Seminar 3.3.2016: Katarina Bodova

Seminar on Qualitative Theory of Differential Equations
organized by P.Quittner, M.Fila and R.Kollar

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Seminar 3.3.2016: Katarina Bodova

Postby quittner » Wed Feb 24, 2016 10:14 am

Seminár z kvalitatívnej teórie diferenciálnych rovníc
Seminar on Qualitative Theory of Differential Equations

Štvrtok 3.3.2016 o 14:00, poslucháreň M-223

Katarína Boďová (IST Austria, Klosterneuburg):
A dynamical maximum entropy approximation for the evolution of quantitative traits

One of the main goals in evolutionary biology is to understand and to predict how quantitative traits
as a bacteria growth rate, or a birds wing span, evolve, in realistically changing environment.
However, it is a difficult problem since dynamics of quantitative traits is a complex process
that involves various mechanisms as selection, mutation, and random effects.
These factors affect allele frequencies on the microscopic scale and consequently the trait
on the macroscopic scale. I will outline the underlying mathematical problem and present
an approximation that reduces it to a tractable dynamical system that emulates the macroscopic
dynamics in response to a change in the evolutionary forces. The approximation is based on
a method well known in statistical physics, the maximum entropy approximation, combined with
a quasi-stationarity assumption. Contrary to our intuition the approximation is remarkably accurate
not only in the adiabatic regime when the evolutionary forces, rate of selection and mutation,
change slowly but also in the extreme case of rapid changes of these parameters.
We will discuss benefits and limitations of such a method and resulting mathematical and biological challenges.
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