| Abstract: | Self-organized criticality (SOC) occurs in systems consisting of a substrate or medium which can be locally stressed to a critical state. When the critical threshold is exceeded, the stress is distributed to the neighborhood around the locale, which can lead to critical states in the neighboring locations thereby propagating the disturbance. The SOC system manifests its behavior in distinctive temporal and spatial relationships. Diagnostic behaviors include conformity of dynamics to a power law (F(s) = βsα) relating the frequency distribution function to the observed behavior (1/f noise) and fractal behavior or spatial self-similarity. We analyzed 40 to 50 years of grasshopper infestations in Idaho and Montana for evidence of SOC. In both states, grasshopper infestations in four of the seven ecoregions statistically fit (the expected frequencies matched the observed with a probability of >95%) the power law relationship. In ecoregions where the model failed to fit the observed behavior, grasshopper infestations were typically rare and small scale. Spatial self-similarity was evident from graphical and statistical analyses. In both states there were statistically significant levels of concordance (among ranks) and correlation (among areas of infestations) between ecoregions. The spatial distributions of grasshopper infestations over time also showed considerable overlaps between ecoregions. However, only in Idaho were the variances in grasshopper infestations among ecoregions homogeneous. If rangeland grasshopper populations are SOC systems, then the management of outbreaks may need to be dramatically restructured. This system appears to be an example of “complex complexity,” in which multiple dynamics (i.e., the appearance of SOC with partial blockage of outbreaks, catastrophic dynamics, and perhaps chaos) give rise to a rich set of behaviors which arise at different scales and certainly necessitate further theoretical developments in order to understand. © 1997 John Wiley & Sons, Inc. |
