Age correlation between mates and average consanguinity in age-structured human populations

When population geneticists wish to determine the genetic consequences of some aspect of mating behavior, it is often necessary to compare observed levels of consanguinity to the level expected when mating is random with respect to the factor being studied. Expectations under random mating are often derived from discrete generation models that ignore age structure. Observed frequencies of consanguineous matings are due to processes that are continuous in time and are affected by variables that are functions of age structure. The extent to which this discrepancy between the models and reality might distort conclusions drawn from comparisons of observed and expected behavior has received insufficient attention. One potential source of error is the tendency for people to choose mates whose ages differ from their own by a certain amount; this tendency influences the frequency of consanguineous matings. Age correlation between mates should therefore also affect average consanguinity between mates and average inbreeding in the population. Expected levels of consanguinity might then differ depending on whether or not age structure has been taken into account. Hajnal developed a model that predicts the frequencies of consanguineous matings in age-structured populations. Hajnal's model is extended here to include relationships that are defined by lineal descent as well as by common ancestry, and to allow calculation of the frequencies of consanguineous matings in the absence of age correlation between mates. The extended model is then used to determine the effect of age correlation between mates on average consanguinity under various sets of conditions. The magnitude of this effect depends on the degree to which the increased frequency of some types of consanguineous matings is offset by the decrease in other types of matings. There is a fairly wide range of conditions under which this compensation is nearly complete and therefore under which the overall effect of age correlation is small. But the size of this effect is sensitive to many factors, especially the distribution of age differences between mates and the variances of ages at maternity and paternity. Under some conditions, age correlation between mates will have a substantial effect on average consanguinity.