Taxonomic sampling
A total of 154 specimens were included in the present study (Additional file 1), comprising 132 genera within 23 orders. The majority of these taxa are eutherians, including placental mammals and their stem relatives. Within placental mammals, the four superorders were all sampled. The “southern” superorders Xenarthra (sloths, armadillos and anteaters) and Afrotheria (elephants, hyraxes, sirenians and allies) were each represented by two genera. Euarchontoglires was represented by two scandentians (tree shrews), two dermopterans (colugos), three primates and ten rodents. The best sampled of the four superorders was Laurasiatheria, with three sampled from Carnivora (cats, dogs, bears and allies), ten from Perissodactyla (horses, rhinoceroses, and tapirs), fifteen from Eulipotyphla (shrews, moles and allies), and seventeen from Artiodactyla (cows, pigs, camels and allies).
In addition to those taxa known to fit unambiguously within extant placental orders, several stem taxa and taxa of uncertain affinities were included. Among those sampled taxa of less certain affinities are three genera of Arctostylopidae, a group which has traditionally been placed with the notoungulates (e.g. [17]), but which more recent studies place near the stem of Glires (rodents, rabbits and pikas) [18]. Notoungulates (two representatives) is one of several South American ungulate clades [19] generally treated as Mammalia incertae sedis[20], although they have been reconstructed as close to Afrotheria based on shared dental, vertebral and astragalar synapomorphies [21]. Cimolesta (11 representatives) is a diverse order, thought to be ancestral or closely related to Ferae (e.g. [22]), the clade containing the extant orders Carnivora and Pholidota (pangolins), but have also been placed as a stem placental clade (e.g. [23]), as has Leptictida [24–26], of which there are three representatives in this dataset. Pantodonta (6 representatives) are sometimes considered to be related to Cimolesta (e.g. [27]), and are reconstructed by others as comprising an entirely separate order of placental mammal (e.g. [28]). Plesiadapiformes, of which there were two genera in this dataset, are often, but not uncontentiously, considered to be close to the origin of Primates [29]. Also included in this dataset were two palaeanodonts, a group which has been considered ancestral to pangolins [30], and two creodonts, which are often reconstructed as a paraphyletic group of stem carnivorans (e.g. [31–33]). By far the most troublesome polyphyletic grouping is that of “Condylarthra” (seventeen representatives), as well as “Acreodi” (five representatives), which have been commonly referred to as “archaic ungulates” [34]. Once thought to be ancestral to the now abandoned group “Ungulata” (a polyphyletic collection of extant hoofed mammals), these Palaeogene omnivores and herbivores have been suggested to be ancestral to several extant placental clades. For instance, phenacodontid “condylarths” have been affiliated with perissodactyls [35] as well as Afrotheria [36]. Arctocyonid “condylarths” such as Chriacus have been suggested to be ancestral to artiodactyls [37], with “Acreodi” often suggested as ancestral specifically to Cetacea [38]. Apheliscid “condylarths” have recently been suggested to be ancestral to Macroscelidea (elephant shrews or sengis), within Afrotheria [39, 40].
Lastly within the eutherian sample were two genera of Zhelestidae, a small, herbivorous clade that has been placed as stem placentals, outside of the crown group, in a recent analysis [24], but have also been considered primitive “ungulatomorphs” by some (e.g. [41]).
Four unambiguous members of the placental stem were included (Zalambdalestes, Bobolestes, Montanalestes, and Zhangolestes), as was a single metatherian (Asiatherium) and two members of the therian stem lineage (Arguimus and Kielantherium), all of which are from the Cretaceous (145 to 66 Ma).
Finally, outside of Theria, a sample of Jurassic and Cretaceous australosphenidan mammals were included, comprised of two Cretaceous members of Monotremata (Kollikodon and Steropodon) and two members of the sister group Ausktribosphenida (Asfaltomylos and Ausktribosphenos). These extinct forms are generally considered to be closely related to modern monotremes (echidnas and the platypus) [15, 42], although this has been disputed by some [43], and represent the final major division of crown mammalian diversity. Sampling, therefore, covers the majority of crown mammalian clades (see Figure 1).
All time periods from the Cretaceous to the Recent were well-represented in this sample. One taxon (Asfaltomylos) is known from the Middle Jurassic (174 to 163 Ma), 14 are known from the Cretaceous (145 to 66 Ma), 95 from the Palaeogene (66 to 23 Ma), and 25 from the Neogene (23 to 2.6 Ma). 9 taxa are extant. Twelve genera are known from both the Palaeogene and Neogene or from both the Neogene and Recent.
Measurements
Measurements of lower molar length and width were obtained from the literature, either from published measurements or specimen images, or directly from museum specimens (both high-quality casts and original material) (Additional file 1). Area was estimated for each tooth as the product of length and width, following the method of both Polly [10] and Wilson [13]. For specimens that were measured directly, length and width were obtained from occlusal-view photographs in ImageJ v1.45s [44]. In addition, measurements for several taxa were obtained from the Palaeobiology Database (http://www.paleodb.org) on the 13th of May 2012, using the taxonomic group name ‘Mammalia’ and the following parameters: Taxonomic resolution = ‘certainly identified to genus’, Body Parts = ‘m1, m2, m3’, with ‘all parts must be measured’ ticked. Output fields were ‘length’, ‘width’, ‘specimens measured’. All measurements were corrected for size by using the ratio of respective tooth area to that of m1 area, such that a posterior decrease in molar sizes would give values lower than 1, and an increase would give values larger than 1. Only specimens with two or all three adjacent molars present were included in the final dataset, and where multiple specimens were available, averages of molar ratios were analysed. All taxa which were composed solely of isolated molars, regardless of whether all three were represented, were removed from the dataset, due to inability to control for intraspecific variation. Ratios of m1:m2, m2:m3 and m1:m3 were quantified for each specimen, and averages of these ratios were then calculated for each genus. For taxa with more than three lower molars, only the first three were measured. Taxa with fewer than three lower molars were excluded from the analysis. Taxa for which either length or width were unavailable due to preservation were also excluded, such that length was not used as a proxy for area in any of the analyses.
While the approach used here, and in the studies noted above, estimated tooth area as a product of maximum length and width, some other studies [8, 11, 12, 14] have measured tooth occlusal area directly. In order to establish the comparability of these area measurements, we also directly measured molar area in 41 genera (41 specimens) for which specimens were available. For this analysis, only values from the second lower molar were used, in order to reduce non-independence in the dataset, and molar area was measured from occlusal-view photographs using the outline tool in ImageJ v1.45s [44].
Data analysis
Correlations among measurements of tooth size
For many fossil taxa, the nature of their preservation results in two-dimensional specimens, for which tooth widths (and hence areas) are unable to be assessed, except where preservation is in occlusal aspect. These specimens cannot be plotted in a tooth area ratio graph, although there is the potential for important size information to nonetheless be extracted. In order to identify whether molar length or width alone could be used as an accurate proxy for area, and hence increase the sample size in future studies, non-parametric Spearman Rank correlation analyses were performed among the relative lengths, widths and areas (scaled against the respective measure for m1) for each pair of molars. A strong length-area correlation would support the use of length as a proxy for molar area, and would imply that the major axis of increase in size is the antero-posterior axis. Such a result would further mean that the length ratios between teeth should follow the same pattern as area, although with differing regression parameters. All analyses were conducted in R [45].
Testing the inhibitory cascade model
Each taxon was plotted in a morphospace described by the ratios of molar areas of m2:m1 and m3:m1, as in previous studies (e.g. [8, 10]), and a reduced major axis linear regression line was calculated (Figure 2). This regression line was then compared with the model predicted by Kavanagh et al. [8], as well as with the regression line of their original dataset, using 95% confidence intervals to test whether the two datasets were significantly different from one another or from the IC Model.
In order to test the second prediction of the IC Model – that m2 should occupy one third of total molar occlusal area – the proportion of total molar area occupied by m2 was calculated for all 154 specimens (132 genera) included in this study. Averages of this proportion were then taken for each genus. A two-tailed Student’s t-test was used to test whether the mean proportion of occlusal area taken up by the m2 was significantly different from 33%. This was then compared with the murine data ([8], supplementary information), to which the same method was applied.
Phylogeny and diet
Non-parametric MANOVA were conducted in R [45] using the ‘adonis’ command line in the ‘vegan’ package [46], in order to test for significant clustering of different dietary guilds and of taxonomic orders within the morphospace. The 101 taxa from higher-level groups with five or more representatives (with a pooled Creodonta-Carnivora group and a Primates-Plesiadapiformes group) were included in the analysis of phylogenetic clustering, comprising 10 groups in total. Phylogenetic group and dietary assignments are detailed in Additional file 2. Decisions on taxonomic grouping follow McKenna and Bell [27] where possible, and otherwise refer to the original descriptive literature for any given genus. Dietary information was extracted from the Paleobiology Database where possible, and otherwise directly from the original descriptive literature. Where dietary assignments were not available for a particular genus, family- or subfamily-level dietary estimates were used. Because precise diets can be difficult to discern in extinct organisms and are continually debated, broad categories (folivorous, carnivorous, omnivorous, insectivorous, frugivorous and durophagous) were used, which, despite some inevitable overlap, should be relatively accurate. Moreover, some inaccuracy in dietary assignations should not obscure a strong pattern with regard to morphospace position and diet, if one exists.