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Entropy in Landscape Ecology II
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Entropy in Landscape Ecology II

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Entropy and Biology".

Deadline for manuscript submissions: closed (1 May 2021) | Viewed by 25241

Special Issue Editor

Prof. Dr. Samuel A. Cushman

E-Mail Website
Guest Editor
Rocky Mountain Research Station, USDA Forest Service, 2500 S. Pine Knoll Dr., Flagstaff, AZ 86001, USA
Interests: landscape ecology; landscape genetics; forest ecology; climate change; wildlife ecology; disturbance ecology; population biology; landscape dynamic simulation modeling; landscape pattern analysis
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleague,

Entropy and the second law of thermodynamics are the central organizing principles of nature, but the ideas and implications of the second law are still poorly developed in landscape ecology, despite a large recent upsurge in interest in the topic. The purpose of this second Special Issue on “Entropy in Landscape Ecology” in Entropy is to continue to build on the momentum we created in the first Special Issue to advance thermodynamic research in landscape ecology. The central goal is to bring together current research on applications of thermodynamics in landscape ecology, to consolidate current knowledge and identify key areas for future research. Formalizing the connections between entropy and ecology are still in an early stage, and this Special Issue will contain papers that address several centrally important ideas and provide seminal work that will be a foundation for the future development of ecological and evolutionary thermodynamics.

Prof. Dr. Samuel A. Cushman
Guest Editor

Manuscript Submission Information

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Keywords

  • landscape
  • scale
  • spatial
  • entropy
  • thermodynamics

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Related Special Issues

Published Papers (7 papers)

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12 pages, 3626 KiB  
Article
Generalizing Boltzmann Configurational Entropy to Surfaces, Point Patterns and Landscape Mosaics
by Samuel A. Cushman
Entropy 2021, 23(12), 1616; https://doi.org/10.3390/e23121616 - 1 Dec 2021
Cited by 8 | Viewed by 2716
Abstract
Several methods have been recently proposed to calculate configurational entropy, based on Boltzmann entropy. Some of these methods appear to be fully thermodynamically consistent in their application to landscape patch mosaics, but none have been shown to be fully generalizable to all kinds [...] Read more.
Several methods have been recently proposed to calculate configurational entropy, based on Boltzmann entropy. Some of these methods appear to be fully thermodynamically consistent in their application to landscape patch mosaics, but none have been shown to be fully generalizable to all kinds of landscape patterns, such as point patterns, surfaces, and patch mosaics. The goal of this paper is to evaluate if the direct application of the Boltzmann relation is fully generalizable to surfaces, point patterns, and landscape mosaics. I simulated surfaces and point patterns with a fractal neutral model to control their degree of aggregation. I used spatial permutation analysis to produce distributions of microstates and fit functions to predict the distributions of microstates and the shape of the entropy function. The results confirmed that the direct application of the Boltzmann relation is generalizable across surfaces, point patterns, and landscape mosaics, providing a useful general approach to calculating landscape entropy. Full article
(This article belongs to the Special Issue Entropy in Landscape Ecology II)
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22 pages, 69224 KiB  
Article
Entropy in Landscape Ecology: A Quantitative Textual Multivariate Review
by Samuel A. Cushman
Entropy 2021, 23(11), 1425; https://doi.org/10.3390/e23111425 - 28 Oct 2021
Cited by 11 | Viewed by 3092
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Entropy in Landscape Ecology II)
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10 pages, 2211 KiB  
Article
Thermodynamic Consistency of the Cushman Method of Computing the Configurational Entropy of a Landscape Lattice
by Samuel A. Cushman
Entropy 2021, 23(11), 1420; https://doi.org/10.3390/e23111420 - 28 Oct 2021
Cited by 9 | Viewed by 1726
Abstract
There has been a recent surge of interest in theory and methods for calculating the entropy of landscape patterns, but relatively little is known about the thermodynamic consistency of these approaches. I posit that for any of these methods to be fully thermodynamically [...] Read more.
There has been a recent surge of interest in theory and methods for calculating the entropy of landscape patterns, but relatively little is known about the thermodynamic consistency of these approaches. I posit that for any of these methods to be fully thermodynamically consistent, they must meet three conditions. First, the computed entropies must lie along the theoretical distribution of entropies as a function of total edge length, which Cushman showed was a parabolic function following from the fact that there is a normal distribution of permuted edge lengths, the entropy is the logarithm of the number of microstates in a macrostate, and the logarithm of a normal distribution is a parabolic function. Second, the entropy must increase over time through the period of the random mixing simulation, following the expectation that entropy increases in a closed system. Third, at full mixing, the entropy will fluctuate randomly around the maximum theoretical value, associated with a perfectly random arrangement of the lattice. I evaluated these criteria in a test condition involving a binary, two-class landscape using the Cushman method of directly applying the Boltzmann relation (s = klogW) to permuted landscape configurations and measuring the distribution of total edge length. The results show that the Cushman method directly applying the classical Boltzmann relation is fully consistent with these criteria and therefore fully thermodynamically consistent. I suggest that this method, which is a direct application of the classical and iconic formulation of Boltzmann, has advantages given its direct interpretability, theoretical elegance, and thermodynamic consistency. Full article
(This article belongs to the Special Issue Entropy in Landscape Ecology II)
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13 pages, 4217 KiB  
Article
Distributions of Hyper-Local Configuration Elements to Characterize, Compare, and Assess Landscape-Level Spatial Patterns
by Tarmo K. Remmel
Entropy 2020, 22(4), 420; https://doi.org/10.3390/e22040420 - 8 Apr 2020
Cited by 2 | Viewed by 3294
Abstract
Even with considerable attention in recent decades, measuring and working with patterns remains a complex task due to the underlying dynamic processes that form these patterns, the influence of scales, and the many further implications stemming from their representation. This work scrutinizes binary [...] Read more.
Even with considerable attention in recent decades, measuring and working with patterns remains a complex task due to the underlying dynamic processes that form these patterns, the influence of scales, and the many further implications stemming from their representation. This work scrutinizes binary classes mapped onto regular grids and counts the relative frequencies of all first-order configuration components and then converts these measurements into empirical probabilities of occurrence for either of the two landscape classes. The approach takes into consideration configuration explicitly and composition implicitly (in a common framework), while the construction of a frequency distribution provides a generic model of landscape structure that can be used to simulate structurally similar landscapes or to compare divergence from other landscapes. The technique is first tested on simulated data to characterize a continuum of landscapes across a range of spatial autocorrelations and relative compositions. Subsequent assessments of boundary prominence are explored, where outcomes are known a priori, to demonstrate the utility of this novel method. For a binary map on a regular grid, there are 32 possible configurations of first-order orthogonal neighbours. The goal is to develop a workflow that permits patterns to be characterized in this way and to offer an approach that identifies how relatively divergent observed patterns are, using the well-known Kullback–Leibler divergence. Full article
(This article belongs to the Special Issue Entropy in Landscape Ecology II)
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15 pages, 685 KiB  
Article
Use of Entropy in Developing SDG-based Indices for Assessing Regional Sustainable Development: A Provincial Case Study of China
by Xiangyu Wang, Peichao Gao, Changqing Song and Changxiu Cheng
Entropy 2020, 22(4), 406; https://doi.org/10.3390/e22040406 - 2 Apr 2020
Cited by 22 | Viewed by 4131
Abstract
Sustainable development appears to be the theme of our time. To assess the progress of sustainable development, a simple but comprehensive index is of great use. To this end, a multivariate index of sustainable development was developed in this study based on indicators [...] Read more.
Sustainable development appears to be the theme of our time. To assess the progress of sustainable development, a simple but comprehensive index is of great use. To this end, a multivariate index of sustainable development was developed in this study based on indicators of the United Nations Sustainable Development Goals (SDGs). To demonstrate the usability of this developed index, we applied it to Fujian Province, China. According to the China SDGs indicators and the Fujian situation, we divided the SDGs into three dimensions and selected indicators based on these dimensions. We calculated the weights and two indices with the entropy weight coefficient method based on collecting and processing of data from 2007 to 2017. We assessed and analyzed the sustainable development of Fujian with two indices and we drew three main conclusions. From 2007 to 2017, the development index of Fujian showed an increasing trend and the coordination index of Fujian showed a fluctuating trend. It is difficult to smoothly improve the coordination index of Fujian because the development speeds of Goal 3 (Good Health and Well-being) and Goal 16 (Peace, Justice, and Strong Institutions) were low. The coordination index of Fujian changed from strong coordination to medium coordination from 2011 to 2012 because the development speed of the environmental dimension suddenly improved. It changed from strong coordination to medium coordination from 2015 to 2016 because the values of the development index of the social dimension were decreasing. To the best of our knowledge, these are the first SDGs-based multivariate indices of sustainable development for a region of China. These indices are applicable to different regions. Full article
(This article belongs to the Special Issue Entropy in Landscape Ecology II)
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14 pages, 5486 KiB  
Article
Calculating the Wasserstein Metric-Based Boltzmann Entropy of a Landscape Mosaic
by Hong Zhang, Zhiwei Wu, Tian Lan, Yanyu Chen and Peichao Gao
Entropy 2020, 22(4), 381; https://doi.org/10.3390/e22040381 - 26 Mar 2020
Cited by 15 | Viewed by 3484
Abstract
Shannon entropy is currently the most popular method for quantifying the disorder or information of a spatial data set such as a landscape pattern and a cartographic map. However, its drawback when applied to spatial data is also well documented; it is incapable [...] Read more.
Shannon entropy is currently the most popular method for quantifying the disorder or information of a spatial data set such as a landscape pattern and a cartographic map. However, its drawback when applied to spatial data is also well documented; it is incapable of capturing configurational disorder. In addition, it has been recently criticized to be thermodynamically irrelevant. Therefore, Boltzmann entropy was revisited, and methods have been developed for its calculation with landscape patterns. The latest method was developed based on the Wasserstein metric. This method incorporates spatial repetitiveness, leading to a Wasserstein metric-based Boltzmann entropy that is capable of capturing the configurational disorder of a landscape mosaic. However, the numerical work required to calculate this entropy is beyond what can be practically achieved through hand calculation. This study developed a new software tool for conveniently calculating the Wasserstein metric-based Boltzmann entropy. The tool provides a user-friendly human–computer interface and many functions. These functions include multi-format data file import function, calculation function, and data clear or copy function. This study outlines several essential technical implementations of the tool and reports the evaluation of the software tool and a case study. Experimental results demonstrate that the software tool is both efficient and convenient. Full article
(This article belongs to the Special Issue Entropy in Landscape Ecology II)
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13 pages, 2120 KiB  
Technical Note
belg: A Tool for Calculating Boltzmann Entropy of Landscape Gradients
by Jakub Nowosad and Peichao Gao
Entropy 2020, 22(9), 937; https://doi.org/10.3390/e22090937 - 26 Aug 2020
Cited by 7 | Viewed by 5693
Abstract
Entropy is a fundamental concept in thermodynamics that is important in many fields, including image processing, neurobiology, urban planning, and sustainability. As of recently, the application of Boltzmann entropy for landscape patterns was mostly limited to the conceptual discussion. However, in the last [...] Read more.
Entropy is a fundamental concept in thermodynamics that is important in many fields, including image processing, neurobiology, urban planning, and sustainability. As of recently, the application of Boltzmann entropy for landscape patterns was mostly limited to the conceptual discussion. However, in the last several years, a number of methods for calculating Boltzmann entropy for landscape mosaics and gradients were proposed. We developed an R package belg as an open source tool for calculating Boltzmann entropy of landscape gradients. The package contains functions to calculate relative and absolute Boltzmann entropy using the hierarchy-based and the aggregation-based methods. It also supports input raster with missing (NA) values, allowing for calculations on real data. In this study, we explain ideas behind implemented methods, describe the core functionality of the software, and present three examples of its use. The examples show the basic functions in this package, how to adjust Boltzmann entropy values for data with missing values, and how to use the belg package in larger workflows. We expect that the belg package will be a useful tool in the discussion of using entropy for a description of landscape patterns and facilitate a thermodynamic understanding of landscape dynamics. Full article
(This article belongs to the Special Issue Entropy in Landscape Ecology II)
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