Math @ Duke

Publications [#303549] of Jonathan C. Mattingly
search arxiv.org.Papers Published
 Luo, S; Mattingly, JC, Scaling limits of a model for selection at two scales
(2015) [1507.00397v1]
(last updated on 2018/11/12)
Abstract: The dynamics of a population undergoing selection is a central topic in
evolutionary biology. This question is particularly intriguing in the case
where selective forces act in opposing directions at two population scales. For
example, a fastreplicating virus strain outcompetes slowerreplicating strains
at the withinhost scale. However, if the fastreplicating strain causes host
morbidity and is less frequently transmitted, it can be outcompeted by
slowerreplicating strains at the betweenhost scale. Here we consider a
stochastic ballandurn process which models this type of phenomenon. We prove
the weak convergence of this process under two natural scalings. The first
scaling leads to a deterministic nonlinear integropartial differential
equation on the interval $[0,1]$ with dependence on a single parameter,
$\lambda$. We show that the fixed points of this differential equation are Beta
distributions and that their stability depends on $\lambda$ and the behavior of
the initial data around $1$. The second scaling leads to a measurevalued
FlemingViot process, an infinite dimensional stochastic process that is
frequently associated with a population genetics.


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