Speed of adaptation and genomic footprints of host-parasite coevolution under arms race and trench warfare dynamics

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.