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273
Coalescents With Multiple Collisions
 Ann. Probab
, 1999
"... For each finite measure on [0 ..."
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Comparison of Bayesian and maximumlikelihood inference of population genetic parameters
 Bioinformatics
, 2006
"... doi:10.1093/bioinformatics/bti803 ..."
Estimating Species Phylogenies Using Coalescence Times among Sequences
, 2009
"... The estimation of species trees (phylogenies) is one of the most important problems in evolutionary biology, and recently, there has been greater appreciation of the need to estimate species trees directly rather than using gene trees as a surrogate. A Bayesian method constructed under the multispec ..."
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Cited by 66 (9 self)
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The estimation of species trees (phylogenies) is one of the most important problems in evolutionary biology, and recently, there has been greater appreciation of the need to estimate species trees directly rather than using gene trees as a surrogate. A Bayesian method constructed under the multispecies coalescent model can consistently estimate species trees but involves intensive computation, which can hinder its application to the phylogenetic analysis of largescale genomic data. Many summary statistics–based approaches, such as shallowest coalescences (SC) and Global LAteSt Split (GLASS), have been developed to infer species phylogenies for multilocus data sets. In this paper, we propose 2 methods, species tree estimation using average ranks of coalescences (STAR) and species tree estimation using average coalescence times (STEAC), based on the summary statistics of coalescence times. It can be shown that the 2 methods are statistically consistent under the multispecies coalescent model. STAR uses the ranks of coalescences and is thus resistant to variable substitution rates along the branches in gene trees. A simulation study suggests that STAR consistently outperforms STEAC, SC, and GLASS when the substitution rates among lineages are highly variable. Two real genomic data sets were analyzed by the 2 methods and produced species trees that are consistent with previous results. [Coalescent model; gene tree; species tree.]
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.
Coalescent Theory
 Handbook of Statistical Genetics, volume II
, 1986
"... The coalescent process is a powerful modeling tool for population genetics. The allelic states of all homologous gene copies in a population are determined by the genealogical and mutational history of these copies. The coalescent approach is based on the realization that the genealogy is usually ea ..."
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Cited by 52 (1 self)
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The coalescent process is a powerful modeling tool for population genetics. The allelic states of all homologous gene copies in a population are determined by the genealogical and mutational history of these copies. The coalescent approach is based on the realization that the genealogy is usually easier to model backward in time, and that selectively neutral mutations can then be superimposed afterwards. A wide range of biological phenomena can be modeled using this approach. Whereas almost all of classical population genetics considers the future of a population given a starting point, the coalescent considers the present, while taking the past into account. This allows the calculation of probabilities of sample configurations under the stationary distribution of various population genetic models, and makes full likelihood analysis of polymorphism data possible. It also leads to extremely efficient computer algorithms for generating simulated data from such distributions, data which can then be compared with observations as a form of exploratory data analysis.
Construction Of Markovian Coalescents
 Ann. Inst. Henri Poincar'e
, 1997
"... Partitionvalued and measurevalued coalescent Markov processes are constructed whose state describes the decomposition of a finite total mass m into a finite or countably infinite number of masses with sum m, and whose evolution is determined by the following intuitive prescription: each pair of ma ..."
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Cited by 49 (16 self)
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Partitionvalued and measurevalued coalescent Markov processes are constructed whose state describes the decomposition of a finite total mass m into a finite or countably infinite number of masses with sum m, and whose evolution is determined by the following intuitive prescription: each pair of masses of magnitudes x and y runs the risk of a binary collision to form a single mass of magnitude x+y at rate (x; y), for some nonnegative, symmetric collision rate kernel (x; y). Such processes with finitely many masses have been used to model polymerization, coagulation, condensation, and the evolution of galactic clusters by gravitational attraction. With a suitable choice of state space, and under appropriate restrictions on and the initial distribution of mass, it is shown that such processes can be constructed as Feller or Fellerlike processes. A number of further results are obtained for the additive coalescent with collision kernel (x; y) = x + y. This process, which arises fro...
Betacoalescents and continuous stable random trees
, 2006
"... Coalescents with multiple collisions, also known as Λcoalescents, were introduced by Pitman and Sagitov in 1999. These processes describe the evolution of particles that undergo stochastic coagulation in such a way that several blocks can merge at the same time to form a single block. In the case t ..."
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Cited by 47 (15 self)
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Coalescents with multiple collisions, also known as Λcoalescents, were introduced by Pitman and Sagitov in 1999. These processes describe the evolution of particles that undergo stochastic coagulation in such a way that several blocks can merge at the same time to form a single block. In the case that the measure Λ is the Beta(2 − α, α) distribution, they are also known to describe the genealogies of large populations where a single individual can produce a large number of offspring. Here we use a recent result of Birkner et al. to prove that Betacoalescents can be embedded in continuous stable random trees, about which much is known due to recent progress of Duquesne and Le Gall. Our proof is based on a construction of the DonnellyKurtz lookdown process using continuous random trees which is of independent interest. This produces a number of results concerning the smalltime behavior of Betacoalescents. Most notably, we recover an almost sure limit theorem of the authors for the number of blocks at small times, and give the multifractal spectrum corresponding to the emergence of blocks with atypical size. Also, we are able to find exact asymptotics for sampling formulae corresponding to the site frequency spectrum and allele frequency spectrum associated with mutations in the context of population genetics.
Bayesian Agglomerative Clustering with Coalescents
 In Advances in Neural Information Processing Systems
"... We introduce a new Bayesian model for hierarchical clustering based on a prior over trees called Kingman’s coalescent. We develop novel greedy and sequential Monte Carlo inferences which operate in a bottomup agglomerative fashion. We show experimentally the superiority of our algorithms over the s ..."
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Cited by 45 (3 self)
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We introduce a new Bayesian model for hierarchical clustering based on a prior over trees called Kingman’s coalescent. We develop novel greedy and sequential Monte Carlo inferences which operate in a bottomup agglomerative fashion. We show experimentally the superiority of our algorithms over the stateoftheart, and demonstrate our approach in document clustering and phylolinguistics. 1
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.