2 6
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Probab. 31, 1002–1026, 1999.
[22] J.R. Chazottes, P. Collet, S. Méléard. Sharp asymptotics for the quasi-stationary
distribution of birth-and-death processes. Probab. Theory and Rel. Fields, 2015.
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[24] P. Collet, S. Méléard, J.A.J. Metz. A rigorous model study of the adaptative dynamics
of Mendelian diploids. J. Math. Biol. Volume 67, Issue 3, Page 569–607, 2013.
[25] F. Comets, T. Meyre. Calcul stochastique et modèles de diffusion. Dunod, 2006.
[26] C. Coron, S. Méléard, E. Porcher, A. Robert. Quantifying the mutational meltdown
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[27] C. Coron. Stochastic modeling of density-dependent diploid populations and extinction vortex. Adv. Appl. Prob. 46, 446–477, 2014.
[28] C. Coron. Slow-fast stochastic diffusion dynamics and quasi-stationary distributions
for diploid populations. J. Math. Biol., 2015.
[29] J. N. Darroch and E. Seneta. On quasi-stationary distributions in absorbing discretetime finite Markov chains. J. Appl. Prob., Volume 2 (1965), pages 88–100.
[30] J.F. Delmas, B. Jourdain. Modèles aléatoires : applications aux sciences de l’ingénieur
et du vivant. Springer, 2006.
[31] R. Durrett. Probability Models for DNA Sequence Evolution, 2nde édition. Springer,
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[32] S.N. Ethier, T.G. Kurtz. Markov Processes, Characterization and Convergence.
Springer, 1986.
[33] S.N. Evans, A. Hening, S.J. Schreiber. Protected polymorphisms and evolutionary
stability of patch-selection strategies in stochastic environments. J. Math. Biol., 2015.
[34] W.J. Ewens. Mathematical Population Genetics. Second Edition. Springer, 2004.
[35] W. Feller. An introduction to Probability Theory and its Applications, 2 Vol. Wiley,
1957.
[36] C. Graham. Chaînes de Markov, Dunod, 2008.
[37] P. Haccou, P. Jagers, V.A. Vatutin. Branching Processes : Variation, growth and
extinction of populations. Cambridge University Press, 2005.
6
BIBLIOGRAPHIE
[18] N. Champagnat, R. Ferrière, S. Méléard. Unifying evolutionary dynamics : from
individual stochastic processes to macroscopic models. Theoret. Popul. Biol. 69 297–
321, 2006.
[19] N. Champagnat. A microscopic interpretation for adaptive dynamics trait substitution sequence models. Stoch. Proc. Appl. 116, 1127–1160 (2006).
[20] N. Champagnat, S. Méléard. Invasion and adaptive evolution for individual-based
spatially structured populations. J. Math. Biol. 55, no. 2, 147–188, 2007.
[21] J.T. Chang. Recent common ancestors of all present-day individuals. Adv. Appl.
Probab. 31, 1002–1026, 1999.
[22] J.R. Chazottes, P. Collet, S. Méléard. Sharp asymptotics for the quasi-stationary
distribution of birth-and-death processes. Probab. Theory and Rel. Fields, 2015.
[23] P. Collet, S. Martinez, J. San Martin. Quasi-Stationary Distributions : Markov
Chains, Diffusions and Dynamical Systems. Probability and Its Applications, Springer, 2013.
[24] P. Collet, S. Méléard, J.A.J. Metz. A rigorous model study of the adaptative dynamics
of Mendelian diploids. J. Math. Biol. Volume 67, Issue 3, Page 569–607, 2013.
[25] F. Comets, T. Meyre. Calcul stochastique et modèles de diffusion. Dunod, 2006.
[26] C. Coron, S. Méléard, E. Porcher, A. Robert. Quantifying the mutational meltdown
in diploid populations. Am. Nat. 181(5) : 623–636, 2013.
[27] C. Coron. Stochastic modeling of density-dependent diploid populations and extinction vortex. Adv. Appl. Prob. 46, 446–477, 2014.
[28] C. Coron. Slow-fast stochastic diffusion dynamics and quasi-stationary distributions
for diploid populations. J. Math. Biol., 2015.
[29] J. N. Darroch and E. Seneta. On quasi-stationary distributions in absorbing discretetime finite Markov chains. J. Appl. Prob., Volume 2 (1965), pages 88–100.
[30] J.F. Delmas, B. Jourdain. Modèles aléatoires : applications aux sciences de l’ingénieur
et du vivant. Springer, 2006.
[31] R. Durrett. Probability Models for DNA Sequence Evolution, 2nde édition. Springer,
2007.
[32] S.N. Ethier, T.G. Kurtz. Markov Processes, Characterization and Convergence.
Springer, 1986.
[33] S.N. Evans, A. Hening, S.J. Schreiber. Protected polymorphisms and evolutionary
stability of patch-selection strategies in stochastic environments. J. Math. Biol., 2015.
[34] W.J. Ewens. Mathematical Population Genetics. Second Edition. Springer, 2004.
[35] W. Feller. An introduction to Probability Theory and its Applications, 2 Vol. Wiley,
1957.
[36] C. Graham. Chaînes de Markov, Dunod, 2008.
[37] P. Haccou, P. Jagers, V.A. Vatutin. Branching Processes : Variation, growth and
extinction of populations. Cambridge University Press, 2005.
6