ously better than the others (0.4 for distance correlation, 0.38 for medoid partitioning, and 0.39 for fuzzy analysis). The three-cluster results for both medoid partitioning and fuzzy analysis have nearly identical silhouette widths than the two-cluster results (0.38 for medoid partitioning, 0.37 for fuzzy analysis). In both of the three-cluster partitions, all three Paranthropus species are separated into their own cluster with members of Australopithecus. As with previous character subsets, three-dimensional MDS again does not reveal any obvious clusters (Figure 11). Distance correlation using Jaccard distances and the EAO characters separates Paranthropus into their own cluster, leaving Homo species and Au. sediba in a cluster and H. floresiensis in a cluster with gorilla and chimpanzee (Figure 12). Three-cluster medoid partition closely resembles the distance correlation, except Au. africanus and Au. garhi are moved into the cluster with H. sapiens. This move results in a drop in the average silhouette width from 0.42 for the distance correlation to 0.36 for the medoid partition. Three-cluster fuzzy analysis moves Au. africanus and Au. garhi along with Au. sediba into the Paranthropus cluster for an even lower average silhouette width of 0.34. The two-cluster medoid partition places all Paranthropus taxa, Au. africanus, and Au. garhi in the human cluster, for an average silhouette width of only 0.36. In contrast, the hard partition from the two-cluster fuzzy analysis places Au. garhi, Au. africanus, H. floresiensis, and Par. aethiopicus in the cluster with chimpanzee and gorilla but keeps Par. robustus and Par. boisei in the cluster with Homo sapiens. Visual inspection of three-dimensional MDS again reveals no obvious clusters (Figure 13). Distance correlation using simple matching distances from the FA characters reveals two clusters (Figure 14). Homo sapiens is placed in a cluster with other members of Homo and Au. sediba. The rest of the australopiths and Homo floresiensis are placed in a cluster with gorilla, chimpanzee, and the Paranthropus species. The two-cluster medoid partition and fuzzy analysis exactly match the partition from the distance correlation, except in moving Par. robustus into the same cluster with Homo sapiens. The average silhouette width is the same for fuzzy analysis and medoid partitioning (0.52). The three-cluster medoid partition appears to be the best partition of all with an average silhouette width of 0.57. In this partition, Paranthropus are separated into their own cluster, H. floresiensis is placed in a cluster with chimpanzee and gorilla, and the remaining Homo taxa and Au. sediba appear the third cluster. The three-cluster fuzzy analysis is worse with an average silhouette width of 0.51, resulting from the shift of Homo habilis from the Homo sapiens cluster to the Paranthropus cluster. Again, the three-dimensional MDS reveals a diffuse cloud of taxa with no obvious clustering (Figure 15). Distance correlation with FA characters and Jaccard distances reveals an identical clustering as seen with the simple matching distances (Figure 16). With Jaccard distances, the two-cluster medoid partitioning exactly matches the distance correlation partition. The hard partition from two-cluster fuzzy analysis differs by placing Par. robustus and Par. boisei in the same cluster with Homo sapiens. The average silhouette widths reveal a very slight preference for the fuzzy analysis partition (0.54) vs. the medoid partition (0.52). The three-cluster medoid partition using the Jaccard distances was identical to the three cluster medoid partition using the simple matching distances, with a matching average silhouette width of 0.57. Again, the three-cluster fuzzy analysis is worst of all with an average silhouette width of 0.38. Three-dimensional MDS again reveals a diffuse set of taxa with no obvious clustering (Figure 17). Distance correlation for the control set of PO characters using simple matching distances reveals three clusters with an average silhouette width of 0.44 (Figure 18). Unsurprisingly, the three Paranthropus species form one cluster, with a second cluster containing all eleven members of Homo and Au. sediba. Three-cluster medoid partitioning moves Kenyanthropus into the Homo cluster. The hard partition from the three-cluster fuzzy analysis moves H. floresiensis into the cluster with chimpanzee and gorilla. The average silhouette width of 0.44 for the distance correlation and 0.45 for the three-cluster fuzzy analysis were comparable, but the average silhouette width for the three-cluster medoid partition was lower at 0.41. Two-cluster medoid partition and fuzzy analysis were both lower than their three-cluster counterparts with average silhouette widths of 0.3 and 0.38 respectively. Three-dimensional MDS does show a moderate separation of Paranthropus from the other taxa but otherwise poor clustering (Figure 19). Distance correlation for the PO characters using Jaccard distances closely resembled the simple matching partition, except for the placement of H. floresiensis in the cluster with gorilla and chimpanzee (Figure 20). All partitions from fuzzy analysis and medoid partitioning were identical to the corresponding partitions generated using simple matching distances. Three-dimensional MDS of the Jaccard distances also closely resembles that of the simple matching distances, with a slight offset of Paranthropus (Figure 21). Figure 3. Orthogonal views of the 3D MDS results for the simple matching distances using the SO character subset. WOOD Essentialism and Human Kind 2023 ICC 96
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