Morphometric (‘log sem’) analysis of anatomical measurements of Galápagos finches (Geospiza), chimpanzees (Pan) and Plio-Pleistocene hominins (Paranthropus, Australopithecus and early Homo)

A morphometric method has been used in analyses of linear measurements obtained from crania of modern hominoids1-3 as well as Plio-Pleistocene hominins,1,4,5 based on pairwise comparisons associated with least squares linear regression to quantify the degree of scatter around a regression line of the form y= mx+c, where m is the slope and c is the intercept. The log-transformed standard error of the m-coefficient, known as ‘log sem’, serves to quantify the degree of scatter around the regression line, associated with the degree of variability in shape. The effect of size is associated with the m-coefficient.


PUBLISHED:
27 January 2022 Significance: • The 'log sem' morphometric method can be shown to be justified in the context of its use in the analysis of anatomical measurements of three sets of data: Galápagos finches (six species of Geospiza); two species of chimpanzees (Pan troglodytes and P. paniscus); and three hominin genera (Australopithecus, Paranthropus and early Homo).
A morphometric method has been used in analyses of linear measurements obtained from crania of modern hominoids 1-3 as well as Plio-Pleistocene hominins, 1,4,5 based on pairwise comparisons associated with least squares linear regression to quantify the degree of scatter around a regression line of the form y= mx+c, where m is the slope and c is the intercept. The log-transformed standard error of the m-coefficient, known as 'log sem', serves to quantify the degree of scatter around the regression line, associated with the degree of variability in shape. The effect of size is associated with the m-coefficient.
For many taxa, a mean log sem value of -1.61 has been recognised as a typical degree of intraspecific morphological variation in extant species. 2,3 With a standard deviation of 0.1, it has been used as a frame of reference for assessing probabilities of conspecificity when pairs of specimens are compared (e.g. Thackeray and Dykes 3 and Thackeray 4 ).
In this analysis, the results of an UPGMA (unweighted pair group method with arithmetic mean) cluster analysis were obtained from log sem statistics calculated from anatomical measurements from the following three sets of data as examples of method: Galápagos finches (Geospiza), chimpanzees (Pan troglodytes and P. paniscus), and Plio-Pleistocene hominins (Australopithecus africanus, A. sediba, Homo habilis, H. erectus, H. rudolfensis and H. naledi). The objective was to demonstrate that the log sem statistic has biological significance, reflecting variability in shape in a diversity of taxa.

UPGMA tree for six species of Galápagos ground finches
Using UPGMA, a log sem matrix was analysed for the six generally accepted species of ground finches, namely Geospiza magnirostris, G. fortis, G. fulginosa, G. difficilis, G. conirostris and G. scandens. 6,7 The log sem matrix was based on measurements of the lengths of wing, tail, culmen, gonys, depth of bill at base, width of mandible at base, tarsus and middle toe with claw, from a database compiled by the California Academy of Sciences. Measurements were obtained from 36 specimens (an equal number of male and female specimens) resulting in more than 1200 regressions. A computer program for analysing large data sets (https://github.com/chdwck9/ professorRegressor) was used to calculate log sem statistics. 8 Figure 1 presents the resulting phenetic tree. This tree corresponds closely to a phylogeny obtained by Burns et al. 9 and Reaney et al. 10 based on genetic data.     UPGMA tree for two chimpanzee species Figure 2 presents a phenetic tree obtained from UPGMA cluster analysis of log sem statistics based on pairwise linear regression analyses of Pan troglodytes and P. paniscus cranial measurements (n=68 specimens, more than 4500 regressions), using measurements published as supplementary material by Gordon and Wood 11 . The log sem approach generally distinguishes the two taxa, reflecting robusticity of the log sem method. Although 3 out of 34 specimens attributed to P. troglodytes group with others attributed to the closely related P. paniscus, this lack of a clear boundary is consistent with genetic evidence of hybridisation between chimpanzees and bonobos within the last million years. 12,13 UPGMA tree for Plio-Pleistocene hominin specimens Figure 3 presents a phenetic tree obtained from UPGMA cluster analysis of log sem data of the kind published by Thackeray and Odes 5 , generated from pairwise comparisons of Plio-Pleistocene hominin specimens attributed to Australopithecus, early Homo and Paranthropus, using measurements published by Wood 14 , with the addition of log sem data associated with A. sediba 15

Conclusion
The three UPGMA analyses of log sem data, calculated for Galápagos finches (Geospiza), chimpanzees (Pan) and Plio-Pleistocene hominins (Paranthropus, Australopithecus and early Homo) reflect groups that have biological significance, serving at the same time to demonstrate that the log sem morphometric method has merit, based on anatomical measurements using landmarks.