Red Queen evolution driven by asymmetric competition

Abstract

The Red Queen hypothesis states that biological entities rather than abiotic factors constitute the larger part of the selective environment experienced by individual organisms, and that species as a consequence undergo continual evolution. Such non-stationary evolutionary dynamics can exist on a fine evolutionary scale, where a constant number of co-evolving species engage in fixed ecological interactions. Phenotypic models of evolution can reflect such continuous evolution through limit cycles in the evolution of traits. Here a dynamic phenotypic model of trait evolution under asymmetric intra- and interspecific competition is presented and analyzed. The model comprises two species or populations competing for resources, where the value of a trait, such as body size, of the interacting individuals determines the competitive effects. A cost for having a trait size different from a defined ecological optimum (i.e. optimal in the absence of competition) is included. The degrees of intra- and inter-specific asymmetry affect evolutionary dynamics in very different ways. The model exhibits Red Queen dynamics in some parts of the investigated parameter space. However, evolutionary limit cycles only occur when there is a certain degree of asymmetry in the inter-specific competitive interactions and when the two populations have different rates of evolution. A shortcut for finding equilibria where such continual dynamics can be achieved in adaptive dynamics models is also presented. This shortcut applies weak convergence stable equilibrium points in any adaptive dynamics model with two species with one evolving trait each.