Community Ecology
Equilibrium/nonequilibrium
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Outline:
1. Definition of equilibrium, including static equilibrium and dynamic equilibrium
A. Three aspects to equilibrium: resistance, resilience, and persistence
2. Equilibrium assumed because animal population numbers seem to remain constant over time
3. Nonequilibrium and chaos
4. Three alternatives to equilibrium in explaining why population numbers remain steady: spatial effects (spreading of risk), refugia, artifact of dealing with long-lived organisms
5. Discussion of the usefulness of the equilibrium concept, despite its lack of realism
A. (Some) types of models: structural, conceptual, analytical, simulation
Terms/people:
equilibrium nonequilibrium chaos
Robert May resistanceresilience
persistence DeAngelis and Waterhousestatic vs. dynamic equilibrium
cycle (oscillation) "butterfly effect" (Lorenz) "spreading of risk" (den Boer)
refugia model (and types)
People have always noticed and marveled at the variety of species that can be found in a prairie, pond, or forest, and so people have also wondered why there were repeated and relatively predictable patterns of species co-occurrences. So community ecology emerged as a scientific discipline at the end of the 19th century as an attempt to understand this "balance of nature."
Equilibrium:
resistance -
resilience -
persistence -
"Balance of nature" is a long-standing idea. Roots of equilibrium thinking:
1) Aristotlean idea that living organisms are components of a "super being"; therefore, all parts must be in balance (homeostasis)
2) essentialism
Evidence needed to demonstrate equilibrium is present is difficult to obtain:
Must show that following a perturbation, numbers will return to a value seen before the perturbation à but logistically and ethically difficult to perturb a system, and need to follow it for a long time after perturbation.
Steady-state (static) equilibrium vs. dynamic equilibrium
alternative stable states: different configurations of communities (different species, different abundances) can occur even in response to identical environmental conditions à see Mittelbach text for more information
Equilibrium began to be questioned in 1800s after extinctions became known (fossil evidence): how could equilibrium exist if some species go extinct?
instable equilibrium = nonequilibrium
Equilibrium-nonequilibrium is a continuum, with the extremes characterized by:
nonequilibrium:
biotic decoupling
unsaturated
species independence
abiotic limitation
density independence
opportunism
large stochastic effects
loose patterns
equilibrium:
biotic coupling
saturated
competition
resource limitation
density dependence
optimality
few stochastic effects
tight patterns
Chaos theory = special form of nonequilibrium
-origins with H. Poincaré, coined by J. Yorke, popularized by R. May:
French mathematician Henri Poincaré in the 1880s pointed out that it is impossible to calculate the precise trajectories of the planets and stars of our solar system because they are continually pulling and pushing on each other via gravity, making their future positions impossible to determine with precision: this is contrary to the Newtonian view of the cosmos at that time that everything can be determined with mathematical precision
Robert May (Australian physicist turned biologist at Princeton and then Oxford) was examining population growth à recall that a population was assumed to grow towards a stable value known as carrying capacity, at which point the population’s demand for resources will match the resources available, and population growth will level off à but May found that if he increased r (pop. growth rate) even more, there was no single stable value reached (instead, the pop. size alternated around several values) (May 1976) à May showed these patterns to James Yorke (Univ. MD mathematician), who coined the term chaos
-randomness in chaos is deterministic in origin because it arises from discrete causes and is not simply extraneous noise/variance, so predictions from chaotic eqns are accurate only in the short term à remind you of weather forecasting?
-famous "butterfly effect" of Edward Lorenz (1972):
George Sugihara (Ph.D. student of May’s, 1983; now at the Scripps Inst. of Oceanography in La Jolla, CA) - although chaos precludes long-term prediction, chaos ¹ randomness (Sugihara and May 1990)
randomness is informationless noise; chaos, in contrast, contains information that can be used to predict the short-term future of a non-linear system
Sugihara has used chaos theory to model short-term stock futures for Deutsche Bank, in a very profitable deal for both parties
More recently he has been examining chaos in marine fishery stocks (Hsieh et al. 2005)
Gleick 1987 - magnify chaos and can get a regular pattern again! So equilibrium is probably just an epiphenomenon of scale.
So how do many communities remain so constant over time?
1) spatial effects
“spreading of risk” - den Boer 1968
2) refugia
3) illusion à the apparent constancy of many communities may seem like unchanging communities with stable equilibria, but they may in fact reflect the nearly imperceptible responses of long-lived organisms to gradually changing surroundings
Is equilibrium a useful concept? Should we abandon it, now that we know about nonequilibrium?
Equilibrium as a model
Types of models
References:
Berryman, A.A. 1987. Equilibrium or nonequilibrium: is that the question? Bull. Ecol. Soc. Amer. 68:500-502.
Connell, J.H. 1978. Diversity in tropical rainforests and coral reefs. Science 199:1302-1310.
DeAngelis, D.L., and J.C. Waterhouse. 1987. Equilibrium and nonequilibrium concepts in ecological models. Ecol. Monogr. 57:1-21. [excellent overview of the subject]
den Boer, P.J. 1968. Spreading of risk and stabilization of animal numbers. Acta Biotheor. 18:165- 194.
Gleick, J. 1987. Chaos: Making a New Science. Viking Press, New York, NY.
Hsieh, C., S.M. Glaser, A.J. Lucas, and G. Sugihara. 2005. Distinguishing random environmental fluctuations from ecological catastrophes for the North Pacific Ocean. Nature 435:336-340.
Lorenz, E. 1972. "Predictability: Does the Flap of a Butterfly's Wings in Brazil Set Off a Tornado in Texas?" Presentation given at the annual meeting of AAAS, Boston, MA, 29 Dec.
May, R.M. 1976. Simple mathematical models with very complicated dynamics. Nature 261:459-467.
Sugihara, G. and R.M. May. 1990. Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series. Nature 344:734-741.
Turchin, P. 1990. Rarity of density dependence or population regulation with lags. Nature 344:660- 663.
Turchin, P. 1995. Population regulation: old arguments and a new synthesis. Pp. 19-41 in: Population Dynamics: New Approaches and Synthesis (N. Cappuccino and P.W. Price, eds.). Academic Press, San Diego, CA.
Wiens, J.A. 1984. On understanding a non-equilibrium world: myth and reality in community patterns and processes. Pp. 439-457 in: Ecological Communities: Conceptual Issues and the Evidence (D.R. Strong, D. Simberloff, L.G. Abele, and A.B. Thistle, eds.), Princeton University Press, Princeton, NJ.