Predator–Prey Evolution from an Eco-evolutionary Trade-off Model: The Role of Trait Differentiation

We develop a novel eco-evolutionary modelling framework and demonstrate its efficacy by simulating the evolution of trait distributions in predator and prey populations. The eco-evolutionary modelling framework assumes that population traits have beta distributions and defines canonical equations for the dynamics of each total population size, the population’s average trait value, and a measure of the population’s trait differentiation. The trait differentiation is included in the modelling framework as a phenotype analogue, Q, of Wright’s fixation index FST\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F_\mathrm{ST}$$\end{document}, which is inversely related to the sum of the beta distribution shape parameters. The canonical equations may be used as templates to describe the evolution of population trait distributions in many ecosystems that are subject to stabilising selection. The solutions of the “population model” are compared with those of a “phenotype model” that simulates the growth of each phenotype as it interacts with every other phenotype under the same trade-offs. The models assume no sources of new phenotypic variance, such as mutation or gene flow. We examine a predator–prey system in which each population trades off growth against mortality: the prey optimises devoting resources to growth or defence against predation; and the predator trades off increasing its attack rate against increased mortality. Computer solutions with stabilising selection reveal very close agreement between the phenotype and population model results, which both predict that evolution operates to stabilise an initially oscillatory system. The population model reduces the number of equations required to simulate the eco-evolutionary system by several orders of magnitude, without losing verisimilitude for the overarching population properties. The population model also allows insights into the properties of the system that are not available from the equivalent phenotype model.