 The Λ-lookdown model with selectionB. Bah and E. Pardoux Stochastic Processes and their Applications, 2015, vol. 125, issue 3, 1089-1126 Abstract: The goal of this paper is to study the lookdown model with selection in the case of a population containing two types of individuals, with a reproduction model which is dual to the Λ-coalescent. In particular we formulate the infinite population “Λ-lookdown model with selection”. When the measure Λ gives no mass to 0, we show that the proportion of one of the two types converges, as the population size N tends to infinity, towards the solution to a stochastic differential equation driven by a Poisson point process. We show that one of the two types fixates in finite time if and only if the Λ-coalescent comes down from infinity. We give precise asymptotic results in the case of the Bolthausen–Sznitman coalescent. We also consider the general case of a combination of the Kingman and the Λ-lookdown model. Keywords: Look-down with selection; Lambda coalescent; Fixation and non fixation (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:125:y:2015:i:3:p:1089-1126 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spa.2014.10.014 Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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