New Australian sauropods shed light on Cretaceous dinosaur palaeobiogeography

Australian dinosaurs have played a rare but controversial role in the debate surrounding the effect of Gondwanan break-up on Cretaceous dinosaur distribution. Major spatiotemporal gaps in the Gondwanan Cretaceous fossil record, coupled with taxon incompleteness, have hindered research on this effect, especially in Australia. Here we report on two new sauropod specimens from the early Late Cretaceous of Queensland, Australia, that have important implications for Cretaceous dinosaur palaeobiogeography. Savannasaurus elliottorum gen. et sp. nov. comprises one of the most complete Cretaceous sauropod skeletons ever found in Australia, whereas a new specimen of Diamantinasaurus matildae includes the first ever cranial remains of an Australian sauropod. The results of a new phylogenetic analysis, in which both Savannasaurus and Diamantinasaurus are recovered within Titanosauria, were used as the basis for a quantitative palaeobiogeographical analysis of macronarian sauropods. Titanosaurs achieved a worldwide distribution by at least 125 million years ago, suggesting that mid-Cretaceous Australian sauropods represent remnants of clades which were widespread during the Early Cretaceous. These lineages would have entered Australasia via dispersal from South America, presumably across Antarctica. High latitude sauropod dispersal might have been facilitated by Albian–Turonian warming that lifted a palaeoclimatic dispersal barrier between Antarctica and South America.

C397. Pedal digit I, proximal articular surface of ungual (phalanx I-2): perpendicular to long axis of ungual (0); bevelled so that the proximal articular surface faces proximolaterally and thus lies at a distinct angle to the long axis of the ungual (1) (Upchurch and Mannion 53 ; Wilson and Upchurch 101 ). Characters 11,14,15,27,40,51,104,122,147,148,177,195,205 and 259 were treated as ordered multistate characters. The data matrix was then analysed using the 'Stabilize Consensus' option in the 'New Technology Search' in TNT vs. 1.1 (Goloboff et al. 102 ). Searches were carried out using sectorial searches, drift, and tree fusing, with the consensus stabilized five times, prior to using the resultant trees as the starting trees for a 'Traditional Search' using Tree Bisection-Reconstruction. This resulted in 456,528 MPTs of 1,544 steps, with little resolution.
We also analysed this data matrix using implied weights in TNT vs. 1.1 with a k-value of 3 (Goloboff et al. 103 ), following the same protocol as our equally weighted analysis. This resulted in 54 MPTs of 160.73 steps, with a fairly resolved tree ( Figure S3), including a fully resolved Lithostrotia, with polytomies restricted to: (1) derived brachiosaurids; (2) the base of Euhelopodidae; and (3) the base of Titanosauria. The agreement subtree required the a posteriori pruning of five taxa (Abydosaurus, Angolatitan, Daxiatitan, Huanghetitan, Liubangosaurus) ( Figure S4).
In both sets of analyses, symmetric resampling was used to generate the relative frequencies of groups of taxa in the trees, expressed as a GC value, using 5,000 replicates in TNT, with all tree searches run using a 'Traditional Search' with TBR 104 . GC values were also recalculated for the taxa in the agreement subtrees. We also calculated Bremer supports for our equal weights analysis.

Equal weights analysis
Bremer supports vary from 1 to 3 throughout the tree, with the best supported clades including Euhelopodidae and Lithostrotia. GC values are in general low, with only 15 nodes displaying values higher than zero ( Figure S5), with a slight increase in numbers of nodes (16) and values ( Figure S6) for the taxa in our agreement subtree. Most of the tree topology is largely congruent with that presented in previous iterations of this data 2,8,35,36 , and here we focus on results pertaining to Titanosauria and the Australian taxa. Wintonotitan is recovered as a non-titanosaurian somphospondylan, just outside of the titanosaur radiation, similar to its position in previous versions of this data matrix 2,8,35 . In contrast to previous analyses, the East Asian taxa Baotianmansaurus and Dongyangosaurus are not members of Opisthocoelicaudiinae, but instead form a clade of basal titanosaurs, outside of Lithostrotia. Similarly, whereas Diamantinasaurus was recovered as an opisthocoelicaudine by Poropat et al. 2 , here it is placed as a non-lithostrotian titanosaur, forming the clade Savannasaurus + (Diamantinasaurus + AODF 836) (Bremer support=2). As in previous analyses, Daxiatitan and Xianshanosaurus form a clade just outside Lithostrotia. The placement of Epachthosaurus within Lithostrotia is congruent with the analyses of most authors (e.g. González Riga et al. 54 ; Curry Rogers 61 ; Salgado et al. 81 ), and contrasts with the basal titanosaurian position recovered by some (e.g. Martínez et al. 40 ; Upchurch et al. 52 ; Carballido et al. 60 ). It forms the clade Muyelensaurus + (Epachthosaurus + Futalognkosaurus). Although its exact placement is uncertain, Aeolosaurus is recovered as a non-saltasaurid lithostrotian. Nemegtosauridae is recovered as the sister taxon to Isisaurus + Saltasauridae. Nemegtosauridae comprises Nemegtosaurus + Tapuiasaurus, supporting the conclusions of Zaher et al. 51 regarding the affinities of the latter taxon. Although pruned to produce our agreement subtree, Rapetosaurus is also recovered as a nemegtosaurid if we exclude Tapuiasaurus a priori, supporting previous work 44, 61 . Alamosaurus + Jiangshanosaurus forms a clade, as in all previous versions of this data matrix, but this is the sister taxon to Opisthocoelicaudia, rather than Saltasaurus (which lies outside of this clade), contrasting with previous iterations. Below, we provide recovered synapomorphies for the clade of Australian titanosaurs, through character mapping in TNT. Each character number is placed in parentheses.
• Radius, maximum diameter of the proximal end divided by proximodistal length is 0.3 or greater (45).
• Scapula, ventrolateral margin of acromion forms an anteroposteriorly concave region posterior to glenoid, followed by a flattened area (358) [note that this might instead be an autapomorphy of Diamantinasaurus].
• Pubis, anterior margin of distal end strongly concave in lateral view, such that the distal end forms a prominent, anteriorly expanded boot (251).

Implied weights analysis
GC values are in general low, with only 16 nodes displaying values higher than zero ( Figure  S7), with a slight increase in numbers of nodes (18) and values ( Figure S8) for the taxa in our agreement subtree. In general, the overall topology ( Figure S4) is not too dissimilar to that presented in Mannion et al. 35 , and we focus primarily on titanosaur interrelationships and the position of the Australian taxa. Novel results outside of these parts of the tree include: (1) Haestasaurus is the sister taxon to Janenschia, at the base of Macronaria, rather than a titanosaur, supporting the conclusions of Upchurch et al. 36 ; (2) the recovery of a diverse Euhelopodidae that closely matches the equal weights topology, although Fusuisaurus, Liubangosaurus, 'Huanghetitan' ruyangensis and Mongolosaurus are also placed in this clade; (3) Australodocus occupies a similar relative position in the tree as that recovered by Mannion et al. 35 , but the change in placement of Andesaurus (see below) means that the former is now a non-titanosaurian somphospondylan. In contrast to Mannion et al. 35 , there is no longer an Andesauroidea composed of taxa generally regarded as non-titanosaurs (e.g. Chubutisaurus, Sauroposeidon, Wintonotitan). Instead these taxa are recovered as nontitanosaurian somphospondylans. Ruyangosaurus and Daxiatitan are recovered as nonlithostrotian titanosaurs, more derived than Andesaurus. All other titanosaurs are lithostrotians, with Xianshanosaurus positioned as the sister taxon to Malawisaurus. Aeolosaurus + Muyelensaurus forms a basal lithostrotian clade that is the sister taxon of Nemegtosauridae + all remaining titanosaurs. Nemegtosauridae comprises Rapetosaurus + (Nemegtosaurus + Tapuiasaurus). Futalognkosaurus is recovered at the base of the clade comprising the remaining titanosaurs, with the latter forming two clades. One consists of (Baotianmansaurus + Dongyangosaurus) + (Savannasaurus + (Diamantinasaurus + AODF 836)), and the other comprises Epachthosaurus + (Isisaurus + Saltasauridae). The interrelationships of Isisaurus + Saltasauridae do not differ from our equal weights analysis. Below, we provide recovered synapomorphies based on our implied weights analysis for the clade of Australian titanosaurs, as well as the clade they form with Baotianmansaurus + Dongyangosaurus, through character mapping in TNT. Each character number is placed in parentheses.
• Middle-posterior dorsal neural arches, neural canal in anterior view enclosed in a deep fossa in the dorsal surface of the centrum (i.e. much of the canal is enclosed laterally by pedicels that are part of the centrum rather than the neural arch) (338).
• Middle-posterior dorsal neural spines (single, not bifid), SPRLs remain separate or converge at about spine mid-height (or above) to form a dorsally restricted median composite lamina (SPRF well-developed and occupies the ventral half of the anterior spine surface) (342 [reversal]).
• Pubis, anterior margin of distal end strongly concave in lateral view, such that the distal end forms a prominent, anteriorly expanded boot (251).

Data sets and methodological approach
In order to reconstruct the biogeographic history of macronarian sauropods, we have applied the maximum likelihood approach implemented in BioGeoBEARS 105,106 in R 107 . The R script used to run the analyses is provided in the file 'PoropatetalBioGeoBEARSRscript.txt' (N.B. readers wishing to replicate the analyses will need to change the names of some files in this script if, for example, they wish to run the 'relaxed' or 'harsh' versions of our dispersal multiplier matrices).

Calibrated trees
A BioGeoBEARS analysis requires a time-calibrated phylogeny. BioGeoBEARS cannot deal with phylogenetic topologies that contain polytomies (as is also the case for nearly all phylogenetic biogeographic methods). Given that our pruned phylogenetic analysis yielded 12 MPTs, we consider it impractical to run divergence time and biogeographic analyses on every topology. In order to reduce the time required for analyses, the time-calibrated trees are based on the agreement subtree resulting from our cladistic analysis ( Figure S2). We have only included macronarian taxa in our biogeographic analysis because this clade is thoroughly sampled for Late Jurassic and Early Cretaceous taxa, whereas other sauropods (i.e. diplodocoids and some basal eusauropods) are only represented by a few taxa for the purposes of outgroup comparison. The resulting phylogeny contains 48 out of the original 62 macronarian taxa included in the data set employed in this study.
Our data set suffers from a common problem that affects the dating of many extinct vertebrate taxa (especially those recovered from non-marine formations). Such taxa are often known from only a single individual, or single locality, so that they represent point occurrences rather than a taxon's true stratigraphic range. Moreover, limits on the dating of many terrestrial formations mean that the age of a given point occurrence might not be known more precisely than, for example, 'Cenomanian-Santonian'. This problem is clearly present in our sauropod data set. Of the 48 taxa included in our sample of macronarians, only Camarasaurus and Alamosaurus are regarded as having stratigraphic ranges based on numerous specimens from multiple horizons. The remaining 46 taxa are typically known from a single individual or small number of specimens, whose geological age can only be determined to sub-stage level at best (and often much less precisely -see Table S1). Recent studies have dealt with this issue by regarding each taxon as occurring at the mid-point of its possible age range 137,138 , and we have applied this assumption here in our 'srpdmidtree.newick' tree. However, the ages of fossils provide only a minimum divergence time for each set of sister taxa, so it is likely that the true divergence times were older than those implied by a simple reading of the fossil record. We have therefore created a 'maximum' divergence time tree (see the file named 'srpdmaxtree.newick'), using the assumption that point occurrence taxa first appear at the oldest point within the uncertainty of their age estimate. Thus, for example, Xianshanosaurus has been dated as occurring at some point during the Cenomanian-Santonian (Table S1) Our two time-calibrated trees were created using the R package strap 110 . In order to convert the Stage-based ages of taxa into absolute ages, we have used the 2015 Chronostratigraphic Timescale of the International Commission on Stratigraphy 111 . For both trees, we used the 'equal' method for re-distributing the node ages of adjacent zero-length branches 112 , implemented in a slightly modified form in strap (see discussion of this issue in Bell and Lloyd 110 ). The 'equal' method in strap also requires a root length ('rLen') to be defined. Here we have assumed that Macronaria diverged from other sauropod lineages by the beginning of the Bajocian (170.3 Ma), which also represents the start of our first palaeogeographic time slice (see below). This assumption is based on the recommendation of Bell and Lloyd 110 , who suggested that the root length for the ingroup clade should be based on the first appearance date of the nearest outgroup, provided that this outgroup is older than the root node of the ingroup. In the case of our data set, Diplodocoidea is the nearest outgroup, but it appears slightly after the first known macronarian (i.e. in the Kimmeridgian). Thus, we have used taxa such as Atlasaurus and Lapparentosaurus, from the Bathonian-Callovian and Bathonian respectively (Table S1), to support the view that macronarians are likely to have been present by the beginning of the Bajocian. This seems reasonable, given that the presence of a late Oxfordian brachiosaurid (French "Bothriospondylus") means that only approximately 10 million years is allowed for the clade to diversify into the lineages leading to Camarasaurus, brachiosaurids and somphospondylans. The root length for each of the two trees is therefore defined as the time (in millions of years) from the start of the Bajocian to the first appearance of the oldest macronarian in our data set (i.e. French "Bothriospondylus").

Geographic areas
Each terminal sauropod taxon in the time-calibrated trees has been assigned to one of seven palaeocontinental areas (N.B. there are no widespread taxa that occupy two or more areas). These areas and their abbreviations are: A, Asia (excluding India); E, Europe; F, Africa; I, Indo-Madagascar; N, North America; S, South America; U, Australia. The file containing information on the geographic ranges of terminal taxa is 'srpdgeogranges.txt'. The maximum range size is set to 7: this means that the ancestral range estimations in BioGeoBEARS, for a given node or lineage, can include all seven specified areas if required.

Time-stratified analyses and dispersal multiplier matrices
BioGeoBEARS allows stratified analyses in which the dispersal probabilities between areas can vary from one time-slice to the next 105,106 . This allows researchers to use palaeogeographic data to constrain or otherwise inform the analysis. The probability of dispersing from one area to another is modified in the 'dispersal multiplier matrix', with one matrix per time slice in a time-stratified analysis (see below).
Here we have created 22 time slices in order to reflect palaeogeographic events that occurred during the Late Jurassic and Cretaceous. The end of the Cretaceous (time slice 22) is treated as time 0, so all dates that define time-slice boundaries are in millions of years prior to that (1) We assume that trans-oceanic dispersal was a very low probability event for sauropods. It is always difficult to assess the dispersal abilities of extinct organisms, especially those with body plans and/or physiologies that are not fully represented among living descendants or analogous taxa. However, large-bodied terrestrial mammals have been estimated to have very limited over-water dispersal abilities (e.g. Lawver et al. 187 and references therein). Moreover, the observation that dinosaurs display statistically significant patterns indicative of continental-scale vicariance (e.g. Upchurch et al. 188 , Ezcurra and Agnolin 189 ) also suggests that these animals did not disperse across marine barriers very frequently or, at least, not frequently enough to overprint the vicariance patterns (see also Csiki-Sava et al. 190 ). We therefore propose that the assumption of no trans-oceanic dispersal in sauropods is reasonable given our current knowledge of these animals. Therefore, when two of our continental areas are completely separated by ocean according to palaeogeographic maps or other geological data, the probability of jump dispersal between these areas is set to 0.000001. We use 0.000001 rather than 0 for two reasons. First, this is a pragmatic measure because BioGeoBEARS analyses sometimes crash or 'hang' when dispersal multiplier values of 0 are used (see http://phylo.wikidot.com/biogeobears). Second, a value of 0.000001 models the scenario that trans-oceanic dispersal of sauropods was not completely impossible, but might have occurred very infrequently. When land areas are separated by shallow and potentially episodic epicontinental seas, or where island chains might have provided 'stepping-stones' for dispersal, we evaluate the case for allowing dispersal to occur (see assumption 8 and the descriptions of each time-slice below).
(2) Two land areas are assumed to be completely isolated from each other by an oceanic barrier at approximately the time of the onset of sea floor spreading between those areas (provided the proposed oceanic crust completely severs all connections between the continental crust of the two landmasses). However, we also take into account other geological and palaeontological evidence pertinent to the nature of an oceanic barrier. For example, support for the disconnection of two continental regions can be provided by the onset of dispersal of marine taxa between two previously separate areas of ocean (as occurred when the South and Central Atlantic were connected during the mid-Cretaceous by the final separation of Africa and South America [see time slice 12]).
(3) Although climatic zones might have hindered or promoted dispersal between areas, we have not built this information into our dispersal constraints. It is probable that sauropods could not tolerate prolonged and extreme cold, and this might have meant that they generally avoided high latitudes. Indeed, sauropods appear to be absent from higher latitudes in the northern hemisphere during the Late Cretaceous, though this might reflect historical and biotic factors, such as the dominance of ornithischians 191,192 , rather than climate. Nevertheless, generally warm conditions during the Cretaceous (e.g. Hay 193 ), coupled with the observation that sauropod remains are known from a wide variety of terrestrial and freshwater environments 194 with a palaeolatitudinal range of 66° N-63.5° S 7,195 , suggest that it would be premature to impose stringent constraints on this group's dispersal based on latitudinal climatic zones given our current knowledge.
(4) Dispersal is only allowed between 'adjacent' areas. For example, if North America is in contact with Europe, and the latter is in contact with Asia, but Asia is not in direct contact with North America, then any taxon dispersing between North America and Asia would have to do so via Europe. This is consistent with the prohibition on trans-oceanic dispersal (see assumption '(1)' above), which would severely restrict direct dispersal between North America and Asia in this situation.
(5) All dispersal probabilities between two areas are symmetrical (i.e. if dispersal from North America to Europe is allowed, then dispersal from Europe to North America is also allowed with the same level of probability). Asymmetrical dispersal probabilities can be modelled in BioGeoBEARS, and are certainly plausible in reality. For example, Sanmartin and Ronquist 196 showed that prevailing wind currents have meant that seed dispersal from 26 Australia to New Zealand has been more prevalent than vice versa. However, we currently have no strong grounds for proposing asymmetrical dispersal of terrestrial taxa between Mesozoic continental areas. Russell 197 employed one of the principles of 'dispersal biogeography' that states that taxa will tend to disperse from a larger geographic area to a smaller one (see also Weishampel and Jianu 198 ), but we suggest that this is a phenomenon that it would be better to test a posteriori, than assume a priori. Even if the assumption of asymmetrical dispersal probabilities was desirable, it is not clear what values should be assigned to represent such a process in the case of terrestrial dinosaurs dispersing from one continent to another.
(6) None of the sauropods in our analysis occur in Antarctica. Therefore, when two of our designated areas are in contact with each other only via Antarctica (e.g. South America and Indo-Madagascar during the Early Cretaceous), we treat them as being 'adjacent' (see assumption ' (4)' above).  201 and references therein). Narrow and shallow epicontinental seas separated these islands and, at present, there is insufficient information available to allow a detailed model of the sequence and timing of the connections and disconnections between these islands (although resolution is improving, especially for the Late Cretaceous -see Csiki-Sava et al. 190 ). In any case, even if it were possible to capture a more detailed palaeogeographic history of Europe, there are so few European sauropods in our phylogeny that further division of this area into smaller units is likely to result in insufficient data to resolve their biogeographic relationships. Here, therefore, we treat Europe as a single area for pragmatic reasons, pending the development of more detailed palaeogeographic and biogeographic data sets.
(8) Dispersal multiplier values are typically set to 0.000001 (effectively no dispersal allowed between the two areas concerned) when there is clear and unequivocal evidence for a barrier to terrestrial dispersal, or 1 (dispersal is allowed between the two areas, with the maximum probability used by the analytical model) when there is strong evidence that two areas were connected. In several cases, such as when palaeogeographic events are temporally or spatially poorly constrained, epicontinental seas are shallow and potentially ephemeral, and/or the presence of a barrier has been inferred mainly on palaeontological (rather than geological/geophysical) data, we have used an intermediate value of 0.5. The version of our dispersal constraints, which includes these 0.5 values, is referred to here as the 'Starting' model and can be found in the file 'srpddispersalmultipliersstarting.txt'. In order to explore the sensitivity of our results to this particular set of assumptions about dispersal, we have also applied two more extreme versions of the dispersal multiplier probabilities. In the 'Relaxed' model, all 0.5 values are reset to 1.0, so that dispersal across the 'doubtful' barriers is allowed with the same probability as dispersal between adjacent land areas (see the file 'srpddispersalmultipliersrelaxed.txt'). In the 'Harsh' model, the 0.5 values are set to 0.000001, so that effectively no dispersal is allowed across the 'doubtful' barriers (see the file 'srpddispersalmultipliersharsh.txt').
(9) We have not used an 'areas allowed' matrix to exclude one or more areas during any of the time slices. This is because we are dealing with continental areas that were present throughout the period under investigation.

27
(10) We have not imposed any assumptions about the probability of dispersal events based on the relative distances between areas (apart from the 'adjacent areas' rule set out in assumption 4).
The time-slice constraints on dispersal (Tables S2-23), and the palaeogeographic data that justify them, are briefly outlined below and summarised in Table S24. Note that all constraints on dispersal defined in a given time slice are retained in subsequent time slices except where stated otherwise. The timescale used here is the same as that employed when producing the time-calibrated phylogenies (see above). The boundaries between time slices are defined in the 'mid' and 'max' versions of the file 'srpdtimeperiods.txt'. The 'mid' version of this time periods file is identical to the 'max' version, except that somes dates in the former have been reduced by 0.0001 million years (e.g. 3.05 Ma. becomes 3.0499 Ma.). This has been done because several of the nodes in the srpdmidtree were exactly the same age as the boundary between two time slices, making it impossible for BioGeoBEARS to temporally-partition the tree (the algorithm cannot determine which of the two time slices should be allocated the node).

Time slice 1: 104.3-91.3 million years prior to the K/Pg boundary (= Bajocian-Oxfordian [170.3-157.3 Ma])
During much of the early Mesozoic, Laurasia and Gondwana were joined to form Pangaea, but the Tethys Ocean created a barrier between Europe and Asia to the North, and Africa and East Gondwana continental areas to the south 199,202,203 . However, a land connection existed between North America and Africa+South America during the Triassic and Early Jurassic 187,199,[202][203][204] . According to Bardet et al. 201 , the Hispanic corridor (separating northwest Africa and South America from North America) potentially dates back to the Pliensbachian, but this marine dispersal route between Tethys and eastern Panthalassa was probably sporadic until the opening of the Gulf of Mexico in approximately the Callovian (see below).
Bardet et al. 201 (and references therein) noted the presence of the Viking Corridor during the Early Jurassic (a narrow area of epicontinental sea corresponding approximately in position with the future North Atlantic rift), which might have hindered North America-Europe terrestrial dispersal at this time. However, the palaeogeographic reconstructions of Scotese 202 and Smith et al. 199 indicate that land connections between North America and at least some portions of Europe existed during the Middle Jurassic (see also Golonka et al. 205 ).
The Turgai Sea (also known as the Obik Sea 206 or Uralian Sea 207 ), or other areas of ocean in the vicinity of the Russian Basin, potentially produced a longitudinally oriented marine barrier separating Europe from Central (and therefore also East) Asia during the middle and Late Jurassic 199,202 . These areas of epicontinental sea have been linked to geographic isolation of Chinese and other East Asian faunas from approximately the Bajocian-Bathonian onwards 62,101,188,197,206,207 , although the palaeocoastline reconstructions of Smith et al. 199  In this time slice, therefore, we allow dispersal between all adjacent areas apart from Europe to Asia and vice versa. In our 'starting' model, the Europe-Asia dispersal multiplier is set to 0.5 during time slices 1-3 (i.e. Bajocian-Tithonian) in order to reflect the uncertain impact of the Turgai Sea/Russian Basin regions.  212 . Here, we assume that an oceanic barrier separated North and South America from the start of the Oxfordian based on these rifting event dates, and also the palaeocoastline reconstructions of Smith et al. 199 and Blakey 203 (N.B. the Bajocian map in Smith et al. 199 suggests that a marine barrier separated North and South America at this time, while a Laurasia-Gondwana land connection was maintained via North America and Africa -but this reconstruction is not supported by some recent assessments of the timing and sequence of sea floor spreading events [e.g. Seton et al. 212 , and references therein]). Both Wilf et al. 204 and Lawver et al. 187 proposed the existence of land connections between Gondwana and Laurasia until well into the Late Jurassic or even the earliest Cretaceous, but the former study argued that a climatic barrier imposed an effective separation between northern and southern terrestrial biotas earlier in the Late Jurassic. Thus, we accept that during the Late Jurassic, direct dispersal of terrestrial animals between Laurasia and Gondwana would have been greatly reduced or impossible from the start of the Kimmeridgian onwards, but it must be acknowledged that there is considerable uncertainty about the exact timing of this biotic separation.
The timing of the opening of the North Atlantic is debated, and its effectiveness as a marine barrier to Late Jurassic North America-Europe dispersal is even more problematic. According to Seton et al. 212 (and references therein), rifting and subsequent sea floor spreading in the North Atlantic region occurred in several phases during the Jurassic, Cretaceous and Cenozoic. Initially, rift basins formed in the region between Iberia and Newfoundland during the Late Triassic and Early Jurassic, but this was followed by a tectonically quiet period until the Late Jurassic 212 . This is consistent with the reconstructions of Golonka et al. 205 226 , corresponding to the oldest magnetic anomalies identified in the Riiser-Larsen Sea by Jokat et al. 225 . The rate of spreading accelerated at ~133 Ma, apparently corresponding to the onset of the opening of the South Atlantic 226 . The palaeocoastline reconstructions of Smith et al. 199 suggest that the last land connection between southern Africa and Antarctica was present during the Tithonian, which is somewhat later than predicted on the basis of the onset of sea floor spreading. In contrast, the palaeogeographic reconstructions of Blakey 203 indicate the presence of at least a shallow sea between Africa and Antarctica during the Late Jurassic. In the Tithonian, Madagascar was probably already fully isolated from Africa by an area of ocean 203 , and these two continents are estimated to have been separated by approximately 400 km of ocean by ~130-120 Ma (late Hauterivian-early Aptian) according to Ali and Krause 228 . The Mozambique Ridge is interpreted to have formed between 140-120 Ma but probably did not act as an island for terrestrial dispersal between Africa and Antarctica 228 . Therefore, during this time slice, we set the Africa-Indo-Madagascar and Africa-Australia dispersal multiplier values at 1.0, but this is changed to 0.5 in the Tithonian to reflect the uncertainty concerning the exact separation of Africa from East Gondwana. From the Berriasian onwards, however, these dispersal multipliers are set to 0.
The palaeogeography of the Patagonia-West Antarctica Peninsula region during the Late Jurassic and Cretaceous is problematic. As a result, there are at least two main competing models for the earliest stages of Gondwana fragmentation 229 . These alternatives have been termed the 'Samafrica' and 'Africa-first' models 229 . Both models involve rifting between southern Africa and Antarctica, and between eastern Africa and Madagascar, commencing in the Late Jurassic (see above). It is also generally accepted that rifting further west started to open the Weddell Sea between southwest Africa, southern South America, and the West Antarctic Peninsula (see Seton et al. 212 and references therein). This rifting commenced at approximately 167-160 Ma, with sea floor spreading initiating at around 146 Ma according to Seton et al. 212 and references therein. The difficulty for those wishing to model the biogeographic consequences of these events stems from the lack of clarity regarding whether or not the land connection between South America and Antarctica was severed during the Late Jurassic, or much later. Under the Samafrica model, the Jurassic rifting results in the separation of the southern tip of South America from the West Antarctic Peninsula, so that Gondwana was initially divided into separate western (Africa+South America) and eastern (Antarctica+Indo-Madagascar+Australia) portions as early as 150 Ma 199,203,[230][231][232][233][234][235][236] . In contrast, the Africa-first model proposes that the South America-West Antarctic Peninsula connection was maintained throughout the Jurassic and Cretaceous, and was not lost until the opening of the Drake Passage during the Cenozoic at around 52 Ma 204,228,237 . Ali and Krause 228 (p. 1860) stated that, "At the Early/Late Cretaceous transition (start of the Cenomanian, 99.6 Ma; Fig.  4b), South America, Antarctica and Australia remained joined…," but the cited palaeogeographic map depicts areas of shallow and deep sea between the southern tip of Patagonia and the West Antarctic Peninsula. J. Ali (pers. comm. to PU in 2014) has confirmed that this discrepancy is the result of an error in the palaeogeographic reconstructions. He also goes on to note that there appears to have been very little movement between these two regions until the Cenozoic, ~35-40 Ma, as can be seen in the reconstructions presented by Schettino and Scotese 238 . Vérard et al. 239 more-or-less supported this interpretation; however, they did suggest that South America and Antarctica were separated for an unspecified length of time between 103 and 84 Ma. The only map in which Vérard et al. 239 depict the separation is their 95 Ma map (Vérard et al. 239 : fig. 5h), and it is only in their description of this map (Vérard et al. 239 : p. 50) that it is explicitly stated that the two continents were separated; both their 103 and 84 Ma maps depict South America and Antarctica united (Vérard et al. 239 : figs. 5g and 5i). It should be noted that, even if there was a continental crust connection between South America and Antarctica during all or part of the Cretaceous, this does not necessarily mean that this provided a viable landbridge for dispersal of terrestrial taxa: changes in sea level might have periodically flooded this region, creating epicontinental seas (J. Ali pers. comm. 2014), and its relatively high latitude might also have transformed this dispersal corridor into a 'filter barrier' at times 229 . Because of this uncertainty, we have set the dispersal multiplier for dispersal between South America and Indo-Madagascar/Australia (both via Antarctica) at 0.5 in our starting model, so that the relaxed and harsh models can be used to examine, respectively, the effects of allowing and prohibiting dispersal across this landbridge in time slice 3 onwards (but note that the nature of the South America-Antarctica connection becomes less important from time slice 9 onwards because of the loss of contact between Antarctica and Indo-Madagascar).

Time slice 3: 86.1-79 million years prior to the K/Pg boundary (= Tithonian [152.1-145 Ma])
As noted in time slice 2, the dispersal multipliers for North America-Europe, Africa-Australia/Indo-Madagascar and South America-Australia/Indo-Madagascar dispersals are set to 0.5 in our starting model for this time slice.

Time slice 4: 79-76.4 million years prior to the K/Pg boundary (= early Berriasian [145-142.4 Ma])
Baraboshkin et al. 240 presented evidence that the marine connection between the Boreal and Tethys Oceans, in the region of the Russian Basin, was interrupted during the early Berriasian. Therefore, the Europe-Asia dispersal multiplier is set at 1.0 for this interval.
There is some palaeogeographic support for a land connection between Africa and Europe during the Early Cretaceous (approximately Berriasian-Barremian). This is the 'Apulian Route', supposedly created by a series of microplates lying between northern Africa and southern Europe at a time of sea-level lowstand (see Ezcurra and Agnolin 189 and references therein). This is consistent with apparent dispersal of terrestrial taxa, such as dinosaurs and mammals, between Africa and Europe during the Early Cretaceous 99,189,207,241 . This land connection seems to have been severed by the Aptian at the latest (but possibly earlier, during the Barremian, as a result of a rise in sea level), though it might have reappeared during the Campanian (Ezcurra and Agnolin 189 and references therein). Therefore, during time slices 4-6 (Berriasian-Hauterivian) we allow Europe-Africa dispersal to occur with a dispersal multiplier value of 1.0. During time slice 7 (Barremian) this value is reduced to 0.5, and from the Aptian onwards this is set to 0.000001 (but see time slices covering the Campanian).
The Africa-India/Australia dispersal multiplier values are set to 0.000001 in this time slice and all subsequent ones (see time slice 2 for details).

Time slice 5: 76.4-65.15 million years prior to the K/Pg boundary (= late Berriasian-early Hauterivian [142.4-131.15 Ma])
The marine connection between the Boreal and Tethys Oceans in the Russian Basin/Turgai regions was re-established during the late Berriasian and persisted throughout the Valanginian, although it became more restricted 240 . The existence of this marine barrier has been inferred partly on geological data and partly on biotic interchanges between the Boreal and Tethyan realms (Baraboshkin et al. 240 and references therein). We therefore prohibit Europe-Asia dispersal during this time slice.

Time slice 6: 65.15-63.4 million years prior to the K/Pg boundary (= late Hauterivian [131.15-129.4 Ma])
During this time slice, the Russian Basin/Turgai marine barrier was again interrupted by a land connection between Europe and Asia, which apparently persisted until approximately the end of the Aptian 240 . We therefore set the dispersal multiplier value to 1 for Europe-Asia dispersals at this time and also in time slices 7-9.

Time slice 7: 63.4-59 million years prior to the K/Pg boundary (= Barremian [129.4-125 Ma])
As noted in time slice 4, the Europe-Africa dispersal multiplier is set at 0.5 during the Barremian, in order to reflect the waning importance of the Apulian Route (Ezcurra and Agnolin 189 and references therein).
In this time slice, we set the North America-Europe dispersal multiplier to 0.000001, reflecting the presence of a well-developed North Atlantic marine barrier between these two continents (see time slice 2).

Time slice 8: 59-53 million years prior to the K/Pg boundary (= early Aptian [125-119 Ma])
The Europe-Africa dispersal multiplier value is set to 0.000001 to reflect the absence of the Apulian Route (see time slices 4 and 7). The dispersal multiplier for North America-Asia dispersal is set to 0.5 for this time slice (see time slice 10 for details).
The timing of the separation and complete biogeographic isolation of Indo-Madagascar is controversial (see the review in Ali and Krause 228 ). However, Ali and Krause 228 present strong palaeogeographic evidence to support the view that Indo-Madagascar became separated from Antarctica by a marine barrier at approximately 119 Ma. This view was also supported by Lawver et al. 187 , although they set the latest possible date for an Antarctica-Indo-Madagascar land connection at 108 Ma. Thus, from the late Aptian time slice onwards we prohibit terrestrial dispersal between Indo-Madagascar and South America/Australia. According to Baraboshkin et al. 240 , the Russian Basin/Turgai Sea regions again formed a marine barrier to Europe-Asia terrestrial dispersal during the early Albian. The Europe-Asia dispersal multiplier for this time slice is therefore set to 0.000001.
There is some palaeogeographic support for the presence of the Bering landbridge between North America and Asia during the Aptian-Albian 242 . Zanno and Makovicky 243 (and references therein) argued for this, partly on the basis of biogeographic data (e.g. the presence of tyrannosauroid material in North America at ~108 Ma). This Bering landbridge probably allowed North America-Asia dispersal during the early Albian, perhaps during a 10 million year interval. Therefore, the North America-Asia dispersal multiplier value is set to 1.0 for this time slice, and 0.5 for the late Aptian and late Albian in order to reflect the uncertainties surrounding the exact dates for the presence of this late Early Cretaceous Bering landbridge.
In time slice 12, we suggest that the final land connection between South America and Africa was severed at approximately 103 Ma, as a result of the joining of the Central and South Atlantic Oceans. However, recent work by Lawver et al. 187 has presented evidence that some form of marine barrier between Brazil and west Africa was present as early as 112 Ma. To reflect this uncertainty, we have set the South America-Africa dispersal multiplier to 0.5 during time slices 10 and 11.

Time slice 11: 40.75-37 million years prior to the K/Pg boundary (= the early portion of the late Albian [106.75-103 Ma])
According to Baraboshkin et al. 240 , the Turgai Sea was again interrupted by a Europe-Asia land connection during the late Albian and Early Cenomanian. Therefore, the Europe-Asia dispersal multiplier value is set to 1.0 for this time slice and the next two.
The North America-Asia dispersal multiplier is set to 0.5 during this time slice (see time slice 10 for details).

million years prior to the K/Pg boundary (= latest Albian [103-100.5 Ma])
The Europe-Asia dispersal multiplier for this time slice is set to 1.0 (see time slice 11).
A key event in the palaeogeographic and biogeographic history of Gondwana during the Cretaceous concerns the final separation of South America from Africa. Some workers have proposed that a land connection persisted until as late as 80 Ma (e.g. Ezcurra and Agnolin 189 [and references therein], Sereno et al. 244 ). Such a late connection depends on the presence of a landbridge created by the Walvis Ridge and Rio Grande Rise, but this seems improbable according to Gheerbrant and Rage 241 and Lawver et al. 187 . The biogeographic support for such a late land connection has also been criticised by Upchurch 229

Time slice 13: 34.5-31.2 million years prior to the K/Pg boundary (= early Cenomanian [100.5-97.2 Ma])
The Europe-Asia dispersal multiplier for this time slice is set to 1.0 (see time slice 11 for details).  The Europe-Asia dispersal multiplier is set to 1.0 for this time slice (see time slice 14 for details). The Europe-Asia dispersal multiplier is set to 0.5 (see time slice 14 for details). The Europe-Asia dispersal multiplier is set to 1.0 for this time slice (see time slice 14 for details).

Time slice 18: 20.3-17.6 million years prior to the K/Pg boundary (= Santonian [86.3-83.6 Ma])
The Europe-Asia dispersal multiplier is set to 0.5 (see time slice 14 for details). The Turgai Sea apparently went through a relatively deep phase during the Campanian 240 . In this time slice, and in the following one, the Europe-Asia dispersal multiplier is set to 0.000001, and is then set to 0.5 for the two Maastrichtian time slices.
Ezcurra and Agnolin 189 (and references therein) suggested that biotic interchange occurred between Africa and Europe during the Campanian and Maastrichtian via a re-emergent Apulian Route (see time slice 4). Although Ezcurra and Agnolin 189 cite some geological/palaeogeographic studies to support this claim, much of the evidence for the proposed land connection is based on biogeographic data. Palaeocoastline reconstructions for the Campanian and Maastrichtian typically do not depict a land connection, and in fact there appears to have been quite a wide area of ocean between Africa and Europe at this time 199,203 .
Because of the uncertainties surrounding the presence/absence of this landbridge, we set the dispersal multiplier for Europe-Africa dispersal to 0.5 during the Campanian and Maastrichtian time slices.
Zanno and Makovicky 243 (and references therein) suggested that a second phase of North America-Asia biotic interchange occurred across the Bering landbridge during the Campanian and Maastrichtian. However, Brikiatis 249 has argued that Beringia was not fully exposed during the Maastrichtian, based on floristic data. We therefore set the dispersal multiplier for North America-Asia dispersal to 1.0 for the two Campanian time slices and 0.5 for the two Maastrichtian time slices.  234 suggested that this land connection was frequently breached as a result of sea level changes so that it fluctuated between being a landbridge, a filter barrier, and a true barrier (probably on time scales that are too fine to resolve in large-scale palaeogeographic reconstructions). Ezcurra and Agnolin 189 also rejected the evidence for biotic interchange between North and South America during the latest Cretaceous, partly on the basis of the absence of a satisfactory palaeogeographic mechanism, and partly because their statistically significant biogeographic patterns did not support such an event. Here, therefore, we set the North America-South America dispersal multiplier value to 0.5 during the late Campanian and early Maastrichtian.
Rifting between Antarctica and Australia commenced as early as 165 Ma, with the onset of breakup between 125 and 83 Ma (Seton et al. 212 and references therein). However, these two areas apparently remained connected throughout the Jurassic and Cretaceous 267,268 . Smith et al. 199 , Scotese 202 and Blakey 203 depict a widening ocean between these two areas from the Campanian onwards (consistent with sea floor spreading between around 84 and 61 Maya according to Seton et al. 212 ). By the end of the Maastrichtian, the land bridge between Antarctica and Australia appears to have been limited to a relatively narrow strip corresponding to modern day Tasmania 269 . Although we might expect terrestrial dispersal between Antarctica and Australia to have been at least partially hindered by this growing oceanic barrier in the latest Cretaceous, we provisionally allow dispersal to occur in our models (N.B. this assumption will not affect our analyses because the Australian sauropods in our data set all predate the Campanian).

Time slice 22: 3.05-0 million years prior to the K/Pg boundary (= late Maastrichtian [69.05-66 Ma])
The North America-Europe dispersal multiplier is set to 0 for this time slice (see time slice 17).

Background
BioGeoBEARS can implement six different models of how the spatial distributions of organisms might evolve with respect to their phylogenetic relationships 105 . These models are known as DEC, DEC+J, DIVALIKE, DIVALIKE+J, BAYAREALIKe and BAYAREALIKe+J. In all models, 'd' (dispersal) and 'e' (extinction) are free parameters that represent the rate of range expansion and contraction, respectively, along a lineage. The models differ, however, in how they deal with the inheritance of ancestral ranges at cladogenesis. DEC (Dispersal, Extinction, Cladogenesis) was proposed by Ree 270 and Ree and Smith 271 . This model allows a restricted form of vicariance in which one of the areas occupied by an ancestor is passed onto one of its two daughter lineages at cladogenesis, whereas the other daughter lineage inherits all of the other areas (e.g. if ancestor z occupies areas ABCD, then daughters x and y can inherit areas A and BCD respectively). Subset speciation is also allowed in DEC (e.g. daughters x and y could inherit areas A and ABCD from z). However, vicariance in the form in which x and y inherit AB and CD respectively, is not permitted in DEC. DIVALIKE is based on DIVA (Dispersal-Vicariance Analysis) created by Ronquist 272 : however, it is termed 'DIVA-like' in BioGeoBEARS because it is a maximum likelihood implementation of the parsimony-based DIVA. DIVALIKE allows vicariance of any form to occur at cladogenesis, but prohibits subset speciation. BAYAREALIKE is a maximum likelihood implementation of BAYAREA, a Bayesian approach to biogeography proposed by Landis et al. 273 . In BAYAREALIKE, only range duplication is allowed at cladogenesis (e.g. ancestor z in areas ABCD, would pass ABCD to both daughters x and y). The +J versions of DEC, DIVALIKE and BAYAREALIKE, were proposed by Matzke 105,106 . J is a third free parameter that represents the rate of founder-event speciation (a process that has previously been omitted from other biogeographic analytical approaches). Founder-event speciation occurs at cladogenesis, as a result of 'jump' dispersal across a barrier, followed by allopatry (e.g. ancestor z living in areas ABCD disperses to E, so that daughters x and y occur in ABCD and E respectively after cladogenesis). BioGeoBEARS uses each of these six models to estimate the ancestral ranges of taxa, and then applies log likelihood ratio tests and AIC analyses in order to assess which model is best fitted by the data 105,106 .

Analyses
We have carried out eight analyses, each of which applies the six biogeographic models outlined above. These eight analyses were generated by applying the starting, harsh, and relaxed versions of the time-stratified dispersal multiplier matrices, as well as no constraints on dispersal, to the maximum age and midpoint age phylogenetic trees. The results are summarised in Tables S25 and S26, and the ancestral range estimations for the best fitting models for each analysis are shown in the supplementary files Figures S9-S22.

Results and interpretation
For reasons of brevity, we use the analysis name abbreviations listed in the legend to Table  S25 in the following discussion. The term 'node' is used in the conventional cladistic sense, but it should be noted that the ancestral range estimates at a given node indicate the area (s) occupied by that ancestor just prior to cladogenesis. The range estimates shown at 'corners' (i.e. where a branch changes direction from vertical to horizontal in the plots shown in Figures  S6-S18), indicate the area (s) occupied by the lineage just after cladogenesis (see http://phylo.wikidot.com/biogeobears). The reader should also note that some caution is required in interpreting the ancestral range estimates produced by BioGeoBEARS. Other combinations of areas might be nearly as probable as those actually shown in the plots. The accompanying figures showing pie charts (at each node or corner) summarise the relative probabilities of various area combinations that could occur. Thus, the area(s) shown at a node or corner as the most probable range estimate might have a relatively low probability, but this probability is higher than that of any other possible range.
Comparisons of the results produced by the maximum age and midpoint age trees indicate that the differences in estimated node dates have had little impact on the biogeographic analyses (especially the unconstrained ones). The main effect is that, whereas BAYAREALIKE and BAYAREALIKE+J models are preferred in the MXst, MXha and MXre analyses, DEC+J (sometimes also with BAYAREALIKE+J) is supported as best fitting the data in the MDst and MDre analyses. Whether or not constraints on dispersal (based on palaeogeography) are applied, and the nature of those constraints, has a more marked effect (see below). Table S25 shows that, when no constraints on dispersal are applied, the data fit the three +J models significantly better than they do the models that lack founder-event speciation. Furthermore, the three +J models fit the data almost equally well. Although there is a slightly better fit between the data and the DIVALIKE+J model (based on the lowest AIC value), the AIC analyses indicate that DEC+J and BAYAREALIKE+J perform nearly as well, and we suggest that there are no grounds for favouring one of these +J models over either of the other two. Thus, when no constraint on dispersal is applied, the data are insufficient to allow a determination of the extent to which continent-scale vicariance did, or did not, play a role in the evolution of Cretaceous titanosauriforms, but do support a major role for founderevent speciation. In terms of the biogeographic origins of the two Australian lineages, the ancestral range estimations support a dispersal event from Asia to Australia (Table S26). This is based on the estimation of Asia as the range for the most recent common ancestor of Diamantinasaurus+Savannasaurus and other titanosaurs, and that of Wintonotitan and other somphospondylans, in the MXun and MDun analyses ( Figures S9-S14). Table S25 shows that, when time-stratified dispersal constraints are implemented, the +J version of each model still performs better than the non+J version in most cases. However, the support for +J models over non+J ones is greatly reduced: indeed, there are several instances when there is no statistically significant difference between them (e.g. BAYAREALIKE and BAYAREALIKE+J in the MDre) or when the non+J version is actually better supported based on AIC scores (e.g. BAYAREALIKE and BAYAREALIKE+J in the MDst and MDha). Thus, application of dispersal constraints significantly reduces the role of founder-event speciation in the biogeographic evolution of macronarian sauropods. This is a reasonable result given that Matzke 105 reported that estimated rates of founder-event speciation are 2-4 times higher in island clades compared to continental ones. The second major effect of imposing palaeogeography-based dispersal constraints is that BAYAREALIKE and BAYAREALIKE+J are much better supported than DEC, DEC+J, DIVALIKE and DIVALIKE+J in the MXst, MXha, MXre and MDha analyses (Table S25). If this accurately reflects the processes governing Cretaceous sauropod evolution, then it suggests very little role for continent-scale vicariance. However, this result is sensitive to how the uncertainty in taxon ages is treated: DEC+J is the best fitting model in the MDst and MDre analyses.
The palaeogeographic constraints have also had a marked impact on the biogeographic histories estimated for the two lineages leading to Diamantinasaurus+Savannasaurus and Wintonotitan (Compare Figs S9-14 with S15-22). With regard to the most recent common ancestor of Diamantinasaurus+Savannasaurus and other titanosaurs, all of the best supported constrained MX analyses estimate a geographic range encompassing at least Asia and South America (Table S26). In the MDst and MDre analyses, where DEC+J is supported, this ancestral range is estimated to include Asia, Africa, Indo-Madagascar, South America and Australia (Figs S18 and S21). A virtually identical set of ancestral area estimations is generated for the most recent common ancestor of Wintonotitan and other somphospondylans (Table S26). These results suggest that the two Australian lineages were derived from ancestral stocks that were widespread across several continents during the Early Cretaceous (i.e. prior to the Aptian). This is a reasonable interpretation even for those results where these ancestors are estimated to have lived solely in Asia+South America at this time.
Palaeogeographic information (see above) demonstrates that a single area composed exclusively of Asia and South America did not exist during the Mesozoic: therefore, an estimated ancestral range comprising just these two areas is most plausibly interpreted as representing a much more widespread range that has been obscured by missing data caused by sampling failure)). If the Australian sauropod lineages belong to groups that were widespread during the pre-Aptian Early Cretaceous, then their existence during the early Late Cretaceous can be explained through processes such as geodispersal and regional extinction and does not require the direct trans-oceanic dispersal from Asia that is implied by the results of the unconstrained analyses.
The results outlined above raise the issue of whether we should give preference to those generated with, or without, palaeogeographic constraints. Here, we propose that the constrained analyses should be given more credence, for several reasons: 1. The unconstrained analyses support some rather unlikely events in sauropod biogeographic history. For example, it seems improbable that such large-bodied terrestrial animals could have crossed thousands of kilometres of ocean in order to disperse from Asia to Australia directly.
2. The constrained analyses have produced more realistic estimates of the rates of dispersal (d), extinction (e) and founder event speciation (J), than the unconstrained ones. In the latter, when the +J models are applied, d and e are estimated to be 0, so that J is a dominant factor (see Figures S9-S14). It seems improbable that range expansion and contraction along evolving lineages played no role in determining the biogeographic ranges of sauropods, and that the latter were largely the product of founder-event speciation. As noted by Matzke 105 , there is some prima facie evidence that J has lower values in continental clades compared to island ones. Thus, the constrained analyses, with their higher values for d and e, and lower values for J, appear to provide more realistic estimates of the factors controlling the spatial distribution of a terrestrial continental clade such as sauropods.
3. The addition of palaeogeographic data to a biogeographic analysis can be supported on the basis of a 'total evidence' argument. We know that sauropod evolution took place against the backdrop of profound changes in palaeogeography resulting from the break-up of Pangaea and fluctuations in sea level. Provided it is reasonable to assume that sauropods could not cross wide ocean barriers, we are justified in informing the biogeographic analyses of the positions and ages of such barriers.
If our constrained analyses have produced accurate estimates of macronarian biogeographic history, then our results have four main implications.
1. The main processes controlling the geographic distributions of Cretaceous macronarians appear to be geodispersal (which produced widespread clades during the earliest Cretaceous), and regional extinction (which was at least partially responsible for continent-scale endemism in the Late Cretaceous). Vicariance driven by continental fragmentation and changes in sea level might also have played a role, but the support for this is sensitive to how the uncertainty in terminal taxon ages is handled (i.e. DEC+J is only the best fitting model when mid-point ages are used). It would be premature, however, to dismiss the role of vicariance. First, several studies (e.g. Upchurch et al. 188 , Ezcurra and Agnolin 189 ) have found statistically significant area relationships, in several dinosaurian clades, indicative of vicariance patterns. Second, it is also possible that a poorly sampled fossil record has destroyed some of the signal for vicariance, and it should be noted that the latter process is perhaps more sensitive to 'noise' in a data set than is, for example, dispersal 229 .
2. Although the existence of one or more pre-Aptian titanosauriform radiations (extending across several continents) is compatible with our current knowledge of the fossil record, our ancestral range estimates nonetheless imply a hitherto unappreciated diversity of taxa that have yet to be found. For example, several of our results suggest that true titanosaurian taxa were present in the pre-Aptian Cretaceous of Indo-Madagascar, even though at present they are only known in this region from the latest Cretaceous. Presumably these gaps in our knowledge reflect poor sampling during the early Cretaceous, particularly in Gondwana (e.g. Upchurch et al. 36 ), and in the mid-Cretaceous in general 274 .
3. Our results mean that we must envisage a series of regional extinction events occurring from the Aptian onwards, as implied by the range contractions seen in our constrained biogeographic analyses. This scenario of earlier cosmopolitanism followed by regional extinction is reminiscent of the proposals made by Sereno et al. 275 , which attempted to explain Late Cretaceous continent-scale endemism among dinosaurs. The potential role of mid-Cretaceous climate change in some of these regional extinctions is discussed briefly in the main text of this article.
4. The apparent close similarity between the mid-Cretaceous dinosaurian faunas of East Asia and Australia (which is discussed in our main text) has been explained as a result of longdistance dispersals by some workers 276 . However, our results only support such an interpretation when palaeogeographic data are ignored. Moreover, our phylogenetic results do not reconstruct either of the two Australian lineages as having sister-taxa in East Asia, as would be predicted by the long-distance dispersal hypothesis. Here, we offer an alternative biogeographic scenario that provides a more plausible explanation for the occurrence of the Australian taxa. We suggest that the Australian lineages represent mid-Cretaceous remnants of clades that were widespread during the Early Cretaceous, with these lineages entering East Gondwana via dispersal from South America (presumably across Antarctica).