Document: BAI-3-92-9

Fractals in ecology: Where is the ecology?

LI, B.*

University of New Mexico, Albuquerque, NM 87131 USA ¹

Abstract:
A log-log plot of ecological data has the great property of displaying, more often than not, a straight line over a certain range of parameters. There is a widely spread tendency to look for simple, ideal explanation; one often interprets a straight line as a scaling law (or scale invariance) reflecting some important information. In this paper, I will analytically demonstrate how deeply misleading this quest for simple interpretation can be. I will show that many different things can produce a power-law distribution. In many cases, there is no single ecological mechanism behind the scale invariance. The distributions which are usually classified as power-law may actually correspond to stretched exponential ones. Using Sevilleta LTER data, I argue that the departures from the power-law should not necessarily be explained by the finite size of the data set, but could result from a deeper departure from the power-law hypothesis. I also argue that current fractal approach is inconsistent with ecological hierarchy theory because of no existence of a hierarchy of characteristic scales in space/time and all scales treated as playing the same role. Ecologically, spatiotemporal scales give us access to additional information and clues about the underlying processes and the existence of a hierarchy of preferred scales; discrete-scale invariance and scale covariance should be applied. Studies of fractals in ecology have now evolved from descriptive to the beginning of understanding.

Keywords: Fractals, scaling, power-law, hierarchy theory

This abstract is being presented at: 10:45 AM in session:
Oral Session #39: Theoretical Ecology.