A review on the use of entropy in landscape ecology: heterogeneity, unpredictability, scale dependence and their links with thermodynamics

Abstract

The identification of a universal law that can predict the spatiotemporal structure of any entity at any scale has long been pursued. Thermodynamics have targeted this goal, and the concept of entropy has been widely applied for various disciplines and purposes, including landscape ecology. Within this discipline, however, the uses of the entropy concept and its underlying assumptions are various and are seldom described explicitly. In addition, the link between this concept and thermodynamics is unclear. The aim of this paper is to review the various interpretations and applications of entropy in landscape ecology and to sort them into clearly defined categories. First, a retrospective study of the concept genesis from thermodynamics to landscape ecology was conducted. Then, 50 landscape ecology papers that use or discuss entropy were surveyed and classified by keywords, variables and metrics identified as related to entropy. In particular, the thermodynamic component of entropy in landscape ecology and its various interpretations related to landscape structure and dynamics were considered. From the survey results, three major definitions (i.e., spatial heterogeneity, the unpredictability of pattern dynamics and pattern scale dependence) associated with the entropy concept in landscape ecology were identified. The thermodynamic interpretations of these definitions are based on different theories. The thermodynamic interpretation of spatial heterogeneity is not considered relevant. The thermodynamic interpretation related to scale dependence is also questioned by complexity theory. Only unpredictability can be thermodynamically relevant if appropriate measurements are used to test it.

Discussing Landscape Compositional Scenarios Generated with Maximization of Non-Expected Utility Decision Models Based on Weighted Entropies

“…There are two distinct uses for the word entropy in landscape ecology, either related to the scientific field of thermodynamics or to information theory, and though there is a formal analogy these concepts are claimed to represent scientific disciplines [1].…”

“…Landscape composition can be defined as the variety and abundance of different land cover types within the landscape [22] and different diversity indices measure distinct aspects of the partition of abundance between landscape elements [23]. In this paper, we will not deal with landscape spatial entropy measures related with heterogeneity and fragmentation of the habitats (see [1]). …”

Thermodynamics in landscape ecology: the importance of integrating measurement and modeling of landscape entropy

“…In a review paper published in this issue Vranken et al (2014) present an overview of the use of entropy in landscape ecology. They identified three main uses of the entropy concept in past landscape ecology research, including: spatial heterogeneity, unpredictability of pattern dynamics, and pattern dependence on scale.…”

“…The Vranken et al (2014) review, in my opinion, shows how poorly the universally important topics of the second law of thermodynamics and the entropy principle have penetrated landscape ecology. There are many examples in the literature of informal linkage to the entropy concept, but virtually no formal, quantitative efforts to develop explicit theory derived from the second law.…”

“…Such a formal analysis and definition of landscape entropy may facilitate understanding the linkages between landscape pattern-process relationships and entropy and the second law of thermodynamics. Such a definition and linkage is necessary for using thermodynamic principles to understand and predict landscape dynamics and thermodynamic controls on the propagation of pattern-process relationships across scales, which are other areas Vranken et al (2014) identify as topics mentioned in past landscape ecology literature, but that are incoherently and inconsistently presented due to lack of a rigorous theoretical framework in which to analyze and interpret data on these topics.…”