Stochastic effects in LMC models

LMC (local mate competition) was first introduced by W. D. Hamilton to expl ain extraordinary female-biased sex ratios observed in a variety of insects and mites. In the original model, the population is subdivided into an inf inite number of colonies founded by a fixed number of inseminated females p roducing the same very large number of offspring. The male offspring compet e within the colonies to inseminate the female offspring and then these dis perse at random to found new colonies. An unbeatable sex ratio strategy is found to be female-biased. In this paper, the effects of having colonies of random size and foundresses producing a random finite number of offspring are considered. The exact evolutionarily stable strategy (ESS) sex ratio is deduced and comparisons with previous approximate or numerical results are made. As the mean or the variance of brood size increases, the ESS sex rat io becomes more female-biased. An increase in the variance of colony size i ncreases the ESS proportion of males when the mean brood size and colony si ze are both small, but decreases this proportion when the mean brood size o r the mean colony size is large. (C) 1999 Academic Press.