A. Bordbar, J. M. Monk, Z. A. King, and B. Palsson, Constraint-based models predict metabolic and associated cellular functions, Nature Reviews Genetics, vol.84, issue.2, pp.107-120, 2014.
DOI : 10.1038/ng.2355

N. E. Lewis, H. Nagarajan, and B. 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 : 10.1371/journal.pone.0016274

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

N. Tepper and T. Shlomi, Predicting metabolic engineering knockout strategies for chemical production: accounting for competing pathways, Bioinformatics, vol.165, issue.3, pp.536-543, 2010.
DOI : 10.1006/jtbi.1993.1203

A. Larhlimi, G. Basler, S. Grimbs, J. Selbig, and Z. Nikoloski, Stoichiometric capacitance reveals the theoretical capabilities of metabolic networks, Bioinformatics, vol.13, issue.18, pp.502-508, 2012.
DOI : 10.1016/j.ymben.2011.03.002

URL : https://hal.archives-ouvertes.fr/hal-01177860

C. Pál, B. Papp, and M. J. Lercher, Adaptive evolution of bacterial metabolic networks by horizontal gene transfer, Nature Genetics, vol.428, issue.12, pp.1372-1375, 2005.
DOI : 10.1038/nature02424

B. Papp, C. Pál, and L. D. Hurst, Metabolic network analysis of the causes and evolution of enzyme dispensability in yeast, Nature, vol.51, issue.6992, pp.661-664, 2004.
DOI : 10.1093/NAR/30.1.31

R. U. Ibarra, J. S. Edwards, and B. Palsson, Escherichia coli K-12 undergoes adaptive evolution to achieve in silico predicted optimal growth, Nature, vol.143, issue.6912, pp.186-189, 2002.
DOI : 10.1099/00221287-143-5-1567

E. V. Koonin, The Logic of Chance: The Nature and Origin of Biological Evolution, 2011.

L. Van-valen, A new evolutionary law. Evolutionary theory 1, pp.1-30, 1973.

L. Van-valen, Molecular evolution as predicted by natural selection, Journal of Molecular Evolution, vol.28, issue.2, pp.89-101, 1974.
DOI : 10.1016/B978-1-4832-2734-4.50017-6

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

H. Yang, C. M. Roth, and M. G. Ierapetritou, A rational design approach for amino acid supplementation in hepatocyte culture, Biotechnology and Bioengineering, vol.225, issue.5, pp.1176-1191, 2009.
DOI : 10.1038/nbt1094-994

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.2, issue.Pt 2, pp.3158-3165, 2009.
DOI : 10.1038/nchembio816

Y. A. Goldstein and A. Bockmayr, A Lattice-Theoretic Framework for Metabolic Pathway Analysis, p.14, 2013.
DOI : 10.1007/978-3-642-40708-6_14

A. Chowdhury, A. Zomorrodi, and C. Maranas, Bilevel optimization techniques in computational strain design Computers and Chemical Engineering, pp.363-372, 2015.

G. K. Saharidis and M. G. Ierapetritou, Resolution method for mixed integer bilevel linear problems based on decomposition technique, J Glob Optim, vol.44, issue.29, p.51, 2008.

P. Xu and L. Wang, An exact algorithm for the bilevel mixed integer linear programming problem under three simplifying assumptions, Computers & Operations Research, vol.41, pp.309-318, 2014.
DOI : 10.1016/j.cor.2013.07.016

K. D. Georgios, A. J. Saharidis, and . Conejo, George Kozanidis Exact Solution Methodologies for Linear and (Mixed) Integer Bilevel Programming Chapter, Metaheuristics for Bi-level Optimization, 2013.

M. Microbial, C. Whitman, W. Coleman, D. Wiebe, and W. , Accounting for Multiple Metabolic Networks References 1 Prokaryotes: the unseen majority, Proceedings of the National Academy of Sciences of the United States of America, vol.95, issue.12, p.9618454, 1998.

J. Kallmeyer, R. Pockalny, R. Adhikari, D. Smith, D. Hondt et al., Global distribution of microbial abundance and biomass in subseafloor sediment, Proceedings of the National Academy of Sciences, vol.79, issue.45, Suppl., pp.16213-16216, 2012.
DOI : 10.1029/98EO00426

B. Lin, A. Sakoda, R. Shibasaki, N. Goto, and M. Suzuki, Modelling a global biogeochemical nitrogen cycle in terrestrial ecosystems, Ecological Modelling, vol.135, issue.1, pp.89-110, 2000.
DOI : 10.1016/S0304-3800(00)00372-0

J. Rullkötter, . Organic, and . Matter, The Driving Force for Early Diagenesis In: Marine Geochemistry, pp.125-168, 2006.

C. Jessup, R. Kassen, S. Forde, B. Kerr, A. Buckling et al., Big questions, small worlds: microbial model systems in ecology, Trends in Ecology & Evolution, vol.19, issue.4, pp.189-197, 2004.
DOI : 10.1016/j.tree.2004.01.008

B. Mcgill, B. Enquist, E. Weiher, and M. Westoby, Rebuilding community ecology from functional traits, Trends in Ecology & Evolution, vol.21, issue.4, pp.178-185, 2006.
DOI : 10.1016/j.tree.2006.02.002

S. Krause, L. Roux, X. Niklaus, P. , V. Bodegom et al., Trait-based approaches for understanding microbial biodiversity and ecosystem functioning, Frontiers in Microbiology, vol.406, issue.209, p.24904563, 2014.
DOI : 10.1038/35021046

E. Litchman and C. Klausmeier, Trait-Based Community Ecology of Phytoplankton, Annual Review of Ecology, Evolution, and Systematics, vol.39, issue.1, pp.615-639, 2008.
DOI : 10.1146/annurev.ecolsys.39.110707.173549

N. Segata, D. Boernigen, T. Tickle, X. Morgan, W. Garrett et al., Computational meta'omics for microbial community studies, Molecular Systems Biology, vol.109, issue.1, p.23670539, 2013.
DOI : 10.1073/pnas.1120577109

URL : http://msb.embopress.org/content/msb/9/1/666.full.pdf

M. Waldor, G. Tyson, E. Borenstein, H. Ochman, A. Moeller et al., Where Next for Microbiome Research?, PLOS Biology, vol.19, issue.1, p.25602283, 2015.
DOI : 10.1016/j.mib.2014.05.022

URL : http://journals.plos.org/plosbiology/article/file?id=10.1371/journal.pbio.1002050&type=printable

A. Steunou, S. Jensen, E. Brecht, E. Becraft, M. Bateson et al., Regulation of nif gene expression and the energetics of N2 fixation over the diel cycle in a hot spring microbial mat, The ISME Journal, vol.62, issue.4, pp.364-378, 2008.
DOI : 10.1186/1471-2229-6-15

M. Oberhardt, A. Chavali, and J. Papin, Flux Balance Analysis: Interrogating Genome-Scale Metabolic Networks, In: Systems Biology, pp.61-80, 2009.
DOI : 10.1007/978-1-59745-525-1_3

Y. Kim, S. Nowack, M. Olsen, E. Becraft, J. Wood et al., Diel metabolomics analysis of a hot spring chlorophototrophic microbial mat leads to new hypotheses of community member metabolisms, Frontiers in Microbiology, vol.95, issue.226, pp.1-14, 2015.
DOI : 10.1016/0009-2541(92)90021-V

S. Nash, A survey of truncated-Newton methods, Journal of Computational and Applied Mathematics, vol.124, issue.1-2, pp.45-59, 2000.
DOI : 10.1016/S0377-0427(00)00426-X

J. Hunter and . Matplotlib, Matplotlib: A 2D Graphics Environment, Computing in Science & Engineering, vol.9, issue.3, pp.90-95, 2007.
DOI : 10.1109/MCSE.2007.55

M. Tawarmalani and N. Sahinidis, A polyhedral branch-and-cut approach to global optimization, Mathematical Programming, vol.14, issue.2, pp.225-249, 2005.
DOI : 10.1007/s101079900106

J. Czyzyk, M. Mesnier, and J. Moré, The NEOS Server, IEEE Computational Science and Engineering, vol.5, issue.3, pp.68-75, 1998.
DOI : 10.1109/99.714603

E. Dolan, The NEOS Server 4.0 Administrative Guide, 2001.
DOI : 10.2172/822567

W. Gropp and J. Moré, Optimization Environments and the NEOS Server In: Approximation Theory and Optimization, Buhmann MD and Iserles A, pp.167-182, 1997.

C. Klatt, Z. Liu, M. Ludwig, M. Kuhl, S. Jensen et al., Temporal metatranscriptomic patterning in phototrophic Chloroflexi inhabiting a microbial mat in a geothermal spring, The ISME Journal, vol.675, issue.9, pp.1775-1789, 2013.
DOI : 10.1128/AEM.00705-11

E. Borenstein, M. Kupiec, M. Feldman, and E. Ruppin, Large-scale reconstruction and phylogenetic analysis of metabolic environments, Proceedings of the National Academy of Sciences, vol.13, issue.10, pp.14482-14487, 2008.
DOI : 10.1101/gr.1589103

P. Bordron, M. Latorre, M. Cortés, M. González, S. Thiele et al., Putative bacterial interactions from metagenomic knowledge with an integrative systems ecology approach, MicrobiologyOpen, vol.3, issue.1, pp.106-117, 2016.
DOI : 10.1021/sb4001307

URL : https://hal.archives-ouvertes.fr/hal-01246173

R. Schuetz, N. Zamboni, M. Zampieri, M. Heinemann, and U. Sauer, Multidimensional Optimality of Microbial Metabolism, Science, vol.224, issue.1, pp.601-604, 2012.
DOI : 10.1016/S0022-5193(03)00146-2

J. England, Statistical physics of self-replication, The Journal of Chemical Physics, vol.1, issue.12, p.24089735, 2013.
DOI : 10.1146/annurev.bb.16.060187.001451

N. Toy, illustrating aerobic and anaerobic utilization of glucose. Grey ring represents cell membrane. Circles represent chemical species inside the microorganism, whereas triangles represent chemical species outside cell membrane. Different colors represent different chemical species. Arrows indicate transport from media to intracellular space and vice versa, whereas chemical reactions are represented by curved lines, p.18

T. Achterberg, T. Koch, and A. Martin, Branching rules revisited, Operations Research Letters, vol.33, issue.1, pp.42-54, 2005.
DOI : 10.1016/j.orl.2004.04.002

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, A. Marchetti-spaccamela, M. Sagot, and L. Stougie, A note on the complexity of finding and enumerating elementary modes, Biosystems, issue.3, pp.99210-214, 2010.

E. Adams and G. Rosso, Alpha-ketoglutaric semialdehyde dehydrogenase of Pseudomonas. Properties of the purified enzyme induced by hydroxyproline and of the glucarate-induced and constitutive enzymes, Journal of Biological Chemistry, issue.8, pp.2421802-1814, 1967.

S. F. Altschul, W. Gish, W. Miller, E. W. Myers, and D. J. Lipman, Basic local alignment search tool, Journal of Molecular Biology, vol.215, issue.3, pp.403-410, 1990.
DOI : 10.1016/S0022-2836(05)80360-2

J. F. Bard, Some properties of the bilevel programming problem, Journal of Optimization Theory and Applications, vol.15, issue.2, pp.371-378, 1991.
DOI : 10.1007/BF00941574

C. L. Barrett, T. Y. Kim, H. U. Kim, B. O. Palsson, L. et al., Systems biology as a foundation for genome-scale synthetic biology, Current Opinion in Biotechnology, vol.17, issue.5, pp.488-492, 2006.
DOI : 10.1016/j.copbio.2006.08.001

H. P. Benson, An Outer Approximation Algorithm for Generating AllEfficient Extreme Points in the Outcome Set of a Multiple ObjectiveLinear Programming Problem, Journal of Global Optimization, vol.13, issue.1, 1998.

M. B. Biggs, G. L. Medlock, G. L. Kolling, and J. A. And-papin, Metabolic network modeling of??microbial communities, Wiley Interdisciplinary Reviews: Systems Biology and Medicine, vol.23, issue.183, pp.317-334, 2015.
DOI : 10.1016/j.copbio.2012.02.001

A. Bordbar, J. M. Monk, Z. A. King, and B. O. Palsson, Constraint-based models predict metabolic and associated cellular functions, Nature Reviews Genetics, vol.84, issue.2, pp.107-120, 2014.
DOI : 10.1038/ng.2355

P. Bork, C. Bowler, C. De-vargas, G. Gorsky, E. Karsenti et al., Tara Oceans. Tara Oceans studies plankton at planetary scale, Introduction. Science, issue.6237, p.348873, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01258211

S. P. Boyd and L. Vandenberghe, Convex optimization, 2004.

M. Budinich, J. Bourdon, A. Larhlimi, and D. Eveillard, OPINION PAPER Evolutionary Constraint-Based Formulation Requires New Bi-level Solving Techniques, Computational Methods in Systems Biology, pp.279-281, 2015.
DOI : 10.1007/978-3-319-23401-4_23

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

M. J. Burk and S. Van-dien, Biotechnology for Chemical Production: Challenges and Opportunities, Trends in Biotechnology, vol.34, issue.3, pp.187-190, 2016.
DOI : 10.1016/j.tibtech.2015.10.007

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, pp.42-459, 2014.

S. Chaffron, H. Rehrauer, J. Pernthaler, V. Mering, and C. , A global network of coexisting microbes from environmental and whole-genome sequence data, Genome Research, vol.20, issue.7, pp.947-959, 2010.
DOI : 10.1101/gr.104521.109

URL : https://hal.archives-ouvertes.fr/hal-01518389

M. W. Covert, C. H. Schilling, and B. Palsson, Regulation of Gene Expression in Flux Balance Models of Metabolism, Journal of Theoretical Biology, vol.213, issue.1, pp.73-88, 2001.
DOI : 10.1006/jtbi.2001.2405

J. G. Dillon, S. Fishbain, S. R. Miller, B. M. Bebout, K. S. Habicht et al., High Rates of Sulfate Reduction in a Low-Sulfate Hot Spring Microbial Mat Are Driven by a Low Level of Diversity of Sulfate-Respiring Microorganisms, Applied and Environmental Microbiology, vol.73, issue.16, pp.735218-5226, 2007.
DOI : 10.1128/AEM.00357-07

M. R. Droop, Vitamin B12 and Marine Ecology. IV. The Kinetics of Uptake, Growth and Inhibition in Monochrysis Lutheri, Journal of the Marine Biological Association of the United Kingdom, vol.33, issue.03, pp.689-733, 1968.
DOI : 10.1038/191868a0

URL : https://link.springer.com/content/pdf/10.1007%2FBF01609935.pdf

J. S. Edwards and B. O. Palsson, The Escherichia coli MG1655 in silico metabolic genotype: Its definition, characteristics, and capabilities, Proceedings of the National Academy of Sciences, vol.17, issue.7, pp.975528-5533, 2000.
DOI : 10.1016/S0167-7799(99)01316-5

M. Ehrgott, L. Shao, and A. Schöbel, An approximation algorithm for convex multi-objective programming problems, Journal of Global Optimization, vol.68, issue.3, pp.397-416, 2010.
DOI : 10.1007/s00186-008-0220-2

M. Ehrgott and M. M. Wiecek, Mutiobjective Programming, Multiple Criteria Decision Analysis: State of the Art Surveys, pp.667-708, 2005.
DOI : 10.1007/0-387-23081-5_17

J. L. England, Statistical physics of self-replication, The Journal of Chemical Physics, vol.1, issue.12, p.121923, 2013.
DOI : 10.1146/annurev.bb.16.060187.001451

K. Faust and J. Raes, Microbial interactions: from networks to models, Nature Reviews Microbiology, vol.393, issue.8, pp.538-550, 2012.
DOI : 10.1038/30918

A. M. Feist, C. S. Henry, J. L. Reed, M. Krummenacker, A. R. Joyce et al., A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information, Molecular Systems Biology, vol.64, 2007.
DOI : 10.1093/jb/mvh147

S. S. Fong, Computational approaches to metabolic engineering utilizing systems biology and synthetic biology, Computational and Structural Biotechnology Journal, vol.11, issue.18, pp.28-34, 2014.
DOI : 10.1016/j.csbj.2014.08.005

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

M. Gebser, R. Kaminski, B. Kaufmann, and T. Schaub, Answer Set Solving in Practice, Synthesis Lectures on Artificial Intelligence and Machine Learning, vol.6702, issue.2, 2012.
DOI : 10.1109/ICCAD.2001.968634

P. Glansdorff and I. Prigogine, On a general evolution criterion in macroscopic physics, Physica, vol.30, issue.2, 1964.
DOI : 10.1016/0031-8914(64)90009-6

V. Grimm, U. Berger, F. Bastiansen, S. Eliassen, V. Ginot et al., A standard protocol for describing individual-based and agent-based models, Ecological Modelling, vol.198, issue.1-2, pp.115-126, 2006.
DOI : 10.1016/j.ecolmodel.2006.04.023

L. Guidi, S. Chaffron, L. Bittner, D. Eveillard, A. Larhlimi et al., Plankton networks driving carbon export in the oligotrophic ocean, Nature, vol.18, issue.7600, pp.532465-470, 2016.
DOI : 10.18637/jss.v018.i02

URL : https://hal.archives-ouvertes.fr/hal-01275276

O. Hädicke and S. Klamt, CASOP: A Computational Approach for Strain Optimization aiming at high Productivity, Journal of Biotechnology, vol.147, issue.2, pp.88-101, 2010.
DOI : 10.1016/j.jbiotec.2010.03.006

J. B. Hagen, The origins of bioinformatics, Nature Reviews Genetics, vol.1, issue.3, pp.231-236, 2000.
DOI : 10.1038/35042090

J. B. Hagen, The Origin and Early Reception of Sequence Databases, Data Mining in Proteomics: From Standards to Applications, pp.61-77, 2011.
DOI : 10.1007/978-1-60761-987-1_4

A. H. Hamel, A. Löhne, R. , and B. , Benson type algorithms for linear vector optimization and applications, Journal of Global Optimization, vol.68, issue.3, pp.811-836, 2013.
DOI : 10.1007/s00186-007-0194-5

M. Hanemaaijer, W. F. Rã-ling, B. G. Olivier, R. A. Khandelwal, B. Teusink et al., Systems modeling approaches for microbial community studies: from metagenomics to inference of the community structure, Frontiers in Microbiology, vol.5, issue.125, 2015.
DOI : 10.1038/ismej.2010.117

T. J. Hanly and M. A. Henson, Dynamic flux balance modeling of microbial co-cultures for efficient batch fermentation of glucose and xylose mixtures, Biotechnology and Bioengineering, vol.56, issue.1, pp.376-385, 2010.
DOI : 10.1007/s002530100624

M. Huerta, F. Haseltine, Y. Liu, G. Downing, and B. Seto, NIH Working Definition of, Bioinformatics and Computational Biology, 2000.

R. Jain, M. C. Rivera, and J. A. Lake, Horizontal gene transfer among genomes: The complexity hypothesis, Proceedings of the National Academy of Sciences, vol.226, issue.5252, pp.963801-3806, 1999.
DOI : 10.1038/2261214a0

URL : http://www.pnas.org/content/96/7/3801.full.pdf

C. W. Johnson, What are emergent properties and how do they affect the engineering of complex systems? Reliability Engineering & System Safety, pp.911475-1481, 2006.

A. R. Joyce and B. O. Palsson, The model organism as a system: integrating 'omics' data sets, Nature Reviews Molecular Cell Biology, vol.103, issue.Suppl. 1, pp.198-210, 2006.
DOI : 10.1073/pnas.0509715102

J. Kallmeyer, R. Pockalny, R. R. Adhikari, D. C. Smith, D. Hondt et al., Global distribution of microbial abundance and biomass in subseafloor sediment, Proceedings of the National Academy of Sciences, pp.16213-16216, 2012.
DOI : 10.1029/98EO00426

M. Kanehisa, S. Goto, Y. Sato, M. Kawashima, M. Furumichi et al., Data, information, knowledge and principle: back to metabolism in KEGG, Nucleic Acids Research, vol.42, issue.D1, pp.42-199, 2013.
DOI : 10.1021/ci200367w

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, p.580, 2012.
DOI : 10.1016/S0022-5193(03)00168-1

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

R. A. Khandelwal, B. G. Olivier, W. F. Röling, B. Teusink, and F. J. Bruggeman, Community Flux Balance Analysis for Microbial Consortia at Balanced Growth, PLoS ONE, vol.21, issue.5, p.64567, 2013.
DOI : 10.1371/journal.pone.0064567.s004

T. Y. Kim, S. B. Sohn, Y. Bin-kim, W. J. Kim, L. et al., Recent advances in reconstruction and applications of genome-scale metabolic models, Current Opinion in Biotechnology, vol.23, issue.4, pp.617-623, 2012.
DOI : 10.1016/j.copbio.2011.10.007

S. Kirner, S. Krauss, G. Sury, S. T. Lam, J. M. Ligon et al., The non-haem chloroperoxidase from Pseudomonas fluorescens and its relationship to pyrrolnitrin biosynthesis, Microbiology, vol.142, issue.8, pp.1422129-2135, 1996.
DOI : 10.1099/13500872-142-8-2129

H. Kitano, Computational systems biology, Nature, vol.14, issue.6912, pp.206-210, 2002.
DOI : 10.1038/35002125

H. Kitano, Systems Biology: A Brief Overview, Science, vol.295, issue.5560, pp.2951662-1664, 2002.
DOI : 10.1126/science.1069492

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 and J. Stelling, Two approaches for metabolic pathway analysis? Trends in biotechnology, pp.64-69, 2003.

N. Klitgord and D. Segrè, THE IMPORTANCE OF COMPARTMENTALIZATION IN METABOLIC FLUX MODELS: YEAST AS AN ECOSYSTEM OF ORGANELLES, Genome Informatics 2009, pp.41-55, 2009.
DOI : 10.1142/9781848165786_0005

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

URL : http://doi.org/10.1371/journal.pcbi.1001002

N. Klitgord and D. Segrè, Ecosystems biology of microbial metabolism, Current Opinion in Biotechnology, vol.22, issue.4, pp.541-546, 2011.
DOI : 10.1016/j.copbio.2011.04.018

D. Kondepudi and I. Prigogine, Modern thermodynamics: from heat engines to dissipative structures, 2014.
DOI : 10.1002/9781118698723

S. Krause, L. Roux, X. Niklaus, P. A. Van-bodegom, P. M. Lennon et al., Trait-based approaches for understanding microbial biodiversity and ecosystem functioning, Frontiers in Microbiology, vol.406, issue.209, p.251, 2014.
DOI : 10.1038/35021046

URL : http://journal.frontiersin.org/article/10.3389/fmicb.2014.00251/pdf

A. Larhlimi, G. Basler, S. Grimbs, J. Selbig, and Z. Nikoloski, Stoichiometric capacitance reveals the theoretical capabilities of metabolic networks, Bioinformatics, vol.13, issue.18, pp.28-502, 2012.
DOI : 10.1016/j.ymben.2011.03.002

URL : https://hal.archives-ouvertes.fr/hal-01177860

A. Larhlimi, L. David, J. Selbig, and A. Bockmayr, F2C2: a fast tool for the computation of flux coupling in genome-scale metabolic networks, BMC Bioinformatics, vol.13, issue.1, p.57, 2012.
DOI : 10.1186/1471-2105-13-57

B. L. Lin, A. Sakoda, R. Shibasaki, N. Goto, and M. Suzuki, Modelling a global biogeochemical nitrogen cycle in terrestrial ecosystems, Ecological Modelling, vol.135, issue.1, pp.89-110, 2000.
DOI : 10.1016/S0304-3800(00)00372-0

D. J. Lipman and W. R. Pearson, Rapid and sensitive protein similarity searches, Science, vol.227, issue.4693, pp.2271435-1441, 1985.
DOI : 10.1126/science.2983426

F. Magne, M. L. Oryan, R. Vidal, and M. Farfan, The human gut microbiome of Latin America populations, Current Opinion in Infectious Diseases, vol.29, issue.5, pp.29528-537, 2016.
DOI : 10.1097/QCO.0000000000000300

R. Mahadevan, J. S. Edwards, D. , and F. J. , Dynamic Flux Balance Analysis of Diauxic Growth in Escherichia coli, Biophysical Journal, vol.83, issue.3, pp.1331-1340, 2002.
DOI : 10.1016/S0006-3495(02)73903-9

R. Mahadevan and C. H. Schilling, The effects of alternate optimal solutions in constraint-based genome-scale metabolic models, Metabolic Engineering, vol.5, issue.4, pp.264-276, 2003.
DOI : 10.1016/j.ymben.2003.09.002

R. S. Mandal, S. Saha, and S. Das, Metagenomic Surveys of Gut Microbiota, Genomics, Proteomics & Bioinformatics, vol.13, issue.3, pp.148-158, 2015.
DOI : 10.1016/j.gpb.2015.02.005

P. D. Martins-conde, T. Sauter, and T. Pfau, Constraint Based Modeling Going Multicellular, Frontiers in Molecular Biosciences, vol.8, issue.491, pp.158-111, 2016.
DOI : 10.1371/journal.pcbi.1002363

A. Mas, S. Jamshidi, Y. Lagadeuc, D. Eveillard, and P. Vandenkoornhuyse, Beyond the Black Queen Hypothesis, The ISME Journal, vol.1, issue.9, pp.1-7, 2016.
DOI : 10.1073/pnas.1421834112

URL : https://hal.archives-ouvertes.fr/hal-01290210

J. Monk, J. Nogales, and B. O. Palsson, Optimizing genome-scale network reconstructions, Nature Biotechnology, vol.10, issue.5, pp.447-452, 2014.
DOI : 10.1093/bioinformatics/btt036

J. Monod, The growth of bacterial cultures, Annual Reviews in Microbiology, 1949.

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, 2013.
DOI : 10.1093/bioinformatics/btl267

D. Nagrath, M. Avila-elchiver, F. Berthiaume, A. W. Tilles, A. Messac et al., Integrated Energy and Flux Balance Based Multiobjective Framework for Large-Scale Metabolic Networks, Annals of Biomedical Engineering, vol.7, issue.6, pp.35863-885, 2007.
DOI : 10.1007/s10439-007-9283-0

D. Nagrath, M. Avila-elchiver, F. Berthiaume, A. W. Tilles, A. Messac et al., Soft constraints-based multiobjective framework for flux balance analysis, Metabolic Engineering, vol.12, issue.5, pp.429-445, 2010.
DOI : 10.1016/j.ymben.2010.05.003

Y. Oh, D. Lee, S. Y. Lee, and S. Park, Multiobjective flux balancing using the NISE method for metabolic network analysis, Biotechnology Progress, vol.79, issue.4, pp.999-1008, 2009.
DOI : 10.1007/s00449-002-0309-6

Y. Oh, D. Lee, H. Yuri, S. Y. Lee, and S. Park, Multi-product trade-off analysis of E. coli by multiobjective flux balance analysis, European Symposium on Computer-Aided Process Engineering-14, 37th European Symposium of the Working Party on Computer-Aided Process Engineering, pp.1099-1104, 2004.
DOI : 10.1016/S1570-7946(04)80249-9

J. D. Orth, T. M. Conrad, J. Na, J. A. Lerman, H. Nam et al., A comprehensive genome-scale reconstruction of Escherichia coli metabolism&mdash, Molecular Systems Biology, vol.7, pp.1-9, 2011.

O. Perez-garcia, G. Lear, and N. Singhal, Metabolic Network Modeling of Microbial Interactions in Natural and Engineered Environmental Systems, Frontiers in Microbiology, vol.428, issue.379, pp.93-123, 2016.
DOI : 10.1016/j.jmb.2015.10.019

P. Pharkya, A. P. Burgard, and C. D. Maranas, OptStrain: A computational framework for redesign of microbial production systems, Genome Research, vol.14, issue.11, pp.2367-2376, 2004.
DOI : 10.1101/gr.2872004

P. Pharkya and C. D. Maranas, An optimization framework for identifying reaction activation/inhibition or elimination candidates for overproduction in microbial systems, Metabolic Engineering, vol.8, issue.1, pp.1-13, 2006.
DOI : 10.1016/j.ymben.2005.08.003

C. Picioreanu, M. C. Van-loosdrecht, and J. J. Heijnen, Mathematical modeling of biofilm structure with a hybrid differential-discrete cellular automaton approach, Biotechnology and Bioengineering, vol.22, issue.1, pp.101-116, 1998.
DOI : 10.1111/j.1574-6941.1997.tb00351.x

C. Picioreanu, J. B. Xavier, and M. C. Van-loosdrecht, Advances in mathematical modeling of biofilm structure, Biofilms, vol.1, issue.4, pp.337-349, 2004.
DOI : 10.1017/S1479050505001572

J. Poggiale, P. Dantigny, R. De-wit, and C. Steinberg, Modeling in Microbial Ecology, Environmental Microbiology: Fundamentals and Applications, pp.847-882, 2014.
DOI : 10.1007/978-94-017-9118-2_19

C. Pozo, G. Guillén-gosálbez, A. Sorribas, and L. Jiménez, Identifying the Preferred Subset of Enzymatic Profiles in Nonlinear Kinetic Metabolic Models via Multiobjective Global Optimization and Pareto Filters, PLoS ONE, vol.7, issue.9, pp.43487-43498, 2012.
DOI : 10.1371/journal.pone.0043487.s001

J. Raes, I. Letunic, T. Yamada, L. J. Jensen, and P. Bork, Toward molecular trait-based ecology through integration of biogeochemical, geographical and metagenomic data, Molecular Systems Biology, vol.1, issue.1, pp.1-9, 2011.
DOI : 10.1371/journal.pbio.0050016

K. Raman and N. Chandra, Flux balance analysis of biological systems: applications and challenges, Briefings in Bioinformatics, vol.4, issue.16, pp.435-449, 2009.
DOI : 10.1186/1752-0509-2-20

S. Ranganathan, P. F. Suthers, and C. D. Maranas, OptForce: An Optimization Procedure for Identifying All Genetic Manipulations Leading to Targeted Overproductions, PLoS Computational Biology, vol.68, issue.72, pp.1000744-1000755, 2010.
DOI : 10.1371/journal.pcbi.1000744.s007

C. Rinke, P. Schwientek, A. Sczyrba, N. N. Ivanova, I. J. Anderson et al., Insights into the phylogeny and coding potential of microbial dark matter, Nature, vol.45, issue.7459, pp.499431-437, 2014.
DOI : 10.1093/bib/bbs031

J. Rullkötter, Organic Matter: The Driving Force for Early Diagenesis, Marine Geochemistry, pp.125-168, 2006.

J. Schellenberger, R. Que, R. M. Fleming, I. Thiele, J. D. Orth et al., Quantitative prediction of cellular metabolism with constraint-based models: the COBRA Toolbox v2.0, Nature Protocols, vol.249, issue.9, pp.1290-1307, 2011.
DOI : 10.1165/rcmb.2007-0306OC

C. H. Schilling, D. Letscher, and B. O. 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. Schrijver, Theory of Linear and Integer Programming, 1998.

A. Schrijver, Combinatorial Optimization, 2011.

R. Schuetz, N. Zamboni, M. Zampieri, M. Heinemann, and U. Sauer, Multidimensional Optimality of Microbial Metabolism, Science, vol.224, issue.1, pp.336601-604, 2012.
DOI : 10.1016/S0022-5193(03)00146-2

S. Schuster, D. A. Fell, and T. Dandekar, A general definition of metabolic pathways useful for systematic organization and analysis of complex metabolic networks, Nature Biotechnology, vol.15, issue.3, pp.326-332, 2000.
DOI : 10.1093/bioinformatics/15.3.251

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

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

R. Taffs, J. E. Aston, K. Brileya, Z. Jay, C. G. Klatt et al., In silico approaches to study mass and energy flows in microbial consortia: a syntrophic case study, BMC Systems Biology, vol.3, issue.1, p.114, 2009.
DOI : 10.1186/1752-0509-3-114

E. Talbi, A Taxonomy of Metaheuristics for Bi-level Optimization, Metaheuristics for Bi-level Optimization, chapter 1, pp.1-34, 2013.
DOI : 10.1007/978-3-642-37838-6_1

M. Terzer and J. Stelling, Large-scale computation of elementary flux modes with bit pattern trees, Bioinformatics, vol.89, issue.19, pp.242229-2235, 2008.
DOI : 10.1529/biophysj.104.055129

I. Thiele, A. Heinken, F. , and R. M. , A systems biology approach to studying the role of microbes in human health, Current Opinion in Biotechnology, vol.24, issue.1, pp.4-12, 2013.
DOI : 10.1016/j.copbio.2012.10.001

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

T. J. Treangen and E. P. Rocha, Horizontal Transfer, Not Duplication, Drives the Expansion of Protein Families in Prokaryotes, PLoS Genetics, vol.13, issue.1, pp.1001284-1001296, 2011.
DOI : 10.1371/journal.pgen.1001284.s007

URL : https://hal.archives-ouvertes.fr/pasteur-00578535

E. Tzamali, P. Poirazi, I. G. Tollis, and M. Reczko, A computational exploration of bacterial metabolic diversity identifying metabolic interactions and growth-efficient strain communities, BMC Systems Biology, vol.5, issue.1, p.167, 2011.
DOI : 10.1126/science.1133755

L. Van-valen, A new evolutionary law. Evolutionary theory, pp.1-30, 1973.

L. Van-valen, Molecular evolution as predicted by natural selection, Journal of Molecular Evolution, vol.28, issue.2, pp.89-101, 1974.
DOI : 10.1016/B978-1-4832-2734-4.50017-6

A. Varma and B. O. Palsson, Metabolic Flux Balancing: Basic Concepts, Scientific and Practical Use, Bio/Technology, vol.43, issue.10, 1994.
DOI : 10.1042/bst0121093

A. Varma and B. O. Palsson, Stoichiometric flux balance models quantitatively predict growth and metabolic by-product secretion in wild-type Escherichia coli W3110, Applied and Environmental Microbiology, issue.10, pp.603724-3731, 1994.

L. Vicente, G. Savard, J. , and J. , Descent approaches for quadratic bilevel programming, Journal of Optimization Theory and Applications, vol.7, issue.2, pp.379-399, 1994.
DOI : 10.1287/ijoc.3.1.63

S. Vieira-silva, G. Falony, Y. Darzi, G. Lima-mendez, R. G. Yunta et al., Species???function relationships shape ecological properties of the human gut microbiome, Nature Microbiology, vol.72, issue.8, pp.1-8, 2016.
DOI : 10.1080/10635150701472164

URL : https://hal.archives-ouvertes.fr/hal-01518385

T. D. Vo, H. J. Greenberg, and B. O. Palsson, Reconstruction and Functional Characterization of the Human Mitochondrial Metabolic Network Based on Proteomic and Biochemical Data, Journal of Biological Chemistry, vol.264, issue.38, pp.27939532-39540, 2004.
DOI : 10.1021/bi0261490

V. Volterra, Fluctuations in the Abundance of a Species considered Mathematically, Nature, vol.118, issue.2972, pp.558-560, 1926.
DOI : 10.1038/118558a0

A. J. Wargacki, E. Leonard, M. N. Win, D. D. Regitsky, C. N. Santos et al., An Engineered Microbial Platform for Direct Biofuel Production from Brown Macroalgae, Science, vol.339, issue.8, pp.335308-313, 2012.
DOI : 10.1016/j.carres.2004.03.010

W. B. Whitman, D. C. Coleman, and W. J. Wiebe, Prokaryotes: The unseen majority, Proceedings of the National Academy of Sciences, vol.26, issue.1-2, pp.956578-6583, 1998.
DOI : 10.1007/BF02111285

S. Widder, R. J. Allen, T. Pfeiffer, T. P. Curtis, C. Wiuf et al., Challenges in microbial ecology: building predictive understanding of community function and dynamics, The ISME Journal, vol.11, issue.11, pp.102557-2568, 2016.
DOI : 10.1038/ismej.2011.11

URL : https://hal.archives-ouvertes.fr/hal-01512087

E. H. Wintermute and P. A. Silver, Emergent cooperation in microbial metabolism, Molecular Systems Biology, vol.180, pp.1-7, 2010.
DOI : 10.1111/j.1420-9101.2006.01258.x

L. Yang, W. R. Cluett, and R. Mahadevan, EMILiO: A fast algorithm for genome-scale strain design, Metabolic Engineering, vol.13, issue.3, pp.272-281, 2011.
DOI : 10.1016/j.ymben.2011.03.002

J. Zanghellini, D. E. Ruckerbauer, M. Hanscho, and C. Jungreuthmayer, Elementary flux modes in a nutshell: Properties, calculation and applications, Biotechnology Journal, vol.279, issue.9, pp.1009-1016, 2013.
DOI : 10.1111/j.1742-4658.2012.08700.x

B. Zhang and S. Horvath, A general framework for weighted gene co-expression network analysis. Statistical applications in genetics and molecular biology, p.17, 2005.

A. R. Zomorrodi, M. M. Islam, and C. D. Maranas, d-OptCom: Dynamic Multi-level and Multi-objective Metabolic Modeling of Microbial Communities, ACS Synthetic Biology, vol.3, issue.4, pp.247-257, 2014.
DOI : 10.1021/sb4001307

A. R. Zomorrodi and C. D. Maranas, OptCom: A Multi-Level Optimization Framework for the Metabolic Modeling and Analysis of Microbial Communities, PLoS Computational Biology, vol.6, issue.2, p.1002363, 2012.
DOI : 10.1371/journal.pcbi.1002363.s002