The multielement apparatus of the Spathian (late Early Triassic) to Carnian (early Late Triassic) conodont Gladigondolella tethydis (Huckriede, 1958) is reconstructed here using multivariate statistical analysis to determine the co-occurrence of elements previously assigned to the Gl. tethydis apparatus by other authors. Disagreements on the apparatus composition of Gl. tethydis have focussed around whether or not the species contained two pairs of P2 elements, or only one pair. Some reconstructions consider elements referred to Cratognathodus as belonging to the multielement apparatus of Gladigondolella, whereas other workers consider these elements to belong to their own multielement apparatus. In the absence of fused clusters or bedding plane assemblages, multivariate statistical analysis of isolated elements provides the best method for constraining apparatus composition. Examination of collections from the Anisian (early Middle Triassic) of China and Romania, together with published occurrences from the Anisian and Carnian from around the world, has allowed the development of a database for both abundance and presence/absence of elements assigned to the Gladigondolella tethydis apparatus. Bray-Curtis indices for abundance data and Jaccard indices for presence/absence data both demonstrate that Cratognathodus elements occur as frequently with other elements belonging to the Gladigondolella tethydis apparatus as those elements do with each other. This lends support to the hypothesis that Cratognathodus elements also belong to the Gladigondolella tethydis apparatus. Therefore, the Gladigondolella tethydis apparatus proposed herein consists of the following elements: Gladigondolella tethydis (P1); Cratognathodus sp. (P2a): Ozarkodina saginata (Huckriede, 1958) (P2b); Roundya lautissima (Huckriede, 1958) (S0); Lonchodina spengleri (Huckriede, 1958) (S1); an enantiognathid element (S2); Hindeodella petrae-viridis (Huckriede, 1958) (S3); Hindeodella multihamata (Huckriede, 1958) (S4); and Lonchodina venusta (Huckriede, 1958) (M). Several of the elements assigned to the apparatus exhibit morphological variability, including the P1 element of Gladigondolella tethydis.
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