Successional state dynamics: A novel approach to modeling nonequilibrium foodweb dynamics

Journal of Theoretical Biology

Volumn 262, Issue 4, 2010, Pages 584-595

  Klausmeier, C A ^a  

^a MICHIGAN STATE UNIVERSITY   (United States)

Author keywords

Nonequilibrium dynamics; Seasonality; Succession; Theory

Indexed keywords

COMPETITION (ECOLOGY); FACILITATION; FOOD WEB; NUMERICAL MODEL; PREDATOR-PREY INTERACTION; SEASONALITY; SUCCESSION; THEORETICAL STUDY;

ARTICLE; COMMUNITY DYNAMICS; COMMUNITY SUCCESSION; FOOD WEB; INTERSPECIFIC COMPETITION; NONHUMAN; PLANKTON; PREDATOR PREY INTERACTION; PRIORITY JOURNAL; SEASONAL VARIATION; SUCCESSIONAL STATE DYNAMICS; THEORETICAL MODEL;

ALGORITHMS; ANIMALS; BIODIVERSITY; COMPETITIVE BEHAVIOR; ECOSYSTEM; ENVIRONMENT; FOOD CHAIN; MODELS, BIOLOGICAL; MODELS, STATISTICAL; MODELS, THEORETICAL; PLANKTON; POPULATION DYNAMICS; PREDATORY BEHAVIOR; SEASONS;

HEXAPODA;

EID: 77649339743     PISSN: 00225193     EISSN: 10958541     Source Type: Journal    
DOI: 10.1016/j.jtbi.2009.10.018     Document Type: Article

References (43)

1. Armstrong R.A., McGehee R. Competitive exclusion. American Naturalist 1980, 115:151-170.
2. Candaten M., Rinaldi S. Peak-to-peak dynamics in food chain models. Theoretical Population Biology 2003, 63:257-267.
3. Chesson P. Multispecies competition in variable environments. Theoretical Population Biology 1994, 45:227-276.
4. Connell J.H., Slatyer R.O. Mechanisms of succession in natural communities and their role in community stability and organization. American Naturalist 1977, 111:1119-1144.
5. DeAngelis D.L., Waterhouse J.C. Equilibrium and nonequilibrium concepts in ecological models. Ecological Monographs 1987, 57:1-21.
6. Dhooge A., Govaerts W., Kuznetsov Yu.A. MatCont: A MATLAB package for numerical bifurcation analysis of ODEs. ACM Transactions on Mathematical Software 2003, 29:141-164.
7. Doedel, E.J., Paffenroth, R.C., Champneys, A.R., Fairgrieve, T.F., Kuznetsov, Yu.A., Oldeman, B.E., Sandstede, B., Wang, X.J., 2001. AUTO2000: continuation and bifurcation software for ordinary differential equations. https://sourceforge.net/projects/auto2000/.
8. Doveri F., Scheffer M., Rinaldi S., Muratori S., Kuznetsov Yu. Seasonality and chaos in a plankton-fish model. Theoretical Population Biology 1993, 43:159-183.
9. Earn D.J.D., Rohani P., Bolker B.M., Grenfell B.T. A simple model for complex dynamical transitions in epidemics. Science 2000, 287:667-670.
10. Grover J.P. Resource competition in a variable environment: phytoplankton growing according to Monod's model. American Naturalist 1990, 136:771-789.
11. Hastings A. Transients: the key to long-term ecological understanding?. Trends in Ecology and Evolution 2004, 19:39-45.
12. Hsu S.-B. A competition model for a seasonally fluctuating nutrient. Journal of Mathematical Biology 1980, 9:115-132.
13. Huppert A., Blasius B., Olinky R., Stone L. A model for seasonal phytoplankton blooms. Journal of Theoretical Biology 2005, 236:276-290.
14. King A.A., Schaffer W.M. The rainbow bridge: Hamiltonian limits and resonance in predator-prey dynamics. Journal of Mathematical Biology 1999, 39:439-469.
15. Klausmeier C.A. Floquet theory: a useful tool for understanding nonequilibrium dynamics. Theoretical Ecology 2008, 1:153-161.
16. Kuznetsov Yu.A., Muratori S., Rinaldi S. Bifurcations and chaos in a periodic predator-prey model. International Journal of Bifurcations and Chaos 1992, 2:117-128.
17. Kuznetsov, Yu.A., Levitin, V.V., 1996. CONTENT: a multiplatform environment for analyzing dynamical systems. Dynamical Systems Laboratory, Centrum voor Wiskunde en Informatica, Amsterdam. http://www.math.uu.nl/people/kuznet/CONTENT/.
18. Litchman E., Klausmeier C.A. Competition of phytoplankton under fluctuating light. American Naturalist 2001, 157:170-187.
19. Lotka A.J. Elements of Physical Biology 1925, Williams and Wilkins, Baltimore.
20. May R.M. Regulation of populations with nonoverlapping generations by microparasites: a purely chaotic system. American Naturalist 1985, 125:573-584.
21. Metz J.A.J., Nisbet R.M., Geritz S.A.H. How should we define "fitness" for general ecological scenarios?. Trends in Ecology and Evolution 1992, 7:198-202.
22. Murdoch, W.W., Nisbet, R.M., McCauley, E., deRoos, A.M., Gurney, W.S.C., 1998. Plankton abundance and dynamics across nutrient levels: tests of hypotheses. Ecology 79, 1339-1356.
23. Murdoch W.M., Briggs C.J., Nisbet R.M. Consumer-Resource Dynamics 2003, Princeton University Press, Princeton.
24. Nisbet R.M., Gurney W.S.C. Modelling Fluctuating Populations 1982, Wiley, New York.
25. Ohnishi M., Inaba N. A singular bifurcation into instant chaos in a piecewise-linear circuit. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 1994, 41:433-442.
26. Piccardi C. Bifurcations of limit cycles in periodically forced nonlinear systems: the harmonic balance approach. IEEE Transactions on Circuits and Systems I 1994, 41:315-320.
27. Rinaldi S., Muratori S., Kuznetsov Yu. Multiple attractors, catastrophes and chaos in seasonally-perturbed predator-prey communities. Bulletin of Mathematical Biology 1993, 55:15-35.
28. Rinaldi S., Solidoro C. Chaos and peak-to-peak dynamics in a plankton-fish model. Theoretical Population Biology 1998, 54:62-77.
29. Sanders J.A., Verhulst F., Murdock J. Averaging Methods in Nonlinear Dynamical Systems 2007, Springer, New York. second ed.
30. Savkin A.V., Evans R.J. Hybrid Dynamical Systems 2002, Birkhäuser, Boston.
31. Scheffer M., Rinaldi S., Kuznetsov Yu.A., van Nes E.H. Seasonal dynamics of Daphnia and algae explained as a periodically forced predator-prey system. Oikos 1997, 80:519-532.
32. Segel L.A. Simplification and scaling. SIAM Review 1972, 14:547-571.
33. Snyder R.E. Spatiotemporal population distributions and their implications for species coexistence in a variable environment. Theoretical Population Biology 2007, 72:7-20.
34. Sommer U., Gliwicz Z.M., Lampert W., Duncan A. The PEG-model of seasonal succession of planktonic events in fresh waters. Archiv für Hydrobiologie 1986, 106:433-471.
35. Sommer U. Plankton Ecology: Succession in Plankton Communities 1989, Springer, Berlin.
36. Steiner, C.F., Schwaderer, A.S., Huber, V., Klausmeier, C.A., Litchman, E., 2009. Periodically forced food chain dynamics: model predictions and experimental validation. Ecology 90, 3099-3107.
37. Strogatz, S.H., 1994. Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering. Perseus Books.
38. Stone L., Olinky R., Huppert A. Seasonal dynamics of recurrent epidemics. Nature 2007, 446:533-536.
39. Tilman D. Resource Competition and Community Structure 1982, Princeton University Press, Princeton.
40. Turchin P. Complex Population Dynamics: A Theoretical/Empirical Synthesis 2003, Princeton University Press, Princeton.
41. van der Schaft, A.J., Schumacher, J.M., 2000. An Introduction to Hybrid Dynamical Systems. In: Springer Lecture Notes in Control and Information Sciences, vol. 251. Springer, Berlin.
42. Volterra V. Variazioni e fluttuazioni del numero d'individui in specie animali conviventi. Memorie della R. Accademia Nazionale dei Lincei 1926, 2:31-113.
43. Yoshida T., Moire H., Shigematsu H. Analytic study of chaos of the tent map: band structures, power spectra, and critical behaviors. Journal of Statistical Physics 1983, 31:279-308.