Do Eve's alleles live on?

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 allel...

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Автори: Watterson, G, Donnelly, P
Формат: Journal article
Мова:English
Опубліковано: 1992
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author Watterson, G
Donnelly, P
author_facet Watterson, G
Donnelly, P
author_sort Watterson, G
collection OXFORD
description 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 of the results for human mitochondrial DNA.
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spelling oxford-uuid:46be1a3e-db5b-42cd-a3cd-017c013d56e62022-03-26T15:15:34ZDo Eve's alleles live on?Journal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:46be1a3e-db5b-42cd-a3cd-017c013d56e6EnglishSymplectic Elements at Oxford1992Watterson, GDonnelly, PConsider 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 of the results for human mitochondrial DNA.
spellingShingle Watterson, G
Donnelly, P
Do Eve's alleles live on?
title Do Eve's alleles live on?
title_full Do Eve's alleles live on?
title_fullStr Do Eve's alleles live on?
title_full_unstemmed Do Eve's alleles live on?
title_short Do Eve's alleles live on?
title_sort do eve s alleles live on
work_keys_str_mv AT wattersong doevesallelesliveon
AT donnellyp doevesallelesliveon