Although it is possible to assign specific values to the timing of developmental events, ontogenetic age ranges are more appropriate for describing the timing of developmental events in the life history of S. fatalis. Tooth development and the fusion of cranial sutures are known to occur at various ontogenetic ages for different individuals of other felid species due to factors such as sexual dimorphism [ 20 , 52 ]. For instance, the timing of initial permanent tooth eruption in P. leo differs by as much as 6 weeks between males and females [ 53 ]. In S. fatalis, studies suggest that there is either no sexual dimorphism in skull size or that the degree of size sexual dimorphism in S. fatalis is less than that observed in P. leo [ 54 – 56 ]. However, S. fatalis skulls do appear to exhibit a degree of shape variation that is equivalent to the degree of morphometric sexual dimorphism in Panthera [ 56 ]. The exact nature of S. fatalis sexual dimorphism notwithstanding, the timing of developmental events in the life histories of mammalian species can be influenced by other differences that exist between individuals, such as disparities in nutritional health that alter the rate of cranial suture fusion [ 57 ]. Thus, even though there may be a popular desire to bestow fixed ontogenetic ages to the developmental events in the life history of S. fatalis, we believe that calculated ontogenetic age ranges serve as more appropriate guidelines.

Studies have generally shown that deciduous tooth mineralization and permanent tooth mineralization do not begin during the early stages of gestation [ 45 – 49 ]. For example, in the small felid, Felis silvestris catus, tooth buds begin developing at about 28 to 32 days of its 63 day gestation period [ 29 , 46 ]. Similarly, calcified tooth germs are not perceptible in fetuses of the rodent Myocaster coypus before 100 to 105 days of its 125 day gestation period [ 50 ]. Given that approximately 1cm of the forming C 1 crown is present in S. fatalis at about the time of birth [ 24 ] and given that the average C 1 enamel growth rate is 5.8mm/month [ 19 ], it appears likely that the C 1 of S. fatalis began to mineralize roughly one month prior to birth. Utilizing one month prior to birth as the point of initial C 1 growth, absolute ontogenetic age ranges were calculated for developmental events using a C 1 enamel growth rate range of 5 to 7.5 mm/month determined previously through examination of stable oxygen isotope values incorporated into tooth enamel [ 19 , 51 ] and C 1 crown lengths previously assigned to particular S. fatalis developmental events [ 13 ] (see S1 Text ).

Determining the absolute ontogenetic age at which C 1 growth began is necessary for calculating the absolute ontogenetic ages of development for particular features of S. fatalis. Because the C 1 growth appears to have begun prior to birth [ 24 ], a conservative estimate for the duration of gestation in S. fatalis can be used to estimate the absolute ontogenetic timing of C 1 growth initiation. In mammals, gestation is correlated with body mass and the duration of gestation tends to be rather consistent within carnivoran families [ 21 , 25 ]. The gestation periods of the extant large felids Panthera tigris (104 to 106 days), P. leo (110 days), P. onca (101 days), P. pardus (88 to 112 days), P. uncia (90 to 103 days), Puma concolor (82 to 96 days), and Acinonyx jubatus (90 to 95 days), exemplify this consistency [ 26 – 32 ]. The hyaenids, Hyaena hyaena, H. brunnea, and Crocuta crocuta, have periods of gestation that average 91 days, 97 days, and 110 days, respectively [ 33 – 36 ]. The gestation periods for large viverrids are 60 to 81 days for Civettictis civetta and approximately 91 days for Arctictis binturong [ 21 , 37 – 38 ]. Considering that gestation is associated with body mass and that the extant large felids and other feliforms exhibit relatively similar gestation periods, it seems unlikely that the gestation period of S. fatalis deviated drastically from those observed in the extant large felids ( Table 1 ) [ 21 , 25 ]. Because the estimated body mass of S. fatalis (approximately 160 to 280 kg) [ 39 ] is most similar to the body mass of P. tigris [ 26 , 29 ], P. tigris appears to be the best modern analog for S. fatalis gestation.

To calculate absolute ontogenetic ages for the development of particular morphological features in ancient species, it is necessary to find a structure (e.g., a tooth) that has a growth period that overlaps the development of the features of interest, and to have data on the timing of growth initiation and the growth rate of the key feature. It is possible to use C 1 growth rate to calculate the absolute ontogenetic ages of initiation and conclusion of eruption for nearly all of the permanent teeth of S. fatalis because the eruption of these teeth occurs while the C 1 forms in this species [ 13 ]. What is more, the C 1 growth rate can be used to calculate the absolute ontogenetic timing of other coinciding developmental events (e.g., cranial suture closures and loss of most of the deciduous dentition).

C1 Eruption Rate Calculation

In S. fatalis, C1 enamel formation was completed before the loss of the dC1 and the completion of C1 eruption. Thus, another approach, beyond using the canine growth rate calculated using stable oxygen isotopes [19], was necessary to determine the absolute ontogenetic ages for these two developmental events, and that was the calculation of the C1 eruption rate. It should be noted that C1 growth rate and C1 eruption rate are closely connected processes, but dissimilar from one another in that C1 growth rate describes the rate of tooth formation, whereas C1 eruption rate describes the rate at which the distal-most portion of the C1 moves in relation to its alveolar border. It was not possible to calculate the C1 eruption rate by merely measuring the C1 length in specimens of different ontogenetic stages. Preservation of the un-mineralized portion of this tooth can be inconsistent between specimens. In addition, because the formation of tooth enamel is a two-part process consisting of matrix formation and subsequent mineralization that affects stable oxygen isotope values [58], C1 eruption rate calculation using the previously published C1 growth rate [19] should be more accurate if based on C1 mineralized enamel lengths (S1 Text). Therefore, calculation of the C1 eruption rate required determination of the proximodistal lengths of C1 mineralized enamel, which were determined ultimately by using micro-computed tomography (μCT) to examine the proximal portion of the C1 of each specimen (see Fig 1).

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larger image TIFF original image Download: Fig 1. Smilodon fatalis specimen UCMP 152565 with partially formed permanent upper canine. (A) Photograph of UCMP 152565. Scale bar represents 1 cm. (B) Image of the 3D model created from the uCT data of UCMP 152565. The model represents the proximal-most portion of the canine. Dark brown color indicates completely mineralized enamel, whereas light brown is unfinished or unmineralized portion of canine. Scale bar represents 1cm. (C) A slice from the uCT data of UCMP 152565. https://doi.org/10.1371/journal.pone.0129847.g001

Although the number of identified specimens and number of individuals of S. fatalis at Rancho La Brea is quite large, certain criteria (e.g., C1 of different ontogenetic stages) were needed to calculate the C1 eruption rate, which severely limited the number of specimens that were relevant for analysis. ZJT and RSF identified a total of six specimens (LACM A-3748, LACM A3775, LACMHC 2001–9, LACMHC 2003-R-1, UCMP 152565, and UCMP 152566) as suitable for C1 eruption rate calculation on the basis that each of these specimens has at least one intact, erupting C1. Due to the spatial constraints of the μCT bore, the large size of the specimens, and similarity in ontogenetic stage between some specimens, only three specimens (LACM A-3748, UCMP 152565, and UCMP 152566) were able to be scanned. For this study, a SCANCO Medical Viva CT40 μCT scanner was utilized at the Center for Biotechnology and Interdisciplinary Studies at Rensselaer Polytechnic Institute (Troy, NY). Specimens were scanned at an energy of 70kVp, an intensity of 114 uA, and a 199 ms integration time. Scanning was performed near the proximal portion of the C1 with voxel size of 19 μm. The resulting image stacks had maximum dimensions of 2048 x 2048 pixels. 2100 slices were produced for UCMP 152565, which was scanned in two parts. 3036 slices were produced for UCMP 152566, and 5039 slices were produced for LACM A-3748. Three-dimensional reconstructions of enamel and dentin were created using Mimics version 13.1. Because of the spatial constraints of the μCT, two specimens (UCMP 152565 and UCMP 152566) yielded data (S1 and S2 Datasets) that were sufficient for creating three-dimensional reconstructions usable in this study. LACM A-3748 was able to be scanned; however the data were incomplete because the specimen was too large to fit properly within the μCT bore, thereby making it impossible to generate a complete three-dimensional reconstruction for LACM A-3748 (see S3 Dataset).

Density differences in the form of intensity grayscale values (with fully mineralized enamel appearing white, and dentin and other bones appearing as darker shades of gray) were utilized to segment the dentin versus enamel structures in the μCT data. As a consequence of limitations in computing resources, the reconstructions were built from reduced datasets that were 50% of original resolution in the x and y dimensions, and 10–30% in the z direction. The reductions resulted in an effective x-y pixel size of 38 μm and interslice distance of 57–190 μm, providing a maximum error of +/-190 μm (i.e., the exact location of the proximal borders of dentin and mineralized enamel are not resolved below the interslice distance of the reduced dataset) in the placement of measurement points.

To determine the C1 mineralized enamel length of each specimen, the distance from the most proximal border of preserved dentin to the most proximal border of mineralized enamel along the anterior edge of the C1 was subtracted from the overall C1 length. Measurements of the distance between the most proximal border of preserved dentin and the most proximal border of mineralized enamel along the anterior edge of the C1 were made within the 3D window in Mimics to the nearest 0.01 mm. Digital calipers were used to measure the overall C1 length of each specimen, as well as the length of erupted C1 from the alveolar border. The alveolar border, defined as an anteroposterior straight line across the alveolus on the maxilla and premaxilla at its distal-most point, represented 0.0 mm. Using the previously published average C1 enamel growth rate of 5.8 mm/month (range = 5 to 7.5 mm/month) [19, 51], we estimated S. fatalis C1 eruption rate, utilizing the following equation: (1)

The C1 mineralized enamel lengths of two specimens (UCMP 152565 and UCMP 152566) were used to calculate the C1 eruption rate. The C1 eruption rate and associated lengths of erupted C1 (which are known via the previously published tooth replacement sequence of Tejada-Flores and Shaw (1984) [13]) were used to determine the period of time (in months) from initial C1 eruption to the loss of the dC1, as well as the period of time from initial C1 eruption to the completion of C1 eruption. The period of time from initial C1 eruption to the loss of the dC1 was added to the absolute ontogenetic age at which the C1 begin to erupt (calculated using the C1 enamel growth rate range of 5–7.5mm/month [19]) in order to calculate the absolute ontogenetic age range of dC1 loss. Similarly, the period of time from initial C1 eruption to the completion of C1 eruption was added to the absolute ontogenetic age at which the C1 begin to erupt in order to calculate the absolute ontogenetic age range for the completion of C1 eruption.