A TIME-SERIES ANALYSIS OF THE POPULATION-GENETICS OF THE SELF-INCOMPATIBILITY POLYMORPHISM .1. ALLELE FREQUENCY-DISTRIBUTION OF A POPULATION WITH OVERLAPPING GENERATIONS AND VARIATION IN PLANT SIZE

A mathematical theory of the population genetics of the self-incompati bility polymorphism is developed for the case where self-incompatibili ty is controlled by a single, multiallelic gene, S, expressed gametoph ytically in the pollen. The theory is based on the probability of a pa rticular allele occurring in a new-plant and an approximate equation f or this is compared, using computer simulation, with the true value, w hich depends upon the frequencies of the genotypes of the parental gen eration. This probability is used to express the frequency of a single established allele, from a population with both overlapping generatio ns and variation in plant size, as a time series. The frequency is sho wn to follow closely the normal distribution which leads to a simple e quation for the variance of the distribution. This variance is approxi mately equal to the average variance of the frequencies of the differe nt alleles in a single generation and the values closely match the com puter simulation results of Brooks er al. (1996). The theory allows al ternative scenarios to be investigated easily and the effects of varyi ng the parameter values are discussed. The time to steady state can al so be calculated.