The Proceedings of the Eighth International Conference on Creationism (2018)

character sets studied (Wood, et. al , 2011). A more targeted study demonstrated discontinuity betweenAvialae and Deinonychosauria for most datasets, though some BDC and MDS results indicated continuity (Garner et al. 2013). Beyonddinosaurs, statistical baraminologyhas alsobeenquestioned within creationist circles for other reasons. One concern was that baraminic distance methods group dissimilar morphospecies, such as Australopithecus sediba and Homo sapiens , into the same holobaramin (DeWitt 2010; Habermaehl 2010; Menton 2010). A more careful critique acknowledged value in the methodology but called for more attention to genetics and genetic programs including hybridization and synapomorphies (Wilson 2010). Though Wilson’s argument has validity, genetic and hybridization criteria cannot be applied to the fossil record. Here, we survey the baraminic status of the Dinosauria using the approaches of statistical baraminology while particularly exploring Senter’s questions about morphospace. One valid question raised by the previous work is whether holobaramins identified by statistical baraminology include hidden discontinuities ( e.g., how much more division are apobaraminic groupings, such as dinosaurs, capable of?). To address these questions, we offer an additional approach to visualize morphological space: Principal Component Analysis (PCA). Examination of character morphospace allows the visualization of holobaramins, morphological continuity and discontinuity, and even potential identification of stratomorphic series of taxa. As a survey of the Dinosauria this work re-contextualizes previous creationist questions. Previous work on tyrannosauroids and bird- dinosaur relationships (e.g., Aaron 2014b; Garner et al. 2013) is addressed in the context of dinosaurs, as a whole. In other words, in addition to the multivariate analyses on tyrannosauroids and maniraptorans we can address whether our patterns were typical – or unique – in the broadest context. The Dinosauria also provide an opportunity to examine broad questions regarding issues of the systematics of a large, terrestrial pre-Flood fauna, and post- Creation intrabaraminic diversification. MATERIALS AND METHODS Analyses included traditional approaches to baraminology, including baraminic distance correlation (BDC) and multidimensional scaling (MDS). Principal components analysis (PCA) was employed to further visualize morphological continuity and discontinuity. The most recent datasets, those compiled after 2004, were mostly analyzed by PCA alone. 1. Baraminic Distance BDISTMDS version 2.0 was used to carry out BDC calculations on datasets (Wood 2005; 2008b). Baraminic distance is a measure of correlation any two organisms share in their character states (Robinson and Cavanaugh 1998; Wood 2001). BDC obtains a distance based on linear regression as a measure of similarity. The goal is to identify groups united by significant, positive correlation (interpreted as continuity between groups) and those separated by significant, negative correlation (interpreted as discontinuity between groups). Characters that do not have a minimum standard of relevance (i.e., percentage of taxa for which the character state is known) are removed from analyses. Since a purpose of this study involved an interest in minimizing missing data, groups that retained the highest relevance were chosen. Cutoffs ranged from 95% relevance to 75%. A hypothetical outgroup was added to each data matrix to provide a consistent and easily visualized reference location. The position labeled OUTGROUP included character states of “0” and was added for visual reference to all datasets, but particularly for PCA. This outgroup assignment provided a common visual reference point for all analyses ( i.e., BDIST, MDS, and PCA). 2. Multidimensional Scaling As commonly employed in baraminic distance studies, three- dimensional classical MDS was used for comparison (Wood 2005). MDS converts a matrix of Euclidean distances between objects into k -dimensional coordinates of the objects. In this study, k represents three dimensions. Unlike previous baraminic studies, this study introduces a small difference in the MDS analyses. Data points were colored and plotted in the software environment R using a three-dimensional grid rotated to highlight maximum point separations. The rotational grid is a different way to visualize data but has identical spatial interpretation as other studies in baraminology. Secondly, the classical MDS function utilized here employed scree plots – rather than stress plots – to visualize the influence of dimensionality reduction. Scree plots employed graphs showing the eigenvalues of each component as a ratio of the eigenvalue sum over all eigenvalues. The relative eigenvalue of each component then represents the proportion of data variance explained by the component. The scree plot shows the decrease in eigenvalue with each component, with the components prior to the “break” in the plot showing the optimal number of components needed to explain the data. Explanation of the data is greatest prior to where the “scree” line levels off (i.e., axes with highest values explain the most). An eigenvalue equation describes an eigenvector, v , of a linearly transformed matrix ( T ) that does not change the direction of T . T applied to the eigenvector scales the eigenvector by a scalar multiple, λ, with the following relationship: T (v) = λ v A linear transformation of a spatial grid is a type of shear mapping. Eigenvectors provide direction of shear distortions while eigenvalues are the measure of distortion generated by a transformation Eigenvalues show variances. The scree plot depicts the eigenvalues plotted in the order they are factored, by component axes, with the first largest values explaining the majority of the variance and others showing progressively less. Scree plots display the most important components as those lying above a scree, or gradually tapering, line. Plots often depict a sharp drop followed by gradual decline. 3. Principal component analysis In addition to BDC and 3D MDS, this study employed PCA as a second means of visualizing discontinuity. One advantage of PCA is that each component axis is biologically meaningful. Since each component axis is a multivariate combination of Doran et al. ◀ Dinosaur baraminology ▶ 2018 ICC 405