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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.
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.
THE COALESCENT EFFECTIVE SIZE OF AGESTRUCTURED POPULATIONS 1
, 2005
"... We establish convergence to the Kingman coalescent for a class of agestructured population models with timeconstant population size. Time is discrete with unit called a year. Offspring numbers in a year may depend on mother’s age. 1. Introduction. The ..."
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Cited by 4 (0 self)
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We establish convergence to the Kingman coalescent for a class of agestructured population models with timeconstant population size. Time is discrete with unit called a year. Offspring numbers in a year may depend on mother’s age. 1. Introduction. The
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"... Convergence to the coalescent and its relation to the time back to the most recent common ancestor ..."
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Convergence to the coalescent and its relation to the time back to the most recent common ancestor
© Institute of Mathematical Statistics, 2005 THE COALESCENT EFFECTIVE SIZE OF
"... We establish convergence to the Kingman coalescent for a class of agestructured population models with timeconstant population size. Time is discrete with unit called a year. Offspring numbers in a year may depend on mother’s age. 1. Introduction. The ..."
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We establish convergence to the Kingman coalescent for a class of agestructured population models with timeconstant population size. Time is discrete with unit called a year. Offspring numbers in a year may depend on mother’s age. 1. Introduction. The
Expected Coalescence Time for a Nonuniform Allocation Process
, 809
"... We study a process where balls are repeatedly thrown into n boxes independently according to some probability distribution p. We start with n balls, and at each step all balls landing in the same box are fused into a single ball; the process terminates when there is only one ball left (coalescence). ..."
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We study a process where balls are repeatedly thrown into n boxes independently according to some probability distribution p. We start with n balls, and at each step all balls landing in the same box are fused into a single ball; the process terminates when there is only one ball left (coalescence). Let c: = P j p2j, the collision probability of two fixed balls. We show that the expected coalescence time is asymptotically 2c −1, under two constraints on p that exclude a thin set of distributions p. One of the constraints is c ≪ ln −2 n. This ln −2 n is shown to be a threshold value: for c ≫ ln −2 n, there exists p with c(p) = c such that the expected coalescence time far exceeds c −1. Connections to coalescent processes in population biology and theoretical computer science are discussed.
EXCHANGEABLE COALESCENTS
, 2010
"... The purpose of this series of lectures is to introduce and develop some of the main aspects of a class of random processes evolving by coalescence, which arise in the study of the genealogy of certain large populations. Let us first present the naive idea. For many years, probability theory has prov ..."
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The purpose of this series of lectures is to introduce and develop some of the main aspects of a class of random processes evolving by coalescence, which arise in the study of the genealogy of certain large populations. Let us first present the naive idea. For many years, probability theory has provided models of population which evolve forward in time: GaltonWatson processes, branching processes, WrightFisher processes, birth and death processes, etc., so roughly speaking the genealogy is view from the ancestor(s). Kingman has been the first to investigate the dual point of view point, i.e. from the offspring going backward in time. Typically, consider a population at the present date. For the sake of simplicity, let us assume that this population is haploid with nonoverlapping generations. We can decompose it into siblings (brothers and sisters), or families of grandchildren, and so on. For each integer n, we have a natural partition into families of individuals having the same ancestor n generations backwards. Plainly, these partitions get coarser as n increases, and more precisely a merging of subfamilies corresponds to coalescence of ancestral lineages. Loosely speaking, we are interested in the study of such coalescent processes for large