Impact of the purposeful kinesis on running waves

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Abstract

The basic model of purposeful kinesis was developed recently (Gorban and Cabukoglu, Ecol. Complex. 2018, 33, 75 83) on the basis of the let well enough alone idea. According to this model the diffusion drops while the reproduction coefficient is increasing. That is, species prefer to stay in a good condition and the population gives birth; otherwise, in the bad situation individuals want to run away because of the fatal conditions. In this study, we analyse the impact of the purposeful kinesis model on running waves. The running waves in the population with kinesis are studied using numerical experiments. Both monotonic and non monotonic (Allee effect) dependence of the reproduction coefficient on the population density are studied. The possible benefits of the purposeful kinesis are demonstrated: with the higher diffusion, while the population without kinesis ends up with extinction, the population with kinesis stays alive and has the running wave behavior. While the kinesis of the prey population is decreasing, the wave amplitude gets smaller. On the other hand, for the lower kinesis of predators they have a sharp increase.

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How should we define 'fitness' for general ecological scenarios?

J. A. Metz, R. Nisbet, S A Geritz (1992)

Beginners in life history theory or evolutionary ecology seemingly face a variety of almost unrelated approaches. Yet the biomathematical literature of the last 10-20 years reflects the implicit acceptance of a common evolutionary framework, the core idea being that there exists a unique general fitness measure that concisely summarizes the overall time course of potential invasions by initially rare mutant phenotypes. Using such an invasion criterion to characterize fitness implicitly presupposes a scenario in which, during periods o f clear evolutionary change, the rate of evolution is set primarily by the random occurrence (and initial establishment) of favourable mutations. Evolutionarily stable life history strategies (ESSs) may then be regarded as traps for the evolutionary random walk. Copyright © 1992. Published by Elsevier Ltd.