Despite the exclusion of several placental taxa with unusual cranial morphologies (notably whales, bats, and elephants), and the limited fossil taxa included, we found in the current study that marsupial crania are, on the whole, significantly less disparate compared with placentals. Although inclusion of the enigmatic Tarsipes could potentially increase the variance of the extant marsupials in future studies, we are confident that this one taxon would not alter the substantial difference in variance between marsupials and placentals reported here. Thus, the results of this study support the hypothesis that marsupial crania are developmentally constrained, and that this constraint is likely to have limited the morphological evolution of marsupials relative to their placental sister groups. In particular, the observation that the viscerocranial region, which includes the early-ossifying bones of the oral region, is significantly less disparate in marsupials than in placentals, whereas the late-ossifying neurocranial region has similar disparity in both clades, is consistent with the hypothesis that the differential evolutionary success of these two groups was shaped by developmental strategy rather than by extrinsic factors.
Developmental timing, integration, and lability
Although relative cranial ossification sequence is largely conserved across mammals [23, 24], there is a delay in raw timing between the development of bones in the oral region and those in the neurocranium of marsupials compared with placentals [25–27]. Anterior elements of the skull also tend to show less heterochronic variation and basicranial elements show the most . As we tested here, these differences in raw timing and rank variability in ossification sequences correlate with differential cranial disparity for the viscerocranial and neurocranial regions, with the former showing significantly less disparity in marsupials than in placentals. These regional differences in amount of heterochronic variation may possibly relate to the different evolutionary lability of these regions , although this hypothesis has yet to be tested with quantitative data on ontogenetic or morphological variation.
Post-weaning ontogeny of marsupial cranial morphology has been studied in several omnivorous and carnivorous species [28–32]. These studies have shown the existence of some common developmental patterns across marsupials, including a faster-growing viscerocranium than neurocranium in early post-weaning development, negative allometry across the entire braincase and in the height of the occipital plate, and positive allometry in the height of the dentary . That these major aspects of post-weaning growth differentiate skull regions is suggestive of the modular nature of cranial development [33–35]. Moreover, that a common growth pattern was found across the full viscerocranium, rather than only in the early-ossifying oral bones of this region, suggests that this region is developmentally integrated, and provides a possible mechanism by which the functional constraints imposed on the oral bones translate to the lower disparity across the entire viscerocranium seen in the current study.
A recent study  found that cranial variance in a marsupial (Monodelphis) remained constant through ontogeny, whereas in a placental (Cryptoprocta), variance decreased markedly from the early to the later stages. Moreover, Monodelphis also showed a decrease in integration of the oral region through ontogeny. This led to a tentative hypothesis by the authors that the combination of high integration of the oral region early in ontogeny, alongside functional demands on those early-developing oral bones, may result in low and constant variance of that region through marsupial ontogeny, in contrast to placentals. Although further data are needed to test that hypothesis, a possible extension suggested by the data from the current study could be that, if the marsupial skull is indeed constrained in the oral region during early development, and if the viscerocranial elements of the skull are strongly integrated, as some studies have suggested [36–38], then the remainder of the viscerocranium (for example, those elements that do not ossify early in development) would also be likely to be constrained as a result of integration, rather than by direct developmental or functional constraint.
Not only is the developmental strategy of marsupials very different to that of placentals, but the nature and timing of development also varies between marsupial groups. Peremelemorphs in particular represent the most unusual condition among extant marsupials in having evolved a chorioallantoic placenta, convergent with that of placentals, and also showing the fastest developmental rate of all marsupials . Peramelemorphians also lack a pronounced crawl, as noted above, and this divergent strategy is reflected in their scapular ontogeny, which has been shown to differ significantly from that of other marsupials . Interestingly, the PC analyses presented here show that peramelemorphians fall further outside of placental cranial morphospace than do other marsupial clades. For this reason, we hypothesize that the unusual development of peramelemorphians (which have a much shorter period during which the oral region develops and functions in isolation from the rest of the quickly developing viscerocranium and the rest of the skull), is related to the evolution of their distinct cranial morphology, relative to that of other marsupials. Future work on peremelemorphian cranial ontogeny thus represents an interesting avenue for research to further address the role of ossification timing and functional constraints on cranial evolution. A specific question of interest is whether peramelemorphians follow or deviate from the developmental trajectory of Monodelphis, discussed above, which is often used to represent a generalized marsupial condition.
It is important to remember that we cannot say for certain whether extinct forms shared the unique developmental strategy of extant marsupials, or indeed, with which group of marsupials they shared most developmental similarities. Of particular interest in this regard are the sparassodonts, included in this analysis and previous studies . These form a group of South American metatherians of uncertain phylogenetic position, although recent analyses have placed them outside of crown marsupials . It is possible that these taxa do not share the same developmental strategy, and thus might not be subject to the same developmental constraints on morphology, as crown marsupials. Nonetheless, the inclusion of fossil taxa did not significantly affect our results, and so we tentatively suggest that the developmental constraint hypothesis may apply to all of the metatherian clades sampled here.
Comparisons with previous studies
Our findings are consistent with those of Prevosti et al.  who also found evidence to support the hypothesis of morphological constraint in the oral region (albeit in the dentary, not tested here) of extant marsupial carnivores. Functionally, this is logical, as the upper and lower jaws should be morphologically coupled for both mechanical and developmental reasons. Conversely, the results of this study concerning the marsupial carnivore/insectivore skull are in contrast to those of Goswami et al. , who included a broader sampling of living and extinct insectivorous and carnivorous species. Because our study compared only ecological groupings of recent taxa, it is possible that this disagreement indicates a greater diversity of carnivorous/insectivorous metatherians in the fossil record than in the present. Indeed, many carnivorous marsupials (or, more generally, metatherians) have become extinct relatively recently . The inclusion of six metatherian fossil taxa (three of which are probably carnivorous/insectivorous) with the Recent marsupials in this study similarly did not significantly increase the overall variance. However, ecological groups were not analyzed separately when fossils were included, nor were placentals and metatherians, as no fossil eutherians (the clade including placentals and their stem relatives) were sampled. Thus, the difference in results between these studies may be a reflection of the limited sample sizes of the fossil taxa and the much broader sampling of extant taxa and different ecological groups in the analysis presented here. Nonetheless, developmental constraints may limit variation, but need not represent absolute barriers to evolution. Even if metatherian and placental disparity is comparable in a few ecological groups (possibly carnivorous and fossorial taxa), the results presented here suggest that a developmental constraint has limited marsupial cranial evolution for most, if not all, of the history of this clade.
Expanding these studies to include fossils representing other ecological groups is central to assessing whether fossil metatherians were subject to similar constraints to those found here for extant forms. For example, it has been shown that large placental omnivores, but not hypercarnivores, have been constrained, in terms of taxonomic diversity, on the southern continents since the late Oligocene . Whether such a pattern also applies to metatherians, possibly in combination with the geographic constraint hypothesis discussed further below, is a promising avenue for future study that will benefit from a broadening of focus beyond comparisons of carnivorous fossil metatherians.
The metatherian fossil record and alternative hypotheses for differential mammalian diversity
It has been suggested that functional requirements around birth bear little relevance to adult metatherian morphology [13, 40], and that other factors are primarily responsible for the observed differences in marsupial and placental diversity. The first alternative hypothesis concerns the relative ages of crown placentals and crown marsupials, while an alternative hypothesis is that the diversification of metatherians has been limited by their biogeographical history and resulting ‘isolation’ on the southern continents.
The earliest metatherians (marsupials and their closest fossil relatives) are known to have existed from the Early Cretaceous of China , and may have been restricted to the northern continents, with an especially rich record in North America, until the end Cretaceous, although there are some debated occurrences in Africa and Madagascar [41, 42]. Non-marsupial metatherians (or possible early didelphimorphs), such as herpetotheriids continued to inhabit the northern continents, although at much reduced numbers, well into the Cenozoic [7, 43]. Molecular approaches estimate the first divergences of the extant marsupial clades around 69 Ma, with the divergences of the Australian orders occurring around 60 Ma . The first paleontological evidence for the extant orders is found in the Paleocene (around 65 to 63.3 Ma) of North America with the appearance of the peradectids, the first known members of Didelphimorphia. Didelphimorphia, Paucituberculata, and Microbiotheria appear in the Palaeocene (around 64.5 to 62.5 Ma) of Brazil. Marsupials first appear in scarce numbers in the fossil record of Australia in the early Eocene , but it is not until the prolific Riversleigh deposits of the Oligo-Miocene that all remaining extant marsupial orders (Diprotodontia, Notoryctemorphia, Peramelemorphia, and Dasyuromorphia) appear. However, a more precise understanding of Gondwanan metatherian biogeography, particularly with regard to the biogeographic origin of the enigmatic Microbiotheria (a small clade of South American marsupials that is a sister group to Australodelphia) is yet hindered  in large part by an extremely poor pre-Oligocene terrestrial vertebrate record from Australia and Antarctica.
Placental phylogenetics and biogeography are somewhat better understood, with a growing body of evidence over the past decade supporting the division of modern placental clades into four superorders, Afrotheria, Xenarthra, Laurasiatheria, and Euarchontoglires, with the latter two combined in Boreoeutheria [47–53]. This divergence of superorders is thought to have been near-simultaneous, and has been linked, albeit contentiously, to their semi-isolation in Africa, South America, and Laurasia, respectively  (although this hypothesis is not congruent with the presence of early afrotherians in the fossil record of North America ). According to recent molecular divergence date estimates, the placental superorders diverged around 88 to 90 Ma, but most extant orders seem to have originated near to or soon after the Cretaceous-Paleogene extinction, around 65 Ma [2, 55]. Although there is as yet no confirmed paleontological evidence for crown placentals in the Late Cretaceous (Nishihara et al.  Meredith et al. , and references therein), crown placentals are known from the earliest Paleocene (around 63 to 64 Ma) of North America, and are found on most continents by the mid Paleocene.
The difference in timing between the basal divergences of crown marsupials and crown placentals has been suggested as one reason for the lower diversity seen in marsupials , although the difference in crown-clade age is out of proportion with the difference in taxonomic diversity between these clades. It has also been suggested that marsupials were hit harder by the K-Pg mass extinction than were placentals (or their respective stem groups), but this has never been explicitly tested. Moreover, paleontological evidence suggests that both groups experienced great losses in diversity, with most Cretaceous metatherian and eutherian families becoming extinct during that event [56–59].
The second alternative, the geographic constraint hypothesis, is based on the observation that placentals are currently more taxonomically diverse throughout the northern continents, and that the northern continents have been in more frequent contact during the Cenozoic [8, 10]. Indeed there are many episodes of dispersal among North America, Asia, and Europe, but both Australia and, until the closure of the Isthmus of Panama (around 3 Ma , but see Montes et al. ), South America, have been almost entirely isolated since the final breakup of Gondwana and opening of the Drake Passage, around 30 Ma . If competition and faunal exchange drive evolution, then geographic isolation and lack of competition may certainly contribute to the current state of marsupial taxonomic diversity. The relatively low diversities of the ‘southern’ placental superorders Xenarthra and Afrotheria may provide further evidence for the possible, but as of yet untested, importance of geographic isolation.
More importantly, however, neither clade age nor the geographic constraint hypothesis can account for the differential disparities of the viscerocranium and neurocranium described here. If extrinsic factors are primarily responsible for the low taxonomic diversity and low morphological disparity of marsupials, then all regions of the skull, not just the early-ossifying viscerocranial elements, should show lower disparity in marsupials than in placentals. The results of the study presented here are consistent with the hypothesis of developmental constraint in the marsupial skull, but do not exclude the possibility of some geographical component also limiting metatherian evolution. Ideally, future work combining both aspects would more fully sample from the metatherian fossil record, including that of the northern continents, but at present, there is a paucity of complete and undeformed metatherian cranial material from those regions.