Remarks on the maximum entropy principle with application to the Maximum Entropy Theory of Ecology

Abstract

In the first part of the paper we work out the consequences of the fact that Jaynes' Maximum Entropy Principle, when translated in mathematical terms, is a constrained extremum problem for an entropy function H(p) expressing the uncertainty associated with the probability distribution p. Consequently, if two observers use different independent variables p or g(p), the associated entropy functions have to be defined accordingly and they are different in the general case. In the second part we apply our findings to an analysis of the foundations of the Maximum Entropy Theory of Ecology (M.E.T.E.) a purely statistical model of an ecological community. Since the theory has received considerable attention by the scientific community, we hope to give a useful contribution to the same community by showing that the procedure of application of MEP, in the light of the theory developed in the first part, suffers from some incongruences. We exhibit an alternative formulation which is free from these limitations and that gives different results.