Evolution of condition-dependent dispersal: A genetic-algorithm search for the ESS reaction norm

Many insects produce two types twinged and wingless) of offspring that greatly differ in dispersal ability. The ratio of the two types often depends on the quality of the local habitat and the crowding experienced by the mother. Here we studied the condition-dependent dispersal that is evolutionarily stable. The model is also applicable to annual plants that produce two types of seeds differing in dispersal rates. The model assumptions are: the population is composed of a number of sites each occupied by a single adult. The total number of offspring produced by a mother depends on the environmental quality of the site that varies over the years and between sites. The ESS fraction of dispersing type as a function of the quality of the habitat (or ESS reaction norm) states that dispersers should not be produced if habitat quality m is smaller than a critical value k. If m is larger than k, the number of dispersers should increase with m and that of nondispersers should be kept constant. Second, we developed an alternative way of searching for the ESS: the reaction norm is represented as a three-layered neural network, and the parameters (weights and biases) are chosen by genetic algorithm (GA). This method can be extended easily to the cases of multiple environmental factors. There was an optimal (relatively wide) range of mutation rates for weights and biases, outside of which the convergence of the network to the valid ESS was likely to fail. Recombination, or crossing-over, was not effective in improving the success rate. The learned network often shows several characteristic ways of deviation from the ESS. We also examined the case in which the quality of different sites was correlated. In this case the ESS fraction of dispersers increases both with the quality of the site and with the average quality of the whole population in that year.