Abstract
Quantifying the strength, sign, and origin of species interactions, along with their dependence on environmental context, is at the heart of prediction and understanding in ecological communities. Pairwise interaction models like Lotka-Volterra provide an important and flexible foundation, but notably absent is an explicit mechanism mediating interactions. Consumer-resource models incorporate mechanism, but describing competitive and mutualistic interactions is more ambiguous. Here, we bridge this gap by modeling a coarse-grained version of a species’ true cellular metabolism to describe resource consumption via uptake and conversion into biomass, energy, and byproducts. This approach does not require detailed chemical reaction information, but it provides a more explicit description of underlying mechanisms than pairwise interaction or consumer-resource models. Using a model system, we find that when metabolic reactions require two distinct resources we recover Liebig’s Law and multiplicative co-limitation in particular limits of the intracellular reaction rates. In between these limits, we derive a more general phenomenological form for consumer growth rate, and we find corresponding rates of secondary metabolite production, allowing us to model competitive and non-competitive interactions (e.g., facilitation). Using the more general form, we show how secondary metabolite production can support coexistence even when two species compete for a shared resource, and we show how differences in metabolic rates change species’ abundances in equilibrium. Building on these findings, we make the case for incorporating coarse-grained metabolism to update the phenomenology we use to model species interactions.
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Abrams PA (1982) Functional responses of optimal foragers. Am Nat 120(3):382–390. https://doi.org/10.1086/283996
Abrams PA (1983) Arguments in favor of higher order interactions. Am Nat 121(6):887–891. https://doi.org/10.1086/284111
Abrams PA (2009) Determining the functional form of density dependence: deductive approaches for Consumer-Resource systems having a single resource. Am Nat 174(3):321–330. https://doi.org/10.1086/603627
Allesina S, Tang S (2012) Stability criteria for complex ecosystems. Nature 483(7388):205–8. https://doi.org/10.1038/nature10832
Barabás G, Michalska-Smith MJ, Allesina S (2017) Self-regulation and the stability of large ecological networks. Nature Ecology & Evolution 1(12):1870–1875. https://doi.org/10.1038/s41559-017-0357-6
Barner AK, Coblentz KE, Hacker SD, Menge BA (2018) Fundamental contradictions among observational and experimental estimates of non-trophic species interactions. Ecology 99(3):557–566. https://doi.org/10.1002/ecy.2133
Brooker RW, Callaghan TV (1998) The balance between positive and negative plant interactions and its relationship to environmental gradients: a model. Oikos 81(1):196. https://doi.org/10.2307/3546481
Butler S, O’Dwyer JP (2018) Stability criteria for complex microbial communities. Nat Commun 9(1):2970. https://doi.org/10.1038/s41467-018-05308-z
Butler S, O’Dwyer JP (2019) Cooperation and stability for complex systems in resource limited environments. Theoretical Ecology In Press
Callaway RM, Walker LR (1997) Competition and facilitation: a synthetic approach to interactions in plant communities. Ecology 78(7):1958–1965. https://doi.org/10.1890/0012-9658(1997)078[1958:CAFASA]2.0.CO;2
Cardinale BJ, Palmer MA, Collins SL (2002) Species diversity enhances ecosystem functioning through interspecific facilitation. Nature 415(6870):426–9. https://doi.org/10.1038/415426a
Cardinale BJ, Duffy JE, Gonzalez A, Hooper DU, Perrings C, Venail P, Narwani A, GM MacE, Tilman D, Wardle DA, Kinzig AP, Daily C, Loreau M, Grace JB, Larigauderie A, Srivastava DS, Naeem S (2012) Biodiversity loss and its impact on humanity. Nature 486 (7401):59–67. https://doi.org/10.1038/nature11148
Carini P, Campbell EO, Morré J, Sañudo-Wilhelmy SA, Thrash JC, Bennett SE, Temperton B, Begley T, Giovannoni SJ (2014) Discovery of a SAR11 growth requirement for thiamin’s pyrimidine precursor and its distribution in the Sargasso Sea. ISME J 8(8):1727–1738. https://doi.org/10.1038/ismej.2014.61
Carrara F, Giometto A, Seymour M, Rinaldo A, Altermatt F (2015) Inferring species interactions in ecological communities: a comparison of methods at different levels of complexity. Methods Ecol Evol 6(8):895–906. https://doi.org/10.1111/2041-210X.12363
Chakraborty S, Nielsen LT, Andersen KH (2017) Trophic strategies of unicellular plankton. Am Nat 189(4):E77–E90. https://doi.org/10.1086/690764
Cherif M, Loreau M (2007) Stoichiometric constraints on resource use, competitive interactions, and elemental cycling in microbial decomposers. Am Nat 169(6):709–724. https://doi.org/10.1086/516844
Cherif M, Loreau M (2010) Towards a more biologically realistic use of Droop’s equations to model growth under multiple nutrient limitation. Oikos 119(6):897–907. https://doi.org/10.1111/j.1600-0706.2010.18397.x
De Ruiter PC, Neutel AM, Moore JC (1995) Energetics, patterns of interaction strengths, and stability in real ecosystems. Science (80- ) 269(5228):1257–1260. https://doi.org/10.1126/science.269.5228.1257
DeAngelis DL, Goldstein RA, O’Neill RV (1975) A model for tropic interaction. Ecology 56(4):881–892. https://doi.org/10.2307/1936298
DeAngelis DL, Mulholland PJ, Palumbo AV, Steinman AD, Huston M A, Elwood JW (1989) Nutrient dynamics and Food-Web stability. Annu Rev Ecol Syst 20:71–95. https://doi.org/10.1146/annurev.es.20.110189.000443
Droop MR (1974) The nutrient status of algal cells in continuous culture. J Mar Biol Assoc U K 54(04):825. https://doi.org/10.1017/S002531540005760X
D’Souza G, Shitut S, Preussger D, Yousif G, Waschina S, Kost C (2018) Ecology and evolution of metabolic cross-feeding interactions in bacteria. Nat Prod Rep 35(5):455–488. https://doi.org/10.1039/c8np00009c
Duffy JE, Cardinale BJ, France KE, McIntyre PB, Thébault E, Loreau M (2007) The functional role of biodiversity in ecosystems: incorporating trophic complexity. Ecol Lett 10(6):522–38. https://doi.org/10.1111/j.1461-0248.2007.01037.x
Duncan SH, Louis P, Flint HJ (2004) Lactate-Utilizing Bacteria, isolated from human feces, that produce butyrate as a major fermentation product. Appl Environ Microbiol 70(10):5810–5817. https://doi.org/10.1128/AEM.70.10.5810-5817.2004
Embree M, Liu JK, Al-Bassam MM, Zengler K (2015) Networks of energetic and metabolic interactions define dynamics in microbial communities. Proc Natl Acad Sci 112(50):15450–15455. https://doi.org/10.1073/pnas.1506034112. arXiv:1011.1669v3
Falkowski PG, Jelen B, Giovannelli D (2016) The role of microbial electron transfer in the coevolution of the geosphere and biosphere. Annu Rev Microbiol 70(1) https://doi.org/10.1146/annurev-micro-102215-095521.
Flynn DFB, Mirotchnick N, Jain M, Palmer MI, Naeem S (2011) Functional and phylogenetic diversity as predictors of biodiversity–ecosystem-function relationships. Ecology 92(8):1573–1581. https://doi.org/10.1890/10-1245.1. arXiv:http://arxiv.org/1011.1669v3
Freilich S, Zarecki R, Eilam O, Segal ES, Henry CS, Kupiec M, Gophna U, Sharan R, Ruppin E (2011) Competitive and cooperative metabolic interactions in bacterial communities. Nat Commun 2:589. https://doi.org/10.1038/ncomms1597
Gause GF, Witt AA (1935) Behavior of mixed populations and the problem of natural selection. Am Nat 69(725):596–609. https://doi.org/10.1086/280628
Glass JB, Orphan VJ (2012) Trace metal requirements for microbial enzymes involved in the production and consumption of methane and nitrous oxide. Front Microbiol 3:1–20. https://doi.org/10.3389/fmicb.2012.00061. http://journal.frontiersin.org/article/10.3389/fmicb.2012.00061/abstract
Gottschalk G (1986) Bacterial metabolism, 2nd edn. Springer, New York
Grilli J, Barabás G, Michalska-Smith MJ, Allesina S (2017) Higher-order interactions stabilize dynamics in competitive network models. Nature 548:210–213. https://doi.org/10.1038/nature23273
Grover JP (1990) Resource competition in a variable environment: phytoplankton growing according to monod’s model. Am Nat 136(6):771–789. https://doi.org/10.1086/285131
Grover JP (2011) Resource storage and competition with spatial and temporal variation in resource availability. Am Nat 178(5):E124–48. https://doi.org/10.1086/662163
Hall SR (2009) Stoichiometrically explicit food webs: feedbacks between resource supply, elemental constraints, and species diversity. Ann Rev Ecol Evol Syst 40(1):503–528. https://doi.org/10.1146/annurev.ecolsys.39.110707.173518
Harpole WS, Ngai JT, Cleland EE, Seabloom EW, Borer ET, Bracken ME, Elser JJ, Gruner DS, Hillebrand H, Shurin JB, Smith JE (2011) Nutrient co-limitation of primary producer communities. Ecol Lett 14(9):852–862. https://doi.org/10.1111/j.1461-0248.2011.01651.x
He Q, Bertness MD, Altieri AH (2013) Global shifts towards positive species interactions with increasing environmental stress. Ecol Lett 16(5):695–706. https://doi.org/10.1111/ele.12080. 2666
Holling CS (1959) The components of predation as revealed by a study of Small-Mammal predation of the european pine sawfly. Can Entomol 91(05):293–320. https://doi.org/10.4039/Ent91293-5
Holt RD (1977) Predation, apparent competition, and the structure of prey communities. Theor Popul Biol 12:197–229. https://doi.org/10.1016/0040-5809(77)90042-9
Ives A, Dennis B, Cottingham K, Carpenter S (2003) Estimating community stability and ecological interactions from time-series data. Ecol Monogr 73(2):301–330. https://doi.org/10.1890/0012-9615(2003)073[0301:ECSAEI]2.0.CO;2
Jiao Y, Navid A, Stewart BJ, McKinlay JB, Thelen MP, Pett-Ridge J (2012) Syntrophic metabolism of a co-culture containing Clostridium cellulolyticum and Rhodopseudomonas palustris for hydrogen production. Int J Hydrog Energy 37(16):11719–11726. https://doi.org/10.1016/j.ijhydene.2012.05.100
Kauffman KJ, Prakash P, Edwards JS (2003) Advances in flux balance analysis. Curr Opin Biotechnol 14(5):491–496. https://doi.org/10.1016/j.copbio.2003.08.001. www.nature.com/nature/journal/v473/n7346/abs/10.1038-nature10011-unlocked.html#supplementary-information
Keller KR, Lau JA (2018) When mutualisms matter: Rhizobia effects on plant communities depend on host plant population and soil nitrogen availability. J Ecol 106(3):1046–1056. https://doi.org/10.1111/1365-2745.12938
Kempes CP, Dutkiewicz S, Follows MJ (2012) Growth, metabolic partitioning, and the size of microorganisms. Proc Natl Acad Sci 109(2):495–500. https://doi.org/10.1073/pnas.1115585109
Koffel T, Boudsocq S, Loeuille N, Daufresne T (2018) Facilitation- vs. competition-driven succession: the key role of resource-ratio. Ecol Lett 21(7):1010–1021. https://doi.org/10.1111/ele.12966
Kooijman SA (1998) The synthesizing unit as model for the stoichiometric fusion and branching of metabolic fluxes. Biophys Chem 73(1–2):179–188. https://doi.org/10.1016/S0301-4622(98)00162-8
Kooijman SA (2001) Quantitative aspects of metabolic organization: a discussion of concepts. Philos Trans R Soc B Biol Sci 356(1407):331–349. https://doi.org/10.1098/rstb.2000.0771
Leibold M, McPeek M (2006) Coexistence of the niche and neutral perspectives in community ecology. Ecology 87(6):1399–1410. https://doi.org/10.1890/0012-9658(2006)87[1399:COTNAN]2.0.CO;2
Litchman E (2003) Competition and coexistence of phytoplankton under fluctuating light: experiments with two cyanobacteria. Aquat Microb Ecol 31:241–248. https://doi.org/10.3354/ame031241
Litchman E, Edwards KF, Klausmeier CA (2015) Microbial resource utilization traits and trade-offs: implications for community structure, functioning, and biogeochemical impacts at present and in the future. Front Microbiol 06:1–10. https://doi.org/10.3389/fmicb.2015.00254
Loreau M (2001) Microbial diversity, producer-decomposer interactions and ecosystem processes: a theoretical model. Proc R Soc 268(1464):303–9. https://doi.org/10.1098/rspb.2000.1366
Loreau M (2010) From populations to ecosystems: theoretical foundations for a new ecological synthesis. Princeton University Press, Princeton
Lotka AJ (1932) The growth of mixed populations: two species competing for a common food supply. J Wash Acad Sci 22(16/17):461–469. https://doi.org/10.1007/978-3-642-50151-7_12
MacArthur R (1970) Species packing and competitive equilibrium for many species. Theor Popul Biol 1(1):1–11. https://doi.org/10.1016/0040-5809(70)90039-0
Marino S, Baxter NT, Huffnagle GB, Petrosino JF, Schloss PD (2014) Mathematical modeling of primary succession of murine intestinal microbiota. Proc Natl Acad Sci 111(1):439–444. https://doi.org/10.1073/pnas.1311322111. arXiv:1011.1669v3
Mee M T, Collins JJ, Church GM, Wang HH (2014) Syntrophic exchange in synthetic microbial communities. Proc Natl Acad Sci USA 111(20):E2149–56. https://doi.org/10.1073/pnas.1405641111
Moore JC, Ruiter PCD, Hunt HW (1993) Influence of productivity on the stability of real and model ecosystems. Science (80- ) 261(5123):906–908. http://www.jstor.org/stable/2882122
Moore JC, McCann K, De Ruiter PC (2005) Modeling trophic pathways, nutrient cycling, and dynamic stability in soils. Pedobiologia (Jena) 49(6):499–510. https://doi.org/10.1016/j.pedobi.2005.05.008
Morris JJ (2015) Black Queen evolution: the role of leakiness in structuring microbial communities. Trends Genet 31(8):475–482. https://doi.org/10.1016/j.tig.2015.05.004
Morris JJ, Lenski RE, Zinser ER (2012) The black queen hypothesis: evolution of dependencies through adaptive gene loss. MBio 3(2):e00036–12. https://doi.org/10.1128/mBio.00036-12
Mougi A, Kondoh M (2012) Diversity of interaction types and ecological community stability. Science 337(6092):349–351. https://doi.org/10.1126/science.1220529
Murdoch WW, Briggs CJ, Nisbet RM (2003) Consumer-resource dynamics, vol 36. Princeton University Press, Princeton
Nisbet RM, Muller EB, Lika K, Kooijman SaLM (2008) From molecules to ecosystems through dynamic energy budget models. J Anim Ecol 69(6):913–926. https://doi.org/10.1111/j.1365-2656.2000.00448.x
Odum EP (1959) Fundamentals of ecology. WB Saunders company
O’Dwyer JP (2018) Whence Lotka-Volterra? Theoretical Ecology 1–12. https://doi.org/10.1007/s12080-018-0377-0
Orth JD, Thiele I, Palsson BO (2010) What is flux balance analysis? Nat Biotechnol 28(3):245–248. https://doi.org/10.1038/nbt.1614, NIHMS150003
Pacheco AR, Moel M, Segrè D (2019) Costless metabolic secretions as drivers of interspecies interactions in microbial ecosystems. Nat Commun 10(1):103. https://doi.org/10.1038/s41467-018-07946-9
Pande S, Merker H, Bohl K, Reichelt M, Schuster S, de Figueiredo LF, Kaleta C, Kost C (2014) Fitness and stability of obligate cross-feeding interactions that emerge upon gene loss in bacteria. ISME J 8:953–62. https://doi.org/10.1038/ismej.2013.211. http://www.ncbi.nlm.nih.gov/pubmed/24285359
Pfeiffer T, Bonhoeffer S (2004) Evolution of cross-feeding in microbial populations. Am Nat 163(6):E126–E135. https://doi.org/10.1086/383593
Price PB, Sowers T (2004) Temperature dependence of metabolic rates for microbial growth, maintenance, and survival. Proc Natl Acad Sci 101(13):4631–4636. https://doi.org/10.1073/pnas.0400522101
Ramírez-Flandes S, González B, Ulloa O (2019) Redox traits characterize the organization of global microbial communities. Proc Natl Acad Sci 116(9):3630–3635. https://doi.org/10.1073/pnas.1817554116
Russell JB, Cook GM (1995) Energetics of bacterial growth: balance of anabolic and catabolic reactions. Microbiol Mol Biol Rev 59(1):48–62
Schimel JP, Weintraub MN (2003) The implications of exoenzyme activity on microbial carbon and nitrogen limitation in soil: a theoretical model. Soil Biol Biochem 35(4):549–563. https://doi.org/10.1016/S0038-0717(03)00015-4
Schoener TW (1983) Field experiments on interspecific competition. Am Nat 122(2):240–285. https://doi.org/10.1086/284133
Sterner RW, Elser JJ (2002) Ecological stoichiometry: the biology of elements from molecules to the biosphere. Princeton University Press, Princeton
Sun Z, Koffel T, Stump S M, Grimaud G M, Klausmeier C A (2019) Microbial cross-feeding promotes multiple stable states and species coexistence, but also susceptibility to cheaters. J Theor Biol 465:63–77. https://doi.org/10.1016/j.jtbi.2019.01.009
Tasoff J, Mee MT, Wang HH (2015) An economic framework of microbial trade. PLoS ONE 10(7):1–20. https://doi.org/10.1371/journal.pone.0132907
Terry JCD, Morris RJ, Bonsall MB (2017) Trophic interaction modifications: an empirical and theoretical framework. Ecol Lett 20(10):1219–1230. https://doi.org/10.1111/ele.12824
Tilman D (1977) Resource competition between plankton algae: an experimental and theoretical approach. Ecology 58(2):338–348
Tilman D (1980) Resources: a graphical-mechanistic approach to competition and predation. Am Nat 116(3):362–393
Tilman D (1987) The importance of the mechanisms of interspecific competition. Am Nat 129(5):769–774. https://doi.org/10.1086/284672
Tilman D, Kilham SS, Kilham P (1982) Phytoplankton community ecology: the role of limiting nutrients. Annu Rev Ecol Syst 13(1):349–372. https://doi.org/10.1146/annurev.es.13.110182.002025
Vellend M (2010) Conceptual synthesis in community ecology. Q Rev Biol 85(2):183–206. https://doi.org/10.1086/652373
Vellend M (2016) The theory of ecological communities. Princeton University Press, Princeton
Volterra V (1926) Fluctuations in the abundance of a species considered mathematically. Nature 118(2972):558–560. https://doi.org/10.1038/118558a0
von Liebig JF, Gregory W (1842) Animal chemistry: or, organic chemistry in its application to physiology and pathology. John Owen
Wiegert RG, Owen DF (1971) Trophic structure, available resources and population density in terrestrial vs. aquatic ecosystems. J Theor Biol 30(1):69–81. https://doi.org/10.1016/0022-5193(71)90037-3
Xiao Y, Angulo MT, Friedman J, Waldor MK, Weiss ST, Liu YY (2017) Mapping the ecological networks of microbial communities. Nat Commun 8(1):2042. https://doi.org/10.1038/s41467-017-02090-2
Zelezniak A, Andrejev S, Ponomarova O, Mende DR, Bork P, Patil KR (2015) Metabolic dependencies drive species co-occurrence in diverse microbial communities. Proc Natl Acad Sci 112 (20):6449–6454. https://doi.org/10.1073/pnas.1421834112,1408.1149
Zomorrodi AR, Segrė D (2016) Synthetic ecology of microbes: mathematical models and applications. J Mol Biol 428(5):837–861. https://doi.org/10.1016/j.jmb.2015.10.019
Acknowledgments
We thank Jake McKinlay, Thomas Koffel, and two anonymous reviewers for critical feedback on an earlier version of this manuscript. This work was supported by the Simons Foundation Grant # 376199 and the James S. McDonnell Foundation Grant # 220020439.
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Muscarella, M.E., O’Dwyer, J.P. Species dynamics and interactions via metabolically informed consumer-resource models. Theor Ecol 13, 503–518 (2020). https://doi.org/10.1007/s12080-020-00466-7
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DOI: https://doi.org/10.1007/s12080-020-00466-7