Research activities
Short presentation:
I work on mathematical models from evolutionary biology and ecology.
I am interested in the description of joint demographic and evolutionary dynamics of populations structured by quantitative traits in heterogeneous environments. Such phenomena can be modeled by nonlocal parabolic Lotka-Volterra type equations or by nonstandard kinetic equations depending on whether or not mixing of the gene pool (due for instance to the exchange of genetic information between bacteria or to sexual reproduction) is taken into account. Such models have typically various temporal regimes. Some characteristics of such multi-scale equations are that they lead to some concentration phenomena (occurrence of dominant traits) or propagation phenomena (spatial invasions).
Articles:
Adaptation in homogeneous environments and asexual reproduction:
- C. Guinet, S. Mirrahimi and J.-M. Roquejoffre, Concentration in selection-mutation models: error estimates and asymptotic expansion, preprint (pdf)
- S. Mirrahimi and J.-M. Roquejoffre, A class of Hamilton-Jacobi equations with constraint: uniqueness and constructive approach, Journal of differential equations, Vol. 250.5 (2016), pp. 4717-4738. (pdf)
- S. Mirrahimi and J.-M. Roquejoffre, Uniqueness in a class of Hamilton-Jacobi equations with constraints, Comptes Rendus Mathematique, Vol. 353, (2015), pp. 489-494: (Online version) (pdf)
- S. Mirrahimi, G. Barles, B. Perthame and P. E. Souganidis, Singular Hamilton-Jacobi equation for the tail problem, SIAM J. Math. Anal. Vol. 44.6, (2012) pp. 4297-4319 (pdf)
- A. Lorz, S. Mirrahimi and B. Perthame, Dirac mass dynamics in a multidimensional nonlocal parabolic
equation, Communications in Partial Differential Equations, Vol. 36, Issue 6, (2011) pp. 1071-1098 (pdf)
- G. Barles, S. Mirrahimi and B. Perthame, Concentration in Lotka-Volterra parabolic or integral equations: a general convergence result. Methods and Applications of Analysis (MAA) Vol. 16.3, (2009) pp. 321-340 (pdf)
Taking into account demographic stochasticity:
- N. Champagnat, S. Méléard, S. Mirrahimi and V.-C. Tran, From stochastic individual-based models to free-boundary
Hamilton-Jacobi equations, preprint (pdf)
- N. Champagnat, S. Méléard, S. Mirrahimi and V.-C. Tran, Filling the gap between individual-based evolutionary models and Hamilton-Jacobi equations, Journal de l'École Polytechnique-Mathématiques, Vol. 10, (2023), pp. 1247-1275. (pdf)
Adaptation of quantitative traits with mixing of the gene pool:
- M. Hillairet and S. Mirrahimi, Analysis of the steady solutions of the Fisher's infinitesimal model; a Hilbertian approach, preprint (pdf)
- A. Garriz and S. Mirrahimi, A Hamilton-Jacobi approach for the evolutionary dynamics of
a model with gene transfer: characterizing monomorphic
dynamics for non-concave fitness functions, accepted in Journal of Differential Equations, (2026) (pdf)
- J. Guerand, M. Hillairet and S. Mirrahimi, A moment-based approach for the analysis of the infinitesimal model in the regime of small variance, Kinetic and Related Models, Vol. 18(3) (2025) pp. 389-425. (pdf)
- A. Garriz, A. Léculier and S. Mirrahimi, Impact of a unilateral horizontal gene transfer on the evolutionary
equilibria of a population, Mathematical Models and Methods in Applied Sciences, Vol. 34(5) (2024) pp. 951-991 (pdf)
- S. Mirrahimi and L. Dekens, Dynamics of Dirac concentrations in the evolution of
quantitative alleles with sexual reproduction, Nonlinearity, Vol. 35(11) (2022) pp. 5781 (pdf)
- S. Mirrahimi and G. Raoul, Population structured by a space variable and a phenotypical trait, Theoretical Population Biology, Vol. 84 (2013) pp. 87-103 (pdf)
Adaptation in temporally heterogeneous environments:
- S. Figueroa Iglesias and S. Mirrahimi, Selection and mutation in a shifting and fluctuating environment, Comm. Math. Sci., Vol. 19 (2021) pp. 1761-1798. (pdf)
- M. Costa, C. Etchegaray and S. Mirrahimi, Survival criterion for a population subject to selection and mutations; Application to temporally piecewise constant environments, Nonlinear Analysis: Real World Applications, Vol. 59 (2021) 103239. (pdf)
- S. Figueroa Iglesias and S. Mirrahimi, Long time evolutionary dynamics of phenotypically structured populations in time-periodic environments, SIAM J. Math. Anal., Vol. 50.5 (2018) pp. 5537-5568. (pdf)
- S. Mirrahimi, B. Perthame and P. E. Souganidis, Time fluctuations in a population model of adaptative dynamics, Annales de l'Institut Henri Poincare (C) Analyse Non Linéaire, Vol. 32.1, (2015) pp. 41-58. (pdf)
Adaptation in spatially heterogeneous environments:
- A. Léculier and S. Mirrahimi, Adaptation to a heterogeneous patchy environment with nonlocal
dispersion, Annales de l'Institut Henri Poincare (C) Analyse Non Linéaire, (2022). (pdf)
- S. Mirrahimi and S. Gandon, Evolution of specialization in heterogeneous environments:
equilibrium between selection, mutation and migration, Genetics, Vol. 214.2 (2020) pp. 479-491, https://doi.org/10.1534/genetics.119.302868.
(Main text)(Supplementary information)
- S. Mirrahimi, A Hamilton-Jacobi approach to characterize the evolutionary equilibria in heterogeneous environments, Mathematical Models and Methods in Applied Sciences, Vol. 27.13 (2017) pp. 2425-2460. (pdf)
- 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 - Mathematique, Vol. 355.2, (2016), pp. 155-160, (Online version) (pdf)
- S. Mirrahimi and B. Perthame, Asymptotic analysis of a selection model with space,
J. Math. Pures Appl., Vol. 104 (2015), pp. 1108-1118. (Online version) (pdf)
- H. Leman, S. Méléard and S. Mirrahimi, Influence of a spatial structure on the long time behavior of a competitive Lotka-Volterra type system, Discrete and Continuous Dynamical System - B (DCDS-B), Vol. 20.2 (2015) pp. 469-493. (pdf)
- E. Bouin and S. Mirrahimi, A Hamilton-Jacobi limit for a model of population stuctured by space and trait, Comm. Math. Sci., Vol. 13.6 (2015)
pp. 1431-1452. (pdf)
- S. Mirrahimi, Adaptation and migration of a population between patches, Discrete and Continuous Dynamical System - B (DCDS-B), Vol. 18.3, (2013) 753-768. (pdf)
Evolution of dispersal:
- V. Calvez, C. Henderson, S. Mirrahimi, O. Turanova and T. Dumont, Non-local competition slows down front acceleration during dispersal evolution, Ann. H. Lebesgue, Vol. 5 (2022) pp. 1-71. (pdf)
- E. Bouin, V. Calvez, N. Meunier, S. Mirrahimi, B. Perthame, G. Raoul, and R. Voituriez, Invasion fronts with variable motility: phenotype selection, spatial sorting and wave acceleration, Comptes rendus - Mathématique Vol. 350 (2012) pp. 761-766. (pdf)
Models with heavy-tailed diffusion:
- A. Léculier, J.-M. Roquejoffre, S. Mirrahimi, Propagation in a fractional reaction-diffusion equation in a
periodically hostile environment, J Dyn Diff Equat (2020), https://doi.org/10.1007/s10884-020-09837-4. (pdf)
- S. Mirrahimi, Singular limits for models of selection and mutations with heavy-tailed mutation distribution, J. Math. Pures Appl., Vol. 134 (2020) pp. 179-203 (pdf)
- S. Méléard and S. Mirrahimi, Singular limits for reaction-diffusion equations with fractional Laplacian and local or nonlocal nonlinearity, Communications in Partial Differential Equations, Vol. 40.5, (2015), pp. 957-993: (Online version) (pdf)
Interaction with resources:
- S. Mirrahimi, B. Perthame and J. Y. Wakano, Direct competition results from strong competition for limited resource , J. Math. biol., Vol. 68(4) (2014) pp. 931-949.
(pdf)
- S. Mirrahimi, B. Perthame and J. Y. Wakano, Evolution of species trait through resource competition, J. Math. biol., Vol. 64(7) (2012) pp. 1189
-1223 (pdf)
Other contributions:
- P. Degond, M. Herda and S. Mirrahimi, A Fokker-Planck approach to the study of robustness in gene expression, Mathematical Biosciences and Engineering, (2020) 17(6): 6459-6486.doi:10.3934/mbe.2020338. (pdf)
- S. Mirrahimi and P. E. Souganidis, A homogenization approach for the motion of motor proteins, Nonlin. Diff. Eq. Appl. (NoDEA), Vol. 20(1) (2013) pp. 129--147 (pdf)
Dissertations and book chapter