Measuring biological diversity using Euclidean metrics

By Stephane Champely, Daniel Chessel. Environmental and Ecological Statistics, 2002

200 citations recorded by the source corpus.

Subfields: Ecology, Ecology, Evolution, Behavior and Systematics, Nature and Landscape Conservation

View Paper: https://www.semanticscholar.org/paper/135831da88be479a41437fa977083a3b76b3e603

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In Ecology

In Ecology, Evolution, Behavior and Systematics

In Nature and Landscape Conservation

Citations in the corpus

A note on functional diversity measures (2005, background): “For instance, if the species distance matrix D is Euclidean, then Q is concave (Champely & Chessel, 2002).”
An attribute‐diversity approach to functional diversity, functional beta diversity, and related (dis)similarity measures (2019, background): “Indeed, in real study cases, there are many more species than functional traits used to describe them (usually more than 30 species and less than 10 traits), while representing M maximally distinct species at the upper bound of the Euclidean space requires at least M 1 axes (e.g., equilateral triang”
Changes in assembly rules along a stress gradient from open dry grasslands to wetlands (2016, methodology): “…variance (Sonnier, Shipley & Navas 2010; Bernard-Verdier et al. 2012), the mean quadratic difference of species’ trait values from the CWM weighted by their relative abundances equals RaoQ if half of the squared Euclidean distance is applied in its calculation (Champely & Chessel 2002).”
Contrasted impacts of climate change on stream fish assemblages along an environmental gradient (2009, methodology): “To measure ﬁsh trait diversity, we followed Champely & Chessel (2002) by using biological information about the dissimilarity between species.”
Functional diversity measures: an overview of their redundancy and their ability to discriminate community assembly rules (2010, background): “The correlation between FDiv and Q is explained by Champely & Chessel (2002) who emphasized that, in an Euclidean space, Rao’s quadratic entropy is the ‘weighted average of the square distances between the underlying Euclidean representation of D [a distance matrix] and the corresponding centre of…”
Quantifying the relevance of intraspecific trait variability for functional diversity (2011, unknown): “For example, as demonstrated by Champely & Chessel (2002), for the dissimilarity between pairs of species: XNsp i¼1 piðxi xcomÞ2 ¼ 1 2 XNsp i¼1 XNsp j¼1 pipjd 2 ij eqn 2 where dij = ||xi-xj|| expresses the trait dissimilarity between each pair of species i and j, i.e. the Euclidian trait value…”
Functional diversity: back to basics and looking forward. (2006, background): “A significant advantage of measures based on pair-wise distances is the large amount of study they have received (Rao 1982; Weitzman 1992; Champely & Chessel 2002) and their relative mathematical simplicity.”
Taxonomic and biological trait differences of stream macroinvertebrate communities between mediterranean and temperate regions: implications for future climatic scenarios (2007, methodology): “Rao’s quadratic diversity was computed using the Champely & Chessel (2002) index as developed by Pavoine & Dole ´dec (2005).”
The apportionment of quadratic entropy: a useful alternative for partitioning diversity in ecological data (2005, methodology): “In order to assure its concavity, we only consider dissimilarity matrices D such that the matrix noted D 1 2, which contains the square root of the values in D, is Euclidean (Rao, 1984; Rao and Nayak, 1985; Champely and Chessel, 2002) that is to say n points Mk (k=1,2,...,n) can be embedded in a Euc”