Host-parasite coevolution in populations of constant and variable size.

Yixian Song,Hinrich Schulenburg,Andrei Papkou,Chaitanya S Gokhale,Arne Traulsen

doi:10.1186/s12862-015-0462-6

Yixian Song, Hinrich Schulenburg + Show 3 more

Open Access

https://doi.org/10.1186/s12862-015-0462-6

Copy DOI

Abstract

BackgroundThe 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.ResultsHere, 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.ConclusionOur 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.

Highlights

The matching-allele and gene-for-gene models are widely used in mathematical approaches that study the dynamics of host-parasite interactions
No host/parasite type is superior to the other. This case corresponds to the matching-allele model, which under the assumption of constant population density is equivalent to the evolutionary game of matching pennies [21, 22]
Short overview Host-parasite interactions are acknowledged as a driving evolutionary force promoting biological diversity and sexual reproduction [10, 11], with the MA and GfG model being the most popular models to describe the genetic interaction for coevolving hosts and parasites [26,27,28,29,30,31,32]

Summary

Introduction

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. Agrawal and Lively [14] developed a general model that interpolates between a pure matching-allele model and a pure gene-for-gene model, as a single parameter is tuned between 0 and 1. This model was introduced for haplotypes of two loci with mutation and recombination. Instead of tackling the dynamics from an analytical perspective to allow for general statements for all parameter sets, subsequent theoretical approaches have increased complexity of the assumed interaction in order to increase the biological realism, for instance by defining a multilocus model that deals with various combinations of MA loci and GfG loci [15]

Objectives

Results

Discussion

Conclusion