
Minicourse by Benoît Perthame  'Adaptive evolution: a population view', Warsaw 811 December 2009 

Benoît Perthame
Pierre & Marie Curie University, Paris,

Abstract of lectures:

The two processes of mutations and selection, proposed by C. Darwin,
can be written in mathematical words.
In a very simple, general and idealized 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 newborn
individuals undergo small variations of the trait under the effect
of mutations. In these circumstances, is it possible to observe
'speciation' and to describe the dynamical evolution of the 'fittest'
traits?
We will give a class of selfcontained mathematical models of such
population dynamics and show that an asymptotic view allows us to
formalize precisely the concepts of monomorphic or polymorphic
populations. We can describe the evolution of the 'fittest traits'
and various forms of branching points. We will also show that
numerical solutions are consistant with individual based stochastic
simulations.
Eventhough the model is very simple, its analysis relates to
remarkable recent progresses of nonlinear analysis.

All lectures will take place at the Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2.


Date 
Time 
Room 
8th December  14:15 
2180

9th December  10:15 
2180

9th December  16:15 
5440

10th December  8:30 
2180


