The origin of new alleles

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Genes G1 and G2 may be connected by other compound paths of this sort (paths that do not pass through the zygote more than once). Thus:
(7:10) F=SUM(0.5^n(1+FA))
where the summation is with respect to all such paths (Wright 1922a).

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The symbol F is to be interpreted as the correlation between pairs of homologous genes in the class of uniting gametes that trace in the way indicated by the pedigree to the foundation stock, relative to the array of genes at any neutral locus in this stock. It has, of course, no relevance to loci that are homoallelic. When F is derived in this way it may be referred to as pedigree F.

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The relativity referred to above has sometimes been overlooked or misinterpreted (Fisher 1949, p 43). A correlation coefficient is, of course, always relative. It is a property of the population as well as of the two variables. In the case of F as an inbreeding coefficient, relating to all heterallelic neutral loci, its primary function is that of a parameter in the specification of population structure. This is still largely true in other applications in which the peculiarities of a particular locus to which it pertains are important.

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There may seem to be a difficulty in the likelihood that the foundation stock may be itself more or less inbred relative to a more remote stock. If, however, there is any heterallelism in the foundation stock in neutral loci, avearge F of a later period measures the correlation between uniting gametes relative to the array of gene frequencies at such loci, and the decline in the heterozygosis relative to an immediate panmictic derivative of the foundation stock. It does not necessarily measure the decline relative to the actual heterozygosis. The foundation stock might conceivable consist of a mixture of homoallelic lines (F=1). If the initial matings are made a random, F falls at once to zero and then, on breeding wholly within the stock, gradually rises. It is the decline in heterozygosis that occurs during such a rise in F that is measured.

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Malecot (1948) has pointed out that the formulat for pedigree F may be interpreted as the probability that the two genes in question are identical by descent from the foundation stock. This holds because the compound path coefficient, ba’ =.05, is interpretable as the probability of identity by descent of a gene with one of those back of it a generation earlier, because the compound path coefficient bA^2 =0.5(1+FA) is interpretable as the probability that the homologous genes in two random gametes of zygote A are identical by descent, and because of the fact that probabilities, like path coefficients, compound along paths of multiplication. Many who use F solely as a measure of inbreeding, relative to the genes of the foundation stock, prefer the simple concept of probability of identity of descent to that of correlation of homologous genes of a certain class. The latter concept, however is required from the broader standpoint of a group of parameters useful for the identification of population structure in general. This is because a correlation coefficient can vary between -1 and +1, whereas a probability can vary only between 0 and 1. There will be occasion later to discuss cases of negative F and . ”

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