  Species sharing a prey or a predator species may go extinct due to
exploitative or apparent competition. We examine whether evolution of the
shared species acts as a coexistence mechanism and to what extent the answer
depends on the genetic architecture underlying trait evolution. In our models
of exploitative and apparent competition, the shared species evolves its
defense or prey use. Evolving species are either haploid or diploid. A single
locus pleiotropically determines prey nutritional quality and predator attack
rates. When pleiotropy is sufficiently antagonistic (e.g. nutritional prey are
harder to capture), eco-evolutionary assembly culminates in one of two stable
states supporting only two species. When pleiotropy is weakly antagonistic or
synergistic, assembly is intransitive: species-genotype pairs are cyclically
displaced by rare invasions of the missing genotypes or species. This
intransitivity allows for coexistence if, along its equilibria, the geometric
mean of recovery rates exceeds the geometric mean of loss rates of the rare
genotypes or species. By affecting these rates, synergistic pleiotropy can
mediate coexistence, while antagonistic pleiotropy does not. For diploid
populations experiencing weak antagonistic pleiotropy, superadditive allelic
contributions to fitness can mitigate coexistence via an eco-evolutionary
storage effect. Density-dependence and mutations also promote coexistence.
These results highlight how the efficacy of evolution as a coexistence
mechanism may depend on the underlying genetic architecture.
