The interpretation of population structure by F-statistics with special regard to systems of mating

TLDR: It was found that there is no equilibrium in either case short of complete fixation locally, in spite of the linear increase in number of different ancestors with increasing number of ancestral generations, in contrast to systems (half first cousin or second cousin) in which this increase is more than linear and a steady state is rapidly attained with respect to heterozygosis.

Abstract: Kimura and Crow (1963b) have recently made an interesting comparison between two classes of systems of mating within populations of constant size: ones in which there is maximum avoidance of consanguine mating and ones in which all matings are between close relatives around an unbroken circle. These are illustrated in Figs. 1 and 2 in populations of eight. The rate of decrease of heterozygosis in the former class had, as they note, been found long before to approach 1/(4N) asymptotically with increasing size of population, N (Wright, 1921, 1933a). Two cases with patterns of mating similar to those of Kimura and Crow's second class, except that the matings were between neighbors along infinitely extended lines instead of around a circle, had also been considered in these papers. These systems consisted of exclusive mating of half-sibs or of first cousins, otherwise with a minimum of relationship. It was found that there is no equilibrium in either case short of complete fixation locally, in spite of the linear increase in number of different ancestors with increasing number of ancestral generations. This was in contrast to systems (half first cousin or second cousin) in which this increase is more than linear and a steady state is rapidly attained with respect to heterozygosis. Kimura and Crow were surprised to find that the limiting rates of decrease of heterozygosis in their circular systems are much less than under maximum avoidance approaching [v/(2N + 4)]2 in the case of half-sib matings and [7/ (N + 12)]2 under first-cousin matings with large N. Maxi-