Special Issue "Entropy in Landscape Ecology"

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

Deadline for manuscript submissions: closed (28 February 2017).

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 86001, AZ, USA
Interests: landscape ecology; landscape genetics; forest ecology; climate change; wildlife ecology; disturbance ecology; population biology; landscape dynamic simulation modeling; landscape pattern analysis
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Special Issue Information

Dear Colleagues,

Entropy and the second law of thermodynamics are the central organizing principles of nature. However, strangely, the ideas and implications of the second law are poorly developed in the landscape ecology literature. This is particularly strange given the focus of landscape ecology on understanding pattern-process relationships across scales in space and time. Every interaction between entities leads to irreversible change, which increases the entropy and decreases the free energy of the closed system in which they reside. Descriptions of landscape patterns, processes of landscape change, and propagation of pattern-process relationships across space and through time are all governed, constrained, and, in large part, directed by thermodynamics. This direct linkage to thermodynamics and entropy was noted in several pioneering works in the field of landscape ecology, yet, in subsequent decades, our field has largely failed to embrace and utilize these relationships and constraints, with a few exceptions. The purpose of this Special Issue in Entropy is to bring together the best scientists across the world, who are working on applications of thermodynamics in landscape ecology, to consolidate current knowledge and identify key areas for future research. A recent editorial in Landscape Ecology on thermodynamics in landscape ecology identified the following topics as deserving particular focus for future work, and we hope the Entropy Special Issue will address many of these in depth.

1) There is a critical need to define the configurational entropy of landscape mosaics as a benchmark and measuring stick, which subsequently can be used to quantify entropy changes in landscape dynamics and the interactions of patterns and processes across scales of space and time.

2) The second law and entropy are of direct relevance to landscape dynamics as all changes in nature result in increases in system disorder and reduction in free energy of the closed system. Therefore, landscape time series data record this process. In a closed system, all time series will show increasing disorder and reduction in free energy over time, but ecological systems are open systems, and thus time series may show dynamic patterns without directional changes in disorder or free energy.

3) Ecological systems are driven by continual inflow of energy from the sun, and are not thermodynamically closed systems. This inflow of energy enables biological processes to function, driving photosynthesis “uphill” against the current of entropy, with ecological food webs then providing a “cascade” back down the free energy ladder, reducing free energy and increasing thermodynamic disorder. Landscape ecologists should more formally associate landscape dynamics with changes in entropy and quantify the function of ecological dissipative structures.

4) Observing a dynamic equilibrium in a landscape does not imply absence of increasing entropy. Just as an organism maintains homeostasis by functioning as a dissipative structure consuming and degrading high free energy organic molecules and releasing heat and highly oxidized metabolic products, a landscape maintains a dynamic equilibrium under a disturbance-succession regime through the collective emergent property of many organismal dissipative structures in interaction with abiotic drivers, such as solar energy, temperature, and moisture.

5) In forest systems, the dynamics range from gap-phase replacement of individual trees as windfall and senescence occurs to large-scale patterns of patch dynamics in response to wild fire and other large contagious disturbances. In each of these there is a dynamic equilibrium of landscape patterns, with different kinds of heterogeneity at different scales. In neither is there any trend to decrease in macrostructural stage, but rather a characteristic range of variation in landscape structure over time (e.g., change in macrostate within a characteristic range), as a function of the nature of the disturbance-succession process in that system. Linking the scale dependence of landscape dynamics to thermodynamic constraints across different ecosystem types would be central to generalizing the application of entropy in landscape ecology.

6) The linkage of the second law of thermodynamics and the entropy principle with the concepts of resistance, resilience and recovery seems important, as is linkage to ideas of dynamic equilibrium and dissipative structures.

7) There are more ways to be broken than to be fixed, more ways to be dead than alive, more ways to be disordered than to be ordered, and thus thermodynamic changes always lead to less predictability in the future state than the current state. All increases in entropy result in increasing disorder and lower potential energy in the closed system. This by definition decreases predictability, as there are more ways to be disordered than ordered and more ways to have dissipated energy than ‘‘concentrated’’ energy. This is always the case, and increase in entropy always leads to decrease in predictability in the closed system. However, landscapes are open stems and understanding the flow of energy and resulting patterns of order and disorder may result in increase or decrease in system predictability over time depending on whether the energy flow results in net decrease in entropy of the landscape or a net increase.

8) Fractal dimension seems directly related to entropy. Fractal dimension is a measure of a pattern-process scaling law and the relationships of such scaling laws to the thermodynamics of dissipative structures is a topic that should be explored. One may conjecture that the reason there are fractal scaling laws at all is because of the thermodynamic behavior of dissipative structures.

9) The scale challenges in landscape ecology are not a source of “departure” from thermodynamics, but rather are products of the action of dissipative structures organized across a range of scales or hierarchical levels. Attention should be given to entropy, complexity theory and the organization of ecological systems as a multilevel or multi-scale system of dissipative structures.

10) Thermodynamic irreversibility is a fundamental attribute of the universe and all things in it, including landscapes. If landscapes appear to not follow irreversibility laws then it is an indication of an insufficiency of how landscape ecological analysis reflects the reality of the universe. When ecological systems are properly viewed as multiscale and hierarchically organized dissipative structures then it is clear that thermodynamic irreversibility does apply.

11) The application of thermodynamic entropy concepts in landscape ecology has not addressed the true thermodynamic nature of the actions of dissipative structures across scales, and this has been limited by failure to measure energy transformations, changes in free energy, changes in configurational entropy of landscape mosaics. As a result, there has been a nebulous and inconsistent application and interpretation of these ideas in the field.

Prof. Dr. Samuel A. Cushman
Guest Editor

Manuscript Submission Information

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Published Papers (7 papers)

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Editorial

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Open AccessEditorial
Editorial: Entropy in Landscape Ecology
Entropy 2018, 20(5), 314; https://doi.org/10.3390/e20050314 - 25 Apr 2018
Cited by 5
Abstract
Entropy and the second law of thermodynamics are the central organizing principles of nature, but the ideas and implications of the second law are poorly developed in landscape ecology. The purpose of this Special Issue “Entropy in Landscape Ecology” in Entropy is to [...] Read more.
Entropy and the second law of thermodynamics are the central organizing principles of nature, but the ideas and implications of the second law are poorly developed in landscape ecology. The purpose of this Special Issue “Entropy in Landscape Ecology” in Entropy is to bring together current research on applications of thermodynamics in landscape ecology, to consolidate current knowledge and identify key areas for future research. The special issue contains six articles, which cover a broad range of topics including relationships between entropy and evolution, connections between fractal geometry and entropy, new approaches to calculate configurational entropy of landscapes, example analyses of computing entropy of landscapes, and using entropy in the context of optimal landscape planning. Collectively these papers provide a broad range of contributions to the nascent field of ecological thermodynamics. Formalizing the connections between entropy and ecology are in a very early stage, and that this special issue contains papers that address several centrally important ideas, and provides seminal work that will be a foundation for the future development of ecological and evolutionary thermodynamics. Full article
(This article belongs to the Special Issue Entropy in Landscape Ecology)

Research

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Open AccessFeature PaperArticle
Calculation of Configurational Entropy in Complex Landscapes
Entropy 2018, 20(4), 298; https://doi.org/10.3390/e20040298 - 19 Apr 2018
Cited by 11
Abstract
Entropy and the second law of thermodynamics are fundamental concepts that underlie all natural processes and patterns. Recent research has shown how the entropy of a landscape mosaic can be calculated using the Boltzmann equation, with the entropy of a lattice mosaic equal [...] Read more.
Entropy and the second law of thermodynamics are fundamental concepts that underlie all natural processes and patterns. Recent research has shown how the entropy of a landscape mosaic can be calculated using the Boltzmann equation, with the entropy of a lattice mosaic equal to the logarithm of the number of ways a lattice with a given dimensionality and number of classes can be arranged to produce the same total amount of edge between cells of different classes. However, that work seemed to also suggest that the feasibility of applying this method to real landscapes was limited due to intractably large numbers of possible arrangements of raster cells in large landscapes. Here I extend that work by showing that: (1) the proportion of arrangements rather than the number with a given amount of edge length provides a means to calculate unbiased relative configurational entropy, obviating the need to compute all possible configurations of a landscape lattice; (2) the edge lengths of randomized landscape mosaics are normally distributed, following the central limit theorem; and (3) given this normal distribution it is possible to fit parametric probability density functions to estimate the expected proportion of randomized configurations that have any given edge length, enabling the calculation of configurational entropy on any landscape regardless of size or number of classes. I evaluate the boundary limits (4) for this normal approximation for small landscapes with a small proportion of a minority class and show it holds under all realistic landscape conditions. I further (5) demonstrate that this relationship holds for a sample of real landscapes that vary in size, patch richness, and evenness of area in each cover type, and (6) I show that the mean and standard deviation of the normally distributed edge lengths can be predicted nearly perfectly as a function of the size, patch richness and diversity of a landscape. Finally, (7) I show that the configurational entropy of a landscape is highly related to the dimensionality of the landscape, the number of cover classes, the evenness of landscape composition across classes, and landscape heterogeneity. These advances provide a means for researchers to directly estimate the frequency distribution of all possible macrostates of any observed landscape, and then directly calculate the relative configurational entropy of the observed macrostate, and to understand the ecological meaning of different amounts of configurational entropy. These advances enable scientists to take configurational entropy from a concept to an applied tool to measure and compare the disorder of real landscapes with an objective and unbiased measure based on entropy and the second law. Full article
(This article belongs to the Special Issue Entropy in Landscape Ecology)
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Open AccessArticle
Horton Ratios Link Self-Similarity with Maximum Entropy of Eco-Geomorphological Properties in Stream Networks
Entropy 2017, 19(6), 249; https://doi.org/10.3390/e19060249 - 30 May 2017
Cited by 5
Abstract
Stream networks are branched structures wherein water and energy move between land and atmosphere, modulated by evapotranspiration and its interaction with the gravitational dissipation of potential energy as runoff. These actions vary among climates characterized by Budyko theory, yet have not been integrated [...] Read more.
Stream networks are branched structures wherein water and energy move between land and atmosphere, modulated by evapotranspiration and its interaction with the gravitational dissipation of potential energy as runoff. These actions vary among climates characterized by Budyko theory, yet have not been integrated with Horton scaling, the ubiquitous pattern of eco-hydrological variation among Strahler streams that populate river basins. From Budyko theory, we reveal optimum entropy coincident with high biodiversity. Basins on either side of optimum respond in opposite ways to precipitation, which we evaluated for the classic Hubbard Brook experiment in New Hampshire and for the Whitewater River basin in Kansas. We demonstrate that Horton ratios are equivalent to Lagrange multipliers used in the extremum function leading to Shannon information entropy being maximal, subject to constraints. Properties of stream networks vary with constraints and inter-annual variation in water balance that challenge vegetation to match expected resource supply throughout the network. The entropy-Horton framework informs questions of biodiversity, resilience to perturbations in water supply, changes in potential evapotranspiration, and land use changes that move ecosystems away from optimal entropy with concomitant loss of productivity and biodiversity. Full article
(This article belongs to the Special Issue Entropy in Landscape Ecology)
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Open AccessArticle
Entropy in the Tangled Nature Model of Evolution
Entropy 2017, 19(5), 192; https://doi.org/10.3390/e19050192 - 27 Apr 2017
Cited by 7
Abstract
Applications of entropy principles to evolution and ecology are of tantamount importance given the central role spatiotemporal structuring plays in both evolution and ecological succession. We obtain here a qualitative interpretation of the role of entropy in evolving ecological systems. Our interpretation is [...] Read more.
Applications of entropy principles to evolution and ecology are of tantamount importance given the central role spatiotemporal structuring plays in both evolution and ecological succession. We obtain here a qualitative interpretation of the role of entropy in evolving ecological systems. Our interpretation is supported by mathematical arguments using simulation data generated by the Tangled Nature Model (TNM), a stochastic model of evolving ecologies. We define two types of configurational entropy and study their empirical time dependence obtained from the data. Both entropy measures increase logarithmically with time, while the entropy per individual decreases in time, in parallel with the growth of emergent structures visible from other aspects of the simulation. We discuss the biological relevance of these entropies to describe niche space and functional space of ecosystems, as well as their use in characterizing the number of taxonomic configurations compatible with different niche partitioning and functionality. The TNM serves as an illustrative example of how to calculate and interpret these entropies, which are, however, also relevant to real ecosystems, where they can be used to calculate the number of functional and taxonomic configurations that an ecosystem can realize. Full article
(This article belongs to the Special Issue Entropy in Landscape Ecology)
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Open AccessArticle
Entropies of the Chinese Land Use/Cover Change from 1990 to 2010 at a County Level
Entropy 2017, 19(2), 51; https://doi.org/10.3390/e19020051 - 25 Jan 2017
Cited by 10
Abstract
Land Use/Cover Change (LUCC) has gradually became an important direction in the research of global changes. LUCC is a complex system, and entropy is a measure of the degree of disorder of a system. According to land use information entropy, this paper analyzes [...] Read more.
Land Use/Cover Change (LUCC) has gradually became an important direction in the research of global changes. LUCC is a complex system, and entropy is a measure of the degree of disorder of a system. According to land use information entropy, this paper analyzes changes in land use from the perspective of the system. Research on the entropy of LUCC structures has a certain “guiding role” for the optimization and adjustment of regional land use structure. Based on the five periods of LUCC data from the year of 1990 to 2010, this paper focuses on analyzing three types of LUCC entropies among counties in China—namely, Shannon, Renyi, and Tsallis entropies. The findings suggest that: (1) Shannon entropy can reflect the volatility of the LUCC, that Renyi and Tsallis entropies also have this function when their parameter has a positive value, and that Renyi and Tsallis entropies can reflect the extreme case of the LUCC when their parameter has a negative value.; (2) The entropy of China’s LUCC is uneven in time and space distributions, and that there is a large trend during 1990–2010, the central region generally has high entropy in space. Full article
(This article belongs to the Special Issue Entropy in Landscape Ecology)
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Open AccessArticle
Radiative Entropy Production along the Paludification Gradient in the Southern Taiga
Entropy 2017, 19(1), 43; https://doi.org/10.3390/e19010043 - 21 Jan 2017
Cited by 6
Abstract
Entropy production (σ) is a measure of ecosystem and landscape stability in a changing environment. We calculated the σ in the radiation balance for a well-drained spruce forest, a paludified spruce forest, and a bog in the southern taiga of the [...] Read more.
Entropy production (σ) is a measure of ecosystem and landscape stability in a changing environment. We calculated the σ in the radiation balance for a well-drained spruce forest, a paludified spruce forest, and a bog in the southern taiga of the European part of Russia using long-term meteorological data. Though radiative σ depends both on surface temperature and absorbed radiation, the radiation effect in boreal ecosystems is much more important than the temperature effect. The dynamic of the incoming solar radiation was the main driver of the diurnal, seasonal, and intra-annual courses of σ for all ecosystems; the difference in ecosystem albedo was the second most important factor, responsible for seven-eighths of the difference in σ between the bog and forest in a warm period. Despite the higher productivity and the complex structure of the well-drained forest, the dynamics and sums of σ in two forests were very similar. Summer droughts had no influence on the albedo and σ efficiency of forests, demonstrating high self-regulation of the taiga forest ecosystems. On the contrary, a decreasing water supply significantly elevated the albedo and lowered the σ in bog. Bogs, being non-steady ecosystems, demonstrate unique thermodynamic behavior, which is fluctuant and strongly dependent on the moisture supply. Paludification of territories may result in increasing instability of the energy balance and entropy production in the landscape of the southern taiga. Full article
(This article belongs to the Special Issue Entropy in Landscape Ecology)
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Other

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Open AccessConcept Paper
Discussing Landscape Compositional Scenarios Generated with Maximization of Non-Expected Utility Decision Models Based on Weighted Entropies
Entropy 2017, 19(2), 66; https://doi.org/10.3390/e19020066 - 10 Feb 2017
Cited by 5
Abstract
The search for hypothetical optimal solutions of landscape composition is a major issue in landscape planning and it can be outlined in a two-dimensional decision space involving economic value and landscape diversity, the latter being considered as a potential safeguard to the provision [...] Read more.
The search for hypothetical optimal solutions of landscape composition is a major issue in landscape planning and it can be outlined in a two-dimensional decision space involving economic value and landscape diversity, the latter being considered as a potential safeguard to the provision of services and externalities not accounted in the economic value. In this paper, we use decision models with different utility valuations combined with weighted entropies respectively incorporating rarity factors associated to Gini-Simpson and Shannon measures. A small example of this framework is provided and discussed for landscape compositional scenarios in the region of Nisa, Portugal. The optimal solutions relative to the different cases considered are assessed in the two-dimensional decision space using a benchmark indicator. The results indicate that the likely best combination is achieved by the solution using Shannon weighted entropy and a square root utility function, corresponding to a risk-averse behavior associated to the precautionary principle linked to safeguarding landscape diversity, anchoring for ecosystem services provision and other externalities. Further developments are suggested, mainly those relative to the hypothesis that the decision models here outlined could be used to revisit the stability-complexity debate in the field of ecological studies. Full article
(This article belongs to the Special Issue Entropy in Landscape Ecology)
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