THE INBREEDING EFFECTIVE POPULATION NUMBER AND THE EXPECTED HOMOZYGOSITY FOR AN X-LINKED LOCUS

Thomas Nagylaki ¹

¹ Department of Biophysics and Theoretical Biology, The University of Chicago, 920 East 58th Street, Chicago, Illinois 60637

Assuming random mating and discrete nonoverlapping generations, the inbreeding effective population number, (see PDF), is calculated for an X-linked locus. For large populations, the result agrees with the variance effective population number. As an application, the maintenance of genetic variability by the joint action of mutation and random drift is investigated. It is shown that, if every allele mutates at rate u to new types, then the probabilities of identity in state (and hence the expected homozygosity of females) converge to the approximate value (see PDF) at the approximate asymptotic rate (see PDF).