Geometric Models for Seed Shape Description and Quantification in the Cactaceae

Seed shape in species of the Cactaceae is described by comparison with geometric models. Three new groups of models are presented, two for symmetric seeds, and a third group for asymmetric seeds. The first two groups correspond, respectively, to superellipses and the combined equations of two semi-e...

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Autores principales:	José Javier Martín-Gómez, Diego Gutiérrez del Pozo, Ángel Tocino, Emilio Cervantes
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	Archimedean spiral cactaceae geometry models morphology seed shape Botany QK1-989
Acceso en línea:	https://doaj.org/article/159f4b1d94ae4194a4e6a71b3a640af6
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spelling	oai:doaj.org-article:159f4b1d94ae4194a4e6a71b3a640af62021-11-25T18:47:33ZGeometric Models for Seed Shape Description and Quantification in the Cactaceae10.3390/plants101125462223-7747https://doaj.org/article/159f4b1d94ae4194a4e6a71b3a640af62021-11-01T00:00:00Zhttps://www.mdpi.com/2223-7747/10/11/2546https://doaj.org/toc/2223-7747Seed shape in species of the Cactaceae is described by comparison with geometric models. Three new groups of models are presented, two for symmetric seeds, and a third group for asymmetric seeds. The first two groups correspond, respectively, to superellipses and the combined equations of two semi-ellipses. The third group contains models derived from the representation of polar equations of Archimedean spirals that define the shape of asymmetric seeds in genera of different subfamilies. Some of the new models are geometric curves, while others are composed with a part resulting from the average silhouettes of seeds. The application of models to seed shape quantification permits the analysis of variation in seed populations, as well as the comparison of shape between species. The embryos of the Cactaceae are of the peripheral type, strongly curved and in contact with the inner surface of the seed coat. A relationship is found between seed elongation and the models, in which the genera with elongated seeds are represented by models with longer trajectories of the spiral. The analysis of seed shape opens new opportunities for taxonomy and allows quantification of seed shape in species of the Cactaceae.José Javier Martín-GómezDiego Gutiérrez del PozoÁngel TocinoEmilio CervantesMDPI AGarticleArchimedean spiralcactaceaegeometrymodelsmorphologyseed shapeBotanyQK1-989ENPlants, Vol 10, Iss 2546, p 2546 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Archimedean spiral cactaceae geometry models morphology seed shape Botany QK1-989
spellingShingle	Archimedean spiral cactaceae geometry models morphology seed shape Botany QK1-989 José Javier Martín-Gómez Diego Gutiérrez del Pozo Ángel Tocino Emilio Cervantes Geometric Models for Seed Shape Description and Quantification in the Cactaceae
description	Seed shape in species of the Cactaceae is described by comparison with geometric models. Three new groups of models are presented, two for symmetric seeds, and a third group for asymmetric seeds. The first two groups correspond, respectively, to superellipses and the combined equations of two semi-ellipses. The third group contains models derived from the representation of polar equations of Archimedean spirals that define the shape of asymmetric seeds in genera of different subfamilies. Some of the new models are geometric curves, while others are composed with a part resulting from the average silhouettes of seeds. The application of models to seed shape quantification permits the analysis of variation in seed populations, as well as the comparison of shape between species. The embryos of the Cactaceae are of the peripheral type, strongly curved and in contact with the inner surface of the seed coat. A relationship is found between seed elongation and the models, in which the genera with elongated seeds are represented by models with longer trajectories of the spiral. The analysis of seed shape opens new opportunities for taxonomy and allows quantification of seed shape in species of the Cactaceae.
format	article
author	José Javier Martín-Gómez Diego Gutiérrez del Pozo Ángel Tocino Emilio Cervantes
author_facet	José Javier Martín-Gómez Diego Gutiérrez del Pozo Ángel Tocino Emilio Cervantes
author_sort	José Javier Martín-Gómez
title	Geometric Models for Seed Shape Description and Quantification in the Cactaceae
title_short	Geometric Models for Seed Shape Description and Quantification in the Cactaceae
title_full	Geometric Models for Seed Shape Description and Quantification in the Cactaceae
title_fullStr	Geometric Models for Seed Shape Description and Quantification in the Cactaceae
title_full_unstemmed	Geometric Models for Seed Shape Description and Quantification in the Cactaceae
title_sort	geometric models for seed shape description and quantification in the cactaceae
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/159f4b1d94ae4194a4e6a71b3a640af6
work_keys_str_mv	AT josejaviermartingomez geometricmodelsforseedshapedescriptionandquantificationinthecactaceae AT diegogutierrezdelpozo geometricmodelsforseedshapedescriptionandquantificationinthecactaceae AT angeltocino geometricmodelsforseedshapedescriptionandquantificationinthecactaceae AT emiliocervantes geometricmodelsforseedshapedescriptionandquantificationinthecactaceae
_version_	1718410696343945216

Geometric Models for Seed Shape Description and Quantification in the Cactaceae

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