title: Eutacticity in sea urchin evolution.
abstract: An eutactic star, in a n-dimensional space, is a set of N vectors which can be viewed as the projection of N orthogonal vectors in a N-dimensional space. By adequately associating a star of vectors to a particular sea urchin, we propose that a measure of the eutacticity of the star constitutes a measure of the regularity of the sea urchin. Then, we study changes of regularity (eutacticity) in a macroevolutive and taxonomic level of sea urchins belonging to the Echinoidea class. An analysis considering changes through geological time suggests a high degree of regularity in the shape of these organisms through their evolution. Rare deviations from regularity measured in Holasteroida order are discussed.
authors.affiliation: Departamento de Nanotecnología, Centro de Física Aplicada y Tecnología Avanzada, Universidad Nacional Autónoma de México, Apartado Postal 1-1010, Querétaro 76000, Mexico.
authors.forename: J
authors.initials: J
authors.lastname: López-Sauceda
authors.forename: J L
authors.initials: JL
authors.lastname: Aragón
mesh_terms: D000718:Anatomy, Regional; D000719:Anatomy, Veterinary; D000818:Animals; D049628:Body Size / Q000235:genetics; D019143:Evolution, Molecular; D015870:Gene Expression; D009929:Organ Size / Q000235:genetics; D010641:Phenotype; D010802:Phylogeny; D011157:Population Dynamics; D012617:Sea Urchins / Q000033:anatomy & histology* / Q000235:genetics*