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361
Coalescents With Multiple Collisions
 Ann. Probab
, 1999
"... For each finite measure on [0 ..."
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Inconsistency of Phylogenetic Estimates from Concatenated Data under Coalescence
, 2007
"... Although multiple gene sequences are becoming increasingly available for molecular phylogenetic inference, the analysis of such data has largely relied on inference methods designed for single genes. One of the common approaches to analyzing data from multiple genes is concatenation of the individua ..."
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Cited by 104 (2 self)
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Although multiple gene sequences are becoming increasingly available for molecular phylogenetic inference, the analysis of such data has largely relied on inference methods designed for single genes. One of the common approaches to analyzing data from multiple genes is concatenation of the individual gene data to form a single supergene to which traditional phylogenetic inference procedures—e.g., maximum parsimony (MP) or maximum likelihood (ML)—are applied. Recent empirical studies have demonstrated that concatenation of sequences from multiple genes prior to phylogenetic analysis often results in inference of a single, wellsupported phylogeny. Theoretical work, however, has shown that the coalescent can produce substantial variation in singlegene histories. Using simulation, we combine these ideas to examine the performance of the concatenation approach under conditions in which the coalescent produces a high level of discord among individual gene trees and show that it leads to statistically inconsistent estimation in this setting. Furthermore, use of the bootstrap to measure support for the inferred phylogeny can result in moderate to strong support for an incorrect tree under these conditions. These results highlight the importance of incorporating variation in gene histories into multilocus phylogenetics. [Coalescence; concatenation; gene tree; maximum likelihood; species tree; statistical inconsistency; supergene.]
Estimating Recombination Rates from Population Genetic Data
, 2000
"... We introduce a new method for estimating recombination rates from population genetic data. The method uses a computationallyintensive statistical procedure (importance sampling) to calculate the likelihood under a coalescentbased model. Detailed comparisons of the new algorithm with two existing m ..."
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Cited by 89 (11 self)
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We introduce a new method for estimating recombination rates from population genetic data. The method uses a computationallyintensive statistical procedure (importance sampling) to calculate the likelihood under a coalescentbased model. Detailed comparisons of the new algorithm with two existing methods (one based on importance sampling and one based on MCMC) show it to be substantially more efficient. (The improvement over the existing importance sampling scheme is typically by four orders of magnitude.) The existing approaches not infrequently led to misleading results on the problems we investigated. We also performed a simulation study to look at the properties of the maximum likelihood estimator (mle) of the recombination rate, and its robustness to misspecification of the demographic model.
Comparison of Bayesian and maximumlikelihood inference of population genetic parameters
 Bioinformatics
, 2006
"... doi:10.1093/bioinformatics/bti803 ..."
Constructing summary statistics for approximate Bayesian computation: semiautomatic approximate Bayesian computation
, 2012
"... ar ..."
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Estimating species phylogeny from genetree probabilities despite incomplete lineage sorting: an example from Melanoplus grasshoppers
 Syst. Biol
, 2007
"... Abstract. — Estimating phylogenetic relationships among closely related species can be extremely difficult when there is incongruence among gene trees and between the gene trees and the species tree. Here we show that incorporating a model of the stochastic loss of gene lineages by genetic drift int ..."
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Cited by 59 (6 self)
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Abstract. — Estimating phylogenetic relationships among closely related species can be extremely difficult when there is incongruence among gene trees and between the gene trees and the species tree. Here we show that incorporating a model of the stochastic loss of gene lineages by genetic drift into the phylogenetic estimation procedure can provide a robust estimate of species relationships, despite widespread incomplete sorting of ancestral polymorphism. This approach is applied to a group of montane Melanoplus grasshoppers for which genealogical discordance among loci and incomplete lineage sorting obscures any obvious phylogenetic relationships among species. Unlike traditional treatments where gene trees estimated using standard phylogenetic methods are implicitly equated with the species tree, with the coalescentbased approach the species tree is modeled probabilistically from the estimated gene trees. The estimated species phylogeny (the ESP) is calculated for the grasshoppers from multiple gene trees reconstructed for nuclear loci and a mitochondrial gene. This empirical application is coupled with a simulation study to explore the performance of the coalescentbased approach. Specifically, we test the accuracy of the ESP given the data based on analyses of simulated data matching the multilocus data collected in Melanoplus (i.e., data were simulated for each locus with the same number of base pairs and locusspecific mutational models). The results of the study show that ESPs can be computed using the coalescentbased approach long before reciprocal monophyly has been achieved, and that these statistical estimates are accurate. This contrasts with analyses of the empirical data collected in Melanoplus and simulated data based on concatenation of multiple loci, for which the
Coalescent Random Forests
 J. COMBINATORIAL THEORY A
, 1998
"... Various enumerations of labeled trees and forests, including Cayley's formula n n\Gamma2 for the number of trees labeled by [n], and Cayley's multinomial expansion over trees, are derived from the following coalescent construction of a sequence of random forests (R n ; R n\Gamma1 ; : ..."
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Cited by 53 (15 self)
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Various enumerations of labeled trees and forests, including Cayley's formula n n\Gamma2 for the number of trees labeled by [n], and Cayley's multinomial expansion over trees, are derived from the following coalescent construction of a sequence of random forests (R n ; R n\Gamma1 ; : : : ; R 1 ) such that R k has uniform distribution over the set of all forests of k rooted trees labeled by [n]. Let R n be the trivial forest with n root vertices and no edges. For n k 2, given that R n ; : : : ; R k have been defined so that R k is a rooted forest of k trees, define R k\Gamma1 by addition to R k of a single edge picked uniformly at random from the set of n(k \Gamma 1) edges which when added to R k yield a rooted forest of k \Gamma 1 trees. This coalescent construction is related to a model for a physical process of clustering or coagulation, the additive coalescent in which a system of masses is subject to binary coalescent collisions, with each pair of masses of magnitude...
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...