Dynamics of concentration in a population model structured by age and a phenotypical trait

These equations, which admit trav- eling fronts as solutions, can be used as models in ecology to describe dynamics of a population structured by a space variable.. A related,

Taking the large population and rare mutations limits under a well- chosen time-scale separation condition, we obtain a jump process that generalizes the Trait Substitution

We observe that the Substitution Fleming-Viot Process includes the three qualitative be- haviors due to the three different time scales: deterministic equilibrium for the size of

Our approach is based on duality arguments (see Proposition 2.7 which is adapted from a result due to Krein-Rutman [14]) and allows us to obtain the existence of eigenvectors in

Under concavity assumptions on the reaction term, we prove that the solution converges to a Dirac mass whose evolution in time is driven by a Hamilton-Jacobi equation with

Using a theory based on Hamilton-Jacobi equations with constraint, we prove that, as the effect of the mutations vanishes, the solu- tion concentrates on a single Dirac mass, while

Finally, we study in detail the particular case of multitype logistic branching populations and seek explicit formulae for the invasion fitness of a mutant deviating slightly from

Adaptive dynamics as a jump process The derivation of the canonical equation (1) by Dieckmann and Law (1996) stems from modeling the dynamics of a population as a Markov process