For the second control character subset, I identified 30 characters for which the Homo sapiens state differs from the state in Neandertal (HN characters). These characters were selected as a means of evaluating the results of separately partitioning taxa that belong in the same group. The remaining taxa shared between 1 (Ardipithecus, Kenyanthropus, Sahelanthropus, Au. garhi, and Au. anamensis) and 19 (Asian H. erectus) of the HN character states. As with the PO character states, the linear array of simple matching distances revealed one significantly long gap between Homo sapiens and Asian H. erectus (gap length 0.367, p=1.04 × 10-7, Weibull shape parameter 1, Weibull scale parameter 0.04). A second significantly long gap of 0.2 occurs between Neandertal and Sahelanthropus and between Neandertal and Au. anamensis, both of which share only one of five HN characters scored for those taxa. The gap length of 0.2 has a p value of 0.00674 (Weibull shape parameter 1, Weibull scale parameter 0.04). Unsurprisingly, this procedure again merely partitioned Homo sapiens from all other taxa and Neandertals from all other taxa (Figure 1). Overall, this procedure of defining “essential” characters fails to define sets of characters that can be used to correctly classify taxa not included in the original character partitioning. All subsets tested here either show ape-specific character states in putatively human taxa like Neandertals or show human-specific character states in putatively nonhuman taxa like Au. africanus. Even if we approach these character subsets by looking for a threshold percentage of shared character states that might be used to separate putatively human from putatively nonhuman taxa, no such threshold has been found. A comparison of partitions derived from the simple matching distances reveals little consistency. Instead, these character subsets excel at defining only the taxa used in making the subset (SO, LC, EAO, PO, and HN), and where they do not, the partitions mix humans and nonhumans in the same partition (FA). Examining a single dimension of simple matching distances does not partition taxa sensibly, but could the subsets be used in true cluster analysis to group human and nonhuman taxa? Cluster analysis. Instead of treating these character subsets as essential characters that diagnose taxa merely by their presence or absence, we might instead think of them as heavily weighted character subsets that could be used in cluster analysis. Effectively, the character subset maximizes the distance between the ingroup and the outgroup used to select the characters for the subset. Secondarily, it also minimizes the distance between the members of the ingroup by requiring that they all have identical character states. Cluster analysis can be done using the standard methods of distance correlation, medoid partitioning, and fuzzy analysis. Since this character matrix has already been coded so that the state 0 exclusively represents the absence of a character, Jaccard distances can be evaluated in addition to simple matching distances. For all of these cluster analyses, no characters were omitted for low relevance, and all characters were used for distance calculations. Distance correlation results for the SO character subset using simple matching distances are shown in Figure 2. Three clusters are apparent. First, Homo floresiensis stands as a singleton with no significant, positive correlation with any other taxa. The second cluster contains a set of apes: Sahelanthropus, Au. garhi, Au. anamensis, chimpanzee, Au. afarensis, Ardipithecus, gorilla, Kenyanthropus, and Au. africanus. The remaining species of Homo belong to the third cluster, along with Au. sediba and all three species of Paranthropus. Two-cluster medoid partitioning and fuzzy analysis place members of Homo, including Homo sapiens, in the same cluster as members of Paranthropus (Figure 2). Three-cluster medoid partitioning places members of Homo together with Au. sediba, Par. robustus, and Par. boisei in a single cluster, but three-cluster fuzzy analysis places Par. robustus and Par. boisei in a separate cluster. Medoid partitioning (two- and three-cluster) places H. floresiensis in the same cluster with H. sapiens, but fuzzy analysis places H. floresiensis in the same cluster with Au. africanus for both two and three cluster partitions. The average silhouette width for all partitions is relatively low, with the highest average 0.37 seen for the two-cluster fuzzy analysis hard partition. Distance correlation has the worst average silhouette width at 0.22. Visual inspection of three-dimensional MDS reveals no obvious clustering, which explains the discordant cluster analysis results (Figure 3). Using Jaccard distances on the same SO character subset reveals a similar pattern of positive and negative correlation, but the resulting partition is quite different (Figure 4). Homo floresiensis shares significant, positive correlation with Kenyanthropus, placing it in a cluster of apes, and the three Paranthropus taxa are separated into their own cluster. The resulting partition has an average silhouette width of 0.39, which is slightly higher than the average silhouette width of 0.35 from the two-cluster partition of the fuzzy analysis and medoid partitioning. In the two-cluster medoid partition, Par. robustus, Par. boisei, Kenyanthropus, and H. floresiensis are placed in a cluster with H. sapiens. The three-cluster medoid partition separates all Paranthropus species into a single cluster by themselves Figure 1. Linear representation of shared fractions of character states by each subset as indicated. All scales place putative “humans” at the bottom and putative “nonhumans” at the top. Significant gaps are shown in red. For more information on the calculation of statistical significance, see the Methods. WOOD Essentialism and Human Kind 2023 ICC 93
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