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Duchamps JJ, Lambert A. Mutations on a random binary tree with measured boundary. ANN APPL PROBAB 2018. [DOI: 10.1214/17-aap1353] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Recurrence Equations for the Probability Distribution of Sample Configurations in Exact Population Genetics Models. J Appl Probab 2016. [DOI: 10.1017/s0021900200007038] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
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 Λ-coalescent with nonrecurrent mutation as long as the probability of multiple mergers and the mutation rate are small enough.
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Abstract
Λ-coalescents model the evolution of a coalescing system in which any number of components randomly sampled from the whole may merge into larger blocks. This survey focuses on related combinatorial constructions and the large-sample behaviour of the functionals which characterize in some way the speed of coalescence.
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Abstract
Λ-coalescents model the evolution of a coalescing system in which any number of components randomly sampled from the whole may merge into larger blocks. This survey focuses on related combinatorial constructions and the large-sample behaviour of the functionals which characterize in some way the speed of coalescence.
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Freund F. Almost sure asymptotics for the number of types for simple
$\Xi$-coalescents. ELECTRONIC COMMUNICATIONS IN PROBABILITY 2012. [DOI: 10.1214/ecp.v17-1704] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Möhle M. Asymptotic results for coalescent processes without proper frequencies and applications to the two-parameter Poisson–Dirichlet coalescent. Stoch Process Their Appl 2010. [DOI: 10.1016/j.spa.2010.07.004] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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Lessard S. Recurrence Equations for the Probability Distribution of Sample Configurations in Exact Population Genetics Models. J Appl Probab 2010. [DOI: 10.1239/jap/1285335406] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
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 Λ-coalescent with nonrecurrent mutation as long as the probability of multiple mergers and the mutation rate are small enough.
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