are seen with both simple matching distances and Jaccard distances. All medoid partitions are very similar when using simple matching or Jaccard distances (Figure 11). Medoid partitioning places chimpanzee, gorilla, and Ardipithecus in a single cluster for all cluster counts. With two clusters, all other taxa are placed in a single cluster, giving an average silhouette width of 0.35 for simple matching distances and 0.34 for Jaccard distances. At three clusters, Au. africanus s.l. and Au. afarensis are placed in a separate cluster, lowering the average silhouette width to 0.32 for simple matching distances and 0.3 for Jaccard distances. With four clusters, Au. sediba is separated from all other taxa into a singleton cluster, lowering the average silhouette width even further to 0.25 for simple matching distances and 0.23 for Jaccard distances. The hard partition from two-cluster fuzzy analysis is nearly identical for both simple matching and Jaccard distances (Figure 11). In both cases, all Homo taxa are placed in a cluster with Au. sediba, and the remaining outgroup taxa are placed in the second cluster. The average silhouette width for this partition is 0.34 for simple matching distances and 0.32 for Jaccard distances. With three clusters, fuzzy analysis once again splits up the Homo + Au. sediba cluster, resulting in a drop in average silhouette width to 0.17 for simple matching distances and 0.15 for Jaccard distances. The 3D MDS results resemble those of both craniodental matrices shown above, using both Jaccard and simple matching distances (Figure 12). There is a group of Homo in proximity to Au. sediba, and the other two Australopithecus lie at some distance from Au. sediba. Chimpanzee, gorilla, and Ardipithecus are not particularly close to one another and are at distance from the Homo group. The same patterns are seen with Jaccard and simple matching distances. Clustering summary. Since the clusters from our analyses do not agree on the details, we evaluated the frequency that each pair of taxa clusters together in the 44 different cluster partitions from medoid partitioning, fuzzy analysis, and distance correlation using the high-relevance craniodental, postcranial, and combined character sets. Partitions of the full craniodental set were omitted from this assessment in order to prevent bias towards craniodental characters. Our results are shown in Table 2. We can see that the outgroup taxa chimpanzee and gorilla and Ardipithecus cluster together in all of our Figure 10. Distance correlation results for the combined character set. Correlations and distance metrics are shown in the diagram. Filled squares indicate significant, positive distance correlation. Open circles indicate significant, negative correlation. WOOD AND BRUMMEL Hominin Baraminology Reconsidered 2023 ICC 261
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