Results 1  10
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224
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 58 (9 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.
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 41 (18 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...
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 36 (17 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 32 (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.
PoissonDirichlet and GEM invariant distributions for splitandmerge transformations of an interval partition
, 2001
"... This paper introduces a splitandmerge transformation of interval partitions which combines some features of one model studied by Gnedin and Kerov [10, 11] and another studied by Tsilevich [30, 29] and MayerWolf, Zeitouni and Zerner [20]. The invariance under this splitandmerge transformatio ..."
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Cited by 29 (0 self)
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This paper introduces a splitandmerge transformation of interval partitions which combines some features of one model studied by Gnedin and Kerov [10, 11] and another studied by Tsilevich [30, 29] and MayerWolf, Zeitouni and Zerner [20]. The invariance under this splitandmerge transformation of the interval partition generated by a suitable Poisson process yields a simple proof of the recent result of [20] that a PoissonDirichlet distribution is invariant for a closely related fragmentationcoagulation process. Uniqueness and convergence to the invariant measure are established for the splitandmerge transformation of interval partitions, but the corresponding problems for the fragmentationcoagulation process remain open.
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 25 (9 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 24 (2 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