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bioRxiv · 10.1101/012435

Host-parasite coevolution in populations of constant and variable size

Yixian Song·Chaitanya Gokhale·Andrei Papkou·Hinrich Schulenburg·Arne Traulsen
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Abstract

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. 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. 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.

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Yixian Song, Chaitanya Gokhale, Andrei Papkou, Hinrich Schulenburg, Arne Traulsen. 2014-12-09. Host-parasite coevolution in populations of constant and variable size. https://doi.org/10.1101/012435

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