M. M. Abang, M. Baum, S. Ceccarelli, S. Grando, C. C. Linde et al., During Parasitic and Saprophytic Phases in the Barley Scald Disease Cycle, Phytopathology, vol.96, issue.11, pp.1214-1222, 2006.
DOI : 10.1094/PHYTO-96-1214

G. N. Agrios, Plant pathology, 2005.

A. R. Akhmetzhanov, F. Grognard, and L. Mailleret, OPTIMAL LIFE-HISTORY STRATEGIES IN SEASONAL CONSUMER-RESOURCE DYNAMICS, Evolution, vol.246, issue.11, 2011.
DOI : 10.1111/j.1558-5646.2011.01381.x
URL : https://hal.archives-ouvertes.fr/hal-00848376

S. Alizon and M. Van-baalen, Multiple Infections, Immune Dynamics, and the Evolution of Virulence, The American Naturalist, vol.172, issue.4, pp.150-168, 2008.
DOI : 10.1086/590958

N. Alvarez, L. Mercier, M. Hossaert-mckey, J. Contreras-garduño, G. Kunstler et al., Ecological distribution and niche segregation of sibling species: the case of bean beetles, Acanthoscelides obtectus Say and A. obvelatus Bridwell, Ecological Entomology, vol.2, issue.6, pp.582-590, 2006.
DOI : 10.1111/j.1461-0248.2004.00569.x

P. Amarasekare, Competitive coexistence in spatially structured environments: a synthesis, Ecology Letters, vol.158, issue.12, pp.1109-1122, 2003.
DOI : 10.1046/j.1461-0248.2003.00530.x

D. J. Bailey and C. A. Gilligan, Dynamics of Primary and Secondary Infection in Take-All Epidemics, Phytopathology, vol.89, issue.1, pp.84-91, 1999.
DOI : 10.1094/PHYTO.1999.89.1.84

B. Boldin and O. Diekmann, Superinfections can induce evolutionarily stable coexistence of pathogens, Journal of Mathematical Biology, vol.74, issue.178, pp.635-672, 2008.
DOI : 10.1007/s00285-007-0135-1

M. L. Carson, from North Carolina, Plant Disease, vol.82, issue.9, pp.1043-1047, 1998.
DOI : 10.1094/PDIS.1998.82.9.1043

S. Daval, L. Lebreton, K. Gazengel, A. Guillerm-erckelboudt, and A. Sarniguet, into two major groups, Plant Pathology, vol.86, issue.Web Server Issu, pp.165-178, 2010.
DOI : 10.1111/j.1365-3059.2009.02158.x

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

O. Diekmann, A beginners guide to adaptive dynamics. Pages 47 Mathematical modelling of population dynamics, 2004.

B. D. Fitt, Y. Huang, F. Van-den, J. S. Bosch, and . West, Coexistence of Related Pathogen Species on Arable Crops in Space and Time, Annual Review of Phytopathology, vol.44, issue.1, pp.163-182, 2006.
DOI : 10.1146/annurev.phyto.44.070505.143417

E. Fournier and T. Giraud, Sympatric genetic differentiation of populations of a generalist pathogenic fungus, Botrytis cinerea, on two different host plants, grapevine and bramble, Journal of Evolutionary Biology, vol.21, pp.122-132, 2008.

S. Gandon, EVOLUTION OF MULTIHOST PARASITES, Evolution, vol.32, issue.3, pp.455-469, 2004.
DOI : 10.1111/j.0014-3820.2004.tb01669.x

G. F. Gause, The Struggle for Existence, Soil Science, vol.41, issue.2, 1934.
DOI : 10.1097/00010694-193602000-00018

S. A. Geritz and E. Kisdi, On the mechanistic underpinning of discrete-time population models with complex dynamics, Journal of Theoretical Biology, vol.228, issue.2, pp.261-269, 2004.
DOI : 10.1016/j.jtbi.2004.01.003

S. A. Geritz, E. Kisdi, G. Mesze´namesze´na, and J. A. Metz, Evolutionarily singular strategies and the adaptive growth and branching of the evolutionary tree, Evolutionary Ecology, vol.34, issue.1, pp.35-57, 1998.
DOI : 10.1023/A:1006554906681

T. Giraud, P. Gladieux, and S. Gavrilets, Linking the emergence of fungal plant diseases with ecological speciation, Trends in Ecology & Evolution, vol.25, issue.7, pp.387-395, 2010.
DOI : 10.1016/j.tree.2010.03.006

I. Gudelj, F. Van-den, B. D. Bosch, and . Fitt, Evolution of Sibling Fungal Plant Pathogens in Relation to Host Specialization, Phytopathology, vol.94, issue.7, pp.789-795, 2004.
DOI : 10.1094/PHYTO.2004.94.7.789

I. Gudelj, F. Van-den, C. A. Bosch, and . Gilligan, Transmission rates and adaptive evolution of pathogens in sympatric heterogeneous plant populations, Proceedings of the Royal Society B: Biological Sciences, vol.271, issue.1553, pp.2187-2194, 2004.
DOI : 10.1098/rspb.2004.2837

M. Gyllenberg and R. Service, Necessary and sufficient conditions for the existence of an optimisation principle in evolution, Journal of Mathematical Biology, vol.380, issue.3, pp.359-369, 2011.
DOI : 10.1007/s00285-010-0340-1

A. J. Inman, A. Sivanesan, B. D. Fitt, and R. L. Evans, The biology of Mycosphaerella capsellae sp. nov., the teleomorph of Pseudocercosporella capsellae, cause of white leaf spot of oilseed rape, Mycological Research, vol.95, issue.11, pp.1334-1342, 1991.
DOI : 10.1016/S0953-7562(09)80586-8

K. Koelle, M. Pascual, and M. Yunus, Pathogen adaptation to seasonal forcing and climate change, Proceedings of the Royal Society B: Biological Sciences, vol.99, issue.2, pp.971-977, 2005.
DOI : 10.1046/j.1365-2958.2001.02195.x
URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1564099

L. V. Madden, G. Hughes, F. Van-den, and . Bosch, The study of plant disease epidemics, 2007.

L. V. Madden, F. Van-den, and . Bosch, A Population-Dynamics Approach to Assess the Threat of Plant Pathogens as Biological Weapons against Annual Crops, BioScience, vol.52, issue.1, pp.65-74, 2002.
DOI : 10.1641/0006-3568(2002)052[0065:APDATA]2.0.CO;2

L. Mailleret, M. Castel, J. Montarry, and F. M. Hamelin, From elaborate to compact seasonal plant epidemic models and back; is competitive exclusion in the details? Theoretical Ecology, 2011.

L. Mailleret and V. Lemesle, A note on semi-discrete modelling in the life sciences, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.4, issue.10, pp.4779-4799, 2009.
DOI : 10.1094/PHYTO.2001.91.10.924

J. A. Metz, S. A. Geritz, G. Mesze´namesze´na, F. J. Jacobs, and J. S. Van-heerwarden, Adaptive dynamics: a geometrical study of the consequences of nearly faithful replication. Pages 183?231 in S, Stochastic and spatial structures of dynamical systems, 1996.

J. A. Metz, S. D. Mylius, and O. Diekmann, When does evolution optimize, Evolutionary Ecology Research, vol.10, pp.629-654, 2008.

J. A. Metz, R. M. Nisbet, and S. A. Geritz, How should we define ???fitness??? for general ecological scenarios?, Trends in Ecology & Evolution, vol.7, issue.6, pp.198-202, 1992.
DOI : 10.1016/0169-5347(92)90073-K

M. Hamdane, A. , X. Giresse, C. Dutech, and M. Desprez-loustau, Distribution spatiale de lign??es d???o??dium des ch??nes en France analys??e ?? l???aide d???outils rapides de caract??risation mol??culaire, Annals of Forest Science, vol.6, issue.1650, p.212, 2010.
DOI : 10.1051/forest/2009105

S. D. Mylius and O. Diekmann, On Evolutionarily Stable Life Histories, Optimization and the Need to Be Specific about Density Dependence, Oikos, vol.74, issue.2, pp.218-224, 1995.
DOI : 10.2307/3545651

S. Schreiber and J. Tobiason, The evolution of resource use, Journal of Mathematical Biology, vol.47, issue.1, pp.56-78, 2003.
DOI : 10.1007/s00285-003-0195-9

M. W. Shaw, Seasonally induced chaotic dynamics and their implications in models of plant disease, Plant Pathology, vol.94, issue.5, pp.790-801, 1994.
DOI : 10.1016/0167-2789(85)90011-9

R. J. Smith, Modelling disease ecology with mathematics, 2008.

M. Tachikawa, F. Van-den-berg, N. Bacaer, J. A. Metz, C. Lannou et al., Fluctuation induces evolutionary branching in a mathematical model of ecosystems Periodic host absence can select for both higher or lower parasite transmission rates Periodicity in host availability does not account for evolutionary branching as observed in many plant pathogens: an application to Gaeumannomyces graminis var. tritici, PLoS ONE Evolutionary Ecology Phytopathology, vol.3, issue.100, pp.121-1371169, 2008.