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Derivations of the Core Functions of the Maximum Entropy Theory of Ecology
Version 1
: Received: 6 May 2019 / Approved: 7 May 2019 / Online: 7 May 2019 (11:24:30 CEST)
A peer-reviewed article of this Preprint also exists.
Brummer, A.B.; Newman, E.A. Derivations of the Core Functions of the Maximum Entropy Theory of Ecology. Entropy 2019, 21, 712. Brummer, A.B.; Newman, E.A. Derivations of the Core Functions of the Maximum Entropy Theory of Ecology. Entropy 2019, 21, 712.
Abstract
The Maximum Entropy Theory of Ecology, or METE, is a theoretical framework of macroecology that makes a variety of realistic ecological predictions about how species richness, abundance of species, metabolic rate distributions, and spatial aggregation of species interrelate in a given region. In the METE framework, "ecological state variables" (representing total area, total species richness, total abundance, and total metabolic energy) describe macroecological properties of an ecosystem. METE incorporates these state variables into constraints on underlying probability distributions. The method of Lagrange multipliers and maximization of information entropy (MaxEnt) lead to predicted functional forms of distributions of interest. We demonstrate how information entropy is maximized for the general case of a distribution, which has empirical information that provides constraints on the overall predictions. We then show how METE’s two core functions are derived. These
functions, called the "Spatial Structure Function" and the "Ecosystem Structure Function" are the core pieces of the theory, from which all the predictions of METE follow (including the Species Area Distribution, the Species Abundance Distribution, and various metabolic distributions). Primarily, we consider the discrete distributions predicted by METE.We also explore the parameter space defined by the METE’s state variables and Lagrange multipliers. We aim to provide a comprehensive resource for ecologists who want to understand the derivations and assumptions of basic mathematical structure of METE.
Keywords
information entropy, information theoretics, macroecology, metabolic theory, scaling, species abundance distribution, species-area relationship
Subject
Biology and Life Sciences, Ecology, Evolution, Behavior and Systematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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