Simulation of ‘hitch-hiking’ genealogies

Slade, Paul F.

doi:10.1007/pl00000072

“…Nevertheeral expression for the effect of selection on the genealogy, which can be seen as an extension of Price's less, this method does not seem likely to lead to a deeper analytical understanding, which would extend to more (1970) equation . The analysis is of a neutral locus that is linked to a general kinds of selection and more complex genetics. Donnelly and Kurtz (1999a) and Slade (2001) have single selected locus that carries two alternative alleles.…”

Section: W E Develop a Diffusion Approximation First Intro-mentioning

confidence: 99%

The Effect of Selection on Genealogies

Barton¹,

Etheridge²

2004

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The coalescent process can describe the effects of selection at linked loci only if selection is so strong that genotype frequencies evolve deterministically. Here, we develop methods proposed by Kaplan, Darden, and Hudson to find the effects of weak selection. We show that the overall effect is given by an extension to Price's equation: the change in properties such as moments of coalescence times is equal to the covariance between those properties and the fitness of the sample of genes. The distribution of coalescence times differs substantially between allelic classes, even in the absence of selection. However, the average coalescence time between randomly chosen genes is insensitive to the current allele frequency and is affected significantly by purifying selection only if deleterious mutations are common and selection is strong (i.e., the product of population size and selection coefficient, Ns Ͼ 3). Balancing selection increases mean coalescence times, but the effect becomes large only when mutation rates between allelic classes are low and when selection is extremely strong. Our analysis supports previous simulations that show that selection has surprisingly little effect on genealogies. Moreover, small fluctuations in allele frequency due to random drift can greatly reduce any such effects. This will make it difficult to detect the action of selection from neutral variation alone. W E develop a diffusion approximation, first intro- (Maynard Smith and Haigh 1974;Kaplan et al. 1988;Barton 1998). However, the deterministic approximaduced by Kaplan et al. (1988), which extends the coalescent to take account of arbitrary forms of selection plainly fails when selection is weak or absent. Consider the relationships between genes that can be of two tion. Kingman (1982) introduced the coalescent process as a simple description of the genealogical relationallelic types. Even if these alleles are neutral, and so represent an arbitrary labeling of the genes, two genes ships among a set of neutral genes. Although the theory of the coalescent has developed largely independently, of the same allelic type are likely to be substantially more closely related than are two genes of different type. it is closely related to the classical concept of identity Moreover, the average relationship between randomly by descent (Nagylaki 1989). The coalescent extends chosen genes depends on the allele frequency, since an naturally to describe structured populations, in which allele that happens to have increased by chance will genes may be found in different places or embedded cause a selective sweep just as if it had increased by sein different genetic backgrounds. The effects of seleclection. Although relationships averaged over the distrition can easily be included, provided that it is so strong bution of allele frequencies and over allelic classes must relative to random drift that the frequencies of different be unaffected by the labeling of neutral alleles, relationgenetic backgrounds can be approximated as changing shi...

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“…Contemporary studies focus on models involving, along with drift, other forces of population genetics: mutation, selection, and recombination [13], [14], [15], [34], [42]. Such Fisher-Wright-type models are of growing interest for both mathematicians and geneticists, but their 'forward' mathematical analysis is quite complicated.…”

Section: Feller Evolution Familymentioning

confidence: 99%

“…These distributions are the main focus of our study. Generalizations of Kingman's coalescent include models with recombination, but in models involving drift, mutation, and recombination it is difficult, if possible at all, to find an equation for the joint distributions [6], [34], [39], [42].…”

Section: Feller Evolution Familymentioning

confidence: 99%

Asymptotic behavior of a Feller evolution family involved in the Fisher-Wright model

Bobrowski

¹

2008

Adv. Appl. Probab.

0

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We study the evolution in time of the joint distribution of a pair of Feller processes, related by the fact that some random time ago they were identical, evolving as a single Feller process; from that time on, they began to evolve independently, conditional on a state at the time of split, according to the same Feller transition probabilities. Such processes are involved in the Fisher-Wright model: the distribution of the time counted backwards from the present to the time of split in the past is a function of deterministic but time-varying effective size 2N of the population from which the two processes are sampled. In terms of a corresponding family of Feller operators, assuming asymptotic stability or ergodicity of the process of mutation, we find the limit form of the distribution of such pairs of processes sampled from decaying, asymptotically constant, and growing populations. In the case where mutation is not asymptotically stable or ergodic, limit distributions are found for the distribution of relative differences.

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“…In the presence of mutation these two forces compete, with mutation introducing new variants to the population and drift striving to make the population uniform. Contemporary studies focus on models involving, along with drift, other forces of population genetics: mutation, selection, and recombination [13], [14], [15], [34], [42]. Such Fisher-Wright-type models are of growing interest for both mathematicians and geneticists, but their 'forward' mathematical analysis is quite complicated.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic behavior of a Feller evolution family involved in the Fisher-Wright model

Bobrowski

¹

2008

Advances in Applied Probability

1

0

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We study the evolution in time of the joint distribution of a pair of Feller processes, related by the fact that some random time ago they were identical, evolving as a single Feller process; from that time on, they began to evolve independently, conditional on a state at the time of split, according to the same Feller transition probabilities. Such processes are involved in the Fisher-Wright model: the distribution of the time counted backwards from the present to the time of split in the past is a function of deterministic but time-varying effective size 2N of the population from which the two processes are sampled. In terms of a corresponding family of Feller operators, assuming asymptotic stability or ergodicity of the process of mutation, we find the limit form of the distribution of such pairs of processes sampled from decaying, asymptotically constant, and growing populations. In the case where mutation is not asymptotically stable or ergodic, limit distributions are found for the distribution of relative differences.

show abstract

Simulation of ‘hitch-hiking’ genealogies

Cited by 10 publications

References 7 publications

The Effect of Selection on Genealogies

The Effect of Selection on Genealogies

Asymptotic behavior of a Feller evolution family involved in the Fisher-Wright model

Asymptotic behavior of a Feller evolution family involved in the Fisher-Wright model

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