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Recent Progress in Coalescent Theory
"... Coalescent theory is the study of random processes where particles may join each other to form clusters as time evolves. These notes provide an introduction to some aspects of the mathematics of coalescent processes and their applications to theoretical population genetics and in other fields such ..."
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Coalescent theory is the study of random processes where particles may join each other to form clusters as time evolves. These notes provide an introduction to some aspects of the mathematics of coalescent processes and their applications to theoretical population genetics and in other fields such as spin glass models. The emphasis is on recent work concerning in particular the connection of these processes to continuum random trees and spatial models such as coalescing random walks.
The total external branch length of beta coalescents. Preprint available on http://arxiv.org/abs/1212.6070
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ON THE EXTENDED MORAN MODEL AND ITS RELATION TO COALESCENTS WITH MULTIPLE COLLISIONS
, 2011
"... We study the asymptotics of the extended Moran model as the total population size N tends to infinity. Two convergence results are provided, the first result leading to discretetime limiting coalescent processes and the second result leading to continuoustime limiting coalescent processes. The lim ..."
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Cited by 10 (4 self)
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We study the asymptotics of the extended Moran model as the total population size N tends to infinity. Two convergence results are provided, the first result leading to discretetime limiting coalescent processes and the second result leading to continuoustime limiting coalescent processes. The limiting coalescent processes allow for multiple mergers of ancestral lineages (Λcoalescent). It is furthermore verified that any continuous time Λcoalescent (with Λ any probability distribution) can arise in the limit. Typical examples of extended Moran models are discussed, with an emphasis on models being in the domain of attraction of beta coalescents or Λcoalescents with Λ being log infinitely divisible.
Analysis of DNA sequence variation within marine species using Beta–coalescents
 Theor. Popln Biol
, 2013
"... Abstract. We apply recently developed inference methods based on general coalescent processes to DNA sequence data obtained from various marine species. Several of these species are believed to exhibit socalled shallow gene genealogies, potentially due to extreme reproductive behaviour, e.g. via H ..."
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Abstract. We apply recently developed inference methods based on general coalescent processes to DNA sequence data obtained from various marine species. Several of these species are believed to exhibit socalled shallow gene genealogies, potentially due to extreme reproductive behaviour, e.g. via Hedgecock’s “reproduction sweepstakes”. Besides the data analysis, in particular the inference of mutation rates and the estimation of the (real) time to the most recent common ancestor, we briefly address the question whether the genealogies might be adequately described by socalled Beta coalescents (as opposed to Kingman’s coalescent), allowing multiple mergers of genealogies. The choice of the underlying coalescent model for the genealogy has drastic implications for the estimation of the above quantities, in particular the realtime embedding of the genealogy.
On the speed of coming down from infinity for Ξcoalescent processes
, 2010
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On the total length of external branches for beta coalescents
, 2012
"... Abstract. In this paper, we consider Beta(2 − α,α) (with 1 < α < 2) and related Λcoalescents. If T (n) denotes the length of an external branch of the ncoalescent, we prove the convergence of n α−1 T (n) when n tends to ∞, and give the limit. To this aim, we give asymptotics for the number σ ..."
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Cited by 5 (4 self)
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Abstract. In this paper, we consider Beta(2 − α,α) (with 1 < α < 2) and related Λcoalescents. If T (n) denotes the length of an external branch of the ncoalescent, we prove the convergence of n α−1 T (n) when n tends to ∞, and give the limit. To this aim, we give asymptotics for the number σ (n) of collisions which occur in the ncoalescent until the end of the chosen external branch, and for the block counting process associated with the ncoalescent.
Wiehe T: Simulation of DNA sequence evolution under models of recent directional selection. Brief Bioinform 2009
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DIFFUSION VERSUS JUMP PROCESSES ARISING AS SCALING LIMITS IN POPULATION GENETICS
"... Abstract. When the reproduction law of a discrete branching process preserving the total size N of a population is ‘balanced’, scaling limits of the forward and backward in time processes are known to be the WrightFisher diffusion and the Kingman coalescent. When the reproduction law is ‘unbalance ..."
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Abstract. When the reproduction law of a discrete branching process preserving the total size N of a population is ‘balanced’, scaling limits of the forward and backward in time processes are known to be the WrightFisher diffusion and the Kingman coalescent. When the reproduction law is ‘unbalanced’, depending on extreme reproduction events occurring either occasionally or systematically, then various forward and backward jump processes, either in continuous time or in discrete time arise as scaling limits in the large N limit. This is in sharp contrast with diffusion limits whose sample paths are continuous. We study some aspects of these limiting jump processes both forward and backward, especially the discretetime ones. In the forward in time approach, because the absorbing boundaries are not hit in finite time, the analysis of the models together with the conclusions which can be drawn deviate significantly from the ones available in the diffusion context. Running title: Diffusion and jump processes in population genetics.
Computational inference beyond Kingman’s coalescent
, 2014
"... Copyright and reuse: The Warwick Research Archive Portal (WRAP) makes this work by researchers of the University of Warwick available open access under the following conditions. Copyright © and all moral rights to the version of the paper presented here belong to the individual author(s) and/or othe ..."
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Copyright and reuse: The Warwick Research Archive Portal (WRAP) makes this work by researchers of the University of Warwick available open access under the following conditions. Copyright © and all moral rights to the version of the paper presented here belong to the individual author(s) and/or other copyright owners. To the extent reasonable and practicable the material made available in WRAP has been checked for eligibility before being made available. Copies of full items can be used for personal research or study, educational, or notfor profit purposes without prior permission or charge. Provided that the authors, title and full bibliographic details are credited, a hyperlink and/or URL is given for the original metadata page and the content is not changed in any way. A note on versions: The version presented here may differ from the published version or, version of record, if you wish to cite this item you are advised to consult the publisher’s version. Please see the ‘permanent WRAP url ’ above for details on accessing the published version and note that access may require a subscription.