Although contemporary models of Müllerian mimicry have considered the movement of interfacial boundaries between two distinct mimetic forms, and even the possibility of polymorphisms in two patch systems, no model has considered how multiple forms of Müllerian mimics might evolve and be maintained over large geographical areas. A spatially explicit individual-based model for the evolution of Müllerian mimicry is presented, in which two unpalatable species are distributed over discrete cells within a regular lattice. Populations in each cell are capable of genetic drift and experience localized dispersal as well as frequency-dependent selection by predators. When each unpalatable prey species was introduced into a random cell and allowed to spread, then mimicry evolved throughout the system in the form of a spatial mosaic of phenotypes, separated by narrow "hybrid zones". The primary mechanism generating phenotypic diversity was the occasional establishment of new mutant forms in unoccupied cells and their subsequent maintenance (and spread) through frequency-dependent selection. The mean number of discrete clusters of the same morph that formed in the lattice was higher the higher the intensity of predation, and higher the lower the dispersal rate of unpalatable prey. Under certain conditions the hybrid zones moved, in a direction dependent on the curvature of their interfacial boundaries. However, the mimetic mosaics were highly stable when the intensity of predation was high and the rate of prey dispersal was low. Overall, this model highlights how a stable mosaic of different mimetic forms can evolve from a range of starting conditions through a combination of chance effects and localized frequency-dependent selection.

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Keywords Anti-apostatic selection, Genetic drift, Heliconius, Polymorphism, Predation
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Journal Journal of Theoretical Biology
Sherratt, T. (2006). Spatial mosaic formation through frequency-dependent selection in Müllerian mimicry complexes. Journal of Theoretical Biology, 240(2), 165–174. doi:10.1016/j.jtbi.2005.09.017