G. Ainsworth, Introduction to the History of Plant Pathology, 1981.

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

D. Andrivon, F. Pilet, J. Montarry, M. Hafidi, R. Corbire et al., to Partial Resistance in Potato: Evidence from French and Moroccan Populations, Phytopathology, vol.97, issue.3, pp.338-381, 2007.
DOI : 10.1094/PHYTO-97-3-0338

G. Azzimonti, Diversification de la résistance quantitative la rouille brune du blé, ` a partir de la caractérisation des composantes de la résistance

G. Azzimonti, C. Lannou, I. Sache, and H. Goyeau, Components of quantitative resistance to leaf rust in wheat cultivars: diversity, variability and specificity, Plant Pathology, vol.162, issue.5, 2013.
DOI : 10.1111/ppa.12029
URL : https://hal.archives-ouvertes.fr/hal-01003394

N. Barton, Linkage and the limits to natural selection, Genetics, vol.140, pp.821-862, 1995.

F. Berg, C. Lannou, C. Gilligan, and F. Bosch, Quantitative resistance can lead to evolutionary changes in traits not targeted by the resistance QTLs, Evolutionary Applications, 2013.

R. Bourget, L. Chaumont, and N. Sapoukhina, Timing of Pathogen Adaptation to a Multicomponent Treatment, PLoS ONE, vol.84, issue.8, 2013.
DOI : 10.1371/journal.pone.0071926.s002
URL : https://hal.archives-ouvertes.fr/hal-00700540

H. Brun, A. Chvre, B. Fitt, S. Powers, A. Besnard et al., Quantitative resistance increases the durability of qualitative resistance to Leptosphaeria maculans in Brassica napus, New Phytologist, vol.50, issue.1, pp.285-299, 2010.
DOI : 10.1111/j.1469-8137.2009.03049.x

V. Caffier, P. Lasserre-zuber, M. Giraud, M. Lascostes, R. Stievenard et al., Erosion of quantitative host resistance in the apple??Venturia inaequalis pathosystem, Infection, Genetics and Evolution, vol.27, 2014.
DOI : 10.1016/j.meegid.2014.02.003
URL : https://hal.archives-ouvertes.fr/hal-01210000

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

C. Cowger and C. Mundt, Isolates from Susceptible and Partially Resistant Wheat Cultivars, Phytopathology, vol.92, issue.6, pp.624-630, 2002.
DOI : 10.1094/PHYTO.2002.92.6.624

J. Dangl and J. Jones, Plant pathogens and integrated defence responses to infection, Nature, vol.411, issue.6839, pp.826-833, 2001.
DOI : 10.1038/35081161

D. Ebert, Experimental Evolution of Parasites, Science, vol.282, issue.5393, pp.1432-1436, 1998.
DOI : 10.1126/science.282.5393.1432

H. Flor, Current Status of the Gene-For-Gene Concept, Annual Review of Phytopathology, vol.9, issue.1, pp.275-296, 1971.
DOI : 10.1146/annurev.py.09.090171.001423

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

S. Gandon, M. Mackinnon, S. Nee, and A. Read, Imperfect vaccines and the evolution of pathogen virulence, Nature, vol.414, issue.6865, pp.751-756, 2001.
DOI : 10.1038/414751a

S. Gandon and Y. Michalakis, Evolution of parasite virulence against qualitative or quantitative host resistance, Proceedings of the Royal Society of London. Series B, pp.985-990, 2000.
DOI : 10.1098/rspb.2000.1100

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

A. Hoffmann and C. Sgro, Climate change and evolutionary adaptation, Nature, vol.120, issue.7335, pp.479-485, 2011.
DOI : 10.1038/nature09670

G. Iacono, F. Van-den-bosch, and N. Paveley, The evolution of plant pathogens in response to host resistance: Factors affecting the gain from deployment of qualitative and quantitative resistance, Journal of Theoretical Biology, vol.304, pp.152-163, 2012.
DOI : 10.1016/j.jtbi.2012.03.033

C. Lannou, Variation and Selection of Quantitative Traits in Plant Pathogens, Annual Review of Phytopathology, vol.50, issue.1, pp.319-338
DOI : 10.1146/annurev-phyto-081211-173031
URL : https://hal.archives-ouvertes.fr/hal-01019819

J. Lehman and G. Shaner, Genetic variation in latent period among isolates of Puccinia recondita f. sp. tritici on partially resistant wheat cultivars, pp.633-641, 1996.

G. Martin and T. Lenormand, THE FITNESS EFFECT OF MUTATIONS ACROSS ENVIRONMENTS: A SURVEY IN LIGHT OF FITNESS LANDSCAPE MODELS, Evolution, vol.157, issue.12, pp.2413-2440, 2006.
DOI : 10.1534/genetics.104.030031
URL : https://hal.archives-ouvertes.fr/halsde-00353457

E. Massad, F. Coutinho, M. Burattini, L. Lopez, and C. Struchiner, The impact of imperfect vaccines on the evolution of HIV virulence, Medical Hypotheses, vol.66, issue.5, pp.907-911, 2006.
DOI : 10.1016/j.mehy.2005.11.042

D. Metzgar and C. Wills, Evolutionary changes in mutation rates and spectra and their influence onthe adaptation of pathogens, Microbes and Infection, vol.2, issue.12, pp.1513-1522, 2000.
DOI : 10.1016/S1286-4579(00)01306-X

C. Mundt, C. Cowger, and K. Garrett, Relevance of integrated disease management to resistance durability, Euphytica, vol.124, issue.2, pp.245-252, 2002.
DOI : 10.1023/A:1015642819151

M. Nair and P. Pollett, On the relationship between µ-invariant measures and quasistationary distributions for continuous-time Markov chains, Advances in Applied Probability, vol.25, issue.1, pp.82-102, 1993.

I. Novella, E. Duarte, S. Elena, A. Moya, E. Domingo et al., Exponential increases of RNA virus fitness during large population transmissions., Proceedings of the National Academy of Sciences, vol.92, issue.13, pp.5841-5844, 1995.
DOI : 10.1073/pnas.92.13.5841

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

S. Otto and T. Day, A Biologist's Guide to Mathematical Modeling in Ecology and Evolution, 2007.

A. Palloix, V. Ayme, and B. Moury, Durability of plant major resistance genes to pathogens depends on the genetic background, experimental evidence and consequences for breeding strategies, New Phytologist, vol.34, issue.1, pp.190-199, 2009.
DOI : 10.1111/j.1469-8137.2009.02827.x

B. Pariaud, V. Ravign, F. Halkett, H. Goyeau, J. Carlier et al., Aggressiveness and its role in the adaptation of plant pathogens, Plant Pathology, vol.15, issue.3, pp.409-424, 2009.
DOI : 10.1111/j.1365-3059.2009.02039.x

J. Poland, B. Kurti, R. Wisser, R. Pratt, and R. Nelson, Shades of gray: the world of quantitative disease resistance, Trends in Plant Science, vol.14, issue.1, pp.21-29, 2009.
DOI : 10.1016/j.tplants.2008.10.006

I. Rouzine, E. Brunet, and C. Wilke, The traveling-wave approach to asexual evolution: Muller's ratchet and speed of adaptation, Theoretical Population Biology, vol.73, issue.1, pp.24-46, 2008.
DOI : 10.1016/j.tpb.2007.10.004

R. Sanjuán, Mutational fitness effects in RNA and single-stranded DNA viruses: common patterns revealed by site-directed mutagenesis studies, Philosophical Transactions of the Royal Society B: Biological Sciences, vol.268, issue.1475, pp.1975-82, 2010.
DOI : 10.1098/rspb.2001.1690

. St and D. Clair, Quantitative Disease Resistance and Quantitative Resistance Loci in Breeding, Annual Review of Phytopathology, vol.48, pp.247-268, 2010.

M. Van-boven, F. Mooi, J. Schellekens, H. De-melker, and M. Kretzschmar, Pathogen adaptation under imperfect vaccination: implications for pertussis, Proceedings of the Royal Society B: Biological Sciences, vol.35, issue.5, pp.1617-1624, 2005.
DOI : 10.1046/j.1365-2958.2000.01785.x

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

N. Young, . Qtl, . And, . Disease, . In et al., QTL MAPPING AND QUANTITATIVE DISEASE RESISTANCE IN PLANTS, Annual Review of Phytopathology, vol.34, issue.1, pp.479-501
DOI : 10.1146/annurev.phyto.34.1.479