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Abstract

Long term oscillations of genotype abundances in host-parasite systems are difficult to confirm experimentally. Therefore, much of our current understanding of these dynamics is based on theoretical concepts explored in mathematical models. However, the same biological assumptions can lead to very different mathematical models with diverging properties. The precise model can depend on the level of abstraction from reality, on the educational background and taste of the modeler, and on the current trends and conventions in the field. Here, we first review the current literature in the light of mathematical approaches. We then propose and compare our own framework of biologically similar, yet mathematical very different models that can all lead to host-parasite Red Queen dynamics. We highlight the different mathematical properties and use analytical and numerical tools to understand the long term dynamics. We focus on (i) the difference between deterministic and stochastic models and (ii) how ecological aspects, in our case population size, can influence the evolutionary dynamics. Our results show not only that stochastic effects can lead to extinction of subtypes, but that a changing population size speeds up this extinction. The loss of strain diversity can be counteracted with random mutations which then allow the populations to recurrently undergo fluctuating selection dynamics and selective sweeps.