Sloths present some anatomical features which are unique in mammals (Hautier et al., 2014; Galliari & Carlini, 2018), such as the variation in the number of cervical vertebrae the specific sequence of cranial suture closure (Rager et al., 2014; Montilla-Rodríguez et al., 2016), the synsacral number (Montilla-Rodríguez et al., 2016; Galliari & Carlini, 2018), the early ossification of the pubis and the phalanges and late ossification of the sternum (Hautier et al., 2011; Tague, 2019), architectural properties of forelimb muscles (Olson et al., 2018). With no deciduous teeth, they have a single set of high-crowned, open-rooted teeth, which grow continuously throughout life. Incisors are absent, and it is not really possible to distinguish between premolars and molars in the cheek series, which are quite similar (Hautier et al., 2016).

Sloths are included in the superorder Xenarthra Cope, 1889. Xenarthra is a mammalian group that includes a wide variety of locomotions and lifestyles, including the digging armadillos and anteaters, completely arboreal modern sloths and extinct terrestrial giant ground sloths (Hautier et al., 2014). They are grouped together with anteaters in the order Pilosa Flower, 1883 (Hautier et al., 2014). Extant sloths consist of only two genera, Choloepus Illiger, 1811 and Bradypus Linnaeus, 1758 (Hautier et al., 2014). One of their differences is found in the number of fingers. Three-fingered genus Bradypus comprises four extant species: B. tridactylus Linnaeus, 1758, B. torquatus Illiger, 1811, B. variegatus Schinz, 1825, and B. pygmaeus Anderson & Handley, 2001. Bradypus is native to the rainforests of South America where, as arboreal herbivores, they spend much of their time in the tree tops eating leaves and fruit (Sampedro-Marín et al., 2018). The head is the centre of the primary sense organs, with outer ears (pinnae) being tiny and hardly visible on the head and eyes having the possibility to retract in their sockets. Both of these characteristics reveal externally a partially muted function of the head within the whole animal (Montilla-Rodríguez et al., 2016).

Despite the extensive literature on the ecology and behaviour related to sloths, research on their developmental basis, and particularly centred on the skull, is rare. Cartelle & De Iuliis (2006) studied the skull ontogeny in the extinct Eremotherium laurillardi (Lund, 1842), the Pan-American giant ground sloth. Hautier et al. (2014) explored the patterns of the intra- and interspecific morphological variation of the skull. Riesco López & Bastir (n.d.) studied virtually the morphology of extincted Megatherium americanum Cuvier, 1796. In an ancient publication, Parker (1885) stated only that sloth skulls grow greatly from birth to full adulthood. In the complete sloths monography by Naples (1989), she does not focus on allometry.

Allometry is the statistical association between size and shape (Mosimann, 1970). In an extended meaning, allometry can be understood as differential change of a quantitative character with variation in overall body size. According to Klingenberg, ontogenetic allometry (or growth allometry, changes of shape versus size) deals with covariation among anatomical features during growth (Klingenberg & Zimmermann, 1992). Static allometry, on the other hand, denotes size-related shape changes, measured in different individuals at the same developmental stage within a population or species. Allometric relationships are important sources of information for many types of biological research. The baseline for an allometric relationship is isometry (or geometric similarity), i.e. that shape is invariant of size. This is why, here, we explore skull allometry in the brown-throated sloth Bradypus variegatus. Thus, this work tries to contribute to the knowledge of ontogenetic skull growth in sloths, based on a geometric morphometrics new approach.

Variation of the specimens in shape space was perfectly correlated with tangent space for all anatomical landmarks. This allowed us the use of the plane approximation in statistical analysis and interpretation of results.

Modifications of patterns of ontogenetic allometry have been shown to affect the magnitude of morphological change in many clades (Wilson, 2018), although it has been frequently underappreciated. Geometrical similarity in B. variegatus skull is maintained with size increase, e.g. skull development is isometric. Constant area-to-volume ratios, an adaptive necessity for many organic relationships, can only be maintained by altering shape. However, in sloths, growth produces individuals of no detectably different form, at least along the allometric range studied, e.g. they preserve the shape with no differential changes of anatomical points. With growth having no significant effect on skull shape, the size of an animal does not determine different mechanical functions; in other words, adult individuals are only a scaled version of juveniles These mechanical cranial functions, which are the same throughout the animal’s life, are probably related to arboreal behaviour (for instance, neck and trunk muscles inserting on skull, skull muscles and the connecting ligament system, frontal sinus, and upper cheek teeth). More research is, however, needed to elucidate such functional aspects derived from skull isometry.

Scaling predictions state that isometric changes in kinematics result from isometric changes in size. This prediction is difficult to support in B. variegatus. In any case, the non-geometric scaling of skull form that has been stated in this research can be seen as another uniqueness of sloths. It would now be interesting to test whether this “algebraic identity of ontogeny” (the maintenance of geometrical similarity with size increase) could also have different phylogenetic differences in the superorder Xenarthra skulls. Another benefit can arise from this general conclusion. Although sloths show great diversity in the combination of their cranial characters, both within and between the three fossil families and the family of recent tree sloths, if we had the ability to reconstruct morphometric data for key fossil taxa, their integration into comparative phylogenetic analyses would be of paramount importance to understand the evolution of body size.