Complexity and Stability of Adaptive Ecological Networks: A Survey of the Theory in Community Ecology

  • Pietro Landi
  • Henintsoa O. Minoarivelo
  • Åke Brännström
  • Cang Hui
  • Ulf Dieckmann
Chapter

Abstract

Background and Significance of the topic: The planet is changing at paces never observed before. Species extinction is happening at faster rates than ever, greatly exceeding the five mass extinctions in the fossil record. Nevertheless, human life is strongly based on services provided by ecosystems, thus the responses to global change of the planet’s natural heritage are of immediate concern. Understanding the relationship between complexity and stability of ecosystems is of key importance for the maintenance of the balance of human growth and the conservation of all the natural services that ecosystems provide. Methodology: The concept of ecological networks and their characteristics are first introduced, followed by central and occasionally contrasting definitions of complexity and stability. The literature on the relationship between complexity and stability in different types of models and few real ecosystems is then reviewed, highlighting the theoretical debate and the lack of consensual agreement. Application/Relevance to systems analysis: This chapter uses ecological-network models to study the relationship between complexity and stability of natural ecosystems. Policy and/or practice implications: Mathematical network models can be used to simplify the vast complexity of the real world, to formally describe and investigate ecological phenomena, and to understand ecosystems propensity of returning to its functioning regime after a stress or a perturbation. Discussion and conclusion: The chapter concludes by summarising the importance of this line of research for the successful management and conservation of biodiversity and ecosystem services.

Keywords

Ecosystem services Community ecology Network complexity Food webs Connectance 

Notes

Acknowledgements

The authors are grateful to the National Research Foundation (NRF) of South Africa and the International Institute for Applied Systems Analysis (IIASA) for organizing the Southern African Young Scientist Summer Program (SA-YSSP). The contribution of two anonymous reviewers is acknowledged. This chapter is based on a review paper by the same authors submitted to Population Ecology.

References

  1. Allesina, S., & Pascual, M. (2008). Network structure, predator-prey modules, and stability in large food webs. Theoretical Ecology, 1, 55–64.CrossRefGoogle Scholar
  2. Allesina, S., & Tang, S. (2012). Stability criteria for complex ecosystems. Nature, 483, 205–208.CrossRefGoogle Scholar
  3. Almeida-Neto, M., Guimarães, P., Guimarães Jr., P. R., et al. (2008). A consistent metric for nestedness analysis in ecological systems: Reconciling concept and measurement. Oikos, 117, 1227–1239.CrossRefGoogle Scholar
  4. Atmar, W., & Patterson, B. D. (1993). The measure of order and disorder in the distribution of species in fragmented habitat. Oecologia, 96, 373–382.CrossRefGoogle Scholar
  5. Bascompte, J., Jordano, P., Melián, C. J., et al. (2003). The nested assembly of plant-animal mutualistic networks. Proceedings of the National Academy of Sciences of the United States of America, 100, 9383–9387.CrossRefGoogle Scholar
  6. Bascompte, J., Jordano, P., & Olesen, J. M. (2006). Asymmetric coevolutionary networks facilitate biodiversity maintenance. Science, 312, 431–433.CrossRefGoogle Scholar
  7. Bastolla, U., Fortuna, M. A., Pascual-Garcia, A., et al. (2009). The architecture of mutualistic networks minimizes competition and increases biodiversity. Nature, 458, 1018–1021.CrossRefGoogle Scholar
  8. Baird, D., Luczkovich, J. J., & Christian, R. R. (1998). Assessment of spatial and temporal variability in ecosystem attributes of the St. Marks National Wildlife Refuge, Apalachee Bay, Florida. Estuarine Coastal Shelf Science, 47, 329–349.CrossRefGoogle Scholar
  9. Baird, D., & Mehta, A. (Eds.). (2011). Estuarine and coastal ecosystem modeling, Volume 9 in Treatise on estuarine and coastal science. Amsterdam: Elsevier.Google Scholar
  10. Banašek-Richter, C., Bersier, L. F., Cattin, M. F., et al. (2009). Complexity in quantitative food webs. Ecology, 90, 1470–1477.CrossRefGoogle Scholar
  11. Beckerman, A., Petchey, O. L., & Morin, P. J. (2010). Adaptive foragers and community ecology: Linking individuals to communities and ecosystems. Functional Ecology, 24, 1–6.CrossRefGoogle Scholar
  12. Berlow, E. L. (1999). Strong effects of weak interactions in ecological communities. Nature, 398, 330–334.CrossRefGoogle Scholar
  13. Berlow, E. L., Neutel, A. M., Cohen, J. E., et al. (2004). Interaction strengths in food webs: Issues and opportunities. Journal of Animal Ecology, 73, 585–598.CrossRefGoogle Scholar
  14. Bersier, L. F., Banašek-Richter, C., & Cattin, M. F. (2002). Quantitative descriptors of food-web matrices. Ecology, 83, 2394–2407.CrossRefGoogle Scholar
  15. Bonchev, D., & Buck, G. A. (2007). Quantitative measures of network complexity. In Complexity in chemistry, biology, and ecology. Berlin: Springer.Google Scholar
  16. Borrelli, J. J., Allesina, S., Amarasekare, P., et al. (2015). Selection on stability across ecological scales. Trends in Ecology & Evolution, 30, 417–425.CrossRefGoogle Scholar
  17. Borrvall, C., Ebenman, B., & Jonsson, T. (2000). Biodiversity lessens the risk of cascading extinction in model food webs. Ecology Letters, 3, 131–136.CrossRefGoogle Scholar
  18. Brännström, Å., Loeuille, N., Loreau, M., et al. (2011). Emergence and maintenance of biodiversity in an evolutionary food-web model. Theoretical Ecology, 4, 467–478. CrossRefGoogle Scholar
  19. Brännström, Å., Johansson, J., Loeuille, N., et al. (2012). Modelling the ecology and evolution of communities: A review of past achievements, current efforts, and future promises. Evolutionary Ecology Research, 14, 601–625.Google Scholar
  20. Brown, J. H., Calder III, W. A., & Kodric-Brown, A. (1978). Correlates and consequences of body size in nectar-feeding birds. American Zoologist, 68, 687–700.CrossRefGoogle Scholar
  21. Campbell, C., Yang, S., Shea, K., et al. (2012). Topology of plant-pollinator networks that are vulnerable to collapse from species extinction. Physical Review E, 86, 02192.CrossRefGoogle Scholar
  22. Camacho, J., Guimerà, R., & Amaral, L. A. N. (2002). Robust patterns in food web structure. Physical Review Letters, 88, 228102.CrossRefGoogle Scholar
  23. Cattin, M. F., Bersier, L. F., Banašek-Richter, C., et al. (2004). Phylogenetic constraints and adaptation explain food-web structure. Nature, 427, 835–839.CrossRefGoogle Scholar
  24. Chen, X., & Cohen, J. E. (2001). Global stability, local stability and permanence in model food webs. Journal of Theoretical Biology, 212, 223–235.CrossRefGoogle Scholar
  25. Christianou, M., & Kokkoris, G. D. (2008). Complexity does not affect stability in feasible model communities. Journal of Theoretical Biology, 253, 162–169.MathSciNetCrossRefGoogle Scholar
  26. Cohen, J. E., & Briand, F. (1984). Trophic links of community food webs. Proceedings of the National Academy of Sciences of the United States of America, 81, 4105–4109.MATHCrossRefGoogle Scholar
  27. Cohen, J. E., & Newman, C. M. (1985). A stochastic theory of community food webs. Proceedings of the Royal Society of London B, 224, 421–448.CrossRefGoogle Scholar
  28. Cohen, J. E., Briand, F., & Newman, C. M. (1990). Community food webs: Data and theory. Biomathematics 20. Berlin: Springer.MATHCrossRefGoogle Scholar
  29. D’Alelio, D., Libralato, S., Wyatt, T., et al. (2016). Ecological-network models link diversity, structure and function in the plankton food-web. Scientific Reports, 6, 21806.CrossRefGoogle Scholar
  30. Darwin, C. (1862). On the various contrivances by which British and foreign orchids are fertilized by insect. London: Murray.Google Scholar
  31. De Angelis, D. L. (1975). Stability and connectance in food web models. Ecology, 56, 238–243.CrossRefGoogle Scholar
  32. De Ruiter, P. C., Neutel, A.-M., & Moore, J. C. (1995). Energetics, patterns of interaction strengths, and stability in real ecosystems. Science, 269, 1257–1260.CrossRefGoogle Scholar
  33. Donohue, I., Petchey, O. L., Montoya, J. M., et al. (2013). On the dimensionality of ecological stability. Ecology Letters, 16, 421–429.CrossRefGoogle Scholar
  34. Dormann, C. F., Fründ, J., Blüthgen, N., et al. (2009). Indices, graphs and null models: Analysing bipartite ecological networks. The Open Ecology Journal, 2, 7–24.CrossRefGoogle Scholar
  35. Dunne, J. A., & Williams, R. J. (2009). Cascading extinctions and community collapse in model food webs. Philosophical Transactions of the Royal Society of London B, 364, 1711–1725.CrossRefGoogle Scholar
  36. Dunne, J. A., Williams, R. J., & Martinez, N. D. (2002a). Food-web structure and network theory: The role of connectance and size. Proceedings of the National Academy of Sciences of the United States of America, 99, 12917–12922.CrossRefGoogle Scholar
  37. Dunne, J. A., Williams, R. J., & Martinez, N. D. (2002b). Network structure and biodiversity loss in food webs: Robustness increases with connectance. Ecology Letters, 8, 558–567.CrossRefGoogle Scholar
  38. Dunne, J. A., Williams, R. J., & Martinez, N. D. (2004). Network structure and robustness of marine food webs. Marine Ecology Progress Series, 273, 291–302.CrossRefGoogle Scholar
  39. Dupont, Y. L., & Olesen, J. M. (2012). Stability of modularity and structural keystone species in temporal cumulative plant-flower-visitor networks. Ecological Complexity, 11, 84–90.CrossRefGoogle Scholar
  40. Ehrlich, P. R., & Raven, P. H. (1964). Butterflies and plants: A study in coevolution. Evolution, 18, 586–608.CrossRefGoogle Scholar
  41. Elton, C. S. (1958). Ecology of invasions by animals and plants. London: Chapman and Hall.CrossRefGoogle Scholar
  42. Emmerson, M. C., & Raffaelli, D. (2004). Predator-prey body size, interaction strength and the stability of a real food web. Journal of Animal Ecology, 73, 399–409.CrossRefGoogle Scholar
  43. Emmerson, M. C., & Yearsley, J. M. (2004). Weak interactions, omnivory and emergent food-web properties. Proceedings of the Royal Society of London B, 271, 397–405.CrossRefGoogle Scholar
  44. Feng, W., & Takemoto, K. (2014). Heterogeneity in ecological mutualistic networks dominantly determines community stability. Scientific Reports, 4, 5912.CrossRefGoogle Scholar
  45. Ferrière, R., Bronstein, J. L., Rinaldi, S., et al. (2002). Cheating and the evolutionary stability of mutualisms. Proceedings of the Royal Society of London B, 269, 773–780.CrossRefGoogle Scholar
  46. Fowler, M. S. (2009). Increasing community size and connectance can increase stability in competitive communities. Journal of Theoretical Biology, 258, 179–188.MathSciNetCrossRefGoogle Scholar
  47. Fussman, G. F., Loreau, M., & Abrams, P. (2007). Eco-evolutionary dynamics of communities and ecosystems. Functional Ecology, 21, 465477.CrossRefGoogle Scholar
  48. Goldwasser, L., & Roughgarden, J. (1993). Construction of a large Caribbean food web. Ecology, 74, 1216–1233.CrossRefGoogle Scholar
  49. Gravel, D., Massol, F., & Leibold, M. A. (2016). Stability and complexity in model meta-communities. Nature Communications, 7, 12457.CrossRefGoogle Scholar
  50. Grilli, J., Rogers, T., & Allesina, S. (2016). Modularity and stability in ecological networks. Nature Communications, 7, 12031.CrossRefGoogle Scholar
  51. Gross, T., Rudolf, L., Levin, S. A., et al. (2009). Generalized models reveal stabilizing factors in food webs. Science, 325, 747–750.CrossRefGoogle Scholar
  52. Gross, T., & Sayama, H. (Eds.). (2009). Adaptive networks: Theory, models and applications. Berlin: Springer.Google Scholar
  53. Havens, K. (1992). Scale and structure in natural food webs. Science, 257, 1107–1109.CrossRefGoogle Scholar
  54. Haydon, D. (1994). Pivotal assumptions determining the relationship between stability and complexity: An analytical synthesis of the stability-complexity debate. American Naturalist, 144, 14–29.CrossRefGoogle Scholar
  55. Haydon, D. (2000). Maximally stable model ecosystems can be highly connected. Ecology, 81, 2631–2636.CrossRefGoogle Scholar
  56. Heckmann, L., Drossel, B., Brose, U., et al. (2012). Interactive effects of body-size structure and adaptive foraging on food-web stability. Ecology Letters, 15, 243–250.CrossRefGoogle Scholar
  57. Heleno, R., Devoto, M., & Pocock, M. (2012). Connectance of species interaction networks and conservation value: Is it any good to be well connected? Ecological Indicators, 14, 7–10.CrossRefGoogle Scholar
  58. Herrera, C. M. (1985). Determinants of plant-animal coevolution: The case of mutualistic dispersal of seeds by vertebrates. Oikos, 44, 132–141.CrossRefGoogle Scholar
  59. Hughes, J. B., & Roughgarden, J. (1998). Aggregate community properties and the strength of species’ interactions. Proceedings of the National Academy of Sciences of the United States of America, 95, 6837–6842.CrossRefGoogle Scholar
  60. Hui, C., & Richardson, D. M. (2017). Invasion dynamics. Oxford University Press.Google Scholar
  61. Hui, C., Richardson, D. M., Landi, P., et al. (2016). Defining invasiveness and invasibility in ecological networks. Biological Invasions, 18, 971–983.CrossRefGoogle Scholar
  62. Ingram, T., Harmon, L. J., & Shurin, J. B. (2009). Niche evolution, trophic structure, and species turnover in model food webs. American Naturalist, 174, 56–67.CrossRefGoogle Scholar
  63. Ives, A. R., Klug, J. L., & Gross, K. (2000). Stability and species richness in complex communities. Ecology Letters, 3, 399–411.CrossRefGoogle Scholar
  64. Jacquet, C., Moritz, C., Morissette, L., et al. (2016). No complexity-stability relationship in empirical ecosystems. Nature Communications, 7, 12573.CrossRefGoogle Scholar
  65. James, A., Pitchford, J. W., & Plank, M. J. (2012). Disentangling nestedness from models of ecological complexity. Nature, 487, 227–230.CrossRefGoogle Scholar
  66. Jordano, P. (1987). Patterns of mutualistic interactions in pollination and seed dispersal: Connectance, dependence asymmetries, and coevolution. American Naturalist, 129, 657–677.CrossRefGoogle Scholar
  67. Jordano, P., Bascompte, J., & Olesen, J. M. (2003). Invariant properties in coevolutionary networks of plant animal interactions. Ecology Letters, 6, 69–81.CrossRefGoogle Scholar
  68. Kaiser-Bunbury, C. N., & Blutghen, N. (2015). Integrating network ecology with applied conservation: A synthesis and guide to implementation. AoB Plants, 7, plv076.CrossRefGoogle Scholar
  69. Kokkoris, G. D., Troumbis, A. Y., & Lawton, J. H. (1999). Patterns of species interaction strength in assembled theoretical competition communities. Ecology Letters, 2, 70–74.CrossRefGoogle Scholar
  70. Kokkoris, G. D., Jansen, V. A. A., Loreau, M., et al. (2002). Variability in interaction strength and implications for biodiversity. Journal of Animal Ecology, 71, 362–371.CrossRefGoogle Scholar
  71. Kondoh, M. (2003). Foraging adaptation and the relationship between food-web complexity and stability. Science, 299, 1388–1391.CrossRefGoogle Scholar
  72. Kondoh, M. (2005). Is biodiversity maintained by food-web complexity? The adaptive food-web hypothesis. In Acquatic food webs: An ecosystem approach (pp. 130–142). Oxford University Press.CrossRefGoogle Scholar
  73. Kondoh, M. (2006). Does foraging adaptation create the positive complexity-stability relationship in realistic food-web structure? Journal of Theoretical Biology, 238, 646–651.MathSciNetCrossRefGoogle Scholar
  74. Kondoh, M. (2007). Anti-predator defence and the complexity-stability relationship of food webs. Proceedings of the Royal Society of London B, 274, 1617–1624.CrossRefGoogle Scholar
  75. Krause, A. E., Frank, K. A., Mason, D. M., et al. (2003). Compartments revealed in food-web structure. Nature, 426, 282–285.CrossRefGoogle Scholar
  76. Landi, P., Dercole, F., & Rinaldi, S. (2013). Branching scenarios in eco-evolutionary prey-predator models. SIAM Journal on Applied Mathematics, 73, 1634–1658.MathSciNetMATHCrossRefGoogle Scholar
  77. Landi, P., & Piccardi, C. (2014). Community analysis in directed networks: In-, out-, and pseudocommunities. Physical Review E, 89, 012814.CrossRefGoogle Scholar
  78. Lawlor, L. R. (1978). Comment on randomly constructed model ecosystems. American Naturalist, 111, 445–447.CrossRefGoogle Scholar
  79. Lawlor, L. R. (1980). Structure and stability in natural and randomly constructed competitive communities. American Naturalist, 116, 394–408.MathSciNetCrossRefGoogle Scholar
  80. Lehman, C. L., & Tilman, D. (2000). Biodiversity, stability, and productivity in competitive communities. American Naturalist, 156, 534–552.CrossRefGoogle Scholar
  81. Logofet, D. O. (2005). Stronger-than-Lyapunov notions of matrix stability, or how “flowers” help solve problems in mathematical ecology. Linear Algebra and its Applications, 398, 75–100.MathSciNetMATHCrossRefGoogle Scholar
  82. Loreau, M., & de Mazancourt, C. (2013). Biodiversity and ecosystem stability: A synthesis of underlying mechanisms. Ecology Letters, 16, 106–115.CrossRefGoogle Scholar
  83. Lyapunov, A. M. (1992). The general problem of the stability of motion. London: Taylor & Francis.MATHGoogle Scholar
  84. May, R. M. (1973). Stability and complexity in model ecosystems. Princeton University Press.Google Scholar
  85. MacArthur, R. H. (1955). Fluctuations of animal populations and a measure of community stability. Ecology, 36, 533–536.CrossRefGoogle Scholar
  86. Martinez, N. D. (1992). Constant connectance in community food webs. American Naturalist, 139, 1208–1218.CrossRefGoogle Scholar
  87. McCann, K., Hastings, A., & Huxel, G. R. (1998). Weak trophic interactions and the balance of nature. Nature, 395, 794–798.CrossRefGoogle Scholar
  88. Martinez, N. D. (1994). Scale-dependent constraints on food-web structure. American Naturalist, 144, 935–953.CrossRefGoogle Scholar
  89. Mello, M. A. R., Marquitti, V. M. D., Guimarães Jr., P. R., et al. (2011). The modularity of seed dispersal: Differences in structure and robustness between bat– and bird–fruit networks. Oecologia, 167, 131–140.CrossRefGoogle Scholar
  90. Memmott, J. (1999). The structure of a plant-pollinator food web. Ecology Letters, 2, 276–280.CrossRefGoogle Scholar
  91. Memmott, J., Waser, N. M., & Price, M. V. (2004). Tolerance of pollination networks to species extinctions. Proceedings of the Royal Society of London B, 271, 2605–2611.CrossRefGoogle Scholar
  92. Memmot, J. (2009). Food webs: A ladder for picking strawberries or a practical tool for practical problems? Philosophical Transactions of the Royal Society of London B, 364, 1693–1699.Google Scholar
  93. Millennium Ecosystem Assessment. (2005). Ecosystems and human well-being: Synthesis. Washington: Island Press.Google Scholar
  94. Minoarivelo, H. O., & Hui, C. (2016). Trait-mediated interaction leads to structural emergence in mutualistic networks. Evolutionary Ecology, 30, 105–121.CrossRefGoogle Scholar
  95. Montoya, J. M., & Solé, R. V. (2002). Small world patterns in food webs. Journal of Theoretical Biology, 214, 405–4012.CrossRefGoogle Scholar
  96. Moore, J. C., & Hunt, H. W. (1988). Resource compartmentation and the stability of real ecosystems. Nature, 333, 261–263.CrossRefGoogle Scholar
  97. Neubert, M. G., & Caswell, H. (1997). Alternatives to resilience for measuring the responses of ecological systems to perturbations. Ecology, 78, 653–665.CrossRefGoogle Scholar
  98. Neutel, A.-M., Heesterbeek, J. A. P., & de Ruiter, P. C. (2002). Stability in real food webs: Weak links in long loops. Science, 296, 1120–1123.CrossRefGoogle Scholar
  99. Neutel, A.-M., Heesterbeek, J. A. P., van de Koppel, J., et al. (2007). Reconciling complexity with stability in naturally assembling food webs. Nature, 449, 599–603.CrossRefGoogle Scholar
  100. Newman, M., & Girvan, M. (2004). Finding and evaluating community structure in networks. Physical Review E, 69, 026113.CrossRefGoogle Scholar
  101. Nuwagaba, S., Zhang, F., & Hui, C. (2015). A hybrid behavioural rule of adaptation and drift explains the emergent architecture of antagonistic networks. Proceedings of the Royal Society of London B, 282, 20150320.CrossRefGoogle Scholar
  102. Odum, E. P. (1953). Fundamentals of ecology. Philadelphia: Saunders.Google Scholar
  103. Okuyama, T. (2008). Do mutualistic networks follow power distributions? Ecological Complexity, 5, 59–65.CrossRefGoogle Scholar
  104. Okuyama, T., & Holland, J. N. (2008). Network structural properties mediate the stability of mutualistic communities. Ecology Letters, 11, 208–216.CrossRefGoogle Scholar
  105. Olesen, J. M., & Jordano, P. (2002). Geographic patterns in plant-pollinator mutualistic networks. Ecology, 83, 2416–2424.Google Scholar
  106. Olesen, J. M., Eskildsen, L. I., & Venkatasamy, S. (2002). Invasion of pollination networks on oceanic islands: Importance of invader complexes and endemic super generalists. Diversity and Distributions, 8, 181–192.CrossRefGoogle Scholar
  107. Olesen, J. M., Bascompte, J., Dupont, Y. L., et al. (2007). The modularity of pollination networks. Proceedings of the National Academy of Sciences of the United States of America, 104, 19891–19896.CrossRefGoogle Scholar
  108. Olff, H., Alonso, D., Berg, M. P., et al. (2009). Parallel ecological networks in ecosystems. Philosophical Transactions of the Royal Society of London B, 364, 1755–1779.CrossRefGoogle Scholar
  109. Olito, C., & Fox, J. W. (2014). Species traits and relative abundances predict metrics of plant-pollinator network structure, but not pairwise interactions. Oikos, 124, 428–436.CrossRefGoogle Scholar
  110. Olivier, T. H., Leather, S. R., & Cook, J. M. (2009). Tolerance traits and the stability of mutualism. Oikos, 118, 346–352.CrossRefGoogle Scholar
  111. Otto, S. B., Rall, B. C., & Brose, U. (2007). Allometric degree distributions facilitate food-web stability. Nature, 450, 1226–1229.CrossRefGoogle Scholar
  112. Paine, R. T. (1992). Food-web analysis through field measurement of per capita interaction strength. Nature, 355, 73–75.CrossRefGoogle Scholar
  113. Petanidou, T., Kallimanis, A. S., Tzanopoulos, J., et al. (2008). Long-term observation of a pollination network: Fluctuation in species and interactions, relative invariance of network structure and implications for estimates of specialization. Ecology Letters, 11, 564–575.CrossRefGoogle Scholar
  114. Pimm, S. L. (1979). Complexity and stability: Another look at MacArthur’s original hypothesis. Oikos, 33, 251–257.CrossRefGoogle Scholar
  115. Pimm, S. L. (1980a). Properties of food webs. Ecology, 61, 219–225.CrossRefGoogle Scholar
  116. Pimm, S. L. (1980b). Food web design and the effect of species deletion. Oikos, 35, 139–149.CrossRefGoogle Scholar
  117. Pimm, S. L. (1984). The complexity and stability of ecosystems. Nature, 307, 321–326.CrossRefGoogle Scholar
  118. Pimm, S. L., & Lawton, J. H. (1978). On feeding on more than one trophic level. Nature, 275, 542–544.CrossRefGoogle Scholar
  119. Pimm, S. L., Lawton, J. H., & Cohen, J. E. (1991). Food web patterns and their consequences. Nature, 350, 669–674.CrossRefGoogle Scholar
  120. Pocock, M. J. O., Evans, D. M., Fontaine, C., et al. (2016). The visualization of ecological networks, and their use as a tool for engagement, advocacy and management. Advances in Ecological Research, 54, 41–85.CrossRefGoogle Scholar
  121. Poisot, T., & Gravel, D. (2014). When is an ecological network complex? Connectance drives degree distribution and emerging network properties. PeerJ, 2, e251.CrossRefGoogle Scholar
  122. Polis, G. (1991). Complex trophic interactions in deserts: An empirical critique of food web theory. American Naturalist, 138, 123–155.CrossRefGoogle Scholar
  123. Ramos-Jiliberto, R., Valdovinos, F. S., de Espanés, P. M., et al. (2012). Topological plasticity increases robustness of mutualistic networks. Journal of Animal Ecology, 81, 896–904.CrossRefGoogle Scholar
  124. Rezende, E. L., Jordano, P., & Bascompte, J. (2007). Effects of phenotypic complementarity and phylogeny on the nested structure of mutualistic networks. Oikos, 116, 1919–1929.CrossRefGoogle Scholar
  125. Rinaldi, S., Della Rossa, F., Dercole, F., et al. (2015). Modeling love dynamics. Singapore: World Scientific.Google Scholar
  126. Rohr, R. P., Saavedra, S., & Bascompte, J. (2014). On the structural stability of mutualistic systems. Science, 345, 1253497.CrossRefGoogle Scholar
  127. Rosvall, M., & Bergstrom, C. T. (2007). An information-theoretic framework for resolving community structure in complex networks. Proceedings of the National Academy of Sciences of the United States of America, 104, 7327–7331.CrossRefGoogle Scholar
  128. Rooney, N., McCann, K., Gellner, G., et al. (2006). Structural asymmetry and the stability of diverse food webs. Nature, 444, 265–269.CrossRefGoogle Scholar
  129. Saint-Béat, B., Baird, D., Asmus, H., et al. (2015). Trophic networks: How do theories link ecosystem structure and functioning to stability properties? A review. Ecological Indicators, 52, 458–471.CrossRefGoogle Scholar
  130. Shannon, C. E. (1948). A mathematical theory of communication. AT&T Technology Journal, 27, 379–342.MathSciNetMATHCrossRefGoogle Scholar
  131. Schoener, T. W. (1989). Food webs from the small to the large. Ecology, 70, 1559–1589.CrossRefGoogle Scholar
  132. Small, M., Judd, K., & Stemler, T. (2013). The stability of networks—Towards a structural dynamical systems theory. ArXiv.Google Scholar
  133. Solé, R. V., & Montoya, J. (2001). Complexity and fragility in ecological networks. Proceedings of the Royal Society of London B, 268, 2039–2045.CrossRefGoogle Scholar
  134. Song, Z., & Fledman, M. W. (2014). Adaptive foraging behaviour of individual pollinators and the coexistence of co-flowering plants. Proceedings of the Royal Society of London B, 281, 20132437.CrossRefGoogle Scholar
  135. Sprules, W. G., & Bowerman, J. E. (1988). Omnivory and food chain length in zooplankton food webs. Ecology, 69, 418–426.CrossRefGoogle Scholar
  136. Strona, G., & Lafferty, K. D. (2016). Environmental change makes robust ecological networks fragile. Nature Communications, 7, 12462.CrossRefGoogle Scholar
  137. Stouffer, D. B., & Bascompte, J. (2011). Compartmentalization increases food-web persistence. Proceedings of the National Academy of Sciences of the United States of America, 108, 3648–3652.CrossRefGoogle Scholar
  138. Suweis, S., Grilli, J., Banavar, J. R., et al. (2015). Effect of localization on the stability of mutualistic ecological networks. Nature Communications, 6, 10179.CrossRefGoogle Scholar
  139. Thébault, E., & Fontaine, C. (2010). Stability of ecological communities and the architecture of mutualistic and trophic interactions. Science, 329, 853–856.CrossRefGoogle Scholar
  140. Tylianakis, J. M., Tscharntke, T., & Lewis, O. T. (2007). Habitat modification alters the structure of tropical host-parasitoid food webs. Nature, 445, 202–205.CrossRefGoogle Scholar
  141. Tylianakis, J. M., Laliberte, E., Nielsen, A., et al. (2010). Conservation of species interaction networks. Biological Conservation, 143, 2270–2279.CrossRefGoogle Scholar
  142. Valdovinos, F. S., de Espanés, P. M., Flores, J. D., et al. (2013). Adaptive foraging allows the maintenance of biodiversity of pollination networks. Oikos, 122, 907–917.CrossRefGoogle Scholar
  143. Valdovinos, F. S., Ramos-Jiliberto, R., Garay-Narvaez, L., et al. (2010). Consequences of adaptive behaviour for the structure and dynamics of food webs. Ecology Letters, 13, 1546–1559.CrossRefGoogle Scholar
  144. van Altena, C., Hemerik, L., & de Ruiter, P. C. (2016). Food web stability and weighted connectance: The complexity stability debate revisited. Theoretical Ecology, 9, 49–58.CrossRefGoogle Scholar
  145. Vázquez, D. P., & Aizen, M. A. (2003). Null model analyses of specialization in plant–pollinator interactions. Ecology, 84, 2493–2501.CrossRefGoogle Scholar
  146. Vieira, M. C., & Almeida-Neto, M. (2015). A simple stochastic model for complex coextinctions in mutualistic networks: Robustness decreases with connectance. Ecology Letters, 18, 144–152.CrossRefGoogle Scholar
  147. Visser, A. W., Mariani, P., & Pigolotti, S. (2012). Adaptive behaviour, tri-trophic food-web stability and damping of chaos. Journal of the Royal Society, Interface, 9, 1373–1380.CrossRefGoogle Scholar
  148. Waser, N. M., Chittka, L., Price, M. V., et al. (1996). Generalization in pollination systems, and why it Matters. Ecology, 77, 1043–1060.CrossRefGoogle Scholar
  149. West, S. A., Kiers, E. T., Pen, I., et al. (2002). Sanctions and mutualism stability: When should less beneficial mutualists be tolerated? Journal of Evolutionary Biology, 15, 830–837.CrossRefGoogle Scholar
  150. Williams, R. J., & Martinez, N. D. (2000). Simple rules yield complex food web. Nature, 404, 180–183.CrossRefGoogle Scholar
  151. Wheelwright, N. T., & Orians, G. H. (1982). Seed dispersal by animals: Contrasts with pollen dispersal, problems of terminology, and constraints on coevolution. American Naturalist, 119, 402–413.CrossRefGoogle Scholar
  152. Wolanski, E., & McLusky, D. (Eds.). (2011). Treatise on estuarine and coastal science. Amsterdam: Elsevier.Google Scholar
  153. Wootton, J. T., & Emmerson, M. (2005). Measurement of interaction strength in nature. Annual Reviews of Ecology and Systematics, 36, 419–444.CrossRefGoogle Scholar
  154. Yodzis, P. (1981). The stability of real ecosystems. Nature, 289, 674–676.CrossRefGoogle Scholar
  155. Zhang, F., Hui, C., & Terblanche, J. S. (2011). An interaction switch predicts the nested architecture of mutualistic networks. Ecology Letters, 14, 797–803.CrossRefGoogle Scholar
  156. Zhang, F., Hui, C., & Pauw, A. (2013). Adaptive divergence in Darwin’s race: how coevolution can generate trait diversity in a pollination system. Evolution, 67, 548–560.CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Pietro Landi
    • 1
    • 2
  • Henintsoa O. Minoarivelo
    • 1
    • 3
  • Åke Brännström
    • 2
    • 4
  • Cang Hui
    • 1
    • 5
  • Ulf Dieckmann
    • 2
  1. 1.Department of Mathematical SciencesStellenbosch UniversityStellenboschSouth Africa
  2. 2.Evolution and Ecology ProgramInternational Institute for Applied Systems AnalysisLaxenburgAustria
  3. 3.Centre of Excellence in Mathematical and Statistical SciencesWits UniversityJohannesburgSouth Africa
  4. 4.Department of Mathematics and Mathematical StatisticsUmeå UniversityUmeåSweden
  5. 5.Mathematical and Physical BiosciencesAfrican Institute for Mathematical SciencesMuizenbergSouth Africa

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