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Saturday, January 5, 2008

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.


  1. Greetings!

    Some recent work I've done on this issue in nematodes (soon to be submitted?) has led me to a couple of special cases that may be of interest: all full-sib inbreeding and all half-sib inbreeding. An authority on this is Dr. Thomas Nagylaki, of the Univ. of Chicago. In Chapter 9 of his 1992 book, Introduction to Theoretical Population Genetics (Springer-Verlag, Biomathematics series), Nagylaki derives precise expressions for these two cases.

    If all individuals in every generation were full-sibs, the extent of expected heterozygosity (ht) is given by ht ≈ 1.17h0 (0.809)t, when t»1, where h0 is the initial extent of heterozygosity and t is the number of generations of inbreeding. If the offspring in every generation were exclusively half-sibs, then ht ≈ 1.106h0 (0.890)t.

    So, after 20 generations of inbreeding, ht is approximately 1.7 % of h0 in the full-sib case and 10.8 % in the half-sib case.

  2. Please see A Systematic Approach to Mapping Recessive Disease Genes in Individuals from Outbred Populations

  3. Thanks CGJ.
    Your profile is currently not available. We do ask that those who comment identify themselves. "We are looking for answers from people with some expertise, and you will be asked to log in so that we know who you are."

    The paper you cite, Hildebrandt et al. , is more about localized homozygosity around disease loci, whereas the question was more about residual heterozygosity after systematic inbreeding.