Evolution of mutualism through spatial effects

Mutualism among species is ubiquitous in natural ecosystems but its evolution is not well understood. We provided a simple lattice model to clarify the importance of spatial structure for the evolution of mutualism. We assumed reproductive rates of two species are modified through interaction between species and examine conditions where mutualists of both species, that give some benefit to the other species with their own cost, invade non-mutualists populations. When dispersal of offspring is unlimited, we verified the evolution of mutualism is impossible under any condition. On the other hand, when the dispersal is limited to neighboring lattice sites, mutualists can invade if the ratio of cost to benefit is low and the intrinsic reproductive rate is low in case where the parameter values are symmetric between species. Under the same conditions, non-mutualists cannot invade mutualist populations, that is, the latter are evolutionarily stable. In case of asymmetric parameters, mutualists tend to invade if the average value of costs to two species is low or that of benefits is high, and if the intrinsic reproductive rate is low for one of the two species. A mechanistic explanation of why mutualists increase when the dispersal is limited is given by showing that mutualist pairs of the two species at the same lattice site rapidly increase at the initial phase of the invasion.