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Conflict between dynamical and evolutionary stability in simple ecosystems

Abstract

Here, we address the essential question of whether, in the context of evolving populations, ecosystems attain properties that enable persistence of the ecosystem itself. We use a simple ecosystem model describing resource, producer, and consumer dynamics to analyze how evolution affects dynamical stability properties of the ecosystem. In particular, we compare resilience of the entire system after allowing the producer and consumer populations to evolve to their evolutionarily stable strategy (ESS) to the maximum attainable resilience. We find a substantial reduction in ecosystem resilience when producers and consumers are allowed to evolve compared to the maximal attainable resilience. This study illustrates the inherent difference and possible conflict between maximizing individual-level fitness and maximizing resilience of entire ecosystems.

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References

  • Abrams PA, Matsuda H (1996) Fitness minimization and dynamic instability as a consequence of predator-prey coevolution. Evol Ecol 10:167–186

    Article  Google Scholar 

  • Allen TFH, Hoekstra T (1992) Toward a unified ecology. Columbia University Press, New York

    Google Scholar 

  • Allesina S, Tang S (2012). Stability criteria for complex ecosystems. Nature 483(7388):205–208

    Google Scholar 

  • Armstrong RA (1979) Prey species replacement along a gradient of nutrient enrichment: a graphical approach. Ecology 60(1):76–84

    Article  Google Scholar 

  • Bassar RD, Marshall MC, López-Sepulcre A, Zandonà E, Auer SK, Travis J, Pringle CM, Flecker AS, Thomas SA, Fraser DF, Reznick DN (2010) Local adaptation in trinidadian guppies alters ecosystem processes. Proc Natl Acad Sci 107(8):3616–3621

    CAS  PubMed Central  PubMed  Article  Google Scholar 

  • Branco P, Stomp M, Egas M, Huisman J (2010) Evolution of nutrient uptake reveals a trade-off in the ecological stoichiometry of plant-herbivore interactions. Am Nat 176(6):E162–E176

    PubMed  Article  Google Scholar 

  • Cortez MH, Ellner SP (2010) Understanding rapid evolution in predator-prey interactions using the theory of fast-slow dynamical systems. Am Nat 176(5):E109–E127

    PubMed  Article  Google Scholar 

  • Cottingham KL, Carpenter SR (1994) Predictive indexes of ecosystem resilience in models of north temperate lakes. Ecology 75(7):2127–2138

    Article  Google Scholar 

  • Cropp R, Gabric A (2002) Ecosystem adaptation: do ecosystems maximize resilience?. Ecology 83(7):2019–2026

    Article  Google Scholar 

  • DeAngelis DL (1980) Energy-flow, nutrient cycling, and ecosystem resilience. Ecology 61(4):764–771

    Article  Google Scholar 

  • DeAngelis DL, Bartell SM, Brenkert AL (1989) Effects of nutrient recycling and food-chain length on resilience. Am Nat 134(5):778–805

    Article  Google Scholar 

  • Dieckmann U, Law R (1996) The dynamical theory of coevolution: a derivation from stochastic ecological processes. J Math Biol 34:579–612

    CAS  PubMed  Article  Google Scholar 

  • Doebeli M (2011) Adaptive diversification. Princeton University Press, Princeton

    Google Scholar 

  • Doebeli M, Koella J (1995) Evolution of simple population dynamics. Proc R Soc Biol Sci 260(1358):119–125

    Article  Google Scholar 

  • Ellner S, Becks L (2011) Rapid prey evolution and the dynamics of two-predator food webs. Theor Ecol 4:133–152

    Article  Google Scholar 

  • Ellner SP, Geber MA, Hairston NGJr (2011) Does rapid evolution matter? Measuring the rate of contemporary evolution and its impacts on ecological dynamics. Ecol Lett 14(6):603–614

    PubMed  Article  Google Scholar 

  • Estes J, Tinker M, Williams T, Doak D (1998) Killer whale predation on sea otters linking oceanic and nearshore ecosystems. Science 282(5388):473–476

    CAS  PubMed  Article  Google Scholar 

  • Ferrière R, Gatto M (1993) Chaotic population dynamics can result from natural selection. Proc R Soc Biol Sci 251(1330):33–38

    Article  Google Scholar 

  • Geritz S, Kisdi E, Meszena G, Metz J (1998) Evolutionarily singular strategies and the adaptive growth and branching of the evolutionary tree. Evol Ecol 12(1):35–57

    Article  Google Scholar 

  • Grover J (1994) Assembly rules for communities of nutrient-limited plants and specialist herbivores. Am Nat 143(2):258–282

    Article  Google Scholar 

  • Harmon L, Matthews B, Des Roches S, Chase JM, Shurin J, Schluter D (2009) Evolutionary diversification in stickleback affects ecosystem functioning. Nature 458:1167–1170

    CAS  PubMed  Article  Google Scholar 

  • Hastings KMA, Huxel GR (1998) Weak interactions and the balance of nature. Nature 395:794–798

    Article  Google Scholar 

  • Hochberg M, Holt R (1995) Refuge evolution and the population dynamics of coupled host-parasitoid associations. Evol Ecol 9:633–661

    Article  Google Scholar 

  • Holt RD (1977) Predation, apparent competition, and the structure of prey communities. Theor Popul Biol 12(2):197–229

    Google Scholar 

  • Hulot FD, Loreau M (2006) Nutrient-limited food webs with up to three trophic levels: feasibility, stability, assembly rules, and effects of nutrient enrichment. Theor Popul Biol 69(1):48–66

    PubMed  Article  Google Scholar 

  • Jorgenson SE (2000) Thermodynamics and ecological modeling. CRC Press, Boca Raton

    Google Scholar 

  • Lawlor LR, Smith JM (1976) The coevolution and stability of competing species. Am Nat 110(971):79–99

    Article  Google Scholar 

  • Leibold MA (1996) A graphical model of keystone predators in food webs: trophic regulation of abundance, incidence, and diversity patterns in communities. Am Nat 147(5):784–812

    Article  Google Scholar 

  • Loeuille N (2010) Influence of evolution on the stability of ecological communities. Ecol Lett 13:1536–1545

    PubMed  Article  Google Scholar 

  • Loeuille N, Loreau M (2004) Nutrient enrichment and food chains: can evolution buffer top-down control? Theor Popul Biol 65(3):285–298

    PubMed  Article  Google Scholar 

  • Loeuille N, Loreau M, Ferriere R (2002) Consequences of plant-herbivore coevolution on the dynamics and functioning of ecosystems. J Theor Biol 217(3):369–381

    PubMed  Article  Google Scholar 

  • Loreau M (1998) Biodiversity and ecosystem functioning: a mechanistic model. Proc Natl Acad Sci USA 95:5632–5636

    CAS  PubMed Central  PubMed  Article  Google Scholar 

  • Loreau M (2010) From populations to ecosystems Monographs in population biology. Princeton University Press, Princeton

  • Marrow P, Dieckmann U, Law R (1996) Evolutionary dynamics of predator-prey systems: an ecological perspective. J Math Biol 34:556–578

    CAS  PubMed  Article  Google Scholar 

  • May RM (1973) Stability and complexity in model ecosystems. Princeton University Press, Princeton

    Google Scholar 

  • de Mazancourt C, Dieckmann U (2004) Trade-off geometries and freqency dependent selection. Am Nat 164(6):765–778

    Article  Google Scholar 

  • Miner B, De Meester L, Pfrender M, Lampert W, Hairston NGJr (2012) Linking genes to communities and ecosystems: Daphnia as an ecogenomic model. Proc R Soc Biol Sci 279(1735):1873–1882

    Article  Google Scholar 

  • Müller F, Hoffmann-Kroll R, Wiggering H (2000) Indicating ecosystem integrity—from ecosystem theories to eco targets, models, indicators and variables. Ecol Model 130:13–23

    Article  Google Scholar 

  • Neubert MG, Caswell H (1997) Alternatives to resilience for measuring the responses of ecological systems to perturbations. Ecology 78(3):653–665

    Article  Google Scholar 

  • Odum EP (1969) Strategy of ecosystem development. Science 164(3877):262–&

    Google Scholar 

  • Pattee HH (1972) The relevance of general systems theory, Braziller, New York, chap The evolution of self-simplifying systems pp 33–41

  • Pimm SL (1984) The complexity and stability of ecosystems. Nature 307(5949):321–326

    Article  Google Scholar 

  • Rosenzweig M (1971) Paradox of enrichment—destabilization of exploitation ecosystems in ecological time. Science 171(3969):385–&

    CAS  PubMed  Article  Google Scholar 

  • Schneider ED, Kay JJ (1994) Life as a manifestation of the second law of thermodynamics. Math Comput Model 19(6–8):25–48

    Article  Google Scholar 

  • Schoener T (2011) The newest synthesis: understanding the interplay of evolutionary and ecological dynamics. Science 331(6016):426–429

    CAS  PubMed  Article  Google Scholar 

  • Steiner CF, Long ZT, Krumins JA, Morin PJ (2006) Population and community resilience in multitrophic communities. Ecology 87(4):996–1007

    PubMed  Article  Google Scholar 

  • Thèbault E, Loreau M (2007) Trophic interactions and the relationship between species diversity and ecosystem stability. Am Nat 166(4):E95–E114

    PubMed  Article  Google Scholar 

  • Tilman D, Reich PB, Knops J, Wedin D, Mielke T, Lehman C (2001) Diversity and productivity in a long-term grassland experiment. Science 294:843–845

    CAS  PubMed  Article  Google Scholar 

  • Ulanowicz R (1997) Ecology, the ascendent perspective. Columbia University Press, New York

    Google Scholar 

  • Valdovinos FS, Ramos-Jiliberto R, Garay-Narvaez L, Urbani P, Dunne JA (2010) Consequences of adaptive behaviour for the structure and dynamics of food webs. Ecol Lett 13(12):1546–1559

    PubMed  Article  Google Scholar 

  • Vallina SM, Le Quere C (2011) Stability of complex food webs: resilience, resistance and the average interaction strength. J Theor Biol 272(1):160–173

    PubMed  Article  Google Scholar 

  • Vitousek P, Cassman K, Cleveland C, Crews T, Field CB, Grimm N, Howarth R, Marino R, Martinelli L, Rastetter E, Sprent J (2002) Towards an ecological understanding of biological nitrogen fixation. Biogeochemistry 57/58:1–45

    CAS  Article  Google Scholar 

  • Walsh JJ (1981) A carbon budget for overfishing off Peru. Nature 290:300–304

    Article  Google Scholar 

  • Webb C (2003) A complete classification of Darwinian extinction in ecological interactions. Am Nat 161:181–U1

    PubMed  Article  Google Scholar 

  • Wilson HB, Hassell MP, Godfray HCJ (1996) Host-parasitoid food webs: dynamics, persistence, and invasion. Am Nat 148(5):787–806

    Article  Google Scholar 

  • Yoshida T, Hairston NGJr, Ellner SP (2004) Evolutionary trade-off between defence against grazing and competitive ability in a simple unicellular alga, Chlorella vulgaris. Proc R Soc Lond Ser B-Biol Sci 271:1947–1953

    Article  Google Scholar 

Download references

Acknowledgments

The authors would like to acknowledge several anonymous reviewers for providing helpful comments that led to improvements of the manuscript. The Centre for Biodiversity Theory and Modelling is supported by the TULIP Laboratory of Excellence (ANR-10-LABX-41).

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Correspondence to Jarad P. Mellard.

Appendix

Appendix

Stability of ecological equilibrium

We classify the stability of the interior equilibrium. The elements of the Jacobian matrix at equilibrium (8) from the characteristic equation

$$ a_{3} \lambda^3+a_{2} \lambda^2+a_{1} \lambda+a_0=0. $$
(14)

In order to be a stable equilibrium, the coefficients must satisfy the following Routh-Hurwitz criteria (May 1973): a n > 0 and a 2 a 1 > a 3 a 0. It is easy to show that a 3 > 0 and a 2 > 0. For the other coefficients, a 1 > 0 if \(\frac {I \Omega (k l + b)}{q + \Omega \Psi } > m b\) and a 0 > 0 if I Ω > m(q + ΩΨ). The second Routh-Hurwitz criterion, a 2 a 1 > a 3 a 0, can be simplified to kl > 0, which is always true since both of these parameters are always (+).

Interpreting the CSS-example, location of producer CSS with producer evolution only

The CSS s P of the producer is partly determined by the consumer strategy s H because the consumer trait s H determines which s P strategies get grazed on most heavily. In this model, the producers are limited by grazing, which means that although there is a trade-off between nutrient uptake and susceptibility to grazing, the producer CSS strategy mainly conforms to what strategy reduces grazing the most (while keeping nutrient uptake as high as possible). For example, in Fig. 8, the producer CSS strategies are all located on the tails of the grazing versus s P curve. Note that no consumers in the system leads to runaway selection for maximum nutrient uptake of the producers.

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Mellard, J.P., Ballantyne, F. Conflict between dynamical and evolutionary stability in simple ecosystems. Theor Ecol 7, 273–288 (2014). https://doi.org/10.1007/s12080-014-0217-9

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Keywords

  • Dynamical stability
  • Evolutionary stability
  • Resilience
  • ESS
  • Ecosystem properties