The stability–complexity relationship at age 40: a random matrix perspective

Population Ecology

Volumn 57, Issue 1, 2015, Pages 63-75

  Allesina, Stefano ^a   Tang, Si ^a  

^a UNIVERSITY OF CHICAGO   (United States)

Author keywords

Complexity; Eigenvalue; Food web; Random matrix; Stability

Indexed keywords

EID: 84939964828     PISSN: 14383896     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10144-014-0471-0     Document Type: Review

References (46)

1. Allesina S, Pascual M (2008) Network structure, predator–prey modules, and stability in large food webs. Theor Ecol 1:55–64
2. Allesina S, Pascual M (2009) Food web models: a plea for groups. Ecol Lett 12:652–662
3. Allesina S, Tang S (2012) Stability criteria for complex ecosystems. Nature 483:205–208
4. Allesina S, Alonso D, Pascual M (2008) A general model for food web structure. Science 320:658–661
5. Anderson GW, Guionnet A, Zeitouni O (2010) An introduction to random matrices. Cambridge University Press, Cambridge
6. Backstrom L, Boldi P, Rosa M, Ugander J, Vigna S (2012) Four degrees of separation. In: Proceedings of the 3rd annual ACM web science conference. ACM, New York, pp 33–42
7. Bai Z (1997) Circular law. Ann Probab 25:494–529
8. Bai Z, Silverstein JW (2009) Spectral analysis of large dimensional random matrices. Springer, New York
9. Dunne JA, Williams RJ, Martinez ND (2002) Food-web structure and network theory: the role of connectance and size. Proc Natl Acad Sci USA 99:12917–12922
10. Gardner MR, Ashby WR (1970) Connectance of large dynamic (cybernetic) systems: critical values for stability. Nature 228:784
11. Ginibre J (1965) Statistical ensembles of complex, quaternion, and real matrices. J Math Phys 6:440–449
12. Girko VL (1985) Circular law. Theor Probab Appl 29(4):694–706
13. Girko VL (1986) Elliptic law. Theor Probab Appl 30(4):677–690
14. Hanski I, Ovaskainen O (2000) The metapopulation capacity of a fragmented landscape. Nature 404:755–758
15. Hastings A (2001) Transient dynamics and persistence of ecological systems. Ecol Lett 4:215–220
16. Hiai F, Petz D (2000) The semicircle law, free random variables and entropy, vol 77. American Mathematical Society, Providence
17. Kondoh M (2003) Foraging adaptation and the relationship between food-web complexity and stability. Science 299:1388–1391
18. Levins R (1968) Evolution in changing environments: some theoretical explorations. Princeton University Press, Princeton
19. Magurran AE, Henderson PA (2003) Explaining the excess of rare species in natural species abundance distributions. Nature 422:714–716
20. May RM (1972) Will a large complex system be stable? Nature 238:413–414
21. May RM (2001) Stability and complexity in model ecosystems. Princeton University Press, Princeton
22. McCann KS (2000) The diversity–stability debate. Nature 405:228–233
23. McCann KS, Hastings A, Huxel GR (1998) Weak trophic interactions and the balance of nature. Nature 395:794–798
24. Metha M (1967) Random matrices and the statistical theory of energy levels. Academic, New York
25. Moore JC, Hunt HW (1988) Resource compartmentation and the stability of real ecosystems. Nature 333:261–263
26. Naumov A (2012) Elliptic law for real random matrices. arXiv:1201.1639
27. Neubert MG, Caswell H (1997) Alternatives to resilience for measuring the responses of ecological systems to perturbations. Ecology 78:653–665
28. Neutel AM, Heesterbeek JA, van de Koppel J, Hoenderboom G, Vos A, Kaldeway C, Berendse F, de Ruiter PC (2007) Reconciling complexity with stability in naturally assembling food webs. Nature 449:599–602
29. Nguyen H, O’Rourke S (2012) The elliptic law. arXiv:1208.5883
30. Pimm SL (1979) The structure of food webs. Theor Popul Biol 16:144–158
31. Pimm SL (1984) The complexity and stability of ecosystems. Nature 307:321–326
32. Pimm SL, Lawton JH, Cohen JE (1991) Food web patterns and their consequences. Nature 350:669–674
33. Roberts A (1974) The stability of a feasible random ecosystem. Nature 251:607–608
34. Sinha S, Sinha S (2005) Evidence of universality for the May–Wigner stability theorem for random networks with local dynamics. Phys Rev E 71(020):902
35. Solé RV, Alonso D, McKane A (2002) Self-organized instability in complex ecosystems. Philos Trans R Soc B-Biol Sci 357:667–681
36. Sommers H, Crisanti A, Sompolinsky H, Stein Y (1988) Spectrum of large random asymmetric matrices. Phys Rev Lett 60:1895
37. Stouffer DB, Bascompte J (2011) Compartmentalization increases food-web persistence. Proc Natl Acad Sci USA 108:3648–3652
38. Stouffer DB, Camacho J, Amaral LAN (2006) A robust measure of food web intervality. Proc Natl Acad Sci USA 103:19015–19020
39. Tang S, Allesina S (2014) Reactivity and stability of large ecosystems. Front Ecol Evol 2:21
40. Tang S, Pawar S, Allesina S (2014) Correlation between interaction strengths drives stability in large ecological networks. Ecol Lett 17:1094–1100
41. Tao T, Vu V, Krishnapur M (2010) Random matrices: universality of ESDs and the circular law. Ann Probab 38:2023–2065
42. Van Mieghem P, Cator E (2012) Epidemics in networks with nodal self-infection and the epidemic threshold. Phys Rev E 86(016):116
43. Wang Y, Chakrabarti D, Wang C, Faloutsos C (2003) Epidemic spreading in real networks: an eigenvalue viewpoint. In: Proceedings of 22nd international symposium on reliable distributed systems. IEEE, New York, pp 25–34
44. Wigner EP (1958) On the distribution of the roots of certain symmetric matrices. Ann Math 67:325–327
45. Williams RJ, Martinez ND (2000) Simple rules yield complex food webs. Nature 404:180–183
46. Wood PM (2012) Universality and the circular law for sparse random matrices. Ann Appl Probab 22:1266–1300