A fundamental problem in the biological and social sciences is understanding how phenotypic characteristics and behavioural traits of single individuals shape patterns of evolution and adaptation at the population level. Mathematical modelling can help to address this fundamental question by enabling extrapolation beyond scenarios analysed through in vitro and in vivo experiments, and by revealing emergent phenomena that would otherwise remain unobserved.
Partial differential equations (PDEs) for structured populations and equivalent stochastic individual-based (IB) models can be used as in silico laboratories to test hypotheses, and decide which postulated qualitative attributes of a population are consistent with the observed behaviours. As the name implies, IB models track the evolution of individual organisms, and allow individual-level mechanisms to be scaled up to their population-level consequences. As such, they offer a precise and flexible description of population dynamics. However, IB models can be explored mainly through numerical simulations only. This impinges on the robustness of the conclusions that can be drawn from their outputs. On the other hand, PDEs can be derived from stochastic IB models through suitable limiting procedures and describe population dynamics in terms of the evolution of population densities across phenotypic and physical spaces. Therefore, compared with IB models, PDEs provide a less exhaustive description, but they make it possible to complement numerical simulations with rigorous analytical results, to achieve conclusions with broad structural stability under parameter changes.
Combining numerical simulation of stochastic IB models with analysis and numerical simulation of PDEs, my research aims to understand how the interplay between variation, selection and evolution of individual traits is mirrored in the adaptive dynamics of structured populations. I currently collaborate with cell biologists to elucidate the connections between phenotypic adaptation and the emergence of resistance to therapies in cancer cell populations, and with evolutionary biologists to study the evolution of social behaviours in spatially structured populations.