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

Abstract

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.

Paradoxes of Competition in Periodic Environments: Delta Functions in Ecological Models

“…In mathematical ecology, the reaction-diffusion equations are traditionally used to describe spatio-temporal effects [33][34][35][36]. These are quite complex mathematical objects.…”

Modeling Study of Factors Determining Efficacy of Biological Control of Adventive Weeds

“…Model ( 1)-( 4) is a modification of the system presented previously in [15,16], which did not consider effect of the cultivated plant but accounted for the genetic structure of the phytophagous population. Since apart from the weed there present also other plants in terrestrial ecosystems, inclusion of a cultivated plant in the model makes it more realistic and appropriate for solving applied problems of weed biocontrol.…”

“…Aside from the diffusive dispersal of densities of all modeled species, the advection term in the balance equation of the phytophage population density (3) describes directed movements of the insect density as indirect trophotaxis (prey taxis) toward gradient of the taxis stimulus S = S(t, x). Parameters ν, κ, and η determine intensity of the consumer taxis; see details in [15,16]. All parameters of the model are presented in Table 1, which also provides four sets of the parameter values that are used in numerical simulations discussed in the next chapters.…”

“…The first mathematical model describing the SPW of the ragweed leaf beetle was suggested by Vechernin and Kovalev [14]. Later, Tyutyunov and coauthors [15,16] elaborated a more detailed demogenetical model capable of reconstructing the formation and movement of the phytophage SPW and explaining other phenomena observed after the introduction of the ragweed leaf beetle, including the rapid transformation of the genetic structure of the leaf beetle population caused by selection of traits enhancing the flight ability of the beetle, which had been evolutionarily lost in its homeland.…”

The Evolutionary Dynamics of a Sex-Structured Population with Non-Overlapping Generations

“…On the other hand, as a rule, fluctuations in abundance are caused by changes in the population structure caused by the combined effects of environmental factors and self-regulatory mechanisms [12][13][14]. Therefore, when modeling population dynamics, it is advisable to use an ecological-genetic approach that allows us to study the interconnected changes in the abundance and genetic structure of a population [15][16][17][18][19][20][21][22][23][24][25][26][27].…”