scholarly journals A New Formulation of Maximum Diversification Indexation Using Rao's Quadratic Entropy

2015 ◽  
Author(s):  
Benoit Carmichael ◽  
Gilles Koumou ◽  
Kevin Moran
Keyword(s):  
Quadratic Entropy ◽  
Rao’S Quadratic Entropy ◽  
New Formulation

scholarly journals The Effect of Climate and Human Pressures on Functional Diversity and Species Richness Patterns of Amphibians, Reptiles and Mammals in Europe

Diversity ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 275
Author(s):  
Mariana A. Tsianou ◽  
Maria Lazarina ◽  
Danai-Eleni Michailidou ◽  
Aristi Andrikou-Charitidou ◽  
Stefanos P. Sgardelis ◽  
...  
Keyword(s):  
Species Richness ◽  
Functional Diversity ◽  
Agricultural Land ◽  
Influential Factor ◽  
Climatic Variables ◽  
Quadratic Entropy ◽  
Functional Richness ◽  
Precipitation Seasonality ◽  
Rao’S Quadratic Entropy ◽  
Richness Patterns

The ongoing biodiversity crisis reinforces the urgent need to unravel diversity patterns and the underlying processes shaping them. Although taxonomic diversity has been extensively studied and is considered the common currency, simultaneously conserving other facets of diversity (e.g., functional diversity) is critical to ensure ecosystem functioning and the provision of ecosystem services. Here, we explored the effect of key climatic factors (temperature, precipitation, temperature seasonality, and precipitation seasonality) and factors reflecting human pressures (agricultural land, urban land, land-cover diversity, and human population density) on the functional diversity (functional richness and Rao’s quadratic entropy) and species richness of amphibians (68 species), reptiles (107 species), and mammals (176 species) in Europe. We explored the relationship between different predictors and diversity metrics using generalized additive mixed model analysis, to capture non-linear relationships and to account for spatial autocorrelation. We found that at this broad continental spatial scale, climatic variables exerted a significant effect on the functional diversity and species richness of all taxa. On the other hand, variables reflecting human pressures contributed significantly in the models even though their explanatory power was lower compared to climatic variables. In most cases, functional richness and Rao’s quadratic entropy responded similarly to climate and human pressures. In conclusion, climate is the most influential factor in shaping both the functional diversity and species richness patterns of amphibians, reptiles, and mammals in Europe. However, incorporating factors reflecting human pressures complementary to climate could be conducive to us understanding the drivers of functional diversity and richness patterns.

scholarly journals From zero to infinity: minimum to maximum diversity of the planet by spatio-parametric Rao’s quadratic entropy

2021 ◽  
Author(s):  
Duccio Rocchini ◽  
Matteo Marcantonio ◽  
Daniele Da Re ◽  
Giovanni Bacaro ◽  
Enrico Feoli ◽  
...  
Keyword(s):  
Satellite Image ◽  
Diversity Indices ◽  
Spatial Uncertainty ◽  
Species Determination ◽  
Quadratic Entropy ◽  
In Situ Data ◽  
Rao’S Quadratic Entropy ◽  
Work Done ◽  
First Time

AbstractAimThe majority of work done to gather information on Earth diversity has been carried out by in-situ data, with known issues related to epistemology (e.g., species determination and taxonomy), spatial uncertainty, logistics (time and costs), among others. An alternative way to gather information about spatial ecosystem variability is the use of satellite remote sensing. It works as a powerful tool for attaining rapid and standardized information. Several metrics used to calculate remotely sensed diversity of ecosystems are based on Shannon’s Information Theory, namely on the differences in relative abundance of pixel reflectances in a certain area. Additional metrics like the Rao’s quadratic entropy allow the use of spectral distance beside abundance, but they are point descriptors of diversity, namely they can account only for a part of the whole diversity continuum. The aim of this paper is thus to generalize the Rao’s quadratic entropy by proposing its parameterization for the first time.InnovationThe parametric Rao’s quadratic entropy, coded in R, i) allows to represent the whole continuum of potential diversity indices in one formula, and ii) starting from the Rao’s quadratic entropy, allows to explicitly make use of distances among pixel reflectance values, together with relative abundances.Main conclusionsThe proposed unifying measure is an integration between abundance- and distance-based algorithms to map the continuum of diversity given a satellite image at any spatial scale.

scholarly journals From zero to infinity: Minimum to maximum diversity of the planet by spatio‐parametric Rao’s quadratic entropy

2021 ◽  
Vol 30 (5) ◽  
pp. 1153-1162
Author(s):  
Duccio Rocchini ◽  
Matteo Marcantonio ◽  
Daniele Da Re ◽  
Giovanni Bacaro ◽  
Enrico Feoli ◽  
...  
Keyword(s):  
Quadratic Entropy ◽  
Rao’S Quadratic Entropy

scholarly journals On a functional equation connected with Rao’s quadratic entropy

1994 ◽  
Vol 120 (3) ◽  
pp. 843-843 ◽  
Author(s):  
J. K. Chung ◽  
B. R. Ebanks ◽  
C. T. Ng ◽  
P. K. Sahoo
Keyword(s):  
Functional Equation ◽  
Quadratic Entropy ◽  
Rao’S Quadratic Entropy
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