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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...

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Autores principales: Morimoto, Juliano, Conceição, Pedro, Smoczyk, Knut
Formato: Online Artículo Texto
Lenguaje:English
Publicado: The Royal Society 2022
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.
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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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