In this thesis, we study two classes of interacting particle systems arising from population genetics, focusing on the behaviour of their scaling limits and the biological implications of thisbehaviour. We consider populations with additional structure — either spatial or temporal —which impacts the evolution of genetic traits in non-trivial ways. We first analyse spatially structured populations, where the survival probability of an individual depends both on the fitnessof its genetic type and on the local population density near its location. In such systems, highlocal density may decrease survival due to competition or increase it due to cooperation. Oneconsequence of this complex interaction is gene surfing — the propagation of neutral mutationsthrough large spatial regions during range expansions, supported by both experimental dataand theoretical models. We study a generalisation of a model introduced by Foutel-Rodier andEtheridge (2020) to rigorously investigate whether gene surfing of deleterious mutations is possible during range expansions. We prove that the interacting particle system is well-posed evenwhen started with infinitely many particles and that, under an appropriate scaling, the processconverges weakly to an infinite system of partial differential equations, confirming non-rigorouscomputations by Foutel-Rodier and Etheridge. The second model developed in this thesis addresses the evolution of seed banks in plants. We study under which environmental conditionsit is advantageous for plants to produce seeds that remain dormant across multiple generations.To rigorously analyse this question, we develop new techniques for stochastic dynamical systemswith multiple time scales.
Fitness in Expanding Populations: (Alternative Format Thesis)
De Oliveira Madeira, J. L. (Author). 22 Apr 2026
Student thesis: Doctoral Thesis › PhD