Séminaire

The Kimura Equation

Fabio Chalub (Universidade Nova de Lisboa)

17 novembre 2016, 09h30–11h00

Toulouse

Salle MC 202

MAD-Stat. Seminar

Résumé

The Kimura Equations was introduced in the 60's by the Japanese geneticist Motoo Kimura and is considered one of the most important models in population genetics. It is a degenerated partial differential equation of drift diffusion type modelling the evolution of the probability distribution among different genotypes in a population. In this talk we will derive this equation from basic stochastic models, showing not only that it approximates in all time scales important models as the Moran and the Wright-Fisher model but in also enclosed the well know replicator equation (a first order ordinary differential equation used in evolutionary game theory). We will also show that the correct formulation of the Kimura equation include two linearly independent conservation laws to be satisfied at all times. In the final part, we will discuss generalizations and new formulations of the same problem.