### Seminar 3.3.2016: Katarina Bodova

Posted:

**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

Abstract:

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.

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

Abstract:

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.