Figure 3. Distance correlation results using the Pugh (2022) characters. Correlations and distance metrics are shown in the diagram. Filled squares indicate significant, positive distance correlation. Open circles indicate significant, negative correlation. larger hominid group. Average silhouette widths for fuzzy analysis of both simple matching and Jaccard distances were poor (0.27 and 0.29 respectively). Distance correlation was repeated on the Pugh (2022) characters using only hominid taxa (and Oreopithecus), but the results did not reveal clear or consistent clustering (Figure 5). All cluster analyses by medoid partitioning and fuzzy analysis had poor average silhouette widths <0.3 (Figure 6). The highest average silhouette widths occur in the two-cluster partitions. However, the medoid partitions do not agree with each other or the fuzzy analyses on the precise membership of taxa. The two fuzzy analyses produce identical results for Jaccard and simple matching distances. Generally, one cluster contains the hominins and the other taxa are placed in a separate cluster. Fuzzy analysis places Pongo and Gigantopithecus in the hominin cluster. The Gilbert et al. (2020) character matrix was filtered at a taxic relevance of 0.25, leaving 41 taxa for analysis. Distance correlation results revealed little clear clustering with Jaccard or simple matching distances or Spearman or Pearson correlations (Figure 7). Likewise, cluster analysis of the simple matching distances revealed partitions with exceptionally poor average silhouette widths ≤0.21 (Figure 8). Cluster analysis with Jaccard distances was even worse, with no average silhouette width >0.16. Reducing the Gilbert et al. (2020) character matrix to include only taxa from his Hominidae and Proconsulidae, the distance correlation results reveal consistent clusters. With simple matching distances, the same three clusters are revealed with both Pearson and Spearman correlations (Figure 9). The first cluster contains Oreopithecus with Turkanapithecus and two species of Nyanzapithecus, all of which Gilbert et al. (2020) place in the Proconsulidae. The second cluster contains the extant great apes together with the fossil taxa Sivapithecus, Lufengpithecus, Kenyapithecus, Ouranopithecus, Pierolapithecus, and Hispanopithecus, all of which are placed in the Hominidae by Gilbert et al. (2020). The third cluster contains the remaining proconsulids Afropithecus, Equatorius, Morotopithecus, Kalepithecus, and two species each of Proconsul and Ekembo. Using Jaccard distances on the Gilbert et al. (2020) reduced character matrix, the distance correlation results separate the taxa into slightly different clusters (Figure 9). The smaller proconsulid cluster is retained, along with the hominid cluster. With Pearson correlations, Equatorius, Morotopithecus, and Afropithecus are separated out from the second proconsulid cluster. With Spearman correlations, Morotopithecus and Afropithecus fall in the hominid cluster, while Equatorius shares significant correlation with members of both the BRUMMEL AND WOOD Preliminary Evaluation of Ape Baramins 2023 ICC 152
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