Coevolution can stabilize a mutualistic interaction

Interspecific mutualisms are ubiquitous in nature, despite their ecological and evolutionary instability. Recent studies have developed coevolutionary theory of mutualisms, which coupled population and evolutionary dynamics, to resolve the longstanding puzzle. However, earlier studies assumed a time-scale separation between these dynamics, leaving an unanswered question of how a relaxation in the time-scale separation affects the coevolutionary dynamics of mutualism. Here I relax the strong assumption to theoretically show that ecological and evolutionary dynamics occurring in a similar time scale can stabilize an otherwise unstable mutualism. I show that the coevolutionary dynamics can cause a stable limit cycle or stable equilibrium in the population sizes, even if the population sizes increase unbounded in the absence of evolutionary adaptation. In contrast, coevolution can also cause stable limit cycle even if the population dynamics is stable in the absence of evolutionary adaptation. Furthermore, the model predicts that the population dynamics is likely to converge to equilibrium when the evolutionary speed of two species is similar and fast or highly dissimilar. The results suggest that the ease of the evolutionary ‘arms race’ is of crucial importance to maintain mutualism.