Integro-Differential Equations from EVolutionary biology – DEEV

We propose to develop new approaches to solve unconventional mathematical questions inspired by the evolutionary dynamics of structured populations. The evolutionary dynamics of phenotypically structured populations are governed by stochastic and deterministic processes. These processes describe individual or collective dynamics and typically have various temporal regimes. We are interested in a class of models based on multi-scale integro-differential equations, describing large populations, with possible stochastic components. We will focus on the study of the impact of spatial heterogeneity, interaction of species or mixing of the gene pool on the Darwinian evolution of species. Such phenomena can be modeled by nonlocal parabolic Lotka-Volterra type equations or by nonstandard kinetic equations depending on whether or not mixing of the gene pool is taken into account. In the study of these unconventional equations several original features arise which require the development of new ideas and tools.