Article Contents

2012, Volume 7, Issue 4: 805-836. Doi: 10.3934/nhm.2012.7.805

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Small populations corrections for selection-mutation models

Pierre-Emmanuel Jabin^1,

1.
CSCAMM and Department of Mathematics, University of Maryland, College Park, MD 20742-4015

Received: March 2012

Revised: August 2012

Published: December 2012

Abstract / Introduction Related Papers Cited by

Abstract

We consider integro-differential models describing the evolution of a population structured by a quantitative trait. Individuals interact competitively, creating a strong selection pressure on the population. On the other hand, mutations are assumed to be small. Following the formalism of [20], this creates concentration phenomena, typically consisting in a sum of Dirac masses slowly evolving in time. We propose a modification to those classical models that takes the effect of small populations into accounts and corrects some abnormal behaviours.

Keywords:

Adaptive dynamics,
Hamilton-Jacobi equation with constraints,
Dirac concentration,
small populations.

Mathematics Subject Classification: Primary: 35B25, 35K55, 92D15.

Citation:

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