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Dynamics of Simple Food Webs

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An Erratum to this article was published on 11 February 2016

Abstract

We consider a simple food web with commensal relationship, where organisms utilize both external resources and resources produced by other organisms. We show that in such a community with no competition, there is at most one possible equilibrium for each fixed set of surviving species, and develop a natural condition that determines which species survive based on available resource. Our main result shows that among all possible communities described by equilibria, the one which is stable has the largest number of surviving species and largest combined biomass and hence maximizes utilization of available resources.

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References

  • Aota Y, Nakajima H (2001) Mutualistic relationships between phytoplankton and bacteria caused by carbon excretion from phytoplankton. Ecol Res 16:289–299

    Article  Google Scholar 

  • Beardmore R, Gudelj I, Lipson D, Hurst L (2011) Metabolic trade-offs and the maintenance of the fittest and the flattest. Nature 472:342–346

    Article  Google Scholar 

  • Bernstein H, Paulson S, Carlson R (2012) Synthetic Escherichia coli consortia engineered for syntrophy demonstrate enhanced biomass productivity. J Biotechnol 157:159–166

    Article  Google Scholar 

  • Bull J, Harcombe W (2009) Population dynamics constrain the cooperative evolution of cross-feeding. PLoS One 4:e4115

    Article  Google Scholar 

  • Burchard A (1994) Substrate degradation by a mutualistic association of two species in the chemostat. J Math Biol 32:465–489

    Article  MathSciNet  MATH  Google Scholar 

  • de Mazancourt C, Schwartz MW (2010) A resource ratio theory of cooperation. Ecol Lett 13:349–359

    Article  Google Scholar 

  • DeLong JP (2008) The maximum power principle predicts the outcomes of two-species competition experiments. Oikos 117(9):1329–1336. doi:10.1111/j.0030-1299.2008.16832.x

    Article  Google Scholar 

  • Doebeli M (2002) A model for the evolutionary dynamics of cross-feeding polymorphisms in microorganisms. Popul Ecol 44:59–70

    Article  Google Scholar 

  • Eiteman M, Lee S, Altman E (2008) A co-fermentation strategy to consume sugar mixtures effectively. J Biol Eng 2:3

    Article  Google Scholar 

  • Elkhader A (1991) Global stability in a synthrophic chain model. Math Biosci 104:203–245

    Article  MathSciNet  MATH  Google Scholar 

  • Estrela S, Gudejl I (2010) Evolution of cooperative cross-feeding could be less challenging than originally thought. PLoS One 5(e14):121

    Google Scholar 

  • Fierer N, Jackson R (2006) The diversity and biogeography of soil bacterial communities. PNAS 103:626–631

    Article  Google Scholar 

  • Gill S, Pop M, DeBoy R, Eckburg P, Turnbaugh P, Samuel B, Gorden J, Relman D, Fraser-Liggett C, Nelson K (2006) Metagenomic analysis of the human distal gut microbiome. Science 312:1355–1359

    Article  Google Scholar 

  • Helling R, Vargas C, Adams J (1987) Evolution of Escherichia coli during growth in a constant environment. Genetics 116:349–358

    Google Scholar 

  • Kassen R, Buckling A, Bell G, Rainey P (2000) Diversity peaks at intermediate productivity in a laboratory microcosm. Nature 406:508–512

    Article  Google Scholar 

  • Katsuyama C, Nakaoka S, Takeuchi Y, Tago K, Hayatsu M, Kato K (2009) Complementary cooperation between two syntrophic bacteria in pesticide degradation. J Theor Biol 256:644–654

    Article  Google Scholar 

  • Lotka AJ (1922) Contribution to the energetics of evolution. Proc Natl Acad Sci USA 8(147):151

    Article  Google Scholar 

  • Odum HT, Pinkerton RC (1955) Times speed regulator: the optimal efficiency for maximum power output in physical and biological systems. Am Sci 43(321):343

    Google Scholar 

  • Peralta-Yahya P, Zhang F, del Cardayre S, Keasling J (2012) Microbial engineering for the production of advanced biofuels. Nature 488:320–328

    Article  Google Scholar 

  • Pfeiffer T, Bonhoeffer S (2004) Evolution of cross-feeding in microbial populations. Am Nat 163:E126–E135

    Article  Google Scholar 

  • Powell G (1985) Stable coexistence of syntrophic associations in continuous culture. J Chem Technol Biotechnol 35B:46–50

    Article  Google Scholar 

  • Powell G (1986) Stable coexistence of synthrophic chains in continuous culture. Theor Popul Biol 30:17–25

    Article  MATH  Google Scholar 

  • Reilly P (1974) Stability of commensalistic systems. Biotechnol Bioeng 16:1373–1392

    Article  Google Scholar 

  • Rosenzweig F, Sharp R, Treves D, Adams J (1994) Microbial evolution in a simple unstructured environment: genetic differentiation in Escherichia coli. Genetics 137:903–917

    Google Scholar 

  • Rozen D, Lenski R (2000) Long-term experimental evolution in Escherichia coli. VIII. Dynamics of a balanced polymorphism. Am Nat 155:24–35

    Article  Google Scholar 

  • Sari T, El Hajji M, Harmand J (2012) The mathematical analysis of a syntrophic relationship between two microbial species in a chemostat. Math Biosci Eng 9:627–645

    Article  MathSciNet  MATH  Google Scholar 

  • Schink B (1997) Energetics of syntrophic cooperation in methanogenic degradation. Microbiol Mol Biol Rev 61:262–280

    Google Scholar 

  • Seitz H, Schink B, Pfennig N, Conrad R (1990a) Energetics of syntrophic ethanol oxidation in defined chemostat cocultures—1. Energy requirement for H\(_2\) production and H\(_2\) oxidation. Arch Microbiol 155:82–88

    Article  Google Scholar 

  • Seitz H, Schink B, Pfennig N, Conrad R (1990b) Energetics of syntrophic ethanol oxidation in defined chemostat cocultures—2. Energy sharing in biomass production. Arch Microbiol 155:89–93

    Article  Google Scholar 

  • Shong J, Diaz M, Collins C (2012) Towards synthetic microbial consortia for bioprocessing. Curr Opin Biotechnol 23:1–5

    Article  Google Scholar 

  • Smith H, Li B (2003) Competition for essential resources: a brief review. Fields Inst Commun 3:213–227

    MathSciNet  Google Scholar 

  • Tilman D (1982) Resource competition and community structure. Princeton University Press, Princeton

    Google Scholar 

  • Treves D, Manning S, Adams J (1998) Repeated evolution of an acetate-crossfeeding polymorphism in long-term populations of Escherichia coli. Mol Biol Evol 15:789–797

    Article  Google Scholar 

  • Venail P, MacLean R, Bouvier T, Brockhurst M, Hochberg M, Mouguet N (2008) Diversity and productivity peak at intermediate dispersal rate in evolving metacommunities. Nature 452:210–214

    Article  Google Scholar 

  • Venter J, Remingtion K, Heidelberg J, Halpern A, Rusch D, Eisen J, Wu D, Paulsen I, Nelson K, Nelson W, Fouts D, Levy S, Knap A, Lomas M, Nealson K, White O, Peterson J, Hoffman J, Parsons R, Baden-Tillson H, Pfannkock C, Rogers Y, Smith HO (2004) Environmental genome shotgun sequencing of the Sargasso Sea. Science 304:66–74

    Article  Google Scholar 

  • Zuroff T, Curtis W (2012) Developing symbiotic consortia for lignocellulosic biofuel production. Appl Microbiol Biotechnol 93:1423–1435

    Article  Google Scholar 

Download references

Acknowledgments

We would like to thank Jeff Heys and Ross Carlson for many stimulating discussions on microbial consortia. We would also like to thank anonymous referees whose comments significantly improved the presentation of the paper.

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Authors and Affiliations

  1. Department of Mathematics, Montana State University, Bozeman, MT, 59717, USA

    Tomas Gedeon & Patrick Murphy

Authors
  1. Tomas Gedeon
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  2. Patrick Murphy
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Correspondence to Tomas Gedeon.

Additional information

This work was partially supported by NSF Grant DMS-1361240.

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Gedeon, T., Murphy, P. Dynamics of Simple Food Webs. Bull Math Biol 77, 1833–1853 (2015). https://doi.org/10.1007/s11538-015-0106-4

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  • DOI: https://doi.org/10.1007/s11538-015-0106-4

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