Seminario di Equazioni Differenziali e Applicazioni: “Eigen's model in the long chain regime”

Mercoledì 12 Aprile 2017, ore 12:00 - Aula 2BC30 - Joseba Dalmau


Mercoledì 12 Aprile 2017 alle ore 12:00 in Aula 2BC30, Joseba Dalmau (Ecole Polytechnique, Parigi) terrà un seminario dal titolo “Eigen's model in the long chain regime”.

In the early 70s Manfred Eigen proposed a mathematical model for the evolution of the first living creatures in earth. The evolution is governed by a system of differential equations, obtained from the reproduction and mutation rates of the different genotypes. When the length of the genotypes goes to infinity, the model shows two phenomena of interest. The first is an error threshold phenomenon : a critical mutation rate above which the population at equilibrium is totally random. The second phenomenon is a quasispecies distribution : for subcritical mutaion rates, the population contains a positive fraction of the most adapted genotype, along with a cloud of close mutants. We will analyse both Eigen's original model and the infinite system obtained for genotypes of infinite length. We will give explicit formulas for the distribution of the quasispecies under different fitness functions and we will explore the different convergences that arise.

Rif. Int. M. Bardi, C. Marchi, C. Mariconda

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