Spatial Heterogeneity Analysis: Introducing a New Form of Spatial Entropy

Abstract

Distinguishing and characterizing different landscape patterns have long been the primary concerns of quantitative landscape ecology. Information theory and entropy-related metrics have provided the deepest insights in complex system analysis, and have high relevance in landscape ecology. However, ideal methods to compare different landscape patterns from an entropy view are still lacking. The overall aim of this research is to propose a new form of spatial entropy ( H s ) in order to distinguish and characterize different landscape patterns. H s is an entropy-related index based on information theory, and integrates proximity as a key spatial component into the measurement of spatial diversity. Proximity contains two aspects, i.e., total edge length and distance, and by including both aspects gives richer information about spatial pattern than metrics that only consider one aspect. Thus, H s provides a novel way to study the spatial structures of landscape patterns where both the edge length and distance relationships are relevant. We compare the performances of H s and other similar approaches through both simulated and real-life landscape patterns. Results show that H s is more flexible and objective in distinguishing and characterizing different landscape patterns. We believe that this metric will facilitate the exploration of relationships between landscape patterns and ecological processes.

Information Theory as a consistent framework for quantification and classification of landscape patterns

“…We suggested a simple explanation of why this must be so. This shortcoming of orderings has not been noticed before because proposed orderings were tested on either synthetic patterns or on small and incomplete samples of real-life patterns (Wang and Zhao, 2018; Cushman, 2018). In contrast, we used an evaluation set of landscapes that includes all types land cover configurations.…”

“…Recently, several works (Claramunt, 2012; Altieri et al, 2018; Wang and Zhao, 2018) proposed to order landscapes using a concept of spatial entropy. Spatial entropy is a modification of the Shannon entropy designed to measure spatial intricacy of a pattern.…”

“…Most of the evaluations done so far used simulated landscapes which lack the character and diversity of form found in real-life landscapes. Demonstrations of orderings on real-life landscapes (Wang and Zhao, 2018; Gao et al, 2017) used two few landscapes to make a judgment.…”

Quantifying Effects of Changing Spatial Scale on Spatial Entropy Index: Use of Fractal Dimension

“…Since introducing the seminal work of Shannon entropy to the field of landscape ecology, entropyrelated metrics have been rapidly developed and represent an efficient tool to quantify and characterize landscape patterns (Vranken et al, 2015), for example, Shannon diversity index, Simpson diversity index, contagion index (Li and Reynolds, 1994), quadratic entropy index (Dí az-Varela et al, 2016), etc. A recent derivation is the Spatial Entropy index (Hs), and it incorporates proximity as a key spatial component into the measurement of spatial heterogeneity (Wang and Zhao, 2018). Hs has been validated as flexible and effective in characterizing landscape patterns, however, the effects of changing spatial scale (or scale sensitivity) on this index has not been quantified.…”

Calculating the Wasserstein Metric-Based Boltzmann Entropy of a Landscape Mosaic

“…To the best of our knowledge, there are two solutions to this limitation of Shannon entropy. The first is to improve Shannon entropy, and many improved forms of Shannon entropy have been proposed in the last few decades, e.g., [29][30][31]; see a recent review published by this journal [32]. Although most of the improved forms of Shannon entropy are valid means of quantifying configurational information, there is no definite correlation between Shannon entropy and thermodynamics [33][34][35].…”