  Coevolution is expected to follow two alternative dynamics, often called
trench warfare and arms races in plant-pathogen systems. Trench warfare
situations are stable cycles of allele frequencies at the coevolving loci of
both host and parasite, and it is predicted that the loci will show molecular
evolutionary signatures of balancing selection, while arms races involve
successive selective sweeps at the interacting loci. We study a haploid
gene-for-gene model that includes mutation and genetic drift due to finite
population size. We study the outcomes under different coevolutionary
parameters to quantify the frequency of fixation of alleles, i.e. occurrence of
an arms race dynamics. We find that contrary to the conventional wisdom, trench
warfare situations do not imply larger numbers of coevolutionary cycles per
unit time than arms races. Therefore, one cannot infer the nature of the
dynamics in such systems based on the speed of coevolution estimated from cycle
times. We subsequently perform coalescent simulations to generate sequences at
the host and parasite loci. We ask whether the signatures expected under
balancing selection or selective sweeps (unexpectedly high or low diversity,
and high or low Tajima D values, respectively) are likely to be observable in
genomic data. Genomic footprints of recurrent selective sweeps are often found,
whereas trench warfare yields signatures of balancing selection only in
parasite sequences, and only in a limited parameter space with high effective
population sizes and long-term selection. Therefore, the existence of a
deterministic polymorphic equilibrium does not imply long-term trench warfare
necessary for the signature of balancing selection to be observed in the
coevolving genes sequence. Our results suggest that to search for signatures of
coevolution via population genomics, it is best to study pathogen rather than
host genomes.
