Stability in multispecies community models

Abstract First, we consider a simple mathematical model for a many-predator-many-prey system, and show it to be in general less stable, and never more stable, than the analogous one-predator-one-prey community. This result would seem to caution against any simple belief that increasing population stability is a mathematical consequence of increasing multispecies complexity. Second, we take up the question of the relation between stability in any one trophic level by itself and stability of the total trophic web. We find that in a simple mathematical model the criteria for isolated single-level stability and for total web stability are not identical, but they tend to be similar, so that usually stability (or instability) at one level goes with stability (or instability) of the whole. It is possible, however, to construct examples where either stability at one level occurs in an overall unstable system, or alternatively instability at one level goes with total web stability. This model points the way to a synthesis of the diverse views that have been expressed on this subject.

[1]  W. Murdoch.  Switching in General Predators: Experiments on Predator Specificity and Stability of Prey Populations , 1969 .

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

[3]  V. Engstrom-Heg.  Predation, competition and environmental variables: some mathematical models. , 1970, Journal of theoretical biology.

[4]  D. A. Chant,et al.  THE PRACTICE AND THEORY OF BIOLOGICAL CONTROL OF INSECTS IN CANADA , 1961 .

[5]  E. J. Kormondy,et al.  Concepts of Ecology , 1970 .

[6]  S B Saila,et al.  Interspecific competition, predation and species diversity. , 1970, Journal of theoretical biology.

[7]  E. Forbush,et al.  The gypsy moth. Porthetria dispar (Linn.). , 1896 .

[8]  G. E. Hutchinson,et al.  Homage to Santa Rosalia or Why Are There So Many Kinds of Animals? , 1959, The American Naturalist.

[9]  E. Pianka.  Latitudinal Gradients in Species Diversity: A Review of Concepts , 1966, The American Naturalist.

[10]  R. Paine.  Food Web Complexity and Species Diversity , 1966, The American Naturalist.

[11]  William W. Murdoch,et al.  "Community Structure, Population Control, and Competition"-A Critique , 1966, The American Naturalist.

[12]  E. H. Kerner,et al.  A statistical mechanics of interacting biological species , 1957 .

[13]  V. S. Ivlev,et al.  Experimental ecology of the feeding of fishes , 1962 .

[14]  Anthony F. Bartholomay,et al.  The Mathematical Approach to Biology and Medicine , 1967 .

[15]  A. J. Lotka,et al.  Elements of Physical Biology. , 1925, Nature.

[16]  L. Slobodkin,et al.  Community Structure, Population Control, and Competition , 1960, The American Naturalist.

[17]  H. Zwolfer.  The structure of the parasite complexes of some Lepidoptera. , 1970 .

[18]  Kenneth E. F. Watt,et al.  Ecology and Resource Management , 1968 .

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

[20]  E. Leigh.  ON THE RELATION BETWEEN THE PRODUCTIVITY, BIOMASS, DIVERSITY, AND STABILITY OF A COMMUNITY. , 1965, Proceedings of the National Academy of Sciences of the United States of America.

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

[22]  G. E. Hutchinson,et al.  The Balance of Nature and Human Impact: The paradox of the plankton , 2013 .

[23]  R. Levins.  Evolution in Changing Environments , 1968 .