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The increasing availability of large databases of pathogen genomes requires the development of mathematical frameworks integrating different features of pathogen evolution. In the case of rapidly-evolving viruses, many assumptions concerning the diversification process are no longer valid: the heterogeneous nature of viral transmission raises the question of whether neutral models based on binary trees are adequate to represent viral evolution. In this context, I propose to use ?-coalescents to model phylogenies of viral populations. I will use this model to quantify viral adaptive dynamics and to estimate the bias on ancestral population inference caused by current methods not including selection.
My first contact with biology-inspired mathematics came during my master’s thesis, when I was working on the relationship of exchangeable coalescents and measurevalued processes used in population genetics, such as the Fleming-Viot process. I then wrote my PhD thesis on random trees theory, focusing especially on the scaling limits of large branching trees (so-called Lévy trees). After graduating, my interest for mathematical structures in biology led me to an 8-month postdoc in the SMILE (Stochastic Models for the Inference of Life Evolution) team at Collège de France, in Paris. There, I learned about the recent advances in using phylogenetic data to infer characteristics of species diversification. In 2013, I joined the MaIAGE research unit (UR 1404, Mathématiques et Informatique Appliquées du Génome à l’Environnement). My research interests lies mainly in epidemiology: epidemic processes on random graphs, spatial spread and, most importantly, phylogenetic methods for the inference of epidemiological parameters (phylodynamics).
Hoscheit, P., Geeraert, S., Beaunee, G., Monod, H., Gilligan, CA., Filipe, JAN., Vergu, E., Moslonka-Lefebvre, M, 2017. Dynamical network models for cattle trade: towards economy-based epidemic risk assessment. Journal of Complex Networks, 5 (4), 604-624.
Abraham, R., Delmas, J.-F. & Hoscheit, P., 2014. Exit times for an increasing Lévy tree-valued process. Probab. Theory Relat. Fields 159, 357-403.
Abraham, R., Delmas, J.-F. & Hoscheit, P., 2013. A note on the Gromov-Hausdorff-Prokhorov distance between (locally) compact metric measure spaces. Electron. J. Probab. 18, 1-21.
Hoscheit, P., 2013.Fluctuations for the number of records on subtrees of the Continuum Random Tree. ALEA - Lat. Am. J. Probab. Math. Stat. 10, 783-811.