Detecting morphological gaps in tooth outlines of a Pachyrukhinae (Hegetotheriidae, Notoungulata) lineage: systematic and palaeobiogeographical significance of the records from Northwestern Argentina Author Armella, Matías A. Instituto de Estratigrafía y Geología Sedimentaria Global (IESGLO-CONICET), Facultad de Ciencias Naturales e IML, Universidad Nacional de Tucumán, Miguel Lillo 205, T 4000 JFE San Miguel de Tucumán (Argentina) and Cátedra de Paleontología, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Catamarca, Avenida Belgrano 300, K 4700 AAP, San Fernando del Valle de Catamarca, Catamarca (Argentina) and Instituto Superior de Correlación Geológica (INSUGEO-CONICET), Universidad Nacional de Tucumán, Avenida Presidente Perón s / n, T 4105 XAY, Horco Molle, Tucumán (Argentina) m.armella@conicet.gov.ar & matiasarmella@yahoo.com.ar Author Ercoli, Marcos D. Instituto de Ecorregiones Andinas (INECOA), Instituto de Geología y Minería, Universidad Nacional de Jujuy, CONICET, Avenida Bolivia 1661, Y 4600 GNE, San Salvador de Jujuy (Argentina marcos.ercoli@conicet.gov.ar & marcosdarioercoli@hotmail.com Author Bonini, Ricardo A. Instituto de Investigaciones Arqueológicas y Paleontológicas del Cuaternario Pampeano (INCUAPA-CONICET), Universidad Nacional del Centro de la provincia de Buenos Aires, Avenida del Valle 5737, B 7400 JWI, Olavarría (Argentina rbonini@fcnym.unlp.edu.ar Author García-López, Daniel A. Instituto Superior de Correlación Geológica (INSUGEO-CONICET), Universidad Nacional de Tucumán, Avenida Presidente Perón s / n, T 4105 XAY, Horco Molle, Tucumán (Argentina dgarcialopez@csnat.unt.edu.ar text Comptes Rendus Palevol 2022 2022-05-02 21 16 323 348 https://doi.org/10.5852/cr-palevol2022v21a16 journal article 315524 10.5852/cr-palevol2022v21a16 3402fecd-0984-4829-b5d2-6975155e83be 1777-571X 20746332 urn:lsid:zoobank.org:pub:1819D600-1B6E-49A2-A016-44C9119C6AA7

TABLE 2. — Clusters and morphological gaps of the upper dentition. Principal components scores (resulting from EFA and PCA) retained for statistical procedures, clustering algorithms used to determine the optimal number of groups under gap statistic methods (K-means, Ward, and centroid indices), Shapiro-Wilk test values for each cluster (α = 0.05), and tolerance regions (γ = 0.05; β = 0.1). Note that the overlap is calculated using the upper limit of Cluster A and the lower limit of Cluster B on their probability distributions along the canonical axis resulting from the LDA. Groups without overlap are highlighted in bold font, providing statistical evidence for the existence of a morphological gap (Fig. 5).

Morphological gaps data	M1	M2	M3	UMM	P2	P3	P4	UPM
PC scores	PC1-8	PC1-8	PC1-8	PC1-9	PC1-7	PC1-8	PC1-7	PC1-8
K-means index (N clusters)	–0.55 (2)	–0.37 (2)	–0.87 (2)	–0.51 (2)	–0.56 (2)	–0.61 (2)	–0.47 (2)	–0.56 (2)
Ward index (N clusters)	–0.60 (2)	–0.25 (2)	–0.86 (2)	–0.49 (2)	–0.47 (2)	–0.18 (2)	–0.49 (2)	–0.46 (2)
Centroid index (N clusters)	–0.86 (2)	–0.68 (2)	–1.16 (2)	–0.58 (2)	–0.69 (2)	–1.06 (2)	–1.07 (2)	–0.54 (2)
Cluster A (W / p-value)	0.96 / 0.82	0.94 / 0.37	0.88 / 0.02	0.89 / 0.06	0.94 / 0.36	0.97 / 0.89	0.91 / 0.10	0.94 / 0.39
Cluster B (W / p-value)	0.95 / 0.35	0.93 / 0.20	0.94 / 0.55	0.95 / 0.62	0.95 / 0.66	0.95 / 0.53	0.94 / 0.28	0.95 / 0.71
Upper limit (Cluster A)	0.37	0.32	–	0.25	–0.40	0.08	0.23	–1.14
Lower limit (Cluster B)	–0.18	–0.21	–	–0.54	–0.76	0.04	0.36	–0.22