Eutacticity in sea urchin evolution

TL;DR

This paper introduces a mathematical measure of shape regularity in sea urchins using eutacticity, revealing high shape stability over evolutionary time with some deviations in specific groups.

Contribution

It proposes a novel eutacticity-based metric to quantify sea urchin shape regularity and applies it to evolutionary data across geological periods.

Findings

High regularity in sea urchin shapes over time

Deviations observed in Holasteroida order

Eutacticity correlates with morphological stability

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.