Statistical mechanics of complex ecological aggregates

A fundamental limitation of classical science was its inability to explain how order could emerge out of uncertainty and indeterminism. The approach to solving this dilemma has been to develop theories of how properties of aggregated systems arise from the properties and interactions of their parts. The basic assumption of such ideas is that there is a tension between the tendency of an aggregated system to change and the constraints that are imposed upon that system by virtue of the behavior of and interactions among the parts. The balance between constraint and change gives rise to a hierarchy of aggregated structures that exhibit regular, repeatable attributes to the degree that constraints are able to maintain change across time within boundaries that define the nature of the structure. This basic view of causality in complex systems suggests an approach to defining a statistical mechanics for ecological systems that can be used to generate new theoretical descriptions of biological diversity. This approach is illustrated by introducing the idea of a “geographic population system” of a species and illustrating how change and constraints interact within this system to determine statistical properties such as geographic range size, and mean-variance scalings. The concept of a geographic population system is then used to develop alternative descriptions of the kinetics of biological diversity. Assuming that these alternatives are complimentary, it is possible to develop a general description for biological diversity that shows how lower level change (geographical population dynamics of species) are constrained by the environment and genetic systems of species to determine rates of origination and extinction of taxa over long periods of time.