F. Van-den-bosch and C. Gilligan, Models of Fungicide Resistance Dynamics, Annual Review of Phytopathology, vol.46, issue.1, pp.123-147, 2008.
DOI : 10.1146/annurev.phyto.011108.135838

R. Maclean, A. Hall, G. Perron, and A. Buckling, The population genetics of antibiotic resistance: integrating molecular mechanisms and treatment contexts, Nature Reviews Genetics, vol.55, issue.6, pp.405-414, 2010.
DOI : 10.1038/nrg2778

M. Lipsitch and B. Levin, The population dynamics of antimicrobial chemotherapy, Antimicrob Agents Ch, vol.41, pp.363-73, 1997.

U. Dieckmann, J. Metz, M. Sabelis, and S. K. , Adaptive Dynamics of Infectious Diseases: In Pursuit of Virulence Management. Cambridge Studies in Adaptive Dynamics, 2005.
DOI : 10.1017/CBO9780511525728

A. Hill, Vaccines against malaria, Philosophical Transactions of the Royal Society B: Biological Sciences, vol.6, issue.1, pp.2806-2814, 2011.
DOI : 10.4161/hv.6.1.9931

B. Bloom and C. Murray, Tuberculosis: Commentary on a Reemergent Killer, Science, vol.257, issue.5073, pp.1055-1064, 1992.
DOI : 10.1126/science.257.5073.1055

M. Boni, Vaccination and antigenic drift in influenza, Vaccine, vol.26, issue.3, pp.8-14, 2008.
DOI : 10.1016/j.vaccine.2008.04.011

C. Mundt, Probability of Mutation to Multiple Virulence and Durability of Resistance Gene Pyramids., Phytopathology, vol.80, issue.2, pp.221-223, 1990.
DOI : 10.1094/Phyto-80-221

P. Zur-wiesch, R. Kouyos, J. Engelstdter, R. Regoes, and S. Bonhoeffer, Population biological principles of drug-resistance evolution in infectious diseases, The Lancet Infectious Diseases, vol.11, issue.3, pp.236-247, 2011.
DOI : 10.1016/S1473-3099(10)70264-4

S. Bonhoeffer, M. Lipsitch, and B. Levin, Evaluating treatment protocols to prevent antibiotic resistance, Proceedings of the National Academy of Sciences, vol.94, issue.22, pp.12106-12111, 1997.
DOI : 10.1073/pnas.94.22.12106

F. Van-den-bosch and C. Gilligan, Measures of Durability of Resistance, Phytopathology, vol.93, issue.5, pp.616-641, 2003.
DOI : 10.1094/PHYTO.2003.93.5.616

S. Gandon and T. Day, The evolutionary epidemiology of vaccination, Journal of The Royal Society Interface, vol.17, issue.7-8, pp.803-817, 2007.
DOI : 10.1016/S0264-410X(98)00313-2

M. Castle and C. Gilligan, An Epidemiological Framework for Modelling Fungicide Dynamics and Control, PLoS ONE, vol.7, issue.8, p.40941, 2012.
DOI : 10.1371/journal.pone.0040941.t003

F. Débarre, T. Lenormand, and S. Gandon, Evolutionary Epidemiology of Drug-Resistance in Space, PLoS Computational Biology, vol.4, issue.4, p.1000337, 2009.
DOI : 10.1371/journal.pcbi.1000337.s001

F. Fabre, E. Rousseau, L. Mailleret, and B. Moury, Durable strategies to deploy plant resistance in agricultural landscapes, New Phytologist, vol.77, issue.4, pp.1064-1075, 2012.
DOI : 10.1111/j.1469-8137.2011.04019.x
URL : https://hal.archives-ouvertes.fr/hal-01019383

T. Day and S. Gandon, THE EVOLUTIONARY EPIDEMIOLOGY OF MULTILOCUS DRUG RESISTANCE, Evolution, vol.7, issue.5, pp.1582-97, 2012.
DOI : 10.1111/j.1558-5646.2011.01533.x

C. Bergstrom, M. Lo, and M. Lipsitch, From The Cover: Ecological theory suggests that antimicrobial cycling will not reduce antimicrobial resistance in hospitals, Proceedings of the National Academy of Sciences, vol.101, issue.36, pp.13285-13290, 2004.
DOI : 10.1073/pnas.0402298101

E. Massad, S. Lundberg, and H. Yang, Modeling and simulating the evolution of resistance against antibiotics, International Journal of Bio-Medical Computing, vol.33, issue.1, pp.65-81, 1993.
DOI : 10.1016/0020-7101(93)90060-J

R. Hermsen and T. Hwa, Sources and Sinks: A Stochastic Model of Evolution in Heterogeneous Environments, Physical Review Letters, vol.105, issue.24, p.248104, 2010.
DOI : 10.1103/PhysRevLett.105.248104

S. Rice and A. Papadopoulos, Evolution with Stochastic Fitness and Stochastic Migration, PLoS ONE, vol.54, issue.10, p.7130, 2009.
DOI : 10.1371/journal.pone.0007130.t001

O. Restif and B. Grenfell, Integrating life history and cross-immunity into the evolutionary dynamics of pathogens, Proceedings of the Royal Society B: Biological Sciences, vol.39, issue.12, pp.409-416, 2006.
DOI : 10.1128/JCM.39.12.4396-4403.2001

D. Agata, E. Magal, P. Olivier, D. Ruan, S. Webb et al., Modeling antibiotic resistance in hospitals: The impact of minimizing treatment duration, J Theor Biol, vol.249, pp.487-499, 2007.

G. Reuter, Competition processes. Univ. California Press, II of Proc. 4th Berkeley Sympos. Math. Statist. and Prob, pp.421-430, 1961.

P. Phillips, Epistasis ??? the essential role of gene interactions in the structure and evolution of genetic systems, Nature Reviews Genetics, vol.1, issue.11, pp.855-867, 2008.
DOI : 10.1038/nrg2452

S. Trindade, A. Sousa, K. Xavier, F. Dionisio, and M. Ferreira, Positive Epistasis Drives the Acquisition of Multidrug Resistance, PLoS Genetics, vol.9, issue.7, p.1000578, 2009.
DOI : 10.1371/journal.pgen.1000578.s005

L. Allen, An Introduction to Stochastic Processes with Biology Applications, 2003.

R. Bourget, Modélisation stochastique des processus d'adaptation d'une population de pathogène aux rsistances génétiques des hôtes, 2013.

D. Gillespie, Exact stochastic simulation of coupled chemical reactions, The Journal of Physical Chemistry, vol.81, issue.25, pp.2340-2361, 1977.
DOI : 10.1021/j100540a008

S. Ethier and T. Kurtz, Markov processes: characterization and convergence. Wiley series in probability and statistics, 2005.
DOI : 10.1002/9780470316658

A. Novozhilov, G. Karev, and E. Koonin, Biological applications of the theory of birth-and-death processes, Briefings in Bioinformatics, vol.7, issue.1, pp.70-85, 2006.
DOI : 10.1093/bib/bbk006

R. Bourget, L. Chaumont, and N. Sapoukhina, Exponentiality of First Passage Times of Continuous Time Markov Chains, Acta Applicandae Mathematicae, vol.72, issue.1, 2012.
DOI : 10.1007/s10440-013-9854-z
URL : https://hal.archives-ouvertes.fr/hal-01209975

N. Sapoukhina, C. Durel, L. Cam, and B. , Spatial deployment of gene-for-gene resistance governs evolution and spread of pathogen populations, Theoretical Ecology, vol.406, issue.4, pp.229-238, 2009.
DOI : 10.1007/s12080-009-0045-5

A. Handel, R. Regoes, and R. Antia, The Role of Compensatory Mutations in the Emergence of Drug Resistance, PLoS Computational Biology, vol.156, issue.10, p.137, 2006.
DOI : 0016-6731(2000)156[1471:CEIREC]2.0.CO;2

T. Rhodes, O. Nikolaitchik, J. Chen, D. Powell, and W. Hu, Genetic Recombination of Human Immunodeficiency Virus Type 1 in One Round of Viral Replication: Effects of Genetic Distance, Target Cells, Accessory Genes, and Lack of High Negative Interference in Crossover Events, Journal of Virology, vol.79, issue.3, pp.1666-1677, 2005.
DOI : 10.1128/JVI.79.3.1666-1677.2005

Y. Collingham and B. Huntley, IMPACTS OF HABITAT FRAGMENTATION AND PATCH SIZE UPON MIGRATION RATES, Ecological Applications, vol.10, issue.1, pp.131-144, 2000.
DOI : 10.2307/3545811

W. Otten, D. Bailey, and C. Gilligan, Empirical evidence of spatial thresholds to control invasion of fungal parasites and saprotrophs, New Phytologist, vol.83, issue.1, pp.125-132, 2004.
DOI : 10.1038/35021046

A. Ohtsuki and A. Sasaki, Epidemiology and disease-control under gene-for-gene plant???pathogen interaction, Journal of Theoretical Biology, vol.238, issue.4, pp.780-794, 2006.
DOI : 10.1016/j.jtbi.2005.06.030

S. Suzuki and A. Sasaki, How does the resistance threshold in spatially explicit epidemic dynamics depend on the basic reproductive ratio and spatial correlation of crop genotypes?, Journal of Theoretical Biology, vol.276, issue.1, pp.117-125, 2011.
DOI : 10.1016/j.jtbi.2011.02.002

A. Scherer and A. Mclean, Mathematical models of vaccination, British Medical Bulletin, vol.62, issue.1, pp.187-199, 2002.
DOI : 10.1093/bmb/62.1.187

M. Michea-hamzehpour, J. Pechere, B. Marchou, and R. Auckenthaler, Combination therapy: a way to limit emergence of resistance?, The American Journal of Medicine, vol.80, issue.6, pp.138-142, 1986.
DOI : 10.1016/0002-9343(86)90491-2

N. Anderson, P. Martin, and R. Jarrett, Mixtures of anthelmintics: A strategy against resistance, Australian Veterinary Journal, vol.63, issue.2, pp.62-64, 1988.
DOI : 10.1071/AR9721113

J. Hooper, D. Custer, C. Schmaljohn, and A. Schmaljohn, DNA Vaccination with Vaccinia Virus L1R and A33R Genes Protects Mice against a Lethal Poxvirus Challenge, Virology, vol.266, issue.2, pp.329-339, 2000.
DOI : 10.1006/viro.1999.0096
URL : http://doi.org/10.1006/viro.1999.0096

J. Kelly, P. Gepts, P. Miklas, and D. Coyne, Tagging and mapping of genes and QTL and molecular marker-assisted selection for traits of economic importance in bean and cowpea, Field Crops Research, vol.82, issue.2-3, pp.135-154, 2003.
DOI : 10.1016/S0378-4290(03)00034-0

R. Michelmore and J. Wong, Classical and molecular genetics of Bremia lactucae, cause of lettuce downy mildew, European Journal of Plant Pathology, vol.71, issue.1, pp.19-30, 2008.
DOI : 10.1007/s10658-008-9305-2

Y. Carriére and B. Tabashnik, Reversing insect adaptation to transgenic insecticidal plants, Proceedings of the Royal Society B: Biological Sciences, vol.268, issue.1475, pp.1475-1480, 2001.
DOI : 10.1098/rspb.2001.1689

E. Berkhoff, E. De-wit, M. Geelhoed-mieras, A. Boon, and J. Symons, Fitness costs limit escape from cytotoxic T lymphocytes by influenza A viruses, Vaccine, vol.24, issue.44-46, pp.6594-6596, 2006.
DOI : 10.1016/j.vaccine.2006.05.051

F. Fabre, C. Bruchou, A. Palloix, and B. Moury, Key determinants of resistance durability to plant viruses: Insights from a model linking within- and between-host dynamics, Virus Research, vol.141, issue.2, pp.140-149, 2009.
DOI : 10.1016/j.virusres.2008.11.021

C. Lannou and C. Mundt, Evolution of a pathogen population in host mixtures: rate of emergence of complex races, TAG Theoretical and Applied Genetics, vol.94, issue.8, pp.991-999, 1997.
DOI : 10.1007/s001220050506

J. Cuevas, A. Moya, and R. Sanjuán, Following the very initial growth of biological RNA viral clones, Journal of General Virology, vol.86, issue.2, pp.435-443, 2005.
DOI : 10.1099/vir.0.80359-0

V. Ayme, S. Souche, C. Caranta, M. Jacquemond, and J. Chadoeuf, Different mutations in the genome-linked protein vpg of potato virus y confer virulence on the pvr2 3 resistance, 2006.

P. Carrasco, J. Dars, P. Agudelo-romero, and E. S. , A real-time RT-PCR assay for quantifying the fitness of tobacco etch virus in competition experiments, Journal of Virological Methods, vol.139, issue.2, pp.181-188, 2007.
DOI : 10.1016/j.jviromet.2006.09.020

P. Labbé, N. Sidos, R. M. Lenormand, and T. , Resistance Gene Replacement in the Mosquito Culex pipiens: Fitness Estimation From Long-Term Cline Series, Genetics, vol.182, issue.1, pp.303-312, 2009.
DOI : 10.1534/genetics.109.101444

M. Kimura, Evolutionary Rate at the Molecular Level, Nature, vol.16, issue.5129, pp.624-626, 1968.
DOI : 10.1038/217624a0

R. Sanjuán, M. Nebot, N. Chirico, L. Mansky, and R. Belshaw, Viral Mutation Rates, Journal of Virology, vol.84, issue.19, pp.9733-9748, 2010.
DOI : 10.1128/JVI.00694-10