L. Alio and R. Doney, Wiener - hopf factorization revisited and some applications, Stochastics An International Journal of Probability and Stochastic Processes, vol.66, issue.1, pp.87-102, 1999.
DOI : 10.1080/17442509908834187

V. I. Afanasyev, J. Geiger, . Goetz, V. A. Kersting, and . Vatutin, Criticality for branching processes in random environment, The Annals of Probability, vol.33, issue.2, pp.645-673, 2005.
DOI : 10.1214/009117904000000928

B. Krishna, S. Athreya, and . Karlin, Branching processes with random environments : 2 : limit theorems, The Annals of Mathematical Statistics, pp.1843-1858, 1971.

B. Krishna, S. Athreya, and . Karlin, On branching processes with random environments : I : Extinction probabilities, The Annals of, Mathematical Statistics, vol.42, issue.5, pp.1499-1520, 1971.

B. Krishna, . Athreya, E. Peter, and . Ney, Branching processes, 1972.

A. Marjorie and . Asmussen, The dynamics of interlocus associations in the three-locus hitchhiking model, Journal of mathematical biology, vol.24, issue.4, pp.361-380, 1986.

V. Bansaye, Proliferating parasites in dividing cells: Kimmel???s branching model revisited, The Annals of Applied Probability, vol.18, issue.3, pp.967-996, 2008.
DOI : 10.1214/07-AAP465

H. Nicholas and . Barton, The effect of hitch-hiking on neutral genealogies, Genetical Research, vol.72, issue.2, pp.123-133, 1998.

V. Bansaye and C. Böinghoff, Upper large deviations for branching processes in random environment with heavy tails, Electron, J. Probab, vol.16, pp.1900-1933, 2011.

[. Barton, . Etheridge, A. Kelleher, and . Veber, Genetic hitchhiking in spatially extended populations, Theoretical Population Biology, vol.87, pp.75-89, 2013.
DOI : 10.1016/j.tpb.2012.12.001

S. Billiard, R. Ferrière, S. Méléard, and V. Tran, Stochastic dynamics of adaptive trait and neutral marker driven by eco-evolutionary feedbacks, arXiv preprint arXiv :1310, p.6274, 2013.

[. Birkner, J. Geiger, and G. Kersting, Branching processes in random environment : a view on critical and subcritical cases, Interacting stochastic systems, pp.269-291, 2005.

C. Boeinghoff and M. Hutzenthaler, Branching diffusions in random environment, Markov Proc. Rel. Fields, pp.269-310, 2012.

M. John, . Braverman, R. Richard, . Hudson, L. Norman et al., The hitchhiking effect on the site frequency spectrum of dna polymorphisms, Genetics, vol.140, issue.2, pp.783-796, 1995.

I. Bienaymé, De la loi de multiplication et de la durée des familles, Soc. Philomat. Paris Extraits, Sér, vol.5, pp.37-39, 1845.

H. Nicholas and . Bingham, Continuous branching processes and spectral positivity, Stochastic Processes Appl, vol.4, issue.3, pp.217-242, 1976.

J. Bertoin and J. Gall, The Bolthausen-Sznitman coalescent and the genealogy of continuous-state branching processes, Probab. Theory Related Fields, vol.117, issue.2, pp.249-266, 2000.

[. Böinghoff, Limit theorems for strongly and intermediately supercritical branching processes in random environment with linear fractional offspring distributions, Stochastic Processes and their Applications, 2014.
DOI : 10.1016/j.spa.2014.05.009

M. Benjamin, . Bolker, W. Stephen, and . Pacala, Spatial moment equations for plant competition : understanding spatial strategies and the advantages of short dispersal, The American Naturalist, vol.153, issue.6, pp.575-602, 1999.

J. C. Vincent-bansaye, C. Pardo, and . Smadi, On the extinction of continuous state branching processes with catastrophes, Electron. J. Probab, vol.18, issue.106, pp.1-31, 2013.

J. Peter and . Brockwell, The extinction time of a birth, death and catastrophe process and of a related diffusion model, Adv. in Appl. Probab, vol.17, issue.2, pp.42-52, 1985.

D. Rowan, D. Barrett, and . Schluter, Adaptation from standing genetic variation, Trends in Ecology & Evolution, vol.23, issue.1, pp.38-44, 2008.

V. Bansaye and F. Simatos, On the scaling limits of galton watson processes in varying environment, arXiv preprint, 2011.

[. Brink-spalink and C. Smadi, Abstract, Advances in Applied Probability, vol.123, issue.01, 2015.
DOI : 10.1016/0040-5809(92)90045-U

[. Brink-spalink and A. Sturm, An approximate sampling distribuion for multiple neutral loci after a selective sweep, 2015.

V. Bansaye and V. Tran, Branching Feller diffusion for cell division with parasite infection, ALEA Lat, Am. J. Probab. Math. Stat, vol.8, pp.95-127, 2011.

J. Bertoin and M. Yor, Exponential functionals of L??vy processes, Probability Surveys, vol.2, issue.0, pp.191-212, 2005.
DOI : 10.1214/154957805100000122

S. Chevin and . Billiard, Hitchhiking Both Ways: Effect of Two Interfering Selective Sweeps on Linked Neutral Variation, Genetics, vol.180, issue.1, pp.301-316, 2008.
DOI : 10.1534/genetics.108.089706
URL : https://hal.archives-ouvertes.fr/hal-00305316

[. Champagnat, R. Ferrière, 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

[. Champagnat, P. Jabin, and S. Méléard, Adaptation in a stochastic multi-resources chemostat model, Journal de Math??matiques Pures et Appliqu??es, vol.101, issue.6, pp.755-788, 2014.
DOI : 10.1016/j.matpur.2013.10.003
URL : https://hal.archives-ouvertes.fr/hal-00784166

N. Champagnat and S. Méléard, Polymorphic evolution sequence and evolutionary branching, Probability Theory and Related Fields, pp.45-94, 2011.
DOI : 10.1007/s00440-010-0292-9
URL : http://arxiv.org/abs/0812.1655

P. Collet, S. Méléard, A. Johan, and . Metz, A rigorous model study of the adaptive dynamics of Mendelian diploids, Journal of Mathematical Biology, vol.60, issue.3, pp.1-39, 2011.
DOI : 10.1007/s00285-012-0562-5

C. Coron, S. Méléard, E. Porcher, and A. Robert, Quantifying the Mutational Meltdown in Diploid Populations, The American Naturalist, vol.181, issue.5, pp.623-636, 2013.
DOI : 10.1086/670022

C. Coron, Slow-fast stochastic diffusion dynamics and quasi-stationary distributions for diploid populations, arXiv preprint, 2013.

P. Carmona, F. Petit, and M. Yor, On the distribution and asymptotic results for exponential functionals of Lévy processes, Exponential functionals and principal values related to Brownian motion, Bibl. Rev. Mat. Iberoamericana, Rev. Mat. Iberoamericana, pp.73-130, 1997.

G. Coop and P. Ralph, Patterns of Neutral Diversity Under General Models of Selective Sweeps, Genetics, vol.192, issue.1, pp.205-224, 2012.
DOI : 10.1534/genetics.112.141861

[. Dekking, On the survival probability of a branching process in a finite state iid environment, Stochastic processes and their applications, pp.151-157, 1987.

E. Danchin, L. Giraldeau, and F. Cézilly, Behavioural ecology : An evolutionary perspective on behaviour, 2008.

J. D. Souza and B. Hambly, On the survival probability of a branching process in a random environment, Advances in Applied Probability, pp.38-55, 1997.

A. Ron, R. A. Doney, and . Maller, Stability and attraction to normality for Lévy processes at zero and at infinity, J. Theoret. Probab, vol.15, issue.3, pp.751-792, 2002.

M. Durinx, H. Metz, and G. Meszéna, Adaptive dynamics for physiologically structured population models, Journal of Mathematical Biology, vol.20, issue.041903, pp.673-742, 2008.
DOI : 10.1007/s00285-007-0134-2

A. Marcio, A. Diniz, and . Polpo, A simple proof for the multinomial version of the representation theorem, The Contribution of Young Researchers to Bayesian Statistics, pp.15-18, 2014.

R. Durrett and J. Schweinsberg, Approximating selective sweeps, Theoretical population biology 66, pp.129-138, 2004.
DOI : 10.1016/j.tpb.2004.04.002

. Dtr-+-10-]-eléonore-durand, I. Maud, C. Tenaillon, D. Ridel, P. Coubriche et al., Alain Charcosset, and Christineh Dillmann, Standing variation and new mutations both contribute to a fast response to selection for flowering time in maize inbreds, BMC evolutionary biology, vol.10, issue.1 2, 2010.

[. Durrett, Probability models for dna sequence evolution [DVS11] Elena Dyakonova, Vladimir Vatutin, and Serik Sagitov, Survival of branching processes in random environments, arXiv preprint arXiv :1110, p.6139, 2008.

E. B. Dynkin, Branching Particle Systems and Superprocesses, The Annals of Probability, vol.19, issue.3, pp.1157-1194, 1991.
DOI : 10.1214/aop/1176990339
URL : http://projecteuclid.org/download/pdf_1/euclid.aop/1176990339

A. Eriksson, P. Fernström, B. Mehlig, and S. Sagitov, An Accurate Model for Genetic Hitchhiking, Genetics, vol.178, issue.1, pp.439-451, 2008.
DOI : 10.1534/genetics.107.076018

T. [. Ethier and . Kurtz, Markov processes : characterization and convergence, 1986.
DOI : 10.1002/9780470316658

M. Éppel and '. , A local limit theorem for first passage time, Siberian Mathematical Journal, vol.15, issue.No. 3, pp.130-138, 1979.
DOI : 10.1007/BF00976138

A. Etheridge, P. Pfaffelhuber, and A. Wakolbinger, An approximate sampling formula under genetic hitchhiking, The Annals of Applied Probability, vol.16, issue.2, pp.685-729, 2006.
DOI : 10.1214/105051606000000114

W. Feller, An introduction to probability theory and its applications, 1971.

]. R. Fis30 and . Fisher, Genetical theory of natural selection, 1930.

Z. Fu and Z. Li, Stochastic equations of non-negative processes with jumps, Stochastic Processes and their Applications, pp.306-330, 2010.
DOI : 10.1016/j.spa.2009.11.005

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

C. Justin, C. Fay, and . Wu, Detecting hitchhiking from patterns of dna polymorphism , Selective Sweep, pp.65-77, 2005.

[. Galton, Problem 4001, p.17, 1873.

P. Guttorp, . Albertsen, E. Steffensen, and . Kristensen, Three papers on the history of branching processes, International statistical review, vol.63, issue.2, pp.233-245, 1995.

H. John and . Gillespie, Junk ain't what junk does : neutral alleles in a selected context, Gene, vol.205, issue.1, pp.291-299, 1997.

J. Geiger and G. Kersting, The Survival Probability of a Critical Branching Process in a Random Environment, Theory of Probability & Its Applications, vol.45, issue.3, pp.607-615, 2000.
DOI : 10.1137/S0040585X97978440

J. Geiger, G. Kersting, and V. A. Vatutin, Th??or??mes limites pour des processus de branchement sous-critiques en environnement al??atoire, Annales de l'Institut Henri Poincare (B) Probability and Statistics, vol.39, issue.4, pp.593-620, 2003.
DOI : 10.1016/S0246-0203(02)00020-1

Y. Guivarc-'h and Q. Liu, Propri??t??s asymptotiques des processus de branchement en environnement al??atoire, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.332, issue.4, pp.339-344, 2001.
DOI : 10.1016/S0764-4442(00)01783-3

A. Stefan, . Geritz, A. Johan, É. Metz, G. Kisdi et al., Dynamics of adaptation and evolutionary branching, Physical Review Letters, vol.78, issue.10, 1997.

R. David and . Grey, Asymptotic behaviour of continuous time, continuous state-space branching processes, J. Appl. Probability, vol.11, pp.669-677, 1974.

A. Grimvall, On the Convergence of Sequences of Branching Processes, The Annals of Probability, vol.2, issue.6, pp.1027-1045, 1974.
DOI : 10.1214/aop/1176996496

K. Hirano, Determination of the limiting coefficient for exponential functionals of random walks with positive drift, J. Math. Sci. Univ. Tokyo, vol.5, issue.2, pp.299-332, 1998.

J. Hermisson, S. Pleuni, and . Pennings, Soft Sweeps: Molecular Population Genetics of Adaptation From Standing Genetic Variation, Genetics, vol.169, issue.4, pp.2335-2352, 2005.
DOI : 10.1534/genetics.104.036947

J. Hermisson and P. Pfaffelhuber, The pattern of genetic hitchhiking under recurrent mutation, Electronic Journal of Probability, vol.13, issue.0, pp.2069-2106, 2008.
DOI : 10.1214/EJP.v13-577

J. Hofbauer and K. 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

[. Hutzenthaler, Supercritical branching diffusions in random environment, Electronic Communications in Probability, vol.16, issue.0, pp.781-791, 2011.
DOI : 10.1214/ECP.v16-1685

N. Ikeda and S. Watanabe, Stochastic differential equations and diffusion processes, 1989.

M. Jirina, Stochastic branching processes with continuous state space, Czechoslovak Math, J, vol.8, issue.83, pp.292-313, 1958.

N. Kaplan, A note on the supercritical branching processes with random environments, The Annals of Probability, pp.509-514, 1974.

G. David and . Kendall, Branching processes since 1873, Journal of the London Mathematical Society, vol.1, issue.1, pp.385-406, 1966.

L. Norman, . Kaplan, C. Hudson, and . Langley, The" hitchhiking effect" revisited, Genetics, vol.123, issue.4, pp.887-899, 1989.

Y. Kim and R. Nielsen, Linkage Disequilibrium as a Signature of Selective Sweeps, Genetics, vol.167, issue.3, pp.1513-1524, 2004.
DOI : 10.1534/genetics.103.025387

V. Mikhail and . Kozlov, On the asymptotic behavior of the probability of non-extinction for critical branching processes in a random environment, Theory of Probability and Its Applications, pp.791-804, 1976.

E. Andreas, J. Kyprianou, and . Pardo, Continuous-state branching processes and self-similarity, Journal of Applied Probability, pp.1140-1160, 2008.

Y. Kim and W. Stephan, Detecting a local signature of genetic hitchhiking along a recombining chromosome, Genetics, vol.160, issue.2, pp.765-777, 2002.

G. Thomas and . Kurtz, Diffusion approximations for branching processes, Branching processes (Conf., Saint Hippolyte, Que, pp.269-292, 1976.

A. E. Kyprianou, Introductory lectures on fluctuations of Lévy processes with applications, 2006.

J. Lamperti, Continuous state branching processes, Bulletin of the American Mathematical Society, vol.73, issue.3, pp.382-386, 1967.
DOI : 10.1090/S0002-9904-1967-11762-2

A. Lambert, Quasi-stationary distributions and the continuous-state branching process conditioned to be never extinct, Electron, J. Probab, vol.12, issue.14, pp.420-446, 2007.

]. R. Lan93 and . Lande, Risks of population extinction from demographic and environmental stochasticity and random catastrophes, American Naturalist, pp.911-927, 1993.

I. Gregory, D. Lang, . Botstein, M. Michael, and . Desai, Genetic variation and the fate of beneficial mutations in asexual populations, Genetics, vol.188, issue.3, pp.647-661, 2011.

R. Law and U. Dieckmann, Moment approximations of individual-based models, The geometry of ecological interactions : simplifying spatial complexity, pp.252-270, 2000.

[. Leocard, Selective sweep and the size of the hitchhiking set, Advances in Applied Probability, vol.175, issue.03, pp.731-764, 2009.
DOI : 10.1007/s00285-007-0085-7

[. Lande, S. Engen, and B. Saether, Stochastic population dynamics in ecology and conservation, 2003.
DOI : 10.1093/acprof:oso/9780198525257.001.0001

[. Li, Measure-valued branching markov processes, 2010.
DOI : 10.1007/978-3-642-15004-3

É. Le, P. , M. Peigné, R. , R. et al., A local limit theorem on the semi-direct product of, Inst. H. Poincaré Probab. Statist, vol.33, issue.2, pp.223-252, 1997.

I. Gregory, . Lang, P. Daniel, . Rice, J. Mark et al., Pervasive genetic hitchhiking and clonal interference in forty evolving yeast populations, Nature, vol.500, issue.7464, pp.571-574, 2013.

G. Mcvean, The Structure of Linkage Disequilibrium Around a Selective Sweep, Genetics, vol.175, issue.3, pp.1395-1406, 2007.
DOI : 10.1534/genetics.106.062828

A. Johan, . Metz, A. Stefan, G. Geritz, . Meszéna et al., Adaptive dynamics, a geometrical study of the consequences of nearly faithful reproduction, Stochastic and spatial structures of dynamical systems, pp.45-183, 1996.

W. Philipp, D. A. Messer, and . Petrov, Population genomics of rapid adaptation by soft selective sweeps, Trends in ecology & evolution 28, pp.659-669, 2013.

S. Méléard and D. Villemonais, Quasi-stationary distributions and population processes, Probability surveys, pp.340-410, 2012.

I. Nhh-+-07-]-rasmus-nielsen, M. Hellmann, C. Hubisz, . Bustamante, G. Andrew et al., Recent and ongoing selection in the human genome, Nature Reviews Genetics, vol.18, issue.11, pp.857-868, 2007.
DOI : 10.1038/nrg2187

C. Neuhauser, M. Stephen, and . Krone, The genealogy of samples in models with selection, Genetics, vol.145, issue.2, pp.519-534, 1997.

[. Orr and A. J. Betancourt, Haldane's sieve and adaptation from the standing genetic variation, Genetics, vol.157, issue.2, pp.875-884, 2001.

T. Ohta and M. Kimura, The effect of selected linked locus on heterozygosity of neutral alleles (the hitch-hiking effect), Genetical Research, vol.18, issue.03, pp.313-325, 1975.
DOI : 10.2307/2406613

M. Prezeworski, G. Coop, D. Jeffrey, and . Wall, THE SIGNATURE OF POSITIVE SELECTION ON STANDING GENETIC VARIATION, Evolution, vol.164, issue.11, pp.2312-2323, 2005.
DOI : 10.1016/S0169-5347(00)01994-7

S. Pleuni, J. Pennings, and . Hermisson, Soft sweeps ii-molecular population genetics of adaptation from recurrent mutation or migration, Molecular biology and evolution, vol.23, issue.5, pp.1076-1084, 2006.

M. Benjamin, E. Peter, R. Huerta-sanchez, and . Nielsen, Distinguishing between selective sweeps from standing variation and from a de novo mutation, PLoS genetics, vol.8, issue.10, 2012.

J. Parsch, C. D. Meiklejohn, L. Daniel, and . Hartl, Patterns of dna sequence variation suggest the recent action of positive selection in the janus-ocnus region of drosophila simulans, Genetics, vol.159, issue.2, pp.647-657, 2001.

M. Przeworski, The signature of positive selection at randomly chosen loci, Genetics, vol.160, issue.3, pp.1179-1189, 2002.

P. Pfaffelhuber and A. Studeny, Approximating genealogies for partially linked neutral loci under a selective sweep, Journal of Mathematical Biology, vol.41, issue.3, pp.299-330, 2007.
DOI : 10.1007/s00285-007-0085-7

O. Nicolas, . Rode, J. Eva, E. Lievens, A. Flaven et al., Roula Jabbour- Zahab, Marta I Sanchez, and Thomas Lenormand, Why join groups ? lessons from parasite-manipulated artemia, Ecology letters, 2013.

R. [. Schweinsberg and . Durrett, Random partitions approximating the coalescence of lineages during a selective sweep, The Annals of Applied Probability, vol.15, issue.3, pp.1591-1651, 2005.
DOI : 10.1214/105051605000000430

J. Maynard, S. , and J. Haigh, The hitch-hiking effect of a favourable gene, Genetical Research, vol.89, issue.5-6, pp.23-35, 1974.
DOI : 10.1017/S0016672308009579

L. Martin and . Silverstein, A new approach to local times, J. Math. Mech, vol.17, pp.1023-1054, 1967.

[. Slatkin, Linkage disequilibrium ??? understanding the evolutionary past and mapping the medical future, Nature Reviews Genetics, vol.29, issue.6, pp.477-485, 2008.
DOI : 10.1038/nrg2361

C. Smadi, An eco-evolutionary approach of adaptation and recombination in a large population of varying size, arXiv preprint arXiv :1402, p.4104, 2014.

C. Pardis, . Sabeti, E. David, . Reich, M. John et al., Detecting recent positive selection in the human genome from haplotype structure, Nature, vol.419, issue.6909, pp.832-837, 2002.

. Sabeti, . Sf-schaffner, . Fry, . Lohmueller, . Varilly et al., Positive Natural Selection in the Human Lineage, Science, vol.312, issue.5780, pp.312-1614, 2006.
DOI : 10.1126/science.1124309

[. Stephan, S. Yun, . Song, H. Charles, and . Langley, The Hitchhiking Effect on Linkage Disequilibrium Between Linked Neutral Loci, Genetics, vol.172, issue.4, pp.2647-2663, 2006.
DOI : 10.1534/genetics.105.050179

L. Walter, . Smith, E. William, and . Wilkinson, On branching processes in random environments, The Annals of Mathematical Statistics, pp.814-827, 1969.

W. Stephan, H. Thomas, . Wiehe, W. Marcus, and . Lenz, The effect of strongly selected substitutions on neutral polymorphism: Analytical results based on diffusion theory, Theoretical Population Biology, vol.41, issue.2, pp.237-254, 1992.
DOI : 10.1016/0040-5809(92)90045-U

[. Thomson and W. Klitz, Disequilibrium pattern analysis. i. theory, Genetics, vol.116, issue.4, pp.623-632, 1987.

B. Wallace, Hard and Soft Selection Revisited, Evolution, vol.29, issue.3, pp.465-473, 1975.
DOI : 10.2307/2407259

C. John, X. Wootton, . Feng, T. Michael, . Ferdig et al., Genetic diversity and chloroquine selective sweeps in plasmodium falciparum, Nature, vol.418, issue.6895, pp.320-323, 2002.

H. William-watson and F. Galton, On the Probability of the Extinction of Families., The Journal of the Anthropological Institute of Great Britain and Ireland, vol.4, pp.138-144, 1875.
DOI : 10.2307/2841222