Basic Model of Purposeful Kinesis

TL;DR

This paper introduces new minimal models of purposeful kinesis where organism movement depends on local fitness, exploring how this influences dispersal, resource assimilation, and invasion dynamics through numerical experiments.

Contribution

It presents novel models of purposeful kinesis with diffusion dependent on local fitness, incorporating an additional parameter for kinesis intensity, and analyzes their properties.

Findings

Kinesis can enhance resource patch assimilation and respond to periodic fluctuations.

Kinesis may delay invasion for species with the Allee effect.

Kinesis does not alter the stability of positive steady states.

Abstract

The notions of taxis and kinesis are introduced and used to describe two types of behavior of an organism in non-uniform conditions: (i) Taxis means the guided movement to more favorable conditions; (ii) Kinesis is the non-directional change in space motion in response to the change of conditions. Migration and dispersal of animals has evolved under control of natural selection. In a simple formalisation, the strategy of dispersal should increase Darwinian fitness. We introduce new models of purposeful kinesis with diffusion coefficient dependent on fitness. The local and instant evaluation of Darwinian fitness is used, the reproduction coefficient. New models include one additional parameter, intensity of kinesis, and may be considered as the {\em minimal models of purposeful kinesis}. The properties of models are explored by a series of numerical experiments. It is demonstrated how kinesis could be beneficial for assimilation of patches of food or of periodic fluctuations. Kinesis based on local and instant estimations of fitness is not always beneficial: for species with the Allee effect it can delay invasion and spreading. It is proven that kinesis cannot modify stability of positive homogeneous steady states.