A population dynamic model of Batesian mimicry

A population dynamic model of Batesian mimicry, in which populations of both model and mimetic species were considered, was analyzed. The probability of a predator catching prey on each encouter was assumed to depend on the frequency of the mimic. The change in population size of each species was considered to have two components, growth at the intrinsic growth rate and carrying capacity, and reduction by predation. For simplicity in the analyses, three assumptions were made concerning the carrying capacities of each population: (1) with no density effects on the mimic population growth rate; (2) with no density effects on the model species; and (3) with density effects on both species. The first and second cases were solved analytically, whereas the last was, for the most part, investigated numerically. Under assumption (1), two stable equilibria are possible, in which both species either coexist or go to extinction. Under assumption (2), there are also two stable equilibria possible, in which either only the mimic persists or both go to extinction. These results explain the field records of butterflies (Pachliopta aristolochiae and its mimic Papilio polytes) in the Ryukyu Islands, Japan.