  Between-species coevolution, and in particular antagonistic host-parasite
coevolution, is a major process shaping within-species diversity. In this paper
we investigate the role of various stochastic processes affecting the outcome
of the deterministic coevolutionary models. Specifically, we assess 1) the
impact of genetic drift and mutation on the maintenance of polymorphism at the
interacting loci, and 2) the change in neutral allele frequencies across the
genome of both coevolving species due to co-demographic population size
changes. We find that genetic drift decreases the likelihood to observe classic
balancing selection signatures, and that for most realistic values of the
coevolutionary parameters, balancing selection signatures cannot be seen at the
host loci. Further, we reveal that contrary to classic expectations, fast
changes in parasite population size due to eco-evo feedbacks can be tracked by
the allelic site-frequency spectrum measured at several time points. Changes in
host population size are, however, less pronounced and thus not observable.
Finally, we also review several understudied stochastic processes occurring in
host-parasite coevolution which are of importance to predict maintenance of
polymorphism at the underlying loci and the genome-wide nucleotide diversity of
host and parasite populations.
