Abstracts

Evolution of Species and Ecosystems: Theoretical Analysis and Computer-Assisted Modeling

An ecological system is characterized by a complex scheme of interactions between its elements. One of the main factors in these interactions is mutual inhibition of elements. Inhibition may be realized through competition for food resources, living space, consuming of one species by another (trophic pyramid), or intoxication of one species by metabolic products of the other species. We have considered the latter case under condition of temporal non-coincidence (shift) of stages in ontogenesis of related species (that is, those species with almost similar parameters considered). However, each of these species suppresses the preceding stages of development of several other species by the products of its vital activity. Then, under condition of the transit time, in population compiled by several asynchronous species, we observe a situation of subsequent cyclic mutual inhibition of reproduction. Let there be n species and n>=k>1. Suppose that the i-th species is an inhibitor of reproduction of species numbered as modn(i+1),…, modn(i+k-1). Here modn(*) denotes positive remainder of division the number (*) by n. If remainder of division equals to zero, then modn(*) is set to be equal to n. Then for this system we may deduce the following conclusions: if n is entirely divided by k, then there exist such threshold parameters of inhibition and reproduction of m0 and a0 that for every m>m0 and a>a0 the model of an ecosystem has k stable critical points. The stable limit cycles are absent in this model. If n is not divided by k without remainder, then there exist such m0 and a0 that for every m>m0 and a>a0, the model has d (d is the greatest common divisor of n and k) stable limit cycles and it lacks stable critical points. This fact was supported by numerous computer simulation experiments. Analogous result could be obtained for the species, which mutually inhibit reproduction at different stages of ontogenesis. For example, for the pair of organisms frog-dragonfly, adult frog consumes adult dragonflies, but dragonfly larvae consumes the frog spawn.

Note. Abstracts are published in author's edition

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