Quantifying shell outline variability in extant and fossil Laqueus (Brachiopoda: Terebratulida): are outlines good proxies for long-looped brachidial morphology and can they help us characterize species?

Extant and extinct terebratulide brachiopod species have been defined
primarily on the basis of morphology. What is the fidelity of
morphological species to biological species? And how can we test this
fidelity with fossils? Taxonomically and phylogenetically, the most
informative internal feature in the brachiopod suborder Terebratellidina
is the geometrically complex long-looped brachidium, which, given their
fragile nature, are not commonly preserved in the fossil record. In their
absence, it is essential to test other sources of morphological data when
trying to recognize and identify species. We analyzed valve outlines and
brachidia in the genus Laqueus to explore the utility of
shell shape in discriminating extant and fossil species. Using geometric
morphometric methods, we quantified valve outline variability using
elliptical Fourier methods and tested whether long-looped brachidial
morphology correlates with shell outline shape. We then built
classification models based on machine learning algorithms using outlines
as shape variables to predict fossil species’ identities. Our results
demonstrate that valve outline shape is significantly correlated with
long-looped brachidial shape and that even relatively simple outlines are
sufficiently morphologically distinct to enable
extant Laqueus species to be identified, validating
current taxonomic assignments. These are encouraging results for the study
and delimitation of fossil terebratulide species, and their recognition as
biological species. In addition, machine learning algorithms can be
successfully applied to help solve species recognition and delimitation
problems in paleontology, especially when morphology can be characterized
quantitatively and analyzed statistically.