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SUMMARY:Exponent dynamics for branching processes
DTSTART;VALUE=DATE-TIME:20230126T130000Z
DTEND;VALUE=DATE-TIME:20230126T140000Z
DTSTAMP;VALUE=DATE-TIME:20230324T184900Z
UID:indico-event-8297@indico.math.cnrs.fr
DESCRIPTION:Speakers: Sylvie Méléard (École Polytechnique)\n\nWe consid
er a stochastic model for the evolution of a discrete population structure
d by a trait taking finitely many values on a grid of [0\, 1] with mutatio
n and selection. Our aim is the study of the dynamics of the population in
logarithm size and time scales\, under a large population assumption.In t
he first part of the talk\, individual mutations are rare but the global m
utation rate tends to infinity. Then negligible sub-populations may have a
strong contribution to evolution. The traits can also be horizontally tra
nsferred\, leading to a trade-off between natural evolution to higher birt
h rates and transfer which drives the population towards lower birth rates
. We prove that the stochastic discrete exponent process converges to a pi
ecewise affine continuous function\, which can be described along successi
ve phases determined by dominant traits.In the second part of the talk\, t
he individual mutations are small but not rare\, we don’t have transfer
and we assume the grid mesh for the trait values becoming smaller and smal
ler. Here again\, the contribution of small sub-populations is important.
We establish that under our rescaling\, the stochastic discrete exponent p
rocess converges to the viscosity solution of a Hamilton-Jacobi equation\,
filling the gap between individual-based evolutionary models and Hamilton
-Jacobi equations.Joint works with N. Champagnat and V.C. Tran\, and S. Mi
rrahimi for the second part.\n\nhttps://indico.math.cnrs.fr/event/8297/
LOCATION:Fokko du Cloux (ICJ\, Bâtiment Braconnier)
URL:https://indico.math.cnrs.fr/event/8297/
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