How genotype-by-environment interactions can maintain variation in mutualisms

Coevolution requires reciprocal genotype-by-genotype (GXG) interactions for fitness, which occur when the fitnesses of interacting species depend on the match between their genotypes. However, in mutualisms, when GXG interactions are mutually beneficial, simple models predict that positive feedbacks will erode genetic variation, weakening or eliminating the GXG interactions that fuel ongoing coevolution. This is inconsistent with the ample trait and fitness variation observed within real-world mutualisms. Here, we explore how genotype-by-environment (GXE) interactions, which occur when different genotypes respond differently to different environments, maintain variation in mutualisms. We employ a game theoretic model in which the fitnesses of two partners depend on mutually beneficial GXG and GXE interactions. Variation is maintained via migration-selection balance when GXE interactions are slightly stronger than GXG interactions or when they are much stronger than GXG interactions for just one partner. However, unexpectedly, when GXE interactions are much stronger than GXG interactions for both partners and dispersal is high, genotypically mismatched partners can fix, eroding variation and leading to apparent maladaptation between partners. We parameterize our model using data from three published reciprocal transplant experiments and find that the observed strengths of GXE interactions can maintain or erode variation in mutualisms via these mechanisms.