During my defense, I will explain how my research bridges applied mathematics and theoretical ecology by exploring and developing mathematical models based on Partial Differential Equations (PDEs), integro-differential equations, and stochastic processes, to gain insights into ecological and evolutionary questions. My mathematical developments are strongly motivated by biological problems arising in conservation biology, ecology and population dynamics, evolutionary biology and population genetics, as well as eco-evolutionary biology, which integrates ecological and evolutionary perspectives. The main objective of this presentation is to understand how species can adapt to changing environments. Specifically, it aims to shed new light on biological propagation and adaptation phenomena across various scales -- such as spatial or ecosystemic -- and within heterogeneous or changing environments.
My HDR is structured around four biological applications: Propagation dynamics and their consequences on genetic diversity (Chapter~I); Long-distance dispersal, with a focus on fast propagation, gene mixing, and ecological rescue (Chapter~II); Evolutionary adaptation of populations to heterogeneous or changing environments (Chapter~III); Eco-evolutionary dynamics of mutualism in host-symbiont ecosystems (Chapter~IV).