Computational protocol: Craniofacial ontogeny in Centrosaurus apertus

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Protocol publication

[…] This study follows and modifies the method used by . Specimens with different morphologies were identified in the primary literature and through first-hand observations in order to define potential hypothetical growth characters. The study sample was restricted to Centrosaurus specimens derived from the lower 30 m of the Dinosaur Park Formation, representing less than a one million year range (). This stratigraphic constraint reduced potential phylogenetic effects by limiting the analysis to specimens found only in similar depositional environments, which produces the best approximation of a single species of Centrosaurus. This stratigraphic restriction is ideal because it contains limited geologic overlap with other centrosaurine species (). It should be noted, however, that this restriction represents the vast majority of the known geologic range of C. apertus.A majority of the growth characters used in this study fall into three main categories: bone fusion, bone texture, and development of ornamentations. These character types have been used as proxies for growth by other authors (; ; ; ; ). Bone fusion refers to the closure of sutures seen externally between adjacent bones. Scoring for these characters follows : sutures were considered open if bones were separate along their entire margin of contact, partially obliterated if the bones were fused incompletely or if a deep groove or trough was still present along the margin, and fully obliterated if the two bones were conjoined into a single unit with a surface nearly level with the surrounding bone (). 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 (; ; ) and confirmed by histological study (). Textures were coded based on a modified method of , where the most mature texture that exceeded a 1 × 1 cm2 continuous area on the exterior surface of the bone was considered the representative state. Ornamentation refers to the horns, hooks, and processes found on the snout, the jugal, the supraorbital region, and the frill. Ornamentation characters include measurements of structure length, and aspects of structure shape, orientation, and surface texture. The numbering of these processes on the frill follows . Other growth characters that are not categorized into the previous three groups include additional structures, such as the presence of foramina and fenestrae which have not previously been used to determine the relative maturity of individual C. apertus, but are otherwise seen to be variable within C. apertus specimens.Taphonomic distortion can further contribute to morphological variation in fossils. Many large Centrosaurus skulls are asymmetrically distorted (e.g., CMN 348) and/or crushed (e.g., CMN 11837), giving these specimens vastly different shaped skulls, a problem that may not be as readily identifiable in specimens that are modified to a lesser extent. To reduce taphonomic bias in the data set, characters based on overall skull shape and orientation were not used. Characters regarding horn shape and orientation were retained, but not scored in specimens that are obviously distorted.All specimens and characters were compiled into a data matrix using MacClade v. 3.0 (), where the nascent (primitive) state for each character is scored 0 and the mature (derived) state is scored 1 or higher. The nascent state was determined using multiple criteria. Specimens with dissimilar character states were first evaluated for major size differences. Size and maturity level are not necessarily equivalent, but specimens that approach average adult sizes are likely to be morphologically more mature than much smaller specimens. In this analysis, size classes follow , with YPM 2015 representing a putative full-grown individual. Skulls less than one-half the maximum length of YPM 2015, or individual bones therein for isolated material, were assumed to possess the nascent condition and were coded 0. Because the length of the skull was used to determine the nascent condition, no other characters related to absolute skull size were included in the analysis. However, characters for display structure (horn) sizes were kept, because these were not included as a measurement of absolute size.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 (). If this second criterion failed to yield a single unequivocal nascent state, the phylogenetic outgroup was used under the assumption that in closely related species ontogeny recapitulates phylogeny, following the methodology of and . For this criterion the morphological feature that most closely resembles the state found in basal neoceratopsians was considered the nascent condition and coded 0.To address instances of characters with more than one mature state two separate data matrices were constructed based on the different coding methods previously used in these types of analyses, one consisting of multistate characters (e.g., ) and the other including only additive binary characters (e.g., ), in order to determine which coding method yields the most parsimonious result. The additive binary coding method tends to force characters into ordered sequences of changes. Under unordered multistate coding the two or more mature states are free to transform in any sequence based on the most parsimonious arrangement. Additive binary coding is a logical assumption for unidirectional and progressive ontogenetic steps for certain characters like bone fusion events (e.g., partial fusion precedes full fusion) and bone textural changes (e.g., mottled texture precedes adult texture). However, other multistate character types are more ambiguous, where full-sized adults contain different character states with no clear indication of the sequence in which these develop (e.g., supraorbital horn shape). To use these features in the additive binary analysis, extra characters were added, so that the two (or more) non-nascent states are each independently scored as the most mature character state. By doing this, the two character states nullify one another, so that only the most parsimonious sequence of characters will be shared on a given internode of the tree. This type of coding was applied to the supraorbital region of the skull in order to test the hypothetical transition proposed by that the supraorbital horns progress from pyramidal-shaped in juveniles, to inflated horns in more mature individuals, to resorbed masses in the most mature individuals. In the present analysis, the inflated horn character state and the resorbed mass character state are each individually considered the most mature state in two different characters.To polarize the characters an all-zero hypothetical embryo was added to the data matrices. Specimens that duplicated identical codings for all characters, or all-zero coding, were removed from the data matrices in order to remove redundancy, because these specimens would, if included, group together and unnecessarily add to the data set. The resulting binary and multistate matrices were each executed in Phylogenetic Analysis Using Parsimony v. 4.0b (PAUP; ) under a heuristic search. Because C. apertus growth cannot be observed firsthand, all characters were equally weighted and left unordered. A heuristic search was used because the sizes of the data sets were too large to efficiently run a branch and bound search with the available computing hardware. The results were then compared for consistencies between the two coding methods in order to find the most parsimonious tree for a given data set.In the analysis of Tyrannosaurus rex by , the authors included an artificial adult alongside the artificial embryo. 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. This provides an independent test in order to orient the tree correctly. The addition of this specimen may yield different results than the same data set without the artificial adult, which is why this technique is only used a posteriori as a heuristic method to determine the ontogenetic axis and hence the most mature specimen. In order to code this specimen the mature states were assumed to follow previous hypotheses of centrosaurine growth (; ).The analyses were also run using both the ACCTRAN and DELTRAN character optimization methods. ACCTRAN optimizes character changes to occur as close to the root of the tree as possible, favoring reversals over convergent character changes farther up the tree. Conversely, DELTRAN optimizes character changes farther up the tree, selecting convergent character changes in lieu of reversals. These methods can therefore produce trees with similar specimen topologies, but different distributions of character changes. It is important to consider both optimization methods to compare character distributions for consistencies and inconsistencies between the two results, because both optimization types may yield a different relative order of development depending on the amount of missing data.The robustness of the results was then tested with Bremer Decay and Bootstrap analyses. For the Bootstrap analysis 1000 replicates were executed using the results from the multistate character matrix in PAUP (). The binary matrix was excluded from the bootstrap analysis because it violates the assumption of character independence (). In the binary data set, characters are not independent because two (or more) characters are necessary to cover all character states for a given feature. If one of these characters is deleted, the corresponding character still remains and contributes to the bootstrap analysis.In order to test the assumption that size is an acceptable proxy for ontogenetic status, a Spearman rank correlation was performed using the results of this cladistic analysis and frill length measurements. Frill length (rostrocaudal length along the midline) was used as a proxy for overall skull size because this portion of the skull is represented in most articulated specimens. Measurements were obtained from and supplemented with measurements for specimens not included in that study. […]

Pipeline specifications

Software tools MacClade, PAUP*
Application Phylogenetics
Diseases Diabetes Mellitus, Type 2, Mitochondrial Diseases