Estimating inbreeding in large, semi-isolated populations: effects of varying generation lengths and of migration.

The purpose of the study reported here was to investigate two important assumptions used in a recently reported new method of estimating inbreeding in large, relatively isolated populations over historic times. The method, based on modeling the genealogical "paradox," produces values of Pearl's coefficients, Z, a measure of inbreeding or genealogical coalescence, as a function of time. In this study, the effects on inbreeding of two important assumptions made in earlier studies, namely those of using a constant generation length and of ignoring migration, have been investigated for the population of Britain. First, by relating the median age of women at childbirth to the development level of various societies, the variation of the generation lengths for different periods in historic Britain were estimated. Values of Z for two types of varying generation lengths were then calculated and compared with the case of constant generation length. Second, the population curve for Britain used in earlier studies was modified to obtain the subpopulation at any time during the past two millennia that was descended from the pre-Roman British Celts. Values of Z for the case with migration were then calculated and compared with the case for no migration. It is shown that these two assumptions may be taken into account if and when required. Both the effect of a varying generation length and the effect of migration on Z were found to be 20-40%, when no known value of inbreeding was used, and 2-5%, when a known value of inbreeding was used.