Term Definition Source 1/f noise S(f)=f—α, where S is the signal and f is the frequency. The constant α, is a positive real number. Lockwood and Lockwood (2008) Alternative Stable States A system in which the equilibrium state can be at more than one distinct value for identical values of the control parameters. Lewontin (1969) Basin of Attraction The region around an attractor (equilibrium point or limit cycle) for which all trajectories lead to the attractor. Holling (1973) Catastrophe Theory The analysis of degenerate critical points of potential functions to describe discontinuous phenomena in normally continuous systems. Seven elementary catastrophic bifurcations exist with the cusp and fold being most commonly applied in ecology. Saunders (1980) Cellular Automata A discrete model consisting of a grid of cells with each cell occupying one of a finite number of states. A set of rules parameterized by the states of the local cells govern the change of states. Wolfram (1984) Characteristic Length Scale Optimum scale at which to monitor a system to establish its deterministic dynamics. Johnson (2009) Fractal Dimension A rough or fragmented geometric shape that can be subdivided in parts, each of which is, at least approximately, a reduced-size copy of the whole. Mandelbrot and Wallis (1969) Nonlinear System System in which either or both additivity and homogeneity fail to hold. Scheffer et al. (2003) Power Law A polynomial relationship that exhibits scale invariance, generally of the form, f(x)=axk. Metabolic ecology is based on the power law relationships of allometry. West et al. (1997) Self-Organized Criticality A spatial system in which a substrate can be locally redistributed to the nearest neighbor patches to propagate further redistribution resulting in arbitrarily large shifts in substrate. The temporal signal of self-organized criticality is 1/f noise and the spatial pattern is fractal. Lockwood and Lockwood (1997)