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SUMMARY:Scaling limits of a model for selection at two scales Joint with S
 hishi Luo - Jonathan Mattingly (Duke University)
DTSTART:20160610T100000Z
DTEND:20160610T110000Z
UID:TALK66444@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:The dynamics of a population undergoing selection is a central
  topic in evolutionary biology. This question is particularly intriguing i
 n the case where selective forces act in opposing directions at two popula
 tion scales. For example\, a fast-replicating virus strain outcompetes slo
 wer-replicating strains at the within-host scale. However\, if the fast-re
 plicating strain causes host morbidity and is less frequently transmitted\
 , it can be outcompeted by slower-replicating strains at the between-host 
 scale. Here we consider a stochastic ball-and-urn process which models thi
 s type of phenomenon. We prove the weak convergence of this process under 
 two natural scalings. The first scaling leads to a deterministic nonlinear
  integro-partial differential equation on the interval [0\,1] with depende
 nce on a single parameter\, &lambda\;. We show that the fixed points of th
 is differential equation are Beta distributions and that their stability d
 epends on &lambda\; and the behavior of the initial data around 1. The sec
 ond scaling leads to a measure-valued Fleming-Viot process\, an infinite d
 imensional stochastic process that is frequently associated with a populat
 ion genetics.
LOCATION:Seminar Room 2\, Newton Institute
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