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

discrete morphological character data, the component axes provide interpretable information. Regardless of the complexity of information reflected in some axes, one thing is clear: taxa with a high degree of morphological similarity ordinate closely while morphologically disparate taxa ordinate at greater spatial distances. As a result, the manner in which taxa cluster reveals important information for baraminology (e.g., large quadrupedal dinosaurs will cluster in one region while smaller, bipedal dinosaurs cluster separately at a spatial distance). Differences between dinosaur groups are revealed by distances in n -dimensional space. PCA is frequently used in biology to visualize morphological relationships and developmental patterns (e.g. , for use with landmark data see Zelditch et al. . 2004, p. 15; for phylogenetic applications see Polly et al . , 2013). Principal component axes (PCs) represent shape variables with the first principal component axis representing the feature(s) that are the most responsible for variation within the class of subjects – here they are character states. Each additional PC is orthogonal to the previous PC and accounts for the next most important source of variation in the data. Thus, the second axis accounts for the second highest source of variation, and so on, until all variation is explained. Since the axes are orthogonal, it can be assumed that the data accounting for the variation along each axis is uncorrelated with the others. The sum of variation accounted for in each axis is cumulative, with most variation typically occurring within the first several components; higher component axes, representing a very small percentage of variation, often amount to little more than “noise” in the data. The advantage of PCA for baraminic studies is that it allows an additional visualization of the relationship between baraminic groups. A simple application of PCA, standard in R, uses a mean-centered ordination of traits and a covariance matrix of variables. Correlation between the principal components, and the original variables, generate component loadings. Loadings are analogous to correlation coefficients and show to what degree each variable is explained by the component. As is true for all statistical analyses, PCA encounters a formidable problem with even the best dinosaur character matrices: missing data. Every dinosaur matrix used in this study had missing data. For example, missing data percentages for the matrices in this study dated after 2004 ranged from 24.1% up to 62.4% (average of 48%). To account for this high proportion of missing data we employed a probabilistic substitution method to replace missing data in every matrix (Stacklies et al . 2007; Stacklies et al . 2017). Missing value substitution allowed entire matrices to be analyzed that would have otherwise been incomplete and provided the most complete analysis of every matrix. In addition to probabilistic replacement, a second step to insure more accurate analyses was to remove species with an unreasonably high proportion of missing data. Unless otherwise stated, data from the 2004 matrices only included taxa with 75% or more complete character data. The most recent matrices included only taxa with 50% or more complete data. PCA results were plotted listing taxon names for easy identification of spatial relationships. When possible, ordinations were presented as biplots containing both taxon names and variable vectors. Variable vectors indicate correlation between morphological features; common vector directions show strong correlation between morphological variables while opposed vectors indicate negative correlation. Ordination of taxa are a function of the total contribution of all positive (and negative) contributions for each variable. As a result, two or more taxa closely grouped within component space share similar morphology, and are interpreted as being biologically continuous. In contrast, spatially-separated taxa lack similarity, and distantly spaced members are interpreted as biologically discontinuous. 4. Data Data from 37 different character matrices were employed for this study. Data sets from 2004 (Weishampel et al . 2004) were analyzed with BDC, MDS, and PCA. The 19 more recent matrices were analyzed by PCA, and two with BDC. Matrices varied in the number of taxa, variables, and proportions of missing data. For example, Weishampel’s matrices ranged from six dinosaurs to 70 while character sets ranged from 20 to more than 600 characters. The highest character relevance cutoffs were used for each BDC analysis (e.g., 0.9 was preferred to 0.8). Though probabilistic replacement routines were employed for all PCAanalyses, taxa with greater than 50% missing character data were generally removed. However, all taxa were analyzed in small datasets. For the 18 BDC analyses, data from Weishampel included the following: The matrix for “basal” Saurischia consisted of 10 taxa and 107 characters. After filtering at the 0.9 character relevance cutoff we used 39 characters to calculate baraminic distances. The matrix for Ceratosauria consisted of 18 taxa and 70 characters. After filtering at the 0.75 character relevance cutoff we used 39 characters to calculate baraminic distances. The matrix for “basal” Tetanurae consisted of 59 taxa and 638 characters. After filtering at the 0.75 character relevance cutoff we used 199 characters to calculate baraminic distances. The matrix for Tyrannosauroidea consisted of 24 taxa and 638 characters. After filtering at the 0.75 character relevance cutoff we used 181 characters to calculate baraminic distances. The matrix for Maniraptoriformes consisted of 12 taxa and 220 characters. After filtering at the 0.95 character relevance cutoff we used 72 characters to calculate baraminic distances. The matrix for Therizinosauroidea consisted of 13 taxa and 40 characters. After filtering at the 0.75 character relevance cutoff we used 18 characters to calculate baraminic distances. The matrix for Oviraptorosauria consisted of 13 taxa and 161 characters. After filtering at the 0.8 character relevance cutoff we used 61 characters to calculate baraminic distances. The matrix for Prosauropoda consisted of 23 taxa and 137 characters. After filtering at the 0.8 character relevance cutoff we used 31 characters to calculate baraminic distances. The matrix for Sauropoda consisted of 12 taxa and 309 characters. After filtering at the 0.8 character relevance cutoff we used 182 characters to calculate baraminic distances. The matrix for “basal” Thyreophora consisted of 7 taxa and 32 characters. After filtering at 0.85 character relevance cutoff we used 24 characters to calculate baraminic distances. Doran et al. ◀ Dinosaur baraminology ▶ 2018 ICC 406