Efficient Computation of Spatial Entropy Measures

Abstract

Entropy indices are commonly used to evaluate the heterogeneity of spatially arranged data by exploiting various approaches capable of including spatial information. Unfortunately, in practical studies, difficulties can arise regarding both the availability of computational tools for fast and easy implementation of these indices and guidelines supporting the correct interpretation of the results. The present work addresses such issues for the most known spatial entropy measures: the approach based on area partitions, the one based on distances between observations, and the decomposable spatial entropy. The newly released version of the R package SpatEntropy is introduced here and we show how it properly supports researchers in real case studies. This work also answers practical questions about the spatial distribution of nesting sites of an endangered species of gorillas in Cameroon. Such data present computational challenges, as they are marked points in continuous space over an irregularly shaped region, and covariates are available. Several aspects of the spatial heterogeneity of the nesting sites are addressed, using both the original point data and a discretised pixel dataset. We show how the diversity of the nesting habits is related to the environmental covariates, while seemingly not affected by the interpoint distances. The issue of scale dependence of the spatial measures is also discussed over these data. A motivating example shows the power of the SpatEntropy package, which allows for the derivation of results in seconds or minutes with minimum effort by users with basic programming abilities, confirming that spatial entropy indices are proper measures of diversity.

Keywords

• Batty’s entropy
• biodiversity
• distance-based entropy
• gorilla nesting sites
• Leibovici’s entropy
• multinomial data