Repeatability of adaptation in interacting species

In many evolving systems, mutations have background-dependent fitness effects due to genetic interactions between loci within a genome (intragenomic epistasis). In coevolving species, genetic interactions can span across genomes, a phenomenon described as intergenomic epistasis. It is known that intragenomic epistasis can make adaptation more repeatable by constraining accessible mutational paths from a specific starting genotype, generating path repeatability. Here, we investigate how endpoint repeatability - how often adaptation from different starting genotypes reaches the same states in the genotype and fitness space - is influenced by the interplay of intra- and intergenomic epistasis. To this end, we model a two-species community in which the fitness of each genotype depends on the combination of present genotypes of both species. We implement this by constructing and simulating adaptation on coevolutionary fitness landscapes using an NKC(S) model, an extension of Kauffman's NK model of evolution that includes intergenomic epistasis. On these fitness landscapes, we simulate adaptive walks that alternate between mutations in a focal and a partner species. To quantify the repeatability of adaptation, we track the endpoints of adaptive walks and record the fitness of both species at the evolutionary endpoints. We find that individual fitness landscapes with intergenomic epistasis can maintain high endpoint repeatability. Yet, intergenomic epistasis causes highly variable fitness outcomes across different fitness landscapes. Thus, patterns of repeatability deviate from expectations based on single-species adaptation in the presence of intragenomic epistasis, due to varying fitness trade-offs between species, which can lead to cycling and large coevolutionary fitness loads.