Geologically calibrated mammalian tree and the corresponding global events, including birth of human

The robust timetree could be constructed using a calibration function of BEAST v1. X released in 2018 simply by applying times of the most recent (= the latest) common ancestors (tMRCAs) for specic monophyletic species groups (clades). The present research is probably the rst trial to fully use the calibration function in BEAST X. The specic node age (child tMRCA) in BEAST X = “minimum age” in conventional MCMCTree, but the “maximum age” in MCMCTree can be equivalent to, e.g., the parent node age (parent tMRCA) in BEAST X. We applied 19 mammalian fossil calibration ages considering Benton et al. (2015; solely their minimum ages), including those of fossil Gorilla and Pan + one geologic event calibration age for otters (= Quaternary isolation time of the Ryukyu islands and start of vicariant speciation), and we estimated our targeted splitting age of Homo and Pan at 5.69 Ma (calibration dates by Benton et al., 2015 were incorrect). After the initial rifting at 120 Ma, the Atlantic Ocean spread over 500 km on Chron 34 (84 Ma), and Afrotheria (Africa) and Xenarthra (South America) started vicariant speciation at this time (~ 70 Ma), reecting the progressed continental isolation. Ordinal-level differentiations started just after the K-Pg boundary (66.0 Ma), and this timing reconrmed that mammalian radiation occurred by rapidly lling the niches left vacant by the non-avian dinosaurs. In addition, we made a base substitution rate vs age diagram using the BEAST X function and showed that the rate exponentially increased and accelerated toward the Holocene, other than having the 55 Ma mild peak reecting the post K-Pg mammalian explosion. The increased rate might have consequently increased the biodiversity, and extensive adaptive radiation might have ultimately birthed Homo sapiens. The basic factor of radiation might be the generation and spreading of C4 grasses since 20 Ma, which has been linked to increasing carbon xation, decreasing atmospheric CO2 concentrations, cooling Earth, and triggering the Quaternary (2.58 Ma ~) glacier-inter glacier cycle and severe climatic change. Note that


Introduction
Modern DNA sequences are an integration of base substitutions, although ancient sequences can be restored using functions such as in MEGA X (maximum likelihood method; Stecher et al., 2020), and recombinant re y proteins were actually made (Oba et al., 2020). The phylogenetic tree built by application of the DNA sequence is a graphical representation of evolutionary history, and the splits re ect organic populations that diverged and evolved independently. The history or tree is, however, shown on a relative timescale, and an absolutely dated tree is only obtained by calibration applying geologically reliable chronological data on speci c nodes. A molecular clock can be used to estimate tree age by assuming typically an approximately constant base substitution rate, and the dated phylogeny can be obtained by such an assumption (e.g., Brower, 1994). However, the molecular clock maintains inaccurate time even in relaxed clocks, as shown in the present paper.
Molecular clock analyses were reviewed by Ho and Duchene (2014), and the concept of geologically determining every node age (= to build a geologically dated tree) was applied to the Bayesian MCMC vicariant speciation simultaneously started at this time and acted on each isolated island population. The Quaternary time of MRCA at 1.55 ± 0.15 Ma is thus a xed, robust and reasonable date for geological event calibration as the isolation of each island of the Ryukyu. Based on the prediction by Osozawa et al. (2012a), we have already applied this calibration date as the tMRCA of insect clades (Osozawa K et al., 2016;Osozawa et al., 2013Osozawa et al., , 2015ab, 2016. These species started vicariance at 1. 55 Ma, and each node-speci c clade was calibrated by 1.55 ± 0.15 Ma. The present study applied this geologic calibration to the Asian continental and Japan island otters (Waku et al., 2016;Fig. 1, calibration point Z).
The mammalian timetree was constructed by many authors (Bininda-Emonds et al., 2007;Meredith et al., 2011;dos Reis et al., 2012dos Reis et al., , 2018O'Leary et al., 2013;Pozzi et al., 2014;Liu et al., 2017). All the above referenced timetrees were motivated to address mammalian ordinal radiation after, across, or before the Cretaceous-Paleogene (K-Pg) boundary (de nition after O' Leary et al., 2013), which was related to considering the effect of mass extinction eliminating non-avian dinosaurs. Additionally, some papers tied the superordinal differentiation with the middle Cretaceous supercontinent break-up (Nishihara et al., 2009) and with the Cretaceous angiosperm radiation (Magallon et al., 2015;Liu et al., 2017;Osozawa et al., 2021b). We can now robustly date the mammalian tree (Figs. 1 and 2) and chronologically correlate the biological divergences with the global geological events.
Another topic is related to the sex-determining region Y (SRY) gene, which is responsible for the initiation of male sex determination in therian mammals (Berta et al., 1990); therefore, the root node age represents the original date of the SRY gene. Additionally, placenta is a de ning characteristic of placental mammals. The rst introgression date may be a node age between Metatheria and Placentalia, although such introgressions were repeated. The protein syncytin, found in the syncytiotrophoblast, has an RNA signature in its genome originating from an ancient endogenous retrovirus that carries out an essential function in placental development (Dupressoir et al., 2012). Syncytin 1 is conserved in all hominoids but has not been characterized in Old World monkeys and lacks in New World monkeys (Caceres et al., 2006). Syncytin 2 is present in Simiiformes and is absent only in prosimians (Blaise et al., 2002). Our timetree correctly shows these evolutionary event dates.
The consequent mammalian timetree calculated by the platform software BEAST was drawn by FigTree. We set BEAUti (associated software in BEAST; see methods section) as selecting relaxed clock model (Ho and Duchene, 2014), and checked variable base substitution rate (rate median of three branches; not constant in a case of relaxed clock model; constant in a case of strict clock model). We made a base substitution rate (rate median) vs age (node age) diagram (Figs. 1 and 2 inset), which indicated that the rate was not random but exponentially increased toward the Holocene, other than having an additional 55 Ma mild peak re ecting mammalian radiation after the K-Pg mass extinction. This phenomenon of exponential increase in the Quaternary has been shown for taxa including primates (Ho et al., 2005(Ho et al., , 2011, and we now try to recon rm and address this basic factor. The implication highlighted that Homo sapiens was created by re ecting the accelerated mutation, partly as a consequence of adaptation to local environment change due to the start of East African rifting (Stevens et al., 2013), and mostly as a consequence of expansion of C4 land grasses (Cerling et al., 1997) triggered global climatic change represented by start of the Quaternary glacial-interglacial cycle (Taira, 2007). Taira (2007) also pointed out that the C4 savanna was tied to Laurasiatheria evolution. We can also precisely estimate the splitting age between Pan and Homo from our newly dated tree.
2. Methods 2.1. Phylogenetic analyses by BEAST v1. X: General A Bayesian inference (BI) tree ( Fig. 1) (Table 1) We used uploaded whole mitochondrial sequence data of most primates and representative mammals analyzed by Pozzi et al. (2014), and the accession numbers are shown in Fig. 1. In addition, we sought other representative mammalian data covering every order available from GenBank/DDJB and included them in our BEAST analyses.
The whole mitochondrial sequences were aligned by ClustalW in MEGA X. Gapped areas of nonprotein cording regions were excluded from the aligned sequences, and the consequent protein cording sequence data had a total of 10,112 bp. Concatenating of genes by SeaView (Gouy et al., 2010) and further partitioning by PartitionFinder 2 (Lanfear et al., 2016) in MCMCTree analyses is not needed in the present BEAST analyses, and the 10,112 bp sequence represents a single long partition. (Table 1) To estimate the evolutionary rate, calibration is essentially necessary, and fossil and geological event calibration is possible (Ho and Duchene, 2014). A node calibration is by the oldest discovered representative fossil of the speci c clade, and the fossil is used to constrain its "minimum age" (Donoghue and Yang, 2016). Due to the fragmentary nature of the fossil record and the oldest fossil relying on negative evidence, the true MRCA of a clade will likely never be found.

Fossil calibration protocols: Competition between BEAST and MCMCTree
For the mammalian fossil calibration in the MCMCTree, however, both the minimum and maximum age constraints for a speci c node were proposed (Benton and Donoghue, 2007). The minimum age is expected to be the oldest fossil age younger than the speci c branch node within the clade. The maximum age is inferred by an additional fossil age older than that speci c node (and the minimum age), i.e., the stem age (or the parent node age at an edge) is representative, although the de nition is sometimes unclear and controversial. Minimum ages are generally more accurate and reliable than maximum ages (Hassanin et al., 2021). In actual mammalian MCMCTree analyses (dos Reis et al., 2012(dos Reis et al., , 2018), a speci c node age (posterior divergence time) is estimated by prior divergence time applying minimum and maximum ages, although maximum age is only roughly estimated (named soft maximum bound). A root node age for the tree = the oldest maximum constraint as the third fossil age, is demanded for the algorithm to converge on a unique solution in MCMCTree.
Calibration protocol of BEAST v1.X. (and v.1.8) is to input a time of the most recent common ancestor (tMRCA) of the ingroup species (clade) on that speci c node, and we can approximate the tMRCA to the single, oldest fossil age known at the time of analyses. The minimum ages proposed by Benton et al. (2015) for MCMCTree coincident with our tMRCA for BEAST X, and the maximum age does not need to be constrained in BEAST X. A root node age in the MCMCTree analyses is simply equivalent to the tMRCA of the root node in BEAST X, and a third fossil age is not needed (the root age should be applied or automatically estimated from the resting child tMRCAs). Note that the BEAST v.1 X and v.1.8 protocol was drastically changed from BEAST v.1.7 with a similar calibration protocol in MCMCTree (several developers are common in these software programs).
We now awake that both BEAST and MCMCTree input prior node ages and output posterior node ages are expected to be coincident. The difference is that the BEAST node age (tMRCA) is younger than the MCMCTree node age, such as the mean (maximum age + minimum age)/2 by standard deviation (maximum age -minimum age)/2, and that the output time tree by MCMCTree as a whole may extend and shift to older dates relative to that by BEAST. Namely, if MCMCTree inputs the same prior node ages as BEAST in the same fashion, it outputs the similarly dated tree as BEAST. The difference may be the calibration protocol considering maximum age or not, and we tested below the effect of applying tMRCA as minimum age or (maximum age + minimum age)/2 (Figs. 3 and 4). Phillips (2016) pointed out that tight calibration across the tree is vital to buffer against rate model errors, and this must include allowing maximum ages to be tight when good fossil records permit.
We employed a normal prior distribution, but the selection of a lognormal distribution may affect node dating (Phillips, 2016), and we also tested and compared these two prior distribution settings (Fig. 5).
We noted above which is the oldest relevant fossil within the clade is in question. Our choice is BEAST analyses including the above testing, and we consider that tMRCA equals the oldest discovered representative fossil age of the speci c clade or the oldest fossil age known at the time of analyses. In the future, if new fossils with older dates may be found, the calibration date should only be modi ed to older dates. Note that famous fossil localities, such as the Burmese amber, are restricted, and the age has recently been well constrained by the efforts of paleontologists and geochronologists, but nding new fossil localities with excellent preservation on Earth may not be easy. The present timetree was made by robust calibration by a total of 20 multiple points covering 0.545 Ma (Quaternary) up to 162.7 m.y.
(Jurassic), and the dated tree is balanced or equilibrated (if not, some branch is folded in the ultimate case in the output gure by FigTree) and nally established. The run time BEAST was more than 5 hours for the present long sequence data, but we needed dozens of runs to obtain a nalized mammalian dated tree. Repeated runs are a problem for command line software such as MCMCTree.
Note that multiple calibration points are particularly helpful in relaxed-clock methods where the rate is allowed to vary among branches in the tree; multiple calibrations throughout the tree act as anchor points, allowing the method to estimate the patterns and degree of rate variation more accurately. Good estimates of rate variation are required from the well-calibrated regions of the tree so that the pattern can be extrapolated to other parts of the tree that are poorly calibrated (Phillips, 2016). In this meaning, the maximum age in MCMCTree can be replaced by the age of the parent node at a step from the speci c child node with tMRCA in BEAST v1. X.
The fossil age should be chronologically checked strictly following the protocol proposed by Parham et al. (2012), which is geologically robust in the opinion of the present authors. Reliable radiometric age by Ar-Ar or U-Pb radiometric dating is recommended, and the age is represented by 98.79 ± 0.62 Ma for the fossiliferous Burmese amber (although no mammalian fossil). In some cases, fossil ages are represented, such as Cenomanian (97.2 ± 3.3 Ma) of chronostratigraphic unit. Ages are after International Chronostratigraphic Chart by International Commission on Stratigraphy (2013).

Actual fossil calibration dates
Calibrations were as follows: the points of prior (input) ages (tMRCAs) are shown in Figs. 1 and 2 green stars, and these dates were input in "Priors" in BEAUti as the mean and standard deviation (in the case of 98.79 ± 0.62 Ma, mean = 98.79, standard deviation = 0.62). Corresponding ingroup species (clade) were included in ingroup taxa by "Taxon Set" on "Taxa" screen in BEAUti.
Figures 3 and 4 were made by prior (input) age of mean: (maximum age + minimum age)/2 and standard deviation: (maximum age -minimum age)/2, in the similar fashion to MCMCTree for testing the affect concerning maximum age. However, note that MCMCTree dating may be statically much more complex. Figure 5 re ects a prior lognormal distribution (Figs. 3 and 4 re ect a normal distribution).
Ingroup species or clade species are monophyletic (a function of BEAUti), although a clade species is obviously monophyletic. This treatment is for con rmation of Afrotheria species should be included in the Afrotheria clade, for example. For convenience in selecting ingroup taxa, we offered headings such as "Afro" in the sequence le. We checked the stem (a function of BEAUti) for four ingroup species (Prototheria, Theria, Bovidae, Eulipotyphla) because the fossil age is explained to not represent tMRCA (within the clade) but its stem (Fig. 2).
Our fossil calibration points were 19 points in total and covered long datums from 0.545 to 162.7 Ma (root age; 162.7 Ma). In every case, we referred to the original study, performed an additional literature search to nd chronological evidence of the data, and modi ed the age. In Figs. 1 and 2, we show fossil calibration points from A to S with the prior input age, but calibration point Z is determined by geological event calibration at 1.55 ± 0.15 Ma (then totally 20). Benton and Donoghue (2007) and Benton et al. (2015) reviewed many calibration data available for animals, and the following mammalian calibration points and dates are addressed by their proposal, except for calibration point X, which cannot be applied, and K, which we ourselves offered. These data were for MCMCTree analyses, and the maximum ages by Benton et al. (2015) are also addressed below to construct Figs. 3 and 4. In Figs. 2 and 4, fossils to adjust minimum ages (= times of MCRA) are also shown (Benton et al., 2015). In Fig. 6, we show our point node ages of A to E and X compared with the corresponding broad node ages by Benton et al. (2015).
Calibration point A: Fossil chimpanzee was reported from the East African Rift and dated by the Ar-Ar method as 0.545 ± 0.003 Ma (McBrearty and Jablonski, 2005). The time of MRCA is a node date between two Pan species ( Fig. 1), although Benton et al. (2015) cited only the above reference and did not address the chimpanzee split. We here set the maximum age at 5.31 ± 0.03 Ma of the calibration point X below.
Calibration point X: Crown Hominini (87) by Benton et al. (2015); Not applied in this paper because chronological evidence was not enough. Benton and Donoghue (2007) and Benton et al. (2015) noted that in the Lukeino Formation of Kenya, the source of Orrorin (Hominina) was dated at 6.56-5.73 m.y. from Ar/Ar ages on volcanic layers, citing Deino et al. (2002). The Lukeino Formation at Kapcherberek, including the fauna, was deposited during chron C3r and can be constrained to the interval 5.88-5.72 Ma (Deino et al., 2002), but this correlation to the magnetic polarity timescale is uncertain. Ar/Ar dating with an age of 5.31 ± 0.03 Ma (Deino et al., 2002) is only available for the ignimbrite and associated air-fall tuff of the basal Chemeron Formation, not the overlying Lukeino Formation. The age constraint for Orrorin loclity is thus only before 5.31 ± 0.03 Ma, and no evidence of lower limit of 6.56 Ma. In addition, Benton and Donoghue (2007) and Benton et al. (2015) noted that dating of the Sahelanthropus (oldest Hominina) beds in Chad is indirect. According to them, biostratigraphic evidence from mammals in particular, but with cross-checking from sh and reptile specimens, only indicates that the unit is de nitely late Miocene (i.e., older than 5.33 m.y.). It is older than the Lukeino Formation of Kenya (thus older than 5.31 ± 0.03 Ma) and may be equivalent (biostratigraphically correlated) to the lower fossiliferous units of the Nawata Formation of Kenya (dated by the traditional K-Ar method as diverse and unreliable ages of 7.4 and 6.5 Ma;Vignaud et al., 2002). Therefore, crown Hominini age is not constrained or only > 5.31 ± 0.03 Ma, and we did not adopt point X for our calibration or prior setting. Conversely, we tried to estimate node X age from the other reliable calibration data. Maximum age at 12.72 ± 1.1 Ma is for Sivapithecus at calibration point C below according to Benton et al. (2015), not 8.072 ± 0.8 Ma for Chororapithecus at calibration point B below (see Fig. 6), although we did not employ these dates to our calibration point X.
Calibration point B: Fossil gorilla (Chororapithecus abyssinicus) was also reported from the East African Rift and combined with the Ar-Ar method and megnetostratigraphy, reliably dated at 8.072 ± 0.8 Ma (Katoh et al., 2016). The time of MRCA is a node date of Homininae (Gorilla, Pan, and Homo). We set maximum age at 12.72 ± 1.1 Ma for Sivapithecus in calibration point C below.
Calibration point C: Crown Hominoidea; great apes (86) by Benton et al. (2015). Sivapithecus (Ponginae) fossil was found in Pakistan and considered to be the Serravallian stage (12.72 ± 1.1 Ma). Benton et al. (2015) proposed a minimum age of 11.62 (12.72-1.1) Ma, and the maximum age is a stem date of fossil Ponginae placed at the base of the Oligocene (33.9 Ma). However, the maximum age at 33.9 Ma should be replaced by younger node D age at 24.93 ± 0.49 Ma (see Fig. 2).
Calibration point E: Crown Primates; Primates (81) by Benton et al. (2015). Fossil Altiatlasius (euprimate) was found in Morocco and considered to be the Thanetian stage (57.6 ± 1.6 Ma). Maximum age at 66.0 Ma is from the Danian primate fossil.
Calibration point F: Crown Euarchonta; Euarchontoglires (74) by Benton et al. (2015), but we excluded the Glires clade to contain Scandentia in the Euarchonta clade (if not, Scandentia becomes the basal clade of Euarchontoglires). Fossil Paromomys (Primates, not Euarchontoglires) were found in Montana, USA, and considered to be the Danian stage (63.8 ± 2.2 Ma). The maximum age was the same as the tMRCA of calibration point R: Crown Theria (59) by Benton et al. (2015) and Juramaia sinensis from Liaoning, Northeastern China, with an Ar-Ar age of 160.7 ± 0.4 Ma (Luo et al., 2011). This too old date compared to the minimum age may not constrain the dating.
Calibration point H: Crown Rodentia (77) by Benton et al. (2015). Fossil Paramys was found in Montana, USA, and considered to be the Thanetian stage (57.6 ± 1.6 Ma). Maximum age: same as above 66.0 Ma. We did not apply Crown Glires (75) by Benton et al. (2015) (77) by Benton et al. (2015) because the age of the Wanghudun Formation with Mimotona, China, is uncertain.
age was assumed to be the Jurassic-Triassic boundary at 201.3 Ma.

Recovering ancient base substitution rates
The consequent mammalian Bayesian Inference tree calculated by the platform software BEAST was drawn by FigTree. We set BEAUti (associated software in BEAST) to select a relaxed clock model (Ho and Duchene, 2014) and checked the variable base substitution rate (rate median of three branches; not constant in the case of a relaxed clock model) in the output tree by FigTree.
We made a base substitution rate (rate median) vs age (node age) diagram (Figs. 1 ~ 5 inset) from the data on the output tree. An approximate curve with its formula is shown on this diagram using the Excel function. The intersection for the curve was 0.0114, the rate median shown on Tracer, in the case of Figs. 1 and 2 inset.

Maximum ages unaffected on dating
Figures 1 and 2 were constructed by calibration by input tMRCA = minimum age, and Figs. 3 and 4 were constructed by calibration by input tMRCA = (maximum age + minimum age)/2. In Figs. 3 and 4, the output dates are not affected by the maximum ages but equal to the input minimum ages, as in Figs. 1 and 2. These two kinds of trees then become similar, unrelated to the two kinds of calibrations. A difference is longer 95% HPD (height posterior density) in Figs. 3 and 4 compared to Figs. 1 and 2 (these bars were not shown in these gures to avoid complexity). Eventually, overestimated maximum ages caused too large and unreasonable standard deviations found at calibration points C, F and N ~ R but did not affect the dating, i.e., the timetree was strongly affected or controlled by the resting calibration points with negligible standard deviations. A minor difference is only that Xenarthra is a sister or not a sister of Afrotheria, but superorder level differentiation almost simultaneously occurred before the K-Pg boundary, common to Figs. 1 and 2.

Mammalian timetree and differentiation
We previously set superorder-to grandorder-level clades with their tMRCAs except for the Glires clade in BEAUti, and the relation of these superorder clades was reasonably restored in Figs. 1 and 2. Prototheria is the basal clade at 160.97 Ma, Metatheria is next at 94.66 Ma. Placentalia were differentiated into superorder clades since 73.42 Ma, and these superorder clades were thereafter differentiated into grandorder ~ species level clades. The relation of grandorder ~ species level clades was reasonably restored in Figs. 1 and 2 by ancestor to descendant node calibrations.
Placentalian superorder level differentiation dates were estimated before the K-Pg boundary (66.0 Ma) except for Euarchontoglires clade at 65.64 Ma. Because prior tMRCAs of Placentalia superorder clades were set younger than 66.0 Ma (K-Pg boundary), all the order-level differentiations were post-K-Pg boundary followed by family-level differentiations.
For great apes, Pongo was differentiated from other great apes at 13.4 Ma. Gorilla was differentiated from Pan and Homo at 8 Ma. Homo sapiens was estimated to have differentiated from Pan at 5.69 Ma (target age), Homo sapiens ssp. Denisova was differentiated from Homo sapiens neanderthalensis and Homo sapiens at 2.09 Ma, and Homo sapiens neanderthalensis was differentiated from Homo sapiens at 0.95 Ma.

Inconsistent Mammalian base substitution rate
The base substitution rate vs age diagram (Figs. 1 ~ 5 inset) shows that the rate was not constant and exponentially increased toward the Recent from ca. 20 Ma, and the heavy red trendline and equation O' Leary et al. (2013) proposed the explosive model by constructing a timetree that emerged from the combined phenomic and molecular parsimony analyses for fossil and living species. They applied multiple fossil ages for the oldest members of the clades to their timetree to determine the minimum divergence dates, and the fossil minimum ages were directly affected on their timetree. We con rmed that only maximum ages did not affect our timetree, but minimum ages were directly affected (Figs. 1 and 2 vs Figs. 3 and 4).
In the following studies, except for older ones, calibration dates were after Benton et al. (2015), and the  Fig. 3), the 12 node calibrations solely by minimum ages (lacking maximum ages) estimated the posterior ages (= posterior density in their Fig. 3) older than the minimum ages, approximate to the presumed maximum age (predicted in MCMCTree but con ict with ours). Therefore, for these 12 node calibrations, the lack of maximum age data produced unexpected older node age estimates that explained the long fuse model. Note that 11 node calibrations both by minimum and maximum ages and 2 node calibrations by solely maximum age put the posterior ages between the minimum and maximum age, as we predicted (but in BEAST analyses, close to the minimam ages as shown by Figs. 3 and 4). MCMCTree analyses actually need to include maximum age data to avoid this disadvantage and obtain accurate timetree, but our opinion is that overestimated maximum ages should be eliminated from dating analyses such as in BEAST v1. X. Application of genome-scale sequence data may be better as dos Raise et al. (2012) did so, but in the present case unrelated to the precision of node dating, calibration method is much more important. Hassanin et al. (2021) applied a lognormal distribution on the calibrated node ages and compared it to the uniform distribution for the minimum and maximum age sets. In BEAST v.1 X, considering maximum ages, we tried to select lognormal for prior distribution to construct Fig. 5 and compared to the normal distribution constructing Figs. 3 and 4. Our trial showed that posterior node ages close to the minimum ages (unaffected by too large standard deviation data) were not controlled by the prior lognormal distribution (Fig. 5), and the discrepancy was not from this distributional setting.

Relation to the middle Cretaceous Pangea breakup
In Eutheria (Placentalia), divergence into Afrotheria, Xenarthra, and Boreoeutheria (Laurasiatheria + Euarchontoglires) was considered to be tied to major-scale vicariant speciation by the breakup of the supercontinent Pangea into Laurasia (Eurashia and North America) and Gondwana (Africa and South America). Although the factor of differentiation into Laurasiatheria and Euarchontoglires has not been addressed, we tentatively assume that Laurasiatheria originated in North America (named the Laurentia continent) + Europe and that Euarchontoglires originated in Eurasia − Europe in the following discussion.
The phylogenetic basal split was considered to have followed the order of continental division between 100 and 120 Ma (Murphy et al., 2001). Nishihara et al. (2009) geologically estimated the date of the Gondwana breakup and proposed simultaneous divergence at approximately 120 Ma. The age of the fossiliferous Santana Formation, Brazil, is coeval with the breakup and initiation of the Atlantic Ocean and may be Aptian, Albian or possibly Cenomanian, although a rather loosely constrained date (125 − 100 Ma;Martill, 2007). Raise et al. (2012) andO'Leary et al. (2013) rejected the possibility of major-scale vicariance; the crown age of Eutheria (Placentalia) was less than 90 Ma, much younger than the above 125 − 100 Ma break-up. We also do not accept the possibility of relation to the Pangea break-up; crown age of Eutheria (Placentalia) was 73.42 Ma, Xenarthra at 57. 26 Ma,and Afrotheria at 57.44 Ma,much younger than the break-up age. However, the factor of Placentalia superordinal differentiations since 73.42 Ma (Figs. 1 and 2) has been remained unsolved.

Reports of dos
The initial rifting and sea oor spreading were complex processes to address the starting age mentioned above. However, marine magnetic anomalies on the Atlantic Ocean oor easily reconstructed the periodic spreading history. The con guration at Chron 34 (84 Ma) after the Cretaceous magnetic quiet zone (long normal polarity epoch; superchron K-T at 118 − 84 Ma) was shown by Moulin et al. (2010), and the South Atlantic Ocean spread over 500 km (minimum distance between Africa and South America) at Chron 34 (84 Ma). Therefore, 84 Ma can be considered to be a starting date of continent-level vicariance and divergence between Afrotheria and Xenarthra, which might have triggered the Placentalia superordinal differentiations shown in Figs. 1 and 2.
The splitting date of Lorisiformes (Africa and Southeast Asia) and Lemuriformes (Madagascar) was estimated at 51.23 Ma and unrelated to the initial break-up, but Lemuriformes in Madagascar is considered by oceanic dispersal from Africa (Horvath et al. 2008). We estimated the divergence time of New World monkeys and Old World monkeys to be 43.21 Ma, and the probable dispersal mechanism was proposed to be rafting on oating islands from Africa to South America (Houle, 1999).
The Panama arc docked and emerged with the Andean arc with crust fracturing during collision with South America (Ferris et al., 2017), and the Central American Seaway that did the Caribbean-Paci c water exchange was closed to form the Panama isthmus. The date was indirectly assumed to be the late Oligocene (25 Ma) from exhumation indicated by (U-Th)/He and ssion track thermochronology coupled with geochemical changes in Panama arc magmatism (Farris et al., 2011), to be the middle Miocene (13 15 Ma) from U-Pb ages of magmatic detrital zircons included in the northern Andean frontal basin (Montes et al., 2015) and to be the middle Miocene (18 Ma) from Ar-Ar ages of ignimbrite (Buchs et al., 2018). This date is concerned with the Great American Biotic Interchange and the vicariance of shallow marine organisms between the Atlantic and Paci c Oceans (Bacon et al., 2015). They demonstrated signi cant waves of dispersal of terrestrial organisms at approximately ca. 20 and 6 Ma and corresponding events separating marine organisms in the Atlantic and Paci c oceans ca. 23 and 7 Ma.
The divergence of Laurasiatheria relative to Xenarthra is possibly related to the partial Pangea breakup into North and South America, i.e., the initial formative time of the Central American Seaway. Marine magnetic anomalies on the Atlantic Ocean oor constrain the ancient relative position of North and South America, but the Caribbean lithosphere obscures the presence of the Central American Seaway. According to Pindell et al. (2011), a proto-Greater Antillean arc was formed along the Paci c side of Central America by entrapping the Caribbean seaway and connecting North and South America ca. 130 Ma, and the seaway was always narrow (maximum: 1000 km) constrained by the present position and distance of 1000 km between North and South America. The Panama arc is younger than 60 Ma (Montes et al., 2015), and the arc is almost connected to South America. Therefore, the Central American Seaway was not wide enough to diverge Laurasiatheria by vicariance within North America, and its origin cannot be addressed.
For Euarchontoglires relative to Laurasiatheria, the northern Atlantic Ocean associated with the Iceland hotspot initiated nal spread since chron 24 (53. For Euarchonta, a component of Euarchontoglires, Scandentia (Southeast Asia) and Dermoptera (Southeast Asia) are the oldest lineages, Lorisiformes (Africa and Southeast Asia) is sister to Lemuriformes (Madagascar), and Tarsiiformes (Southeast Asia) is sister to Simiiformes, including New World monkeys. As we calibrated using crown Primates date (81) by Benton et al. (2015), the oldest fossil Primates were from the Thanetian, Morocco, as calibrated at 57.6 Ma. The origin of Euarchonta was Southeast Asia and Africa, but the Euarchontoglires de nition becomes unclear.
In Metatheria, Dromiciops gliroides is known from Patagonia, South America, but is included in Australidelphia. In the timetree by dos Raise et al. (2012), this species occupied the basal lineage of Australidelphia (pre K-Pg) and a sister relationship with Notoryctes typhlops in Fig. 1 (only 21.27 Ma in Fig. 1; 33.12 Ma in Fig. 3). Nilsson et al. (2010) showed a single marsupial migration from South America to Australia by their phylogenetic study including D. gliroides. Patagonia, the Scotia arc, and the Antarctic Peninsula originally connected and formed a long land bridge because the Drake Passage was formed by the Scotia plate spreading after chron C11n (30 Ma;Riley et al., 2019). Therefore, marsupial migration occurred via Antarctica through the long bridge before 33 Ma and dispersed Australia before 33 Ma when the Tasman Gateway initiated opening (Lagabrielle et al., 2009).
As we applied tMRCA of the Asian continental and Japan island otters at 1.55 Ma, isolation of the Japanese island from the Korean Peninsula by the Tsushima Strait (Osozawa et al., 2012) triggered vicariant speciation on isolated populations in Japan. This process is unrelated to dispersal to Japan, especially through land bridges and subsequent vicariance, although recently found otters on Tsushima Island in 2017 were probably dispersed from the Korean Peninsula by swimming. Similarly, we did not calibrated by 1.55 Ma for wildcat (Prionailurus bengalensis euptilurus) on Tsushima Island (lacking on the Japan main islands) because relatively recent dispersal from Korea is plausible.

Relation to the middle Cretaceous Angiosperm radiation
Angiosperms were diversi ed and radiated in Middle Cretaceous time (Magallon et al., 2015;Osozawa et al., 2021b;approximately 125 Ma), and insect beetles have been clari ed to have contemporaneously coradiated around middle Cretaceous time (McKenna et al., 2015). Mammalian ordinal radiation occurred after the K-P boundary (66.0 Ma) and unrelated to middle Cretaceous angiosperm radiation.

Physiological evolutionary aspects
The SRY gene is a male sex determination in Theria (Berta et al., 1990), and the mammalian root node age is estimated at 160.97 Ma, and this date represents the origin date of the SRY gene. The origin date of the placenta was a Theria crown age of 94.66 Ma, de ning characteristic of placental mammals. The origin date of Syncytin 1 is a crown age of Simiiformes and is estimated at 35.58 Ma. Syncytin 1 is inactive in Old World monkeys, and the inactive date is a crown age of Catarrhini, estimated at 25.2 Ma.
Syncytin 2 is found in Simiiformes, and the date is a crown age of Primates, estimated at 57.14 Ma.

Expanded C4 grasslands and Catarrhini radiation
The calibration of crown Catarrhini was from the African fossil age at 24.93 ± 0.49 Ma (Roberts et al., 2010). Stevens et al. (2013) suggested a possible link between diversi cation of Catarrhini and the prominent East African rift system, uplift of the African plateau, and the consequent climate and environmental changes. If acceptable, Catarrhini was generated in East Africa. However, Hylobatidae and fossils are known from Southeast Asia, including China (Benton et al., 2015).
The East African uplift led to a drastic reorganization of atmospheric circulation, engendering strong aridi cation since ca. 8 Ma (Sepulchre et al., 2006). The consequent progressive increase in open grassland was linked to African Hominidae evolution. We estimated crown age of gorilla at 8.38 Ma as calibrated by point B of 8 Ma (Fig. 1). This fact may support the hypothesis of in situ African evolution of the Gorilla-Pan-human clade (Katoh et al., 2016). However, Ponginae is native to the rainforests of Indonesia and Malaysia, and Sivapithecus (Ponginae) fossils were found in Pakistan (Benton et al., 2015).
Quaternary glaciations may have been triggered by the expansion of land grasses (Poales) because this process increased carbon xation, which consequently decreased atmospheric CO2 concentrations (Taira, 2007). C4 plants are e cient for CO2 xation (Taira, 2007), and C4 Poales plants appeared and started diversi cation at 20.35 Ma (C4 dicots from 31.92 Ma) by our Angiospermae timetree (Osozawa et al., 2021b). Carbon isotope ratios from mammalian fossil tooth enamel show that diet change into C4 plants started at 9.9 Ma in eastern Africa (Uno et al., 2011). Additionally, the mammalian fossil tooth from the sub-Himalayan Siwalik Group, Pakistan, suggests that C4 savanna replaced C3 forest and woodland between 8.5 and 6.0 Ma (Badgley et al., 2008). The expansion of C4 grasses was a global phenomenon, including North America and South America beginning in the late Miocene and persisting to the present day, and generated the glacial-interglacial period (Cerling et al., 1997). This event should have affected Hominidae radiation as well as Laurasiatheria, such as Bovidae and Equidae in tropical savanna and temperate steps (Taira, 2007).
We estimated the most reliable date of the human-chimpanzee speciation event at 5.69 Ma, which is close to the estimate of ca. 6 Ma by Scally et al. (2012)  4.5. Increased base substitution rate toward the Holocene, increased biodiversity, and ultimate human generation The insets in Figs. 1 and 2 show that the base substitution varied, and a constant molecular clock (strict clock model) was not applicable. The light red curve indicated that the base substitution rate has a small peak at approximately 55 Ma, probably re ecting the mammalian radiation event after the K-P boundary following the explosive model. Although Bininda-Emonds et al. (2007) showed diversi cation rates over time with a peak at 93 Ma, their estimates re ected their short fusion model.
The heavy red trendline (Figs. 1 and 2 insets) has an additional interesting character: the rate exponentially increased toward the Holocene since ca. 20 Ma. This phenomenon was rst shown for primates (Ho et al., 2005), and they found that a Quaternary date calibration produced a faster rate than an older date calibration. BEAST v1. X can run simultaneously by applying multiple calibration points, but they employed BEAST v1. 3 (Drummond and Rambaut, 2003) that needed to run repeatedly by applying a date at every calibration point. Note that we instantaneously calibrated by multiple dates, including older dates such as the Jurassic as well as younger dates of the Quaternary, not solely calibrated by the Quaternary date, and the reason for the increasing rate is unrelated only to the Quaternary calibration.
Additionally, note that combined gene analyses were not possible in the old versions of BEAST, and such users needed to discuss the rate for every gene. Therefore, although their trendlines and the equations are similar to ours, their timetrees do not actually re ect drastic changes in base substitution rates over time but assume a constant rate as if the clock is strict. Scally et al. (2012) suggested that the rate was decreased for Hominidae reversal in our analyses, but they pointed out that the evolution was accelerated for African Hominidae. Human timetree calibrated by radiometric carbon data (detection limit: ca. 60 kyr) suggested that the base substitution rate was approximately 1.6-fold higher than that of the older fossil-calibrated tree (Fu et al., 2013), similar to high estimate rates obtained in studies of pedigrees and laboratory mutation-accumulation lines (Ho et al., 2011).
An exponentially increased base substitution rate may be expected to increase biodiversity, as shown by the diversi ed species in Fig. 1. Species diversity might have been a consequence of extensive adaptive radiation triggered by the expansion of C4 grasses, effective decreases in atmospheric CO2 concentrations, global cooling, and severe climatic changes at the start of the Quaternary glacialinterglacial cycle. We moreover suspect that the ultimate effect might be the birth of Homo species.

Conclusion
Maximum ages not strictly de ned in MCMCTree are practically substituted by multiple node calibrations in BEAST v.1 X. The robustly dated tree showed the evolutionary history with a series of global events of the post 70 Ma vicariant speciation between Afrotheria (Africa) and Xenarthra (South America) by progressed spreading of the Atlantic Ocean, the post K-Pg (66 Ma) placentalian radiation, post 20 Ma expansion of C4 grasses, its triggered increase carbon xation, decrease of atmospheric CO2, global cooling, the Quaternary glacial-interglacial cycle, extensive adaptive radiation, exponentially increased base substitution (mutation) rate, and ultimately creating Homo sapiens.   Figure 1 Mammalian timetree built by BEAST v1. X. Fossil calibrations from A to S were solely by minimum ages.

Declarations
The Pan-Homo splitting date was not calibrated but expressed X and was estimated at 5.69 Ma.
Geological event calibration: point Z. Ordinal differentiation was a post K-Pg boundary event. Illustrations were downloaded from silhouette AC. Inset: Base substitution rate (= rate median shown at each node; mutations per bp per million years) vs age (= posterior age shown at each node) diagram. Heavy red curve with equation: trendline drawn by Excel function, and light red curve: trendline drawn by connecting plots with maximum rate through the time. Mammalian timetree built by BEAST v1. X, impli ed from Fig. 1. Fossils with cross marks to adjust minimum ages (Benton et al., 2015) were shown close to each calibration point.

Figure 3
Mammalian timetree built by BEAST v1. X. Prior distribution: normal. Fossil calibrations from A to S were calculated by considering maximum ages in addition to minimum ages. The Pan-Homo splitting date was not calibrated but expressed X and was estimated at 8.79 Ma. Geological event calibration: point Z.
Ordinal differentiation was a post K-Pg boundary event with an exception. Illustrations were downloaded from silhouette AC. Inset: Base substitution rate vs age diagram. Heavy red curve with equation: trendline drawn by Excel function, and light red curve: trendline drawn by connecting plots with maximum rate through the time. Comparison calibration ages for Simiiformes. Our calibrated nodes approximated the minimum ages, and those by Benton et al. (2015) approximated between maximum and minimum ages with wide ranges. Our node B age is at 8.072± 0.8 Ma, but the maximum age can be automatically constrained by its parent node C age at 12.72 ± 1.1 Ma. Node C maximum age should be replaced by node D minimum age, and this de nition of maximum age is inappropriate. From nodes E to Q, maximum ages are mostly di cult to assign and overestimated by Benton et al. (2015).

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