G. Barles, S. Mirrahimi, and B. Perthame, Concentration in Lotka-Volterra Parabolic or Integral Equations: A General Convergence Result, Methods and Applications of Analysis, vol.16, issue.3, pp.321-340, 2009.
DOI : 10.4310/MAA.2009.v16.n3.a4

URL : https://hal.archives-ouvertes.fr/hal-00391982

G. Barles and B. Perthame, Concentrations and constrained Hamilton-Jacobi equations arising in adaptive dynamics, Contemp. Math, vol.439, pp.57-68, 2007.
DOI : 10.1090/conm/439/08463

R. Bürger and I. M. Bomze, Stationary distributions under mutation-selection balance: structure and properties, Advances in Applied Probability, vol.28, issue.01, pp.227-251, 1996.
DOI : 10.1073/pnas.54.3.731

A. Calsina and S. Cuadrado, Small mutation rate and evolutionarily stable strategies in infinite dimensional adaptive dynamics, Journal of Mathematical Biology, vol.48, issue.2, pp.135-159, 2004.
DOI : 10.1007/s00285-003-0226-6

J. A. Carrillo, S. Cuadrado, and B. Perthame, Adaptive dynamics via Hamilton???Jacobi approach and entropy methods for a juvenile-adult model, Mathematical Biosciences, vol.205, issue.1, pp.137-161, 2007.
DOI : 10.1016/j.mbs.2006.09.012

N. Champagnat, A microscopic interpretation for adaptive dynamics trait substitution sequence models, Stochastic Processes and their Applications, vol.116, issue.8, pp.1127-1160, 2006.
DOI : 10.1016/j.spa.2006.01.004

URL : https://hal.archives-ouvertes.fr/hal-00015130

N. Champagnat, R. Ferrì-ere, and G. B. Arous, The Canonical Equation of Adaptive Dynamics: A Mathematical View, Selection, vol.2, issue.1-2, pp.71-81, 2001.
DOI : 10.1556/Select.2.2001.1-2.6

URL : https://hal.archives-ouvertes.fr/inria-00164767

N. Champagnat, R. Ferrì-ere, and S. Méléard, From individual stochastic processes to macroscopic models in adaptive evolution, Stoch. Models, pp.2-44, 2008.

N. Champagnat, P. Jabin, and G. , Convergence to equilibrium in competitive LotkaVolterra and chemostat systems, C. R. Math. Acad
URL : https://hal.archives-ouvertes.fr/inria-00495991

N. Champagnat and S. Méléard, Polymorphic evolution sequence and evolutionary branching, Probability Theory and Related Fields, vol.8, issue.3, 2010.
DOI : 10.1007/s00440-010-0292-9

URL : https://hal.archives-ouvertes.fr/inria-00345399

R. Cressman and J. Hofbauer, Measure dynamics on a one-dimensional continuous trait space: theoretical foundations for adaptive dynamics, Theoretical Population Biology, vol.67, issue.1, pp.47-59, 2005.
DOI : 10.1016/j.tpb.2004.08.001

L. Desvillettes, P. Jabin, S. Mischler, and G. , On selection dynamics for continuous structured populations, Communications in Mathematical Sciences, vol.6, issue.3, pp.729-747, 2008.
DOI : 10.4310/CMS.2008.v6.n3.a10

URL : https://hal.archives-ouvertes.fr/hal-00363138

U. Dieckmann and R. Law, The dynamical theory of coevolution: a derivation from stochastic ecological processes, Journal of Mathematical Biology, vol.39, issue.5-6, pp.579-612, 1996.
DOI : 10.1007/BF02409751

O. Diekmann, A beginner's guide to adaptive dynamics In Mathematical modelling of population dynamics, Polish Acad. Sci, vol.63, pp.47-86, 2004.

O. Diekmann, M. Gyllenberg, H. Huang, M. Kirkilionis, J. A. Metz et al., On the formulation and analysis of general deterministic structured population models, Journal of Mathematical Biology, vol.43, issue.2, pp.157-189, 2001.
DOI : 10.1007/s002850170002

O. Diekmann, P. E. Jabin, S. Mischler, and B. Perthame, The dynamics of adaptation: An illuminating example and a Hamilton???Jacobi approach, Theoretical Population Biology, vol.67, issue.4, pp.257-271, 2005.
DOI : 10.1016/j.tpb.2004.12.003

S. Genieys, N. Bessonov, and V. Volpert, Mathematical model of evolutionary branching, Mathematical and Computer Modelling, vol.49, issue.11-12, pp.11-12, 2009.
DOI : 10.1016/j.mcm.2008.07.018

S. A. Geritz, J. A. Metz, E. Kisdi, and G. Meszéna, Dynamics of Adaptation and Evolutionary Branching, Physical Review Letters, vol.78, issue.10, pp.2024-2027, 1997.
DOI : 10.1103/PhysRevLett.78.2024

S. A. Geritz, E. Kisdi, G. Meszéna, and J. A. Metz, Evolutionarily singular strategies and the adaptive growth and branching of the evolutionary tree, Evolutionary Ecology, vol.34, issue.1, pp.35-57, 1998.
DOI : 10.1023/A:1006554906681

J. Hofbauer and R. Sigmund, Adaptive dynamics and evolutionary stability, Applied Mathematics Letters, vol.3, issue.4, pp.75-79, 1990.
DOI : 10.1016/0893-9659(90)90051-C

P. E. Jabin and G. , Selection dynamics with competition. To appear, J. Math Biol

J. A. Metz, R. M. Nisbet, and S. A. Geritz, How should we define 'fitness' for general ecological scenarios? Trends in Ecology and Evolution, pp.198-202, 1992.

J. A. Metz, S. A. Geritz, G. Meszéna, F. A. Jacobs, and J. S. Van-heerwaarden, Adaptive Dynamics, a geometrical study of the consequences of nearly faithful reproduction, Stochastic and Spatial Structures of Dynamical Systems, pp.183-231, 1996.

]. S. Mirrahimi, G. Barles, B. Perthame, and P. E. Souganidis, A Singular Hamilton--Jacobi Equation Modeling the Tail Problem, SIAM Journal on Mathematical Analysis, vol.44, issue.6
DOI : 10.1137/100819527

B. Perthame and M. Gauduchon, Survival thresholds and mortality rates in adaptive dynamics: conciliating deterministic and stochastic simulations, Mathematical Medicine and Biology, vol.27, issue.3, 2009.
DOI : 10.1093/imammb/dqp018

URL : https://hal.archives-ouvertes.fr/hal-00755201

B. Perthame and S. Génieys, Concentration in the Nonlocal Fisher Equation: the Hamilton-Jacobi Limit, Mathematical Modelling of Natural Phenomena, vol.2, issue.4, pp.135-151, 2007.
DOI : 10.1051/mmnp:2008029

F. Yu, Stationary distributions of a model of sympatric speciation, The Annals of Applied Probability, vol.17, issue.3, pp.840-874, 2007.
DOI : 10.1214/105051606000000916