In order to compare the evolutionary history of a group with global processes of the Earth, an absolute time scale is required. For example, molecular dating studies have severely challenged the commonly assumed role of vicariance (due to plate tectonics) in shaping the biogeographic distribution of many clades (for reviews, see Crisp et al., 2011 and Renner, 2005). Furthermore, current probabilistic approaches to reconstructing biogeographic history typically rely on dated trees, such as the dispersal-extinction-cladogenesis (DEC) model implemented in Lagrange (Ree and Smith, 2008). Another example where molecular dating studies have played an important role is whether past climate change had an influence on the diversification of large clades at a regional scale (Linder, 2003).

Over the last few years, considerable interest has grown in estimating speciation and extinction rates from molecular phylogenies, with the continuous development of increasingly complex models accounting for variable rates through time and across lineages (Alfaro et al., 2009, FitzJohn et al., 2009, Morlon et al., 2011 and Stadler, 2011). All of these methods require an absolute or relative time scale as a prerequisite.

A very wide range of contemporary methods in comparative biology rely on dated trees, for instance to infer ancestral states or to test the correlation between two traits (for reviews, see O’Meara, 2012 and Pagel, 1999). However, for many methods, nonultrametric trees obtained from phylogenetic analyses (i.e., phylograms, with branch lengths proportional to the number of inferred substitutions) are also acceptable and commonly used.

Molecular dates can be used to test whether two clades of interacting organisms, such as parasites and their hosts or plants and their pollinators, have diversified synchronously (Cardinal and Danforth, 2013, Cruaud et al., 2012 and Ramírez et al., 2011).

Molecular dating methods have also been developed for and applied to infraspecific studies to address a wide range of topics, including applications to medicine such as the timing of emergence of HIV strains (Gilbert et al., 2007).

Although absolute divergence times might be interesting in themselves, most researchers will need them for a specific purpose as outlined above. If the clade studied has a rich fossil record and only a few nodes need to be scaled in time, paleontological dating might be sufficient (Magallón and Sanderson, 2001 and Marjanović and Laurin, 2007). If time-scaled trees are needed for comparative analyses without specific attention to absolute time, molecular dating might or might not be necessary. The risk is to increase error compared to using molecular branch lengths only. The gain is to dissociate rates of molecular and morphological evolution, in situations of strong molecular rate variation, where long branches do not necessarily imply long times, and short branches do not necessarily reflect short times. However, if the assumption that molecular and morphological rates are linked can be justified to be biologically sound, then molecular dating can be avoided in comparative analyses. In studies of biogeography, diversification rates, or co-diversification requiring all divergence times to be known in absolute time, molecular dating analyses appear necessary, but results should be interpreted with caution depending on the quality of the data available for estimating divergence times (see below).

There are four main kinds of calibration for molecular dating analyses.

Fossil calibration often involves three sources of uncertainty, which should be properly acknowledged.

A problematic aspect of conducting molecular dating analyses calibrated with the fossil record is that a set of minimum age constraints alone is not sufficient for the analysis to converge on a unique or restricted range of solutions (Ho and Phillips, 2009). Therefore, it is often necessary to add a maximum age constraint on at least one node in the tree, which will effectively restrict the range of solutions for the entire tree. This is often applied to the root node. A maximum age constraint could be the oldest biologically sound age of a clade, argued either from the fossil record or from previous molecular dating analyses. To justify a maximum age based on the fossil record is difficult because many lineages have long sampling gaps (or ghost lineages), which are difficult to quantify, and absence from the fossil record does not mean that the lineage was not there. A case is more easily made when the fossil record is rich, well sampled, and globally distributed, and the clade in question has unmistakably diagnostic features. This is the case, for instance, of tricolpate pollen, diagnostic of the eudicot clade of angiosperms, which appears at the Barremian/Aptian boundary but is completely absent from any older deposits. This has been used extensively to justify a maximum age constraint of 125 million years on crown eudicots in many studies of angiosperm divergence times (e.g., Magallón and Castillo, 2009). Finally, it should be noted that although a single maximum bound is in principle sufficient, multiple maximum bounds would in fact be desirable in order to best inform molecular rate variation across the tree.

Penalized likelihood dating (implemented in r8s; Sanderson, 2002 and Sanderson, 2003) and various other dating methods only allow strict minimum or maximum age constraints for calibration. However, a rising number of dating methods are implemented in Bayesian frameworks that allow more sophisticated age constraints to be applied, in the form of prior distributions (for reviews, see Ho, 2007 and Ho and Phillips, 2009). These priors, such as the lognormal and the exponential priors, allow the user to enforce a strict minimum age (offset value) while specifying that the age of the node is unlikely to be much older (diminishing tail of probability) than the set minimum age (for an exponential prior) or median age (for a lognormal prior). These properties can be particularly useful when modeling the sampling gap discussed above. However, the current practice of using these priors in molecular dating analyses is somewhat debatable. Indeed, in addition to a strict minimum age, the exponential prior requires one additional parameter (mean), and the lognormal prior requires two parameters (mean and standard deviation). These parameters are often set quite arbitrarily (or using the defaults of the software) and how exactly this is preferable to uniform priors (the equivalent of simple strict minimum or maximum age constraints) remains uncertain. All of the priors cited above (uniform, lognormal, exponential) share hard minimum bounds, allowing the enforcement of strict minimum ages. However, additional priors implemented in some (but not all) Bayesian relaxed clocks also allow the specification of soft minimum or maximum bounds (Ho and Phillips, 2009 and Yang and Rannala, 2006). These properties can be interesting when one wishes to use minimum or maximum age constraints without being absolutely certain that these are correct.

The program r8s (http://loco.biosci.arizona.edu/r8s/) is a post-tree dating software with autocorrelated relaxed clock models. r8s was originally written by Sanderson (1997) to implement nonparametric rate smoothing (NPRS), an autocorrelated relaxed clock. NPRS was very popular in the early 2000s and has been used in many molecular dating studies, but has since been replaced by penalized likelihood (PL), another autocorrelated relaxed clock (Sanderson, 2002 and Sanderson, 2003). Penalized likelihood is an interesting trade-off between a strict molecular clock and an entirely uncorrelated clock, with a smoothing value determining the level of autocorrelation. The optimal smoothing value depends on each data set and is typically determined during a cross-validation step prior to the estimation of divergence times. Cross-validation can take a few minutes to a few hours to complete, depending on the number of taxa, whereas divergence time estimation is virtually instantaneous. For very large trees (e.g., 10,000 taxa), a modified, much faster version of PL is now available in the program treePL (Smith and O’Meara, 2012).

The input file is a NEXUS file where a phylogram in Newick format has been pasted from a previous phylogenetic analysis. The choice of a particular phylogram for the dating analysis can be important. The best-scoring tree from a maximum likelihood analysis such as RAxML (Stamatakis, 2006) is an option. The majority-rule consensus tree from a Bayesian analysis such as MrBayes is another one, but polytomies can have a confounding effect on accurate divergence time estimation. Finally, it is not recommended to use a maximum parsimony phylogram as the input tree because parsimony branch lengths typically require additional assumptions. If a maximum parsimony topology is still chosen, branch lengths can be optimized according to an explicit model of molecular evolution in software such as PAUP* (Swofford, 2002). It is important that the input phylogram is rooted correctly and that the most external outgroup lineage is pruned prior to the analysis (either by manually editing the phylogram or by using the prune command of r8s). This is because phylogenetic reconstruction programs work on unrooted trees and are not able to split the outgroup branch length correctly without additional information. In addition, zero-length (or near-zero-length) terminal branches must be pruned prior to the analysis (prune command) and the internal ones must be collapsed (collapse command). Calibrations are set easily in the NEXUS file with the constrain command either in the form of minimum or maximum age constraints. The nodes for calibration must have been previously defined with the mrca command by providing at least two terminal taxa, of which the most recent common ancestor is the node of interest.

One important shortcoming of r8s is that it does not provide confidence intervals on estimated ages, but instead point estimates. However, it is quite easy to obtain confidence intervals by running the analysis on a collection of bootstrapped trees, varying in branch length but not topology. This collection must be generated in another program such as RAxML or PAUP, with the molecular sequence data and the fixed tree topology as input.

The program BEAST (http://beast.bio.ed.ac.uk/) is a simultaneous tree reconstruction and dating software with uncorrelated relaxed clock models. BEAST allows a wide diversity of analyses on rooted timetrees in a Bayesian framework (Drummond and Rambaut, 2007 and Drummond et al., 2012). Although BEAST can also be used to reconstruct phylogenies, it became popular for molecular dating due to its implementation of the uncorrelated lognormal (UCLN) relaxed clock proposed by Drummond et al. (2006). At the time, the UCLN offered a unique uncorrelated alternative to the surge of autocorrelated relaxed clocks, although uncorrelated clocks are now also available in other packages (e.g., PhyloBayes and MCMCTree; Lartillot et al., 2009 and Yang, 2007).

Running BEAST involves several steps, each requiring a different program (but all are distributed as part of the same package). First, the user configures the analysis in a graphical interface called BEAUTi. The input is a molecular sequence alignment. The user is invited to set up data partitions, assign a specific model of substitution to each partition, specify calibrations in the form of prior distributions, and adjust various parameters of the MCMC analysis. The output of BEAUTi is an XML file (very different from a NEXUS file), which is the input for BEAST and can also be edited by hand for further adjustments. Then, the Bayesian analysis is run in BEAST and can take a long time to complete (a few hours up to a few months), depending on the number of taxa, the size of the alignment and number of partitions, the number of generations of the MCMC chain, and the power of your computer. For this reason, many users tend to run BEAST on a multicore server or a remote cluster facility such as CIPRES (Miller et al., 2010). As with other Bayesian phylogenetic software, it is strongly recommended to run and combine multiple independent searches and it is also necessary to check for convergence, for instance by using Tracer (Rambaut and Drummond, 2007). The main outputs of BEAST are a parameter log file (useful, in particular, to check convergence) and a tree file. Log and tree files from multiple runs can be combined and resampled using LogCombiner. Finally, TreeAnnotator is used to summarize the sample of post-burnin trees (chronograms) as a single tree (chronogram) annotated with various relevant statistics, such as mean age and 95% confidence intervals for each node, branch support in the form of posterior probabilities, and estimated rates of substitution for each branch. These metadata can typically be read by a tree viewer such as FigTree (http://tree.bio.ed.ac.uk/software/figtree/).

In spite of the excellent tutorials and manual, the user if often faced with difficult choices, partly because BEAST can perform so many different analyses. First, BEAST does not require an outgroup to be specified and can potentially root the trees simply based on the pattern of branch lengths (i.e., some rooted trees have a better likelihood than others). However, it is possible to specify an outgroup by defining the ingroup as a taxon and constraining this taxon to be monophyletic (easily done in BEAUTi). Second, the fact that BEAST reconstructs the phylogeny at the same time as it estimates divergence times can be an advantage as much as a problem. It is clearly an advantage because, unlike r8s, BEAST accounts for phylogenetic uncertainty in divergence time estimation. It can be a problem because calibration, as outlined earlier, is conditional on a given phylogeny. Indeed, the exact position of fossils may depend on the relationships among extant taxa. A solution is to calibrate only nodes with very strong support in previous phylogenetic analyses and to check, after the BEAST analysis, that these nodes are still receiving strong support, which is generally the case. An alternative is to enforce the presence of the calibrating node by constraining the corresponding group to be monophyletic, or to specify a stem rather than a crown node calibration if appropriate (e.g., if a fossil can be justified to be more closely related to a clade than any other taxon in the phylogeny, but the sister group of this clade is uncertain). Third, the user must choose and parameterize a prior distribution for each calibration, a difficult decision that should always be justified in the methods (see above). Fourth, BEAST requires a tree prior to be set, which will affect the likelihood of the distribution of the nodes across the tree. Typically, for analyses above the population level, a simple birth process (Yule) prior has been used in most molecular dating analyses, although a birth-and-death prior is also an option that has been used by various authors (e.g., Nagalingum et al., 2011). This is a difficult choice because a constant speciation and extinction rate, assumed in both priors, may not be realistic for some analyses, especially at large taxonomic scales (Alfaro et al., 2009). Although this is an area of current concern, especially among the diversification rate community, it has been argued that this choice may not have a strong impact on the analysis after all (Couvreur et al., 2010).

Finally, an important decision must be made when choosing the topology and node ages to be represented in the summary tree generated by TreeAnnotator. Contrary to MrBayes, the philosophy of BEAST is to choose a single tree sampled from the prior rather than build a consensus. The most commonly used rule for selecting a particular tree is to choose the one with the highest product of clade posterior probabilities, termed the maximum clade credibility tree. However, even when choosing this tree for topology, one still has to decide whether to set its node ages to the exact ages in the sampled tree or to the mean or median ages of the nodes calculated across the posterior collection of trees. This decision will depend on the context and have a different impact, whether the tree is only plotted (e.g., for a figure) or it is used in post-dating analyses (e.g., diversification rate or ancestral state reconstruction). Median ages are generally more appropriate than mean ages because estimates of divergence times are lognormally distributed (Morrison, 2008).

It is essential to always report confidence intervals on estimated ages, rather than mean ages or point estimates obtained from a single analysis. This is important because molecular dating is not precise, even when calibrated with multiple fossils (Sauquet et al., 2012 and Yang and Rannala, 2006). Reporting mean estimates to two decimal places without confidence intervals may lead to the impression of illusory precision, which is sometimes misinterpreted by readers not familiar with the field. Likewise, it would be better to compare confidence intervals on the estimated ages of a given node, when comparing different studies or different methods. If confidence intervals do not overlap, then a significant contradiction may be concluded among two analyses, a conclusion that is harder to reach when only mean ages differ.

When comparing results obtained with different methods, for instance different relaxed clocks, it is important to remember the assumptions of each method. In particular, it remains difficult, if not impossible, to assess whether an autocorrelated or an uncorrelated relaxed clock model better suits a given phylogeny. Bayes Factor comparison is a possibility to perform this assessment in some Bayesian frameworks that allow different models to be tested on the same data (e.g., BEAST, MrBayes, or PhyloBayes). However, the computation of Bayes Factors in itself is an area of current active research that has probably not reached maturity yet (Baele et al., 2013 and Xie et al., 2011). In addition, fossil calibrations appear to have a strong impact on best-fit relaxed clock model selection and it is possible that different relaxed clocks best fit different parts of the tree (Ronquist et al., 2012a).

When comparing a molecular dating analysis to previous studies, an important, potentially overlooked rule is to compare the same nodes. Indeed, many researchers have an interest in estimating the crown age of a particular taxon, and it is such ages that are commonly reported in tables of molecular dating papers. However, whether different studies are in fact reporting the age of the same node for a given taxon is highly conditional on taxonomic sampling. Studies focused on a particular taxon will often have included a wide, nonrandom sample of taxa designed to include all of the potentially basal lineages in the phylogeny, and therefore are likely to have the actual crown node of this taxon represented in their study. However, in large-scale studies (e.g., all flowering plants) it is common that the basalmost lineage of a taxon (e.g., an order) has not been included in the sample and therefore that the crown-group age reported for this taxon is in fact that of a subclade (Magallón and Castillo, 2009).

An additional source potentially interfering with direct comparisons of absolute ages obtained in different studies is the variation through time of the geological time scales themselves. As outlined earlier, if the latest time scale has been used in an analysis to convert stratigraphic ages into absolute ages for calibration, it is possible that the same analysis with the same fossils but a different time scale would have led to different results. However, this difference is likely to be thin in comparison to the wide confidence intervals generally obtained and may thus not be so problematic in practice.

A frequent problem with molecular dating results is that they often seem to contradict the fossil record. This contradiction can take two forms. Either the estimated crown-group age of a clade is much older than its oldest known fossils, as was found in many studies of angiosperms (Bell et al., 2005, Magallón, 2010, Magallón and Sanderson, 2005 and Smith et al., 2010) or bilaterian animals (Douzery et al., 2004 and Peterson et al., 2004), or the estimated ages, usually for subclades of the ingroup, are much younger than the fossil record suggests. These discrepancies have led to a large body of debate and discussion in the literature, which have pointed at the limitations of both the fossil record and molecular dating methods (Donoghue and Benton, 2007, Graur and Martin, 2004 and Pulquério and Nichols, 2007). First, it should be stated that such differences can be very interesting as a stimulus for further discovery and methodological improvement if one accepts the limitations of both approaches. Much older molecular ages may indicate that a clade has remained very low in standing diversity for a long time in its early history or was living in an environment that did not favor fossilization. Much younger molecular ages may, on the other hand, signify a failure of the relaxed clock model to represent accurately molecular rate variation without including more fossil calibrations, or that the presumed older fossils (not included as calibrations) belong instead to different clades or represent extinct stem lineages of the clade they were thought to be nested in. Either way, it is important to state that if one is very confident in the fossil record and not ready to accept a contradiction from molecular dating, then one should include the information from these fossils as additional age constraints in the analysis. For this reason, molecular dating should perhaps be named molecular and paleontological dating instead, better reflecting its truly hybrid nature, and any discrepancies between molecular and fossil ages should be regarded as a conflict between the fossils used for calibration and the rest of the fossil record. However, other sources of variation in molecular dates, such as substitution and relaxed clock models, may also contribute to these discrepancies. Finally, a recurrent theme and argument in these comparisons is that molecular ages are always underestimated and should only be taken as minimum ages, since the fossils only provide minimum ages. While this was true of earlier dating analyses using fixed calibration points, it would be incorrect to generalize this to contemporary molecular dating practice because, as stated earlier, some form of maximum age constraint is almost always needed in the analysis (either in the form of a hard maximum constraint, or in the form of priors with a diminishing tail of probability towards older ages).

Given the recently identified critical role of calibration and yet the presently very poor state of its practice and justification, it is not surprising that several different papers have independently come to the same conclusion that an improvement of this aspect of the field is urgently needed (Gandolfo et al., 2008, Parham et al., 2012 and Sauquet et al., 2012). Although each of these papers has proposed guidelines for this improvement, centered around a much more extensive and explicit documentation of the calibrations, one group has gone further by also creating a global Fossil Calibration database (Ksepka et al., 2011). This initiative is particularly interesting because it is associated with a new publication model, whereby articles focused entirely on justifying calibrations will be submitted to a new Fossil Calibrations section of the open access journal Paleontologia Electronica, peer-reviewed, and linked to the entries in the database.

Since fossils can be included as terminal taxa in phylogenetic analyses, they could in principle be included as terminal taxa in molecular dating analyses too, as long as morphological data are combined with molecular data to inform the fossil relationships. Thus, instead of being taken into account in the form of age constraints on nodes of the extant phylogeny, fossils would be part of the whole analysis, without prior hypotheses on their relationships, and with the age of the fossils themselves effectively calibrating and constraining the analysis. This approach, termed total evidence dating (in contrast with traditional node-calibration dating), has recently been tested for the first time in two different Bayesian frameworks. Pyron (2011) implemented it in BEAST to test the temporal origin of Lissamphibia, while Ronquist et al. (2012a) used MrBayes to obtain divergence times in Hymenoptera. More recently, the approach was also used in BEAST for spiders (Wood et al., 2013) and many more examples are likely to come soon. In addition, Lee et al. (2009) implemented an earlier, two-step version of this approach in a case study on lizards. Total evidence dating is particularly attractive because it allows to explicitly take fossil phylogenetic placement uncertainty into account in divergence time estimation. In addition, this approach enforces the phylogenetic analysis of fossils, which is widely recognized as desirable but easily bypassed in traditional calibration analyses, and because the age of the fossils is taken into account in this phylogenetic analysis, it may potentially lead to more accurate or realistic results than traditional, time-free total evidence analysis (e.g., a very old fossil is unlikely to be sister to an extant terminal taxon). However, the approach is not straightforward. It requires a morphological matrix of extant and fossil taxa in addition to the molecular data set of extant taxa, its proper implementation requires many tests and adjustments (Ronquist et al., 2012a), and future methodological improvements are expected. In particular, an area that will need special attention is the modeling of morphological evolution and the level of correlation between morphological and molecular change. In both BEAST and MrBayes, the models used so far are reversible Markov models (Lewis, 2001), which assume that rates of morphological evolution are constant through time and across lineages.