Geometric morphometric approaches become increasingly applied in the fields of biology and paleontology. Taxonomy is a good example, where a long-standing intention of scientists is to eliminate subjectivity as much as possible. In the case of biostratigraphically important conodont elements, the application of such methods is not widespread. Indeed, only a handful of studies attempted to deal with the morphological variance of conodont elements from this aspect. The detailed description of five lower Norian (Upper Triassic) taxa (Ancyrogondolella quadrata, A. rigoi, A. triangularis, A. uniformis and Metapolygnathus mazzai) is presented here based on landmarks and Fourier analysis of the P1 element and keel outlines. Both methods led to similar outcomes regarding taxonomic differentiation and exposing shape variability. Consensus shapes were generated to objectively reveal the typical contour shape of each taxon, which allowed their comparison with each other, and with the members of their respective sample population including the holotypes. The results pointed out that the holotype of a taxon is generally not an average representative, but rather a peripheral form with well-separable morphological characteristics. Ancyrogondolella quadrata and A. rigoi turned out to represent a morphological continuum with ample transitional forms between these two end-members that may cause bias in their biostratigraphic applicability; however, their combined shape variance seems to be too large for uniting them into a single species. Given the results that may be too subtle to realize based solely on qualitative observations, future taxonomic studies and type material designation could greatly benefit from the application of similar methodologies.

Material

The analysis involved a total of 136 lower Norian conodont P1 elements. The material originates from various localities of the western Tethys and western North America. Eighty percent of the specimens were unambiguously assigned to the taxa Ancyrogondolella quadrata, A. rigoi, A. triangularis, A. uniformis and Metapolygnathus mazzai. For specimens bearing morphological characters not fully fitting in the original diagnoses of these species, the open nomenclatural term “ex gr.” (of the group) was used. Holotypes of the listed species were also included in the study based on the best illustrations from the literature. Only non-deformed, complete, adult (GS4-GS6; based on the ontogenetic series defined in Mazza & Martínez-Pérez 2015) specimens were involved in the present study.

Shape descriptors

For the shape description, we chose to analyse the element and the keel outlines. To avoid bias induced by bilaterality, all dextral elements were mirrored into their sinistral counterpart. Outline digitization was carried out manually (as in Sinitsa et al. 2019) using the multi-point tool of the open-access ImageJ software (v1.53; Abramoff et al. 2004; Schneider et al. 2012). Uniform point allocation was achieved by the equidistantCurve function of the Morpho package within the R programming environment (v4.1.2; R Core Team 2013; Schlager 2017). In total, the coordinates of 100 shape descriptors were recorded to describe the element and the keel outlines, separately. In addition, the position of the pit was marked in aboral view. To be able to record the position of the tip of the cusp, which is not visible in this view, images made in oral view were mirrored and projected on the corresponding aboral views. The more posteriorly inclined the cusp is, the further behind the pit its projection falls. 

Landmark analysis

The points related to the location of the cusp and the pit were recognized as type I landmarks (i.e. homologous anatomical points). Type II or geometrical landmarks (sensu Bookstein 1992) were selected on the outlines using automated algorithms that searched for the sharpest inward facing angle between neighbouring equidistant shape descriptors of a specific region. On the element outline the anterior end and the posterolateral corners were marked. On the keel outline the anterior end and the two posterior tips if the keel was bifid or the posterolateral corners if the keel was non-bifid were selected. The sections between the type II landmarks were resampled by a pre-defined number of equidistantly placed non-sliding semilandmarks (6 on the posterior margin and 12 on each lateral margin) to retain finer details of the shape (see Gunz and Mitteroecker 2013). To eliminate variability induced by size and orientational differences a generalized Procrustes superimposition was used: the landmark (LM) configurations were centred, scaled to the same centroid size, and rotated until the minimum sum of squared distances between the LMs and their corresponding average position was reached (Gower 1975). To extract the primary patterns of variation, a principal component analysis (PCA) was performed on the resulting aligned coordinates with the prcomp function of the built-in stats package of R.

Fourier analysis

Fourier descriptors (FDs) were calculated using equation 31.6 of Smith (2002) by a provided custom function (dft) written in the R programming language (v4.1.2; R Core Team 2013). The previously produced coordinate sets containing 100 equidistant shape descriptors were used as the basis of these calculations. Contrary to the LM-based approach, the positions of the pit and the cusp were ignored, and all contour points (including the ones selected before as type II LMs) were treated equally during the Fourier analysis. Following the steps described by Kuhl & Giardina (1981) and Godefroy et al. (2012), the FDs were rescaled so that the major axis of the first ellipse (i.e. the sum of the amplitudes of the first two epicycles) became equal to 1. The centred outlines were rotated until the minor and major axes coincided with the horizontal and vertical axes of the underlying Cartesian coordinate system. The FDs were also corrected so that the starting phase angle of the first two epicycles became 0. These steps were achieved by another provided custom R function (normDft). Similar to the LM configurations, the resulting Fourier coefficients were used as variables in a PCA implemented by the prcomp function of the built-in stats package of R. Only the first 20 pairs of FDs were considered for this analysis to provide a good balance between a satisfying description of the element shape, and an efficient filtering of measurement noise without using excessive epicycles.

To run the provided scripts, the open-access R programming environment (v4.1.2) and the RStudio desktop application (build 353) is recommended. To begin, "Virag_Karadi_2023_CONODONTS_script.R" should be opened with RStudio, and if run step by step, it will load the necessary packages (Morpho), custom functions ("Virag_Karadi_2023_CONODONTS_functions.R") and data files (all provided .csv files), automatically during the session.