DOI: 10.3390/math11153378 ISSN: 2227-7390

Spatial Demo-Genetic Predator–Prey Model for Studying Natural Selection of Traits Enhancing Consumer Motility

Yuri V. Tyutyunov
  • General Mathematics
  • Engineering (miscellaneous)
  • Computer Science (miscellaneous)

Combining explicit modelling of predator movements with the Kostitzin demo-genetic equations, we study conditions promoting natural selection of consumer motility. The model is a system of partial differential equations describing spatial movements of predators pursuing the diffusing prey. Local predator–prey interactions are described by the classical Rosenzweig–MacArthur model, which additionally accounts for the Allee effect affecting reproduction of predators. Spatial activity of predators is determined by the coefficients of diffusion and indirect prey-taxis. The latter characterizes the predator ability to move directionally up the gradient of taxis stimulus (odor, pheromone, exometabolite) continuously emitted by prey. Assuming that the consumer movement ability is governed by a single diallelic locus with recessive ‘mobile’ and dominant ‘settled’ alleles, the predator population in the model consists of three competing genotypes differing by diffusion and taxis coefficients; other parameters characterizing the genotypes are assumed to be equal. Numerical simulations with different spatial patterns imitating habitat deterioration demonstrate that the direction of selection among the consumer genotypes alternates, depending on the degree of habitat deterioration affecting the overall production of the prey population. Theoretical implications of the results are discussed in relation with problems of biological control, predator interference, and evolution of animal motility.

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