RUNX2 tandem repeat ratios
The translated amino acid sequences for the 41 species are provided in the Supplementary Material ( Additional File 1). The RUNX2 amino acid sequences flanking the tandem repeat region were generally conserved across taxa providing evidence that orthologous rather than paralogous sequences were successfully retrieved. In support of this, all publicly-available mammalian genomes contain a single annotated RUNX2 locus, suggesting that this gene has 1:1 orthology across mammals and has not been subject to duplication. QA ratios calculated from the translated sequences range from 0.82 (Choloepus didactylus, Xenarthra) to 5.33 (Equus caballus, Perissodactyla, but see below) (Table 1). With the exception of Equus, these QA ratios were generally lower than those of carnivorans . In their analysis of Carnivora, Sears et al.  report a lowest value of 1.5 for the QA ratio in Potos flavus, which is close to the range of domesticated dog breeds (approximately 1.2 – 1.45; based on Figure 2B in ). Glutamine and alanine amino acid counts for non-carnivoran mammals (glutamines: 14-29, alanines: 13-18) were not markedly different than those of domestic dog breeds (glutamines: 18-20; alanines: 12-17), although carnivorans are on the low end of alanine counts (Table 1). Across the mammals included in our dataset, the majority of the QA ratios lie between 1 and 2 (34 out of 41 species analyzed). Xenarthrans had the lowest variation in QA ratio across sampled species (variance = 0.067) and laurasiatherians had the highest (variance = 1.60). We make such taxonomic comparisons tentatively, as species within clades are not equally distant to each other and the species sampled here represent only a subset of the extant diversity for each clade.
Across the 41 mammals tested, both the polyQ and polyA are variable, but the polyQ has a greater range of values than the polyA repeat (polyQ ranges from 10-31 repeats, polyA ranges from 3-19 repeats) ( Additional File 1). Also, intraspecific variation was detected in two (Myrmecophaga tridactyla, the giant anteater, and Tamandua tetradactyla, the southern tamandua) of the four species where multiple individuals were sequenced (Table 1).
Although RUNX2 is generally conserved across mammals, three of the RUNX2 sequences obtained via genome browsers (three-lined squirrel, bottlenose dolphin and horse) contain distinctive amino acid changes ( Additional File 1). We cannot conclusively exclude the possibility of errors in the online genome sequence annotations, and this is of particular concern for the horse where there is extensive divergence in the 3’ flanking sequence. The unusually high QA ratio of 5.33 for Equus caballus is mostly due to the highly shortened poly A sequence (3 repeats compared to 7-17 repeats for other laurasiatherians), and, thus, this result should be viewed with caution. However, there is no a priori reason to suspect sequence or annotation errors for the three-lined squirrel or bottlenose dolphin; in these cases the sequences flanking the unusual amino acids are highly conserved, as are other mammalian sequences. We also note that the flanking sequences for some of the novel species (Dasypus, Hemicentetes) are short, but in these cases we can confirm the sequence from original trace files. The removal of flanking sequence was done when an ambiguous base pair was present in the sequence trace file. Sequences were only included in both the alignment and further analysis if the QA region of the sequence contained no ambiguous trace file calls; thus the QA ratio is likely to be correct in these cases, even though the flanking sequence was partially truncated.
The polyA repeat was often interrupted by a single valine ( Additional File 1). In fact, the presence of an interrupting amino acid has an interesting phylogenetic distribution (and intraspecific variation in Myrmecophaga), as most afrotherians and xenarthrans exhibit an interrupted polyA sequence but laurasiatherians or euarchontoglires do not. Regarding the polyQ repeat, only Microcebus murinus, the grey mouse lemur, has an interrupted glutamine sequence (by histidine; Table 1). In further analyses (see below), we considered both the total QA ratio (ignoring any interrupting amino acids) and the QA ratio for uninterrupted sequences only. For example, we scored the total QA ratio for the mouse lemur as 1.25 (20Q : 16A) in the initial analysis, but we also ran the analyses with a mouse lemur QA ratio of 0.38 (6Q : 16A) (Table 1). Whether we included total QA ratios or uninterrupted QA ratios, the direction and significance of the correlation results did not change (Table 2).
Since the goal of this study is to examine whether the pattern Sears et al.  describe for carnivorans holds for mammals in general, we took morphological measurements comparable to those described in Sears et al.  (Figure 1). After adjusting measurements relative to body size by dividing by proxy measures of overall size (following ; CBL, condylobasal length; and Oc-Pat, distance from lateral-most point of occipital condyle to caudal margin of palate; Figure 1), Dasypus (armadillo) and Myrmecophaga (giant anteater) had the longest ‘nose’ (measured from anteroventral margin of orbit at lacrimal foramen to anterolateral margin of nasal bone). These taxa, along with Sus (domestic pig) and Tursiops (dolphin) had the longest ‘face’ (measured from anteroventral margin of orbit at lacrimal foramen to the anterior premaxilla). At the other extreme, Callithrix (marmoset), Bradypus (sloth) and Mustela (weasel) showed the shortest face; Callithrix
Pongo (orangutan) and Nomascus (gibbon) had the shortest nose.
Those species with the longest and shortest rostra described above were not those with the largest and smallest RUNX2 QA ratios, especially in xenarthrans and afrotherians (Figure 2). Also, we did not recover a significant correlation between QA ratio and indices of rostrum size in non-carnivorans. None of our phylogenetic generalized linear models showed a significant relationship between QA ratios and relative face and nose lengths (Table 2). This was true regardless of our method of accounting for body size. In fact, closely related pairs of species that differ substantially in relative rostrum size (e.g., the anteaters Myrmecophaga vs. Tamandua; armadillos Priodontes vs. Chlamyphorus; and tenrecs Hemicentetes vs. Microgale) did not show correspondingly different QA ratios (Figure 2). For example, the extraordinarily long-faced Myrmecophaga had a slightly lower QA ratio (1.24) than the short-faced Chlamyphorus (1.53; see Figure 2).
Similar results were found for primates. The hamadryas baboon (Papio hamadryas) and the rhesus macaque (Macaca mulatta) have identical QA ratios (1.41) but the baboons have markedly longer faces (e.g. Face/Oc-Pat for baboon: 1.57, for macaque: 0.99). As is the case for the armadillo, anteater, and tenrec examples mentioned above (Figure 2), gibbons have a QA ratio similar to that of orangutans (1.35) and this also matches the ancestral reconstruction of the ratio at the great ape node. However, gibbons have much shorter faces than the great apes (e.g. Face/Oc-Pat for gibbon: 0.58, for orangutans: 0.89).
Thus, in contrast to the trend apparent among carnivorans in which long-faced species possess high QA ratios , this correlation does not seem to hold across placental mammals in general, and particularly not among xenarthrans or afrotherians (Table 2, Figure 2).
In order to characterize these observations further, we used the newly developed Bayesian comparative method of Lartillot and Poujol  (see Methods) to study the correlation between RUNX2 QA ratios and relative face/nose lengths (Table 3). As a proof of concept example, the method was first applied to the Sears et al. carnivoran dataset . Using 30 MT-CYTB (mitochondrial cytochrome b) sequences and fossil calibrations to control for phylogeny and divergence times, the Bayesian method retrieved the positive correlation between RUNX2 QA ratio and relative facial length in Carnivora with a posterior probability of 0.95 (Table 3). However, similar analyses of our placental dataset using 41 VWF (von Willebrand factor) nuclear sequences and fossil calibrations to control for phylogeny and divergence times showed no significant correlation between RUNX2 QA ratio and the four relative face/nose size-controlled variables tested (Table 3). These results confirm the results of the PGLS (phylogenetic generalized least squares) analyses in demonstrating statistical independence between RUNX2 QA ratio and facial length at the global level of placentals.
Moreover, the Bayesian method also allowed the joint ancestral reconstruction of both QA and facial length ratios under the Brownian assumption (Figure 3). Figure 3a illustrates the relative homogeneity of the RUNX2 QA ratio in non-carnivoran placentals. The 95% credibility interval for the ancestral placental QA ratio is 1.14-1.80, whereas the ancestral carnivoran QA ratio is estimated at a larger value (1.57-2.63). Xenarthrans (1.01-1.65), afrotherians (1.00-1.80), and primates (1.05-1.71) showed remarkably comparable ancestral values. Also the relatively modest value (1.24-1.94) reconstructed for the Laurasiatheria ancestral node suggests that the RUNX2 QA ratio has increased in Carnivora possibly as a response to selection for increasing facial length in this clade. The Bayesian joint reconstruction of relative facial length shows a much greater variability among placentals than the QA ratio (Figure 3b). A larger heterogeneity is observed in both xenarthrans and afrotherians with relatively large ancestral facial ratios being inferred for each group. This contrasts with the homogeneity of their RUNX2 QA ratios (Figure 3a). Also, as previously noted, primates are characterized by relatively reduced facial length ratios compared to the other placental groups. This suggests that the relative facial length has been reduced in the ancestral branch leading to living primates. Overall, the comparison between the two panels of Figure 3 highlights the general lack of correlation between the RUNX2 QA ratio and relative facial length in placental mammals.