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The Concept of Evenness/Unevenness: Less Evenness or More Unevenness?
While evenness is understood to be maximal if all types (species, genotypes, alleles, etc.) are represented equally (via abundance, biomass, area, etc.), its opposite, maximal unevenness, either remains conceptually in the dark or is conceived as the type distribution that minimizes the applied even...
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Formato: | Online Artículo Texto |
Lenguaje: | English |
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Springer Netherlands
2021
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8664801/ https://www.ncbi.nlm.nih.gov/pubmed/34890008 http://dx.doi.org/10.1007/s10441-021-09429-9 |
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author | Gregorius, Hans-Rolf Gillet, Elizabeth M. |
author_facet | Gregorius, Hans-Rolf Gillet, Elizabeth M. |
author_sort | Gregorius, Hans-Rolf |
collection | PubMed |
description | While evenness is understood to be maximal if all types (species, genotypes, alleles, etc.) are represented equally (via abundance, biomass, area, etc.), its opposite, maximal unevenness, either remains conceptually in the dark or is conceived as the type distribution that minimizes the applied evenness index. The latter approach, however, frequently leads to conceptual inconsistency due to the fact that the minimizing distribution is not specifiable or is monomorphic. The state of monomorphism, however, is indeterminate in terms of its evenness/unevenness characteristics. Indeed, the semantic indeterminacy also shows up in the observation that monomorphism represents a state of pronounced discontinuity for the established evenness indices. This serious conceptual inconsistency is latent in the widely held idea that evenness is an independent component of diversity. As a consequence, the established evenness indices largely appear as indicators of relative polymorphism rather than as indicators of evenness. In order to arrive at consistent measures of evenness/unevenness, it seems indispensable to determine which states are of maximal unevenness and then to assess the position of a given type distribution between states of maximal evenness and maximal unevenness. Since semantically, unevenness implies inequality among type representations, its maximum is reached if all type representations are equally different. For given number of types, this situation is realized if type representations, when ranked in descending order, show equal differences between adjacent types. We term such distributions “stepladders” as opposed to “plateaus” for uniform distributions. Two approaches to new evenness measures are proposed that reflect different perspectives on the positioning of type distributions between the closest stepladders and the closest plateaus. Their two extremes indicate states of complete evenness and complete unevenness, and the midpoint is postulated to represent the turning point between prevailing evenness and prevailing unevenness. The measures are graphically illustrated by evenness surfaces plotted above frequency simplices for three types, and by transects through evenness surfaces for more types. The approach can be generalized to include variable differences between types (as required in analyses of functional evenness) by simply replacing types with pairs of different types. Pairs, as the new types, can be represented by their abundances, for example, and these can be modified in various ways by the differences between the two types that form the pair. Pair representations thus consist of both the difference between the paired types and their frequency. Omission of pair frequencies leads to conceptual ambiguity. Given this specification of pair representations, their evenness/unevenness can be evaluated using the same indices developed for simple types. Pair evenness then turns out to quantify dispersion evenness. |
format | Online Article Text |
id | pubmed-8664801 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2021 |
publisher | Springer Netherlands |
record_format | MEDLINE/PubMed |
spelling | pubmed-86648012021-12-27 The Concept of Evenness/Unevenness: Less Evenness or More Unevenness? Gregorius, Hans-Rolf Gillet, Elizabeth M. Acta Biotheor Regular Article While evenness is understood to be maximal if all types (species, genotypes, alleles, etc.) are represented equally (via abundance, biomass, area, etc.), its opposite, maximal unevenness, either remains conceptually in the dark or is conceived as the type distribution that minimizes the applied evenness index. The latter approach, however, frequently leads to conceptual inconsistency due to the fact that the minimizing distribution is not specifiable or is monomorphic. The state of monomorphism, however, is indeterminate in terms of its evenness/unevenness characteristics. Indeed, the semantic indeterminacy also shows up in the observation that monomorphism represents a state of pronounced discontinuity for the established evenness indices. This serious conceptual inconsistency is latent in the widely held idea that evenness is an independent component of diversity. As a consequence, the established evenness indices largely appear as indicators of relative polymorphism rather than as indicators of evenness. In order to arrive at consistent measures of evenness/unevenness, it seems indispensable to determine which states are of maximal unevenness and then to assess the position of a given type distribution between states of maximal evenness and maximal unevenness. Since semantically, unevenness implies inequality among type representations, its maximum is reached if all type representations are equally different. For given number of types, this situation is realized if type representations, when ranked in descending order, show equal differences between adjacent types. We term such distributions “stepladders” as opposed to “plateaus” for uniform distributions. Two approaches to new evenness measures are proposed that reflect different perspectives on the positioning of type distributions between the closest stepladders and the closest plateaus. Their two extremes indicate states of complete evenness and complete unevenness, and the midpoint is postulated to represent the turning point between prevailing evenness and prevailing unevenness. The measures are graphically illustrated by evenness surfaces plotted above frequency simplices for three types, and by transects through evenness surfaces for more types. The approach can be generalized to include variable differences between types (as required in analyses of functional evenness) by simply replacing types with pairs of different types. Pairs, as the new types, can be represented by their abundances, for example, and these can be modified in various ways by the differences between the two types that form the pair. Pair representations thus consist of both the difference between the paired types and their frequency. Omission of pair frequencies leads to conceptual ambiguity. Given this specification of pair representations, their evenness/unevenness can be evaluated using the same indices developed for simple types. Pair evenness then turns out to quantify dispersion evenness. Springer Netherlands 2021-12-10 2022 /pmc/articles/PMC8664801/ /pubmed/34890008 http://dx.doi.org/10.1007/s10441-021-09429-9 Text en © The Author(s) 2021 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) . |
spellingShingle | Regular Article Gregorius, Hans-Rolf Gillet, Elizabeth M. The Concept of Evenness/Unevenness: Less Evenness or More Unevenness? |
title | The Concept of Evenness/Unevenness: Less Evenness or More Unevenness? |
title_full | The Concept of Evenness/Unevenness: Less Evenness or More Unevenness? |
title_fullStr | The Concept of Evenness/Unevenness: Less Evenness or More Unevenness? |
title_full_unstemmed | The Concept of Evenness/Unevenness: Less Evenness or More Unevenness? |
title_short | The Concept of Evenness/Unevenness: Less Evenness or More Unevenness? |
title_sort | concept of evenness/unevenness: less evenness or more unevenness? |
topic | Regular Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8664801/ https://www.ncbi.nlm.nih.gov/pubmed/34890008 http://dx.doi.org/10.1007/s10441-021-09429-9 |
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