The general coalescent with asynchronous mergers of ancestral lines

Sagitov, Serik

doi:10.1017/s0021900200017903

Cited by 170 publications

(221 citation statements)

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“…We redirect the interested reader to the cited literature for rigorous mathematical definitions (see Berestycki 2009;Etheridge 2011). MMC models are derived from the general Cannings model of population dynamics (Cannings 1974;Sagitov 1999;Möhle & Sagitov 2001), from which the Moran and Wright-Fisher models are specific cases. We describe here the recent model of Schweinsberg (2003) which has been used to derive the Λ-coalescent, but which idea captures the essence of the population model underlying the MMC models.…”

Section: Overview Of Existing MMC Modelsmentioning

confidence: 99%

“…1). This class of models was established independently by Donnelly & Kurtz (1999), Pitman (1999), andSagitov (1999). It specifies the genealogy of a sample from a Cannings population model based on the so-called Λ-Fleming-Viot process (Bertoin & Gall .…”

Section: Overview Of Existing MMC Modelsmentioning

confidence: 99%

“…Starting with the Bolthausen-Snitzman coalescent (Bolthausen & Sznitman 1998), followed by the Λ-coalescent (Donnelly & Kurtz 1999;Pitman 1999;Sagitov 1999) and Ξ-coalescent (Schweinsberg 2000;Möhle & Sagitov 2001) there is a recent burst of mathematical theory, which aims to generalize the Kingman model (Wakeley 2013). In a nutshell, these theories allow for the merging (coalescence) of multiple lineages (more than two) at a given generation, and possibly several simultaneous mergers (Fig.…”

Section: Introductionmentioning

confidence: 99%

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Coalescence 2.0: a multiple branching of recent theoretical developments and their applications

Tellier

Lemaire

2014

Preprint

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Population genetics theory has laid the foundations for genomics analyses including the recent burst in genome scans for selection and statistical inference of past demographic events in many prokaryote, animal and plant species. Identifying SNPs under natural selection and underpinning species adaptation relies on disentangling the respective contribution of random processes (mutation, drift, migration) from that of selection on nucleotide variability. Most theory and statistical tests have been developed using the Kingman's coalescent theory based on the Wright-Fisher population model. However, these theoretical models rely on biological and life-history assumptions which may be violated in many prokaryote, fungal, animal or plant species. Recent theoretical developments of the so called multiple merger coalescent models are reviewed here (Λ-coalescent, beta-coalescent, Bolthausen-Snitzman, Ξ-coalescent). We explicit how these new models take into account various pervasive ecological and biological characteristics, life history traits or life cycles which were not accounted in previous theories such as 1) the skew in offspring production typical of marine species, 2) fast adapting microparasites (virus, bacteria and fungi) exhibiting large variation in population sizes during epidemics, 3) the peculiar life cycles of fungi and bacteria alternating sexual and asexual cycles, and 4) the high rates of extinction-recolonization in spatially structured populations. We finally discuss the relevance of multiple merger models for the detection of SNPs under selection in these species, for population genomics of very large sample size and advocate to potentially examine the conclusion of previous population genetics studies.

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Section: Overview Of Existing MMC Modelsmentioning

confidence: 99%

Section: Overview Of Existing MMC Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Coalescence 2.0: a multiple branching of recent theoretical developments and their applications

Tellier

Lemaire

2014

Preprint

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“…In the case of no simultaneous mergers in the limit coalescent, called the -coalescent (see Pitman (1999) and Sagitov (1999)), only the arrays of numbers that have only one element larger than 1, given by c + 1, have to be considered in (21) and (22) Moreover, there exists a nonnegative finite measure on…”

Section: The -Coalescentmentioning

confidence: 99%

Recurrence Equations for the Probability Distribution of Sample Configurations in Exact Population Genetics Models

Lessard

2010

J. Appl. Probab.

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Recurrence equations for the number of types and the frequency of each type in a random sample drawn from a finite population undergoing discrete, nonoverlapping generations and reproducing according to the Cannings exchangeable model are deduced under the assumption of a mutation scheme with infinitely many types. The case of overlapping generations in discrete time is also considered. The equations are developed for the Wright-Fisher model and the Moran model, and extended to the case of the limit coalescent with nonrecurrent mutation as the population size goes to ∞ and the mutation rate to 0. Computations of the total variation distance for the distribution of the number of types in the sample suggest that the exact Moran model provides a better approximation for the sampling formula under the exact Wright-Fisher model than the Ewens sampling formula in the limit of the Kingman coalescent with nonrecurrent mutation. On the other hand, this model seems to provide a good approximation for a -coalescent with nonrecurrent mutation as long as the probability of multiple mergers and the mutation rate are small enough.

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“…Let n = ( n (t), t ≥ 0) be an exchangeable coalescent with multiple collisions, as introduced in [22] and [25]. This is a càdlàg (right continuous with left limits) Markov process that starts at t = 0 with n particles and evolves according to the following dynamics.…”

Section: Introductionmentioning

confidence: 99%

On Asymptotics of Exchangeable Coalescents with Multiple Collisions

2008

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We study the number of collisions, X n , of an exchangeable coalescent with multiple collisions ( -coalescent) which starts with n particles and is driven by rates determined by a finite characteristic measure ν(dx) = x −2 (dx). Via a coupling technique, we derive limiting laws of X n , using previous results on regenerative compositions derived from stick-breaking partitions of the unit interval. The possible limiting laws of X n include normal, stable with index 1 ≤ α < 2, and Mittag-Leffler distributions. The results apply, in particular, to the case when ν is a beta(a − 2, b) distribution with parameters a > 2 and b > 0. The approach taken allows us to derive asymptotics of three other functionals of the coalescent: the absorption time, the length of an external branch chosen at random from the n external branches, and the number of collision events that occur before the randomly selected external branch coalesces with one of its neighbours.

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The general coalescent with asynchronous mergers of ancestral lines

Cited by 170 publications

References 4 publications

Coalescence 2.0: a multiple branching of recent theoretical developments and their applications

Coalescence 2.0: a multiple branching of recent theoretical developments and their applications

Recurrence Equations for the Probability Distribution of Sample Configurations in Exact Population Genetics Models

On Asymptotics of Exchangeable Coalescents with Multiple Collisions

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