The concepts of elasticity, invulnerability and invadability.

Abstract Users of mathematical models in ecological research have emphasized mathematical elegance in elucidating the dynamics of ecosystem models with fixed collections of state variables instead of addressing the equally important question of what effects a changing ecosystem structure has on the system's dynamics. Our work addresses the effect of invasion on the species composition of communities. In the context of a linear model, we found that as communities were made more complex (in terms of the number of species they contained and the number of interactions among these species) the probability of their being stable decreased, but the probability of their being invulnerable to invasion by other species increased. These results are consistent with the hypothesis that, through time, communities approach an intermediate complexity at which the influences of environmental stochasticity (which tends to destabilize complex communities) and invasion pressure (which tends to add species to simple communities) counterbalance one another. At this intermediate complexity the average rate of change of species composition is low.

[1]  H. S. Horn,et al.  The Ecology of Secondary Succession , 1974 .

[2]  ALAN ROBERTS,et al.  The stability of a feasible random ecosystem , 1974, Nature.

[3]  R. May,et al.  Stability and Complexity in Model Ecosystems , 1976, IEEE Transactions on Systems, Man, and Cybernetics.

[4]  Kenneth E. F. Watt,et al.  Ecology and resource management: a quantitative approach , 1968 .

[5]  E. Lewis.  Applications of Discrete and Continuous Network Theory to Linear Population Models , 1976 .

[6]  Bernard C. Patten,et al.  A simulation of the shortgrass prairie ecosystem , 1972 .

[7]  D. L. Angelis,et al.  STABILITY AND CONNECTANCE IN FOOD WEB MODELS , 1975 .

[8]  Daniel Goodman,et al.  The Theory of Diversity-Stability Relationships in Ecology , 1975, The Quarterly Review of Biology.

[9]  B. C. Patten,et al.  Systems Analysis and Simulation in Ecology , 1978, IEEE Transactions on Systems, Man, and Cybernetics.

[10]  Bernard C. Patten,et al.  Ecosystem Linearization: An Evolutionary Design Problem , 1975, The American Naturalist.

[11]  Edwin R. Lewis,et al.  LINEAR POPULATION MODELS WITH STOCHASTIC TIME DELAYS , 1977 .

[12]  MARK R. GARDNER,et al.  Connectance of Large Dynamic (Cybernetic) Systems: Critical Values for Stability , 1970, Nature.

[13]  John Maynard Smith.  Models in ecology , 1974 .

[14]  C. S. Holling.  Resilience and Stability of Ecological Systems , 1973 .

[15]  Karl P. Schmidt,et al.  Principles of Animal Ecology , 1950 .

[16]  N S Goel,et al.  On the extinction of a colonizing species. , 1972, Theoretical population biology.

[17]  D. Pimentel.  Species Diversity and Insect Population Outbreaks , 1961 .

[18]  R. Macarthur.  Fluctuations of Animal Populations and a Measure of Community Stability , 1955 .

[19]  W. H. V. Dobben,et al.  Unifying Concepts in Ecology , 1975, Springer Netherlands.

[20]  A. J. Schwartz,et al.  Systems of ordinary differential equations : an introduction , 1974 .

[21]  M. Gilpin,et al.  Stability of feasible predator-prey systems , 1975, Nature.

[22]  E. Odum.  Fundamentals of ecology , 1972 .

[23]  R. Macarthur,et al.  The Theory of Island Biogeography , 1969 .

[24]  L. Slobodkin.  Growth and regulation of animal populations , 1962 .