Spectral Analysis in Ecology

Abstract

Ecologists, like other biologists, are involved with the study of living systems, and they, again like other biologists, are handicapped in their work by the inadequacy of the conceptual framework to which they must relate their quantitative results, and within which they must generate new and testable hypotheses. One way in which the weakness of this structure manifests itself is in the lack of a theoretical approach consistently applicable to a wide variety of living systems, and able to lead to powerful predictions of high generality. Various such approaches have been tried and found wanting; for example, the most recent candidate, the systems analysis method, requires colossal labor· and expense to produce a solution that is self­ consistent for a particular data set, but for which is guaranteed neither the unique­ ness in the original data set nor the self-consistency in any other data set that may be drawn from the same system ensemble, regardless of the boundary conditions. In other words, both the predictive power and the generality of this inelegant approach are very low. A new foundation for a theoretical biology has been proposed based on nonlinear statistical mechanics (49). This method, which is neither strictly holism nor wholly reductionism, is emerging from attempts to find a general mathematical approach that would account for living as well as nonliving phenomena. It identifies as the most important characteristic of complex systems the property' that the differential equations describing the functional relationships between the system components be of the nonlinear kind. A crucial characteristic of nonlinear systems is their disposition toward periodic behavior, even for non periodic boundary conditions. Therefore, they tend to a periodic (cyclic) organization in time, in space, or in both. According to this view, the biosystem is seen as an ensemble of nonlinear oscillators, coupled together in various functional configurations at each hierarchic level of system description. The