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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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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.
A new model for evolution in a spatial continuum
"... o b a b i l i t y Vol. 15 (2010), Paper no. 7, pages 162–216. Journal URL ..."
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Cited by 20 (5 self)
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o b a b i l i t y Vol. 15 (2010), Paper no. 7, pages 162–216. Journal URL
Genealogical constructions of population models
, 2014
"... Representations of population models in terms of countable systems of particles are constructed, in which each particle has a ‘type’, typically recording both spatial position and genetic type, and a level. For finite intensity models, the levels are distributed on [0, λ], whereas in the infinite i ..."
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Representations of population models in terms of countable systems of particles are constructed, in which each particle has a ‘type’, typically recording both spatial position and genetic type, and a level. For finite intensity models, the levels are distributed on [0, λ], whereas in the infinite intensity limit, at each time t, the joint distribution of types and levels is conditionally Poisson, with mean measure Ξ(t) × l where l denotes Lebesgue measure and Ξ(t) is a measurevalued population process. Key forces of ecology and genetics can be captured within this common framework. Models covered incorporate both individual and event based births and deaths, oneforone replacement, immigration, independent ‘thinning ’ and independent or exchangeable spatial motion and mutation of individuals. Since birth and death probabilities can depend
On a Voter model on Rd: Cluster growth in the Spatial ΛFlemingViot Process
"... ton, Etheridge and Véber, 2010) can be seen as a direct extension of the Voter Model (Clifford and Sudbury, 1973); (Liggett, 1997). As such, it is an Interacting Particle System with configuration spaceMRd, whereM is the set of probability measures on some space K. Such processes are usually studie ..."
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ton, Etheridge and Véber, 2010) can be seen as a direct extension of the Voter Model (Clifford and Sudbury, 1973); (Liggett, 1997). As such, it is an Interacting Particle System with configuration spaceMRd, whereM is the set of probability measures on some space K. Such processes are usually studied thanks to a dual process that describes the genealogy of a sample of particles. In this paper, we propose two main contributions in the analysis of the SΛFV process. The first is the study of the growth of a cluster, and the suprising result is that with probability one, every bounded cluster stops growing in finite time. In particular, we discuss why the usual intuition is flawed. The second contribution is an original method for the proof, as the traditional (backward in time) duality methods fail. We develop a forward in time method that exploits a martingale property of the process. To make it feasible, we construct adequate objects that allow to handle the complex geometry of the problem. We are able to prove the result in any dimension d.
Coalescent simulation in continuous space
"... Summary: Coalescent simulation has become an indispensable tool in population genetics and many complex evolutionary scenarios have been incorporated into the basic algorithm. Despite many years of intense interest in spatial structure, however, there are no available methods to simulate the ancestr ..."
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Summary: Coalescent simulation has become an indispensable tool in population genetics and many complex evolutionary scenarios have been incorporated into the basic algorithm. Despite many years of intense interest in spatial structure, however, there are no available methods to simulate the ancestry of a sample of genes that occupy a spatial continuum. This is mainly due to the severe technical problems encountered by the classical model of isolation by distance. A recently introduced model solves these technical problems and provides a solid theoretical basis for the study of populations evolving in continuous space. We present a detailed algorithm to simulate the coalescent process in this model, and provide an efficient implementation of a generalised version of this algorithm as a freely available Python module. Availability: Package available at