"Branching systems as models for structured populations"Tourniaire, JuliePopulation dynamics is widely documented when it comes to neutral unstructured models. In panmictic populations (no space and no selection), the evolutionary history is usually investigated using standard models such as the Wright-Fisher and Moran models, their backward-in-time counterpart, Kingman's coalescent, and the celebrated Ewens's sampling formula. Despite being mathematically appealing, these models seem unrealistic from a modelling point of view. In many biological systems, structures play a central role. This structure can refer to different features, such as spatial position, type, fitness or age, and generally generates travelling wave phenomena. When studying structured populations, standard mean-field approximations may break down, leading to more complex behaviours than well-mixed systems. The theory of branching processes turned out to be a powerful tool to explore these complex phenomena. First, the principle of "a few guiding the way for many" (see e.g. Hallatschek and Geyrhofer 2016) stating that invasions are often driven by a small number of pioneers is now well established in the biology literature. From a modelling viewpoint, this idea suggests that the precise form of the regulation mechanisms do not impact the dynamics of the population and that these dynamics are dictated by the behaviour of a few leaders, located at the tip of the wave, where the effect of competition is negligible. As a consequence, branching processes seem well-suited models to capture the evolutionary forces and the internal mechanisms leading these travelling wave phenomena. Second, even when the dynamics are driven by ``typical individuals'', that is individuals sitting in the bulk, macroscopic properties (e.g. spatial distribution, survival probability) of interacting particle systems can be understood thanks to comparison with branching processes. Finally, as it is the case for Galton-Watson processes, general branching processes are naturally associated to genealogical structures (backward in time). Therefore, they form a class of tractable systems which can explain and predict genetic patterns in structured populations. The aims of this symposium are both to explore the macroscopic dynamics of different interacting particle systems via branching processes, and, at a microscopic scale, to investigate the interplay between structure and genealogies. This symposium is organised by Zsófia Talyigás and Julie Tourniaire. |
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