A Coevolutionary Predator-Prey Model with Quantitative Characters

Abstract

A new model for coevolution in generalized predator-prey systems is presented by incorporating quantitative characters relevant to predation in both prey and predator. Malthusian fitnesses are derived from ecological models, and they include interspecific frequency and density dependence. Both prey and predator characters are under stabilizing selection even without predation, and predation adds an additional linear selection component to both characters. The nonlinear system of differential equations is studied analytically by using local linearization near the equilibrium points. Parameters related to intrinsic growth and death rates and stabilizing selection determine whether there are zero, one, or two equilibria. Additive genetic variances do not have an effect on the equilibrium points, but genetic variability is crucial for determining their stability. Analysis of the linearized model shows that at most one equilibrium can be stable, and stability is achieved when additive genetic variance is high enough in both the prey and predator populations. The stability properties are illustrated by numerical examples of the full dynamics of the original nonlinear model.

Why intraspecific trait variation matters in community ecology

“…A modest number of theoretical studies have investigated how intraspecific trait variation affects population dynamics [31][32][33][34], interspecific competition [35][36][37], and predator-prey or host-parasitoid systems [38][39][40]. These studies consider variation in diverse traits, including (1) traditional phenotypes like size or morphology; (2) emergent traits like competitive ability [41], prey attack rate [39], or vulnerability to enemies [42]; and (3) fitness-related traits like fecundity or survival [33].…”

“…These studies consider variation in diverse traits, including (1) traditional phenotypes like size or morphology; (2) emergent traits like competitive ability [41], prey attack rate [39], or vulnerability to enemies [42]; and (3) fitness-related traits like fecundity or survival [33]. Variation in these traits might be stochastic [32], environmentally induced [43], or genetic (Mendelian or quantitative; sexual or asexual [31,44]).…”

Multilocus Genetics and the Coevolution of Quantitative Traits

“…Models using phenotypic approximations (Abrams 2001), such as adaptive dynamics (e.g., Dieckmann and Law 1996;Doebeli and Dieckmann 2000;Dercole et al 2003), game theory (e.g., Brown and Vincent 1992), and quantitative genetics (e.g., Saloniemi 1993;Abrams and Matsuda 1997;Gavrilets 1997a;Khibnik and Kondrashov 1997), describe the evolution of phenotypes directly, while skipping over the details of the underlying genetics. Explicit genetic models frequently consider only one locus (Gavrilets and Hastings 1998) or two loci (e.g., Bell and Maynard Smith 1987;Seger 1988;Preigel and Korol 1990;Kirzhner et al 1999) per species.…”

Evolutionary dynamics of predator-prey systems: an ecological perspective

“…(We will see below, however, that a terminus does not necessarily exist.) The third approach, quantitative genetics, focuses on statistical properties of traits with continuous variation caused by the environment and a large (unspecified) number of genes with small effects; see for example Saloniemi (1993). This has the advantage that many of the traits important in coevolution are continuous variables, and the disadvantage that, like much of evolutionary game theory, it lacks an explicit mechanistic basis in genetics.…”