V. Acuña, F. Chierichetti, V. Lacroix, A. Marchetti-spaccamela, M. Sagot et al., Modes and cuts in metabolic networks: Complexity and algorithms, Biosystems, issue.1, pp.9551-60, 2009.

V. Acuña, P. V. Milreu, L. Cottret, A. Marchetti-spaccamela, L. Stougie et al., Algorithms and complexity of enumerating minimal precursor sets in genome-wide metabolic networks, Bioinformatics, vol.28, issue.19, pp.282474-2483, 2012.
DOI : 10.1093/bioinformatics/bts423

R. Andrade, M. Wannagat, C. C. Klein, V. Acuña, A. Marchetti-spaccamela et al., Enumeration of minimal stoichiometric precursor sets in metabolic networks, Algorithms for Molecular Biology, vol.8, issue.1, 2016.
DOI : 10.1371/journal.pone.0053957

URL : https://hal.archives-ouvertes.fr/hal-01368653

M. R. Antoniewicz, Methods and advances in metabolic flux analysis: a mini-review, Journal of Industrial Microbiology & Biotechnology, vol.45, issue.4, pp.317-325, 2015.
DOI : 10.1007/s10295-015-1585-x

M. Archetti and I. Scheuring, Trading public goods stabilizes interspecific mutualism, Journal of Theoretical Biology, vol.318, pp.58-67, 2013.
DOI : 10.1016/j.jtbi.2012.10.022

M. Archetti, I. Scheuring, M. Hoffman, M. E. Frederickson, N. E. Pierce et al., Economic game theory for mutualism and cooperation, Ecology Letters, vol.108, issue.12, pp.141300-1312, 2011.
DOI : 10.1111/j.1461-0248.2011.01697.x

M. Archetti, F. Úbeda, D. Fudenberg, J. Green, N. E. Pierce et al., Let the Right One In: A Microeconomic Approach to Partner Choice in Mutualisms, The American Naturalist, vol.177, issue.1, pp.75-85, 2011.
DOI : 10.1086/657622

G. Ausiello, P. G. Franciosa, and D. Frigioni, Directed Hypergraphs: Problems, Algorithmic Results, and a Novel Decremental Approach, ICTCS, pp.312-327, 2001.
DOI : 10.1007/3-540-45446-2_20

R. Axelrod, The evolution of cooperation, Science, vol.211, issue.4489, 1984.
DOI : 10.1126/science.7466396

J. Bader, E. Mast-gerlach, M. Popovi?, R. Bajpai, and U. Stahl, Relevance of microbial coculture fermentations in biotechnology, Journal of Applied Microbiology, vol.73, issue.103, pp.371-387, 2010.
DOI : 10.1111/j.1365-2672.2009.04659.x

K. Ballerstein, A. Von-kamp, S. Klamt, and U. Haus, Minimal cut sets in a metabolic network are elementary modes in a dual network, Bioinformatics, vol.28, issue.3, pp.28381-387, 2012.
DOI : 10.1093/bioinformatics/btr674

A. D. Bary, Die Erscheinung der Symbiose, 1879.

S. Benomar, D. Ranava, M. L. Cárdenas, E. Trably, Y. Rafrafi et al., Nutritional stress induces exchange of cell material and energetic coupling between bacterial species, Nature Communications, vol.73, 2015.
DOI : 10.1038/ncomms7283

URL : https://hal.archives-ouvertes.fr/hal-01427429

J. D. Bever, S. C. Richardson, B. M. Lawrence, J. Holmes, and M. Watson, Preferential allocation to beneficial symbiont with spatial structure maintains mycorrhizal mutualism, Ecology Letters, vol.17, issue.1, pp.13-21, 2009.
DOI : 10.1111/j.1461-0248.2008.01254.x

A. Brandenburger, Cooperative game theory: Characteristic functions, allocations, marginal contribution, 2007.

M. Broom and J. Rychtar, Game-Theoretical Models in Biology, 2013.

J. J. Bull and W. R. Rice, Distinguishing mechanisms for the evolution of co-operation, Journal of Theoretical Biology, vol.149, issue.1, pp.63-74, 1991.
DOI : 10.1016/S0022-5193(05)80072-4

A. P. Burgard, P. Pharkya, and C. D. Maranas, Optknock: A bilevel programming framework for identifying gene knockout strategies for microbial strain optimization, Biotechnology and Bioengineering, vol.18, issue.6, pp.647-657, 2003.
DOI : 10.1002/bit.10803

P. Carbonell, D. Fichera, S. B. Pandit, and J. And-faulon, Enumerating metabolic pathways for the production of heterologous target chemicals in chassis organisms, BMC Systems Biology, vol.6, issue.1, pp.1-18, 2012.
DOI : 10.1016/j.cor.2003.11.014

R. Caspi, T. Altman, R. Billington, K. Dreher, H. Foerster et al., The metacyc database of metabolic pathways and enzymes and the biocyc collection of pathway/genome databases, Nucleic Acids Research, issue.D1, pp.42-459, 2014.

B. K. Chung and D. Lee, Flux-sum analysis: a metabolite-centric approach for understanding the metabolic network, BMC Systems Biology, vol.3, issue.1, pp.1-10, 2009.
DOI : 10.1186/1752-0509-3-117

S. T. Clark and W. S. Verwoerd, Minimal Cut Sets and the Use of Failure Modes in Metabolic Networks, Metabolites, vol.2, issue.4, pp.567-595, 2012.
DOI : 10.3390/metabo2030567

B. L. Clarke, Stability of Complex Reaction Networks, pp.1-215, 1980.
DOI : 10.1002/9780470142622.ch1

L. Cottret, P. Milreu, V. Acuna, A. Marchetti-spaccamela, F. Viduani-martinez et al., Enumerating Precursor Sets of Target Metabolites in a Metabolic Network, Lecture Notes in Bioinformatics, vol.5251, pp.233-244, 2007.
DOI : 10.1007/978-3-540-87361-7_20

URL : https://hal.archives-ouvertes.fr/hal-00428200

L. David and A. Bockmayr, Computing Elementary Flux Modes Involving a Set of Target Reactions, IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol.11, issue.6, pp.1099-1107, 2014.
DOI : 10.1109/TCBB.2014.2343964

L. F. De-figueiredo, A. Podhorski, A. Rubio, C. Kaleta, J. E. Beasley et al., Computing the shortest elementary flux modes in genome-scale metabolic networks, Bioinformatics, vol.25, issue.23, pp.253158-3165, 2009.
DOI : 10.1093/bioinformatics/btp564

W. Dejonghe, E. Berteloot, J. Goris, N. Boon, K. Crul et al., Synergistic Degradation of Linuron by a Bacterial Consortium and Isolation of a Single Linuron-Degrading Variovorax Strain, Applied and Environmental Microbiology, vol.69, issue.3, pp.691532-1541, 2003.
DOI : 10.1128/AEM.69.3.1532-1541.2003

Y. Deville, D. Gilbert, J. Van-helden, and S. J. Wodak, An overview of data models for the analysis of biochemical pathways, Briefings in Bioinformatics, vol.4, issue.3, pp.246-259, 2003.
DOI : 10.1093/bib/4.3.246

P. Dittrich and P. S. Di-fenizio, Chemical Organisation Theory, Bulletin of Mathematical Biology, vol.96, issue.25, pp.1199-1231, 2007.
DOI : 10.1007/s11538-006-9130-8

M. Doebeli, A model for the evolutionary dynamics of cross-feeding polymorphisms in microorganisms, Population Ecology, vol.44, issue.2, pp.59-70, 2002.
DOI : 10.1007/s101440200008

E. Coli, E.coli core: http://systemsbiology, pp.2016-2020, 2016.

D. P. Edwards, M. Hassall, W. J. Sutherland, Y. , and D. W. , Selection for protection in an ant-plant mutualism: host sanctions, host modularity, and the principal-agent game, Proceedings of the Royal Society B: Biological Sciences, vol.73, issue.1544, pp.273595-602, 1586.
DOI : 10.1098/rspb.2003.2630

S. Eker, M. Krummenacker, A. Shearer, A. Tiwari, I. Keseler et al., Computing minimal nutrient sets from metabolic networks via linear constraint solving, BMC Bioinformatics, vol.14, issue.1, p.114, 2013.
DOI : 10.1006/jtbi.2000.1088

P. J. Enyeart, Z. B. Simpson, and A. D. Ellington, A microbial model of economic trading and comparative advantage, Journal of Theoretical Biology, vol.364, pp.326-343, 2015.
DOI : 10.1016/j.jtbi.2014.09.030

E. Estrada and J. A. Rodríguez-velázquez, Subgraph centrality and clustering in complex hyper-networks. Physica A: Statistical Mechanics and its Applications, pp.581-594, 2006.

A. Fabich, S. A. Jones, F. Z. Chowdhury, A. Cernosek, A. Anderson et al., Comparison of Carbon Nutrition for Pathogenic and Commensal Escherichia coli Strains in the Mouse Intestine, Infection and Immunity, vol.76, issue.3, pp.1143-1152, 2008.
DOI : 10.1128/IAI.01386-07

A. M. Feist and B. O. Palsson, The biomass objective function, Current Opinion in Microbiology, vol.13, issue.3, pp.344-349, 2010.
DOI : 10.1016/j.mib.2010.03.003

D. A. Fell and A. Wagner, Structural properties of metabolic networks: Implications for evolution and modeling of metabolism, Animating the cellular map, pp.79-85, 2000.

A. Finney and M. Hucka, Systems biology markup language: Level 2 and beyond, Biochemical Society Transactions, vol.31, issue.6, pp.311472-1473, 2003.
DOI : 10.1042/bst0311472

J. Gagneur and S. Klamt, Computation of elementary modes: a unifying framework and the new binary approach, BMC Bioinformatics, vol.5, issue.1, pp.1-21, 2004.

G. Gallo, G. Longo, S. Nguyen, and S. Pallottino, Directed hypergraphs and applications, Discrete Applied Mathematics, vol.42, issue.2-3, pp.177-201, 1993.
DOI : 10.1016/0166-218X(93)90045-P

M. P. Gerstl, S. Klamt, C. Jungreuthmayer, and J. Zanghellini, Exact quantification of cellular robustness in genome-scale metabolic networks, Bioinformatics, vol.32, issue.5, 2015.
DOI : 10.1093/bioinformatics/btv649

B. R. Glick, Phytoremediation: synergistic use of plants and bacteria to clean up the environment, Biotechnology Advances, vol.21, issue.5, pp.383-393, 2003.
DOI : 10.1016/S0734-9750(03)00055-7

A. Grafen, Biological signals as handicaps, Journal of Theoretical Biology, vol.144, issue.4, pp.517-546, 1990.
DOI : 10.1016/S0022-5193(05)80088-8

C. M. Guinane and P. D. Cotter, Role of the gut microbiota in health and chronic gastrointestinal disease: understanding a hidden metabolic organ, Therapeutic Advances in Gastroenterology, vol.6, issue.4, pp.295-308, 2013.
DOI : 10.1177/1756283X13482996

V. Gurvich and L. Khachiyan, On generating the irredundant conjunctive and disjunctive normal forms of monotone Boolean functions, Discrete Applied Mathematics, vol.96, issue.97, pp.363-373, 1999.
DOI : 10.1016/S0166-218X(99)00099-2

H. Hamburger, N???person Prisoner's Dilemma???, The Journal of Mathematical Sociology, vol.7, issue.1, pp.27-48, 1973.
DOI : 10.1080/0022250X.1973.9989822

W. Hamilton, The genetical evolution of social behaviour. I, Journal of Theoretical Biology, vol.7, issue.1, pp.1-16, 1964.
DOI : 10.1016/0022-5193(64)90038-4

T. Handorf, N. Christian, O. Ebenhöh, and D. Kahn, An environmental perspective on metabolism, Journal of Theoretical Biology, vol.252, issue.3, pp.530-537, 2008.
DOI : 10.1016/j.jtbi.2007.10.036

URL : https://hal.archives-ouvertes.fr/hal-00428159

C. Hauert, S. De-monte, J. Hofbauer, S. , and K. , Volunteering as Red Queen Mechanism for Cooperation in Public Goods Games, Science, vol.296, issue.5570, pp.2961129-1132, 2002.
DOI : 10.1126/science.1070582

J. D. Hoeksema and M. W. Schwartz, Expanding comparative-advantage biological market models: contingency of mutualism on partner's resource requirements and acquisition trade-offs, Proceedings of the Royal Society B: Biological Sciences, vol.270, issue.1518, pp.270913-919, 1518.
DOI : 10.1098/rspb.2002.2312

J. Hofbauer and K. Sigmund, Evolutionary Games and Population Dynamics, 1998.
DOI : 10.1017/CBO9781139173179

S. Hoops, S. Sahle, R. Gauges, C. Lee, J. Pahle et al., COPASI--a COmplex PAthway SImulator, Bioinformatics, vol.22, issue.24, pp.223067-3074, 2006.
DOI : 10.1093/bioinformatics/btl485

C. Hopla, L. Durden, and J. Keirans, Ectoparasites and classification, Revue Scientifique et Technique de l'OIE, vol.13, issue.4, pp.985-1017, 1994.
DOI : 10.20506/rst.13.4.815

M. Hucka, A. Finney, H. M. Sauro, H. Bolouri, J. C. Doyle et al., The systems biology markup language (SBML): a medium for representation and exchange of biochemical network models, Bioinformatics, vol.19, issue.4, pp.524-531, 2003.
DOI : 10.1093/bioinformatics/btg015

S. Hummert, K. Bohl, D. Basanta, A. Deutsch, S. Werner et al., Evolutionary game theory: cells as players, Mol. BioSyst., vol.64, issue.12, pp.3044-3065, 2014.
DOI : 10.1039/c3mb70601j

K. A. Hunt, J. P. Folsom, R. L. Taffs, and R. P. Carlson, Complete enumeration of elementary flux modes through scalable demand-based subnetwork definition, Bioinformatics, vol.30, issue.11, pp.301569-1578, 2014.
DOI : 10.1093/bioinformatics/btu021

M. Imieli?ski, C. Belta, Á. Halász, R. , and H. , Investigating metabolite essentiality through genome-scale analysis of Escherichia coli production capabilities, Bioinformatics, vol.21, issue.9, pp.2008-2016, 2005.
DOI : 10.1093/bioinformatics/bti245

M. Imieli?ski, C. Belta, H. Rubin, and Á. Halász, Systematic Analysis of Conservation Relations in Escherichia coli Genome-Scale Metabolic Network Reveals Novel Growth Media, Biophysical Journal, vol.90, issue.8, pp.902659-2672, 2006.
DOI : 10.1529/biophysj.105.069278

K. C. Jandér and E. A. Herre, Host sanctions and pollinator cheating in the fig tree-fig wasp mutualism, Proceedings of the Royal Society B: Biological Sciences, vol.81, issue.16, 2010.
DOI : 10.1016/j.cub.2007.06.004

D. Jevremovic, D. Boley, and C. Sosa, Divide-and-Conquer Approach to the Parallel Computation of Elementary Flux Modes in Metabolic Networks, 2011 IEEE International Symposium on Parallel and Distributed Processing Workshops and Phd Forum, pp.502-511, 2011.
DOI : 10.1109/IPDPS.2011.188

A. A. Julius, M. Imielinski, and G. J. Pappas, Metabolic networks analysis using convex optimization, 2008 47th IEEE Conference on Decision and Control, pp.762-767, 2008.
DOI : 10.1109/CDC.2008.4739111

A. Kamp and S. Schuster, Metatool 5.0: fast and flexible elementary modes analysis, Bioinformatics, vol.22, issue.15, pp.221930-1931, 2006.
DOI : 10.1093/bioinformatics/btl267

S. M. Kelk, B. G. Olivier, L. Stougie, and F. J. Bruggeman, Optimal flux spaces of genome-scale stoichiometric models are determined by a few subnetworks, Scientific Reports, 2012.
DOI : 10.1038/srep00580

URL : https://hal.archives-ouvertes.fr/hal-00763439

E. T. Kiers, R. A. Rousseau, S. A. West, and R. F. Denison, Host sanctions and the legume???rhizobium mutualism, Nature, vol.425, issue.6953, pp.42578-81, 2003.
DOI : 10.1038/nature01931

S. Klamt and E. D. Gilles, Minimal cut sets in biochemical reaction networks, Bioinformatics, vol.20, issue.2, pp.226-234, 2004.
DOI : 10.1093/bioinformatics/btg395

S. Klamt, J. Saez-rodriguez, G. , and E. D. , Structural and functional analysis of cellular networks with cellnetanalyzer, BMC Systems Biology, vol.1, issue.1, pp.1-13, 2007.

S. Klamt and J. Stelling, Two approaches for metabolic pathway analysis?, Trends in Biotechnology, vol.21, issue.2, pp.64-69, 2003.
DOI : 10.1016/S0167-7799(02)00034-3

R. Kleerebezem and M. C. Van-loosdrecht, Mixed culture biotechnology for bioenergy production, Current Opinion in Biotechnology, vol.18, issue.3, pp.207-212, 2007.
DOI : 10.1016/j.copbio.2007.05.001

N. Klitgord and D. Segrè, Environments that Induce Synthetic Microbial Ecosystems, PLoS Computational Biology, vol.34, issue.11, pp.1-17, 2010.
DOI : 10.1371/journal.pcbi.1001002.s011

V. Lacroix, L. Cottret, P. Thébault, and M. Sagot, An Introduction to Metabolic Networks and Their Structural Analysis, IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol.5, issue.4, pp.594-617, 2008.
DOI : 10.1109/TCBB.2008.79

URL : https://hal.archives-ouvertes.fr/hal-00355497

A. Larhlimi, S. Blachon, J. Selbig, and Z. Nikoloski, Robustness of metabolic networks: A review of existing definitions, Biosystems, vol.106, issue.1, pp.1-8, 2011.
DOI : 10.1016/j.biosystems.2011.06.002

A. Larhlimi and A. Bockmayr, Minimal Direction Cuts in Metabolic Networks, AIP Conference Proceedings, pp.73-86, 2007.
DOI : 10.1063/1.2793406

A. Larhlimi and A. Bockmayr, A new constraint-based description of the steady-state flux cone of metabolic networks, Discrete Applied Mathematics, vol.157, issue.10, pp.2257-2266, 2009.
DOI : 10.1016/j.dam.2008.06.039

M. Leatham, S. Banerjee, S. M. Autieri, R. Mercado-lubo, T. Conway et al., Precolonized Human Commensal Escherichia coli Strains Serve as a Barrier to E. coli O157:H7 Growth in the Streptomycin-Treated Mouse Intestine, Infection and Immunity, vol.77, issue.7, pp.772876-2886, 2009.
DOI : 10.1128/IAI.00059-09

S. Lee, C. Phalakornkule, M. M. Domach, and I. E. Grossmann, Recursive MILP model for finding all the alternate optima in LP models for metabolic networks, Computers & Chemical Engineering, vol.24, issue.2-7, pp.2-7711, 2000.
DOI : 10.1016/S0098-1354(00)00323-9

N. E. Lewis, H. Nagarajan, and B. O. Palsson, Constraining the metabolic genotype???phenotype relationship using a phylogeny of in silico methods, Nature Reviews Microbiology, vol.6, issue.4, pp.291-305, 2012.
DOI : 10.1038/nrmicro2737

C. Lin, C. Chang, C. Lu, J. Martel, D. Ojcius et al., Impact of the gut microbiota, prebiotics, and probiotics on human health and disease, Biomedical Journal, vol.37, issue.5, pp.259-268, 2014.

H. Ma and A. Zeng, Reconstruction of metabolic networks from genome data and analysis of their global structure for various organisms, Bioinformatics, vol.19, issue.2, pp.270-277, 2003.
DOI : 10.1093/bioinformatics/19.2.270

R. Maltby, M. P. Leatham-jensen, T. Gibson, P. S. Cohen, C. et al., Nutritional Basis for Colonization Resistance by Human Commensal Escherichia coli Strains HS and Nissle 1917 against E. coli O157:H7 in the Mouse Intestine, PLoS ONE, vol.55, issue.4, p.53957, 2013.
DOI : 10.1371/journal.pone.0053957.t004

M. W. Schwartz and J. D. , SPECIALIZATION AND RESOURCE TRADE: BIOLOGICAL MARKETS AS A MODEL OF MUTUALISMS, Ecology, vol.79, issue.3, pp.1029-1038, 1998.
DOI : 10.1126/science.212.4494.562

B. D. Martin and E. Schwab, Current Usage of Symbiosis and Associated Terminology, International Journal of Biology, vol.5, issue.1, 2012.
DOI : 10.5539/ijb.v5n1p32

M. Smith and D. Harper, Animal Signals. Oxford Series in Ecology and Evolution, 2003.

J. Meador, M. E. Caldwell, P. S. Cohen, C. , and T. , Escherichia coli Pathotypes Occupy Distinct Niches in the Mouse Intestine, Infection and Immunity, vol.82, issue.5, pp.1931-1938, 2014.
DOI : 10.1128/IAI.01435-13

R. J. Mitchell, R. E. Irwin, R. J. Flanagan, and J. D. And-karron, Ecology and evolution of plant-pollinator interactions, Annals of Botany, vol.103, issue.9, pp.1355-1363, 2009.
DOI : 10.1093/aob/mcp122

A. Mithani, G. M. Preston, and J. Hein, Rahnuma: hypergraph-based tool for metabolic pathway prediction and network comparison, Bioinformatics, vol.25, issue.14, pp.251831-1832, 2009.
DOI : 10.1093/bioinformatics/btp269

J. Monk, P. Charusanti, R. K. Aziz, J. A. Lerman, N. Premyodhin et al., Genome-scale metabolic reconstructions of multiple Escherichia coli strains highlight strain-specific adaptations to nutritional environments, Proceedings of the National Academy of Sciences, pp.11020338-20343, 2013.
DOI : 10.1073/pnas.1307797110

J. J. Morris, R. E. Lenski, and E. R. Zinser, The Black Queen Hypothesis: Evolution of Dependencies through Adaptive Gene Loss, mBio, vol.3, issue.2, 2012.
DOI : 10.1128/mBio.00036-12

A. C. Müller and A. Bockmayr, Flux modules in metabolic networks, Journal of Mathematical Biology, vol.22, issue.15, pp.1151-1179, 2013.
DOI : 10.1007/s00285-013-0731-1

J. Nash, Non-Cooperative Games, The Annals of Mathematics, vol.54, issue.2, pp.286-295, 1951.
DOI : 10.2307/1969529

A. M. Nedosyko, J. E. Young, J. W. Edwards, B. Da-silva, and K. , Searching for a Toxic Key to Unlock the Mystery of Anemonefish and Anemone Symbiosis, PLoS ONE, vol.73, issue.3, p.98449, 2014.
DOI : 10.1371/journal.pone.0098449.t004

M. A. Nowak, Five Rules for the Evolution of Cooperation, Science, vol.314, issue.5805, pp.3141560-1563, 2006.
DOI : 10.1126/science.1133755

M. A. Nowak and R. M. May, Evolutionary games and spatial chaos, Nature, vol.359, issue.6398, pp.359826-829, 1992.
DOI : 10.1038/359826a0

J. D. Orth, I. Thiele, and B. O. Palsson, What is flux balance analysis?, Nature Biotechnology, vol.19, issue.3, pp.245-248, 2010.
DOI : 10.1038/nbt.1614

M. J. Osborne and A. Rubinstein, A Course in Game Theory, 1994.

J. A. Papin, N. D. Price, S. J. Wiback, D. A. Fell, and B. O. Palsson, Metabolic pathways in the post-genome era, Trends in Biochemical Sciences, vol.28, issue.5, pp.250-258, 2003.
DOI : 10.1016/S0968-0004(03)00064-1

E. Parmentier and L. Michel, Boundary lines in symbiosis forms, Symbiosis, vol.302, issue.3???4, pp.1-5, 2013.
DOI : 10.1007/s13199-013-0236-0

K. A. Peacock, Symbiosis in Ecology and Evolution, Philosophy of Ecology Handbook of the Philosophy of Science, vol.11, pp.219-250, 2011.
DOI : 10.1016/B978-0-444-51673-2.50009-1

N. Pearcy, J. J. Crofts, C. , and N. , Hypergraph models of metabolism, International Journal of Biological, Biomolecular, Agricultural, Food and Biotechnological Engineering, vol.8, issue.8, pp.19-23, 2014.

M. Pelillo, Encyclopedia of Optimization, chapter Replicator dynamics in combinatorial optimization, pp.3279-3291, 2009.

O. Pellmyr and C. J. Huth, Evolutionary stability of mutualism between yuccas and yucca moths, Nature, vol.372, issue.6503, pp.372257-260, 1994.
DOI : 10.1038/372257a0

J. Pey, J. A. Villar, L. Tobalina, A. Rezola, J. M. García et al., TreeEFM: calculating elementary flux modes using linear optimization in a tree-based algorithm, Bioinformatics, vol.31, issue.6, 2014.
DOI : 10.1093/bioinformatics/btu733

T. Pfeiffer and S. Bonhoeffer, Evolution of Cross???Feeding in Microbial Populations, The American Naturalist, vol.163, issue.6, pp.126-135, 2004.
DOI : 10.1086/383593

T. Pfeiffer and S. Schuster, Game-theoretical approaches to studying the evolution of biochemical systems, Trends in Biochemical Sciences, vol.30, issue.1, pp.20-25, 2005.
DOI : 10.1016/j.tibs.2004.11.006

T. Pfeiffer, S. Schuster, and S. Bonhoeffer, Cooperation and Competition in the Evolution of ATP-Producing Pathways, Science, vol.292, issue.5516, pp.292504-507, 2001.
DOI : 10.1126/science.1058079

J. Pramanik and J. D. Keasling, Stoichiometric model of Escherichia coli metabolism: Incorporation of growth???rate dependent biomass composition and mechanistic energy requirements, Biotechnology and Bioengineering, vol.56, issue.4, pp.398-421, 1997.
DOI : 10.1002/(SICI)1097-0290(19971120)56:4<398::AID-BIT6>3.3.CO;2-F

L. Quek and L. K. Nielsen, A depth-first search algorithm to compute elementary flux modes by linear programming, BMC Systems Biology, vol.4, issue.3, pp.1-10, 2014.
DOI : 10.1186/s12918-014-0094-2

W. S. Reeburgh, Oceanic Methane Biogeochemistry, Chemical Reviews, vol.107, issue.2, pp.486-513, 2007.
DOI : 10.1021/cr050362v

D. Ricardo, On the Principles of Political Economy and Taxation, 1817.
DOI : 10.1017/CBO9781107589421

P. Romero and P. Karp, Nutrition-related analysis of pathway/genome databases, Pacific Symposium on Biocomputing'01, pp.470-482, 2001.

R. Noë and P. H. , Biological markets, Behavioral Ecology and Sociobiology, vol.35, issue.1, pp.1-11, 1994.
DOI : 10.1017/CBO9780511752421.007

M. Rothschild and J. Stiglitz, Equilibrium in Competitive Insurance Markets: An Essay on the Economics of Imperfect Information, The Quarterly Journal of Economics, vol.90, issue.4, pp.629-649, 1976.
DOI : 10.2307/1885326

D. E. Rozen and R. E. Lenski, Long-Term Experimental Evolution in Escherichia coli. VIII. Dynamics of a Balanced Polymorphism, The American Naturalist, vol.155, issue.1, pp.24-35, 2000.
DOI : 10.2307/3079013

URL : https://hal.archives-ouvertes.fr/hal-00173266

E. G. Ruby and M. J. Mcfall-ngai, Oxygen-utilizing reactions and symbiotic colonization of the squid light organ by Vibrio fischeri, Trends in Microbiology, vol.7, issue.10, pp.414-420, 1999.
DOI : 10.1016/S0966-842X(99)01588-7

W. H. Sandholm, Population Games and Evolutionary Dynamics, 2010.

J. Sapp, The dynamics of symbiosis: an historical overview, Canadian Journal of Botany, vol.82, issue.8, pp.1046-1056, 2004.
DOI : 10.1139/b04-055

C. H. Schilling, D. Letscher, and B. Ø. Palsson, Theory for the Systemic Definition of Metabolic Pathways and their use in Interpreting Metabolic Function from a Pathway-Oriented Perspective, Journal of Theoretical Biology, vol.203, issue.3, pp.229-248, 2000.
DOI : 10.1006/jtbi.2000.1073

A. Schimper, Die epiphytische Vegetation Amerikas, 1888.

R. Schuetz, L. Kuepfer, and U. Sauer, Systematic evaluation of objective functions for predicting intracellular fluxes in Escherichia coli, Molecular Systems Biology, vol.101, issue.1, 2007.
DOI : 10.1038/msb4100162

S. Schuster, T. Dandekar, and D. A. Fell, Detection of elementary flux modes in biochemical networks: a promising tool for pathway analysis and metabolic engineering, Trends in Biotechnology, vol.17, issue.2, pp.53-60, 1999.
DOI : 10.1016/S0167-7799(98)01290-6

S. Schuster and C. Hilgetag, ON ELEMENTARY FLUX MODES IN BIOCHEMICAL REACTION SYSTEMS AT STEADY STATE, Journal of Biological Systems, vol.02, issue.02, pp.2165-182, 1994.
DOI : 10.1142/S0218339094000131

S. Schuster, C. Hilgetag, J. Woods, and D. Fell, Reaction routes in biochemical reaction systems: Algebraic properties, validated calculation procedure and example from nucleotide metabolism, Journal of Mathematical Biology, vol.45, issue.2, pp.45153-181, 2002.
DOI : 10.1007/s002850200143

S. Schuster, S. Klamt, W. Weckwerth, F. Moldenhauer, and T. Pfeiffer, Use of network analysis of metabolic systems in bioengineering, Bioprocess and Biosystems Engineering, vol.24, issue.6, pp.363-372, 2002.

R. Schwarz, P. Musch, A. Von-kamp, B. Engels, H. Schirmer et al., Yana ? a software tool for analyzing flux modes, gene-expression and enzyme activities, BMC Bioinformatics, vol.6, issue.1, pp.1-12, 2005.

S. Schwendener, Ueber die beziehungen zwischen algen und flechtengonidien, Botanische Zeitung, vol.26, pp.289-292, 1868.

D. Segrè, D. Vitkup, and G. M. Church, Analysis of optimality in natural and perturbed metabolic networks, Proceedings of the National Academy of Sciences, pp.9915112-15117, 2002.
DOI : 10.1073/pnas.232349399

R. S. Senger and E. T. Papoutsakis, : Part I. Metabolic network resolution and analysis, Biotechnology and Bioengineering, vol.71, issue.1, pp.1036-1052, 2008.
DOI : 10.1002/bit.22010

S. Sieuwerts, F. A. De-bok, J. Hugenholtz, and J. E. Van-hylckama-vlieg, Unraveling Microbial Interactions in Food Fermentations: from Classical to Genomics Approaches, Applied and Environmental Microbiology, vol.74, issue.16, pp.744997-5007, 2008.
DOI : 10.1128/AEM.00113-08

. Sigma-aldrich, Metabolic pathway map: http://www.sigmaaldrich.com/content/ dam/sigma-aldrich/docs/Sigma/General_Information/metabolic_pathways_poster. pdf [accessed, pp.2016-2019, 2016.

E. L. Simms, D. L. Taylor, J. Povich, R. P. Shefferson, J. Sachs et al., An empirical test of partner choice mechanisms in a wild legume-rhizobium interaction, Proceedings of the Royal Society B: Biological Sciences, vol.73, issue.1492, pp.27377-81, 1582.
DOI : 10.1098/rspb.2001.1878

J. M. Smith and G. R. Price, The Logic of Animal Conflict, Nature, vol.62, issue.5427, pp.15-18, 1973.
DOI : 10.1038/246015a0

J. Stelling, S. Klamt, K. Bettenbrock, S. Schuster, G. et al., Metabolic network structure determines key aspects of functionality and regulation, Nature, vol.292, issue.6912, pp.420190-193, 2002.
DOI : 10.1103/PhysRevE.64.036106

E. J. Stewart, Growing Unculturable Bacteria, Journal of Bacteriology, vol.194, issue.16, pp.4151-4160, 2012.
DOI : 10.1128/JB.00345-12

K. B. Storey, Functional Metabolism, 2004.
DOI : 10.1002/047167558X

J. Tasoff, M. T. Mee, W. , and H. H. , An Economic Framework of Microbial Trade, PLOS ONE, vol.342, issue.6157, pp.1-20, 2015.
DOI : 10.1371/journal.pone.0132907.s002

M. Terzer and J. Stelling, Large-scale computation of elementary flux modes with bit pattern trees, Bioinformatics, vol.24, issue.19, pp.242229-2235, 2008.
DOI : 10.1093/bioinformatics/btn401

I. Thiele and B. O. Palsson, A protocol for generating a high-quality genome-scale metabolic reconstruction, Nature Protocols, vol.161, issue.1, pp.93-121, 2010.
DOI : 10.1186/1752-0509-3-37

W. W. Toller, R. Rowan, and N. Knowlton, following Experimental and Disease-Associated Bleaching, The Biological Bulletin, vol.201, issue.3, pp.360-373, 2001.
DOI : 10.2307/1543614

A. Traulsen and M. A. Nowak, Evolution of cooperation by multilevel selection, Proceedings of the National Academy of Sciences, pp.10952-10955, 2006.
DOI : 10.1073/pnas.0602530103

C. T. Trinh, A. Wlaschin, and F. Srienc, Elementary mode analysis: a useful metabolic pathway analysis tool for characterizing cellular metabolism, Applied Microbiology and Biotechnology, vol.8, issue.5, pp.813-826, 2008.
DOI : 10.1007/s00253-008-1770-1

R. Urbanczik, Sna ? a toolbox for the stoichiometric analysis of metabolic networks, BMC Bioinformatics, vol.7, issue.1, pp.1-4, 2006.

M. Valls and V. De-lorenzo, Exploiting the genetic and biochemical capacities of bacteria for the remediation of heavy metal pollution, FEMS Microbiology Reviews, vol.26, issue.4, pp.327-338, 2002.
DOI : 10.1111/j.1574-6976.2002.tb00618.x

H. R. Varian, Intermediate Microeconomics: A Modern Approach, 2009.

E. Von-böhm-bawerk, The Positive Theory of Capita, 1891.

A. Von-kamp and S. Klamt, Enumeration of Smallest Intervention Strategies in Genome-Scale Metabolic Networks, PLoS Computational Biology, vol.17, issue.1, p.1003378, 2014.
DOI : 10.1371/journal.pcbi.1003378.t003

J. Von-neumann and O. Morgenstern, Theory of Games and Economic Behavior, 1944.

A. Wagner and D. A. Fell, The small world inside large metabolic networks, Proceedings of the Royal Society B: Biological Sciences, vol.268, issue.1478, pp.1803-1810, 1478.
DOI : 10.1098/rspb.2001.1711

C. Wagner and R. Urbanczik, The Geometry of the Flux Cone of a Metabolic Network, Biophysical Journal, vol.89, issue.6, pp.3837-3845, 2005.
DOI : 10.1529/biophysj.104.055129

M. R. Watson, Metabolic maps for the Apple II, Biochemical Society Transactions, vol.12, issue.6, pp.1093-1094, 1984.
DOI : 10.1042/bst0121093

D. Weininger, SMILES, a chemical language and information system. 1. Introduction to methodology and encoding rules, Journal of Chemical Information and Modeling, vol.28, issue.1, pp.31-36, 1988.
DOI : 10.1021/ci00057a005

G. Welbaum, A. Sturz, Z. Dong, and J. Nowak, Managing Soil Microorganisms to Improve Productivity of Agro-Ecosystems, Critical Reviews in Plant Sciences, vol.112, issue.2, pp.175-193, 2004.
DOI : 10.1023/A:1009998304177

G. D. Werner, J. E. Strassmann, A. B. Ivens, D. J. Engelmoer, E. Verbruggen et al., Evolution of microbial markets, Proceedings of the National Academy of Sciences, pp.1237-1244, 2014.
DOI : 10.1073/pnas.1315980111

URL : https://hal.archives-ouvertes.fr/hal-00939254

S. A. West, E. T. Kiers, E. L. Simms, and R. F. Denison, Sanctions and mutualism stability: why do rhizobia fix nitrogen?, Proceedings of the Royal Society B: Biological Sciences, vol.269, issue.1492, pp.269685-694, 1492.
DOI : 10.1098/rspb.2001.1878

E. G. Weyl, M. E. Frederickson, D. W. Yu, P. , and N. E. , Economic contract theory tests models of mutualism, Proceedings of the National Academy of Sciences, pp.15712-15716, 2010.
DOI : 10.1073/pnas.1005294107

E. H. Wintermute and P. A. Silver, Emergent cooperation in microbial metabolism, Molecular Systems Biology, vol.180, issue.1, 2010.
DOI : 10.1111/j.1420-9101.2006.01258.x

G. A. Wyatt, E. T. Kiers, A. Gardner, and S. A. West, A BIOLOGICAL MARKET ANALYSIS OF THE PLANT-MYCORRHIZAL SYMBIOSIS, Evolution, vol.26, issue.9, pp.682603-2618, 2014.
DOI : 10.1111/evo.12466

G. A. Wyatt, E. T. Kiers, A. Gardner, and S. A. West, Restricting mutualistic partners to enforce trade reliance, Nature Communications, vol.62, 2016.
DOI : 10.1007/s002850050024

R. Zarecki, M. A. Oberhardt, L. Reshef, U. Gophna, and E. And-ruppin, A Novel Nutritional Predictor Links Microbial Fastidiousness with Lowered Ubiquity, Growth Rate, and Cooperativeness, PLoS Computational Biology, vol.6, issue.7, pp.101-113, 2014.
DOI : 10.1371/journal.pcbi.1003726.s003

W. Zhou and L. Nakhleh, Properties of metabolic graphs: biological organization or representation artifacts?, BMC Bioinformatics, vol.12, issue.1, pp.1-12, 2011.
DOI : 10.1038/30918