Alternatives to Lotka-Volterra competition: models of intermediate complexity.

Abstract A family of one-level differential-equation competition models in which two populations are limited by the energy flowing into the system generates the following results. For competitors on the same and only resource: 1) Purely exploitative competition leads to exclusion; which species wins depends on relative abilities to appropriate and extract energy from the resource, and the relative death and maintenance rates. 2) If conspecific interference (e.g., deaths or energy loss from fighting, cannibalism, or display) is sufficiently high relative to abilities to exploit the common resource, competition for the same resource can lead to coexistence. 3) If heterospecific interference is sufficiently high relative to abilities to exploit the common resource, competition for the same resource can lead to a priority effect, in which the outcome depends on initial population sizes. 4) Depending on whether situation (2) or (3) prevails, an increase in the amount of the common resource can convert an outcome in which one species always wins into one giving coexistence (2) or a priority effect (3). 5) If species are similar to one another in their abilities to appropriate and extract energy from the common resource and show reciprocity in intererence costs, competition can have multiple outcomes; either one species wins or the species coexist, depending on initial values. For competition on the same resource, but with each species monopolizing an exclusive resource as well: 1) Purely exploitative competition always leads to a unique point coexistence. 2) If interference is added to the system described in (1), two points of coexistence, separated by a saddle (an “unstable equilibrium”) are possible. This is favored by a) a small yield from the exclusive resources relative to the common one; and b) strong interspecific relative to intraspecific interference.

[1]  J. Sutherland,et al.  Multiple Stable Points in Natural Communities , 1974, The American Naturalist.

[2]  R M May,et al.  On the theory of niche overlap. , 1974, Theoretical population biology.

[3]  J. M. Smith,et al.  Can there be more predators than prey? , 1972, Theoretical population biology.

[4]  S. E. Khaikin,et al.  Theory of Oscillators , 1966 .

[5]  John Vandermeer,et al.  The Competitive Structure of Communities: An Experimental Approach with Protozoa , 1969 .

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

[7]  M E Gilpin,et al.  Competition between species: theoretical models and experimental tests. , 1973, Theoretical population biology.

[8]  T. Schoener,et al.  Competition and the form of habitat shift. , 1974, Theoretical population biology.

[9]  Alfred J. Lotka,et al.  The growth of mixed populations: Two species competing for a common food supply , 1978 .

[10]  J. Roughgarden.  Species packing and the competition function with illustrations from coral reef fish. , 1974, Theoretical population biology.

[11]  T. Schoener,et al.  Some Methods for Calculating Competition Coefficients from Resource-Utilization Spectra , 1974, The American Naturalist.

[12]  H. Wilbur.  Competition, Predation, and the Structure of the Ambystoma-Rana Sylvatica Community , 1972 .

[13]  A. C. Crombie.  Further experiments on insect competition , 1946, Proceedings of the Royal Society of London. Series B - Biological Sciences.

[14]  P. J. Hughesdon,et al.  The Struggle for Existence , 1927, Nature.

[15]  M. Gilpin,et al.  Global models of growth and competition. , 1973, Proceedings of the National Academy of Sciences of the United States of America.

[16]  R. McGehee,et al.  Coexistence of two competitors on one resource. , 1976, Journal of theoretical biology.

[17]  M E Gilpin,et al.  Schoener's model and Drosophila competition. , 1976, Theoretical population biology.

[18]  A. L. Koch,et al.  Competitive coexistence of two predators utilizing the same prey under constant environmental conditions. , 1974, Journal of theoretical biology.

[19]  Robert M. May,et al.  Stability in multispecies community models , 1971 .

[20]  R M May,et al.  Niche overlap as a function of environmental variability. , 1972, Proceedings of the National Academy of Sciences of the United States of America.

[21]  S. Levin.  Dispersion and Population Interactions , 1974, The American Naturalist.

[22]  T. Schoener,et al.  Population growth regulated by intraspecific competition for energy or time: some simple representations. , 1973, Theoretical population biology.

[23]  John Vandermeer,et al.  On the Covariance of the Community Matrix , 1972 .

[24]  G. F. Gause.  The struggle for existence , 1971 .

[25]  J. Neyman,et al.  Struggle for Existence. The Tribolium Model: Biological and Statistical Aspects , 1956 .

[26]  L. Buss,et al.  Alleopathy and spatial competition among coral reef invertebrates. , 1975, Proceedings of the National Academy of Sciences of the United States of America.

[27]  William E. Neill,et al.  The Community Matrix and Interdependence of the Competition Coefficients , 1974, The American Naturalist.