Figure 1. Distance correlation results using the Martin et al. (2021) characters. Correlations and distance metrics are shown in the diagram. Filled squares indicate significant, positive distance correlation. Open circles indicate significant, negative correlation. the Paranthropus cluster is less well-defined. Simple matching distances and Spearman correlation reveals significant, positive correlation between H. habilis and three of the Paranthropus taxa. Jaccard distances and Spearman correlation reveals significant, positive correlation shared between H. habilis and Paranthropus and between H. ergaster and Paranthropus. Silhouette plots for the medoid partitioning and fuzzy analysis are shown in Figure 2. The average silhouette width for all clusterings is quite poor and similar between different cluster numbers. Average silhouette widths range from 0.24 for medoid partitioning of Jaccard distances to 0.31 for medoid partitioning of simple matching distances. At k>2, medoid partitioning separates the four Paranthropus taxa in a single cluster using both simple matching and Jaccard distances, but neither medoid partitioning nor fuzzy analysis distinguish the Paranthropus cluster when k=2. The character matrix from Pugh (2022) was filtered at taxic relevance cutoff of 0.2, leaving 30 taxa for analysis. Distance correlation results are shown in Figure 3. Using both distance metrics (simple matching and Jaccard) and Spearman and Pearson correlations, two groups can be distinguished. The larger group contains all the taxa that Pugh places in Hominidae along with Nacholapithecus and Equatorius. The smaller group consists of the outgroup taxa Cebus, Dendropithecus, Aegyptopithecus, Ekembo, and the hylobatids. Using Spearman correlations, Oreopithecus is part of the smaller group, but Oreopithecus shares no significant, positive Pearson correlation with any other taxa. For all correlations and distance metrics, Nacholapithecus and Equatorius share significant, positive correlation with members of the outgroup cluster. Two-cluster medoid partitioning using Jaccard and simple matching distances gives a partition that closely resembles the groups in the distance correlation (Figure 4). The only difference is the position of Equatorius, which groups with the outgroup taxa rather than the hominids. Three-cluster medoid partitioning divides the hominids into a cluster of hominins + Rudapithecus and a cluster containing the remaining taxa. The outgroup cluster is retained from the two-cluster partition. At k=4, the average silhouette width is lower than the two- or three-cluster medoid partitions (0.25 at k=4 vs. 0.31 and 0.29 for k=2 and k=3 respectively, using simple matching distances). Medoid partitioning using Jaccard distances closely resembles the medoid partitions from simple matching distances. Fuzzy analysis of the Pugh (2022) characters using simple matching distances enlarges the outgroup cluster by adding Nacholapithecus, Equatorius, Griphopithecus, Dryopithecus, and Kenyapithecus. Fuzzy analysis of the Jaccard distances places Dryopithecus with the BRUMMEL AND WOOD Preliminary Evaluation of Ape Baramins 2023 ICC 150
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