Genetic aspects of consanguinity

Abstract

Consanguineous marriages increase the frequency of homozygotes AA and aa among their offspring by the same absolute amount, thus incurring no change in gene frequency. When recessives are originally rare in the population, this would mean a manyfold increase in the frequency of recessives among the inbred offspring. Inbreeding studies usually include consanguineous marriages of all degrees (first cousins, second cousins, etc.). A formula for estimating gene frequency from such data has been given and is a generalization of the one in common use for first cousins. A basic equation for the balanced condition between selection and mutation in a random mating population is given, from which special cases and approximate formulas have been obtained. The average fitness of such a population under a certain notation system is \\ ̄ gw 0 = (1 − qhs)(1 − μ) ; when q is very small, qhs = μ approximately so that \\ ̄ gw 0 = 1 − 2 μ . When this population is rendered to complete homozygosis without changing the gene frequency, the average fitness decreases, being \\ ̄ gw 1 = 1 − sq . To measure the extent of the decrease, it is proposed to use the following ratio (or some function of it): \\ ̄ gw 1 \\ ̄ gw 0 = 1 − sq (1 − hsq)(1 − μ) (mutational) which is independent of the arbitrary notation system for genotypic fitness. The equilibrium condition due to higher fitness of the heterozygote is then given in a new algebraic form to facilitate comparison. (The new expression is, of course, equivalent to the conventional one.) The corresponding ratio of the average fitness at the complete homozygosis state to that at the random mating state is \\ ̄ gw 1 \\ ̄ gw 0 = 1 − sq 1 + hsq (heterotic) The latter ratio is always smaller than the former, indicating that upon inbreeding the average fitness of heterotic population decreases to a greater extent than that of an equilibrium population in mutational balance. Crow's finding is just the opposite to the one stated. It is shown that his is due to an algebraic artefact, incurred by an arbitrary system of notation for genotypic fitness. His “genetic load” as defined by L = 1 − \\ ̄ gw cannot be used directly for comparison or for descriptive purposes. For genes whose deleterious effect on fitness is additive, the balance is necessarily due to recurrent mutations (within the limits of the factors considered in this paper. Other mechanisms could be involved.) For such populations, the average fitness remains the same upon inbreeding, further enhancing our conclusion. Because hsq and μ are both small quantities, the two types of equilibrium populations do not respond differently to inbreeding. The difference may become appreciable only when h and q are large. Whatever difference there is, the offspring of parents who are first cousins have only an inbreeding coefficient of 1 16 , a long way from complete homozygosis and thus inadequate to bring out the difference. Some general considerations concerning inbreeding studies and genetic properties of populations are given.