Using geometry to rank evenness measures: towards a deeper understanding of divergence
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Publication:2235576
DOI10.1016/J.JTBI.2021.110902zbMATH Open1472.92257arXiv2105.11532OpenAlexW3201107166MaRDI QIDQ2235576
Publication date: 21 October 2021
Published in: Journal of Theoretical Biology (Search for Journal in Brave)
Abstract: While recent work has established divergence as a key framework for understanding evenness, there is currently no research exploring how the families of measures within the divergence-based framework relate to each other. This paper uses geometry to show that, holding order and richness constant, the families of divergence-based evenness measures nest. This property allows them to be ranked based on their reactivity to changes in relatively even assemblages or changes in relatively uneven ones. We establish this ranking and explore how the distance-based measures relate to it for both order q=2 and q=1. We also derive a new family of distance-based measures that captures the angular distance between the vector of relative abundances and a perfectly even vector and is highly reactive to changes in even assemblages. Finally, we show that if we only require evenness to be a divergence, then any smooth, monotonically increasing function of diversity can be made into an evenness measure. A deeper understanding of how to measure evenness will require empirical or theoretical research that uncovers which kind of divergence best reflects the underlying concept.
Full work available at URL: https://arxiv.org/abs/2105.11532
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