A mathematical tool to analyze radially symmetrical organisms and its application to a new camerate from Upper Ordovician of South Western Spain

Abstract

We propose a new mathematical technique to describe the morphology of organisms exhibiting radial symmetry. For example, the calyxes of some primitive camerates have a highly regular five-fold symmetry pattern suitable for this analysis. To analyze the plate arrangement, we digitalize the plate diagram codifying the plates with a binary system. After, we expand this binary function as a truncated Fourier-Bessel development. The multimodal structure of the mimic images shows the nonlinear character of patterns. The truncated developments obtained correspond to a regular pentagonal arrangement of five plane waves. This pattern, is stable as it is shown starting from an amplitude equation of gradient form. The above mentioned morphometric tool is useful to study the morphological disparity of different taxa in macroevolutionary trends. This technique has been applied to characterize a new genus and species of Rhodocrinitids which is the oldest camerate from Iberian Peninsula.