Speaker
Description
Recent biological evidence suggests the presence of a 2-phase ageing process in D. Melanogaster. Following these discoveries, we first introduce a stochastic individual-based model and estimate from data the rates of transition between phases.
We then consider a deterministic approximation of the individual model to model an interacting population. We introduce a system of coupled age-structured partial differential equations to model the evolution of a wild population with two distinct age phases. The goal of this work is to try and understand the evolutionary implications of a discontinuous ageing process, and the behaviour of such a model. The model includes birth, death, transition between phases and non linearities due to competition. We study general properties of the system such as well-posedness, positivity and boundedness under few conditions and using general relative entropy methods. We also propose some particular cases of the system, for which we study the existence and stability of steady states with the semi-group approach. By comparing with classical one-phase ageing models, we motivate the presence of a discontinuity from an evolutionary perspective. Finally, we introduce further assumptions and study the global asymptotic behavior of our system without assuming weak non-linearities.
