A Classification of Coalescent Processes for Haploid Exchangeable Population Models

Möhle, Martin; Sagitov, Serik

doi:10.1214/aop/1015345761

Cited by 199 publications

(217 citation statements)

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“…When a large proportion of the population is sampled, multiple coalescent events may occur in a single generation. In such a case, more general coalescent models that the commonly used Kingman coalescent may be more appropriate, which allow multiple 'collisions' of lineages (Pitman 1999;Sagitov 1999Sagitov , 2003Schweinsberg 2000;Mohle & Sagitov 2001). Although populations may deviate from the assumptions of a Wright-Fisher model-for example, they may show geographical structure-in many, but not all cases, the relative size function can be assumed to be proportional to the population size, in which case, it is referred to as the 'effective population size', N e , and the relative size function is n(t) ¼ N e (t).…”

Section: Phylodynamic Patterns Under Different Epidemiological Scenarios (A) the Time-varying Coalescent Modelmentioning

confidence: 99%

Viral phylodynamics and the search for an ‘effective number of infections’

Frost

Volz

2010

Phil. Trans. R. Soc. B

134

157

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Information on the dynamics of the effective population size over time can be obtained from the analysis of phylogenies, through the application of time-varying coalescent models. This approach has been used to study the dynamics of many different viruses, and has demonstrated a wide variety of patterns, which have been interpreted in the context of changes over time in the ‘effective number of infections’, a quantity proportional to the number of infected individuals. However, for infectious diseases, the rate of coalescence is driven primarily by new transmissions i.e. the incidence, and only indirectly by the number of infected individuals through sampling effects. Using commonly used epidemiological models, we show that the coalescence rate may indeed reflect the number of infected individuals during the initial phase of exponential growth when time is scaled by infectivity, but in general, a single change in time scale cannot be used to estimate the number of infected individuals. This has important implications when integrating phylogenetic data in the context of other epidemiological data.

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Section: Phylodynamic Patterns Under Different Epidemiological Scenarios (A) the Time-varying Coalescent Modelmentioning

confidence: 99%

Viral phylodynamics and the search for an ‘effective number of infections’

Frost

Volz

2010

Phil. Trans. R. Soc. B

134

157

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“…For example in certain highly fecund organisms (Hedgecock, 1994; Beckenbach, 1994; Hedgecock and Pudovkin, 2011; Árnason, 2004; Irwin et al, 2016), where individuals have the ability to produce numbers of offspring on the order of the population size and therefore a few individuals may produce the bulk of the offspring in any given generation (Hedgecock, 1994). These population dynamics violate basic assumptions of the Kingman coalescent, and are better modelled by ‘multiple-merger’ coalescents (Donnelly and Kurtz, 1999; Pitman, 1999; Sagitov, 1999; Schweinsberg, 2000; Möhle and Sagitov, 2001), in which more than two lineages can merge in a given event. Multiple-merger coalescent processes have also been shown to be relevant for modelling the effects of selection on gene genealogies (Gillespie, 2000; Durrett and Schweinsberg, 2004; Desai et al, 2013; Neher and Hallatschek, 2013; Schweinsberg, 2017).…”

Section: Resultsmentioning

confidence: 99%

Efficient ancestry and mutation simulation with msprime 1.0

Baumdicker

Bisschop

Goldstein

et al. 2021

Preprint

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Stochastic simulation is a key tool in population genetics, since the models involved are often analytically intractable and simulation is usually the only way of obtaining ground-truth data to evaluate inferences. Because of this necessity, a large number of specialised simulation programs have been developed, each filling a particular niche, but with largely overlapping functionality and a substantial duplication of effort. Here, we introduce msprime version 1.0, which efficiently implements ancestry and mutation simulations based on the succinct tree sequence data structure and tskit library. We summarise msprime's many features, and show that its performance is excellent, often many times faster and more memory efficient than specialised alternatives. These high-performance features have been thoroughly tested and validated, and built using a collaborative, open source development model, which reduces duplication of effort and promotes software quality via community engagement.

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“…Derivations of alternative coalescent processes usually retain the conventional proportionality to N −2 ([21], Theorem 3.2 via Equation (5); [22], Theorem 2.1 via Equation (4)). These generalizations are in turn based on the partition structures of equivalence classes described in terms of sampling distributions not originally connected to genealogy [23][24][25].…”

Section: Coalescent Theory Of Branching Processesmentioning

confidence: 99%

Linearization of the Kingman Coalescent

Slade

2018

Mathematics

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Kingman's coalescent process is a mathematical model of genealogy in which only pairwise common ancestry may occur. Inter-arrival times between successive coalescence events have a negative exponential distribution whose rate equals the combinatorial term ( n 2 ) where n denotes the number of lineages present in the genealogy. These two standard constraints of Kingman's coalescent, obtained in the limit of a large population size, approximate the exact ancestral process of Wright-Fisher or Moran models under appropriate parameterization. Calculation of coalescence event probabilities with higher accuracy quantifies the dependence of sample and population sizes that adhere to Kingman's coalescent process. The convention that probabilities of leading order N −2 are negligible provided n N is examined at key stages of the mathematical derivation. Empirically, expected genealogical parity of the single-pair restricted Wright-Fisher haploid model exceeds 99% where n ≤ √ N/6. The fractional cubic root criterion is practicable, since although it corresponds to perfect parity and to an extent confounds identifiability it also accords with manageable conditional probabilities of multi-coalescence.

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A Classification of Coalescent Processes for Haploid Exchangeable Population Models

Cited by 199 publications

References 20 publications

Viral phylodynamics and the search for an ‘effective number of infections’

Viral phylodynamics and the search for an ‘effective number of infections’

Efficient ancestry and mutation simulation with msprime 1.0

Linearization of the Kingman Coalescent

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