A. S. Abdullah, C. S. Moffat, F. J. Lopez-ruiz, M. R. Gibberd, J. Hamblin et al., Host-multi-pathogen warfare: pathogen interactions in co-infected plants. Frontiers in plant science 8, p.1806, 2017.

F. R. Adler and R. C. Brunet, The dynamics of simultaneous infections with altered susceptibilities, Theoretical population biology, vol.40, issue.3, pp.369-410, 1991.

S. Alizon, Co-infection and super-infection models in evolutionary epidemiology, Interface Focus, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01567919

S. Alizon, J. C. De-roode, and Y. Michalakis, Multiple infections and the evolution of virulence, Ecology letters, vol.16, issue.4, pp.556-567, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01567918

R. A. Armstrong and R. Mcgehee, Coexistence of species competing for shared resources, Theoretical population biology, vol.9, issue.3, pp.317-328, 1976.

K. Auranen, J. Mehtala, A. Tanskanen, S. Kaltoft, and M. , Between-strain competition in acquisition and clearance of pneumococcal carriage: 376 Epidemiologic evidence from a longitudinal study of day-care children, American Journal of Epidemiology, vol.171, issue.2, pp.169-176, 2010.

T. W. Berngruber, R. Froissart, M. Choisy, and S. Gandon, Evolution of virulence in emerging epidemics, PLoS pathogens, vol.9, issue.3, 2013.

I. Billick and T. J. Case, Higher order interactions in ecological communities: what are they and how can they be detected?, Ecology, vol.75, issue.6, pp.1529-1543, 1994.

D. Bogaert, B. Keijser, S. Huse, J. Rossen, R. Veenhoven et al., Variability and diversity of nasopharyngeal microbiota in children: A metagenomic analysis, PLoS ONE, vol.6, issue.2, p.17035, 2011.

I. M. Bomze, Lotka-volterra equation and replicator dynamics: a two-dimensional classification, Biological cybernetics, vol.48, issue.3, pp.201-211, 1983.

I. M. Bomze, Lotka-volterra equation and replicator dynamics: new issues in classification, Biological cybernetics, vol.72, issue.5, pp.447-453, 1995.

C. Bottomley, A. Roca, P. C. Hill, B. Greenwood, and V. Isham, A mathematical model of serotype replacement in pneumococcal carriage following vaccination, Journal of The Royal Society Interface, vol.10, issue.89, 2013.

T. Chawanya and K. Tokita, Large-dimensional replicator equations with antisymmetric random interactions, Journal of the Physical Society of Japan, vol.71, issue.2, pp.429-431, 2002.

L. Chen, F. Ghanbarnejad, and D. Brockmann, Fundamental properties of cooperative contagion proc, New J. of Phys, vol.19, issue.10, 2017.

S. Cobey and M. Lipsitch, Niche and neutral effects of acquired immunity permit coexistence of pneumococcal serotypes, Science, vol.335, pp.1376-1380, 2012.

S. Cobey and M. Lipsitch, Pathogen diversity and hidden regimes of apparent competition, The American naturalist, vol.181, issue.1, pp.12-24, 2012.

T. Cohen, C. Colijn, and M. Murray, Modeling the effects of strain diversity and mechanisms of strain competition on the potential performance of new tuberculosis vaccines, Proceedings of the National Academy of Sciences, vol.105, issue.42, pp.16302-16307, 2008.

G. W. Constable and A. J. Mckane, Exploiting fast-variables to understand population dynamics and evolution, Journal of Statistical Physics, vol.172, issue.1, pp.3-43, 2018.

R. Cressman and Y. Tao, The replicator equation and other game dynamics, Proceedings of the National Academy of Sciences, vol.111, pp.10810-10817, 2014.

N. G. Davies, S. Flasche, M. Jit, and K. E. Atkins, Within-host dynamics shape antibiotic resistance in commensal bacteria, Nature ecology & evolution, vol.3, issue.3, p.440, 2019.

T. Day and S. Gandon, Insights from price?s equation into evolutionary. Disease evolution: models, concepts, and data analyses 71, p.23, 2006.

K. Dietz, The estimation of the basic reproduction number for infectious diseases, Statistical methods in medical research, vol.2, issue.1, pp.23-41, 1993.

E. M. Dunne, H. C. Smith-vaughan, R. M. Robins-browne, E. K. Mulholland, and C. Satzke, Nasopharyngeal microbial interactions in the era of pneumococcal conjugate vaccination, Vaccine, vol.31, pp.2333-2342, 2013.

A. W. Edwards, The fundamental theorem of natural selection, Biological Reviews, vol.69, issue.4, pp.443-474, 1994.

R. A. Fisher, The genetical theory of natural selection, 1958.

J. Friedman, L. M. Higgins, and J. Gore, Community structure follows simple assembly rules in microbial microcosms, Nature ecology & evolution, vol.1, issue.5, p.109, 2017.

M. Gaivão, F. Dionisio, and E. Gjini, Transmission fitness in co-colonization and the persistence of bacterial pathogens, Bulletin of mathematical biology, vol.79, issue.9, pp.2068-2087, 2017.

G. F. Gause, The struggle for existence, 1934.

S. A. Geritz, G. Mesze, and J. A. Metz, Evolutionarily singular strategies and the adaptive growth and branching of the evolutionary tree, 412 Evolutionary ecology, vol.12, issue.1, pp.35-57, 1998.

E. Gjini and S. Madec, A slow-fast dynamic decomposition links neutral and non-neutral coexistence in interacting multi-strain pathogens, 414 Theoretical Ecology, vol.10, issue.1, pp.129-141, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01342432

E. Gjini and S. Madec, The key to complexity in interacting systems with multiple strains, 2020.
URL : https://hal.archives-ouvertes.fr/hal-02470047

E. Gjini, C. Valente, R. Sá-leão, and M. G. Gomes, How direct competition shapes coexistence and vaccine effects in multi-strain pathogen systems, Journal of Theoretical Biology, vol.388, pp.50-60, 2016.

J. R. Gog and B. T. Grenfell, Dynamics and selection of many-strain pathogens, PNAS, vol.99, issue.26, pp.17209-17214, 2002.

S. Gupta and R. Anderson, Population structure of pathogens: the role of immune selection, Parasitology Today, vol.15, issue.12, pp.497-501, 1999.

F. M. Hamelin, L. J. Allen, V. A. Bokil, L. J. Gross, F. M. Hilker et al., Co-infections by non-interacting pathogens are not independent and require new tests of interaction, p.618900, 2019.

L. Hébert-dufresne and B. M. Althouse, Complex dynamics of synergistic coinfections on realistically clustered networks, PNAS, vol.112, issue.33, pp.10551-10556, 2015.

J. Hofbauer and K. Sigmund, Evolutionary game dynamics, Bulletin of the American Mathematical Society, vol.40, issue.4, pp.479-519, 2003.

D. U. Hooper, F. S. Chapin, J. J. Ewel, A. Hector, P. Inchausti et al., Effects 426 of biodiversity on ecosystem functioning: a consensus of current knowledge, Ecological monographs, vol.75, issue.1, pp.3-35, 2005.

F. Hoppensteadt, Singular perturbations on the infinite interval, Transactions of the American Mathematical Society, vol.123, pp.521-535, 1966.

S. P. Hubbell, The unified neutral theory of biodiversity and biogeography (MPB-32), vol.32, 2001.

O. Kogan, M. Khasin, B. Meerson, D. Schneider, and C. R. Myers, Two-strain competition in quasineutral stochastic disease dynamics, Physical Review E, vol.430, issue.4, p.42149, 2014.

A. J. Kucharski, V. Andreasen, and J. R. Gog, Capturing the dynamics of pathogens with many strains, Journal of mathematical biology, vol.432, issue.1-2, pp.1-24, 2016.

S. Lion, Theoretical approaches in evolutionary ecology: environmental feedback as a unifying perspective, The American Naturalist, vol.191, issue.1, pp.434-455, 2018.
URL : https://hal.archives-ouvertes.fr/hal-02122328

M. Lipsitch, Vaccination against colonizing bacteria with multiple serotypes, PNAS, vol.94, issue.12, pp.6571-6576, 1997.

M. Lipsitch, O. Abdullahi, A. D'amour, W. Xie, D. M. Weinberger et al., Estimating rates of carriage acquisition and clearance and competitive ability for pneumococcal serotypes in Kenya with a Markov transition model, Epidemiology, vol.23, issue.4, pp.510-519, 2012.

C. Lobry and T. Sari, On Tykhonov's theorem for convergence of solutions of slow and fast systems, Electronic Journal of Differential Equations, vol.19, pp.1-22, 1998.

C. Lobry and T. Sari, Singular perturbation methods in control theory, Contrôle non linéaire et Applications, vol.64, pp.155-182, 2005.

A. J. Lotka, Elements of physical biology, Science Progress in the Twentieth Century, vol.21, issue.82, pp.341-343, 1919.

R. H. Macarthur, The theory of island biogeography, vol.1, 1967.

G. Meszéna, M. Gyllenberg, F. J. Jacobs, and J. A. Metz, Link between population dynamics and dynamics of darwinian evolution, Physical 444 review letters, vol.95, issue.7, p.78105, 2005.

J. A. Metz, R. M. Nisbet, and S. A. Geritz, How should we define ?fitness? for general ecological scenarios?, Trends in Ecology & Evolution, vol.446, issue.6, pp.198-202, 1992.

R. E. Michod, Darwinian dynamics: evolutionary transitions in fitness and individuality, 2000.

J. C. Miller, Cocirculation of infectious diseases on networks, Physical Review E, vol.87, issue.6, p.60801, 2013.

A. Mougi and M. Kondoh, Diversity of interaction types and ecological community stability, Science, vol.337, issue.6092, pp.349-351, 2012.

M. A. Nowak and R. M. May, Evolutionary games and spatial chaos, Nature, vol.359, issue.6398, p.826, 1992.

M. A. Nowak and K. Sigmund, Evolutionary dynamics of biological games, Science, vol.303, issue.5659, pp.793-799, 2004.

M. Nurhonen, A. C. Cheng, and K. Auranen, Pneumococcal transmission and disease in silico: a microsimulation model of the indirect effects of vaccination, PloS one, vol.8, issue.2, p.56079, 2013.

I. H. Park, D. G. Pritchard, R. Cartee, A. Brandao, M. C. Brandileone et al., Discovery of a new capsular serotype (6c) within serogroup 6 of Streptococcus pneumoniae, Journal of Clinical Microbiology, vol.45, issue.4, pp.1225-1233, 2007.

M. Pascual and J. A. Dunne, Ecological networks: linking structure to dynamics in food webs, 2006.

F. Pinotti, F. Ghanbarnejad, P. Hövel, and C. Poletto, Interplay between competitive and cooperative interactions in a three-player pathogen 458 system, 2019.

G. R. Price, Fisher's 'fundamental theorem' made clear, Annals of human genetics, vol.36, issue.2, pp.129-140, 1972.

W. H. Sandholm, Population games and evolutionary dynamics, 2010.

J. Sanz, C. Xia, S. Meloni, and Y. Moreno, Dynamics of interacting diseases, Physical Review X, vol.4, issue.4, p.41005, 2014.

S. Shrestha, B. Foxman, D. M. Weinberger, C. Steiner, C. Viboud et al., Identifying the interaction between influenza and pneumococcal pneumonia using incidence data, Science translational medicine, vol.5, pp.191-84, 0191.

S. Shrestha, A. A. King, and P. Rohani, Statistical inference for multi-pathogen systems, PLoS Computational Biology, vol.7, issue.8, p.1002135, 2011.

C. Taylor, D. Fudenberg, A. Sasaki, and M. A. Nowak, Evolutionary game dynamics in finite populations, Bulletin of mathematical biology, vol.466, issue.6, pp.1621-1644, 2004.

A. N. Tikhonov, Systems of differential equations containing small parameters in the derivatives, Matematicheskii sbornik, vol.73, issue.3, pp.575-586, 1952.

D. Tilman, The importance of the mechanisms of interspecific competition, The American Naturalist, vol.129, issue.5, pp.769-774, 1987.

A. Traulsen and M. A. Nowak, Evolution of cooperation by multilevel selection, PNAS, vol.103, issue.29, pp.10952-10955, 2006.

C. Valente, J. Hinds, F. Pinto, S. Brugger, D. Gould et al., Decrease in pneumococcal 472 co-colonization following vaccination with the seven-valent pneumococcal conjugate vaccine, PLos ONE, vol.7, issue.1, p.30235, 2012.

V. Volterra, Fluctuations in the abundance of a species considered mathematically, 1926.

J. W. Weibull, Evolutionary game theory, 1997.

D. M. Weinberger, R. Malley, and M. Lipsitch, Serotype replacement in disease after pneumococcal vaccination, The Lancet, vol.378, issue.9807, p.1962, 2011.