Inferring ancestral range reconstruction based on trilobite records: a study-case on Metacryphaeus (Phacopida, Calmoniidae)

Metacryphaeus is a calmoniid trilobite genus from the Devonian Malvinokaffric Realm, exclusive to the Gondwanan regions. It includes eleven species, which are for the first time included here in a single phylogenetic analysis. The resulting hypotheses establish relations among the Metacryphaeus species with few ambiguities, also suggesting the inclusion of both Plesiomalvinella pujravii and P. boulei within the genus, as originally considered. The results of palaeobiogeographic analyses employing the Dispersal-Extinction-Cladogenesis (DEC) model reinforce the hypothesis that Bolivia and Peru form the ancestral home of Metacryphaeus. The radiation of the genus to other Gondwanan areas took place during transgressive eustatic episodes during the Lochkovian–Pragian. The Lochkovian dispersal occurred from Bolivia and Peru to Brazil (Paraná and Parnaíba basins) and the Falklands, and Pragian dispersal occurred towards South Africa. Dispersal events from Bolivia and Peru to the Parnaíba Basin (Brazil) were identified during the Lochkovian–Pragian, suggesting the presence of marine connections between those areas earlier than previously thought.


Results and Discussion
Phylogeny. The parsimony analysis resulted in two MPTs of 132 steps (consistency index = 0.41 and retention index = 0,52; Fig. 4). The only topological difference between these two trees is the placement of Metacryphaeus branisai. The strict consensus is presented in Fig. 5, along with bootstrap probabilities and Bremer decay indices for each node.
Plesiomalvinella boulei and P. pujravii were found deeply nested within a clade of Metacryphaeus species. Accordingly, those two species are here referred to that genus, as previously proposed by Wolfart 13 . Metacryphaeus (including M. boulei and M. pujravii) is here supported by two synapomorphies: frontal lobe projecting beyond the cephalic anterior border in dorsal view (character 4) and uniformly divergent axial furrows from SO to the cephalic margin (character 19).
The present analysis recovered the clades formed by Metacryphaeus giganteus + M. parana (Figs 4 and 5) and M. boulei + M. pujravii (Figs 4 and 5), previously recognized by Lieberman 5 . Synapomorphies of the M. giganteus + M. parana clade are: 60 to 70% ratio between the basal glabellar width and the glabellar length (character 9), convergently acquired in Clarkeaspis; slender genal spine (character 36); dorsoventral height of the pygidium gradually decreasing posteriorly (character 39); 0.65 to 0.80 ratio between the maximum pygidial axial width and the maximum pygidial axial length (character 42). The M. boulei + M. pujravii clade is supported by six synapomorphies which are related to the presence of two symmetrical rows of sagittal spines on the posterior part of the glabella (character 15), the presence of one or two spines on L1 and L2 (characters 17 and 18), 0.15 and 0.25 ratio between the distance of posterior margin of the eyes to the axial furrow and the maximum glabellar width (character 25), the presence of four or five spines on the thoracic axial rings (character 37), and the prosopon covered by spines (character 48).
Our study also recovered new hypotheses for the relationships of Metacryphaeus, including a clade formed by M. allardyceae, M. caffer, M. australis, M. meloi, M. kegeli, and M. tuberculatus. This is supported by four synapomorphies related to the shape and extension of the (cranidial) cephalic anterior border (characters 2 and 3), the ratio between the sagittal length of L1 and the glabellar sagittal length (character 14), and the incision of the occipital furrow medially (character 29). The clade including M. caffer, M. australis, M. meloi, M. kegeli, and M. tuberculatus is supported by four synapomorphies (Fig. 4a): glabella posteriorly elevated and declined anteriorly to S3 (character 8); 65 to 75° α angle (character 22); rounded pygidial terminus (character 45); no spine on the pygidial terminus (character 46). Also, the clade formed by M. tuberculatus, M. meloi, and M. kegeli is supported by four synapomorphies related to L2 and L3 that do not merge distally (character 13), 55 to 64° β angles (character 23), the connection of S2 and the axial furrow (character 24), and the lack of connection between the anterior margin of the eyes and the axial furrow (character 26) (Fig. 5). Two synapomorphies support the M. caffer plus M. australis clade: characters 9 (reverted to the plesiomorphic condition) and 41, which are respectively related to a ratio greater than 80% between the basal glabellar width and the glabellar length, and to 0.25 to 0.35 ratios between the maximum pygidial axial width and the maximum pygidial width.
The  (Fig. 4), probably because its pygidium is unknown, implying the non-codification for characters 38 to 47. In the phylogeny modelled by Lieberman 5 , Metacryphaeus convexus and M. curvigena are not considered sister taxa to all other Metacryphaeus. Instead, M. curvigena is considered the sister taxon to M. branisai and M. convexus the sister taxon to both (Fig. 1a). In our analysis, the clade formed by M. convexus and M. curvigena is supported by five synapomorphies: inclination of 10-20° of S3 in relation to SO (character 12); L2 and L3 not merged distally (character 13); cephalic axial furrows deep and broad (characters 20 and 21); evident connection between S2 and the axial furrow. Likewise, the affinities of M. meloi and M. kegeli are supported by four synapomorphies. This is interesting because these species are endemic to the Parnaíba Basin (Brazil), as is their sister-taxon M. tuberculatus, the only other species of the genus known to that basin. Palaeobiogeography. Likelihood Ratio Test supports DEC M2 (w and j set as free parameters) as the best-fit model to our data ( Table 1). The palaeobiogeographic reconstructions differ only slightly for the two MPTs, so we focus the discussion on the first MPT. The summary of biogeographic stochastic mapping (BSM) counts (Table 2) shows a predominance of dispersals among range change events (33.6% of total events) and, among those, founder events (19.6%) are slightly more frequent than anagenetic dispersals (14.1%). Vicariance was very uncommon according to our model, accounting only for 3.9% of the events ( Table 2). Most dispersals occurred from Bolivia and Peru (A) to other areas, more frequently to the Paraná (B) and Parnaíba (E) basins (Table 3).
All three models estimate a 100% probability for Bolivia and Peru (A) as the ancestral area for the Metacryphaeus clade, as well as for most of its internal clades ( It is interesting to note that those dispersal and expansion events likely occurred before the transgressive events on western Gondwana 14-17 dated between the late Pragian and the early Emsian (Fig. 6). Those areas (A, B, C, D) were eventually connected by transgressive-regressive cycles (Fig. 6), which promoted the faunal similarity observed among the Malvinokaffric fauna of the Early Devonian 15,18 .
The last common ancestor of Metacryphaeus meloi, M. kegeli, and M. tuberculatus, and the node including only the latter two taxa were reconstructed with two almost equal probable ranges, either restricted to Bolivia and Peru (A) or a joint distribution (Fig. 6) also including the Parnaíba and Paraná basins (ABE). These different The arrival of Metacryphaeus in the Parnaíba Basin may have occurred via two alternative routes (Fig. 6). A northern route (surrounding the northern margin of the South American continent) would impose no continental (landmass) barriers, but there would be climatic barriers related to the warmer waters the animals would need to overcome, as the Malvinokaffric Realm marks cooler areas. Also, faunas of this age on the northern margin of South-America belong to other realms, which lack Metacryphaeus. On the other hand, a route through the Amazon Basin (Fig. 6) would have presented no climatic or faunal barriers (cf. 15,18,19 ). Even a continental barrier might not have been in place, as there were transgression events possibly connecting that basin to Bolivia and Peru. The lack of fossils of this age in the Amazon Basin, which could confirm such a dispersal route, is related to the depositional gap present in the upper Lochkovian and lower Emsian of the basin (cf. [20][21][22][23][24][25] ). This absence of Lochkovian-lower Emsian rocks is also observed in the Parnaíba Basin 20,21,24 , which hinders palaeobiogeographical inferences related to the presence/absence of Metacryphaeus in the Lower Devonian of this basin.     and Paraná basins were recurrent by the Middle Devonian (e.g. 15,26 ). However, the dispersal and range expansion events highlighted in our biogeographic analyses (except that related to M. caffer dispersal from the Paraná Basin to South Africa) occurred during the late Lochkovian (Fig. 6). As such, our data suggest an earlier connection between all those Gondwanan regions, allowing Metacryphaeus trilobites to expand into the Paraná and Parnaíba basins via southeastern and northern/northeastern routes, respectively (Fig. 6). Another interesting fact is the diversification of Metacryphaeus in South America occurring earlier than its dispersal to South Africa (where it is represented by M. caffer). This was temporally the latest dispersal of the genus, taking place during the Pragian, and a separate event from the dispersal of M. allardyceae in the same direction (to the Falkland Islands), which occurred earlier. Among the 48 characters employed here (see Appendix 1), 33 were taken or modified from Lieberman 5 and 15 are new (characters 7, 9, 12, 13, 14, 22, 23, 24, 25, 26, 27, 34, 40, 41, and 42), although based on characters used in phylogenetic analyses of other trilobite groups (e.g. [35][36][37][38][39][40][41][42]. The morphological elements of the exoskeleton are shown in Fig. 7 and all morphological relations/angles used in the 15 newly proposed characters were measured as indicated in Fig. 8.

Methods
Among the characters taken from Lieberman 5 , some scores were changed for some taxa based on our own interpretations. This is the case for characters 5 (changed from 0 to 1 in Malvinocooperella pregiganteus, Metacryphaeus giganteus, and Me. branisai), 18 (changed from 0 to 1 in Me. branisai), and 19 (changed from 0 to 1 in Me. giganteus). Other characters from Lieberman 5 , e.g. characters 9, 10, 12, 13, 19, 23, 24, and 34, were not used here because they either have too much variation between individuals of the same species or can be easily affected by taphonomic deformation. Some characters from Lieberman 5 were split into two or more characters, as in case of characters 2 and 3 (=character 1 of Lieberman 5 ), 20 and 21 (=character 18 of Lieberman 5 ), 30 and Characters 1 to 36 are related to the cephalon, character 37 to the thorax, 38 to 47 to the pygidium, and 48 to the prosopon (Appendix 1 and 2). All characters are related to the dorsal surface of the exoskeleton and were treated as ordered. The data matrix was analyzed in search of the Most Parsimonious Trees (MPTs) using the software TNT version 1.1 44 . A heuristic search was conducted with 1,000 replicates, random addition of taxa (random seed 0), Tree Bisection and Reconnection (TBR) as branch swapping algorithm, and "hold" of 10 trees per replica. The recovered MPTs were summarized in a strict consensus tree. Bremer 45 decay indices and bootstrap proportions 46 were calculated using scripts incorporated in TNT. The data matrix was compiled in NEXUS format using the software Mesquite version 3.03 (702) and the tree images were generated with the software FigTree version 1.4.2.
Palaeobiogeographical analysis. We conducted palaeobiogeographic analyses to explore the distribution dynamic and biogeographical events that affected Metacryphaeus distribution through time in five areas pre-defined based on the known occurrences genus: Bolivia and Peru (A); Paraná Basin, Brazil (B); South Africa (C); Falkland Islands (D); and Parnaíba Basin, Brazil (E). Bolivia and Peru were treated as a single area due to their geographical proximity, strong palaeontological association, and co-occurrence of endemic species 2,47 . Only fossil taxa with accurate occurrence data and taxonomic identification were included. For this reason, taxa with doubtful assignation (cf., aff.) were not considered in our analyses (e.g. 48 ). Ancestral area reconstructions were conducted using R (R Development Core Team 2013) package BioGeoBEARS 49 , which allows comparing the likelihood of our data given distinct models, choosing that with better fit 50 . We tested three nested models based on the LAGRANGE Dispersal-Extinction-Cladogenesis (DEC) model 51,52 : M0 contains the default parameters of the DEC models 49 ; M1 has the addition of the free parameter w; and M2 has the addition of the free parameters w and j. The free parameter w is a multiplier of the dispersal matrices and when set to 1 (e.g. in M0) the probabilities of dispersal events are based solely on the dispersal matrices and equal across all events 53 . The founder-event parameter j (included only in M2 and set to 0 in M0 and M1) allows range changes to areas distinct to that of the ancestor during a cladogenetic event 49 . We employed the Likelihood Ratio Test (LRT) to select the best model.
We used time-calibrated versions of the two MPTs, dividing them into two time slices, Silurian to Lower Devonian (430-395 Ma) and Middle to Upper Devonian (395-382 Ma). Based on that, we conducted a time-stratified analyses using time-specific dispersal multiplier and area matrices (see Supplementary supple 2 and supple 3). This allowed changing the distances and probabilities between the areas along these periods, simulating the continental transformations.
We also conducted a biogeographic stochastic mapping (BSM) on BioGeoBEARS 54 to estimate the number and type of biogeographical events. We conducted the BSM only for the first MPT, as the ancestral area reconstruction of both MPTs differ only slightly, and employed the parameters of the best-fit model of the ancestral area reconstruction 53 . The mean and standard deviation of event counts of 100 BSMs were used to estimate the frequencies of range change between the considered areas and of each kind of biogeographic event. The ancestral area reconstructions for Metacryphaeus show dispersal events occurring earlier than expected, i.e. during the Early Devonian, even though the faunal similarities of Bolivia and Peru with the Parnaíba and Amazon basins are more prominent in the Middle Devonian, with the sharing of brachiopod (Tropidoleptus and Australocoelia), crinoid (Exaesiodiscus, Laudonomphalus, Monstrocrinus, and Marettocrinus), and other trilobite (Eldredgeia and Burmeisteria) taxa. The results presented here indicate that these areas were also somehow connected during the beginning of the Devonian, as to allow the dispersal of Metacryphaeus.

Data Availability
The datasets analyzed during the current study are available in: https://figshare.com/s/6b42cf2d4d0cadde7e11.