Supplementary Information 1. Supplementary Methods Phylogenetic and age justifications for fossil calibrations The justifications for each fossil calibration are presented here for the ‘hornworts-sister’ topology (summarised in Table S2). For variations of fossil calibrations for the other hypothetical topologies, see Supplementary Tables S1-S7. Node 104: Viridiplantae; Chlorophyta – Streptophyta: 469 Ma – 1891 Ma. Fossil taxon and specimen: Tetrahedraletes cf. medinensis [palynological sample 7999: Paleopalynology Unit, IANIGLA, CCT CONICET, Mendoza, Argentina], from the Zanjón - Labrado Formations, Dapinigian Stage (Middle Ordovician), at Rio Capillas, Central Andean Basin, northwest Argentina [1]. Phylogenetic justification: Permanently fused tetrahedral tetrads and dyads found in palynomorph assemblages from the Middle Ordovician onwards are considered to be of embryophyte affinity [2-4], based on their similarities with permanent tetrads and dyads found in some extant bryophytes [5-7] and the separating tetrads within most extant cryptogams. Wellman [8] provides further justification for land plant affinities of cryptospores (sensu stricto Steemans [9]) based on: assemblages of permanent tetrads found in deposits that are interpreted as fully terrestrial in origin; similarities in the regular arrangement of spore bodies and size to extant land plant spores; possession of thick, resistant walls that are chemically similar to extant embryophyte spores [10]; some cryptospore taxa possess multilaminate walls similar to extant liverwort spores [11]; in situ cryptospores within Late Silurian to Early Devonian bryophytic-grade plants with some tracheophytic characters [12,13]. The oldest possible record of a permanent tetrahedral tetrad is a spore assigned to Tetrahedraletes cf. medinensis from an assemblage of cryptospores, chitinozoa and acritarchs collected from a locality in the Rio Capillas, part of the Sierra de Zapla of the Sierras Subandinas, Central Andean Basin, north-western Argentina [1]. Minimum age: 469 Ma. Soft maximum age: 1891 Ma. Age justification: The minimum age constraint is based on a palynological sample containing the oldest tetrahedral tetrad, collected from strata in the transition between the upper part of the Zanjón Formation and the Laja Morada Member of the Labrado Formation (level 7999, fig. 1, [1]). This sample was assigned to the Dapinigian Stage of the Middle Ordovician, based on the presence of the chitinozoan Lagenochitina combazi, a biostratigraphical marker of the L. combazi Biozone of southern China [14]. At the Dapingian type sections in the Yichang area of China, the local L. combazi Biozone begins within 1m above the GSSP of the base of Dapingian, as defined by the FAD of the conodont Baltoniodus triangularis [15, 16], currently dated at 470.0 Ma ± 1.4 Myr [17]. The top of the combazi Biozone has been correlated closely to the boundary between the chitinozoan D. ornensis and B. henryi Biozones of Northern Gondwana [14, 18]. Dated at 469 Ma [17], this boundary is the youngest possible age for the top of the correlated L. combazi Biozone, and thus the minimum age of the tetrahedral tetrad record from Argentina, 1 Myr after the beginning of the Dapingian Stage/ Middle Ordovician. The soft maximum constraint is based on the earliest record of eukaryotes [19-21] when, despite the presence of simple eukaryotes, there is no evidence of anything as complex as a multicellular alga. Though the fossils present have been suggested by some to represent some kind of green algae [22]. The maximum age for this formation is based on the igneous and metamorphic rocks that it overlies. These rocks are dated at 1823 Ma ± 68 Myr [23]. Discussion: Parfrey et al. [24] identify Palaeastrum and Proterocladus, from the early Neoproterozoic Svenbergfjellet flora of Spitsbergen [25] as charophytes. However, though the characteristics of these fossils are compatible with Chlorophyaceae, their simple morphology precludes unequivocal assignment to Viridiplantae [26]. Claims of chlorophytes in the Ediaracan Miahoe Biota [27] are even more speculative. Amgaella, Palaeoporella, Yakutina and Seletonella, among many other Cambrian and Ordovician records [28, 29], have variously been considered the oldest Dasycladales, or siphonous algae (Bryopsidales and Dasycladales) [28-30], however, even their algal affinity has been considered uncertain [28, 29]. Palaeocymopolia silurica is considerably younger, but its anatomy is well characterized. Node 205: Chlorophyceae – Prasinophyaceae: 438.3 Ma – 1891 Ma. Fossil taxon and specimen: Palaeocymopolia silurica [TUG 1269-9 (holotype): Natural History Museum of the University of Tartu, Estonia], from the Aeronian (Llandovery; Silurian) Raikküla Stage at a quarry near Kalana, Estonia [31]. Phylogenetic justification: Mastik and Tinn [31] draw comparison between Palaeocymopolia silurica and living dasycladealean Cympolia species based on the shared presence of ‘thalli with dichotomously branching, serially segmented form, segment size, and shape, and size and morphology of filaments in the tufts’ [p. 6: 31]. Minimum age: 438.3 Ma. Soft maximum age: 1891 Ma. Age justification: The Kalana Lagerstätte occurs within the Pribylograptus leptotheca graptolite Biozone [32]. The minimum age can therefore be determined by the base of the succeeding Lituigraptus convolutes graptolite Biozone, dated to 439.21 Ma ± 0.9031 Myr, thus, 438.3 Ma. The soft maximum constraint is based on the earliest record of eukaryotes [19-21] when, despite the presence of simple eukaryotes, there is no evidence of anything as complex as a multicellular alga. Though the fossils present have been suggested by some to represent some kind of green algae [22]. The maximum age for this formation is based on the igneous and metamorphic rocks that it overlies. These rocks are dated at 1823 Ma ± 68 Myr [23]. Discussion: This is the divergence between Uronema versus Nephroselmis, Monomastix, and Pyramimonas, the former a member of the monophyletic Chlorophyceae, and the latter members of the paraphyletic Prasinophyaceae. Hence, we base our node calibration on the oldest certain Chlorophyceae, for which we use the oldest certain record of Dasycladales. Node 105: Streptophyta; Charophyta – Embryophyta: 469 Ma – 1891 Ma. Fossil taxon and specimen: Tetrahedraletes cf. medinensis [palynological sample 7999: Paleopalynology Unit, IANIGLA, CCT CONICET, Mendoza, Argentina], from the Zanjón - Labrado Formations, Dapinigian Stage (Middle Ordovician), at Rio Capillas, Central Andean Basin, northwest Argentina [1]. Phylogenetic justification: Permanently fused tetrahedral tetrads and dyads found in palynomorph assemblages from the Middle Ordovician onwards are considered to be of embryophyte affinity [2-4], based on their similarities with permanent tetrads and dyads found in some extant bryophytes [5-7] and the separating tetrads within most extant cryptogams. Wellman [8] provides further justification for land plant affinities of cryptospores (sensu stricto Steemans [9]) based on: assemblages of permanent tetrads found in deposits that are interpreted as fully terrestrial in origin; similarities in the regular arrangement of spore bodies and size to extant land plant spores; possession of thick, resistant walls that are chemically similar to extant embryophyte spores [10]; some cryptospore taxa possess multilaminate walls similar to extant liverwort spores [11]; in situ cryptospores within Late Silurian to Early Devonian bryophytic-grade plants with some tracheophytic characters [12,13]. The oldest possible record of a permanent tetrahedral tetrad is a spore assigned to Tetrahedraletes cf. medinensis from an assemblage of cryptospores, chitinozoa and acritarchs collected from a locality in the Rio Capillas, part of the Sierra de Zapla of the Sierras Subandinas, Central Andean Basin, north-western Argentina [1]. Minimum age: 469 Ma. Soft maximum age: 1891 Ma. Age justification: The minimum age constraint is based on a palynological sample containing the oldest tetrahedral tetrad, collected from strata in the transition between the upper part of the Zanjón Formation and the Laja Morada Member of the Labrado Formation (level 7999, fig. 1, [1]). This sample was assigned to the Dapinigian Stage of the Middle Ordovician, based on the presence of the chitinozoan Lagenochitina combazi, a biostratigraphical marker of the L. combazi Biozone of southern China [14]. At the Dapingian type sections in the Yichang area of China, the local L. combazi Biozone begins within 1m above the GSSP of the base of Dapingian, as defined by the FAD of the conodont Baltoniodus triangularis [15, 16], currently dated at 470.0 Ma ± 1.4 Myr [17]. The top of the combazi Biozone has been correlated closely to the boundary between the chitinozoan D. ornensis and B. henryi Biozones of Northern Gondwana [14, 18]. Dated at 469 Ma [17], this boundary is the youngest possible age for the top of the correlated L. combazi Biozone, and thus the minimum age of the tetrahedral tetrad record from Argentina, 1 Myr after the beginning of the Dapingian Stage/ Middle Ordovician. The soft maximum constraint is based on the earliest record of eukaryotes [1-3] when, despite the presence of simple eukaryotes, there is no evidence of anything as complex as a multicellular alga. Though the fossils present have been suggested by some to represent some kind of green algae [4]. The maximum age for this formation is based on the igneous and metamorphic rocks that it overlies. These rocks are