Accurate reconstruction of the branching order for the major eukaryotic lineages is an extremely challenging task given the low information content of alignments of highly diverged sequences and the compressed cladogenesis that seems to be characteristic of the primary radiation of eukaryotes [5–7]. Dating these ancient divergences using molecular clock methods is even more difficult [1, 2, 19, 20]. First, estimates of divergence dates are only meaningful if the phylogeny they are based upon is correct. Second, molecular dating requires accurate substitution models for the genes under consideration over billion-year time-scales as well as models that account for substitution rate variation across the tree branches [1, 2, 19, 20]. Finally, divergence time estimation obviously requires reliable calibration points (dates) that only can be extracted from the fossil record and are associated with errors of several types including the error inherent in the dating of the associated geological strata; a systematic bias due to the fact that the true divergence date must be older than the first appearance of the descendant taxa in the fossil record; and the error associated with the extrapolation far outside the range of the calibration points that is inevitable in the estimation of ancient divergence times [2, 19].
The use of RGCs has the potential to alleviate at least one of the key sources of error in molecular dating, namely evolutionary rate variation between branches of the tree (violation of molecular clock). Indeed, here we found that the rate of RGC_CA accumulation showed a stronger linear dependence on calibration divergence times inferred from the fossil record than the overall rate of substitution accumulation, suggesting that the RGC_CAs approximate molecular clock better despite the smaller number of data points. Further, cross-validation analysis supports the approximate molecular clock behavior of RGC_CAs because the rates of RGC_CA accumulation are, approximately, the same in the analyzed terminal and internal branches of the tree except for some extreme cases of rate variability. This conclusion is further buttressed by the narrow distribution of the distances from LECA to extant species measured in RGC_CA units.
A specific advantage of the RGC_CA-based dating is that this approach is relatively robust to errors in the branching order. The overall tree topology is not critical: what matters is only the correct topology of four branches involved in a particular estimate (Figure 3). With respect to the latter requirement, to estimate the age of LECA, we assumed that the divergence of plants and animals/fungi is the most ancient event in the evolution of eukaryotes. This assumption is compatible with the results of the eukaryotic root inference by different methods as well as the detailed phylogenetic analyses that led to the proposals of megagroups [13, 16–18].
Different methods used in this study generally produced highly consistent time estimates for the primary divergence of eukaryotes (age of LECA), divergence of the animal phyla, divergence of opisthokonts and the dicot-monocot divergence. The distributions of all estimates span rather narrow time intervals, with the sole exception of the estimates obtained with maximum parsimony and the human-chicken calibration point at 370 Mya (Additional file 3).
The means of the estimates from all employed methods are 339 Mya for the dicot/monocot split; 619 Mya for the radiation of the Bilaterian animal phyla; 949 Mya for the radiation of opisthokonts; 1130 Mya for LECA (Figure 5). The inclusion of the still controversial red algal calibration date  along with the corresponding sequence data predictably pushed all the dates back (Figure 6). Nevertheless, even with this ancient date included, we obtained indications of a "young" age of LECA, with the mean of 1173 Mya (the implication of this estimate is a rapid, explosive post-LECA divergence of the main eukaryotic lineages so that less than 100 million years separates LECA from the appearance of red algae).
The origin and radiation of the angiosperms is a well-known difficult problem that fascinated biologists since the days of Darwin who called it "an abominable mystery" . The current consensus in the plant evolution community seems to be a relatively late crown angiosperm radiation, at 140-180 Mya . Even these estimates predate the appearance of indisputable angiosperm fossils that date to ~120 Mya . Recently, an uncorrelated relaxed-clock analysis yielded an older, late Triassic date of approximately 217 Mya . This date is at the low boundary of the range see in the present work (Figure 5). However, earlier studies that employed phylogenies of individual, highly conserved genes and a careful interpolation from several calibration points gave an estimate of ~300 Mya for the dicot/monocot split, in a good agreement with our present estimates [72–74]. A recent detailed study has dated the origin of the Coleoptera (beetles), i.e., the radiation of the major lineages of the holometabolous insects, earlier than previously suspected, at ~285 Mya . If the radiation of angiosperms indeed predated the insect radiation, as suggested by the comparison of the respective estimates, the attractive hypothesis of plant-insect coevolution and the dependence of insect diversification on herbivory, that has been dismissed owing to the assumed late date of angiosperm radiation , might become relevant again.
The radiation of animal phyla in relation to the Cambrian explosion is possibly an even more controversial matter that the radiation of angiosperms. The appearance of the bilaterian phyla, which constitutes the "explosion proper", has been dated with considerable precision to 542-520 Mya . Several estimates using molecular clock point to substantially older radiation dates: the extensive variation notwithstanding, all these studies estimated the divergence time between protostomes and deuterostomes to be >700 Mya [75, 82, 83], leading to the idea of a long interval of "invisible" animal evolution before the Cambrian explosion. However, the use of Bayesian relaxed molecular clock approaches yielded younger date estimates of 582 +/- 112 Mya  or 642-761 Mya (mean 695)  which are compatible both with the estimate obtained here and with the fossil record. Similar estimates have been obtained in another study that employed molecular clock but used invertebrate rather than vertebrate calibration points . These younger dates have been subsequently questioned on methodological grounds . Nevertheless, a comprehensive analysis using a variety of molecular clock methods combined with Bayesian techniques yielded estimates for the protostome/deuterostome split in the range of 733-641 Mya  which, taking the confidence intervals into account, is compatible with our RGC_CA-based estimate (although the inclusion of the red algal data yields a wider range that at the outside is compatible with ancient divergence long preceding the explosion). These convergent younger dates for the radiation of the bilaterian phyla support the hypothesis that the bilaterian cladogenesis took place during the latest pre-Cambrian period, the Ediacaran (635-542 Mya), whereas skeletons that are best preserved as fossils evolved during the Cambrian, creating the appearance of explosion [63, 86, 87].
The case of the fungi/metazoan split tells a story similar to that of the bilaterian radiation. Molecular clock methods produce date estimates as ancient as 1,600 Mya  but the Bayesian relaxed molecular clock approach gives much younger dates of 872-1,127 Mya (mean 983 Mya)  which overlaps with our estimate.
The age of LECA arguably is the most consequential date that we estimated. Our results suggests that the primary radiation of eukaryotes occurred about 1.1-1.2 Gya, or around 1.4 Gya at the earliest (when the red algal fossil data are used for calibration), in agreement with the results previously obtained with relaxed Bayesian molecular clock [3, 22] but clearly not with estimates obtained with simpler molecular clock models that point to an ancient radiation of eukaryotes at ~2,500 Mya . Given the convergence of independent dating approaches on the "young LECA", buttressed by the agreement between these methods on other key dates such as the bilaterian radiation and the fungi/metazoa split, it seems that the possibility that the diversification of all extant eukaryotes occurred no earlier than ~1.4 Gya should be taken seriously. The implications of a young LECA are manifold and might substantially affect our understanding of the origin and early evolution of eukaryotes.
The late origin of the extant eukaryotic diversity implies a substantial time gap between LECA and the earliest occurrence of (apparent) eukaryotic fossils which are confidently dated to times in the early Proterozoic (>1,500 Mya) [12, 26–28, 31]. Given that collectively the evidence for the ancient appearance of eukaryotes seems solid, the several hundred years of eukaryotic evolution before LECA requires explanation. A simple, straightforward scenario has been put forward by Philippe and Adoutte  who proposed that the diversification of eukaryotes was intimately linked to the mitochondrial endosymbiosis and that the beginning oxygenenation of the oceans thought to have started ~1,000 Mya  was the principal trigger of the evolution of the aerobic eukaryotes . This scenario implies that the earliest eukaryotes were amitochondrial organisms, sometimes denoted archezoa [91–93]. However, an alternative, potentially more plausible scenario should be considered in light of the arguments that the mitochondrial endosymbiosis probably was the cause of eukaryogenesis rather than a relatively late capture of an α-proteobacterium by an archezoan [94–97]. The conclusion on the young LECA adds credibility to the ideas that the original main function of mitochondria was distinct from aerobic respiration and could involve other forms of metabolic symbiosis between the (archaeal) host and an α-proteobacterium (these hypotheses are also best compatible with the latest geochemical data that date the beginning of ocean oxygenation much later during the Neoproterozoic, perhaps, at 700-800 Mya ). Probably, the most coherent scenario of this type is the hydrogen hypothesis of Martin and Müller according to which the selective advantage of the symbiosis consisted in the production of molecular hydrogen needed for the host metabolism by the endosymbiont .
It seems likely that during the pre-LECA stem phase of eukaryotic evolution, the diversification of the primitive eukaryotes was limited as suggested by the fossil evidence . It remains unclear what factors would trigger the explosive radiation that, according to the current estimates, occurred some 1.1 Gya. Regardless of the exact scenario of the evolution of eukaryotes, young LECA implies that we know next to nothing about a long and formative early part of the history of eukaryotes. Even if the early diversity of eukaryotes is incomparable to that created by the post-LECA radiation, there certainly were multiple lineages, and LECA obviously belonged only to one of these, and we know nothing about the rest. Indeed, inference of events that occurred during these "dark ages" is a formidable task because comparative genomics of eukaryotes cannot directly look past LECA. However, there are still ways to decipher some aspects of that early evolution, in particular, through detailed study of the numerous eukaryote-specific gene duplications  that, under the young LECA scenario, could have accumulated gradually over an extended period of time.