The total joint distribution of gene identities by descent over all the members of a population, relative to some ancestral gene pool, is a complete description of the population's genealogical structure. However, it is one that can never be explicitly found; the number of possible gene identity states between even small numbers of individuals is prohibitive (Thompson, 1974). What is required is some meaningful reduction of this total distribution. Whereas previous authors have considered extensions of kinship and inbreeding based directly on gene identity coefficients, we propose an alternative set of parameters based on the survival and extinction of sets of genes, and correlations in such extinction or survival. These correlations illuminate directly the nonindependence of gene descent in pedigrees, and this is a factor of prime importance in the evolution of small populations. These correlations are investigated under a variety of mating systems, under "outbreeding" and "random-mating" populations, and in the actual population of Tristan da Cunha. © 1979.
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