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55
A classification of coalescent processes for haploid exchangeable population models
 Ann. Probab
, 2001
"... We consider a class of haploid population models with nonoverlapping generations and fixed population size N assuming that the family sizes within a generation are exchangeable random variables. A weak convergence criterion is established for a properly scaled ancestral process as N! 1. It results ..."
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Cited by 63 (4 self)
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We consider a class of haploid population models with nonoverlapping generations and fixed population size N assuming that the family sizes within a generation are exchangeable random variables. A weak convergence criterion is established for a properly scaled ancestral process as N! 1. It results in a full classification of the coalescent generators in the case of exchangeable reproduction. In general the coalescent process allows for simultaneous multiple mergers of ancestral lines.
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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Cited by 48 (3 self)
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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.
Ancestral processes with selection
 Theor. Popul. Biol
, 1997
"... In this paper, we show how to construct the genealogy of a sample of genes for a large class of models with selection and mutation. Each gene corresponds to a single locus at which there is no recombination. The genealogy of the sample is embedded in a graph which we call the ancestral selection gra ..."
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Cited by 42 (1 self)
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In this paper, we show how to construct the genealogy of a sample of genes for a large class of models with selection and mutation. Each gene corresponds to a single locus at which there is no recombination. The genealogy of the sample is embedded in a graph which we call the ancestral selection graph. This graph contains all the information about the ancestry; it is the analogue of Kingman’s coalescent process which arises in the case with no selection. The ancestral selection graph can be easily simulated and we outline an algorithm for simulating samples. The main goal is to analyze the ancestral selection graph and to compare it to Kingman’s coalescent process. In the case of no mutation, we find that the distribution of the time to the most recent common ancestor does not depend on the selection coefficient and hence is the same as in the neutral case. When the mutation rate is positive, we give a procedure for computing the probability that two individuals in a sample are identical by descent and the Laplace transform of the time to the most recent common ancestor of a sample of two individuals; we evaluate the first two terms of their respective power series in terms of the selection coefficient. The probability of identity by descent depends on both the selection coefficient and the mutation rate and is different from the analogous expression in the neutral case. The Laplace transform does not have a linear correction term in the selection coefficient. We also provide a recursion formula that can be used to approximate the probability of a given sample by simulating backwards along the sample paths of the ancestral selection graph, a technique developed by Griffiths and Tavare (1994).] 1997 Academic Press 1.
Inferences from DNA data: population histories, evolutionary processes, and forensic match probabilities.
 Journal of Royal Statistics Society, Series A
, 2003
"... We develop a flexible class of... ..."
A modified lookdown construction for the XiFlemingViot process with mutation and populations with recurrent bottlenecks
 ALEA
, 2009
"... populations with recurrent bottlenecks ..."
Exchangeable partitions derived from Markovian coalescents
 Adv. Appl. Probab
, 2006
"... Kingman derived the Ewens sampling formula for random partitions from the genealogy model defined by a Poisson process of mutations along lines of descent governed by a simple coalescent process. Möhle described the recursion which determines the generalization of the Ewens sampling formula when the ..."
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Cited by 19 (3 self)
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Kingman derived the Ewens sampling formula for random partitions from the genealogy model defined by a Poisson process of mutations along lines of descent governed by a simple coalescent process. Möhle described the recursion which determines the generalization of the Ewens sampling formula when the lines of descent are governed by a coalescent with multiple collisions. In [7] authors exploit an analogy with the theory of regenerative composition and partition structures, and provide various characterizations of the associated exchangeable random partitions. This paper gives parallel results for the further generalized model with lines of descent following a coalescent with simultaneous multiple collisions. 1
Convergence to the Coalescent with Simultaneous Multiple Mergers
, 2002
"... The general coalescent process with simultaneous multiple mergers of ancestral lines was initially characterized in [13] in terms of a sequence of measures de ned on the nitedimensional simplices. A more compact characterization of the general coalescent requiring a single probability measure ..."
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Cited by 14 (1 self)
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The general coalescent process with simultaneous multiple mergers of ancestral lines was initially characterized in [13] in terms of a sequence of measures de ned on the nitedimensional simplices. A more compact characterization of the general coalescent requiring a single probability measure de ned on the in nite simplex was suggested in [17].
A duality approach to the genealogies of discrete nonneutral WrightFisher models
 J. Prob
, 2009
"... Abstract. Discrete ancestral problems arising in population genetics are investigated. In the neutral case, the duality concept has proved of particular interest in the understanding of backward in time ancestral process from the forward in time branching population dynamics. We show that duality fo ..."
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Cited by 11 (3 self)
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Abstract. Discrete ancestral problems arising in population genetics are investigated. In the neutral case, the duality concept has proved of particular interest in the understanding of backward in time ancestral process from the forward in time branching population dynamics. We show that duality formulae still are of great use when considering discrete nonneutral WrightFisher models. This concerns a large class of nonneutral models with completely monotone (CM) bias probabilities. We show that most classical bias probabilities used in the genetics literature fall within this CM class or are amenable to it through some ‘reciprocal mechanism ’ which we define. Next, using elementary algebra on CM functions, some suggested novel evolutionary mechanisms of potential interest are introduced and discussed,
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.