## Abstract

In modern evolutionary divergence analysis the role of geological information extends beyond providing a timescale, to informing molecular rate variation across the tree. Here I consider the implications of this development. I use fossil calibrations to test the accuracy of models of molecular rate evolution for placental mammals, and reveal substantial misspecification associated with life history rate correlates. Adding further calibrations to reduce dating errors at specific nodes unfortunately tends to transfer underlying rate errors to adjacent branches. Thus, tight calibration across the tree is vital to buffer against rate model errors. I argue that this must include allowing maximum bounds to be tight when good fossil records permit, otherwise divergences deep in the tree will tend to be inflated by the interaction of rate errors and asymmetric confidence in minimum and maximum bounds. In the case of placental mammals I sought to reduce the potential for transferring calibration and rate model errors across the tree by focusing on well-supported calibrations with appropriately conservative maximum bounds. The resulting divergence estimates are younger than others published recently, and provide the long-anticipated molecular signature for the placental mammal radiation observed in the fossil record near the 66 Ma Cretaceous–Paleogene extinction event.

Molecular dating has been transformed by relaxed clock methods that allow the rate of molecular evolution to vary across the phylogeny ( Sanderson 1997 ; Thorne and Kishino 2002 ; and see Welch and Bromham 2005 ). Single point calibrations have in turn been superseded by multiple sets of calibration bounds or priors. As a result, geological information, which formerly only gave a temporal scale to molecular branch lengths, now also substantially informs how rates of molecular evolution vary across the tree (see Ho and Phillips 2009 ; Magallón et al. 2013 ). I refer to this modern conception of relaxed clocks and multiple calibrations as “geomolecular dating.”

Despite recent progress in modeling molecular sequence evolution, large apparent conflicts with far younger fossil records remain across the tree of life, such as for the diversification of metazoans ( Aris-Brosou and Yang 2002 ), and the origins of flowering plants ( Bell et al. 2010 ) and birds ( Brown et al. 2008 ). The timing of placental mammal diversification remains especially contentious, with major recent studies reinforcing divisions between older, molecular-based estimates ( Meredith et al. 2011 ; Bininda-Emonds et al. 2012 ) and younger fossil-based estimates ( Wible et al. 2007 ; O'Leary et al. 2013 ).

Direct reading of the fossil record suggests that eutherian mammals, including their crown group (placentals), underwent an extraordinary taxonomic and morphological diversification following the extinction of non-avian dinosaurs at the Cretaceous–Paleogene boundary (KPg), 66 Ma. In the most extensively sampled phylogenetic analysis of living and fossil eutherians O'Leary et al. (2013) argue for the “hard” explosive model ( Fig. 1 a), in which all placentals arose from a single survivor of the KPg mass extinction. Traditionally, however, paleontologists have favored a “soft” explosive model ( Fig. 1 b), which allows Late Cretaceous origins for the deepest few placental lineages ( Simpson 1945 ; Archibald and Deutschman 2001 ). Regardless of these “hard” and “soft” explosive models ( Fig. 1 ), paleontologists agree that all known Cretaceous eutherians were small (<500 g) insectivores or omnivores, and that the earliest accepted crown members are found on the northern continents ( Wible et al. 2009 ; Goswami et al. 2011 ).

F igure 1.

The timing of placental mammal evolution. Dark gray triangles show the pattern of superordinal divergences, beginning with the placental crown origin. Black circles show the crown origins for the 11 orders generally agreed upon as being Paleogene or older, in each case arranged from top to bottom: Xenarthra, Afrosoricida, Lipotyphla, Carnivora, Chiroptera, Perissodactyla, Artiodactyla, Primates, Scandentia, Rodentia, and Lagomorpha. (a) The hard explosive model is based on O'Leary et al. (2013) . (b) The soft explosive model differs only by extending the earliest few placental superordinal divergences into the Cretaceous. (c) The long fuse model is based on dos Reis et al. (2012) . (d) The short fuse model is based on Bininda-Emonds et al. (2007) . (e) The majority consensus of recent molecular dating estimates is represented here by Meredith et al. (2011) .

F igure 1.

The timing of placental mammal evolution. Dark gray triangles show the pattern of superordinal divergences, beginning with the placental crown origin. Black circles show the crown origins for the 11 orders generally agreed upon as being Paleogene or older, in each case arranged from top to bottom: Xenarthra, Afrosoricida, Lipotyphla, Carnivora, Chiroptera, Perissodactyla, Artiodactyla, Primates, Scandentia, Rodentia, and Lagomorpha. (a) The hard explosive model is based on O'Leary et al. (2013) . (b) The soft explosive model differs only by extending the earliest few placental superordinal divergences into the Cretaceous. (c) The long fuse model is based on dos Reis et al. (2012) . (d) The short fuse model is based on Bininda-Emonds et al. (2007) . (e) The majority consensus of recent molecular dating estimates is represented here by Meredith et al. (2011) .

Molecular dating studies present a very different evolutionary history for placentals. Relaxed clock analyses place the crown origin in the mid-Cretaceous (85–115 Ma), and most likely in Africa or at least Gondwana ( Murphy et al. 2001 ; Springer et al. 2011 ). Some 20–45 modern lineages are estimated to predate the KPg mass extinction. An explosive interordinal diversification is predicted, but it predates the dinosaur extinction by nearly 20 myr and has instead been loosely associated with the tail-end of the Cretaceous diversification of flowering plants and insects ( Meredith et al. 2011 ). In this scenario, morphological and ecological specialization were uncoupled from taxonomic diversification and instead occurred gradually, with crown primates and rodents arising 3–15 myr before the KPg, bats and artiodactyls (cow and whale relatives) close to the KPg, and carnivorans and perissodactyls (horse relatives) a further 10 myr later. Molecular estimates are said to support “long fuse” models ( Fig. 1 c) when nearly all of the 18 placental crown order divergences postdate the KPg, although interordinal divergences are mostly Cretaceous (e.g., dos Reis et al. 2012 ). In “short fuse” models ( Fig. 1 d), many more of the crown order divergences also fall in the Cretaceous (e.g., Bininda-Emonds et al. 2007 ).

In the most comprehensive mammalian molecular dating study yet, Meredith et al. (2011) analyzed a 26-gene DNA supermatrix with family-level coverage of mammals across 169 taxa. Their divergence estimates closely match the majority consensus among recent molecular analyses (from here referred to as the “molecular consensus dates,” Fig. 1 e, e.g., Hasegawa 2003 ; Springer et al. 2003 ; Lartillot and Delsuc 2012 ). I use the DNA supermatrix of Meredith et al. (2011) to illustrate both the potential for contemporary calibration practices to mislead divergence estimates, and the expanded role for fossil calibration that modern geomolecular dating offers.

Analyses presented here are based on Meredith et al.'s (2011) most inclusive (protein and non-coding DNA) data set. Except where stated otherwise, I follow their usage of MCMC tree ( Rannala and Yang 2007 ) with the independent rates model, and 82 sets of soft-bound fossil calibrations with upper and lower 2.5% prior probability tails. Autocorrelated rates models may not be appropriate for testing an explosive placental diversification in the wake of the KPg event, because they bias against the rapid rate shifts advocated by proponents of this model ( Benton 1999 ; McKenna 2007 ).

I begin by considering the role of fossil calibrations for informing molecular rate variation across the tree. I particularly focus on the implications of only a small proportion of calibrations being informative, and of asymmetrical confidence in assigning minimum versus maximum bounds. I argue that these factors, in combination with life history correlations with rates of molecular evolution, will tend to inflate deep-level divergence estimates among placentals. I make several recommendations to ameliorate this bias, and incorporate these in an empirical study. The resulting divergence estimates place the major interordinal radiation of placental mammals close to the KPg event, consistent with the traditional soft explosive model based on fossil records.

## T he E xpanded R ole of C alibration in G eomolecular D ating

### Informing Molecular Rate Variation across the Tree

For some time after relaxed clocks were introduced it was still common for molecular dating to employ just one or a few calibrations. The intention was to use those fossils that most closely pinpointed actual clade origins. However, this practice often provided dates at other nodes that contradicted fossil records ( Bromham et al. 1999 ; Waddell et al. 2001 )—highlighting both the inadequacy of our relaxed clock models and the need for additional calibrations. The trend is now moving toward providing bounds or prior distributions for any node that can be informatively calibrated. This calibration drive undoubtedly improves accuracy, at least locally. We should nevertheless be mindful of the importance of correcting the underlying rate model misspecifications ( Ksepka and Phillips 2015 ), which will be especially critical for accurately dating regions of the tree with poorer fossil records.

Large discrepancies among divergence estimates for nodes that are not closely calibrated are predicted by simulation studies ( Ho et al. 2005 ), and corroborated by comparisons of alternative relaxed-clock models ( Brown et al. 2008 ) and coding schemes (e.g., ACTG vs. RY, Phillips 2009 ). Another way to assess the performance of models of molecular rate variation is to remove the assistance of multiple calibrations, by providing only a single, nominal calibration, and then see how closely the relative node ages match the fully calibrated tree. To make such a comparison I repeated Meredith et al.'s (2011) independent rates, relaxed clock analysis with just their (Euteleostomi) root calibration. The resulting “nominally calibrated” timetree was then scaled to minimize the sum of node age differences to the fully calibrated tree (Supplementary Table S2, available on Dryad at http://dx.doi.org/10.5061/dryad.s43f8 ). This scaling prevents any single node (such as the root) pulling all divergences high or low. A similarly root calibrated and scaled strict clock tree was also inferred, to control for the effects of both relaxing the clock and multiple calibrations. The strict clock is rejected by likelihood ratio testing in PAUP*4.0b10 ( Swofford 2002 ) at $P<0.0001$ . Thus, the strict clock model is a very poor fit and is expected to be far inferior to the relaxed clock.

The results instead show that without assistance from multiple calibrations, relaxing the clock provides little improvement over the strict clock. Across placental nodes, the mean age difference between the fully and nominally calibrated relaxed clock trees is 4.35 myr. To put this result in context, the mean node age difference between the fully calibrated relaxed clock tree and the strict clock tree is 5.42 myr. Thus, relaxing the clock contributes less than 20% (1.07 myr) of the overall assumed improvement of the fully calibrated relaxed clock dates over the strict clock dates. This result emphasizes the potential inadequacy of our relaxed clock model of molecular rate variation in the absence of close calibration.

It is well established that rates of DNA sequence evolution are slower in large, long-lived mammals ( Nabholz et al. 2008 ; Welch et al. 2008 ; Bromham 2011 ). It has also been suggested by Kitazoe et al. (2007) and Waddell (2008) that such rate variation systematically misleads relaxed clock models, although the former study was sensitive to model choice and the latter only compared small sets of phylogenetically nearby calibrations. My results in Figure 2 are clearer, showing a strong correlation ( $R2=0.655$ ) between body size/longevity and the disparity between the nominally and fully calibrated placental dates. Thus, rate model misspecification associated with body size and longevity can explain much of this apparent dating error across the placental tree. Misspecification of the tree process prior (e.g., birth–death) also deserves attention (e.g., Zhang et al. 2015 ). However, informative node calibrations spread across the tree should lessen the influence of tree process priors, in contrast to their importance for tip dating without explicit maximum bounds.

F igure 2.

Apparent dating error as a function of body mass and longevity. The apparent dating error is the percentage node age difference between the soft-bound fully and nominally calibrated relaxed clock trees for each placental taxon pair. The average of Sqrt(log(mass) × longevity) for the two taxa in each pair was calculated from average adult body mass ( Jones et al. 2009 ) and maximum longevity ( De Magalhães and Costa 2009 ). $R2=0.655$ . The nominal tree was scaled to minimize the overall node age difference to the fully calibrated tree. The filled circle represents Lorisiformes, and shifts up to 92% apparent dating error if the 37.1 Ma minimum age of Saharagalago is instead hard bound.

F igure 2.

Apparent dating error as a function of body mass and longevity. The apparent dating error is the percentage node age difference between the soft-bound fully and nominally calibrated relaxed clock trees for each placental taxon pair. The average of Sqrt(log(mass) × longevity) for the two taxa in each pair was calculated from average adult body mass ( Jones et al. 2009 ) and maximum longevity ( De Magalhães and Costa 2009 ). $R2=0.655$ . The nominal tree was scaled to minimize the overall node age difference to the fully calibrated tree. The filled circle represents Lorisiformes, and shifts up to 92% apparent dating error if the 37.1 Ma minimum age of Saharagalago is instead hard bound.

The results in Figure 2 are based on one of the most commonly used Bayesian relaxed clock models, the lognormally distributed independent rates model (originally Drummond et al. 2006 ). A second set of analyses show that the autocorrelated rates model delivers a similar pattern associated with body-size/longevity variation. Slightly lower $R2$ (0.596) may relate to autocorrelation affording less freedom for rates to vary among adjacent branches, between the different calibration regimes. The proportionally largest difference between the fully and nominally calibrated dates (for the crown age of Sirenia) is similarly extreme for the independent (395%) and autocorrelated (340%) rates models.

Model misspecification associated with life history rate correlates is again implied by patterns of incongruence between the fossil priors and the fully calibrated divergence estimates. The soft bound analyses of Meredith et al. (2011) applied 2.5% upper and lower prior bounds to 82 nodes. Hence, if these priors appropriately reflect fossil record uncertainty, and if the models of molecular evolution are accurate, we would expect few posterior estimates to fall outside their prior bounds, about two above and two below. Instead on average across their analyses 11.75 date estimates (14%) fell below and 4.75 (6%) fell above. Clades that are older than the maximum bound include small, short-lived (fast molecular rate) taxa; the most extreme overestimates being within rodents and for the divergence of the tarsier from anthropoid primates. Clades that are younger than the minimum bound typically comprise large, long-lived (slow molecular rate) taxa. The most extreme underestimates occur within whales and for the divergence of the walrus from fur seals.

Incongruence between Meredith et al.'s (2011) fossil priors and posterior dates brings into focus the main challenges for dating the adaptive radiation of placentals. The key deep divergences are close to shifts in body size and longevity that may compromise rate models, but are distant from calibrations that could help to correct these rate models.

### Competition between Minimum and Maximum Calibration Bounds

Although Meredith et al.'s (2011) divergence estimates fell outside of their fossil prior bounds more often than expected, most of the estimates still fell within these bounds. So the transfer of errors to uncalibrated nodes could largely be nullified if calibration regimes work as a consensus, but this is not the case. Calibrating certain clades disproportionately influences placental interordinal divergences ( Waddell et al. 2001 ; Hallström and Janke 2010 ).

Selective exclusion of Meredith et al.'s (2011) fossil bounds demonstrates that calibration is more like a competition that is settled between the most informative maximum and minimum bounds ( Table 1 ). As a simplification, calibrations may be “high bidders” with informative minimum bounds that push dates upward, “low bidders” with informative maximum bounds that push dates downward or uninformative “non-bidders” that have little influence either way. Excluding just three “low-bidding” calibrations (tarsier/anthropoid primates and the two basal rodent clades) substantially increases dates at deeper nodes (by up to 9.2 myr for haplorhine primates). Excluding instead the “high-bidding” perissodactyl (horse/rhino), lorisiform (loris/galago), and whale calibrations substantially decreases dates deeper in the tree (by nearly 12 myr for Whippomorpha). Conversely, Meredith et al.'s (2011) dates were barely shifted by excluding all 24 of the “non-bidding” placental calibrations for which the respective original 95% HPDs fell entirely within their soft prior bounds.

T able 1.

Placental mammal posterior mean ages (Ma) from Meredith et al.'s (2011) original calibration set, and excluding alternative sets of calibrations

Meredith et al. (2011) Calibration exclusion sets
Uninformative a  High bidders b  Low bidders c
Placentalia 101.0 100.2 94.6 104.1
Laurasiatheria 84.1 84.0 78.5 86.9
Euarchontoglires 83.9 83.5 79.4 88.2
Afrotheria 79.5 78.3 74.9 81.0
Deep Crown Orders
Primates 71.9 71.8 66.4 79.4
Rodentia 72.9 72.9 70.7 78.5
Chiroptera 65.8 65.7 62.4 66.6
Artiodactyla 64.9 64.9 55.9 65.3
Lipotyphla 76.9 76.5 71.8 79.4
Afrosoricida 70.7 69.5 66.7 72.3
Meredith et al. (2011) Calibration exclusion sets
Uninformative a  High bidders b  Low bidders c
Placentalia 101.0 100.2 94.6 104.1
Laurasiatheria 84.1 84.0 78.5 86.9
Euarchontoglires 83.9 83.5 79.4 88.2
Afrotheria 79.5 78.3 74.9 81.0
Deep Crown Orders
Primates 71.9 71.8 66.4 79.4
Rodentia 72.9 72.9 70.7 78.5
Chiroptera 65.8 65.7 62.4 66.6
Artiodactyla 64.9 64.9 55.9 65.3
Lipotyphla 76.9 76.5 71.8 79.4
Afrosoricida 70.7 69.5 66.7 72.3

Notes: Dates are from soft-bound MCMC tree analyses of 26 nuclear genes under the independent rates model, following Meredith et al. (2011) .

a Exclusion of 24 calibrations considered to be uninformative, because the original 95% HPDs fell entirely within their respective soft prior bounds (see Supplementary Table S1, available on Dryad at http://dx.doi.org/10.5061/dryad.s43f8 ).

b Exclusion of the horse/rhino, lorisiform, and cetacean calibrations, for which fully calibrated posterior 95% HPDs fell entirely below their respective soft prior bounds.

c Exclusion of the tarsier/anthropoid, and the two deepest rodent calibrations, for which fully calibrated posterior 95% HPDs fell entirely above their respective soft prior bounds.

The influence of calibrations also follows life history rate correlates. High bidders, which push dates older, are almost all larger and longer-lived. Low bidders, which push dates younger, are smaller and shorter-lived. One exception is the loris/galago calibration. Members of this clade are among the smallest, shortest-lived and apparently fastest evolving primates ( De Magalhães and Costa 2009 ; Meredith et al. 2011 ; Supplementary Figs. S1–S4, available on Dryad at http://dx.doi.org/10.5061/dryad.s43f8 ). Hence, their extreme “high bidder” status sharply defies the trend (also see Fig. 2 ). In this case the approximately 37 Ma Saharagalago reference fossil has not been considered controversial, but does only have low-to-moderate statistical support for grouping with modern galagos ( Seiffert et al. 2005 ). Calibrations based on erroneous fossil assignments or those unduly influenced by rate model errors will tend to stand out as the highest or lowest bidders to (mis)inform divergence estimation.

### Rate Error Transfer and Calibration Bound Asymmetry

Meredith et al. (2011) noted that when whale calibrations were excluded, divergence estimates among these aquatic giants were up to 5-fold younger than their oldest fossils. Calibrating within crown groups such as whales improves local divergence estimates. However, it transfers the underlying problem (underestimating stem rates relative to crown rates) to the stem divergences, which will then be overestimated. I refer to this phenomenon as “error-shift inflation” (see Fig. 3 ). This bias may be common when calibrating clades of large, long-lived placentals, because each had ancestors that were small and most likely short-lived.

F igure 3.

Rate-shift inflation of divergence estimates. Rates are indicated by branch widths for (a) a hypothetical example similar to placentals (clade 1) being subtended by the cow/whale (clade 2) divergence, with large size and low rates of molecular evolution evolving in parallel. (b) The over-smoothing tendency of relaxed clocks (which helps explain the result in Fig. 2 ) spreads the parallel crown rate deceleration to the stem lineage, such that the age of clade 2 is underestimated. (c) Calibrating clade 2 then shifts the error stemwards, inflating the age of clade 1. This is because the underlying misspecification remains (underestimating stem relative to crown rates for clade 2). In the reverse situation where far higher rates evolved along the node 2 daughter lineages, over-smoothed relaxed clocks would instead induce rate-shift deflation, upon node 2 being calibrated.

F igure 3.

Rate-shift inflation of divergence estimates. Rates are indicated by branch widths for (a) a hypothetical example similar to placentals (clade 1) being subtended by the cow/whale (clade 2) divergence, with large size and low rates of molecular evolution evolving in parallel. (b) The over-smoothing tendency of relaxed clocks (which helps explain the result in Fig. 2 ) spreads the parallel crown rate deceleration to the stem lineage, such that the age of clade 2 is underestimated. (c) Calibrating clade 2 then shifts the error stemwards, inflating the age of clade 1. This is because the underlying misspecification remains (underestimating stem relative to crown rates for clade 2). In the reverse situation where far higher rates evolved along the node 2 daughter lineages, over-smoothed relaxed clocks would instead induce rate-shift deflation, upon node 2 being calibrated.

The extent to which rate model errors or indeed calibration errors are transferred across the tree depends on the buffering capacity of the calibration regime. The dilemma here is that fossil record interpretations that provide the tightest calibration for reining in errors might also be expected to be the most likely to be erroneous. Walking this tightrope is made even more difficult by asymmetry in bounding confidence. Minimum bounds can be more precisely defined by confidently assigned reference fossils than can maximum bounds, which are largely defined by absence of evidence (see Reisz and Müller 2004 ; Barnett et al. 2005 ). Such asymmetry in bound confidence could systematically inflate divergences, with more precise minima keeping a tight rein on rate model errors that would push dates younger, while conservative maxima allow more leeway for errors that would push dates older across the tree.

The potential for inflating dates across the tree may be exacerbated by the implicit primacy in emphasis on minimum bounds, that dominates the field, including in major reviews of calibration. Sauquet (2013) , for example, provides a valuable discussion on minima, but ignores maximum bounds other than suggesting they should be conservative. Benton and Donoghue (2007) , Ho and Phillips (2009) , and Parham et al. (2012) have all advocated soft, conservative maximum bounds, yet allow hard minimum bounds based on reference fossils supported by a single synapomorphy. Hug and Roger (2007) and Marjanović and Laurin (2007) warn of the potential consequences of such bounding asymmetry, showing that arbitrarily old maxima result in unreasonably ancient divergence dates.

Bats provide an informative case of overly conservative maximum bounds limiting the potential for buffering against erroneous rates. The closest external calibrations to bats are among slowly evolving ungulates, leading to apparently inflated divergence estimates. Phillips (2015) showed that even including an appropriate soft maximum for bats (see below) reduced their crown age estimate from approximately 66 Ma to approximately 59 Ma, consistent with analyses that instead avoided error-shift inflation by excluding the ungulate calibrations.

Employing only conservative maximum bounds is most concerning when minimum bounds are defined too liberally, by reference fossils that do not meet the certainty demanded by hard (100%) or even soft (e.g., 97.5%) priors. Ignoring Bayesian prior confidence assumptions across large numbers of calibrations will inevitably lead to stem taxa erroneously calibrating some crown groups, and inflating divergence estimates (e.g., Phillips 2009 ; de Bruyn et al. 2013 ). The extent of this inflation depends on the buffering capacity of the maximum bounds.

In practice, many calibration reference fossils are speculative, having not been tested within a phylogenetic framework, or are justified by a single “unambiguous” synapomorphy, and yet are commonly allotted hard (100% confidence) minimum bounds. Explicit hypothesis tests between trees constrained to place proposed reference fossils within versus outside crown groups may in future help to inform more appropriate prior probability allocation to soft bound minima.

Wilkinson et al. (2011) suggest that the use of speculative reference fossils relates to the fear that better supported crown fossils will grossly underestimate divergence times. This vestige of point calibration is inappropriate for contemporary geomolecular dating, where the minimum is not the expected divergence, but the oldest date for which we can be nearly certain that the crown group had originated. The underestimation concern is instead dealt with in the modern context for relatively fossil rich taxa by applying appropriate phylogenetic caution to a range of calibrated nodes. These are expected to provide a distribution of bound tightness, among which the “high bidders” with apomorphies that arose more rapidly will tend to have an asymptote close to true divergences. Calibration prior peaks may also be fitted around or just earlier than fossils that are close to the crown transition, but that are too uncertain to qualify as minimum bounds ( Yang and Rannala 2006 ; Ho and Phillips 2009 ). Where feasible, these peaked distributions place more weight where the fossil record suggests divergences occurred, without unduly loading the prior.

At the older end of the prior, maximum bounds should be appropriately conservative, not merely “conservative”—an adjective often unfortunately applied as a badge of honor. Conservative maximum bounds may often be necessary, but they are just as much a failure to inform rate variation as conservative minimum bounds. What then is an appropriately conservative maximum bound? As noted by Parham et al. (2012) , the best guide remains the intuitive definition “to cover the time back until relatively well sampled fossil assemblages in potential geographic regions of origin that contain no putative crown group members, but contain stem members or ecological equivalents” ( Barnett et al. 2005 ). A more statistically rigorous framework that retains biological realism has been elusive, although models based on fossil sampling (e.g., Wilkinson and Tavaré 2009 ; Nowack et al. 2013 ; Heath et al. 2014 ; Gavryushkina et al. 2015 ) are promising to add quantitative rigor.

Important challenges facing statistical inference of maximum bounds or for integrating fossil sampling into the tree process prior include (1) incorporating phylogenetic uncertainty for fossil placements, (2) biogeographic and ecological heterogeneity in fossil sampling and diversification patterns, and (3) inferring the quality of the fossil record over the critical missing fossil history for the clade being calibrated, perhaps using proxies such as ecologically similar stem members. Otherwise, these methods tend to provide implausible bounds, such as Nowack et al. (2013) allowing for Jurassic or even Triassic crown rodents. “Total evidence” dating is a new development that circumvents each of these issues (e.g., Pyron 2011 ; Ronquist et al. 2012 ). Instead of defining calibration bounds or priors, fossils are used to stamp time on the tree as terminal taxa (tip dating) in analyses that combine molecular and morphological characters. Total evidence dating is a special case of tip dating. Alternative tip dating methods are being developed that do not require morphological characters. These new tip dating methods (e.g., Heath et al. 2014 ) instead anchor the fossil tips via the tree process prior, although current implementations do not address the fossil sampling biases and phylogenetic uncertainties that total evidence dating addresses or circumvents.

The major challenge for total evidence dating is that in addition to the vagaries of molecular clocks, the approach also depends on the more erratic ticking of morphological clocks. Heterotachy and character covariance are generally far more complex among morphological data than among molecular sequences (e.g., Scotland et al. 2003 ), yet, available models of morphological evolution (e.g., Mkv of Lewis 2001 ) are derivatives of the simplest molecular models and can struggle with truncation of terminal branches ( Lee et al. 2013 ). Moreover, data sets have been borrowed from cladistic analyses that partly reflect historical interest in particular branches, and tend to focus on deeper level variation, ignoring much recent variation, and so present ascertainment biases for estimating evolutionary rates across the tree ( Pagel and Meade 2006 ; Beck and Lee 2014 ). Thus far, total evidence dating has been embraced most warmly for groups with poorer fossil records (e.g., spiders, Wood et al. 2013 ). For mammals, fossil records reveal large errors in total evidence dating ( Beck and Lee 2014 ), perhaps due to biases in obtaining and modeling morphological matrices. However, tip dating (including total evidence dating) is in its infancy. As morphological phylogeny and tree process priors develop it will be important to identify when these new methods should replace or be combined with node dating.

Drawing branch-length information from molecular sequences alone and using fossil bounds on internal nodes remains the most widespread practice. Until we can better model morphological evolution, calibration bounding will also likely remain the most reliable method, at least where bounds are sufficiently tight and numerous to inform rates of molecular evolution across the tree. The onus on calibration then is on limiting the influence of asymmetrical confidence bias between minimum and maximum bounds.

## A lternative C alibration S chemes , M eredith et al. (2011) and dos R eis et al. (2012)

Calibration regimes prevailing among the studies that underpin the recent molecular consensus for mid-Cretaceous (∼100 Ma) placental origins may be encouraging upward dating biases across the tree. This is because due consideration is not given to the burden of confidence implied by Bayesian prior minimum bounds (e.g., 97.5% for soft bounds here), so increasing the likelihood of including fossils that predate their target divergences. Inflated dates are further favored by denying any tight maximum bounds to buffer against error-shift inflation ( Fig. 3 ) related to life history rate correlations and the possible influence of calibration errors.

Several of Meredith et al.'s (2011) minimum bounds are based on reference fossils that have not been subjected to phylogenetic analysis, matrix-based or otherwise (e.g., the tree shrew Eodendrogale and an undescribed putative mormoopid bat). In other cases, reference fossil placements are contradicted by matrix-based analyses, such as for the putative anomaluroid rodent, Pondaungimys (see Marivaux et al. 2011 ) and the putative procyonid carnivoran, Pseudobassaris (see Finarelli 2008 ). In contrast, the maximum bounds that Meredith et al. (2011) use are far more conservative, defined as whichever is oldest among (a) the oldest fossil taxon up to two outgroups distant from the crown clade, (b) two successive fossil-bearing chronologic units (e.g., the 16 Ma base of the Middle Miocene, given a 3 Ma Pliocene crown fossil), and (c) allowing for taxa of uncertain phylogenetic affinities that, at least in some studies, belong to the crown, first outgroup, or second outgroup. This compound definition (especially b) precludes any possibility of providing tight maxima, even when warranted.

Meredith et al. (2011) infer that nearly 30 placental lineages crossed the KPg boundary, including four or five placental crown orders ( Fig. 1 e, Table 2 ), only two fewer than Bininda-Emonds et al.'s (2007 , revised version) modern benchmark for the short-fuse model. dos Reis et al. (2012) instead take greater advantage of the capacity for maximum bounds to inform molecular evolutionary rates. Again they provide several minimum bounds among large body-size/long-lived clades, but partly mitigate against error-shift inflation by placing maximum bounds on several faster rate taxa, including the two deepest rodent clades at 65.8 Ma and 58.9 Ma. Their estimated placental origin (∼90 Ma) and other interordinal divergences fall approximately 10 myr younger than in Meredith et al. (2011) .

T able 2.

Placental mammal posterior mean ages (Ma) for alternative calibration schemes, using Meredith et al.'s (2011) DNA data

Notes: Dates are from soft-bound MCMC tree analyses of 26 nuclear genes under the independent rates model, following Meredith et al. (2011) . Cretaceous ages for crown orders are bold, and identified with an asterisk if their 95% HPD is entirely Cretaceous. Meredith et al. (2011) treat calibration minima for Lagomorpha and three bat clades differently, using stage (age) dates instead of well-established older radiometric/stratigraphic dates. In each case the placement of the reference fossil is highly speculative (see Supplementary Information, available on Dryad at http://dx.doi.org/10.5061/dryad.s43f8 ).

a Four speculative calibrations allowed older minimum dates.

b Four speculative calibrations excluded.

c New maximum bounds applied to Primates, Rodentia, and Chiroptera (see text).

d Number of placental lineages extending back into the Cretaceous.

e Temporal extent of Cretaceous ghost lineage time summed over boreoeutherians.

The genomic data that dos Reis et al. (2012) use cover fewer than half of the 18 placental ordinal crown divergences. Moreover, their sparse taxon sampling limits inference of molecular rate variation across the tree ( Linder et al. 2005 ; Hug and Roger 2007 ). As an alternative, I have employed dos Reis et al. (2012) calibration scheme for reanalyzing Meredith et al.'s (2011) 26-gene DNA data matrix. The combination of denser taxon sampling and maximum bounds that better mitigate against error-shift inflation further reduces the estimate for the placental origin to approximately 81 Ma (95% HPD, 78–84 Ma) and all crown orders fall younger than the KPg boundary ( Table 2 ). However, the calibration scheme of dos Reis et al. (2012) constrained nearly twice as many minimum as maximum bounds. Among the missing maxima are the ancestrally small primates and bats, which, along with rodents, provide arguably the best opportunities for tight, yet appropriately conservative maximum bounds to buffer against rate model errors.

In each case the earliest primate, bat, and rodent crown members are closely preceded by stem members from well-sampled faunas in regions of origin that match molecular biogeographic predictions ( Springer et al. 2011 , 2012 ). Crown primates and rodents both appear first in the latest Paleocene or earliest Eocene (∼55–57 Ma; Asher et al. 2005 ; Ni et al. 2013 ) and crown bats putatively in the Early Eocene (∼52 Ma; Simmons et al. 2008 ). In each case, successive stem members only are found earlier in these ages and putatively in the preceding age, from which I use the base to give soft maximum bounds of 61.1 Ma for primates and rodents, and 58.9 Ma for bats in my reanalysis.

With the new maximum bounds the placental crown origin falls to 77 Ma (95% HPD, 75–80 Ma) and the major diversification that Meredith et al. (2011) place at approximately 83 Ma falls squarely on or just after the 66 Ma KPg event ( Table 2 ; Fig. 4 d), thus supporting the soft explosive model. Limiting the transfer of rate errors deeper into the tree has played an important role here. However, rate model misspecification associated with extreme body-size/longevity shifts remains at shallower nodes. For instance, the 8–10 Ma estimate for the crown age of whales is less than a third of their >30 Ma fossil age ( Fordyce and Barnes 1994 ). One development that is promising in this regard is joint reconstruction of divergence times and life history rate correlates ( Lartillot and Delsuc 2012 ). Although the authors noted that life history correlation signals were compromised by Brownian motion over-smoothing rate shifts, future integration of fossil body size data should improve rate modeling across the tree.

F igure 4.

Timeline of placental mammal evolution. (a) Fossil record species richness of eutherian mammals, and (b) to reduce any sampling biases, expressed as the eutherian percentage of mammal species during the pre-Campanian Cretaceous (30 of 195 species), Campanian–Maastrichtian (34 of 175 species), and Paleocene (591 of 725 species). (c–d) MCMC tree geomolecular dates for placental interordinal divergences, including log lineage through time plots for Boreoeutheria, with circles denoting divergences and lines showing 95% HPDs, for (c) Meredith et al.'s (2011) calibration set, and (d) dos Reis et al. (2012) calibrations, supplemented with revised maximum bounds for primates, rodents, and bats. Each analysis employed the 26-gene matrix of Meredith et al. (2011) , independent rates and soft-bound calibrations. With the autocorrelated rates model the median date among the boreoeutherian diversification cluster (open circles) shifts from 64.6 Ma to 66.9 Ma (see Supplementary Fig. S2d, available on Dryad at http://dx.doi.org/10.5061/dryad.s43f8 ).

F igure 4.

Timeline of placental mammal evolution. (a) Fossil record species richness of eutherian mammals, and (b) to reduce any sampling biases, expressed as the eutherian percentage of mammal species during the pre-Campanian Cretaceous (30 of 195 species), Campanian–Maastrichtian (34 of 175 species), and Paleocene (591 of 725 species). (c–d) MCMC tree geomolecular dates for placental interordinal divergences, including log lineage through time plots for Boreoeutheria, with circles denoting divergences and lines showing 95% HPDs, for (c) Meredith et al.'s (2011) calibration set, and (d) dos Reis et al. (2012) calibrations, supplemented with revised maximum bounds for primates, rodents, and bats. Each analysis employed the 26-gene matrix of Meredith et al. (2011) , independent rates and soft-bound calibrations. With the autocorrelated rates model the median date among the boreoeutherian diversification cluster (open circles) shifts from 64.6 Ma to 66.9 Ma (see Supplementary Fig. S2d, available on Dryad at http://dx.doi.org/10.5061/dryad.s43f8 ).

### Further Testing the Soft Explosive Model

Importantly, the correlation between life history and apparent dating errors ( Fig. 2 ) could be coincident with either inflated or deflated placental origins. If early placental molecular rates were fast, as expected for small Cretaceous eutherians, then over-smoothing rate decelerations among large/long-lived calibrated groups, such as ungulates, would inflate deeper divergences ( Fig. 3 ). Alternatively, if those early rates defy expectations and were slow, then over-smoothing rate accelerations among small/short-lived calibrated groups, such as rodents, could instead deflate deeper divergences. To test this, I calibrated Meredith et al.'s (2011) tree with either high-bidding whale and horse/rhino calibrations or low-bidding rodent and tarsier/anthropoid calibrations (and the Euteleostomi root constraint in each case).

The results confirm that rates from the large, long-lived taxa are not traced reliably back over the KPg. The 95% HPDs for the divergences of placentals to marsupials (214.1–253.7 Ma) and to monotremes (256.4–297.3 Ma) dramatically predate fossil record expectations, respectively, 124.0–171.2 Ma and 162.9–191.1 Ma ( Benton et al. 2009 ; dos Reis et al. 2012 ). The implication is that error-shift inflation from over-smoothing rate deceleration among large, long-lived taxa drives erroneously old placental divergence estimates.

In contrast, employing only the low-bidding calibrations among the faster rate rodents and tarsier/anthropoid clade gave divergences for placentals to marsupials (151.1–179.4 Ma) and to monotremes (181.7–215.0 Ma) that match fossil records. Thus, rates are more reliably traced back into the Cretaceous for mammals that more closely retain ancestral small body size and presumably other life history traits. These results lend confidence to my proposed bounds for these faster rate taxa, and hence, to the revision of dos Reis et al.'s (2012) calibration scheme, which supports the soft explosive model for placental mammal evolution ( Fig. 4 d).

An additional challenge to explosive models of placental evolution is the contention that they necessitate implausibly high rates of molecular evolution in the earliest Paleogene. The argument is compelling, because it focuses on local rate shifts around the divergences of interest, isolating these to some extent from potentially misspecified rate models and calibrations. However, only hard explosive models were tested by Springer et al. (2013) and Beck and Lee (2014) , while Bininda-Emonds et al. (2012) forced all placental crown orders to diverge almost simultaneously.

The soft explosive model allows Cretaceous placental origins, but still requires that the major interordinal diversification occurs after the KPg. To test whether rates of molecular evolution are plausible under the soft explosive model I placed hard maximum bounds at the KPg (66 Ma) for the crown ages of Afrotheria, Xenarthra, and both boreoeutherian clades (Laurasiatheria and Euarchontoglires). These constraints were employed alongside Meredith et al.'s (2011) calibrations, including all the high bidders. Rates of molecular evolution among all lineages that cross or closely follow the KPg fall well within the typical range for other placental lineages ( Fig. 5 ). Thus, the soft explosive model is consistent with “business as usual” rate variation at the KPg boundary.

F igure 5.

Inferred rates of molecular evolution among placentals, with the four basal crown clades: Laurasiatheria, Euarchontoglires, Afrotheria, and Xenarthra constrained to post-date the 66 Ma Cretaceous–Paleogene (KPg) boundary. Otherwise the calibration scheme follows the “exclusion” Meredith et al. (2011) treatment from Table 2 . Rates correspond to the parent lineage of each dated node. The gray box covers superordinal rates for lineages that cross or immediately follow the KPg (all interordinal divergences within Laurasiatheria and Euarchontoglires occur from 62.5 to 66 Ma). Lower rates of molecular evolution over the most recent 20 myr correspond to increased sampling among large/long-lived groups, such as whales and seals.

F igure 5.

Inferred rates of molecular evolution among placentals, with the four basal crown clades: Laurasiatheria, Euarchontoglires, Afrotheria, and Xenarthra constrained to post-date the 66 Ma Cretaceous–Paleogene (KPg) boundary. Otherwise the calibration scheme follows the “exclusion” Meredith et al. (2011) treatment from Table 2 . Rates correspond to the parent lineage of each dated node. The gray box covers superordinal rates for lineages that cross or immediately follow the KPg (all interordinal divergences within Laurasiatheria and Euarchontoglires occur from 62.5 to 66 Ma). Lower rates of molecular evolution over the most recent 20 myr correspond to increased sampling among large/long-lived groups, such as whales and seals.

## M olecular D ates and the F ossil R ecord

Any diversification model for placental mammals should fit both the molecular and fossil evidence. It is important here to consider what evidence the fossil record brings to bear on placental origins, because much recent debate has been polarized between direct reading of the fossil record (e.g., O'Leary et al. 2013 ), and largely dismissing the incomplete fossil record (e.g., Springer et al. 2013 ). Historically, paleontologists have not universally favored explosive models. Cladistic assignments for Cretaceous zhelestids and zalambdalestids within the modern radiation of placentals ( Archibald 1996 ; Archibald et al. 2001 ) support the long-fuse model ( Fig. 3 c). However, this argument for ancient placental origins is now invalid, with both of these fossil taxa now recognized as stem eutherians (e.g., Wible et al. 2009 ; Zhou et al. 2013 ).

Cretaceous origins for crown primates have also been favored by some paleontological models. Tavaré et al. (2002) and Wilkinson et al. (2011) modeled primate diversification and fossil sampling to estimate how far back their origin predates their earliest fossil appearance at approximately 56 Ma. However, key assumptions that were not based on empirical data predispose these studies to recovering ancient divergences. In particular, assuming logistic species accumulation (favoring slow initial diversification), and long times to speciation (2–3 myr) both favor primate diversity being inferred to accumulate gradually over a long missing history. That these parameters are misspecified is suggested by Wilkinson et al.'s (2011) simulations greatly underestimating modern diversity. When Wilkinson (2007) had partly circumvented these questionable assumptions, by using posterior means for lineage birth–death parameters, the median estimate for primate divergence fell from approximately 80 Ma to 59.6 Ma. This is consistent with most other fossil sampling and phylogenetic inferences of missing clade history favoring explosive models with few Cretaceous placental lineages ( Alroy 1999 ; Foote et al. 1999 ; Archibald and Deutschman 2001 ; Hunter and Janis 2006 ; Wible et al. 2009 ; O'Leary et al. 2013 ).

The missing history of placentals implied by the recent molecular consensus ( Fig. 1 e), before the group's first fossil appearance approximately 66 Ma ( Hunter and Janis 2006 ; Archibald et al. 2011 ) is, counterintuitively, most defensible at its deepest extreme, the approximately 100 Ma crown origin. The first of two reasonable explanations is that the earliest crown placentals may have fallen outside the survey of the fossil record ( Springer et al. 1997 ). This is because phylogeographic inference often reconstructs Africa as the origin for placentals (e.g., Springer et al. 2011 ), and Africa has no mammal record for the entire Late Cretaceous (66–100 Ma). The second argument (e.g., Springer et al. 2007 ) is that morphological phylogenetics has been unable to resolve most interordinal placental relationships, such that early placentals may still be hidden among sampled fossils. For example, the well-regarded Novacek (1992) tree and the massive O'Leary et al. (2013) study only recover two to three of the 16 placental interordinal groupings. Hence, Gondwanan or morphologically cryptic origins may explain the basal few placental lineages extending back into the Cretaceous.

However, framing the debate in terms of placental origins distracts from more perplexing mismatches. The first is that the most profound diversification event in the group's history, dated by the molecular consensus at approximately 83 Ma, leaves no trace in the fossil record ( Fig. 4 a–c). What makes this so surprising is that molecular biogeography ( Springer et al. 2011 ) places this explosive radiation, which includes stem members of all 11 boreoeutherian orders, in Eurasia and North America, right beside the best Late Cretaceous fossil faunas. Yet, eutherian species richness is virtually unchanged in these Campanian (∼71–84 Ma) fossil faunas. The only new family to appear, the gypsonictopids, are probable stem eutherians ( Goswami et al. 2011 ).

The absence of diverse placental Cretaceous fossils is not easily explained as undersampling, because overall mammal fossil record completeness during the latest Cretaceous is similar to the subsequent Paleocene record that does reveal the placental radiation ( Alroy 1999 ; Benton 1999 ). The paleobiology database records a similar number of mammal-bearing sites from the geological ages before (Maastrichtian, 232) and after (Danian, 270) the KPg boundary. Meredith et al.'s (2011) dates imply nearly 30 modern placental lineages and a quarter of a billion years of Cretaceous ghost lineages among boreoeutherians alone ( Table 2 ). This is just the tip of the iceberg. Lineage birth–death processes would imply hundreds of ecologically diverse placental species, all somehow hidden in close view of well-sampled fossil faunas.

The second major mismatch is that the recent molecular consensus dates for placentals are blind to the group's fossil record surge in diversity during the ecological opportunity that followed the KPg extinction (see Fig. 4 ). Bininda-Emonds et al. (2007 , 2012 ) and Meredith et al.'s (2011) molecular diversification analyses instead suggest a decline across the KPg and throughout the Paleocene. Bininda-Emonds et al. (2007) hypothesize that diversification of modern placental lineages was suppressed during the Paleocene by multituberculates, and now extinct eutherian Plesiadapiformes and “condylarths.” However, it is unclear why, after diversifying alongside multituberculates, placentals fated to leave modern lineages were initially suppressed by the same multituberculate families, while placental groups fated for later extinction initially diversified. And, instead of suppressing modern clades, the Plesiadapiformes and “condylarths” may actually have given rise to major diversifications, respectively, within Archonta ( Ni et al. 2013 ) and Laurasiatheria ( O'Leary et al. 2013 ). The analyses presented here fit the more parsimonious, traditional fossil record interpretation of a few surviving placental lineages founding an explosive diversification following the KPg extinction event.

## C onclusions

Geomolecular dating describes modern divergence analysis, for which the role of geological information extends beyond providing a timescale, to informing molecular rate variation across the tree. Fossil calibrations can also be used to test the efficacy of models of molecular rate evolution, and in the case presented here, reveal substantial misspecification associated with life history rate correlates. A central dilemma is that cautious calibration is essential to prevent errors, which can disproportionately influence divergence estimates, yet tight calibration is vital to buffer against rate model errors and any calibration errors at other nodes. To help balance this paradox, minimum bounds should emphasize phylogenetic near-certainty and maximum bounds should be appropriately conservative (e.g., Barnett et al. 2005 ; Parham et al. 2012 ), but must be allowed to be tight where good fossil records permit.

Modeling molecular rate evolution remains a great challenge, as evidenced here by relaxed clocks providing little improvement over the strict clock, in the absence of multiple calibrations. As a consequence, statistical modeling of calibration priors and tip dating look set to play important roles in geomolecular dating, although both approaches require considerable development and should currently be viewed with particular caution. My reanalysis of Meredith et al. (2011) seeks to reduce the potential for transferring calibration and rate model errors across the tree. The divergence estimates support the soft explosive model, with a 75–80 Ma origin for crown placentals. The major interordinal diversification spike coincides closely with the 66 Ma KPg event, consistent with ecospace filling in the wake of the extinction of non-avian dinosaurs.

## F unding

This work was supported by the Queensland University of Technology and an Australian Research Council Discovery grant [DP150104659 to M.J.P.].

## A cknowledgments

I am grateful to William Dodt, Alistair Evans, Elizabeth Lindsay, and Rachel Warnock for helpful discussions and comments on the manuscript. Systematic Biology Editor-in-Chief Frank Anderson, Associate Editor Michael Charleston, Nicolas Lartillot, Fredrik Ronquist and an anonymous reviewer provided valuable comments and constructive criticism.

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## Author notes

Associate Editor: Michael Charleston