How quickly does inbreeding produce homozygosity?

What is the probability that locus is homozygous due to inbreeding after a given number of generations? The answer should be an equation expressing this probability as a function of the number of generations.

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.

Is race "real"?

Someone wrote in "wondering what the current stance is with geneticist in regards to whether different human races exist or not." This important question has been discussed at length already, and I refer readers to a Social Sciences Research Council forum on race, the special issue of Nature Genetics on race published in November of 2004, and an edited volume by Jefferson Fish. I side with those who feel that race, as it is normally understood, is a social construct. Those biological definitions that might be partially valid for humans differ significantly from the way the concept is normally used in our society. However, others argue for the importance of considering "ethnicity" in clinical trial design (Taylor et al. 2005), and the drug BiDil has been licensed exclusively for African-Americans (for a recent news report in "The Times" click here).

So, my answer to this questions has been given before.

It seems to me that if a drug differs in either safety or efficacy for one "race" or another, then the underlying basis is probably either a genetic difference or a cultural difference. In the first case, the relevant genetic difference itself, or a related biomarker, would be much more reliable than popular notions of race. On the other hand, if the basis is cultural, the relevant practice (such as lifestyle or diet) should be identified. I was therefore gratified to see Nature Genetics publish this letter from Jonathan Kahn making the case against the misuse of race, as well as a sidebar showing how the media has misrepresented their own statements.

However, additional answers are welcomed.