Isolation by Distance under Diverse Systems of Mating.

HE effects of restricted dispersion on the genetic properties of a continuous T population have been treated mathematically in a previous paper (WRIGHT 1943a). The conclusions have been applied to the interpretation of observed local variability in a population of a plant, Linanthus Parryi (WRIGHT 1943b) and in one of an animal, Drosophila pseudoobscura (DOBZHANSKY and WRIGHT 1943). The mathematical treatment was based on the assumption of completely random union of gametes within each neighborhood and thus would rarely be strictly applicable to actual cases. The purposes of the present paper are to compare the effects of various systems of mating within continuous populations, and to present a more accurate method than before for estimating from data an important theoretical quantity, N, the effective size of population of a “neighborhood” in the sense discussed below. It was postulated in the previous paper that a population of uniform density occupies either an indefinitely large area (area continuity) or a strip of indefinitely great length but of such narrow width that dispersion occurs across it within a single generation (linear continuity). Both uniparental and biparental reproduction were considered. In the former case, it was postulated that the locations of parents a t some phase of the life cycle are distributed, relative to the corresponding locations of their progeny, according to a normal probability curve with a standard deviation U, if there is linear continuity, or in a bivariate normal distribution with standard deviation u, for both x and y coordinates of the parental locations (relative to their progeny) if there is area continuity. I n the case of biparental reproduction the locations of the parents were assumed to be uncorrelated with each other. This is assumed to hold in the present paper except as qualified by self fertilization or brother-sister mating in excess of random. A term is needed to designate the local population of which the parents may be considered as representative. Various terms were used in the preceding paper. (‘Panmictic unit” applies only if there is completely random mating locally and is thus not sufficiently general. “Parental group” is better but is somewhat awkward. An essential property of the population in question is that the individuals are neighbors in the sense that their gametes may come together. The term “neighborhood” is thus an appropriate one for this important unit.