Recurrent selective sweeps versus trench warfare in host-parasitecoevolution: the influence of population size changes

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The goal of this project is to gain insights into the coevolution of host-parasite systems, particularly processes that generate genetic diversity. In the first objective, we analyze an epidemiological model of coevolution with coupled reciprocal changes in allele frequencies and size changes of host and parasite populations. Using these results, we show how signatures of coevolution can be quantified in terms of the site frequency spectrum of genetic polymorphisms observed over the whole genome of both hosts and parasites. To do this, we start from a general model of coevolution that encompasses the well-known matching-allele and gene-for-gene models frequently used in the plant and animal literature. Then we extend this deterministic model by including several parasite generations per host generation. In the second objective, we study the influence of stochasticicity on the maintenance of polymorphism in host and parasite populations as well as the loss and fixation of alleles at coevolving loci. Two stochastic processes of biological relevance are modeled: (i) genetic drift is allowed to occur in the parasite population assuming a large variance in offspring production, which is a common feature of many plant and insect parasites; (ii) the stochastic process of disease transmission is modeled as a Markov process affecting the epidemiological dynamics. We specifically explore the conditions under which co-evolutionary models starting from three alleles in hosts and parasites generate loss or fixation of alleles (thus reducing the system to two-allele or monomorphic populations). We focus on conditions under which we observe the two extreme cases of coevolution that are both described by our generalized models and were the subject of the work of the first funding period, the arms race (recurrent selective sweeps) and trench warfare scenarios.