2012/03/19 by Pierre-Emmanuel Jabin, Pierre‐Emmanuel Jabin, Jabin, Pierre-Emmanuel
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #Analysis of PDEs (math.AP) #Evolution and Genetic Dynamics #FOS: Mathematics #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models #math.AP
paper · pdf · doi:10.48550/arxiv.1203.4123
arxiv created 2012/03/19 · openalex publication_date 2012/03/19 · arxiv updated 2012/03/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Diekmann, Jabin, Mischler, and Perthame, 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.