2007/10/26 by Sylvie Méléard, Viet Chi Tran · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #Evolution and Genetic Dynamics #Genetics, Aging, and Longevity in Model Organisms #Mathematical and Theoretical Epidemiology and Ecology Models #math.PR #msc:60F99 #msc:60J80 #msc:60K35 #msc:92D15 #q-bio.PE
paper · pdf · doi:10.1007/s00285-008-0202-2
published as Journal of Mathematical Biology 58, 6 (2009) 881-921
arxiv created 2007/10/26 · openalex publication_date 2008/07/30 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/29
We are interested in a stochastic model of trait and age-structured population undergoing mutation and selection. We start with a continuous time, discrete individual-centered population process. 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 Sequence process describing Adaptive Dynamics for populations without age structure. Under the additional assumption of small mutations, we derive an age-dependent ordinary differential equation that extends the Canonical Equation. These evolutionary approximations have never been introduced to our knowledge. They are based on ecological phenomena represented by PDEs that generalize the Gurtin-McCamy equation in Demography. Another particularity is that they involve a fitness function, describing the probability of invasion of the resident population by the mutant one, that can not always be computed explicitly. Examples illustrate how adding an age-structure enrich the modelling of structured population by including life history features such as senescence. In the cases considered, we establish the evolutionary approximations and study their long time behavior and the nature of their evolutionary singularities when computation is tractable. Numerical procedures and simulations are carried.