PMID: 1286806Dec 1, 1992Paper

Do Eve's alleles live on?

Genetical Research
G A Watterson, P Donnelly

Abstract

Consider a random sample of genes at a locus, drawn from a population evolving according to the infinitely many, neutral, alleles model. The sample will have a most recent common ancestor gene, which we shall call 'Eve'. The probability distribution, for the number of genes of oldest allelic type in a sample, is known and has a neat form. Rather less is known about the distribution for the number of genes in the sample which are of the same allelic type as Eve possessed. If the latter number is positive, then these genes are automatically of the oldest type in the sample. But Eve may have no non-mutant descendants in the sample; then, the oldest allele will be a mutant arising in a line of descent after Eve. The paper studies the number of non-mutant descendants from Eve, its distribution and moments. It seems that there may be few neat results. In large samples, the proportion of genes of Eve's type has an approximate beta-like density, together with a discrete probability atom at zero, if the mutation rate parameter is low. Extinction of the allele of even the population's common ancestor is possible, but not certain, and bounds are obtained for its probability. Some comments are made about the applications and implications o...Continue Reading

References

Nov 1, 1991·Scientific American·L L Cavalli-Sforza
Jan 1, 1990·Journal of Mathematical Biology·M Notohara
Dec 1, 1990·Theoretical Population Biology·N Takahata, M Slatkin
Jan 1, 1989·Journal of Mathematical Biology·R C Griffiths
Apr 1, 1989·Theoretical Population Biology·G A Watterson
Aug 22, 1986·Proceedings of the Royal Society of London. Series B, Containing Papers of a Biological Character·G J Nossal
Jan 1, 1987·Nature·R L CannA C Wilson
Apr 1, 1988·Theoretical Population Biology·B Beder
Dec 1, 1988·Genetical Research·N Takahata
Jan 1, 1987·Journal of Mathematical Biology·F M Hoppe
Jan 1, 1987·Nature·J Wainscoat

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Citations

Mar 1, 1995·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·J A GlazierM H Skolnick

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