Entropy in Landscape Ecology: A Quantitative Textual Multivariate Review

Abstract

This paper presents a multivariate textual analysis of more than 1300 papers on entropy in ecology. There are six main insights that emerged. First, there is a large body of literature that has addressed some aspect of entropy in ecology, most of which has been published in the last 5–10 years. Second, the vast majority of these papers focus on species distribution, species richness, relative abundance or trophic structure and not landscape-scale patterns or processes, pe se. Third, there have been few papers addressing landscape-level questions related to entropy. Fourth, the quantitative analysis with hierarchical clustering identified a strongly nested structure among papers that addressed entropy in ecology. Fifth, there is clear differentiation of papers focused on landscape-level applications of entropy from other papers, with landscape focused papers clustered together at each level of the hierarchy in a relatively small and closely associated group. Sixth, this group of landscape-focused papers was substructured between papers that explicitly adopted entropy measures to quantify the spatial pattern of landscape mosaics, often using variations on Boltzmann entropy, versus those that utilize Shannon entropy measures from information theory, which are not generally explicit in their assessment of spatial configuration. This review provides a comprehensive, quantitative assessment of the scope, trends and relationships among a large body of literature related to entropy in ecology and for the first time puts landscape ecological research on entropy into that context.

Generalizing Boltzmann Configurational Entropy to Surfaces, Point Patterns and Landscape Mosaics

“…Several recent methods have been proposed to calculate configurational entropy, based on Boltzmann entropy. The Cushman [ 3 , 4 ] method directly applies the classic and iconic Boltzmann relation (s = klogW) to spatial patterns. The Boltzmann relation states that the entropy of a system is proportional to the logarithm of the number of macrostate, or unique configurations, that produce the observed macrostate, or global system property.…”

“…Second, as a framework for computing the configurational entropy of landscapes, the Boltzmann relation is particularly appropriate given the direct analogies between particular arrangements of landscape elements and microstates in the Boltzmann system and measured spatial attributes of a landscape pattern as the Boltzmann macrostate. Cushman [ 3 , 4 ] applied this to landscape mosaics. The goal of this paper is to show that the direct application of the Boltzmann relation for computing landscape entropy also applies in the exact same way to measuring the entropy of point patterns and surfaces.…”

“…The essence of the Cushman [ 3 , 4 ] approach is to apply the Boltzmann relation directly to spatial patterns of a landscape mosaic of categorical patches. This is done in three steps.…”

“…Then the total edge length (the linear distance along edges of pixels where two different cover classes touch) is calculated for the actual landscape and the large number of permuted patterns. Next, following the Central Limit Theorem, Cushman [ 4 ] showed that the edge lengths of the permuted landscapes (microstates) are normally distributed. A Gaussian function is fit to this distribution.…”

“…A Gaussian function is fit to this distribution. Cushman [ 4 ] also showed that the entropy function resulting from this distribution is parabolic, given that the logarithm of a normal distribution is a parabola, and entropy is proportional to the logarithm of the number of microstates producing a given macrostate.…”