Host-parasite coevolution in populations of constant and variable size

Abstract

Background:The matching-allele and gene-for-gene models are widely used in mathematical approaches that study the dynamics of host-parasite interactions. Agrawal and Lively (Evolutionary Ecology Research 4:79-90, 2002) captured these two models in a single framework and numerically explored the associated time discrete dynamics of allele frequencies. Results:Here, we present a detailed analytical investigation of this unifying framework in continuous time and provide a generalization. We extend the model to take into account changing population sizes, which result from the antagonistic nature of the interaction and follow the Lotka-Volterra equations. Under this extension, the population dynamics become most complex as the model moves away from pure matching-allele and becomes more gene-for-gene-like. While the population densities oscillate with a single oscillation frequency in the pure matching-allele model, a second oscillation frequency arises under gene-for-gene-like conditions. These observations hold for general interaction parameters and allow to infer generic patterns of the dynamics. Conclusion: Our results suggest that experimentally inferred dynamical patterns of host-parasite coevolution should typically be much more complex than the popular illustrations of Red Queen dynamics. A single parasite that infects more than one host can substantially alter the cyclic dynamics.

Feedback Between Coevolution and Epidemiology Can Help or Hinder the Maintenance of Genetic Variation in Host-Parasite Models

“…In contrast to the constant-size model, the second-order stability arises from the additional feedback between host and parasite dynamics that arises as a result of density-dependent population growth. This is illustrated by the contrast between the dynamics observed here relative to those of Song et al (2015), 155 whose model does not include explicit intra-specific density-dependence and does not exhibit second-order stability (neutrally stable cycles are found around the equilibrium). The second-order stability of system…”

Disentangling eco-evolutionary effects on trait fixation

“…These higher order interactions can be interpreted in terms of multiplayer games from evolutionary game theory. The model explicitly deals with finite and especially fluctuating population sizes which are important in the context of co-evolution [33,73,83,97]. While constant or infinite population size is captured by birth-death processes and the replicator equation we apply stochastic di↵usion theory to tackle the fluctuating size complication.…”

Prophage as a genetic reservoir: Promoting diversity and driving innovation in the host community

“…(); for recent work reconciling these models in a single framework, see Agrawal and Lively (), Song et al. (), Ashby and Boots (). )…”

“…Thus phage P K can infect both H K and H J in the nested model. (For an overview of infection models including empirical support, see Flores et al (2011), Weitz et al (2013); for recent work reconciling these models in a single framework, see Agrawal and Lively (2002), Song et al (2015), Ashby and Boots (2017). )…”