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Shishi Luo

Title: Scaling limits of a model for selection at two scales

Abstract: Natural selection can act in opposing directions at different
biological scales. For example, a fast-replicating virus strain is at
an advantage within a host because it out-competes slower-replicating
strains. It is at a disadvantage at the between-host scale, however,
if it causes host morbidity and is less frequently transmitted. We
model this phenomenon as a particle process and prove the weak
convergence of this stochastic process under two natural scalings. The
first scaling leads to a deterministic nonlinear integropartial
differential equation with dependence on a single parameter directly
related to the prelimiting model parameters. We show that the fixed
points of this differential equation are Beta distributions and that
their stability depends on the parameter value and the behavior of the
initial data around 1. The second scaling leads to a measure-valued
Fleming-Viot process, a stochastic process that is frequently
associated with a population genetics. This is joint work with
Jonathan Mattingly.