different successional are typical  stages local  of mature  disturbances  structure.  Fig.  26  stands where  eventually  lead  illustrates  to  the  an  continuous minor all-aged  development  stand  of  age  structure from the typically tight cohorts of early stages to the all-aged structure in mature forest. a)  b)  O.T  05  E  0  Fig.  4  26.  Q  1:  1U  240  320  400  Years  0  eo  lJ  240  20  400  Years  Typical age structures of stands of different age in the study area; a) a site of age class 2 (51-100 yrs). b) a site of age class 5 (201-300 yrs.). Bar width: 20 yrs.  123  question  The  is  now whether,  in  of  light  this  lower  degree of integration and higher flexibility of ecosystems in to  response interpret  external  signals,  succession  constraints.  What the  words,  succession  not  is  still  adequate  manifestation  according  is,  interpretation, is  a  as  it  reality of  such  to  of  a  internal  thermodynamic  constraints?  sufficiently  to  In  explained  other  by  the  properties of the individual organisms? Internal constraints, according to thermodynamic theory, follow  from  principle.  the  maximum-energy  and  minimum-dissipation  The system configuration is an expression of the  dynamic tension of the two laws, whereby Lotka’s law dominates as energy is abundantly available in unsaturated conditions of the  early  stages,  whereas  with  increasingly  constrained  resources Prigogine’s principle will become more active. Thus, species composition and abundance at the onset of succession will  be  dominated  generalist  species  angustifolium)  In  by  rapidly  and  (forbs later  dispersing  stages  grasses, long-lived  and  fast  e.g. and  growing  Epilobium specialized  species will be favoured, using the available resources more efficiently  and  spending  relatively  production of progeny (trees,  shrubs,  124  less  energy  lichens)  (Fig.  for 27).  the  100  80  ,60 z w 0 cc w °-40  20  0  1  2  4  3  5  8  AGECLASS Fig.  in composition Change (forbs/grasses (F), shrubs bryophytes (B).  27.  One  might  argue,  replacement  the  of (S),  of  ground lichens  r-  cover: (L) and  by K-selected  individuals was entirely predictable from the strategies of the  individual  species  as  determined  by  their  genetic  material. A thermodynamic interpretation of development would point out that organisms have not evolved in a vacuum but in a fabric of interdependency with their living and non-living surroundings. autonomous  The  control  genetic  material  system but  125  as  one  is  not  seen  that preserves  as  an  those  forms that have been previously successful within the system configuration under the specific thermodynamic constraints. Thereby the whole is “more than the sum of its parts because the whole is involved in the very definition of the parts” (Wicken 1987, p.166) Such  interpretation  an  organisms  and  ecosystems.  builds  Organisms,  constituent elements of the system, the  energetic  same  rules  the  of  bridge  between  representing  the  have evolved subject to  thermodynamic  flow  as  the  ecosystem as a whole. The individual interest is embedded in the context of the community dynamics, are  and  preserved  passed  on  to  and successful forms  future  generations.  although differing in degree of integration, thermodynamic  interpretation,  organismic  Thus,  in light of a and  ecosystem  development become essentially comparable. It  was  by  the  phenomenological  symmetries  between  organismic and community development that Clements was led to proposing  his  organismic  interpretations are expect  of  phenomenological  some  processes.  to be  Symmetries  concept.  If  any value,  one would equally  similarities  between  successional  thermodynamic  between and  the  two  organismic  development have been summarized by the following four “rules” (Weber et al.  1)  1989,  Salthe 1991)  after an initial increase,  a monotonic decrease in the  intensity of energy flow per unit biomass occurs; 126  2)  a  continual  (system  hyperbolic  size,  increase  number  and  in  complexity  diversity  of  occurs  components,  connections between elements); 3)  internal stability increases, i.e. the internal tendency towards change decreases;  4)  stability  in  the  face  of  perturbations  gradually  decreases.  The first rule is a restatement of item three in Odum’s catalogue of “trends to be expected” that  biomass  supported  per  unit  (Table 1) which maintains flow  increases  during  succession. For organismic development this rule conforms to the  observation  increase, 1972)  that  metabolic  costs,  after  an  tend to decrease as maturity is approached  initial (Zotin  (Fig. 28) The  decline  efficiency  of  of  the  the  curve  system  as  illustrates maturity  is  the  increasing  approached  predicted by the minimum dissipation principle.  as  Increasing  efficiency can result from increasing differentiation of the constituent  components  of  the  system  and  the  increasing  interactions among them, leading to increased internal cycling of the available energy. Increasing efficiency can also result from a reduction of the number of redundant energy pathways (Ulanowicz 1986, Weber et al.  1989)  127  60  50  40  300 se \‘ 0%  200  0  100  \  Rats 2  \•\  %•‘0.  10  Sheep  0_••,  °—0—.o........o_O_e_, Pigs 0.• oe.—0 Horses Cows  28.  30 month  20  10  Fig.  46  k o4_  20  ‘-,  Chickens  *_0_  Change in basal metabolism during growth of birds and mammals (from Zotin 1972, P. 48).  Whereas differentiation  in  organismic is  brought  differentiation of cells  development about  by  (Ham and Veomett  the 1980),  increasing increasing a similar  trend is observed in ecosystem development as the ecological amplitude of the constituent species decreases in the course of succession (Fig. 24, IDe Pablo et al. 1982, Zorrilla et al. 1986)  In the present study changes in energetic efficiency may be inferred from increasing metabolic efficiencies of growing 128  organisms  (Zotin  Low energetic  1972).  efficiency  in  early  stages may result from the young age and small size of the tree layer. The rule, however, should be applied with caution when plants are involved as,  according to Odum (1971, p. 79)  for plants “it is often difficult to decide what constitutes an ‘individual’  .  Thus, we may commonly regard a large tree as  one individual but actually the leaves may act as ‘functional individuals’  as  far as  size-surface area relationships are  concerned”. Low  energetic  efficiency  in  early  stages  could  also  result from the fact that energetically less efficient small plants of the ground cover constitute a higher proportion of the total biomass than in later stages where biomass is to a very large proportion supplied by the tall growing tree layer. Evidence demonstrating that the systems of this thesis operate  more  construed  efficiently  from  the  in  declining  mature  stages  eccentricity  can of  also the  be  equal  frequency ellipses for ground cover (combined and mesic data) (Figs.  l4a  and  14b).  As  previously  discussed,  decreasing  eccentricity may be interpreted as an expression of a decline in redundancy, a feature expected from developing systems as they approach maturity. Thereby redundant energetic pathways are  sacrificed  efficiency.  in  Xeric  exchange sites  appear  approaching  maturity by being  disturbance  and  therefore  for  are 129  increasing to  subject not  energetic  be  prevented  from  to  continuous  minor  operating  to  minimize  with  dissipation  increasing  stand  age,  as  reflected  by  increasing  complexity  in  increasing eccentricity in later stages.  second  The  developing  rule  relates  systems.  In  to  organismic  development  complexity  increases with increasing size, increasing differentiation of cells  increasingly complicated networks  and  between cells and organs Increasing  interaction  (Ham and Veomett 1980)  complexity  in  course  documented by increasing basal area species diversity  of  (Figs.  7  10).  -  of  (Fig.  succession  4)  was  and increasing  From Lotka’s principle of  “maximum energy” one would expect the system to expand most rapidly during the  early phases,  and biomass production to  level off with increasing age. Calculations of basal area per hectare  living  of  crop  standing  expectations class 4  trees,  per  (Fig.  area, 4)  .  an  expression  were  in  of  the  agreement  amount with  of  these  Basal area reached a maximum in age  (151-200 yrs.) and declined slightly as stands became  older.  This decline is most likely a result of the death of  trees  as  favourable  they  reached  moisture  their  conditions  upper  age  resulted  limit. in  basal  The area  more per  hectare to be higher on mesic than on xeric sites. Noteworthy also is the rapid increase in basal area between age class 1 and 2,  a feature consistent with thermodynamic theory which  would  predict  rapid  system  expansion  during  times  of  abundantly available resources. Biomass production stagnated 130  in  stages  later  and  incoming  energy  appears  to  be  spent  entirely to maintain the status quo. Increasing complexity,  species  was  diversity,  documented  by  Shannon diversity,  ellipses,  an aspect  increasing  of  structural  equal  frequency  and spatial heterogeneity.  alleged hyperbolic shape of this increase,  however,  The  was not  found. Equal frequency ellipses suggested a steady increase up to  age  class  5  (201-300  yrs.)  (Fig.  whereas  7),  Shannon  diversity (Fig. 9) and spatial heterogeneity (Fig. 10) showed a large increase from age class 1 (51-100 yrs.)  and,  (1-50 yrs.)  similar to basal area  relatively constant in later stages. hyperbolic  increase  would  have  It  been  to age class 2  (Fig.  remained  4),  is possible that a found  for  Shannon  diversity and spatial heterogeneity if the first 100 years had been divided into smaller time segments. Although not observed for structural complexity, by  the  cover  quantifications (Fig.  17),  a hyperbolic curve was documented  of  relating  organizational to  the  change  change  in  in  ground  functional  complexity of the system.  Rule  three  development.  relates  to  the  course  and  speed  of  For ecosystem development this rule relates to  the resilience of the system describing the ability and speed of a community to rebound after disturbance. The rule claims that  the  matures  processes of -  development  slow down as  the  system  a tendency implied and illustrated also  in the  131  Brooks et  graph of  al.  (Fig.  (1989)  23)  .  This decrease  in  speed of development leads to a state of “internal stability” (perhaps “internal inertia” would be more appropriate) as the system matures.  In organismic  development  such  a  state of  internal stability is approached in adulthood as growth and development come to an end and the mature form is reached. In classic  succession  models,  changes  gradually  autogenic  such  a  slow  state down  is  and  achieved the  as  ecosystem  approaches a state of climax where species composition and abundance remain relatively stable. Speed and course of recovery after disturbance of the communities of this study were documented by quantifications of organizational change, based on calculations of angle theta and  angles  between  ground cover data phase  eigenvectors.  development  for  the  combined  were in agreement with rule three. After a  intense  of  Results  organizational  slowed  down  change  remarkably  and  successional approached  an  equilibrium as the system matured (Figs. 17a and 18a). For the divided data, down  on  successional  mesic  sites  but  changes also were found to slow on  xeric  sites  the  dynamics  of  recovery showed no sign of approaching an equilibrium (Figs. 17b and 18b). Thus,  speed  and  course  of  recovery  appeared  to  be  significantly influenced by the environmental setting of the communities.  There  are  two  possible  reluctant recovery of xeric sites. 132  explanations  for  the  Xeric sites are rich in  terrestrial  lichen  species,  some  of  which  (Cladina  spp.,  Stereocaulon spp.) are known for their extremely slow recovery after  fire  (Scotter  1964)  Alternatively,  .  the  delay  or  obstruction of the recovery process could also be caused by continuous minor disturbances preventing the communities from ever approaching a state of equilibrium. What could be the nature of such frequent disturbances in later  stages  of  xeric  severity could be  habitats?  a possible  While  agent  droughts  of  of  unusual  disturbance,  such a  scenario is unlikely since xeric sites are rich in extremely drought-tolerant different  lichens.  origin.  The  The  disturbances  area  study  is  the  may  home  have  of  a  central  British Columbia’s largest population of woodland caribou and the mature lichen-rich stands on xeric soils are preferred winter feeding grounds. suggested caribou  continuous grazing,  Thus,  it is quite possible that the  disturbances  a  form  of  are  caused  disturbance  by  excessive  that  becomes  increasingly important in the area owing to extensive logging operations in prime caribou habitat  (Cichowski 1990).  In conclusion, resilience, the process of recovery after disturbance of the communities of this study,  appeared to be  significantly influenced by the environmental conditions of the habitat. Unproductive sites on xeric soils recovered much slower,  whether  as  a  result  of  terrestrial lichens  or of  ungulate  In both cases  herbivory.  the  slow  recovery  of  continuous minor disturbances by  133  it would be  the  lichens  holding up the  recovery process,  quantifications  of  a  organizational  strata which identified the  suspicion  change  lichens  confirmed by  for  the  separate  to be one of  the more  restless components of the ground cover (Figs. 19 and 20)  .  The  slower recovery of the xeric sites is also in agreement with Grime  (1988)  predicting  low  resilience  for  communities  in  chronically unproductive habitats.  Rule  four,  the  behaviour  of  stability  systems requires a more detailed discussion. chapter  implications  to  the  in  developing  In the previous  diversity/stability discussion  have frequently been alluded to.  I will now try to summarize  the most relevant aspects of the results pertinent to this issue in order to assess what the evidence of this study can add to the debate as well as to assess how the behaviour of stability  in  the  investigated  communities  compares  to  stability in organismic development. The area of equal frequency ellipses around PCA scores for ground cover data was interpreted to be an expression of species  diversity,  represent  whereas  “redundancy”,  an  eccentricity expression  was  of  understood  the  presence  to of  alternative energy pathways within a system. High redundancy was  concluded  perturbations.  to  induce  high  stability  in  In an undisturbed environment,  the  face  of  according to  thermodynamic theory, one would expect redundancy to increase during the phases of system expansion and to decline in later 134  H W 01  CD  I-h  0  Cl)  < CD H  CD  •  Y  a  U)  :-•  “  ,  U)  CD  (  H-  U)  CD  Hft  U)  C)  H-  U)  S (D  Pi  CD  H 3 C)  CD  çt  -  H  P  CD  ft  0 $i  CD Cl  ft  d 0 H i  U) Ct  H  H-  CD CD  Cl  H  k<  C)  Cl  CD Cl  Cl  Pi  CD  ft °  <  :CD  Ct  CD CD i  b CD  CD IU) H ft ‘<  <  k<  CD h Cl) H ft  Cl H-  l H-  H-  ‘—  i  CD  I-  CD  H  tQ  H-  <  CD  0  C)  CD  i]:j  .  ft CD U)  U)  H H  Pi  S  U)  Mi  0  ft  P.) C)  Mi  CD  ft  p.)  Mi  0  CD pi  I-  u  CD  U)  d  CD H H H-  H-  PJ U)  -.  ft  p.)  H Mi HC)  H-  CD U)  C)  CD 1 CD  H Hi Mi  Cl  CD  U)  p.) IU) C)CDCDT  U)  P-  ft  H-  CD  H-  ‘1  CD  H  (D  H  H  Pi 5 d  U)  H CD Pi  C)  CD CD  ft  CD  H-  U)  o H-  H  CD  .  Cl)  <  CD  o  —  ft P.)  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CD  U)  -  CD  Mi  H-  C)  <  CD  H  C)  Cl  C) ‘-<  Cl P.)  $3  CD  CD  ft  k<  CD  ft  Mi  0  b  U)  P.)  CD  CD 3 II CD Hi Mi HP.) C) HCD  C1  ft  U) CD 3  CD  Mi I-  d  Hi  CD  CD  II  S  C)  H  CD ft  CD  CD  HN H  S  ft H  0  0  HC.))  P.) U)  Iti  CD  CD  ft  CD  CD  CD U)  ft .)  U)  suggesting that xeric sites were less resistant to external perturbations. Given the foregoing, it would follow that diversity alone in the investigated communities had little effect on levels of stability. This may come as a surprise. Are not redundancy and diversity pointed  an  out,  inseparable stability  couple?  is  a  As  May  function  (1972,  not  has  1973)  only of  species  diversity but also of the amount and strength of interactions in  a  community.  As  redundancy  is  concerned  with  energy  pathways, levels of redundancy will necessarily depend on the degree  and  strength of  such  community  interactions.  Thus,  lower redundancy on xeric sites could be the result of the lower degree of integration of communities in xeric habitats. According  to  Grime  species  (1988)  competition  in  unimportant;  similarly,  unproductive  interactions  habitats  beneficial  are  such  as  relatively  interactions  may  be  negligible as well. Thus, low levels of interaction would lead to a relatively loose community structure where species are only minimally connected with each other. As the presence of redundant pathways implies a relatively elaborate network of community  interactions  redundancy  would  minimum  dissipation  likely  be  insignificant as well. From  the  principle  of  redundancy  would be expected to decrease in later stages as alternative pathways  are  sacrificed  in  order  agreement with such expectations 136  to  gain  efficiency.  In  redundancy on mesic sites  dropped in later stages of succession, but on sites of limited moisture  the  opposite  trend  was  observed  (Fig.  This  14).  unexpected increase in redundancy on mature xeric sites may be a consequence of frequent minor disturbances in later stages of succession. that  Such a conclusion would follow from the fact  disturbance will of  lower  hypothesis”  would  levels  cause a  regression of  efficiency. also  This  explain  the  the  “minor  system to  disturbance  observation  that  the  recovery process on xeric sites shows no sign of approaching a climactic equilibrium (Fig.  17b)  In comparison with organismic development the behaviour of the combined and mesic data appear to conform to the rule that stability in the face of disturbance declines in mature stages. On xeric sites the rule was not followed: redundancy increased in later stages which was explained as a reaction to disturbance in these stages.  Similarly,  rule three,  stating  that the speed of development will slow as the systems mature was followed only in mesic variants or in the combined data where habitat effect had been removed. Although rules one and two,  relating  complexity  to  energetic  appeared  to  be  efficiency followed  by  and both  increasing variants,  considerable differences in degree of agreement were found. Patterns of successional development in the investigated lodgepole pine forests were in reasonable agreement with the four  phenomenological  rules  for  the  combined  data  where  environmental effects had been removed from the data matrix. 137  Mesic sites also often followed the patterns outlined by these rules but on xeric sites little consensus with the rules was found. This poor agreement of unproductive sites may reflect the  lower  decreasing  degree levels  integration of  of of  integration  such  communities.  ecosystems  will  With  become  increasingly subject to external influences which will tend to override the autogenic processes. Thus, follow organismic rules  ecosystems appear to  if autogenic processes are able to  proceed unimpeded but departures from the rules are expected where  there  is  greater  susceptibility  interference.  138  to  external  SUMMARY  Trends in temporal development of a recovery sequence for a lodgepole pine-dominated system in the interior of British Columbia were documented by quantifying order and organization within these communities. Order was defined as a probabilistic concept concerned with pattern or structure and arising from the relationship of the observed or actual randomness complexity (Hmax)  .  with the potential  (Hreat)  Hmax refers to a theoretical state of maximum  randomness and is also defined as the number of potentially available states of  a system.  Order,  applied to ecological  data, was found to have a strong affinity to the more familiar concept  diversity.  of  Organization  on  the  defined to be concerned with functional  other  hand  relationships  was in a  system. Different  aspects of both order and organization were  quantified by means of multivariate techniques and compared to results  obtained by calculations  spatial heterogeneity.  of  Shannon  diversity  and  The area of equal frequency ellipses  around principal component scores of transects was interpreted to represent the observed randomness according  to  calculation,  the to  type  be  an  of  (Hreat)  original  expression  of  of a system and,  variables  used  either  species  for or  structural diversity. Eccentricity  of  the  equal 139  frequency  ellipse,  an  expression  of  the  strength  of  variable  intercorrelations  within a system, was equated with redundancy, a term borrowed from information  theory.  The  term has  been used elsewhere  (Ulanowicz 1986) to describe the presence of multiple pathways in an ecological  system,  eccentricity  95-equal  of  and it was frequency  hypothesized that ellipses  the  provided  a  possible procedure to quantify redundancy in an ecological system. Organizational  change  in the course of  succession was  quantified by the change of orientation of equal  frequency  ellipses as well as by angular comparisons of eigenvectors between adjacent age classes. Based  on  successional  these and  quantifications,  organismic  similarities  development  according to four phenomenological rules Salthe  1991).  Succession  in  the  were  between  evaluated  (Weber et al.  investigated  1989,  communities  followed similar trends as found in organismic development in terms of energetic efficiency,  structural complexity,  speed  and course of development and system stability. The suggested  undivided data a  steady  penultimate phase  (xeric  increase  with a  in  and mesic species  subsequent  stands  combined)  diversity up  decline  as  to  a  climax was  approached. Eccentricity followed a similar pattern, thereby behaving  in  agreement  with  expectations  from  Prigogine’s  minimum dissipation principle predicting a system to sacrifice multiple pathways in exchange for higher energetic efficiency. 140  Order,  quantified based on species data, was found to remain  relatively stable during succession. Organizational dynamics were most pronounced at  the onset of  succession and slowed  down with increasing stand age. Stability and resilience were found to be lower on sites of  environmental  poor  relationship,  conditions  however,  of  than  stability  on or  mesic  sites.  resilience  No  with  diversity could be established as levels of diversity in both mesic and xeric sites were similar. Lower redundancy on xeric sites was  interpreted as an indicator for lower stability,  leading to higher sensitivity to environmental fluctuations during the process of recovery. This in turn could have led to the observed reluctance of such sites of achieving a state of equilibrium. Processes in successional and organismic development were reasonably similar except for sites in unproductive locations. This unanticipated behaviour of xeric sites was hypothesized to  be  a  result  communities however,  of  the  lower  degree  of  integration  in locations of poor productivity.  of  In general,  it was concluded that the recovery process of the  investigated  communities  exhibited  patterns  similar  to  organismic development as long as the autogenic processes were able to proceed undisturbed.  141  CITED LITERATURE Auclair, A. N. and F. G. Goff. 1971. Diversity relations of upland forests in the western Great Lakes area. Am. Nat. 105: 499-528. Banerjee, S., P. R. Sibbald and J. 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Karger, Basel.  150  APPENDIX  COMPOSITION OF GROUND COVER AND STRUCTURE OF THE TREE LAYER  151  GROUND COVER ON MESIC SITES  (Mean Daubenxnire Cover Clas8 Values)  AGECLASS  1  2  3  4  5  6  .28 .29 .43 .36 .33 1.11 .27 .11 1.32 .30 .50 .42 .00 .03 .22 .01 .00 .04 .02 .00 .00 .06 .00 .02 .00 .00 .08 .01 .00 .00 .08 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .85 .01 .00 .01 .22 .00 .00 .00 .02 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .20 .00 .32 .00 .10 .00 .00 .00 .00 .00  .11 .16 .27 .08 .08 .01 .02 .13 .00 .00 .03 .13 .00 .04 .00 .00 .00 .00 .04 .00 .04 .00 .00 .00 .04 .00 .01 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00  .24 .20 .58 .06 .08 .69 .03 .02 .06 .00 .00 .01 .00 .10 .00 .02 .00 .01 .00 .00 .02 .00 .00 .01 .00 .05 .00 .00 .01 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .01  .26 .37 .38 .02 .18 .25 .02 .17 .00 .03 .02 .15 .00 .07 .00 .09 .00 .00 .18 .00 .04 .00 .00 .02 .01 .30 .00 .00 .00 .00 .00 .00 .01 .00 .01 .02 .02 .01 .00 .00 .00  .47 .23 .38 .05 .27 .07 .00 .00 .03 .00 .00 .00 .00 .07 .00 .00 .00 .00 .02 .00 .00 .00 .00 .03 .00 .47 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00  GRASSES AND FORBS  Arnica cordifolia Carex concinnoides Linnaea borealis Rosa acicularis Epilobium angustifolium Cornus canadensis Pyrola chiorantha Achillea millefolium Spiraea betulifolia Oryzopsis asperifolia Oryzopsis pungens Solidago spathulata Phleum pratense Calamagrostis rubescens Aster ciliolatus Aster occidentalis Antennaria neglecta Calypso bulbosa Festuca altaica Festuca saximontana Fragaria virginiana Gentiana amarella Hordeum jubatum Pedicularis racemosa Penstemon fruticosus Petasites palmatus Tragopogon dubius Trisetum spicatum Viola orbiculata Taraxacum officinale Dactylis glomerata Aster conspicuus Anemone multifida Smilacina racemosa Sibbaldia procumbens Senecio triangularis Rubus pedatus Equisetum sylvaticum Galium boreale Polemonium pulcherrimum Lycopodium clavatum 152  GROUND COVER ON MESIC SITES  (Mean Daubenmire Cover Class Values)  AGECLASS  1  2  .00 .03 .00 .00 .00 .00 .12 .40 .45 .00  .10 .00 .18 .04 .00 .02 .86 .00 .00 .00  3  4  5  6  SHRUBS Arctostaphylos uva-ursi Betula glandulosa Empetrum nigrum Juniperus communis Salix spp. Shepherdia canadensis Vaccinium scoparium Vaccinium caespitosum Pinus contorta Picea glauca x engelmannii  .10 .33 .17 .15 .00 .00 .00 .05 .29 1.01 1.03 1.27 .43 .29 .24 .53 .00 .05 .02 .05 .04 .01 .20 .02 .62 1.12 1.27 1.03 .08 .00 .00 .06 .03 .00 .02 .01 .00 .01 .00 .00  BRYOPHYTES  Hylocomium splendens Pleurozium schreberi Polytrichum juniperinum Polytrichum piliferum Dicranum fuscescens Dicranum polysetum Dicranum scoparium Rhytidiopsis robusta Ptilium crista-castrensis Marchantia polymorpha Lepidozia reptans Pohlia nutans Aulacomnium palustre  .00 .00 .82 .00 .00 .00 .00 .02 .00 .05 .00 1.13 .00  153  .00 .00 .29 .15 .07 .56 1.22 2.11 1.32 1.48 .29 .09 .01 .11 .02 .03 .00 .00 .02 .01 .10 .44 .57 .27 .76 .05 .01 .01 .00 .20 .12 .01 .06 .00 .00 .00 .00 .00 .04 .00 .04 .06 .08 .02 .03 .00 .00 .00 .00 .00 .02 .02 .03 .02 .00 .01 .00 .01 .03 .00 .00 .00 .02 .00 .00  GROUND COVER ON MESIC SITES  (Mean Dauberunire Cover Class Values)  AGE CLASS  1  2  3  4  5  6  LICHENS Cladina mitis/arbuscula Cladina rangiferina Cladonia chlorophaea Cladonia coccifera Cladonia coniocraea Peltigera aphthosa Peltigera malacea Peltigera canina Peltigera venosa Stereocaulon tomentosum Cladonia cornuta Cladonia gracilis Cladonia verticillata Cladonia fimbriata Cladonia sulfurina Cladonia pyxidata Cladonia cariosa Cladonia bacillaris Cladonia furcata Cladonia uncialis Cetraria islandica Solorina crocea Cetraria pinastri Parmeliopsis ambigua Parmeliopsis hyperopta Cladonia ecmocyna Cladonia crispata Cladonia cenotea  .00 .26 .22 .17 .00 .16 .12 .29 .04 .00 .09 .06 .17 .00 .12 .00 .00 .02 .03 .00 .00 1.34 1.13 1.17 .00 .12 .32 .08 .05 .00 .02 .00 .00 .00 .00 .00 .21 .00 .08 .05 .00 .50 .24 .13 .66 .00 .31 .19 .10 .00 .12 .02 .00 .09 .16 .03 .26 .00 .22 .13 .00 .00 .07 .02 .02 .00 .02 .00 .01 .00 .01 .00 .01 .00 .00 .01 .00 .00 .00 .00 .00 .40 .14 .30 .00 .00 .00 .00 .06 .00 .02 .00 .46 .00 .14 .14 .29 .00 .09 .06 .12 .00 .11 .18 .00 .00 .01 .00 .24 .00 .01 .00  154  .27 .13 .22 .18 .12 .07 .03 .00 .00 .03 .84 1.25 .20 .18 .00 .00 .00 .00 .08 .03 .20 .07 .27 .25 .10 .00 .10 .02 .17 .05 .03 .03 .02 .00 .02 .00 .00 .01 .00 .00 .10 .12 .00 .00 .03 .03 .13 .08 .12 .04 .18 .28 .00 .00 .00 .00  GROUND COVER ON XERIC SITES  (Mean Daubenmire Cover Class Values)  AGE CLASS  1  2  3  4  5  6  .03  .04 .25 .43 .10 .13 .03 .05 .07 .04 .03 .05 .12 .00 .01 .00 .00 .01 .00 .01 .03 .01 .00 .00 .00 .01 .01 .02 .01 .00 .00 .00 .00 .01 .00 .01 .00 .00 .00 .00 .01 .00  .07 .24 .35 .04 .14 .08 .02 .05 .03 .00 .01 .07 .00 .01 .00 .00 .00 .00 .03 .00 .01 .02 .01 .00 .00 .02 .02 .01 .00 .00 .00 .00 .00 .04 .00 .00 .00 .00 .00 .00 .00  .08 .38 .49 .07 .07 .00 .02 .00 .02 .03 .00 .03 .00 .01 .00 .00 .00 .00 .00 .01 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00  .06 .32 .59 .16 .02 .00 .10 .00 .08 .00 .00 .00 .00 .01 .00 .00 .00 .00 .00 .00 .00 .01 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00  GRASSES AND FORBS  Arnica cordifolia Carex concinnoides Linnaea borealis Rosa acicularis Epilobium angustifolium Cornus canadensis Pyrola chiorantha Achillea millefolium Spiraea betulifolia Oryzopsis asperifolia Oryzopsis pungens Solidago spathulata Phleum pratense Calamagrostis rubescens Aster ciliolatus Aster occidentalis Antennaria neglecta Calypso bulbosa Festuca altaica Festuca saximontana Fragaria virginiana Gentiana amarella Hordeum jubatum Pedicularis racemosa Penstemon fruticosus Petasites palmatus Tragopogon dubius Trisetum spicatum Viola orbiculata Taraxacum of ficinale Dactylis glomerata Aster conspicuus Anemone multifida Smilacina racemosa Sibbaldia procumbens Senecio triangularis Rubus pedatus Equisetum sylvaticum Galium boreale Polemonium puicherrimum Lycopodium clavatum  .66 .58 1.01 .14 1.10 .20 .00 .02 .02 .01 .03 .04 .02 .08 .00 .00 .00 .00 .02 .03 .01 .04 .00 .00 .00 .00 .00 .09 .00 .01 .02 .01 .00 .00 .00 .00 .00 .00 .00 .00 .00 155  .12 .81 .25 .06  .16 .05 .01 .10 .01 .00 .01 .00 .01 .00 .00 .00 .00 .01 .01 .01 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .01 .00 .00 .00 .00 .00 .00 .00 .02  GROUND COVER ON XERIC SITES  (Mean Daubenmire Cover Class Values)  AGECLASS  1  2  3  .19 .00 .00 .01 .02 .06 .34 .21 .35 .01  .17 .00 .07 .22 .02 .01 .57 .02 .02 .00  .00 .00 .97 .09 .01 .00 .00 .01 .00 .00 .00 1.11 .00  .00 .21 .15 .08 .24 .01 .03 .00 .03 .00 .10 .10 .00  4  5  6  .28 .01 .15 .32 .03 .01 .45 .03 .01 .00  .68 1.34 .00 .00 .21 .09 .38 .80 .00 .00 .09 .03 .47 .15 .13 .14 .02 .02 .00 .00  .64 .00 .50 .58 .00 .06 .72 .07 .03 .00  .01 .43 .19 .01 .41 .00 .03 .00 .03 .00 .07 .05 .00  .00 .19 .14 .12 .32 .00 .08 .01 .00 .00 .06 .06 .00  .01 .37 .13 .01 .54 .00 .00 .00 .00 .00 .06 .01 .00  SHRUBS  Arctostaphylos uva-ursi Betula glandulosa Empetrum nigrum Juniperus communis Salix spp. Shepherdia canadensis Vaccinium scoparium Vaccinium caespitosum Pinus contorta Picea glauca x engelmannii  BRYOPHYTES  Hylocomium splendens Pleurozium schreberi Polytrichum juniperinum Polytrichum piliferum Dicranum fuscescens Dicranum polysetum Dicranum scoparium Rhytidiopsis robusta Ptilium crista-castrensis Marchantia polymorpha Lepidozia reptans Pohlia nutans Aulacomnium palustre  156  .01 .11 .06 .01 .41 .01 .01 .01 .00 .00 .01 .00 .00  GROUND COVER ON XERIX SITES  (Mean Dauberimire Cover Class Values)  AGECLASS  1  2  3  4  5  6  .46 .28 .29 .11 .02 .33 .71 .02 .00 .47 .35 .77 .29 .03 .23 .19 .00 .00 .06 .01 .68 .01 .02 .07 .03 .16 .01 .00  .98 .46 .11 .02 .02 .29 .71 .00 .00 .30 .22 .70 .09 .02 .08 .06 .00 .00 .11 .02 .39 .00 .01 .09 .03 .00 .00 .00  .86 .86 .18 .00 .01 .91 .48 .01 .00 .13 .09 .60 .01 .09 .10 .04 .02 .00 .08 .02 .36 .00 .01 .12 .10 .13 .04 .00  LICHENS Cladina mitis/arbuscula Cladina rangiferina Cladonia chlorophaea Cladonia coccifera Cladonia coniocraea Peltigera aphthosa Peltigera malacea Peltigera canina Peltigera venosa Stereocaulon tomentosum Cladonia cornuta Cladonia gracilis Cladonia verticillata Cladonia Eimbriata Cladonia sulfurina Cladonia pyxidata Cladonia cariosa Cladonia bacillaris Cladonia furcata Cladonia uncialis Cetraria islandica Solorina crocea Cetraria pinastri Parmeliopsis arnbigua Parmeliopsis hyperopta Cladonia ecmocyna Cladonia crispata Cladonia cenotea  .00 .23 .65 .00 .07 .28 .00 .14 .13 .00 .03 .10 .00 .03 .06 .00 1.12 1.03 .00 .76 .68 .00 .05 .03 .00 .01 .00 .00 .33 .23 .00 .49 .28 .00 .73 .61 .00 .26 .14 .00 .06 .12 .00 .27 .25 .00 .02 .08 .00 .01 .00 .00 .01 .00 .00 .00 .00 .00 .00 .00 .00 .59 .36 .00 .00 .01 .00 .01 .01 .00 .24 .20 .00 .22 .13 .00 .13 .17 .00 .05 .01 .00 .02 .00  157  STRUCTURE OF THE TREE LAYER ON MESIC SITES (Mean and Standard Deviations)  AGE CLASS DENSITY (trees/ha)  1 2 3 4 5 6  11676 ±12211 9502 ± 3937 2690 ± 1145 2450 ± 1313 412 1390± 1544 ± 333  TREE DIAMETER (cm)  1.0 7.2 12.6 17.4 19.8 16.9  ± 0.0 ± 1.7 ± 2.6 ± 3.5 ±3.3 ± 3.4  CANOPY COVER  (%)  20.4 ± 67.8 ± 58.9 ± 53.0 ± 44.0± 34.2 ±  11.0 10.7 11.1 12.5 9.7 9.1  CROWN HEIGHT (m)  0.5 ± 0.0 8.3 ± 2.2 12.0 ± 1.5 15.0 ± 1.7 16.4±1.2 17.5 ± 1.6  STRUCTURE OF THE TREE LAYER ON XERIC SITES (Mean and Standard Deviations)  AGE CLASS DENSITY (trees/ha)  1 2 3 4 5 6  6749 ± 5331 5851 ± 5289 4634 ±1833 1436 ± 1056 1228 ± 739 429 980±  TREE DIAMETER (cm)  1.0 ± 0.0 11.4 ± 4.6 9.9±1.8 18.9 ± 5.0 16.9 ± 3.7 17.3 ±3.5  158  CANOPY COVER  ()  21.1 ± 6.2 67.8 ± 13.9 6.5 58.9± 53.0 ± 10.8 44.0 ± 7.6 7.5 34.2±  CROWN HEIGHT (m)  0.5 ± 0.0 8.3 ± 2.9 12.0 ±2.2 15.0 ± 3.4 16.4 ± 1.3 17.5±1.8  

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