A hierarchy-based solution to calculate the configurational entropy of landscape gradients

Context: The second law of thermodynamics is fundamental in landscape ecology, and Shannon entropy has been employed as an important means of analyzing landscape patterns. However, the thermodynamic basis of Shannon entropy has been recently questioned because such entropy considers only probability and not configurational information. As a result, Boltzmann entropy (also called configurational entropy), which is the basic measure in thermodynamics, has been revisited, and some thoughts on its calculation have been put forward. Nevertheless, a comprehensive calculation method is still lacking. Objectives: The objective of this study is to propose a feasible solution for the calculation of configurational entropy for landscape gradients. Methods: To calculate the configurational entropy, the first step is to define a good macrostate and then to determine the number of microstates. The macrostate of a landscape gradient is defined as its abstract (i.e., upscaled) representation. The number of microstates is calculated by determining all the possible ways of downscaling from the macrostate to the original. Results: Both simulated and real-life landscape patterns were used for experimental validation. The results show that the entropy calculated using the proposed method successfully captures the disorder of landscape gradients in terms of both composition and configuration. Conclusions: Configurational entropy, calculated using the proposed method, can serve as a thermodynamics-based metric to describe gradient-based landscapes and their changes across space and through time. With this metric, it becomes possible to interpret landscape ecological processes based on thermodynamic insights.