Constructing random matrices to represent real ecosystems

American Naturalist

Volumn 185, Issue 5, 2015, Pages 680-692

  James, Alex ^a,b   Plank, Michael J ^a,b   Rossberg, Axel G ^c,d   Beecham, Jonathan ^c   Emmerson, Mark ^d   Pitchford, Jonathan W ^e  

^a UNIVERSITY OF CANTERBURY   (New Zealand)

^b New Zealand Centre of Research Excellence in Complex Systems and Data Analytics   (New Zealand)

^c CENTRE FOR ENVIRONMENT   (United Kingdom)

^d QUEEN'S UNIVERSITY BELFAST   (United Kingdom)

^e UNIVERSITY OF YORK   (United Kingdom)

Author keywords

Community matrix; Complexity; Food web; Interaction strength; Predator prey interaction; Stability

Indexed keywords

COMMUNITY DYNAMICS; COMPLEXITY; FOOD WEB; INTRASPECIFIC COMPETITION; NUMERICAL MODEL; PREDATOR-PREY INTERACTION; THEORETICAL STUDY;

ANIMAL; COMPETITIVE BEHAVIOR; ECOSYSTEM; FOOD CHAIN; POPULATION DYNAMICS; PREDATION; THEORETICAL MODEL;

ANIMALS; COMPETITIVE BEHAVIOR; ECOSYSTEM; FOOD CHAIN; MODELS, THEORETICAL; POPULATION DYNAMICS; PREDATORY BEHAVIOR;

EID: 84928473798     PISSN: 00030147     EISSN: None     Source Type: Journal    
DOI: 10.1086/680496     Document Type: Article

References (58)

1. Allesina, S., and M. Pascual. 2008. Network structure, predator-prey modules, and stability in large food webs. Theoretical Ecology 1:55–64.
2. Allesina, S., and S. Tang. 2012. Stability criteria for complex ecosystems. Nature 483:205–208.
3. Bastolla, U., M. A. Fortuna, A. Pascual-Garca, A. Ferrera, B. Luque, and J. Bascompte. 2009. The architecture of mutualistic networks minimizes competition and increases biodiversity. Nature 458: 1018–1020.
4. Berlow, E. L., S. A. Navarrete, C. J. Briggs, M. E. Power, and B. A. Menge. 1999. Quantifying variation in the strengths of species interactions. Ecology 80:2206–2224.
5. Brose, U., R. J. Williams, and N. D. Martinez. 2006. Allometric scaling enhances stability in complex food webs. Ecology Letters 9: 1228–1236.
6. Christensen, V., and D. Pauly. 1992. Ecopath II—a software for balancing steady-state ecosystem models and calculating network characteristics. Ecological Modelling 61:169–185.
7. Dalsgaard, J., S. S. Wallace, S. Salas, and D. Preikshot. 1998. Massbalance model reconstructions of the Strait of Georgia: the present, one hundred, and five hundred years ago. Pages 72–91 in D. Pauly, T. Pitcher, D. Preikshot, and J. Hearne, eds. Back to the future: reconstructing the Strait of Georgia ecosystem. Vol. 6. Fisheries Centre Research Reports. University of British Columbia, Vancouver.
8. Dambacher, J. M., H.-K. Luh, H. W. Li, and P. A. Rossignol. 2003. Qualitative stability and ambiguity in model ecosystems. American Naturalist 161:876–888.
9. Datta, S., G. W. Delius, and R. Law. 2010. A jump-growth model for predator-prey dynamics: derivation and application to marine ecosystems. Bulletin of Mathematical Biology 72:1361–1382.
10. de Angelis, D. L. 1975. Stability and connectance in food web models. Ecology 56:238–243.
11. de Ruiter, P. C., A.-M. Neutel, and J. C. Moore. 1995. Energetics, patterns of interaction strengths, and stability in real ecosystems. Science 269:1257–1260.
12. de Ruiter, P. C., J. A. Van Veen, J. C. Moore, L. Brussaard, and H. W. Hunt. 1993. Calculation of nitrogen mineralization in soil food webs. Plant and Soil 157:263–273.
13. Elton, C. S. 1958. The ecology of invasions by animals and plants. Methuen, London.
14. Emmerson, M. C., and D. Raffaelli. 2004. Predator-prey body size, interaction strength and the stability of a real food web. Journal of Animal Ecology 73:399–409.
15. Emmerson, M. C., and J. M. Yearsley. 2004. Weak interactions, omnivory and emergent food-web properties. Proceedings of the Royal Society B: Biological Sciences 271:397–405.
16. Erdös, P., and A. Rényi. 1960. On the evolution of random graphs. Publications of the Mathematical Institute of the Hungarian Academy of Sciences 5:17–61.
17. Gravel, D., E. Canard, F. Guichard, and N. Mouquet. 2011. Persistence increases with diversity and connectance in trophic metacommunities. PLoS ONE 6:e19374. doi:10.1371/journal.pone.0019374.
18. Gribble, N. A. 2005. Ecosystem modelling of the great barrier reef: a balanced trophic biomass approach. Pages 2561–2567 in A. Zerger and R. M. Argent, eds. Modelling and Simulation Society of Australia and New Zealand.
19. Grimm, V., and C. Wissel. 1997. Babel, or the ecological stability discussions: an inventory and analysis of terminology and a guide for avoiding confusion. Oecologia (Berlin) 109:323–334.
20. Guénette, S., and V. Christensen. 2005. Food web models and data for studying fisheries and environmental impacts on eastern Pacific ecosystems. Vol. 13. Fisheries Centre Research Reports. University of British Columbia, Vancouver.
21. 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.
22. Haydon, D. 2000. Maximally stable model ecosystems can be highly connected. Ecology 81:2631–2636.
23. Hofbauer, J., and K. Sigmund. 1998. Evolutionary games and population dynamics. Cambridge University Press, Cambridge.
24. Jacquet, C., C. Moritz, L. Morissette, P. Legagneux, F. Massol, P. Archambault, and D. Gravel. 2013. No complexity-stability relationship in natural communities. arXiv preprint. arXiv:1307.5364.
25. Jansen, W. 1987. A permanence theorem for replicator and Lotka- Volterra systems. Journal of Mathematical Biology 25:411–422.
26. Jonsson, T., J. E. Cohen, and S. R. Carpenter. 2005. Food webs, body size, and species abundance in ecological community description. Advances in Ecological Research 36:1–84.
27. Law, R., and J. C. Blackford. 1992. Self-assembling food webs: a global viewpoint of coexistence of species in Lotka-Volterra communities. Ecology 73:567–578.
28. Levins, R. 1979. Coexistence in a variable environment. American Naturalist 114:765–783.
29. MacArthur, R. 1955. Fluctuations of animal populations and a measure of community stability. Ecology 36:533–536.
30. Mackinson, S., and G. Daskalov. 2007. An ecosystem model of the North Sea to support an ecosystem approach to fisheries management: description and parameterisation. Cefas Science Series Technical Report 142.
31. May, R. M. 1972. Will a large complex system be stable? Nature 238:413–414.
32. McCann, K., A. Hastings, and G. R. Huxel. 1998. Weak trophic interactions and the balance of nature. Nature 395:794–798.
33. McCann, K. S. 2000. The diversity-stability debate. Nature 405:228–233.
34. Meszéna, G., M. Gyllenberg, L. Pásztor, and J. A. J. Metz. 2006. Competitive exclusion and limiting similarity: a unified theory. Theoretical Population Biology 69:68–87.
35. Metha, M. L. 1967. Random matrices and the statistical theory of energy levels. Academic Press, New York.
36. Moellmann, C., and R. Diekmann. 2012. Marine ecosystem regime shifts induced by climate and overfishing: a review for the Northern Hemisphere. Advances in Ecological Research 47:303–347.
37. Moore, J. C., P. C. de Ruiter, and H. W. Hunt. 1993. Influence of productivity on the stability of real and model ecosystems. Science 261:906–908.
38. Moore, J. C., P. C. de Ruiter, H. W. Hunt, D. C. Coleman, and D. W. Freckman. 1996. Microcosms and soil ecology: critical linkages between fields studies and modelling food webs. Ecology 77:694–705.
39. Neutel, A.-M., J. A. P. Heesterbeek, and P. C. de Ruiter. 2002. Stability in real food webs: weak links in long loops. Science 296:1120–1123.
40. Neutel, A.-M., J. A. P. Heesterbeek, J. van de Koppel, G. Hoenderboom, A. Vos, C. Kaldeway, F. Berendse, and P. C. de Ruiter. 2007. Reconciling complexity with stability in naturally assembling food webs. Nature 449:599–602.
41. O’Gorman, E. J., and M. C. Emmerson. 2010. Manipulating interaction strengths and the consequences for trivariate patterns in a marine food web. Advances in Ecological Research 42:301–419.
42. Opitz, S. 1996. Trophic interactions in Caribbean coral reefs. Technical Report 43. International Center for Living Aquatic Resources Management, Makati.
43. Otto, S. B., B. C. Rall, and U. Brose. 2007. Allometric degree distributions facilitate food-web stability. Nature 450:1226–1229.
44. Pawar, S., A. I. Dell, and V. M. Savage. 2012. Dimensionality of consumer search space drives trophic interaction strengths. Nature 486:485–489.
45. Pimm, S. L. 1980. Food web design and the effect of species deletion. Oikos 35:139–149.
46. Pimm, S. L., and J. H. Lawton. 1978. On feeding on more than one trophic level. Nature 275:542–544.
47. Reuman, D. C., C. Mulder, C. Banašek-Richter, M.-F. Cattin Blandenier, A. M. Breure, H. D. Hollander, J. M. Kneitel, D. Raffaelli, G. Woodward, and J. E. Cohen. 2009. Allometry of body size and abundance in 166 food webs. Advances in Ecological Research 41:1–44.
48. Rossberg, A. G. 2013. Food webs and biodiversity: foundations, models, data. Wiley, Hoboken, NJ.
49. Staniczenko, P. P. A., J. C. Kopp, and S. Allesina. 2013. The ghost of nestedness in ecological networks. Nature Communications 4:1391.
50. Tang, S., S. Pawar, and S. Allesina. 2014. Correlation between interaction strengths drives stability in large ecological networks. Ecology Letters 17:1094–1100.
51. Thébault, E., and C. Fontaine. 2010. Stability of ecological communities and the architecture of mutualistic and trophic networks. Science 329:853–856.
52. Twomey, M., U. Jacob, and M. C. Emmerson. 2012. Perturbing a marine food web: consequences for food web structure and trivariate patterns. Advances in Ecological Research 47:349–409.
53. Tylianakis, J. M., E. Laliberté, A. Nielsen, and J. Bascompte. 2010. Conservation of species interaction networks. Biological Conservation 143:2270–2279.
54. Walters, C., S. J. D. Martell, and B. Mahmoudi. 2006. An Ecosim model for exploring ecosystem management options for the Gulf of Mexico: implications of including multistanza life history models for policy predictions. Presentation for Mote Symposium 6:23.
55. Wiggins, S. 2003. Introduction to applied nonlinear dynamical systems and chaos. Vol. 2. Springer, New York.
56. Woodward, G., B. Ebenman, M. Emmerson, J. M. Montoya, J. M. Olesen, A. Valido, and P. H. Warren. 2005a. Body size in ecological networks. Trends in Ecology and Evolution 20:402–409.
57. Woodward, G., D. C. Speirs, and A. G. Hildrew. 2005b. Quantification and resolution of a complex, size-structured food web. Advances in Ecological Research 36:85–135.
58. Yodzis, P. 1981. The stability of real ecosystems. Nature 289:674–676.