Local fluctuations in gene frequencies
Annals of Human Genetics 32 (3): 251--260 (1969)

Most populations are divided into small villages or towns or similar communities. Gene frequencies will certainly vary from community to community, even if only because of random variations. It is possible that selective forces might also cause similar fluctuations. It is therefore important to know how much variability is to be expected, to compare it with the amount actually observed. In work on blood-group frequency the phenotype frequencies in neighbouring populations are often compared by a x2 test, to see whether they differ `significantly'. This test is clearly not appropriate. In comparing samples by x2 the null hypothesis is that they are drawn at random from the same large population, or from large populations with similar constitutions. This does not mean anything reasonable for villages. Each village will continue to develop more or less on its own from generation to generation with only limited migration from nejghbours. The frequency fluctuations in each generation will be added to those of preceding generations. Hence the variability in gene frequency will accumulate. The x2 test would be appropriate if the villages had been at one stroke carved out of a single homogeneous population. Much work has been done on the extent of random drift in populations. Accounts are to be found in, for example, Li (1955, chapter 23)) Moran (1962, chapters 6 and 7) and Kimura (1964). But in order to make the algebra mathematically tractable it has so far been necessary to use rather simple model situations. This makes it difficult a t present to apply the theory to obser- vational data. There seems to be room for an approximate method of dealing with the situation, at least until the exact theory has been successfully extended to deal with more complicated situations. What follows is a first attempt at this. It is based on the idea that variance is introduced into a population in each generation by random drift (and to a small extent by random mutation). The variance may be reduced by selection or mutation, which tend to bring the population back to an equilibrium state, and by migration between communities, which tends to make them uniform. By adding together the amounts of incoming variance, and taking into account that lost by other processes, we should obtain the expected amount of variation in gene frequency present a t any one time.
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