A general model of sexual and natural selection

FISHER in The Genetical Theory of JVatural Selection (1930) described how mating preferences might evolve by natural selection. If mating behaviour varies among different genotypes, some individuals may have an hereditary disposition to mate with others having particular characteristics. Usually of course it is the females who choose the males and their choice is determined by the likelihood that the males' display will release their mating responses. If some females prefer to mate with those males that have characteristics advantageous in natural selection, then the genotypes that determine such matings will also be selected: the offspring will carry both the advantageous genotypes and the genotypes of the mating preference. Once the mating preference is established, it will itself add to the selective advantage of the preferred genotypes: a "runaway process" as Fisher called it develops. In a paper in Heredity (1963) I described a mathematical model of this type of selection. In the simplest case two loci must be involved: one locus determines the preferred character and the other the mating preference. If there are only two alleles segregating at each locus, ten different genotypes can occur if the loci are linked and nine if they are not. If they are sex-linked, there are i possible genotypes. I derived finite difference equations giving the frequencies of the genotypes in terms of parameters describing the degree of dominance of the preferred genotypes and the recombination fractions of the loci. They are complicated, non-linear equations and cannot be solved explicitly. I could only obtain approximate solutions giving the rate of sexual selection at the start of the process and near its final equilibrium. I was unable to incorporate in the model the effects of natural selection which is what starts off the runaway process. But I have now made a detailed numerical study of the equations using the Elliott 803 Computer here at the University College of North Wales and the Atlas i Computer of the Science Research Council at Chilton, Berkshire. The computers were programmed to allow for any intensity of natural selection and for variations in the size of the population.