New method of estimating inbreeding in large semi-isolated populations with application to historic Britain

The purpose of this paper is to introduce a new method of estimating inbreeding in large, relatively isolated, populations over historic times, to demonstrate its application, and indicate some of its limitations and future developments. The method is based on the "paradox" of genealogy, and requires only that the variation of the population size be known, at least reasonably well, over an extended historic period. In this study a method has been developed to model this "paradox" which allows an estimation of the minimum level of inbreeding necessary for a given population curve in terms of values of Pearl's coefficients for each generation. As an example, the method is applied to the population of Britain. It is found that the frequency of siblings occurring in the same generation of a pedigree varies with the population size according to the Fermi-Dirac equation of statistical physics. The effect of introducing a single known estimate of inbreeding into the model is to make the otherwise diverse results for both the actual numbers of ancestors in a generation and the corresponding coefficients of inbreeding to converge.