The most common errors regarding node dating

Many molecular dating studies rely on a few, sometimes poorly understood fossils as age priors to constrain nodes heights (ages) in an ultrametric tree. But do the authors (peers, editors, and – ultimately – readers) know what they do/has been done? Maybe, maybe not; in any case reading the papers can be confusing. In this post, I'll try to give a quick step-in.

The very principle of node dating using fossils

It has been pointed out occassionally that many molecular clocks are too young. This critique is often true but overlooks what node dating does. The oldest (known) representative of a lineage (e.g. genus or family) is used to constrain the possible minimum stem (root) age of that lineage. Since we (typically) do not know how close this oldest (and recognisable) representative is to the actual first member of the lineage, i.e. the common ancestor (CA) of the lineage (the lineage's root), it can only inform a lower boundary (Fig. 1). Thus, node-dating-based estimates can be expected to be underestimating in most of the cases and should always be regarded and treated as minima. The closer the fossil(s) used as constraint is (are) from the actual lineage-CA (root nodes), the less underestimating will be the minimum age estimates.

Fig. 1 A true (ultrametric) tree of a genus with three extant taxa. The genus' crown age is defined by the most recent common ancestor of the modern species; the genus' stem age by the point at which the genus diverged from its sister clade.

Using A’, the oldest known fossil of lineage A, as minimum age constraint for the MRCA of the modern species A, C, and D, one may infer a very young and underestimated divergence age for the sister species C and D or the genus’ stem age. But the estimates – e.g. C and D diverged before 2.5 Ma, the genus diverged latest at 20 Ma – are not wrong, the real divergence ages (10 Ma, 40 Ma) are greater than the estimates.
New palaeontological evidence may show that lineages A and CD were already present at nearly 20 Ma, and accordingly our node-dating minimum estimates will become only slightly underestimating. Since many dating studies rely on conservatively assigned (regarding taxonomy) deep node constraints (not rarely taken from earlier dating studies), it is not overly surprising that estimates towards the tips can be highly underestimating.

Fig. 2 Same tree, but older fossils that are closer to the nodes they can constrain, which automatically leads to less underestimating minimum divergence ages

Sensible node dating requires direct input/control by palaeontologists

Fact is: only palaeontological experts (may) have the overview to decide which fossil is a good candidate for a node-dating constraint. Any (node) dating study stands and falls with the quality of the known fossil record. To get substantially better dating estimates, one primarily needs a better understood fossil record. Nothing else.
Relatively young fossils (A’, B, S1 in Figs 1 and 2) musts result in (severely) underestimated (“too young”) divergence age estimates.
Wrongly assigned/misinterpreted fossils naturally may result in fundamentally wrong estimates (Fig. 3).

Fig. 3 Same tree, x-axis now reflecting evolution of the genus within its morphospace. Showing essentially a D-type morphology, fossil S1 (Fig. 2) is labelled as D', and erroneously used by the dater to constrain a much too high minimum age of the MRCA of C and D (= stem age of D).

Examples of odd, meaningless or even methodologically flawed dating estimates – related to lack of proper age constraints or use of poorly understood molecular data (problematic topologies) – can be found throughout literature, in low- to high-impact journals. The most intriguing example for me was a paper by Larson-Johnson (2016) on rate shifts in Fagales, published last year in New Phytologist, a mid-high-tier, very prestigious journal. Apparently, the paper was waved through with the blessing of high-profile scientist (see Acknowledgments) but without any proper peer review. The node dating is fundamentally flawed, partly because the author uses (the wrong) fossils as absolute age constraints. Overall, it seems the constraints were just filtered from the comprehensive supplement of a not much better paper on Fagales – regarding the purported dating results – published in 2012 in Systematic Biology, a high-tier, also confidentially peer-reviewed journal (Sauquet et al. 2012; the methodology is fine, but the data and tested scenarios are not). In case you are interested in more details, see the Supplemental Files S2, S3 (included in this archive) of Grímsson et al. (2016), and our discussion.

Furthermore, the palaeontologist may have a good idea whether a fossil represents a stem or crown taxon of a lineage. This can help to get more useful estimates, even if it means to bend the rules of node dating. The reason lies in the somewhat different definition of stem and crown when using Hennig’s phylogenetic classification or cladistics as used in molecular dating (Fig. 4).

Fig. 4 Same tree, with two more fossil taxa. A*, the first representative of the lineage leading to A (earliest precursor of A), and S2, a crown fossil (according definition of Doyle & Donoghue 1993), but part of the stem (root branch) in a node-dating framework. Both fossils would give sensible estimates when used to constrain the genus' crown age (MRCA modern species), but in case of S2 they would be overestimating. Note that in the real world, it may be impossible to decide whether a fossil represents A* or S2.

Fossil S2 shows all (syn)apomorphies of the (modern) genus, thus, it can be regarded as a crown taxon. It would make a sensible constraint for the age (absolute, not minimum) of the most recent common ancestor (MRCA) of all modern taxa (A, C, D), i.e. provide a direct constraint for the crown age of the genus. But since it is part of the stem (cladistically speaking) and cannot be assigned to one of the subclades within the genus (A, BCD, CD, C, D), it can only be used to inform a (much too young) minimum stem age for the genus itself following the standard protocol of node dating. Note that when we – against the rules – use S2 to constrain the genus' crown age all subsequent estimates may be (a bit) too old! However, in reality, it is much more likely that such an early crown taxon is not the very last common ancestor of all modern species or stem taxon (S2), but either a precursor (A*) or early (extinct) sibling (like B), hence, likely provides a best-as-possible minimum age constraint for the (modern) genus’ crown age. A real-world example is Fagus langevinii [PDF], used by Sauquet et al. (2012) – methodologically correct – as much too young minimum stem (root) age constraint for the lineage leading to the beech trees, Fagus. Regarding its morphology and the fossil record in general, the fossil is more likely to inform a sensible crown age of the (modern) genus (Denk & Grimm 2009; Grímsson et al. 2016; Renner et al. 2016).

Lineage sampling and topological ambiguity

Something often overlooked in node dating studies, and their interpretation, is lineage sampling and the bias because of the used topology. Let’s assume that we don’t have any data on C and D in our tree, and only A-type/-similar fossils (Fig. 5). There is no genus crown anymore, just a single taxon. Following the node dating rules, A* or S1 can only inform a minimum stem (root) age of the genus (represented by A), which will be too young.

Fig. 5 Same tree, but C and D have not been sampled for the analysis. Accordingly A*, which usually would provide a best-possible constraint for the genus' crown age, only provides a poor constraint for the genus' stem age.

As soon as we add C or D to the dataset, another species of the genus, A* does inform the stem (root) age of lineage A, i.e. one node up, and can provide us with quite a sensible age prior (fix point; Fig. 3). However, if our inferred tree resolves C as sister of A but not D, we'll assign A* to an artificial, too young node.

Fig. 6 A partly wrong tree (just shifted the genus' root); now A* constrains the MRCA of A and C, but not anymore of all modern species A, C, and D as before.

A few real-world examples illustrating these issues.
Liu et al. (2014) argued that an Eocene Alnus fossil is a member of one of the subgenera (subgenus Alnus), and concluded that the Alnus subgenera were already established by that time, i.e. crown group radiation started, contrasting our dating estimates inferring a 15 Ma younger crown age (Grimm & Renner 2013). But in fact, there’s no conflict, as our data set (harvested from gene banks) only included members of subgenus Alnus – as it turned out later. Hence, our crown age only refers to the subgenus Alnus, but not the genus Alnus itself, and stands unchallenged.
Not only the Fagales rate shifts estimated by Larson-Johnson (2016) are based on a pretty wrong topology, in particular when it comes to intra-family relationships (poor genetic data selection). Similar problems can be found in the all-Fagales studies of Xing et al. (2014) and Xiang et al. (2014). Although all three studies use partly the same fossils to constrain node ages – fossils also included by Sauquet et al. (2012) – they place them at different nodes (see Fig. S2-1 in the supplement to Grímsson et al., 2016). Hence, the same fossils are used to inform the age of (substantially) different MRCAs, but all in-line with node dating procedure! Sauquet et al. and Larson-Johnson eliminated some of the topological ambiguity imminent from their data sets by leaving out a couple of genera. Thus, assigning fossil-based age constraints to, actually, too deep nodes in their tree, similar to what I depict in Fig. 5.

If you must do node dating…

The fossilized birth-death dating (FBD; Heath, Huelsenbeck & Stadler 2014) is clearly superior (in principle and practise) and if you have really good morphological data, total-evidence dating (Ronquist et al. 2012) may be an option (not for plants, I'm afraid). Nonetheless, classic node dating may be inevitable in many cases. So, here’s some advice what to do (and what peers should ask when judging a node-dating paper):

• Contact a palaeontologist who worked on the group from which you select your dating constraints and has an overview about fossil record. (If you’re lucky, you get a full fossil record that allows you to do FBD.)
• If nobody is available, many modern groups are still poorly studied regarding their fossil records and palaeontological knowledge is somewhat dying out (at least the number of palaeobotanists and positions is steadily declining), make a proper literature search (i.e. checking original palaeontological literature, not other dating papers), and put up a table listing the fossil records. Provide that table as supplement (open data), so others can elaborate on it (always a nice gesture for future research).
• Given the uncertainty about the actual positions of fossils in the phylogeny (is it a A*, B or S1?), one should play around with different constraints. Rather than using all fossils to constrain many nodes in your chronogram at once, run several chronograms each using just a single constraint and compare the results. If the different fossil constraints end up with similar estimates, they can’t be too wrong. This also serves as test to see which fossil doesn’t fit at all (maybe because they have been misinterpreted, maybe because the molecular-inferred topology has some issues). But if you use them up in one single run, you have no control on their biases.
• Same for topologies. The era of Big Data, next-generation sequencing and (beauti)fully resolved, unambiguous phylogenies may be dawning, but most current data sets used for dating are still oligogene data. They can include (substantial) internal conflict (e.g. the data used in the all-Fagales studies mentioned above) and may be supporting more than one topological alternative; and eventually resulting in a Bayesian highest posterior probability (PP) tree that has some odd branching patterns (watch for low PP, but also branches with high PP and low bootstrap support). Make sure you have a proper tree or several of them and fix the topologies for the dating analysis rather than leave it all to the BEAST.

One last note on the data: if you’re doing dating on genera (species-level), you naturally want to include as many species as possible, but you need good data, too (ideally no data gaps, data with sufficient diversity). If you’re doing families or higher hierarchies, any two genera will give you a crown and allow estimating a crown age, but don’t confuse this with the actual family crown (age); see e.g. some of the youngest alternatives for divergence ages provided on the otherwise brilliant Angiosperm Phylogeny Website (Stevens 2001 onwards). To get a (methodologically) meaningful family crown age one needs to sample all genera/lineages of a family, or at least the (putatively) earliest diverging branches.

And always remember: Whatever the result, it’s all just minimum estimates. But, when thoughfully done, they may be close to the actual point of divergence.

Cited literature

Denk T, Grimm GW. 2009. The biogeographic history of beech trees. Review of Palaeobotany and Palynology 158:83–100.
Grimm GW, Renner SS. 2013. Harvesting GenBank for a Betulaceae supermatrix, and a new chronogram for the family. Botanical Journal of the Linnéan Society 172:465–477.
Heath TA, Huelsenbeck JP, Stadler T. 2014. The fossilized birth–death process for coherent calibration of divergence-time estimates. Proceedings of the National Academy of Sciences 111:E2957–E2966.
Liu X, Manchester SR, Jin J. 2014. Alnus subgenus Alnus in the Eocene of Western North America based on leaves, associated catkins, pollen, and fruits. American Journal of Botany 101:1925–1943.
Renner SS, Grimm GW, Kapli P, Denk T. 2016. Species relationships and divergence times in beeches: New insights from the inclusion of 53 young and old fossils in a birth-death clock model. Philosophical Transactions of the Royal Society B DOI:10.1098/rstb.2015.0135.
Ronquist F, Klopfstein S, Vilhelmsen L, Schulmeister S, Murray DL, Rasnitsyn AP. 2012. A total-evidence approach to dating with fossils, applied to the early radiation of the hymenoptera. Systematic Biology 61:973–999.
Stevens PF. 2001 onwards. Angiosperm Phylogeny Website. Version 8, June 2007 [and more or less continuously updated since]. Available at http://www.mobot.org/MOBOT/research/APweb/ (accessed 30/03/2017.
Xiang X-G, Wang W, Li R-Q, Lin L, Liu Y, Zhou Z-K, Li Z-Y, Chen Z-D. 2014. Large-scale phylogenetic analyses reveal fagalean diversification promoted by the interplay of diaspores and environments in the Paleogene. Perspectives in Plant Ecology, Evolution and Systematics 16:101–110.
Xing Y, Onstein RE, Carter RJ, Stadler T, Linder HP. 2014. Fossils and large molecular phylogeny show that the evolution of species richness, generic diversity, and turnover rates are disconnected. Evolution 68:2821–2832.
Grímsson F, Grimm GW, Zetter R, Denk T. 2016. Cretaceous and Paleogene Fagaceae from North America and Greenland: evidence for a Late Cretaceous split between Fagus and the remaining Fagaceae. Acta Palaeobotanica 56:247–305. http://dx.doi.org/10.1515/acpa-2016-0016
Larson-Johnson K. 2016. Phylogenetic investigation of the complex evolutionary history of dispersal mode and diversification rates across living and fossil Fagales. New Phytologist 209:418–435.
Sauquet H, Ho SY, Gandolfo MA, Jordan GJ, Wilf P, Cantrill DJ, Bayly MJ, Bromham L, Brown GK, Carpenter RJ, Lee DM, Murphy DJ, Sniderman JM, Udovicic F. 2012. Testing the impact of calibration on molecular divergence times using a fossil-rich group: the case of Nothofagus (Fagales). Systematic Biology 61:289–313.