Research

My research is in applied mathematics, mainly motivated by questions in evolutionary biology and ecology. I study the dynamics of structured populations using partial differential equations, kinetic models and stochastic processes.

Topics I am particularly interested in include selection and adaptation, sexual reproduction, spatial population dynamics, and the long-time behaviour of mathematical models. I also work on stochastic models of interacting populations and branching networks.

Research code

Interactive simulator — Explore the asexual and sexual population models studied in Alfaro, Raoul & Ronce (2026), When do leading and rear edges of the range shift slower or faster than climate? (see Selected publications below). Source code on GitHub.

Selected publications

  1. V. Bansaye, G. Raoul and M. Tomašević. Growing random planar network with oriented branching and fusion. Preprint (2026). [PDF]
  2. S. Boucenna, V. Dakos and G. Raoul. A model for a population of trees structured by phenological traits. Mathematical Biosciences 395, 109640 (2026). [PDF]
  3. M. Alfaro, G. Raoul and O. Ronce. When do leading and rear edges of the range shift slower or faster than climate? Insights from a mathematical model. Journal of Evolutionary Biology (accepted). [PDF]
  4. G. Raoul. Exponential convergence to a steady-state for a population genetics model with sexual reproduction and selection. Kinetic and Related Models (accepted). [PDF]
  5. G. Raoul. Macroscopic limit from a structured population model to the Kirkpatrick–Barton model. Bulletin des Sciences Mathématiques 205, 103697 (2025). [PDF]
  6. P. Magal and G. Raoul. Dynamics of a kinetic model describing protein exchanges in a cell population. Journal of Mathematical Biology 91, article 76 (2025). [PDF]
  7. Q. Griette, M. Alfaro, G. Raoul and S. Gandon. Evolution and spread of multiadapted pathogens in a spatially heterogeneous environment. Evolution Letters 8(3), 427–436 (2024). [PDF]
  8. M. Alfaro, H. Berestycki and G. Raoul. The effect of climate shift on a species submitted to dispersion, evolution, growth and nonlocal competition. SIAM Journal on Mathematical Analysis 49(1), 562–596 (2017). [PDF]
  9. R. Aguilée, G. Raoul, F. Rousset and O. Ronce. Pollen dispersal slows geographical range shift and accelerates ecological niche shift under climate change. Proceedings of the National Academy of Sciences USA 113(39), E5741–E5748 (2016). [PDF]
  10. S. Mirrahimi and G. Raoul. Dynamics of sexual populations structured by a space variable and a phenotypical trait. Theoretical Population Biology 84, 87–103 (2013). [PDF]

Complete list of publications and preprints →

Teaching

  • École polytechnique (since 2017): part time teaching position, lecturing in analysis, PDEs, and the master's course Partial differential models for ecology.
  • Ho Chi Minh University of Science (since 2022): Theoretical PDEs withinh the Franco-Vietnamese master's programme.
  • Université de Guyane (2023 and 2026): short course Systèmes dynamiques.
  • SEAMS summer school (2026): Wasserstein distances and convergence of stochastic processes.

PhD students

Current: Vianney de la Salle (since 2025, with V. Bansaye); Le Tuyet Nhi Pham (since 2023, with G. Conforti and A. Durmus).

Former: Sirine Boucenna (2021–2024, with V. Dakos); Julie Tourniaire (2018–2021, with P. Maillard); José Méndez (2015–2019, with N. Loeuille and F. Massol); Quentin Griette (2013–2017, with M. Alfaro and S. Gandon).

Contact

Centre de Mathématiques Appliquées (CMAP)
École polytechnique, 91128 Palaiseau, France
gael.raoul@polytechnique.edu