ERC starting grant MESOPROBIO (2015-2020)


The aim of the MESOPROBIO project is to analyse PDE models for biological propagation phenomena at the mesoscale.

By analogy with the kinetic theory of gases, this is an intermediate level of description between the microscale (individual-based models) and the macroscale (parabolic reaction-transport-diffusion equations). The specific feature common to all the models involved in the project is the local heterogeneity with respect to a structure variable (velocity, phenotypical trait, age) which requires new mathematical methods. We propose to push analysis beyond classical upscaling arguments and to track the local heterogeneity all along the analysis.

The biological applications are: concentration waves of bacteria, evolutionary aspects of structured populations (with respect to dispersal ability or life-history traits), and anomalous diffusion.

The mathematical challenges are: multiscale analysis of PDE having different properties in different directions of the phase space, including nonlocal terms (scattering, competition), and possibly lacking basic features of reaction-diffusion equations such as the maximum principle. The outcomes are travelling waves, accelerating fronts, approximation of geometric optics, nonlocal Hamilton-Jacobi equations, optimal foraging strategies and evolutionary dynamics of phenotypical traits. Emphasis will be placed on quantitative results with strong feedback towards biology.

Members of the project

    Permament researchers


  • V. Calvez, DR CNRS, Institut Camille Jordan, Lyon, Principal Investigator
  • J. Garnier, CR CNRS, LAMA, Univ. Savoie, Chambéry, Associate Investigator
  • S. Mirrahimi, CR CNRS, Institut Mathématiques de Toulouse, Associate Investigator

    • PhD students and post-docs (chronological order)


  • Alvaro Mateos González, PhD student (2013-2017)
  • Nils Caillerie, PhD student (2014-2017)
  • Chris Henderson, Post-doc (2015-2016)
  • Thibault Bourgeron, Post-doc (2015-2017)
  • Hélène Hivert, Post-doc (2016–2017)
  • Florian Patout, PhD student (2016–2019)
  • Monika Twarogowska, Post-doc (2016–2018)
  • Bastien Polizzi, Post-doc (2018-)

    • Associated researchers


  • H. Leman, CR Inria, Ecole Normale Supérieure de Lyon
  • Th. Lepoutre, CR Inria, Institut Camille Jordan, Lyon

Publications linked to the project

    Preprints

  • Calvez, V., Débarre, F. and Girardin, L. Catch me if you can: a spatial model for a brake-driven gene drive reversal preprint (2018).
  • Calvez, V., Garnier, J. and Patout, F. A quantitative genetics model with sexual mode of reproduction in the regime of small variance , preprint (2018).
  • Calvez, V., Henderson, C., Mirrahimi, S., Turanova, O. with a numerical appendix by Dumont, T. Non-local competition slows down front acceleration during dispersal evolution , preprint (2018).
  • Mirrahimi, S., Gandon, S. Evolution of specialization in heterogeneous environments: equilibrium between selection, mutation and migration , preprint (2018).
  • Mirrahimi, S. Singular limits for models of selection and mutations with heavy-tailed mutation distribution , preprint (2018).
  • Calvez, V. and Lam, K.-Y Uniqueness of the viscosity solution of a constrained Hamilton-Jacobi equation , preprint (2018).
  • E. Bouin, V. Calvez, E. Grenier, and G. Nadin, Large deviations for velocity- jump processes and non-local Hamilton-Jacobi equations, preprint (2016).

    • Articles

  • A. Sadier, M. Twarogowska, K. Steklikova, L. Hayden, A. Lambert, P. Schneider, V. Laudet, M. Hovorakova*, V. Calvez* and S. Pantalacci*, Modeling Edar expression reveals the hidden dynamics of tooth signaling center patterning, PLOS Biol (2019).
  • V. Calvez Chemotactic waves of bacteria at the mesoscale, J. Eur. Math. Soc. (in press).
  • E. Bouin, M. Chan, C. Henderson and P.S. Kim Influence of a mortality trade-off on the spreading rate of cane toads fronts, Comm. PDE (in press).
  • Calvez, V., Gabriel, P. & González, Á, Limiting Hamilton-Jacobi equation for the large scale asymptotics of a subdiffusion jump-renewal equation, Asymptotic Analysis (in press).
  • Calvez, V., Gosse, L. and Twarogowska, M. Travelling Chemotactic Aggregates at Mesoscopic Scale and Bistability, SIAM Journal on Applied Mathematics (2017).
  • Calvez, V., Gosse, L. and Twarogowska, M. Concentration Waves of Chemotactic Bacteria: The Discrete Velocity Case, in Innovative Algorithms and Analysis (eds. Gosse, L. & Natalini, R.), 2017.
  • Calvez, V., Carrillo, J. A. and Hoffmann, F. The Geometry of Diffusing and Self-Attracting Particles in a One-Dimensional Fair-Competition Regime, in Nonlocal and Nonlinear Diffusions and Interactions: New Methods and Directions, 2017.
  • Calvez, V., Carrillo, J. A. and Hoffmann, F. Equilibria of homogeneous functionals in the fair-competition regime, Nonlinear Analysis (2017).
  • V. Calvez, and T. Gallouët, Blow-up phenomena for gradient flows of discrete homogeneous functionals, Applied Mathematics & Optimization (2017).
  • S. Figueroa Iglesias and S. Mirrahimi, Long time evolutionary dynamics of phenotypically structured populations in time-periodic environments, SIAM J. Math. Anal. (2018).
  • H. Hivert A first-order asymptotic preserving scheme for front propagation in a one-dimensional kinetic reaction–transport equation, Journal of Computational Physics (2018).
  • E. Bouin and N. Caillerie Spreading in kinetic reaction–transport equations in higher velocity dimensions European Journal of Applied Mathematics (2018).
  • E. Bouin, J. Garnier, C. Henderson and F. Patout Thin Front Limit of an Integro-differential Fisher-KPP Equation with Fat-Tailed Kernels, SIAM Journal on Mathematical Analysis (2018).
  • L. Roques, J. Garnier and G. Martin, Beneficial mutation-selection dynamics in finite asexual populations: a free boundary approach, Scientific Reports (2017).
  • S. Mirrahimi A Hamilton–Jacobi approach to characterize the evolutionary equilibria in heterogeneous environments, Mathematical Models and Methods in Applied Sciences (2017).
  • S. Gandon and S. Mirrahimi, A Hamilton–Jacobi method to describe the evolutionary equilibria in heterogeneous environments and with non-vanishing effects of mutations, Comptes Rendus Mathématiques (2017).
  • N. Caillerie Large deviations of a velocity jump process with a Hamilton–Jacobi approach Comptes Rendus Mathématiques (2017).
  • E. Bouin and C. Henderson Super-linear spreading in local bistable cane toads equations. Nonlinearity (2017).
  • E. Bouin, C. Henderson and L. Ryzhik The Bramson logarithmic delay in the cane toads equations, Quarterly of Applied Mathematics (2016).
  • H. Berry, Th. Lepoutre and A.M González, Quantitative Convergence Towards a Self-Similar Profile in an Age-Structured Renewal Equation for Subdiffusion, Acta Applicandae Mathematicae (2016).