Kinesis (biology)

Basic model of kinesis

The kinesis strategy controlled by the locally and instantly evaluated well-being (fitness) can be described in simple words: Animals stay longer in good conditions and leave bad conditions more quickly. If the well-being is measured by the local reproduction coefficient then the minimal reaction-diffusion model of kinesis can be written as follows:

For each population in the biological community,

${\displaystyle {\mathrm{\partial }}_t{u}_i(x,t)=D_{0i}\mathrm{\nabla }\left(e^{-{\alpha }_i{r}_i(u_1,\dots ,u_k,s)}\mathrm{\nabla }{u}_i\right)+r_i(u_1,\dots ,u_k,s)u_i,}$

where: ${\displaystyle u_i}$ is the population density of ith species, ${\displaystyle s}$ represents the abiotic characteristics of the living conditions (can be multidimensional), ${\displaystyle r_i}$ is the reproduction coefficient, which depends on all ${\displaystyle u_i}$ and on s, ${\displaystyle D_{0i}>0}$ is the equilibrium diffusion coefficient (defined for equilibrium ${\displaystyle r_i=0}$). The coefficient ${\displaystyle {\alpha }_i>0}$ characterises dependence of the diffusion coefficient on the reproduction coefficient.

The models of kinesis were tested with typical situations. It was demonstrated that kinesis is beneficial for assimilation of both patches and fluctuations of food distribution. Kinesis may delay invasion and spreading of species with the Allee effect.