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If a population (species) consists of n haploid lines (subpopulations) which reproduce asexually and each of which is subject to random extinction and subsequent replacement, it is shown that, at equilibrium in which mutational production of new alleles and their random extinction balance each other, the genetic diversity (1 minus the sum of squares of allelic frequencies) is given by 2Nev/(1 + 2NeV), where Ne = N + n/(2X) + nNv/X, in which N is the harmonic mean of the population size per line, n is the number of lines (assumed to be large), X is the rate of line extinction, and v is the mutation rate (assuming the infinite neutral allele model) In a diploid population (species) consisting of n colonies, if migration takes place between colonies at the rate m (the island model) in addition to extinction and recolonization of colonies, it is shown that effective population size is Ne =N+n/[4(vv+X+m)]+nN(v+m)/(v+X+m)If the rate of colony extinction (A) is much larger than the migration rate of individuals, the effective population size is greatly reduced compared with the case in which no colony extinctions occur (in which case Ne = nN). The stepping-stone type of recolonization scheme is also considered. Bearing of these results on the interpretation of the level of genetic variability at the enzyme level observed in natural populations is discussed from-the standpoint of the neutral mutation-random drift hypothesis. The concept of effective population size, introduced by Wright (1), has played a fundamental role in treating the process of random gene frequency drift in finite populations. Useful formulae have been derived by him and others (2-6) to compute the effective sizes for various situations such as unequal numbers of males and females, different parents contributing widely different numbers of young, the population size fluctuating from time to time, and overlapping generations (see refs. 7-9 for reviews).It is known that most species in nature have subdivided population structure, and extinction and recolonization of local populations may occur rather frequently in some groups of organisms such as insects (see refs. 10 and 11). This will greatly reduce the effective population size of the species.Wright (12) pointed out that if local populations are liable to frequent extinction with restoration from the progeny of a few stray immigrants, the species may pass repeatedly through extremely reduced state of effective population size even though the species include at all times "countless millions of individuals in its range as a whole." He suggested that mutations such as reciprocal translocations that are very strongly selected against until half-fixed may require some such mechanism to become established.A pioneering study of the effect of local extinction and recolonization of subpopulations on genetic variability of the species was made by Slatkin (11) using two models termed "propagule pool" and "migration pool." By pursuing the same problem further, we obtained some results which we report i...

SUMMARYFollowing Moran's (1962) method, it was shown that the fixation probability of a mutant gene is not altered by the subdivision of a population into partially isolated colonies, if the following conditions are met; fitness is additive, samplings and selection is done separately in each colony, and migration between colonies does not change the gene frequency in the whole population. This conclusion was checked by simulation experiments.

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