This question was inspired by a recent review of mouse genetics (Peters et al. 2007. "The mouse as a model for human biology: a resource guide for complex trait analysis" Nature Reviews Genetics 8, 58-69. doi:10.1038/nrg2025), which states, without qualification, that "Inbred mouse strains are derived from a single parental mating pair with subsequent repeated brother–sister intercrosses and no breeding from non-sibling mice. After 20 generations of inbreeding, the mice are genetically identical and homozygous at all loci." 20 generations is an accepted benchmark that leaves a very low probability of homozygosity, but that probability is not zero. What is it?

This is really three questions (or more).

1) Selfing organisms like Arabidopsis thaliana or Caenorhabditis elegans present a simple case. Here, the probability that a given locus remains heterozygous is simply (1/2)

^{n}, where n is the number of generations.

2) The mouse, which represents all diploid species where crosses between full siblings is possible. Brothers and sisters that share the same two parents. I suspect the equation for this case has been worked out. What is the answer?

3) Species where females store sperm. In this case one can isolate a female each generation. She will have mated with her (possibly half-) brothers prior to isolation. Here the probability of homozygosity is a function not only of the number of generations, but also the probability of the female having mated with a full brother vs. a half-brother.