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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Scaling limits of a model for selection at two sca
les Joint with Shishi Luo - Jonathan Mattingly (Du
ke University)
DTSTART;TZID=Europe/London:20160610T110000
DTEND;TZID=Europe/London:20160610T120000
UID:TALK66444AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/66444
DESCRIPTION:The dynamics of a population undergoing selection
is a central topic in evolutionary biology. This q
uestion is particularly intriguing in the case whe
re selective forces act in opposing directions at
two population scales. For example\, a fast-replic
ating virus strain outcompetes slower-replicating
strains at the within-host scale. However\, if the
fast-replicating strain causes host morbidity and
is less frequently transmitted\, it can be outcom
peted by slower-replicating strains at the between
-host scale. Here we consider a stochastic ball-an
d-urn process which models this type of phenomenon
. We prove the weak convergence of this process un
der two natural scalings. The first scaling leads
to a deterministic nonlinear integro-partial diffe
rential equation on the interval [0\,1] with depen
dence on a single parameter\, &lambda\;. We show t
hat the fixed points of this differential equation
are Beta distributions and that their stability d
epends on &lambda\; and the behavior of the initia
l data around 1. The second scaling leads to a mea
sure-valued Fleming-Viot process\, an infinite dim
ensional stochastic process that is frequently ass
ociated with a population genetics.
LOCATION:Seminar Room 2\, Newton Institute
CONTACT:info@newton.ac.uk
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