AbstractCoevolution is a selective process of reciprocal adaptation between antagonistic or mutualistic symbionts and their host. Classic population genetics theory predicts the signatures of selection at the interacting loci but not the neutral genome-wide polymorphism patterns. We here build a coevolutionary model with cyclic changes in the host and parasite population sizes. Using an analytical framework, we investigate if and when these population size changes can be observed in the neutral

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... site frequency spectrum of the host and parasite full genome data. We show that polymorphism data sampled over time can capture the changes in the population size of the parasite but not of the host because genetic drift and mutations occur on different time scales in the coevolving species. This is due to the small parasite population size at the onset of the coevolutionary history subsequently undergoing a series of strong bottlenecks. We also show that tracking coevolutionary cycles is more likely for a small amount of parasite per host and for multiple parasite generations per host generation. Our results demonstrate that time sampling of host and parasite full genome data are crucial to infer the co-demographic history of interacting species.