Contemporaneous radiations of fungi and plants linked to symbiosis

Interactions between fungi and plants, including parasitism, mutualism, and saprotrophy, have been invoked as key to their respective macroevolutionary success. Here we evaluate the origins of plant-fungal symbioses and saprotrophy using a time-calibrated phylogenetic framework that reveals linked and drastic shifts in diversification rates of each kingdom. Fungal colonization of land was associated with at least two origins of terrestrial green algae and preceded embryophytes (as evidenced by losses of fungal flagellum, ca. 720 Ma), likely facilitating terrestriality through endomycorrhizal and possibly endophytic symbioses. The largest radiation of fungi (Leotiomyceta), the origin of arbuscular mycorrhizae, and the diversification of extant embryophytes occurred ca. 480 Ma. This was followed by the origin of extant lichens. Saprotrophic mushrooms diversified in the Late Paleozoic as forests of seed plants started to dominate the landscape. The subsequent diversification and explosive radiation of Agaricomycetes, and eventually of ectomycorrhizal mushrooms, were associated with the evolution of Pinaceae in the Mesozoic, and establishment of angiosperm-dominated biomes in the Cretaceous.

The accuracy of absolute divergence times estimated with molecular clocks depends heavily on the reliability of independent temporal calibrations 17 , which are most frequently obtained from the fossil record. For any biological group, the availability of useful fossil calibrations depends on the combination of biological factors responsible for the evolution of distinctive morphological features that allow unequivocal clade recognition, and of taphonomic factors that regulate the probability that these distinctive features become preserved as fossils. The utility of available fossils as calibrations also depends on the density of sampling in a phylogenetic tree. Insufficient sampling may preclude accurate recognition of the fossil's phylogenetic position. However, even if its phylogenetic relationship is correctly recognized, its associated temporal information may become irrelevant as the fossil will be placed in a long branch whose subtending node will be much older than the minimum age that the fossil provides. Estimates of most divergence times for land plants have been stable since 2005. This convergence of estimates from various studies can be explained in part by the number, distribution through time, and the taphonomic quality of the fossil record for plants. For fungi, estimations of absolute divergence time have varied greatly among studies. Overall, data sets leaned more heavily toward using multiple loci and few taxa than vice versa. The number of species included in studies published before 2007 ranged from 15 species when based on many genes, to usually fewer than 50 species when based on a single locus (nrRNA gene). The various combinations of using a relatively low number of taxa, low number of genes, and divergence time estimation methods assuming a molecular clock led to drastically different estimations across mycological studies published pre-2007. Here we estimated divergence time based on a data set of six gene regions for nearly 200 fungal species 18 , with representation of fungal phyla more or less proportional to their species richness. Divergence times were estimated using a Bayesian approach 19 and taking into consideration all available fossil records (see Supplementary Note 1). Our estimated divergence times for the fungi converged on the estimations obtained independently from three other studies [14][15][16] . The recent convergence of divergence time estimates for fungi is a combination of the availability of more comprehensive data sets, in terms of both taxon and locus sampling, and better analytical methods 19 . Numbers in parentheses following each citation along the X axes refer to the order in which they appear in the list of Supplementary References.

Supplementary Figure 2.
Detailed chronogram for fungi, depicting median divergence times and associated error (95% highest posterior density) for all nodes. The names of all representative species selected for this study, preceded by their Assembling the Fungal Tree of Life (AFToL) numbers, are shown at the tips of the tree. Numbers with grey shading refer to monophyletic groups listed to the left of the tree. Each taxon name listed on the left of the tree is followed by its known species-richness (in parentheses). Nodes labeled A to M were constrained with age priors as described in the Methods and Supplementary Note 1. The node labeled R indicates the root of the tree. Figure 3. Detailed chronogram for plants, depicting median divergence times and associated error (95% highest posterior density). Numbers with grey shading refer to monophyletic groups listed to the left of the tree, followed by their species richness (in parentheses). Nodes labeled A to Z and a to o were constrained with age priors as described in the Methods and Supplementary Note 2.

Supplementary
Supplementary Figure 4. Topology of fungi, indicating the number of species assigned to each monophyletic group 20 , and used in the diversification analysis in MEDUSA 21 . The height of the terminal cones is proportional to the number of species included in Fig. 1 Figure 5. Topology of plants, indicating the number of species assigned to each monophyletic group [22][23][24][25][26] , and used in the diversification analysis with MEDUSA 21 . The height of the terminal cones is proportional to the number of species included in Fig. 1. Table 1. Estimated species richness 20 , median age, and 95% highest posterior density (HPD) of major fungal clades (crown nodes). Numbers in the first column correspond to clades listed in Fig. 1. These results can also be visualized in Supplementary Fig. 2 Supplementary Table 5. Summary of posterior distribution of differences in divergence times between selected plant and fungal clades (all ages are in millions of years; see Fig. 2).* * The mean difference in the absolute value of the estimated fungal (F) and plant (P) ages, along with credible intervals, is shown under F-P. For each pair of clades, the right portion of the table shows the posterior probabilities that the times of fungal and plant divergences differ in absolute value, by less than, or by more than, six different amounts (x = 1, 5, 10, 20, 40, and 60 million years).

Supplementary Note 1: Fossil constraints for fungi
List of constraints on fungal tree, corresponding to yellow nodes on Supplementary Fig. 2.
Node A: Fungal bodies of the genus Colletotrichum were found in dung of the dinosaur Isisaurus from the Upper Cretaceous. The authors 27 placed the genus in the family Melanconiaceae (Deuteromycetes). Members of Colletotrichum are anamorphs of the genus Glomerella, a genus currently placed in the order Glomerellales (Sordariomycetes) 20 . Therefore, a minimum age constraint of 65.2 Ma was applied to the most recent common ancestor (MRCA) of the Sordariomycetes (see Supplementary Fig. 2). Extant Colletotrichum species are parasites of diverse angiosperms and some Pinaceae, with many species occurring as endophytes.
Node B: Paleopyrenomycites devonicus Taylor, Hass, Kerp, Krings et Hanlin was found in the cortex of aerial stems and rhizomes of the 400 Ma fossilized vascular plant Asteroxylon from the Rhynie Chert 28 . Due to the presence of a perithecial ascoma, an apparently unitunicate ascus, and some centrum features more in common with Xylaria-type centrum development, the fossil appears to have close affinities with extant pyrenomycetes (currently Sordariomycetes). A minimum age constraint of 404.2 Ma was applied to the node from which the Sordariomycetes diverged. 29 dating from the Early Oligocene (55 Ma) to Late Eocene (35 Ma). Because of the exceptional preservation of organisms in amber, the fossil could be identified to the species level. The genus is placed in the family Anziaceae or Parmeliaceae (s. auct.), order Lecanorales. A minimum age constraint of 33.8 Ma was applied to the basal node of a clade including Parmeliaceae and other members of the order Lecanorales.

Node C: Anzia electra Rikkinen & Poinar is a lichenized fungus that was found in Baltic amber
Node D: Aspergillus collembolorum Dörfelt & A.R. Schmidt was found overgrowing a springtail (suborder Entomobryomorpha) in Baltic amber 30 . Excellent preservation of the hyphae and conidiophores allowed the placement of the fossil within the genus Aspergillus (Trichocomaceae, Eurotiales, Eurotiomycetidae, Eurotiomycetes). A minimum age constraint of 33.8 Ma was applied to the node leading to the divergence of Aspergillus and Monascus.
Wunderl. specimens were found in Baltic and Bitterfield amber 31 . As the Bitterfield amber was suggested to have originated by transport and re-deposition of Baltic amber during the Miocene [32][33] , all fossil specimens found in Bitterfield amber should also be 55-35 Ma. Several preserved features showed similarities with extant Metacapnodium (Metacapnodiaceae, Capnodiales, Dothideomycetes) and supported the placement of the fossils within that genus. A minimum age constraint of 33.8 Ma was applied to the basal node of a clade including Capnodiales and Dothideales.
Node F: A Xylaria species was found in Dominican amber dating from the Eocene to the Miocene period 34 . A minimum age constraint of 15.97 Ma was applied to the node that leads to the divergence of the Xylariales.  3 Ma should have been applied to the node from which the Tricholomataceae diverged, however, because that clade was not wellsupported, the constraint was place on the immediate well-supported node deeper in the phylogeny.
Node I: A permineralized ectomycorrhizal fungus was found in association with roots of Pinus in the Princeton Chert of the Middle Eocene 37 . Several features such as presence of a Hartig net and corraloid clusters, and an absence of clamp connections on the emanating hyphae, suggested a close relation of the fungal fossil to Basidiomycota extant genera Rhizopogon and Suillus, both in the Boletales. A minimum age of 40.2 Ma was applied to the node from which the Boletales diverged.
Node J: Quatsinoporites cranhamii Smith, Currah et Stockey is an Early Cretaceous (Barremian) basidiomycete preserved in marine calcareous nodules 38 . It was placed in the family Hymenochaetaceae (Hymenochaetales) due to the poroid hymenophore, the presence of setae, and a monomitic hyphal system lacking clamp connections. A minimum age of 124 Ma should have been applied to the node from which the Hymenochaetaceae diverged, but because that clade was not well supported, the constraint was place on the next, deeper, well-supported clade.
Node K: Glomites rhyniensis Taylor, Remy, Hass et Kerp represents an arbuscular endomycorrhiza in association with the Early Devonian plant Aglaophyton 39 . The authors are almost certain that Glomites belong to the family Glomaceae (currently Glomeraceae) with several characters in common with Glomus. A minimum age of 404.2 Ma was applied to the node from which Glomeraceae diverged.
Node L: Protoascon missouriensis Batra, Segal et Baxter was found associated with the charophyte Palaeonitella in Middle Pennsylvanian permineralization. The fossil represents a Zygosporangium-suspensor complex of a zygomycete comparable to some modern Mucorales 40 . A minimum age of 305.5 Ma was applied to the node from which the Mucorales diverged.

Root (node R):
We applied a lognormal prior distribution on the age of the root of the phylogeny that placed 90% of the prior density between 501 Ma and 1965 Ma ( Supplementary Fig. 2).

Supplementary Note 2: Fossil constraints for Viridiplantae
Root: Age of the MRCA between Rhodophyta and Viridiplantae was estimated in a study of the timing of early eukaryotic diversification 42 . The tree model root height was assigned a uniform prior between 1394 and 1623 Ma, corresponding to the 95% HPD estimated for the MRCA between Rhodophyta and Viridiplantae in Tree E of Parfrey et al. (2011) 42 . This tree was estimated including the largest taxonomic sample in their analysis (109 taxa), using Proterozoic and Phanerozoic fossils as calibrations, considering the calibration for Rhodophyta (Bangiomorpha) to be 1174 Ma, and simultaneously estimating the root of the tree. The prior for the height of the root of the tree was obtained from a uniform distribution between 1394 and 1623 Ma.
Node A: Rhodophyta crown node calibrated with Bangiomorpha pubescens Butterfield, from the late Mesoproterozoic [43][44] . Bangiomorpha pubescens has been considered as the oldest taxonomicallyresolved fossil eukaryote. Its diagnostic characters are the "fourfold radially symmetrical arrangement of wedge-shaped cells that constitute most multisertiate filaments. This arrangement documents the unique pattern of longitudinal intercalary cell division that is otherwise known only in modern Bangia. Likewise, the hierarchical pairing of cells in uniseriate filaments documents the bangiaceaen habit of diffuse growth whereby all vegetative cells contribute to initial filament elongation through transverse intercalary cell division (vs. the apical growth of most other algae and filamentous cyanobacteria)." 43 . Bangiomorpha pubescens was compared with potentially related taxa, including Cyanobacteria, Schizomeridaceae, Porphyridales and the Prasiolalean chlorophyte Rosevingiella, but was found to be almost indistinguishable from the modern bangiophyte red algae Bangia 43 . However, as noted by Yang et al. (2015) 45 "several Bangiomorpha-like, simple filamentous species occur among the deeply diverging Compsopogonophyceae (i.e., Compsopogon, Compopogoniopsis, Erythrotrichia, Rhodochaete) and Stylonematophyceae (i.e., Bangiopsis, Purpureofilum, Stylonema)". Their interpretation is that Bangiomorpha "associates with any one of a number of the deep red algal lineages, possibly even an extinct lineage that evolved characters in parallel to the Bangiophyceae and Compsopogonophyceae. Therefore, it would not be unreasonable to place the Bangiomorpha constraint as a stem taxon to the early branching lineages of red algae." 45 . Bangiomorpha pubescens was found in the Hunting Formation from NW Somerset Island, arctic Canada, in a Proterozoic sedimentary basin. The Hunting Formation is bracketed between 1267-723 Ma based on detailed stable isotope chemostratigraphy, and litho-and biostratigraphy correlations with Mesoproterozoic units in the nearby Baffin Island and Greenland, but a Pb-Pb dating of carbonates from the Hunting-correlative Society Cliffs formation on Baffin Island yielded a more constrained age of 1198 ± 24 Ma [42][43][44]46 Note that the affinity and age of Bangiomorpha pubescens has been debated (e.g., Parfrey et al. 2011 42 ). Its position within the stratigraphic sequence, and other factors would suggest an age closer to 1200 Ma (discussed in Knoll et al. 2013 46 ), whereas a conservatively implemented calibration would require the absolute upper bound of the Hunting Formation, at 720 Ma, as a minimum age 42 . Bangiomorpha pubescens was used to calibrate the crown node of Rhodophyta with a lognormal prior distribution with mean = 4.3239, standard deviation = 0.75, and offset = 1000.
Node B: Prasinophytina stem node was calibrated with Pterospermella spp., from the late Mesoproterozoic/earliest Neoproterozoic 47 . Pterospermella spp. are "oval to circular vesicle consist[ing] of a body surrounded at the equatorial plane by a membrane. The membrane is wide, slightly and transparent and the ratio of overall diameter vs. inner body diameter ranges from 1.3 to 1.8. In some specimens, irregularly distributed thick aristae, up to 99 µm in length, occur." 47 . Pterospermella is similar to extant Pyramimonadales species with a single large ring around the equator of the phycoma. Five specimens of Pterospermella were recorded from the Orlik Fjord and Kap Powell formations of the Dundas Group, and from the Qaanaaq Formation of the Baffin Bay Group, of the Thule Basin in the Canadian-Icelandic shield, which, based on biostratigraphic correlations and independent stable isotope data is of c. 1300 to c. 1200 Ma 47 . Pterospermella spp. were used to calibrate the stem node of Prasinophytina with a lognormal prior distribution with mean = 3.8131, standard deviation = 0.75, and offset = 1200.
Node C: Cladophorales stem node calibrated with species of Proterocladus Butterfield, from the late Riphean (Neoproterozoic) 48 . Proterocladus are "Multicellular, uniseriate and occasionally branched filaments with intercellular septa. Cells thin walled, psilate and cylindrical; length highly variable but typically much longer than wide. Branches usually subjacent to a septum in the primary axis and themselves often septate. Apical terminations simply rounded or capitate." 48 . Proterocladus is considered to be morphologically similar to extant Chlorophyta, in particular the branching septate filaments of Cladophoropsis and Cladophora (Ulvophyceae). It was also compared with simple Rhodophyta (e.g., Rhodoehorton), but Butterfield et al. (1994) 48 considered that the varied cell length in Proterocladus is similar to that in modern Cladophoropsis, whereas its branching pattern and septal structure are similar to those in Cladophora. Butterfield (2009) 49 noted "the generally large cell size (up to 50 m wide and 1000 m long) strongly implies a multinucleate grade of organization" which is consistent with early branching Ulvophyceae. These remains occur in the sediments of the Svanbergfjellet Formation, NE Spitzbergen, which is considered to be 700-750 Ma. Proterocladus spp. were used to calibrate the stem node of Cladophorales with a lognormal prior distribution with mean = 3.2741, standard deviation = 0.75, and offset = 700.
Node D: Sphaeropleales stem node calibrated with Palaeastrum dyptocranum Butterfield, Knoll & Swett, from the late Riphean (Neoproterozoic) 48 . Palaeastrum are spheroidal to ellipsoidal cells with prominent intercellular attachment circular discs with a reinforced rim, which form monostromatic colonies. "The intercellular attachment discs are not simply the product of cell-cell contact but are fully differentiated structures involved in the maintenance of colony structure." 48 . Palaeastrum was described as forming monostromatic colonies from 15 to >100 cells, similar to extant Pediastrum, Hydrodictyon and Coelastrum in grade of multicellular organization, and probably related to sphaeroplealean chlorophytes [48][49] . Palaeastrum was found in the sediments of the Svanbergfjellet Formation, NE Spitzbergen, which is considered to be 700-750 Ma. Palaeastrum dyptocranum was used to calibrate the stem node of Sphaeropleales with a lognormal prior distribution with mean = 3.2741, standard deviation = 0.75, and offset = 700.
Node E: Chlorellales (Trebouxiophyceae) stem node calibrated with Caryosphaeroides pristina Schopf, from the Late Precambrian 50 . Caryospaheroides pristina are spheroidal cells that are solitary or forming small colonies with typical chlorococcoid appearance, similar to modern Chlorococcum or Chlorella 50 . Cells with a single, dense granular body were originally interpreted as a nucleus, but this interpretation was controversial 51 . The cell size (average of 13 μm) and presence of an internal body that was interpreted as a pyrenoid after TEM investigation is consistent with Caryosphaeroides being a green alga [52][53]. Caryosphaeroides pristina was reported from the late Precambrian Bitter Springs Formation, central Australia, which is ca. 800-830 Ma. Age consistent with prior estimated divergence time for group 54 . Caryosphaeroides pristina was used to calibrate the stem node of Chlorellales with a lognormal prior distribution with mean = 3.6308, standard deviation = 0.75, and offset = 1000.
Node F: Embryophytes crown node bounded with a maximum age corresponding to the oldest stem embryophytes (Middle Ordovician, Dapingian 55 ), and a minimum age corresponding to the oldest crown embryophytes (Upper Ordovician 56 ). The maximum age of the embryophyte crown group was bounded by what possibly represent the oldest stem lineage embryophytes, corresponding to assemblages of sporopolleninn-coated monads, dyads and tetrads of cryptospores (spores that lack haptophytic features such as a trilete or monolete mark) with different ornamentations, from Dapingian (early Middle Ordovician) sediments from Argentina (eastern Gondwana 55 ). Their relationship with embryophytes is demonstrated by their ability to produce sporopollenin, which unambiguously represents an attribute of this lineage 55,57 . Their organization as monads, dyads or tetrads, instead as free monads resulting from the dissociation of meiotic tetrads, and the occasional presence of a thin envelope that is difficult to equate with a similar structure among extant plants 57 , suggest that these cryptospores represent embryophyte stem relatives. The minimal age of the embryophyte crown node was bounded by plant fragments including sporangia containing spores, from Ordovician sediments from Oman 56 . Spore wall ultrastructure supports affinities with liverworts, hence, membership into crown group embryophytes 56,58 . The embryophyte crown node was calibrated with a uniform distribution between 485 and 443.8, which correspond to the lower and upper bounds of the Ordovician.
Node G: Metzgeriales stem node calibrated with Metzgeriothallus sharonae VanAller Hernick, Landing & Bartowski, from the Middle Devonian (Givetian) 59 . Metgeriothallus sharonae is the earliest secure liverwort known in the fossil record. It is preserved as a carbonaceous film, and consists of a dorsiventral thallus ca. 32 mm long and 1.5-3.8 mm wide, with a median costa (midrib) and entiremargined wings. The unicellular ribbon-like cells that extend from beneath the costa appear to be typical marchantoid rhizoids. Similarly, the sporophyte capsule that opens with four valves indicates a liverwort 59 . The bifurcating simple thalloid habitus with rhizoids extending from beneath the costa, however, narrow the liverwort appearance to the classic simple thalloid liverworts such as Metzgeria or Pellia. Metzgeriothallus sharonae was found in Middle to Late Devonian Catskill Delta succession. Metzgeriothallus sharonae was used to calibrate the stem node of Metzgeriales with a lognormal prior distribution with mean = 2.6703, standard deviation = 0.75, and offset = 382.7.
Node H: Hypnales stem node calibrated with Capimirinus riopretensis Cortez Christiano de Souza, Ricardi Branco & León Vargas, from the Permian 60 . Dichotomous branching stems with spirally distributed erect-patent-leaves that harbor a well-delimited single costa 60 clearly indicate the fossil as a moss. The leave shape is ovate and slightly asymmetric 60 . The well-preserved sporophyte that is developed at the apex of a short side branch 60 , which defines pleurocarpy, places the fossil at the stem node of the included pleurocarps after the split from the Orthotrichales (compare Bell et al. 2007) 61 . Capimirinus riopretensis was used to calibrate the stem node of Hypnales with a lognormal prior distribution with mean = 2.2531, standard deviation = 0.75, and offset = 252.17.
Node I: Lycophytes stem node (equal to tracheophytes crown node) calibrated with Baragwanathia longifolia Lang & Cookson, from the Upper Silurian (Ludlow) [62][63] . Baragwanathia has been identified as a member of Lycopodiophyta due to the presence of microphylls. Morphology-based phylogenetic analyses placed Baragwanathia on the stem lineage of the extant Lycopodiaceae and Selaginellaceae/Isoetaceae 64 . Baragwanathia was used to calibrate the stem group of Lycopodiophyta (equal to the crown group of tracheophytes) with a lognormal prior distribution with mean = 2.7704, standard deviation = 0.75, and offset = 423.
Node J. Isoletaceae-Selaginellaceae stem node (equal to lycophytes crown node), calibrated with Leclercquia complexa Banks, Bonamo & Grierson, from the Middle Devonian 65 . Morphology-based phylogenetic analyses by Kenrick and Crane (1997) 64 placed Leclerquia in Lycopsida, within a clade that includes the living Isoetaceae and Selaginellaceae, as well as several extinct lineages. Leclerquia was used to calibrate the stem node of Selaginellaceae plus Isoetaceae (equal to the crown group of Lycopodiophyta) with a lognormal prior distribution with mean = 2.6703, standard deviation = 0.75, and offset = 382.7.
Node K: Equisetales stem node calibrated with Ibyka amphikoma Skog & Banks, from the Middle Devonian (Givetian [66][67][68]. Ibyka amphikoma consists of vegetative and reproductive smooth axes that branch pseudomonopodially in three dimensions, and ovoid to pyriform sporangia clustered in terminal pairs. Based on morphology-based phylogenetic analyses, Ibyka was identified as a stem relative of sphenophytes 64 , and represents the oldest member of monilophytes. Ibyka was used to constrain the stem node of Equisetales, which is equal to the divergence between Equisetales and Polypodiales, with a lognormal prior distribution with mean = 2.6703, standard deviation = 0.75, and offset = 382.7. Node L: Osmundaceae stem node (equal to leptosporangiate ferns crown node) calibrated with Thamnopteris schlechtendalii Kidston & Gwynne-Vaughan, from the Upper Permian 69 . Thamnopteris schlechtendalii is a structurally preserved arborescent stem with protostele anatomy, surrounded by a mantle of adventitious roots, similar to that in Osmundaceae 69 . Thamnopteris schlechtendalii was used to calibrate the stem node of Osmundaceae, corresponding to the crown node of leptosporangiate ferns, with a lognormal prior distribution with mean = 2.2531, standard deviation = 0.75, and offset = 252.17.
Node M: Gleichenia stem node calibrated with Gleichenia chaloneri Herendeen & Skog, from the early Albian 70 . Herendeen & Skog (2009) 70 found G. chaloneri to be the sister to Gleichenia glauca; hence, the fossil could calibrate stem node Gleichenia. However, Schuettpelz & Pryer (2009) 71 did not do this, because they considered that presently, Gleichenia is delimited differently. They used G. chaloneri to calibrate a subclade within Gleicheniaceae consisting of Gleichenia, Sticherus and Stromatopteris. However, this clade is represented in our tree only by Gleichenia. Gleichenia chalonerii was used to calibrate the stem node of Gleichenia, with a lognormal prior distribution with mean = 1.3332, standard deviation = 0.75, and offset = 100.5.
Node N: Lygodium stem node calibrated with Stachypteris spicans Pomel from the Middle Jurassic (Bajocian 72 ). Stachypteris spicans were re-studied and described as trilete spores with "rounded-=triangular in equatorial outline: distal surface convex in equatorial view, proximal surface rather flattened: laesurae distinct, reaching almost to the equator, sometimes bordered by an inconspicuous margo: exine thick … distal surface sculptured with muri and irregularly shaped pits, at the bottom of the pits granula visible; proximal surface finely granulate …" 72 . Based on morphological comparisons, Stachypteris spicans was considered most closely similar to reticulate spores of Lygodium 72 . Stachypteris spicans was used to calibrate the stem node of Lygodium, corresponding in our tree to the crown node of Schizaeaceae, with a lognormal prior distribution with mean = 1.8488, standard deviation = 0.75, and offset = 168.3.
Node O: Cyatheaceae stem node calibrated with Cyathocaulis naktongensis Ogura from the Upper Jurassic [73][74] . Cyathocalulis naktongensis is a tree fern stem covered with roots, showing spirallyarranged vascular traces, conspicuously curved meristeles enclosed in schlerenchymatous sheath, numerous medullary bundles mostly close to the center of the pith or near the leaf-gap. Leaf scars are elliptical or fusiform with numerous small bundles, arranged as in living Cyatheaceae 73 . A phylogenetic analysis of extant and fossil tree ferns based on stem anatomy placed C. naktongensis as stem member of a clade that includes Alsophila, Cyathea, Hymenophyllopsis and Sphaeropteris 74 . Cyathocaulis naktongensis was used to calibrate the stem node of Cyatheaceae, with a lognormal prior distribution with mean = 1.6998, standard deviation = 0.75, and offset = 145.
Node P: Pteridaceae stem node calibrated with "Pteris sp." from the Cenomanian 75 . "Pteris sp." are fragments of pinnate leaves with a thin, longitudinally striate rachis that forks distally at an acute angle. Pinnae are alternate, lanceolate, variably dissected, with 1-2 pairs of proximal pinnules. Pinnules are anadromous or catadromous, elliptical to rounded, reduced to lobes in the distal pinnae, with pinnate venation. Fertile pinnae have linear marginal coenosori 75 . Krassilov and Bachia (2000) 75 considered that pinnule morphology and position of the coenosori are typical of the extant genus Pteris. Schuettpelz and Pryer (2009) 71 considered this fossil to be related to Pteridaceae, but not necessarily to genus Pteris. "Pteris sp." was used to calibrate the stem node of Pteridaceae, with a lognormal prior distribution with mean = 1.2652, standard deviation = 0.75, and offset = 93.9.
Node Q: Spermatophytes stem node (equal to euphyllophytes crown node) calibrated with Pertica quadrifaria Kasper & Andrews and P. varia Granoff et al., from the Lower Devonian (Emsian [76][77]. Pertica are distally isotomous, pseudomonopodially branched axes with a decussate lateral branches resulting in a tetrastichious arrangement, and fertile ultimate appendages with terminally-borne clusters of erect sporangia 64,78 . In morphology-based phylogenetic analyses, Pertica is placed within crown euphyllophytes, on lineage leading to seed plants 64 . Pertica quadrifaria was used to calibrate the stem node of spermatophytes (equal to the crown node of euphyllophytes) with a lognormal prior distribution with mean = 2.6976, standard deviation = 0.75, and offset = 393.3.
Node R: Cycads crown node calibrated with Crossozamia Pomel emend. Gao & Thomas, from the Lower Permian [79][80] . Four species of Crossozamia described from compression-impression specimens. The fossils are megasporophylls with fan-shaped to palmate lamina, distal margin divided into tapering segments, with a long and broad stalk, ovoid to oblong ovules attached laterally on each side of the stalk, with one or two ovules borne at proximal lateral margins of the lamina. Hermsen et al. (2006) 80 included Crossozamia in a morphology-based phylogenetic analysis and found it to be sister to extant Cycas. Considering this phylogenetic result, Crossozamia indicates the differentiation of Cycadaceae and Zamiaceae, which corresponds to the cycadophyte crown node. Crossozamia spp. was used to calibrate the crown node of cycads with a lognormal prior distribution with mean = 2.3299, standard deviation = 0.75, and offset = 272.3.
Node S: Conifer stem node (equal to conifers = ginkgophytes crown node) calibrated with Swillingtonia denticulata Scott & Chaloner from the Westphalian B (Middle Pennsylvanian, Carboniferous [81][82]. Swillingtonia denticulata are small leaves and leafy shoots preserved as compressions and charcoal, including epidermal characters, and internal structure. Leaves are hyposotmatic with a denticulate margin, and the lower epidermis has two wide stomatal bands, often with subsidiary cells 81 . Epidermal, stomatal and anatomical features indicate the relationship of these remains to conifers. Swillingtonia denticulata was used to calibrate the stem node of conifers (including gnetophytes), with a lognormal prior distribution with mean = 2.4499, standard deviation = 0.75, and offset = 307.
Node T: Picea stem node calibrated with Picea burtonii Klymiuk & Stockey, and Pinus stem node calibrated with Pinus mundayi Falcon-Lang Mages & Collinson. The calibrations correspond to the divergence between Pinus and Picea in our tree, and both fossils are from the Valanginian [83][84] . Picea burtonii is an anatomically preserved seed cone with a combination of characters present only in Picea. A morphology-based phylogenetic analysis placed Picea burtonii as most closely related to Picea among extant genera 84 . Pinus mundayi are anatomically preserved long shoots with axial resin ducts with thinwalled epithelial cells in the secondary xylem and phloem; fenestriform or pinoid cross-field pits; and helically arranged short-shoots that pass through growth ring boundaries before distally diverging into two separate needle bases. It was interpreted as belonging to an evergreen two-needle pine 83 . The Pinus-Picea divergence was calibrated with a lognormal prior distribution with mean = 1.6126, standard deviation = 0.75, and offset = 132.9.
Node U: Gnetophytes stem node calibrated with Dechellyia gormani Ash, and Maculostrobus clatratus Ash, from the Upper Triassic [85][86] . Dechellyia gormani are sterile and fertile branches with leaves arranged in opposite and decussate pairs, and oval seeds attached to a lanceolate lamina 85 . Masculostrobus clathratus are cones with Equisetosporites-type pollen. Although these organs have not been found in connection, their combined features indicate an affinity with gnetophytes 86 . These fossils are here considered to be stem lineage representatives of gnetophytes, and are used to calibrate their stem node. The stem node of gnetophytes was calibrated with a lognormal prior distribution with mean = 2.0278, standard deviation = 0.75, and offset = 201.3.
Node V: Ephedra stem node (equal to gnetophyte crown node) calibrated with Liaoxia chenii Cao et S.Q. (emend. Rydin, Wu & Friis), and Ephedra archaeorhytidosperma Yang, Geng, Dilcher, Chen & Lott, both from the Early Cretaceous (approximately Barremian [87][88]. Liaoxia chenii corresponds to plants similar to Ephedra with erect striate stems distinct nodes, and opposite decussate branching. Leaves, when present, are linear. Reproductive cones are rounded to ovobate with opposite-decussate bracts, with ovoid to elliptic seeds in the axils of bracts 88 . Ephedra archaeorhytidosperma are fertile branches, including female cones and seeds preserving morphologial and anatomical details, including the mycropilar tube, which can be assigned to Ephedraceae 87 . Liaoxia chenii and Ephedra archaeorhytidosperma are here considered as stem relatives of Ephedra, and used to calibrate the stem node of this genus, equivalent to the crown node of gnetophytes, with a lognormal prior distribution with mean = 1.5513, standard deviation = 0.75, and offset = 125. Node W: Araucariaceae stem node (equal to the divergence between Araucariaceae and Podocarpaceae) calibrated with Araucarites phillipsii Harris and Brachyphyllum mamillare Harris and from the Middle Jurassic (Aalenian [89][90]. Araucarites phillipsii are ovulate cones with seeds fused to the bract for most of its length except at the tip, and covered by cone scale tissue as in extant Araucariaceae 90 . Brachyphyllum mammilare are leaves and attached pollen cones considered to belong to the same plant as Araucarites phillipsii [89][90] . Both taxa show attributes of Araucariaceae 90 . We follow Leslie et al. (2012) 90 in considering both as the earliest fossils that can be confidently assigned to Araucariaceae, and use them to calibrate the stem node of this family with a lognormal prior distribution with mean = 1.8606, standard deviation = 0.75, and offset = 170.3.
Node X: Taxaceae stem node calibrated with Palaeotaxus rediviva Florin, from the Lower Jurassic (Hettangian 91 ). Palaeotaxus rediviva is known from vegetative remains and ovulate cones. Leslie et al. (2012) 90 considered Palaeotaxus rediviva similar to extant Taxaceae in having an axillary shoot with sterile scales that terminates in a single ovule. Palaeotaxus rediviva was here used to calibrate the stem node of Taxaceae with a lognormal prior distribution with mean = 2.0178, standard deviation = 0.75, and offset = 199.3.
Node Y: Angiospermae crown node calibrated with pollen grains with infratectal columellae and reticulate tectum, from the Valanginian-Hauterivian. The age of the angiosperm crown node was bounded uniformly between the age of the oldest fossils that can reliably be assigned to the group, and the oldest bound of the age of this node estimated in a diversification analysis based on fossil occurrences 92 . Pollen grains with infratectal columellae and perforate to reticulate tectum from late Valaginian and Hauterivian sediments [93][94][95] . The presence of a collumellate infratectal structure and the distribution of that attribute among early diverging angiosperm lineages indicates affinity with angiosperms 96 . One among several most parsimonious optimizations is that the columellar infratectum and perforate to reticulate tectum observed in the oldest angiosperm fossil pollen grains evolved within crown group angiosperms. If this reconstruction is correct, then the oldest known angiosperm fossils would be members of the angiosperm crown group [97][98] . We used the Valanginian-Hauterivian age of pollen grains with collumellate infratectum and perforate to reticulate tectum to determine the minimum bound of the confidence interval at 132.9 Ma. The maximum age of the inteval was obtained from the upper bound of the age of the angiosperms estimated with a hierarchical Bayesian model to estimate temporal dynamics of speciation and extinction based on fossil occurrences of angiosperm genera, and which jointly models diversification and preservation potential 92,99 . The age of crown group angiosperms was estimated as having a Laplace distribution centered on 143.8 Ma, and with a 95% HPD between 151.8 and 133.0 Ma 92 . We used the oldest limit of the 95% HPD as the maximum bound of the uniform distribution to calibrate the angiosperm crown node. Therefore, the angiosperm crown node was assigned a uniform prior distribution between 132.9 and 151.8.
Node Z: Nymphaeaceae stem node calibrated with Monetianthus mirus Friis, Pedersen, von Balthazar, Grimm & Crane, from the late Aptian-early Albian [100][101] . Monetianthus mirus is known from a single three-dimensionally preserved flower. It is radially symmetrical, perigynous and apparently bisexual. Based on floral traits, an affinity with Nymphaeaceae was initially proposed 102 , and subsequently confirmed by the type of placentation, ovule number and size, revealed by Synchrotron Radiation X-Ray Tomographic Microscopy SRXTM 100 . Monetianthus mirus is considered as a stem representative of Nymphaeaceae, and was used to calibrate the split between Nymphaeaceae and Cabombaceae, with a lognormal prior distribution with mean = 1.4144, standard deviation = 0.75, and offset = 109.
Node a: Schisandraceae stem node calibrated with Anacostia spp. Friis, Crane & Pedersen, from the late Aptian-early Albian 103 . A phylogenetic analysis conducted by Doyle et al. (2008) 104 placed a consensus of the four species of Anacostia described by Friis et al. (1997) 103 within the Austrobaileyales, as the sister taxon of Schisandra plus Illicium. Anacostia is here considered as a stem representative of Schisandraceae, and is used to calibrate the Schisandraceae stem group, which is equivalent to the Austrobaileyales crown node, with a lognormal prior distribution with mean = 1.4144, standard deviation = 0.75, and offset = 109.
Node b: Chloranthales crown node calibrated with the Asteropollis plant, from the late Barremian to the early Aptian [105][106] . The Asteropollis plant consists of epigynous trigonous pistillate flowers and fruits 105 with attached pollen with a star-shaped aperture, corresponding to Asteropollis 106 , and staminate inflorescence and dispersed stamens. The flowers and pollen are very similar to extant Hedyosmum [105][106] . A phylogenetic analysis indicated the placement of the Asteropollis plant among extant species of Hedyosmum 107 . We consider the Asteropollis plant to represent a stem member of Hedyosmum, hence, it would calibrate the stem node of this genus, which is equivalent to the crown node of Chloranthaceae. Because our analysis included a single terminal for Chloranthales, the Asteropollis plant was used to calibrate the divergence between Chloranthales and Magnoliales with a lognormal prior distribution with mean = 1.5188, standard deviation = 0.75, and offset = 121.  112 ] would allow it to calibrate the crown node of Araceae, but because of the sparse sampling in this analysis, it is used to calibrate the stem node of Alismatales with a lognormal prior distribution with mean = 1.5188, standard deviation = 0.75, and offset = 121.
Node g: Arecaceae stem node calibrated with leaves assigned to Sabal magothiensis Berry and stems assigned to Palmoxylon cliffwoodensis Berry, from the Santonian 113 . Leaves, stems and pollen grains from the Magothy Formation were assigned to Arecaceae 113 . These remains exhibit distinctive attributes of Arecaceae, but can belong to the stem group or the crown group of the family. They were used to calibrate the Arecaceae stem group, with a lognormal prior distribution with mean = 1.1491, standard deviation = 0.75, and offset = 83.6.
Node h: Eudicotyledoneae crown node calibrated with tricolpate pollen grains from the Barremian-Aptian. Tricolpate pollen grains from mid-to late Barremian sediments, and from close to the Barremian-Aptian boundary [114][115][116] . Tricolpate pollen grains unequivocally characterize eudicots (Eudicotyledoneae). The records correspond to isolated tricolpate pollen grains from the middle Atherfield Wealden Bed 35, corresponding to the mid-to late Barremian in the Early Cretaceous succession in southern and eastern England 114 , and to aff. Tricolpites micromurus and aff. Tricolpites crassimurus from Pollen Zone C-VII of the Cocobeach sequence, Gabon, corresponding closely to the Barremian-Aptian boundary [115][116] . Because it is very likely that tricoplate pollen evolved along the stem lineage of eudicots, the fossil tricolpate pollen grains are used to calibrate the stem node of Eudicotyledoneae (equivalent to the split with Ceratophyllales) with a lognormal prior distribution with mean = 1.5513, standard deviation = 0.75, and offset = 125.
Node i: Ranunculales crown node calibrated with Teixeiraea lusitanica von Balthazar, Pedersen & Friis, from the late Aptian 117 . Flowers assigned to Teixeiraea lusitanica are actinomorphic, with helical phyllotaxy, with a moderately differentiated perianth, and stamens of two sizes containing tricolpate pollen with a perforate tectum. No carpels were observed; hence, it is interpreted as a unisexual staminate flower. Von Balthazar et al. (2005) 117 considered it to be related to members of Ranunculales, but a possible affinity with Hamamelidaceae and Daphniphyllaceae (Saxifragales) and Berberidopsidaceae (Berberidopsidales) within Pentapetalae was also considered. Teixeiraea lusitanica was used to calibrate the crown node of Ranunculales with a lognormal prior distribution with mean = 1.4504, standard deviation = 0.75, and offset = 113.  118 . Prototinomiscium spp. are endocarps with features corresponding to Menispermaceae. These fossils could belong to the stem lineage or to the crown group of Menispermaceae, and were used to calibrate the Menispermaceae stem node, with a lognormal prior distribution with mean = 0.9127, standard deviation = 0.75, and offset = 66.
Node k: Platanaceae stem node calibrated with leaves of Sapindopsis variabilis Fontaine; staminate inflorescences and flowers assigned to Aquia brookensis Crane, Pedersen, Friis & Drinnan; and pistillate inflorescences and flowers assigned to Platanocarpus brookensis Crane, Pedersen, Friis & Drinnan, from the early-middle Albian 119 . These detached organs were reconstructed by Crane et al. (1993) 119 as belonging to a single plant taxon, referred to as the Sapindopsis plant. Morphology-based phylogenetic analyses placed the reconstructed Sapindopsis plant as sister to extant Platanus (Platanaceae). The reconstructed plant was considered as a stem representative of Platanaceae, and used to calibrate the Platanaceae stem node with a lognormal prior distribution with mean = 1.3741, standard deviation = 0.75, and offset = 104.7.
Node l: Pentapetalae crown node calibrated with the "Rose Creek Flower", from the latest Albian 120 . The Rose Creek Flower is the oldest fossil showing the distictive floral ground plan of Pentapetalae, including a two-whorled perianth differentiated into distinct calyx and corolla, pentamerous merosity, and radial alternation between the organs of concentric whorls. Stamens are clearly differentiated into filament and anther, and the gynoecium is syncarpous and superior 120 . While its floral ground plan confidently documents an affinity with Pentapetalae, a relationship with any major clade within Pentapetalae is equivocal 101 . We used the Rose Creek Flower to calibrate the crown node of Pentapetalae with a lognormal prior distribution with mean = 1.3332, standard deviation = 0.75, and offset = 100.5.
Node m: Ericales crown node calibrated with Paleoenkianthus sayrevillensis Nixon & Crepet, from the Turonian 121 . Paleoenkianthus sayrevillensis are flowers with five sepals, five petals, eight stamens and four carpels 121 . The combination of its floral traits and anatomical features suggested an affinity with several families of Ericales, especially Ericaceae 121 . This fossil was considered to be related to Clethraceae, Cyrillaceae or Ericaceae, and was used to calibrate the crown node of Ericales with lognormal prior distribution with mean = 1.2206, standard deviation = 0.75, and offset = 89.8.
Node n: Brassicales stem node calibrated with Dressiantha bicarpelata Gandolfo, Nixon & Crepet, from the Turonian 122 . The flowers assigned to Dressiantha bicarpelata exhibit a unique combination of attributes relative to extant taxa, including a gynophore, a 2 + 2 arrangement of the sepals, unequal petals, monothecal anthers, and a bicarpellate gynoecium" 122 . Among extant taxa, this combination occurs only among Capparaceae, Brassicaceae, and related families within Brassicales.
Dressiantha bicarpelata was used to calibrate the stem node of Brassicales, with lognormal prior distribution with mean = 1.2206, standard deviation = 0.75, and offset = 89.8.
Node o: Fagales crown node calibrated with pollen grains of the Normapolles complex, from the middle Cenomanian [123][124][125] . Pollen grains of the Normapolles complex are oblate, triangular in polar view, with protruding, complex apertures and tectate, slighlty sculptured pollen wall 126 . These morphological attributes suggested a general affinity with Fagales, which became very strongly supported by the finding of Normapolles grains in situ structurally preserved flowers with affinities to Juglandaceae/Myricaceae, or Betulaceae, all within the core Fagales. Therefore, Normapolles pollen grains are used to calibrate the crown group of Fagales with a lognormal prior distribution with mean = 1.2998, standard deviation = 0.75, and offset = 97.2.