Abstract
The variation of species diversity over space and time has been widely recognised as a key challenge in ecology. However, measuring species diversity over large areas might be difficult for logistic reasons related to both time and cost savings for sampling, as well as accessibility of remote ecosystems. In this paper, we present a new R package - rasterdiv - to calculate diversity indices based on remotely sensed data, by discussing the theory behind the developed algorithms. Obviously, measures of diversity from space should not be viewed as a replacement of in situ data on biological diversity, but they are rather complementary to existing data and approaches. In practice, they integrate available information of Earth surface properties, including aspects of functional (structural, biophysical and biochemical), taxonomic, phylogenetic and genetic diversity. Making use of the rasterdiv package can result useful in making multiple calculations based on reproducible open source algorithms, robustly rooted in Information Theory.
Highlights
Back in 1872, Ludwig Eduard Boltzmann (Boltzmann 1872) introduced the first measure of entropy, later called marginal entropy and restructured by Claude Elwood Shannon under a mathematical theory umbrella (Shannon 1948)
Measuring species diversity over wide areas might be difficult for logistic reasons related both to time and sampling costs (Chiarucci et al 2011; Hernandez-Stefanoni et al 2012) and to theoretical and practical constraints, which are mainly related to two sources of uncertainty
In the absence of such information, it becomes excessively challenging to properly address the modifiable areal unit problem (MAUP), which in this case is the sensitivity of biodiversity to scale (Jelinski and Wu 1996)
Summary
Back in 1872, Ludwig Eduard Boltzmann (Boltzmann 1872) introduced the first measure of entropy, later called marginal entropy and restructured by Claude Elwood Shannon under a mathematical theory umbrella (Shannon 1948). The diversity of a homogeneous surface like water could be overestimated if spectral distances are not considered To overcome this issue, the Rao’s Quadratic diversity (hereafter Rao’s Q, Rao 1982) could be applied by taking into account relative abundance and the spectral distance among different pixel values. Rao et al (2004) proposed a Cumulative Residual Entropy (CRE) to build a consistent Shannon-like index for continuous variables It is based on residual cumulative probability ( P(X >= xi) ), which can be estimated in a robust manner from empirical mono-dimensional distributions by counting for each value the number of observations with equal or larger values and dividing by the total. We refer to Chao et al (2016) for a complete overview of the Hill’s numbers application in ecology
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