M. Alfaro and R. Carles, Replicator-mutator equations with quadratic fitness, Proc. Amer. Math. Soc, vol.145, pp.5315-5327, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01399269

M. Alfaro, J. Coville, and G. Raoul, Bistable travelling waves for nonlocal reaction diffusion equations, Disc. Cont. Dyn. Systems A, vol.34, pp.1775-1791, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00800918

M. Alfaro and M. Veruete, Evolutionary branching via replicator-mutator equations, J. Dyn. Diff. Equations, 2019.
URL : https://hal.archives-ouvertes.fr/hal-01699053

D. G. Aronson and P. Besala, Parabolic equations with unbounded coefficients, J. Diff. Equations, vol.3, pp.1-14, 1967.

E. Baake, A. G. Casanova, S. Probst, and A. Wakolbinger, Modelling and simulating Lenski's long-term evolution experiment, Theor. Popul. Biology, 2019.

H. Berestycki, G. Nadin, B. Perthame, and L. Ryzhik, The non-local Fisher-KPP equation: travelling waves and steady states, Nonlinearity, vol.22, pp.2813-2844, 2009.

A. G. Casanova, N. Kurt, A. Wakolbinger, and L. Yuan, An individual-based model for the Lenski experiment, and the deceleration of the relative fitness, Stoch. Processes Appl, vol.126, pp.2211-2252, 2016.

N. Champagnat, R. Ferrì-ere, and S. Méléard, Unifying evolutionary dynamics: from individual stochastic processes to macroscopic models, Theor. Popul. Biology, vol.69, pp.297-321, 2006.
URL : https://hal.archives-ouvertes.fr/inria-00164784

V. A. De-crécy-lagard, J. Bellalou, R. Mutzel, and P. Marlì, Long term adaptation of a microbial population to a permanent metabolic constraint: overcoming thymineless death by experimental evolution of Escherichia coli, BMC Biotechnology, vol.1, p.10, 2001.

S. Elena and R. Sanjuán, Climb every mountain?, Science, vol.302, pp.2074-2075, 2003.

J. Fang and X. Zhao, Monotone wavefronts of the nonlocal Fisher-KPP equation, Nonlinearity, vol.24, pp.3043-3054, 2011.

G. Faye and M. Holzer, Modulated traveling fronts for a nonlocal Fisher-KPP equation: a dynamical systems approach, J. Diff. Equations, vol.258, pp.2257-2289, 2015.

S. S. Fong and B. Ø. Palsson, Metabolic gene-deletion strains of Escherichia coli evolve to computationally predicted growth phenotypes, Nature Genetics, vol.36, p.1056, 2004.

A. Friedman, Partial Differential Equations of Parabolic Type, 1964.

S. Genieys, V. Volpert, and V. Auger, Pattern and waves for a model in population dynamics with nonlocal consumption of resources, Math. Model. Nat. Phenom, vol.1, pp.63-80, 2006.

P. J. Gerrish and P. D. Sniegowski, Real time forecasting of near-future evolution, J. Royal Soc. Interface, vol.9, pp.2268-2278, 2012.

M. Gil, F. Hamel, G. Martin, and L. Roques, Mathematical properties of a class of integro-differential models from population genetics, SIAM J. Appl. Math, vol.77, pp.1536-1561, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01406163

M. Gil, F. Hamel, G. Martin, and L. Roques, Dynamics of fitness distributions in the presence of a phenotypic optimum: an integro-differential approach, Nonlinearity, 2019.
URL : https://hal.archives-ouvertes.fr/hal-01803741

B. H. Good and M. M. Desai, The impact of macroscopic epistasis on long-term evolutionary dynamics, Genetics, vol.85, pp.177-190, 2015.

S. A. Gourley, Travelling front solutions of a nonlocal Fisher equation, J. Math. Biol, vol.41, pp.272-284, 2000.

F. Hamel and L. Ryzhik, On the nonlocal Fisher-KPP equation: steady states, spreading speed and global bounds, Nonlinearity, vol.27, pp.2735-2753, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00843279

T. Johnson, The approach to mutation-selection balance in an infinite asexual population, and the evolution of mutation rates, Proc. Royal Soc. B: Biol. Sciences, vol.266, pp.2389-2397, 1999.

S. Kryazhimskiy, G. Tka?ik, and J. B. Plotkin, The dynamics of adaptation on correlated fitness landscapes, Proc. Nat. Acad, vol.106, pp.18638-18643, 2009.

R. A. Lacroix, .. E. Sandberg, E. J. O'brien, J. Utrilla, A. Ebrahim et al., Use of adaptive laboratory evolution to discover key mutations enabling rapid growth of Escherichia coli K-12 MG1655 on glucose minimal medium, Appl. Environmental Microbiology, vol.81, pp.17-30, 2015.

R. E. Lenski, M. R. Rose, S. C. Simpson, and S. C. Tadler, Experimental evolution in Escherichia coli. I. Adaptation and divergence during 2,000 generations, The American Naturalist, vol.138, pp.1315-1341, 1991.
URL : https://hal.archives-ouvertes.fr/hal-00171694

R. E. Lenski and M. Travisano, Dynamics of adaptation and diversification: a 10,000-generation experiment with bacterial populations, Proc. Nat. Acad, vol.91, pp.6808-6814, 1994.

A. Lunardi, Schauder theorems for linear elliptic and parabolic problems with unbounded coefficients in R n, Studia Math, vol.128, pp.171-198, 1998.

G. Martin, Fisher's geometrical model emerges as a property of complex integrated phenotypic networks, Genetics, vol.197, pp.237-255, 2014.

G. Martin, S. F. Elena, and T. Lenormand, Distributions of epistasis in microbes fit predictions from a fitness landscape model, Nature Genetics, vol.39, p.555, 2007.
URL : https://hal.archives-ouvertes.fr/halsde-00353548

G. Martin and T. Lenormand, A general multivariate extension of Fisher's geometrical model and the distribution of mutation fitness effects across species, Evolution, vol.60, pp.893-907, 2006.

G. Martin and T. Lenormand, The fitness effect of mutations across environments: Fisher's geometrical model with multiple optima, Evolution, vol.69, pp.1433-1447, 2015.

G. Martin and L. Roques, The non-stationary dynamics of fitness distributions: Asexual model with epistasis and standing variation, Genetics, vol.204, pp.1541-1558, 2016.

D. M. Mccandlish and A. Stoltzfus, Modeling evolution using the probability of fixation: history and implications, Quart. Rev. Biology, vol.89, pp.225-252, 2014.

I. S. Novella, E. A. Duarte, S. F. Elena, A. Moya, E. Domingo et al., Exponential increases of RNA virus fitness during large population transmissions, Proc. Nat. Acad, vol.92, pp.5841-5844, 1995.

L. Perfeito, A. Sousa, T. Bataillon, and I. Gordo, Rates of fitness decline and rebound suggest pervasive epistasis, Evolution, vol.68, pp.150-162, 2014.

M. H. Protter and H. F. Weinberger, Maximum Principles in Differential Equations, 1967.

L. Roques, Modèles de réaction-diffusion pour l'´ ecologie spatiale (Editions Quae, 2013.

F. Rosenzweig and G. Sherlock-;-v-vi, Experimental evolution: prospects and challenges, Genomics, vol.104, 2014.

S. Schoustra, S. Hwang, J. Krug, and J. A. Visser, Diminishing-returns epistasis among random beneficial mutations in a multicellular fungus, Proc. Royal Soc. B: Biol. Sciences, vol.283, pp.2016-1376, 2016.

P. D. Sniegowski and P. J. Gerrish, Beneficial mutations and the dynamics of adaptation in asexual populations, Phil. Trans. Royal Soc. B: Biol. Sciences, vol.365, pp.1255-1263, 2010.

O. Tenaillon, The utility of Fisher's geometric model in evolutionary genetics, Annual Rev. Ecology, Evolution, Systematics, vol.45, pp.179-201, 2014.

L. S. Tsimring, H. Levine, and D. A. Kessler, RNA virus evolution via a fitness-space model, Phys. Rev. Lett, vol.76, pp.4440-4443, 1996.

P. Turchin, Quantitative Analysis of Movement: Measuring and Modeling Population Redistribution in Animals and Plants, 1998.

D. Waxman and J. R. Peck, Pleiotropy and the preservation of perfection, Science, vol.279, pp.1210-1213, 1998.

M. J. Wiser, N. Ribeck, and R. E. Lenski, Long-term dynamics of adaptation in asexual populations, Science, p.1243357, 2013.

A. L. Yakymiv, A generalization of the Curtiss theorem for moment generating functions, Math. Notes, vol.90, pp.920-924, 2011.