Rare alleles and selection

Carsten Wiuf

doi:10.1006/tpbi.2001.1523

Rare alleles and selection

Carsten Wiuf^*

^*Corresponding author for this work

9 Citations (Scopus)

Abstract

A subpopulation D of rare alleles is considered. The subpopulation is part of a large population that evolves according to a Moran model with selection and growth. Conditional on the current frequency, q, of the rare allele, an approximation to the distribution of the genealogy of D is derived. In particular, the density of the age, T₁, of the rare allele is approximated, It is shown that time naturally is measured in units of qN(0) generations, where N(0) is the present day population size, and that the distribution of the genealogy of D depends on the compound parameters ρ=rqN(O) and σ=sqN(O) only. Here, s is the fitness per generation of heterozygote carriers of the rare allele and r is the growth rate per generation of the population. Amongst more, it is shown that for constant population size (ρ=0) the distribution of D depends on σ only through the absolute value |σ|, not the direction of selection.

Original language	English
Journal	Theoretical Population Biology
Volume	59
Issue number	4
Pages (from-to)	287-296
Number of pages	10
ISSN	0040-5809
DOIs	https://doi.org/10.1006/tpbi.2001.1523
Publication status	Published - 1 Jan 2001
Externally published	Yes

Keywords

Birth-death process
Exponential growth
Genealogy
Rare allele
Selection

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10.1006/tpbi.2001.1523

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abstract = "A subpopulation D of rare alleles is considered. The subpopulation is part of a large population that evolves according to a Moran model with selection and growth. Conditional on the current frequency, q, of the rare allele, an approximation to the distribution of the genealogy of D is derived. In particular, the density of the age, T1, of the rare allele is approximated, It is shown that time naturally is measured in units of qN(0) generations, where N(0) is the present day population size, and that the distribution of the genealogy of D depends on the compound parameters ρ=rqN(O) and σ=sqN(O) only. Here, s is the fitness per generation of heterozygote carriers of the rare allele and r is the growth rate per generation of the population. Amongst more, it is shown that for constant population size (ρ=0) the distribution of D depends on σ only through the absolute value |σ|, not the direction of selection.",

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AB - A subpopulation D of rare alleles is considered. The subpopulation is part of a large population that evolves according to a Moran model with selection and growth. Conditional on the current frequency, q, of the rare allele, an approximation to the distribution of the genealogy of D is derived. In particular, the density of the age, T1, of the rare allele is approximated, It is shown that time naturally is measured in units of qN(0) generations, where N(0) is the present day population size, and that the distribution of the genealogy of D depends on the compound parameters ρ=rqN(O) and σ=sqN(O) only. Here, s is the fitness per generation of heterozygote carriers of the rare allele and r is the growth rate per generation of the population. Amongst more, it is shown that for constant population size (ρ=0) the distribution of D depends on σ only through the absolute value |σ|, not the direction of selection.

KW - Birth-death process

KW - Exponential growth

KW - Genealogy

KW - Rare allele

KW - Selection

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Rare alleles and selection

Abstract

Keywords

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