Joseph A. Frederickson; Allison R. Tumarkin-Deratzian

“ Sexual dimorphism, if present, should appear as variable growth characters that are only found in roughly half of the most mature (adult) specimens. Without first determining the ontogenetic progression it is difficult, if not impossible, to distinguish growth characters from other forms of variation. ”

“ Size, as determined by frill length, can also justifiably be used to determine general ontogenetic status. The use of size and bone textural changes are the optimum factors for determining the relative maturity in individuals that have yet to grow to adult size. In the largest individuals, these factors differ insufficiently to determine relative maturity. For these individuals, the order of epiparietal and episquamosal fusion (caudal to rostral) along with the orientation of the nasal horn provides a better indication of ontogenetic status. ”

“ The second best proxy for growth is bone textural changes. Bone textural changes have been shown to be reliable growth proxies in horned dinosaurs, especially in the frill ( [3] ; [4] ; [6] ; [7] ) . In this analysis, bone textural changes were extremely effective at identifying relative ontogenetic stage in the least mature specimens. In all of the full-sized specimens, adult texture covered large portions of the cranial bones, rendering this proxy useless in determining relative maturity among the largest individuals. ”

“ The primary objective of this study is to combine multiple different lines of ontogenetic proxies for growth in Centrosaurus apertus into a cladistic analysis. If a hierarchical signal exists within the known fossil record, then a growth series for this taxon can be reconstructed. Once a growth sequence of ontogenetically informative characters is recovered, characters that are individually variable within the population can be identified. Further, the presence of sexual dimorphism can be tested once the ontogenetic progression is known. ”

“ The remaining most-mature specimens are split into two separate growth series (node J; Fig. 4) . One of the series (node K) is united by a single synontomorphy, the complete fusion of episquamosal one. The other series (node L) , containing YPM 2015, is supported by two synontomorphies: the fusion of the frontal midline suture and the obliteration of the prefrontal suture with the supraorbital unit. The growth series at node L represents the most mature individuals in the analysis because they contain the most cumulative character changes. ”

“ A hypothesis of the patterns of ontogenetic development for estimating relative maturity in Centrosaurus apertus can be derived from the collection and combination of independent growth characters through a cladistic approach. Substantial non-ontogenetic variability was present in the sample, but a growth signal was still recovered once isolated specimens were removed. The resulting growth series compares favorably to previous hypotheses regarding the growth of C. apertus ( [3] ; [4] ) .
(2) Two different coding methods were compared using the same data set. ”

“ Further, the cranial ornamentations reduce in size in the most mature individuals, giving their skulls less distinctive ornamentations than those seen in relatively immature specimens. Although some of these ornamentations (e.g., P1) show a fairly consistent pattern of growth, it does not follow an expected sequence where increasing maturity equates to more elaborate ornamentations. ”

“ This artificial adult was coded for the mature character states for each character in order to polarize the data away from the root and determine the most mature specimen. This additional step is required because the ontogram can be oriented so that any of the specimens above the artificial embryo are located directly opposite the root, which is the position of the most mature specimen. The addition of the artificial adult determines the axis of maturity by identifying the specimen that is recovered as the sister to the artificial adult. ”

“ Proxies for growth
The quantitative results from the three principal maturity indicators (bone fusion, bone texture, and ornamentation) are shown in Tables 4 and 5. For the reduced multistate analysis, bone fusion characters contained the highest cumulative CI, indicating that these are the least variable characters, as they tend to change states comparatively fewer times than the other proxies. In this analysis, bone fusion can be broken down into two types: skull bones and epiparietals/episquamosals. ”

“ The results of the Spearman rank correlation also suggest that large-scale sexual size dimorphism is not present in C. apertus. The strong congruent signal obtained shows a positive relationship between frill size and ontogenetic status, with no specimen exceeding the next by more than 25 mm in length. If sexual size differences were present, it would be assumed that many of the most mature specimens from the smaller sex would have a size rank far below less mature individuals of the larger sex. ”

“ In the most mature specimens, ornamentations may be resorbed so that they are shorter, more rugose in texture, and withered in appearance, in contrast to less mature individuals. This phenomenon is also found in other ceratopsids, pachycephalosaurs, and tyrannosaurids, implying that ontogenetic display structure reduction is a primitive feature for dinosaurs.
(6) Growth characters based upon bone textural changes and bone fusion events are the best proxies for relative development in the skulls of Centrosaurus apertus. ”

“ In adult-sized individuals, the fusion of the epiparietals and episquamosals and the orientation of the nasal horn are the best indicators of relative maturity. This study recovers no clear evidence for sexually specific display structures or size dimorphism in C. apertus. ”

“ If more than one morphology was present among specimens that were less than one-half the length of YPM 2015, other putative juvenile centrosaurines were used as an analog for the morphology found in C. apertus juveniles. The nascent character states for C. apertus are assumed to be similar to the character states found in other juvenile centrosaurines, because closely related centrosaurine species are hypothesized to have followed the same growth pattern ( [3] ) . ”

“ Changes in cranial ornamentations include the development of P2 and a ventrally oriented P1. This growth stage represents the first stage at which a specimen possesses the diagnostic characteristics of Centrosaurus apertus. Prior to this stage, the parietal processes are small and uncurved. Individuals at the first and second growth stages look no different than other juvenile centrosaurines ( [4] ; [3] ) and without stratigraphic evidence these specimens would not be identifiable to C. apertus.
The fourth growth stage (node C; e.g., CMN 1229) is supported by six synontomorphies. ”

“ Size, for example, may be affected by environmental stresses (e.g., [9] ) and becomes useless for relative aging once an animal has reached its largest skeletal proportions. Cranial ornamentations have also classically been used to determine the ontogenetic status of centrosaurines; however, many of these structures do not develop fully until near-maximum sizes are achieved ( [3] ) , and often these data conflict with relative size observations (e.g., larger skulls may have poorly developed cranial ornamentations in contrast to smaller ones ( [5] ) ) . ”

“ Furthermore, the nasal horn in CMN 8795 is also reduced in length and width compared to other similarly sized specimens. This indicates that there is a complete reduction in ornamentations associated with late maturity.
This reduction in ornamentation size with increasing maturity is not unique to C. apertus. The derived chasmosaurine Triceratops similarly reduces the size and shape of ornamentations ( [26] ) . In less mature animals, the epiparietals and episquamosals are tall and triangular. ”

“ Bone textural changes refer to the sequence of three distinct surficial bone textures (striated/long-grained, mottled, or adult/rugose) identified as an ontogenetic progression by previous authors ( [3] ; [4] ; [6] ) and confirmed by histological study ( [7] ) . ”

“ This is consistent with the results of this analysis, where some of the large disarticulated nasals are recovered in the tree as less mature than smaller articulated specimens that possess a closed suture.
The largest individuals show more variation in nasal horn orientation than the smaller ones. Full-sized adult specimens possess nasal horns that are either straight or procurved, with some of these individuals possessing a deep basal constriction. ”

“ Underlined specimens are also found in the reduced analysis.50% majority rule consensus tree for 100,000 MPTs, based on additive binary character coding.This tree is 265 steps long, has a CI of 0.4868. The numbers above each node represent the percent frequency of each grouping out of the 100,000 total trees. Underlined specimens are also found in the reduced analysis. The two coding methods generated trees that differ from one another. Both trees have areas of conflict, with three groups collapsing into polytomies in both data sets. ”