A Model for Tropic Interaction

A nonlinear function general enough to include the effects of feeding saturation and intraspecific consumer interference is used to represent the transfer of material or energy from one trophic level to another. The function agrees with some recent experimental data on feeding rates. A model using this feeding rate function is subjected to equilibrium and stability analyses to ascertain its mathematical implications. The anaylses lead to several observations; for example, increases in maximum feeding rate may, under certain circumstances; result in decreases in consumer population and mutal interference between consumers is a major stabilizing factor in a nonlinear system. The analyses also suggest that realistic classes of consumer—resource models exist which do not obey Kolmogorov's Criteria but are nevertheless globally stable. See full-text article at JSTOR

[1]  M. Hassell,et al.  Mutual Interference between Searching Insect Parasites , 1971 .

[2]  V. Wynne-Edwards.  Animal dispersion in relation to social behaviour , 1962 .

[3]  M. Rosenzweig,et al.  Exploitation in Three Trophic Levels , 1973, The American Naturalist.

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

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

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

[7]  V. Volterra.  Variations and Fluctuations of the Number of Individuals in Animal Species living together , 1928 .

[8]  H. G. Andrewartha,et al.  The distribution and abundance of animals. , 1954 .

[9]  Robert M. May,et al.  Limit Cycles in Predator-Prey Communities , 1972, Science.

[10]  Gerald G. Marten,et al.  An Optimization Equation for Predation , 1973 .

[11]  Frederick E. Smith,et al.  Experimental Methods in Population Dynamics: A Critique , 1952 .

[12]  K. Watt,et al.  A Mathematical Model for the Effect of Densities of Attacked and Attacking Species on the Number Attacked , 1959, The Canadian Entomologist.

[13]  A. Rescigno,et al.  The struggle for life. I. Two species. , 1967, The Bulletin of mathematical biophysics.

[14]  R. Wiegert,et al.  Trophic structure, available resources and population density in terrestrial vs. aquatic ecosystems. , 1971, Journal of theoretical biology.

[15]  C. S. Holling.  The components of prédation as revealed by a study of small-mammal prédation of the European pine sawfly. , 1959 .

[16]  Elliott W. Montroll,et al.  Nonlinear Population Dynamics. (Book Reviews: On the Volterra and Other Nonlinear Models of Interacting Populations) , 1971 .

[17]  G. Salt,et al.  Predator and Prey Densities as Controls of the Rate of Capture by the Predator Didinium Nasutum , 1974 .

[18]  C. S. Holling.  Some Characteristics of Simple Types of Predation and Parasitism , 1959, The Canadian Entomologist.

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

[20]  G. Salt,et al.  Predation in an Experimental Protozoan Population (Woodruffia-Paramecium) , 1967 .