Seminario de Probabilidad y Procesos Estocásticos

Resumen:

The presence of older individuals in natural populations raises critical evolutionary questions: what influence do these individuals exert on population evolution? An example is the so-called Lansing effect, a transgenerational mechanism in which offspring born to older parents have shorter lifespans than those born to younger parents. This phenomenon has been observed across multiple species, but its underlying mechanisms remain debated. From an adaptive dynamics perspective, the persistence of such an effect, which apparently decreases individual fitness, is puzzling. However, if individuals carrying the Lansing mechanism can evolve more rapidly under intermediate mutation rates of power-law order, they could reach a fitter trait faster than those without it, hence ensuring the persistence of this strategy. This scenario is reminiscent of fitness valley crossing, where a population must pass through an intermediate state of reduced fitness to reach a trait of higher fitness. In this talk, I will extend the framework and results of Bovier, Coquille and Smadi (2019) on fitness valley crossing to a non-linear age-structured population dynamics, where individuals are characterized by both their age and a discrete trait. The approach relies on a large-population scaling limit in a small mutation regime: the resident population remains close to its equilibrium, while the small mutant subpopulations crossing the valley can be approximated by linear dynamics. In particular, I will show how accounting for age structure introduces new mathematical challenges, requiring fine results for age-structured populations and renewal equations. Joint work with M. Doumic, M. Esser, and S. Méléard.