Prior expectations from shape-only analyses vs size-and-shape analyses

In the absence of size considerations to distinguish between species, it was expected, based on visual inspections of the images captured for this study and on measurements taken (see Figure 4.1 and paragraph 4.3.1.2 below), that the three great ape species might overlap somewhat on a shape-only analysis, particularly in the case of bonobos (Pan paniscus) and common chimpanzees (Pan troglodytes). Both of these species might also overlap slightly with the gorilla specimens in the absence of size considerations, particularly if the chimpanzee or bonobo specimens were slightly narrower than usual, or if the gorilla specimens were wider than the average. As for the modern Homo sapiens sample, molar shape was much more unpredictable than for the other species.

133 Modern Homo sapiens: rounded and regular; usually relatively wider than the

great ape species, although width is variable

Gorillas: very large, but proportionally, consistently very narrow with uneven,

pronounced cusps

Chimpanzees: consistently narrow;

uneven cusps Bonobos : consistently narrow; uneven cusps

Figure 4.1 Typical shapes of modern human, gorilla, chimpanzee and bonobo mandibular first molars.

To confirm the importance of size when comparing teeth, the principal components analysis was first performed as normal, based on Procrustes “shape space” (with the PCA being based on a full Procrustes superimposition, whereby objects are translated, rotated and scaled to factor size differences out between them) and secondly in

Procrustes “form space” (the log of the centroid is factored in as a variable to the analysis to enable size to be analysed as well as shape (Mitteroecker et al. 2004)).

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4.2.3 Results of the shape-only and size-and-shape analyses

The following figures (Figures 4.2 and 4.3) illustrate the differences between a shape analysis and a size-and-shape analysis, in the context of teeth:

Figure 4.2 – Procrustes shape space analysis of lower first molars of four extant species (n=20 per species; 49 landmarks each specimen); in this analysis, data are rotated, translated and scaled. With size differences between specimens not factored into the analysis, and shape alone determining the covariance results, relative width of tooth becomes a major distinguishing factor as shown by PC1 along the x-axis (reflected by the relative warps wireframe images; PC1: 28% of the covariance). There is significant overlap between species, particularly chimps and bonobos, once size is no longer a factor to differentiate between molars.

Since size has been factored out of this (shape only) analysis, the primary differentiator between species is relative width of tooth, and this is the main factor depicted along the x-axis (PC1= 28.0% of the variance). PCs 2 and 3 accounted mainly for some elements of cusp arrangement changes (PC2= 25.4% of the variance). With no size differentiation, there is overlap between bonobos and gorillas, bonobos and chimpanzees and chimpanzees and gorillas where their relative width is similar, as well as some overlap between modern Homo sapiens, chimpanzees and bonobos.

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A second Principal components analysis was then conducted with the addition of a size factor (log of the centroid size added), to produce a “size-and-shape” analysis (Procrustes “form space”). The results are shown in Figure 4.3 below.

Figure 4.3 – Procrustes form space analysis of lower first molars of four extant species (n=20 per species; 49 landmarks per specimen); in this analysis, data are rotated and translated and size is added to the analysis by means of the log of the centroid size. With size now differentiating between specimens, size itself becomes the major determining differentiator between molars (x-axis, PC1: 90.6% of covariance), with relative width (formerly the main contributor to covariance) now accounting for most of the covariance along the y-axis, PC2. There is less overlap between species, particularly between chimps and bonobos and no longer any overlap at all between gorillas and bonobos; size-related sexual dimorphism between male and female gorillas also now becomes apparent.

In this size-and-shape analysis, size is now the dominating factor along the x-axis (PC1 = 90.6% of the variance), with relative width of the tooth (formerly PC1) now accounting for the second principal component (y-axis: PC2 = 2.8% of the variance). Along both axes there is an element of cusp pattern change and perimeter shape change in addition to the size and relative width components, although size is now highly correlated to PC1 due to the log of the centroid size being a variable in the analysis. The correlations between centroid size and the first principal components axes from both analyses are shown below in figure 4.4.

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a) b)

Figure 4.4 PCA results for 4 extant species: PC1 correlated to centroid size, a) using Procrustes shape space which includes scaling; R2_{= 0.132; b) with size factored in to the variables by means of the log of}

centroid size (Procrustes form space; R2_{= 0.997). The high correlation in b) is to be expected, since the log of centroid size}

is a variable in the shape analysis. There are components of peripheral shape and cusp arrangement also represented within the first principal component.

In the “form space” analysis, there is still some slight overlap between species towards the middle of the chart, but with size factored into the analysis, gorilla specimens no longer overlap with bonobo specimens or chimpanzee specimens. Modern Homo sapiens molars, which overlap in size with a few large bonobo teeth, some similarly-sized chimpanzee teeth and one very small female gorilla tooth are seen to overlap in size range (around the middle of the x-axis, where “medium-sized teeth” are grouped), but the majority of the Modern Homo sapiens sample tends to be wider than the molars of the great ape species, thus they tend to group towards the negative side of the y-axis, where wider teeth are located. In addition to the above, gorilla male molars no longer overlap with gorilla female molars for the sample used. Overall, the results from this principal components plot are in keeping with the observations made in 4.2.2 above, in that the species groups are reasonably differentiated, with some overlap at the extremes, just as is observed in nature.

In sum, the results of these analyses show that size appears to be a major diagnostic feature for differentiating between species, followed by relative width, and then by changes in cusp pattern arrangement. Overlaps on the PC plot concur with potential areas of overlap discussed in 4.2.2 above (small chimpanzees-large bonobos; very

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narrow modern Homo sapiens teeth with medium-sized great ape teeth (i.e. mainly chimpanzee teeth, and the smallest female gorilla tooth).

In light of the above, for the remainder of the study, it was decided to proceed with principal components analyses based on Procrustes form space, in the knowledge that the first principal component in any graph based on form space would have a high correlation with the size of the specimens (because the log of centroid size is included as a variable for each shape in the analysis), together with additional contributions that would be made factors of variability in peripheral shape and of cusp arrangement. The choice of y-axis (the selection of the remaining principal component for depiction in the graphs – PC2 or PC3, for instance) would in each case be based primarily on which principal component was most reflective of relative tooth width, because in the analyses conducted on the extant species based purely on shape (with size factored out), the first principal component then accounted primarily for relative width differences, together with some factor of shape/cusp arrangement variability.

(Furthermore, relative tooth width is, as noted in Figure 4.2 above, a primary diagnostic feature used by morphologists to make taxonomic assessments of lower first molars, so it is useful to ensure that the y-axis reflects relative width as well as some feature of cusp variation in each case).

In Morphologika, it is possible to inspect the shape changes being depicted along each axis using the wireframe tool. Relative warps (showing a visual depiction of shape change) can be examined visually using the slider tool in the software. It is therefore possible to examine PC2, PC3 and additional principal components by selecting them as the y-axis component and viewing the change in the shape of the wireframe relative

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warps as the slider progresses from the minimum value to the maximum value. In this manner, it is possible to determine which of the principal components accounts mainly for changes in width (together with some measure of cusp arrangement variability) and which of the principal components accounts mainly for cusp arrangement variation alone, with little contribution made by tooth width variation.

4.2.4 Fossil hominin species – application of parameters identified in extant