Theoretical Ecology

, Volume 9, Issue 1, pp 27–37 | Cite as

Stability of a diamond-shaped module with multiple interaction types

  • Alix M. C. SauveEmail author
  • Colin Fontaine
  • Elisa Thébault


Indirect interactions among species emerge from the complexity of ecological networks and can strongly affect the response of communities to disturbances. To determine these indirect interactions and understand better community dynamics, ecologists focused on the interactions within small sets of species or modules. Thanks to their analytical tractability, modules bring insights on the mechanisms occurring in complex interaction networks. So far, most studies have considered modules with a single type of interaction although numerous species are involved in mutualistic and antagonistic interactions simultaneously. In this study, we analyse the dynamics of a diamond-shaped module with multiple interaction types: two resource species sharing a mutualist and a consumer. We describe the different types of indirect interaction occurring between the resource species and the conditions for a stable coexistence of all species. We show that the nature of indirect interactions between resource species (i.e. apparent facilitation, competition or antagonism), as well as stable coexistence, depend on the species generalism and asymmetry of interactions, or in other words, on the distribution of interaction strengths among species. We further unveil that a balance between mutualistic and antagonistic interactions at the level of resource species favours stable coexistence, and that species are more likely to coexist stably if there is apparent facilitation between the two resource species rather than apparent competition. Our results echo existing knowledge on the trophic diamond-shaped module, and confirm that our understanding of communities combining different interaction types can gain from module analyses.


Indirect interactions Diversity of interaction types Mutualism Antagonism Diamond-shaped module Stability Species coexistence Interaction strength 



We warmly thank Pierre Collet whose advices greatly contributed to this work, and Nicolas Loeuille whose comments improved the present manuscript. AMCS was supported with a fellowship by the Chaire “Modélisation Mathématique et Biodiversité” of Veolia Environnement – École Polytechnique – Museum National d’Histoire Naturelle – Fondation X.

Supplementary material

12080_2015_260_MOESM1_ESM.docx (288 kb)
ESM 1 (DOCX 287 kb)


  1. Abrams PA (1999) Is predator-mediated coexistence possible in unstable systems? Ecology 80:608–621Google Scholar
  2. Adler LS, Bronstein JL (2004) Attracting antagonists: does floral nectar increase leaf herbivory? Ecology 85:1519–1526CrossRefGoogle Scholar
  3. Adler LS, Karban R, Strauss SY (2001) Direct and indirect effects of alkaloids on plant fitness via herbivory and pollination. Ecology 82:2032–2044CrossRefGoogle Scholar
  4. Adler LS, Wink M, Distl M, Lentz AJ (2006) Leaf herbivory and nutrients increase nectar alkaloids. Ecol Lett 9:960–967CrossRefPubMedGoogle Scholar
  5. Armstrong RA (1979) Prey species replacement along a gradient of nutrient enrichment: a graphical approach. Ecology 60:76–84CrossRefGoogle Scholar
  6. Arroyo MTK, Till-Bottraud I, Torres C et al (2007) Display size preferences and foraging habits of high Andean butterflies pollinating Chaetanthera lycopodioides (Asteraceae) in the subnival of the Central Chilean Andes. Arct Antarct Alp Res 39:347–352CrossRefGoogle Scholar
  7. Bascompte J, Melián CJ (2005) Simple trophic modules for complex food webs. Ecology 86:2868–2873CrossRefGoogle Scholar
  8. Bascompte J, Jordano P, Olesen JM (2006) Asymmetric coevolutionary networks facilitate biodiversity maintenance. Science 312:431–433CrossRefPubMedGoogle Scholar
  9. Bastolla U, Lässig M, Manrubia SC, Valleriani A (2005) Biodiversity in model ecosystems, I: coexistence conditions for competing species. J Theor Biol 235:521–530CrossRefPubMedGoogle Scholar
  10. Bastolla U, Fortuna MA, Pascual-Garcia A et al (2009) The architecture of mutualistic networks minimizes competition and increases biodiversity. Nature 458:1018–1021CrossRefPubMedGoogle Scholar
  11. Berlow E, Neutel AM, Cohen JE et al (2004) Interaction strengths in food webs: issues and opportunities. J Anim Ecol 73:585–598CrossRefGoogle Scholar
  12. Bertness MD, Callaway RM (1994) Positive interactions in communities. Trends Ecol Evol 9:191–193CrossRefPubMedGoogle Scholar
  13. Bonsall M, Hassell M (1997) Apparent competition structures ecological assemblages. Nature 388:371–373CrossRefGoogle Scholar
  14. Brooker RW, Maestre FT, Callaway RM et al (2008) Facilitation in plant communities: the past, the present, and the future. J Ecol 96:18–34CrossRefGoogle Scholar
  15. Burns TP, Rose KA, Brenkert AL (2014) Quantifying direct and indirect effects of perturbations using model ecosystems. Ecol Model 293:69–80CrossRefGoogle Scholar
  16. Camacho J, Stouffer DB, Amaral LAN (2007) Quantitative analysis of the local structure of food webs. J Theor Biol 246:260–268CrossRefPubMedPubMedCentralGoogle Scholar
  17. Carvalheiro LG, Beismeijer JC, Benadi G et al (2014) The potential for indirect effects between co-flowering plants via shared pollinators depends on resource abundance, accessibility and relatedness. Ecol Lett 17(11):1389–1399CrossRefPubMedGoogle Scholar
  18. Casper BB, Jackson RB (1997) Plant competition underground. Annu Rev Ecol Syst 28:545–570CrossRefGoogle Scholar
  19. Chaneton E, Bonsall M (2000) Enemy-mediated apparent competition: empirical patterns and the evidence. Oikos 88:380–394CrossRefGoogle Scholar
  20. Connell JH (1983) Importance of interspecific competition: evidence from field experiments. Am Nat 122:661–696CrossRefGoogle Scholar
  21. De Ruiter PC, Neutel A-M, Moore J (1995) Energetics, patterns of interaction strengths, and stability in real ecosystems. Science 269:1257–1260CrossRefPubMedGoogle Scholar
  22. Elias M, Fontaine C, van Veen FJF (2013) Evolutionary history and ecological processes shape a local multilevel antagonistic network. Curr Biol 23:1355–1359CrossRefPubMedGoogle Scholar
  23. Fontaine C, Thébault E, Dajoz I (2009) Are insect pollinators more generalist than insect herbivores? Proc Biol Sci 276:3027–3033CrossRefPubMedPubMedCentralGoogle Scholar
  24. Fontaine C, Guimarães PR, Kéfi S et al (2011) The ecological and evolutionary implications of merging different types of networks. Ecol Lett 14:1170–1181CrossRefPubMedGoogle Scholar
  25. Georgelin E, Loeuille N (2014) Dynamics of coupled mutualistic and antagonistic interactions, and their implications for ecosystem management. J Theor Biol 346:67–74CrossRefPubMedGoogle Scholar
  26. Ghazoul J (2005) Pollen and seed dispersal among dispersed plants. Biol Rev Camb Philos Soc 80:413–443CrossRefPubMedGoogle Scholar
  27. Ghazoul J (2006) Floral diversity and the facilitation of pollination. J Ecol 94:295–304CrossRefGoogle Scholar
  28. Goh BS (1979) Stability in models of mutualism. Am Nat 113:261–275CrossRefGoogle Scholar
  29. Grover J, Holt R (1998) Disentangling resource and apparent competition: realistic models for plant-herbivore communities. J Theor Biol 191:353–376CrossRefGoogle Scholar
  30. Harrison GW (1979) Stability under environmental stress: resistance, resilience, persistence, and variability. Am Nat 113:659–669CrossRefGoogle Scholar
  31. Holland JN, DeAngelis D, Bronstein J (2002) Population dynamics and mutualism: functional responses of benefits and costs. Am Nat 159:231–244CrossRefPubMedGoogle Scholar
  32. Holland JN, Wang Y, Sun S, DeAngelis DL (2013) Consumer–resource dynamics of indirect interactions in a mutualism–parasitism food web module. Theor Ecol 6:475–493CrossRefGoogle Scholar
  33. Holt RD (1977) Predation, apparent competition, and the structure of prey communities. Theor Popul Biol 12:197–229CrossRefPubMedGoogle Scholar
  34. Holt RD, Lawton JH (1994) The ecological consequences of shared natural enemies. Annu Rev Ecol Syst 25:495–520CrossRefGoogle Scholar
  35. Holt RD, Grover J, Tilman D (1994) Simple rules for interspecific dominance in systems with exploitative and apparent competition. Am Nat 144:741–771Google Scholar
  36. Kéfi S, Berlow EL, Wieters EA et al (2012) More than a meal… integrating non-feeding interactions into food webs. Ecol Lett 15:291–300CrossRefPubMedGoogle Scholar
  37. Leibold MA (1996) A graphical model of keystone predators in food webs: trophic regulation of abundance. Am Nat 147:784–812CrossRefGoogle Scholar
  38. Levins R (1974) The qualitative analysis of partially specified systems. Ann N Y Acad Sci 231:123–138CrossRefPubMedGoogle Scholar
  39. Loxdale H, Lushai G, Harvey J (2011) The evolutionary improbability of ‘generalism’ in nature, with special reference to insects. Biol J Linn Soc 103:1–18CrossRefGoogle Scholar
  40. MacArthur R, Levins R (1967) The limiting similarity, convergence, and divergence of coexisting species. Am Nat 101:377–385CrossRefGoogle Scholar
  41. Maron JL, Crone E (2006) Herbory: effects on plant abundance, distribution and population growth. Proc R Soc B 273:2575–2584CrossRefPubMedPubMedCentralGoogle Scholar
  42. May RM (1973) Stability in randomly fluctuating versus deterministic environments. Am Nat 107:621–650CrossRefGoogle Scholar
  43. McCann KS, Hastings A, Huxel GR (1998) Weak trophic interactions and the balance of nature. Nature 395:794–798CrossRefGoogle Scholar
  44. Melián CJ, Bascompte J, Jordano P, Krivan V (2009) Diversity in a complex ecological network with two interaction types. Oikos 118:122–130CrossRefGoogle Scholar
  45. Menge BA (1995) Indirect effects in marine rocky intertidal interaction webs: patterns and importance. Ecol Monogr 65:21–74CrossRefGoogle Scholar
  46. Milo R, Shen-Orr S, Itzkovitz S et al (2002) Network motifs: simple building blocks of complex networks. Science 298:824–827CrossRefPubMedGoogle Scholar
  47. Milo R, Itzkovitz S, Kashtan N et al (2004) Superfamilies of evolved and designed networks. Science 303:1538–1542CrossRefPubMedGoogle Scholar
  48. Montoya JM, Woodward G, Emmerson MC et al (2009) Press perturbations and indirect effects in real food webs. Ecology 90(9):2426–2433CrossRefPubMedGoogle Scholar
  49. Morris RJ, Lewis OT, Godfray HCJ (2004) Experimental evidence for apparent competition in a tropical forest food web. Nature 428:310–313CrossRefPubMedGoogle Scholar
  50. Mougi A, Kondoh M (2012) Diversity of interaction types and ecological community stability. Science 337(80):349–351CrossRefPubMedGoogle Scholar
  51. Mougi A, Kondoh M (2014a) Instability of a hybrid module of antagonistic and mutualistic interactions. Popul Ecol 56:257–263CrossRefGoogle Scholar
  52. Mougi A, Kondoh M (2014b) Adaptation in a hybrid world with multiple interaction types: a new mechanism for species coexistence. Ecol Res 29(2):113–119CrossRefGoogle Scholar
  53. Pocock MJO, Evans DM, Memmott J (2012) The robustness and restoration of a network of ecological networks. Science 335(80):973–977CrossRefPubMedGoogle Scholar
  54. Ringel MS, Hu HH, Anderson G (1996) The stability and persistence of mutualisms embedded in community interactions. Theor Popul Biol 50:281–297CrossRefPubMedGoogle Scholar
  55. Sahli HF, Conner JK (2006) Characterizing ecological generalization in plant-pollination systems. Oecologia 148:365–372CrossRefPubMedGoogle Scholar
  56. Sauve AMC, Fontaine C, Thébault E (2014) Structure-stability relationships in networks combining mutualistic and antagonistic interactions. Oikos 123:378–384CrossRefGoogle Scholar
  57. Stachowicz JJ (2001) Mutualism, facilitation, and the structure of ecological communities. Bioscience 51:235–246CrossRefGoogle Scholar
  58. Stouffer DB, Bascompte J (2010) Understanding food-web persistence from local to global scales. Ecol Lett 13:154–161CrossRefPubMedGoogle Scholar
  59. Stouffer DB, Camacho J, Jiang W, Amaral LAN (2007) Evidence for the existence of a robust pattern of prey selection in food webs. Proc Biol Sci 274:1931–1940CrossRefPubMedPubMedCentralGoogle Scholar
  60. Strauss SY (1997) Floral characters link herbivores, pollinators, and plant fitness. Ecology 78:1640–1645CrossRefGoogle Scholar
  61. Theis N (2006) Fragrance of Canada thistle (Cirsium arvense) attracts both floral herbivores and pollinators. J Chem Ecol 32:917–927CrossRefPubMedGoogle Scholar
  62. Tilman D (1977) Resource competition between plankton algae: an experimental and theoretical approach. Ecology 58:338–348CrossRefGoogle Scholar
  63. Travis CC, Post WM (1979) Dynamics and comparative statics of mutualistic. 553–571Google Scholar
  64. Vandermeer JH, Boucher DH (1978) Varieties of mutualistic interaction in population models. J Theor Biol 74:549–558CrossRefPubMedGoogle Scholar
  65. Vázquez DP, Morris WF, Jordano P (2005) Interaction frequency as a surrogate for the total effect of animal mutualists on plants. Ecol Lett 8:1088–1094CrossRefGoogle Scholar
  66. Vázquez DP, Melián CJ, Williams NM et al (2007) Species abundance and asymmetric interaction strength in ecological networks. Oikos 116:1120–1127CrossRefGoogle Scholar
  67. Wootton JT (1994) Putting the pieces together: testing the independence of interactions among organisms. Ecology 75:1544–1551CrossRefGoogle Scholar
  68. Wootton JT (2002) Indirect effects in complex ecosystems: recent progress and future challenges. J Sea Res 48:157–172CrossRefGoogle Scholar
  69. Yodzis P (1988) The indeterminacy of ecological interactions as perceived through perturbation experiments. Ecology 69:508–515CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Alix M. C. Sauve
    • 1
    • 2
    Email author
  • Colin Fontaine
    • 1
  • Elisa Thébault
    • 2
  1. 1.Centre d’Ecologie et des Sciences de la Conservation (CESCO UMR 7204)Sorbonne Universités, MNHN, CNRS, UPMC, CP51ParisFrance
  2. 2.Institute of Ecology and Environmental Sciences - Paris (UMR 7618), UPMC, CNRS, INRA, IRD, Université Paris Diderot, UPECParis Cedex 05France

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