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Nutrigonometry III: curvature, area and differences between performance landscapes
Nutrition is one of the underlying factors necessary for the expression of life-histories and fitness across the tree of life. In recent decades, the geometric framework (GF) has become a powerful framework to obtain biological insights through the construction of multidimensional performance landsc...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
The Royal Society
2022
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9709515/ https://www.ncbi.nlm.nih.gov/pubmed/36465681 http://dx.doi.org/10.1098/rsos.221326 |
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author | Morimoto, Juliano Conceição, Pedro Smoczyk, Knut |
author_facet | Morimoto, Juliano Conceição, Pedro Smoczyk, Knut |
author_sort | Morimoto, Juliano |
collection | PubMed |
description | Nutrition is one of the underlying factors necessary for the expression of life-histories and fitness across the tree of life. In recent decades, the geometric framework (GF) has become a powerful framework to obtain biological insights through the construction of multidimensional performance landscapes. However, to date, many properties of these multidimensional landscapes have remained inaccessible due to our lack of mathematical and statistical frameworks for GF analysis. This has limited our ability to understand, describe and estimate parameters which may contain useful biological information from GF multidimensional performance landscapes. Here, we propose a new model to investigate the curvature of GF multidimensional landscapes by calculating the parameters from differential geometry known as Gaussian and mean curvatures. We also estimate the surface area of multidimensional performance landscapes as a way to measure landscape deviations from flat. We applied the models to a landmark dataset in the field, where we also validate the assumptions required for the calculations of curvature. In particular, we showed that linear models perform as well as other models used in GF data, enabling landscapes to be approximated by quadratic polynomials. We then introduced the Hausdorff distance as a metric to compare the similarity of multidimensional landscapes. |
format | Online Article Text |
id | pubmed-9709515 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2022 |
publisher | The Royal Society |
record_format | MEDLINE/PubMed |
spelling | pubmed-97095152022-12-01 Nutrigonometry III: curvature, area and differences between performance landscapes Morimoto, Juliano Conceição, Pedro Smoczyk, Knut R Soc Open Sci Organismal and Evolutionary Biology Nutrition is one of the underlying factors necessary for the expression of life-histories and fitness across the tree of life. In recent decades, the geometric framework (GF) has become a powerful framework to obtain biological insights through the construction of multidimensional performance landscapes. However, to date, many properties of these multidimensional landscapes have remained inaccessible due to our lack of mathematical and statistical frameworks for GF analysis. This has limited our ability to understand, describe and estimate parameters which may contain useful biological information from GF multidimensional performance landscapes. Here, we propose a new model to investigate the curvature of GF multidimensional landscapes by calculating the parameters from differential geometry known as Gaussian and mean curvatures. We also estimate the surface area of multidimensional performance landscapes as a way to measure landscape deviations from flat. We applied the models to a landmark dataset in the field, where we also validate the assumptions required for the calculations of curvature. In particular, we showed that linear models perform as well as other models used in GF data, enabling landscapes to be approximated by quadratic polynomials. We then introduced the Hausdorff distance as a metric to compare the similarity of multidimensional landscapes. The Royal Society 2022-11-30 /pmc/articles/PMC9709515/ /pubmed/36465681 http://dx.doi.org/10.1098/rsos.221326 Text en © 2022 The Authors. https://creativecommons.org/licenses/by/4.0/Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) , which permits unrestricted use, provided the original author and source are credited. |
spellingShingle | Organismal and Evolutionary Biology Morimoto, Juliano Conceição, Pedro Smoczyk, Knut Nutrigonometry III: curvature, area and differences between performance landscapes |
title | Nutrigonometry III: curvature, area and differences between performance landscapes |
title_full | Nutrigonometry III: curvature, area and differences between performance landscapes |
title_fullStr | Nutrigonometry III: curvature, area and differences between performance landscapes |
title_full_unstemmed | Nutrigonometry III: curvature, area and differences between performance landscapes |
title_short | Nutrigonometry III: curvature, area and differences between performance landscapes |
title_sort | nutrigonometry iii: curvature, area and differences between performance landscapes |
topic | Organismal and Evolutionary Biology |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9709515/ https://www.ncbi.nlm.nih.gov/pubmed/36465681 http://dx.doi.org/10.1098/rsos.221326 |
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