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Analysis of Ratios in Multivariate Morphometry
The analysis of ratios of body measurements is deeply ingrained in the taxonomic literature. Whether for plants or animals, certain ratios are commonly indicated in identification keys, diagnoses, and descriptions. They often provide the only means for separation of cryptic species that mostly lack...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Oxford University Press
2011
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3193766/ https://www.ncbi.nlm.nih.gov/pubmed/21828084 http://dx.doi.org/10.1093/sysbio/syr061 |
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author | Baur, Hannes Leuenberger, Christoph |
author_facet | Baur, Hannes Leuenberger, Christoph |
author_sort | Baur, Hannes |
collection | PubMed |
description | The analysis of ratios of body measurements is deeply ingrained in the taxonomic literature. Whether for plants or animals, certain ratios are commonly indicated in identification keys, diagnoses, and descriptions. They often provide the only means for separation of cryptic species that mostly lack distinguishing qualitative characters. Additionally, they provide an obvious way to study differences in body proportions, as ratios reflect geometric shape differences. However, when it comes to multivariate analysis of body measurements, for instance, with linear discriminant analysis (LDA) or principal component analysis (PCA), interpretation using body ratios is difficult. Both techniques are commonly applied for separating similar taxa or for exploring the structure of variation, respectively, and require standardized raw or log-transformed variables as input. Here, we develop statistical procedures for the analysis of body ratios in a consistent multivariate statistical framework. In particular, we present algorithms adapted to LDA and PCA that allow the interpretation of numerical results in terms of body proportions. We first introduce a method called the “LDA ratio extractor,” which reveals the best ratios for separation of two or more groups with the help of discriminant analysis. We also provide measures for deciding how much of the total differences between individuals or groups of individuals is due to size and how much is due to shape. The second method, a graphical tool called the “PCA ratio spectrum,” aims at the interpretation of principal components in terms of body ratios. Based on a similar idea, the “allometry ratio spectrum” is developed which can be used for studying the allometric behavior of ratios. Because size can be defined in different ways, we discuss several concepts of size. Central to this discussion is Jolicoeur's multivariate generalization of the allometry equation, a concept that was derived only with a heuristic argument. Here we present a statistical derivation of the allometric size vector using the method of least squares. The application of the above methods is extensively demonstrated using published data sets from parasitic wasps and rock crabs. |
format | Online Article Text |
id | pubmed-3193766 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2011 |
publisher | Oxford University Press |
record_format | MEDLINE/PubMed |
spelling | pubmed-31937662011-10-17 Analysis of Ratios in Multivariate Morphometry Baur, Hannes Leuenberger, Christoph Syst Biol Regular Articles The analysis of ratios of body measurements is deeply ingrained in the taxonomic literature. Whether for plants or animals, certain ratios are commonly indicated in identification keys, diagnoses, and descriptions. They often provide the only means for separation of cryptic species that mostly lack distinguishing qualitative characters. Additionally, they provide an obvious way to study differences in body proportions, as ratios reflect geometric shape differences. However, when it comes to multivariate analysis of body measurements, for instance, with linear discriminant analysis (LDA) or principal component analysis (PCA), interpretation using body ratios is difficult. Both techniques are commonly applied for separating similar taxa or for exploring the structure of variation, respectively, and require standardized raw or log-transformed variables as input. Here, we develop statistical procedures for the analysis of body ratios in a consistent multivariate statistical framework. In particular, we present algorithms adapted to LDA and PCA that allow the interpretation of numerical results in terms of body proportions. We first introduce a method called the “LDA ratio extractor,” which reveals the best ratios for separation of two or more groups with the help of discriminant analysis. We also provide measures for deciding how much of the total differences between individuals or groups of individuals is due to size and how much is due to shape. The second method, a graphical tool called the “PCA ratio spectrum,” aims at the interpretation of principal components in terms of body ratios. Based on a similar idea, the “allometry ratio spectrum” is developed which can be used for studying the allometric behavior of ratios. Because size can be defined in different ways, we discuss several concepts of size. Central to this discussion is Jolicoeur's multivariate generalization of the allometry equation, a concept that was derived only with a heuristic argument. Here we present a statistical derivation of the allometric size vector using the method of least squares. The application of the above methods is extensively demonstrated using published data sets from parasitic wasps and rock crabs. Oxford University Press 2011-12 2011-08-09 /pmc/articles/PMC3193766/ /pubmed/21828084 http://dx.doi.org/10.1093/sysbio/syr061 Text en © The Author(s) 2011. Published by Oxford University Press on behalf of the Society of Systematic Biologists. This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0), which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. |
spellingShingle | Regular Articles Baur, Hannes Leuenberger, Christoph Analysis of Ratios in Multivariate Morphometry |
title | Analysis of Ratios in Multivariate Morphometry |
title_full | Analysis of Ratios in Multivariate Morphometry |
title_fullStr | Analysis of Ratios in Multivariate Morphometry |
title_full_unstemmed | Analysis of Ratios in Multivariate Morphometry |
title_short | Analysis of Ratios in Multivariate Morphometry |
title_sort | analysis of ratios in multivariate morphometry |
topic | Regular Articles |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3193766/ https://www.ncbi.nlm.nih.gov/pubmed/21828084 http://dx.doi.org/10.1093/sysbio/syr061 |
work_keys_str_mv | AT baurhannes analysisofratiosinmultivariatemorphometry AT leuenbergerchristoph analysisofratiosinmultivariatemorphometry |