Alternatives to resilience for measuring the responses of ecological systems to perturbations

Ecology

Volumn 78, Issue 3, 1997, Pages 653-665

  Neubert, Michaei G ^a   Caswell, Hal ^a  

^a WOODS HOLE OCEANOGRAPHIC INSTITUTION   (United States)

Author keywords

Compartment models; Eigenvalues; Pulse perturbations; Reactivity; Relative stability; Resilience; Return time; Transient vs. asymptotic dynamics

Indexed keywords

ECOLOGICAL SYSTEM; PERTURBATION; RESILIENCE; STABILITY;

EID: 0030616824     PISSN: 00129658     EISSN: None     Source Type: Journal    
DOI: 10.1890/0012-9658(1997)078[0653:ATRFMT]2.0.CO;2     Document Type: Article

References (53)

1. Armstrong, R A. 1982. The effects of connectivity on community stability. American Naturalist 120:391-402.
2. Beddington, J. R., C. A. Free, and J. H. Lawion. 1976. Concepts of stability and resilience in predator- prey models. Journal of Animal Ecology 45:791-816.
3. Carpenter, S. R., J. F. Kitchell, J. R. Hodgson, P. A. Cochran, J. J. Elser, M. M. Elser, D. M. Lodge, D. Kretchmer, X. He, and C. N. von Ende. 1987. Regulation of lake primary productivity by food web structure, Ecology 68:1863-1876.
4. Carpenter, S. R., C. E. Kraft, R. Wright, X. He, P. A. Soranno, and J. R. Hodgson. 1992. Resilience and resistance of a lake phosphorus cycle before and after a food web manipulation. American Naturalist 140:781-798.
5. Caswell, H. 1978. A general formula for the sensitivity of population growth rate to changes in life history parameters. Theoretical Population Biology 14:215-230.
6. Coppel, W. A. 1965. Stability and asymptotic behavior of differential equations. Heath, Boston, Massachusetts. USA.
7. Cottingham, K. L., and S. R. Carpenter. 1994. Predictive indices of ecosystem resilience in models of north temperate lakes. Ecology 75:2127-2138.
8. Dahlquist, G. 1959. Stability and error bounds in the numerical integration of ordinary differential equations. Transactions of the Royal Institute of Technology Number 130, Stockholm, Sweden.
9. DeAngelis, D. L. 1980. Enegry flow, nutrient cycling, and ecosystem resilience. Ecology 61:764-771.
10. _ . 1992. Dynamics of nutrient cycling and food webs. Chapman and Hall. London. England.
11. DeAngelis, D. L., S. M. Bartell, and A. L. Brenkert. 1989a. Effects of nutrient recycling and food chain length on resilience. American Naturalist 134:778-805.
12. DeAngelis, D. L., P. J. Mulholland, A. V. Palumbo, A. D. Steinman, M. A. Huston, and J. W. Elwood. 1989b. Nutrient dynamics and food-web stability. Annual Reviews of Ecology and Systematics 20:71-95.
13. Farrell, B. F. 1989. Optimal excitation of baroclinic waves. Journal of the Atmospheric Sciences 46:1193-1206.
14. Hadeler, K. P., and I. Gerstmann. 1990. The discrete Rosenzweig model. Mathematical Biosciences 98:49-72.
15. Harrison. G. W. 1979. Stability under environmental stress: resistance, resilience, persistence, and variability. American Naturalist 113:659-669.
16. Harte, J. 1979. Ecosystem stability and the distribution of community matrix eigenvalues. Pages 453-465 in E. Halfon. editor. Theoretical systems ecology. Academic Press. New York. New York, USA.
17. Harwell, M. A., W. P. Cropper, and H. L. Ragsdale. 1977. Nutrient recycling and stability: a reevaluation. Ecology 58:660-666.
18. Harwell, M. A., W. P. Cropper, and H. L. Ragsdale. 1981. Analysis of transient characteristics of a nutrient cycling model. Ecological Modelling 12:105-131.
19. Harwell, M. A., and H. L. Ragsdale. 1979. Eigengroup analyses of linear ecosystem models. Ecological Modelling 7:239-255.
20. Hastings, A., and K. Higgins. 1994. Persistence of transients in spatially structured ecological models. Science 263:1133-1136.
21. Hastings, A., C. L. Hom, S. Ellner, P. Turchin, and H. C. J. Godfray. 1993. Chaos in ecology: is Mother Nature a strange attraclor? Annual Reviews of Ecology and Systematics 24:1-33.
22. Higham, D. J., and L. N. Trefethen. 1993. Stiffness of ODEs. Bit 33:285-303.
23. Holling, C. S. 1973. Resilience and stability of ecological systems. Annual Reviews of Ecology and Systematics 4:1-23.
24. Horn, R. A., and C. R. Johnson. 1985. Matrix analysis. Clambridge University Press. Cambridge. UK.
25. Ives, A. R. 1995. Measuring resilience in stochastic systems. Ecological Monographs 65:217-233.
26. Jacobi, C. J. G. 1846. Über ein leichtes Verfahren die in der Theorie der Säcularstörungen vorkommenden Gleichungen numerisch aufzulösen. Journal für die Reine und Angewandte Mathematik 30:51-95.
27. Jordan, C. F., J. R. Kline, and D. S. Sasscer. 1972. Relative stability of mineral cycles in forest ecosystems. American Naturalist 106:237-253.
28. Lee, J. J., and D. L. Inman. 1975. The ecological role of consumers - an aggregated systems view. Ecology 56:1455-1458.
29. Lepš, J., J. Osbornová-Kosinová, and M. Rejmánek. 1982. Community stability, complexity, and species life history strategies. Vegetatio 50:53-63.
30. Loreau, M. 1994. Material cycling and the stability ot ecosystems. American Naturalist 143:508-513.
31. Lozinskij, S. M. 1958. Error estimate for numerical integration of ordinary differential equations. Izvestiya Vysshikh Uchebnykh Zavedeniǐ. Matematika 6:52-90.
32. McGinnis, J. T., F. B. Golley, R. G. Clements, G. I. Child, and M. J. Duever. 1969. Elemental and hydrologic budgets of the Panamanian tropical moist forest. BioScience 19:697-700.
33. May, R. M., and W. Leonard. 1975. Nonlinear aspects of competition between three species. SIAM Journal of Applied Mathematics 29:243-252.
34. Moler, C. B., and C. F. Van Loan. 1978. Nineteen dubious ways to calculate the exponential of a matrix. SIAM Review 20:801-836.
35. Nakajima, H. 1992. Sensitivity and stability of flow networks. Ecological Modelling 62:123-133.
36. National Research Council. 1992. Restoration of aquatic ecosystems. National Academy Press. Washington. D.C., USA.
37. Ncubert, M. G., and M. Kot. 1992. The subcritical collapse of predator populations in discrete-time predator-prey models. Mathematical Biosciences 110:45-66.
38. O'Neill, R. V. 1971. Examples of ecological transfer matrices. Publication 397. Ecological Sciences Division. Oak Ridge National Laboratory, Oak Ridge, Tennessee, USA.
39. _ . 1976. Ecosystem persistence and heterotrophic regulation. Ecology 57:1244-1253.
40. 134cesium kinetics in terrestrial microcosms. Ecology 48:813-824.
41. Pimm, S. L. 1479. The structure of food webs. Theoretical Population Biology 16:144-158.
42. _ . 1982. Food webs. Chapman and Hall. London. UK.
43. _ . 1984. The complexity and stability of ecosystems. Nature 307:321-326.
44. _ . 1991. The balance of nature. University of Chicago Press, Chicago, Illinois, USA.
45. Pimm, S. L., and J. H. Lawton. 1977. Number of trophiclevels in ecological communities. Nature 268:329-331.
46. Pimm, S. L., and J. H. Lawton. 1978. On feeding on more than one trophic level. Nature 275:542-544.
47. Stcinman, A. D., P. J. Mulholland, A. V. Palumbo, T. F. Flum, and D. L. DeAngelis. 1991. Resilience of lotic ecosystems to a light-elimination disturbance. Ecology 72:1299-1313.
48. Strang, G. 1988. Linear algebra and its applications. Harcourt Brace Jovanovich, San Diego, California, USA.
49. Trefethen, L. N. 1992. Pseudospectra of matrices. Pages 234-266 in D. F. Griffiths and G. A. Watson, editors. Numerical analysis 1991. Longman Scientific. New York. New York, USA.
50. Trefethen, L. N., A. E. Trefethen, S. C. Reddy, and T. A. Driscoll. 1993. Hydrodynamic stability without eigenvalues. Science 261:578-584.
51. Van Loan, C. 1977. The sensitivity of the matrix exponential. SIAM Journal of Numerical Analysis 14:971-981.
52. Vincent, T. L., and L. R. Anderson. 1979. Return time and vulnerability for a food chain model. Theoretical Population Biology 15:217-231.
53. Webster, J. R., J. B. Waide, and B. C. Patten. 1975. Nutrient recycling and the stability of ecosystems. Pages 1-27 in F. G. Howell, J. B. Gentry, and M. H. Smith, editors. Mineral cycling in southeastern ecosystems. Energy Research and Development Administration (ERDA) Symposium Series. Technical Information Center, Washington, D.C., USA.