D. Aldous, Stopping Times and Tightness, The Annals of Probability, vol.6, issue.2, pp.335-340, 1978.
DOI : 10.1214/aop/1176995579
URL : http://projecteuclid.org/download/pdf_1/euclid.aop/1176995579

P. Billingsley, Convergence of Probability Measures, 1968.
DOI : 10.1002/9780470316962

N. Champagnat, A microscopic interpretation for adaptive dynamics trait substitution sequence models, Stochastic Processes and their Applications, vol.116, issue.8, 2006.
DOI : 10.1016/j.spa.2006.01.004
URL : https://hal.archives-ouvertes.fr/hal-00015130

N. Champagnat, R. Ferrì-ere, B. Arous, and G. , 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, Unifying evolutionary dynamics: From individual stochastic processes to macroscopic models, Theoretical Population Biology, vol.69, issue.3, pp.297-321, 2006.
DOI : 10.1016/j.tpb.2005.10.004
URL : https://hal.archives-ouvertes.fr/inria-00164784

J. F. Crow and M. Kimura, An Introduction to Population Genetics Theory, 1970.

U. Dieckmann and M. Doebeli, On the origin of species by sympatric speciation, Nature, vol.400, issue.6742, pp.354-357, 1999.
DOI : 10.1038/22521

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

U. Dieckmann and R. Law, Relaxation projections and the method of moments The Geometry of Ecological Interactions: Symplifying Spatial Complexity, pp.412-455, 2000.

R. Durrett and J. Schweinsberg, Approximating selective sweeps, Theoretical Population Biology, vol.66, issue.2, pp.129-138, 2004.
DOI : 10.1016/j.tpb.2004.04.002

A. Etheridge, P. Pfaffelhuber, and A. Wakolbinger, An approximate sampling formula under genetic hitchhiking, The Annals of Applied Probability, vol.16, issue.2, 2006.
DOI : 10.1214/105051606000000114
URL : http://arxiv.org/abs/math/0503485

S. N. Ethier and T. G. Kurtz, Markov Processes, Characterization And Convergence, 1986.

W. Feller, DIFFUSION PROCESSES IN GENETICS, Proc. Second Berkeley Symp. Math. Statist. Prob, pp.227-246, 1951.
DOI : 10.1007/978-3-319-16856-2_8

N. Fournier and S. Méléard, A microscopic probabilistic description of a locally regulated population and macroscopic approximations, The Annals of Applied Probability, vol.14, issue.4, pp.1880-1919, 2004.
DOI : 10.1214/105051604000000882

M. I. Freidlin, On the factorization of non-negative definite matrices. Theory Probab, Appl, vol.13, pp.354-356, 1968.

J. H. Gillespie, Population Genetics: A Concise Guide., Biometrics, vol.54, issue.4, 1998.
DOI : 10.2307/2533705

T. F. Hansen, Stabilizing Selection and the Comparative Analysis of Adaptation, Evolution, vol.51, issue.5, pp.1341-1351, 1997.
DOI : 10.2307/2411186

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
URL : http://doi.org/10.1016/0893-9659(90)90051-c

J. Jacod and A. N. Shiryaev, Limit Theorems for Stochastic Processes, 1987.
DOI : 10.1007/978-3-662-02514-7

M. Kimura, Diffusion models in population genetics, Journal of Applied Probability, vol.153, issue.02, pp.177-232, 1964.
DOI : 10.2307/2405451

M. Kimura, The neutral theory of molecular evolution, 1983.

M. Kimura, Population Genetics, Molecular Evolution, and the Neutral Theory, 1994.

E. Kisdi and M. Gyllenberg, Adaptive dynamics and the paradigm of diversity, Journal of Evolutionary Biology, vol.18, issue.5, pp.1170-1173, 2005.
DOI : 10.1111/j.1420-9101.2004.00852.x

A. Lambert, The branching process with logistic growth, The Annals of Applied Probability, vol.15, issue.2, pp.1506-1535, 2005.
DOI : 10.1214/105051605000000098

A. Lambert, Probability of fixation under weak selection: A branching process unifying approach, Theoretical Population Biology, vol.69, issue.4, pp.419-441, 2006.
DOI : 10.1016/j.tpb.2006.01.002
URL : https://hal.archives-ouvertes.fr/hal-00267511

R. Lande, Natural Selection and Random Genetic Drift in Phenotypic Evolution, Evolution, vol.30, issue.2, pp.314-334, 1976.
DOI : 10.2307/2407703

P. Marrow, R. Law, and C. Cannings, The Coevolution of Predator--Prey Interactions: ESSS and Red Queen Dynamics, Proceedings of the Royal Society B: Biological Sciences, vol.250, issue.1328, pp.133-141, 1992.
DOI : 10.1098/rspb.1992.0141

M. Smith, J. Haigh, and J. , The hitch-hiking effect of a favourable gene, Genetical Research, vol.19, issue.01, pp.23-35, 1974.
DOI : 10.1038/2191114a0

J. A. Metz, R. M. Nisbet, and S. A. Geritz, How should we define 'fitness' for general ecological scenarios ? Trends in Ecology and Evolution, 0202.

J. R. Norris, Markov Chains, 1997.
DOI : 10.1017/CBO9780511810633

H. G. Spencer and M. W. Feldman, Adaptive dynamics, game theory and evolutionary population genetics, Journal of Evolutionary Biology, vol.162, issue.5, pp.1191-1193, 2005.
DOI : 10.1111/j.1420-9101.2004.00842.x