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Adaptive evolution: a population view

Benoît Perthame
Laboratoire J.-L. Lions, Université P. et M.  Curie,
INRIA-Rocquencourt and Institut Universitaire de France

The three processes of multiplication, mutations and selection, proposed by C.Darwin, can be written in mathematical words. In a very simplified description, the  environment can be considered as a 'nutrient' shared by all the population. This alllows certain individuals, characterized by a 'phenotypical trait', to multiply faster because they are better adapted to use the environment. This leads to select the 'fittest trait' in the population. On the other hand, the
new-born individuals undergo small variations of  the trait under the effect of mutations. In these circumstances, is it possible to observ 'speciation' and to describe the dynamical evolution of the 'fittest' traits?

We will give a class of self-contained mathematical models of such population dynamics based on nonlocal-parabolic equations. Introducing a small parameter, we show that asymptotic analysis allows us to formalize precisely the concepts of monomorphic or polymorphic populations. We can describe the evolution of the 'fittest traits' thanks to a form of canonical equation with branching points. We will also show that numerical solutions are consistant with individual based stochastic simulations. The analysis uses a new type of Hamilton-Jacobi equation with constraints.

Viernes 7 Enero, 2011, 14:30 hrs. Sala de seminarios 5to piso, DIM.

Categoría: charla
Lugar: Sala de Seminarios DIM, 5to piso, Viernes 7 Enero 2011, 14.30 hr
Última actualización: 05/enero/2011
Fecha de Inicio: 07/enero/2011
Fecha de Término: 07/enero/2011
Departamento de Ingeniería Matemática, Universidad de Chile.
Facultad de Ciencias Físicas y Matemáticas.
Blanco Encalada 2120, piso 5. - Casilla 170-3. Correo 3. - Santiago, CHILE.
Fono: (562) 671 1530. Fax: (562) 688 3821 - Email: contacto [at]