Molecular Clocks and Fossils: Two Rulers Competing in the Shadows

I Two Numbers That Do Not Add Up

The textbook story goes like this: the dinosaurs died out 66 million years ago, mammals filled the vacancies, and in time there were elephants, whales, bats, and us.

The molecular clock keeps a different timetable. A great many multigene and genome-wide analyses place the separation of the major living placental mammal lineages in the Cretaceous, with the basal nodes often dated to around 100–110 million years ago. In other words, while the dinosaurs were still doing perfectly well, the line that would lead to elephants and the one that would lead to whales had already parted company. They had been apart for 30 or 40 million years.

That is a consequential claim, because it says something else along the way: for those 30 or 40 million years, these lineages were going about their lives on Earth without leaving a single generally accepted fossil.

Paleontology has a name for a branch that must have existed on the tree but has no fossils to show for it: a ghost lineage. Every molecular-clock date older than the fossils draws a stretch of ghost lineage onto the tree. What the two sides have been arguing about, then, has never been an abstract number. It is the length of the ghosts.

Change their length, and you get two entirely different pictures. If the molecular side is right, several lineages that would eventually lead to modern orders were hiding among the mammals of the Cretaceous; no one could have recognized them then, and no one has dug them up since. If the fossil side is right, the entire fan of modern placental mammals unfolded within a few million years after the boundary.

The natural reaction is: two rulers, one saying earlier and one saying later. One of them must be wrong. Nor is this just about dinosaurs and mammals. “The molecular clock gives a date of…” now appears in almost every report about when two lineages split. What this essay is really about is everything packed into that phrase.

What I want to show is that this reaction conceals two assumptions, and neither holds.

The first is that the two rulers are measuring the same thing. The second is that they are independent of each other. They fail in different ways, so we need to take them separately.

This essay will not decide which side is right, either. It asks a different question: once two constructs have become inputs to each other, how much meaning is left in “Which one is right?” We will begin with where the molecular clock came from, because its origins bear directly on the second assumption.

In 1962, two researchers compared differences between protein sequences in different species with the divergence dates supplied by paleontology, and found that the amount of difference accumulated roughly with time. In 1965 they developed the idea into a systematic account. Almost simultaneously, in 1963, another researcher studying cytochromes proposed “genetic equidistance”: viewed from an outgroup, two descendant lineages can have accumulated approximately equal amounts of change since their common ancestor.

Together, these observations supplied the empirical basis for the idea that molecular evolution is approximately clocklike. Notice where this begins. From its very first day, the molecular clock took its time scale from paleontology. This was not a contamination that crept in later. It was how the clock was born. A sequence on its own can tell you how much has changed, not how long the changing took.

The mathematics of a strict molecular clock is simple: if a lineage has a constant substitution rate, molecular distance is proportional to time. If both descendant lineages evolve at that same rate, the distance between them is roughly proportional to twice the time since they diverged.

That “if” is the key to the whole affair, and most of the next five sections are devoted to it. Before we go any further, let us give three terms some substance. We will not get far without them.

The first is a node. A phylogenetic tree keeps branching, with living species at its tips. Each branching point is a node, representing the moment when two lineages separated. To “put a date on it” is to assign a year to one of those forks.

The second is a crown group. Find the last common ancestor of all the living members of a group: that ancestor, together with all its descendants, is the crown group. The third is the stem group: the close relatives that branched off before that ancestor and have no descendants left alive today.

So “the earliest crown-group placental mammal” and “the earliest close relative of placental mammals” refer to two different moments, which may be very far apart. Again and again below, that distinction will determine who is right and who is wrong. It will even do so twice for the same fossil.

II The Clock Is Not Strict, So We Have Many Kinds of Clock

First, put “substitution” on the ground: one base replaces another at a site and becomes fixed in the relevant lineage. The clock infers how many such events have accumulated. Both descendant branches accumulate them. If each evolves at rate r per unit time, their genetic distance after time t apart is approximately 2rt. A difference is not a date: without the rate, we still cannot read the clock.

The conditions a strict clock requires are much more demanding than the “neutral evolution” many people have in mind. The relevant branches must have sufficiently similar average substitution rates, at the sites being analyzed and over the time scale being analyzed.

Yet mutation rate, generation time, selective constraint, repair mechanisms, metabolism, and life history all vary systematically among lineages. A mouse turns over a generation in a few months. A whale takes decades.

Small-bodied lineages with fast metabolisms accumulate more substitutions in the same million years. So, in the great majority of real datasets spanning major groups and long stretches of time, the strict clock is usually rejected.

Rejection does not mean that molecular clocks are unusable. It means that, from then on, every molecular date comes with a choice of model, and the sequence does not uniquely determine that choice.

Modern deep-time dating therefore no longer asks whether the clock is strict. It asks: How should changes in branch rates be modeled? There are three main approaches.

The first is an uncorrelated clock. Every branch has its own rate, drawn independently from the same overall distribution. There is no requirement that a fast parent branch have fast descendants.

The distribution’s mean and dispersion are estimated from the data. This approach suits situations in which there is no clear reason to assume that rates carry a kind of lineage inertia. It also suits trees with frequent rate shifts whose locations cannot be specified in advance.

Its weakness is this: because each branch is allowed to vary independently, a history containing sustained, long-lived blocks of altered rates may be flattened out. One lasting local shift can become random heterogeneity scattered across the tree.

The second is an autocorrelated clock. A daughter branch’s rate is conditionally dependent on its parent’s: close relatives are expected to have similar rates, and larger drifts are allowed only over longer stretches of time.

This suits rate changes with some physiological or life-history inertia. But “rates really are autocorrelated” is itself an empirical assumption, and the scale of that autocorrelation changes with the depth of sampling.

The third is a local clock. It neither lets every branch change at will nor lets the whole tree drift continuously. Instead, it assumes that the tree contains several rate regimes. Early local clocks required researchers to specify in advance which branches shared a rate. Later random local clocks brought the locations of rate shifts, and the number of local clocks, into the statistical inference as well.

Local clocks are particularly well suited to a history in which a group undergoes a substantial change in life history and its descendants maintain the new rate for a long time. The difficulty is a much larger model space and much greater computational cost. All three approaches face the same requirement: the data must decide which fits best. Intuition cannot make the choice for us.

These three approaches may sound like different levels of refinement applied to the same thing. One example will show why they are not.

Australian grass trees are monocots that look like a clump of grass with a thick pole rising from it. They make a clean test case because their crown group hangs from the end of a very long stem branch with no internal calibration anywhere along it. In other words, time information has to be extrapolated from a long way away.

The researchers began with simulated data, setting the true crown-group age at 25 million years, then estimating it with different clocks.

The random local clock returned 28.4 million years, with a 95% interval of 11–42 million years. With a different tree prior, it returned 29.4 million years and an interval of 14–43 million years. Both intervals contained the true value.

The uncorrelated lognormal clock returned 4.1 million years, with an interval of 0.5–11 million years. Changing the tree prior gave 4.9 million years, with an interval of 0.5–10 million years. The true age of 25 million years did not come within either of those intervals.

The results from real sequence data were just as striking. The median age of the same crown group ranged from 3.3 million to 35 million years as the clock model changed, a roughly tenfold difference at the extremes. In most comparisons using the same data and the same tree prior, the two clocks’ 95% intervals did not even overlap. There is a point here that is easy to miss, and we will need it repeatedly.

In that simulation, the uncorrelated clock gave a narrower interval but failed to cover the known truth. The random local clock gave a wider interval and did cover it. A narrow posterior interval within a model, in other words, does not demonstrate that systematic error between models is small.

Both of these things go by the name “uncertainty,” but they are different things. The error bar measures uncertainty within the model. It does not measure uncertainty over the choice of model. Readers are usually shown only the former.

III Which Moment Does a Molecular Clock Measure?

We can now address the first assumption: are the two rulers measuring the same thing? The formal object a molecular clock estimates is the time of a node on a phylogenetic tree. In a species-tree analysis, this is usually interpreted as the moment when two lineages last shared an ancestor and then separated. But that object comes with four qualifications, every one of which can turn into several million years in a real dispute.

First, a single-gene clock directly estimates the coalescence time of gene lineages. That need not equal the actual time at which the species lineages split.

The mechanism is not difficult to understand. When two species separate, their ancestral population already contains polymorphism. After the split, take one copy of a gene from each side and trace them backward. The common ancestor of those two copies may lie a long way before the species split, because they were already two different alleles in the ancestral population.

We can calculate this. In the simplest neutral diploid coalescent model, once two lineages enter the ancestral population, the expected additional wait until they coalesce is on the order of twice the effective population size, measured in generations. With an ancestral effective population of 50,000 and a generation time of twenty years, the expectation from this term alone is about 2 million years. With an effective population of 100,000, it is about 4 million.

In large populations undergoing rapid successive divergences, this term can readily be of the same order as the several-million-year discrepancies debated in paleontology.

Essay Two used the same distinction when discussing the last common ancestor: the gene tree and the species tree are not the same tree. There, it determined whether an ancestor could be reconstructed.

Without gene flow after the species split, gene coalescence is no younger than that split. Concatenating many genes and reading their history directly as species divergence can charge some ancestral coalescent time to the species node. But that direction has a condition: the introgression discussed below can break it. “Always older” is not a rule for every gene history.

Second, the clock does not estimate when a morphology appeared. A lineage can separate from its sister and then retain a highly ancestral morphology for several million years.

In practice, this means that an early member genuinely within the crown group may be impossible for paleontologists to recognize if its teeth and bones still look exactly like those of its stem-group relatives. “Recognizable from diagnostic characters” is a different temporal quantity. Especially when diagnosis depends on a combination of traits, the split may precede the full assembly of that combination.

Third, it does not estimate when an ecological role was established. A split at a node tells us only that two ancestral lineages no longer shared the same branch. A further stretch of time may well separate that step from a change in body size or feeding strategy, the occupation of a new niche, or the development of a highly diverse crown group.

Fourth, it does not estimate when population divergence was “complete.” In speciation with gene flow, a split is not a mathematical instant. Different genomic regions can have different coalescent histories, and introgression can make some sites yield coalescence times later than the actual species split. What, then, does the fossil side measure?

The oldest known fossil first gives us a lower bound on age: the lineage was already present no later than this time. If a fossil reliably assigned to a crown group is 100 million years old, the crown-group split must have happened no later than 100 million years ago. It could perfectly well have happened 105 million years ago, or 120 million, or earlier still.

To treat “the oldest known fossil” directly as “the true age of origin” is to assume that the first preservation, the first discovery, and the first collection all happened to coincide with the moment of origin.

We therefore have a sequence of moments with no reason to be equal: the lineage split; the establishment of recognizable crown-group morphology; the first sampled occurrence in the sedimentary record; the emergence of a conspicuous ecological role. The earlier items are commonly older, the later ones younger.

If that is the situation, the molecular node will naturally be older than the recognizable fossils, and both sides may have measured their own objects accurately.

The “long-fuse” model of placental mammal evolution is built this way: it separates early lineage splits from later morphological and ecological expansion. Under this model, Cretaceous divergence in the molecular account and post-boundary radiation in the fossil account can both be true. They are not talking about the same event.

Nor was the model invented simply to smooth over a disagreement. It has testable consequences. If those splits really occurred in the Cretaceous, members of the lineages should exist in Cretaceous strata, even if their morphology does not yet let us recognize them. That is a prediction you can send people out to investigate, not an excuse.

But this resolution cannot be applied everywhere. It works only when the two sides really are measuring different objects. A genuine conflict over age arises only when both studies claim to be measuring the same historical event at the same node. Such cases do exist. Section Seven will give us several.

IV Three Layers of Error on the Fossil Side

Fossils are often treated as “the hard side”: a rock is as old as it is. That is only one-third right. Using a fossil to calibrate a node requires us to pass through at least three layers of error, and their magnitudes differ enormously.

The first is error in the age of the strata. This is usually the smallest layer, on the scale of hundreds of thousands to a few million years, and the methods are mature. The questions are: which bed did the specimen come from? How is that bed connected to a numerical chronology? Does the age interval come from direct radiometric dating or stratigraphic correlation? Are there regional differences in converting biostratigraphy into numerical ages?

Best practice in node calibration requires an independent argument for this layer, rather than a citation of a round number. Behind a fossil described as “100 million years old” there may be a directly dated ash bed, or there may be a biostratigraphic correlation spanning two continents.

Best practice is itself a checklist: what is the specimen’s catalog number, and where is it housed? What diagnostic evidence places it in that group, and can others test that placement? Which bed did it come from? Where does the age of that bed come from, and how large is the error?

The checklist looks like paperwork. Yet every item marks a place where a date can go wrong by tens of millions of years.

The second layer is error in phylogenetic placement. This is the main character in the story.

The very same bone can change the age of the node it calibrates by tens of millions of years without a single alteration to its stated radiometric age. At first glance that sounds exaggerated. It is not. The change takes place in a paper on morphological systematics, whose authors have not redated a single rock sample.

The reason is that the node a fossil can calibrate depends on its position in the tree, not on how much it looks like a modern member. A fossil securely placed in a crown group proves, at a minimum, that the split which formed that crown group had already occurred. Move the same fossil onto the stem outside the crown, and it ceases to supply any minimum age for the crown node. It can constrain only a deeper stretch of total-group history.

Placental mammals make the point particularly clear. If certain Late Cretaceous mammals are placed within the crown group of living placentals, they provide a Mesozoic minimum constraint on that crown. If those same morphologies are reassigned outside the crown, all they can establish is that the broader total group already existed.

The dispute concerns “where it sits on the tree,” not necessarily “how old the rock is.” The former is determined by a morphological matrix; the latter by a mass spectrometer. Their stability is very different.

This layer also has a direction, and the direction can go either way. Fossils often lack soft tissues, molecular characters, and parts of the skeleton. Preservation bias can systematically shift fossils that retain only hard tissues “toward the stem” on a morphological tree. Thus “it lacks this character of the modern crown group” has two possible explanations: it really is outside the crown, or the character was not preserved, was not coded, or still retained its ancestral state.

Essay Nine’s discipline of “the diagnostic characters are not yet a complete set” becomes calibration uncertainty here. In that essay, it determined whether a fossil counted as a particular kind of organism. In this one, it determines a date.

The opposite direction exists too, with stranger consequences. Misplacing a stem fossil within the crown makes the fossil minimum too old and can even produce a so-called “zombie lineage”: the molecular node is younger than the minimum fossil age assigned to it. That is logically impossible, forcing researchers back to recheck the model, the dating, or the phylogenetic placement.

The third layer is the lag before first appearance. Essay Eleven has already quantified it. Here we need only one sampling-rate estimate to give us a sense of scale.

In the exceptionally well-preserved record of planktonic foraminifera, some estimates put the probability of sampling certain species in each one-million-year time bin at no less than about 80%. This is the high end, not the norm. Foraminifera are abundant, have hard shells, and occur in continuous deep-sea sediments: almost the best conditions the fossil record can offer.

The number is useful because it sets up the next section. If the detection probability really is 80% per million years, absence over several consecutive million years soon becomes strong negative evidence. If a group’s effective detection probability is only a few percent per million years, a gap of the same length can scarcely establish any strong upper bound on age.

Taken together, the three layers tell us this: describing the fossil side as “an error of plus or minus 2 million years” leaves out the layer that actually dominates deep-time disputes. The dominant errors are not in the first layer but in the second and third, neither of which looks like an error bar.

V Is It Circular?

Now for the second assumption: just how independent is this ruler?

First, let us be clear about why the problem exists.

We can count how many substitutions have accumulated along a sequence. That number is the product of two things: rate multiplied by time.

The trouble lies in the multiplication. Double every time and halve every rate, and the product stays exactly the same. The sequence itself cannot tell the difference. Every branch in the tree has exactly the same length under the two readings.

In other words, the sequence can tell the model how many substitutions a branch has accumulated and which nodes are relatively deeper. It cannot give the model years. Those have to come from outside.

At least one absolute scale is therefore needed. Modern node dating usually places fossil minimum ages, maximum ages, or probability densities at several internal nodes. Molecular branch lengths and the rate model then spread that time information through the tree. The 2023 study covered 241 placental species. Its 65-taxon locus-tree dating used 37 soft-bounded fossil calibrations; the concatenated 241-species analysis added another 23. The 37 anchors used below to illustrate the principle are not the total for the full analysis.

Thirty-seven looks like a lot. It also means that there are thirty-seven places on that tree where fossil ages and phylogenetic placements are written directly into the inputs.

This opens the door to a dangerous form of argument. Assume the ages and phylogenetic placements of fossils A, B, and C to calibrate the clock. The clock estimates the target node to be older than its own oldest fossil.

Therefore, molecular evidence “independently” proves that the fossil record is incomplete. That final “independently” does not hold, because the output is already conditional on fossil inputs.

But this does not make every case of “molecules older than fossils” a formal logical circle. Suppose fossils at three places on the tree, A, B, and C, supply time constraints, while the target node has no direct calibration at all. Sequence branch lengths and the clock model extrapolate from A, B, and C to the target. The target’s posterior age is then compared with its own oldest fossil.

There is no tautology here of putting the answer in beforehand and taking it out again. What we have is something else: dependence among lines of evidence, plus model-based extrapolation. There are three common replies to the charge of circularity. We need to assess separately how much each one resolves.

The first reply is that the calibration points come from other groups or other periods. That removes the strongest form of circularity, but not extrapolation bias. If the target node lies far from the calibration nodes, systematic error can travel all the way through the rate model. This is especially true when the calibrations all lie on one side of the tree and the target sits on another long branch that has undergone a major rate shift. “Not the same node” is no guarantee of robust inference.

The grass-tree case has exactly this shape. In Section Two, the Australian grass-tree crown hung at the end of a long stem branch without any internal calibration. Change the clock model, and the estimated age jumps from 3–6 million years to 26–30 million years.

The same sequences, the same calibration points, an almost tenfold difference in age. The only change is how variation in rates is modeled.

The second reply is that calibrations set bounds rather than dictate answers. That is partly true. A hard minimum says only that a node cannot be younger than a particular time. In principle, the posterior can fall anywhere earlier. A soft maximum even allows a small probability of exceeding the upper bound. The node is therefore not simply nailed to the fossil’s age.

But multiple bounds interact with the tree prior to produce what is called an effective prior. Even the time distributions of uncalibrated nodes can be strongly shaped by it. A bound is not a point answer, but it can still supply most of the information in the answer.

The third reply is that the more calibration points there are, the less any single error matters. That holds only if the errors are approximately independent and the points are sensibly distributed across the tree. Several independent, reliable calibrations can indeed constrain one another. A calibration that is conspicuously too old or too young is more likely to conflict with the other data, and soft bounds allow the sequences and other calibrations to reduce its influence.

But if ten calibrations share the same phylogenetic misclassification, the same erroneous maximum age, or simply cluster on one branch, they are not ten independent pieces of information. They are the same systematic error repeated ten times.

Another point is often overlooked: the placement of calibrations matters at least as much as their number. An internal calibration can directly break the trade-off between time and rate along a long branch.

Adding more calibrations only near the root may fail to constrain a distant crown group that has undergone a rate shift of its own. In the grass-tree example, it was precisely the long stem without internal calibration that magnified the problem.

The right verdict, then, is neither “necessarily circular” nor “wholly independent.”

The molecular age of a target node is a prediction conditional on a set of fossils, a clock model, a sequence model, and a tree prior. It can be independent of the target node’s own first fossil appearance, but it is usually not independent of the fossil time scale itself. That is a short statement, but it rejects two common claims at once. One says that a molecular clock merely repeats what the fossils have told it. The other says it is an independent ruler with nothing to do with fossils. Both are wrong, in opposite directions.

Using this prediction to test the completeness of the target node’s record is cross-prediction, and it is legitimate. Describing it as a second clock wholly independent of paleontology overstates its independence.

VI At the Maximum-Age End

Calibration has two ends, supported by arguments of very different strength. A hard minimum has the firmest logic: if a fossil reliably assigned to a crown group is at least 100 million years old, the node that gave rise to the crown group cannot be only 90 million years old.

The issue therefore comes down to two premises: does the fossil really belong to this crown group, and is the rock layer really at least that old? Once those two premises are secure, the direction of the constraint is firm.

A maximum age is different. A minimum comes from “we have found one.” A maximum comes from “we have not found one in older strata where this group ought to have been preserved.” It rests on negative evidence.

Turning absence into an upper bound requires a further chain of arguments. Do the older strata exist? Have they been sampled densely enough? Was the environment suitable? Did the group then possess structures that could both be preserved and diagnosed? Would researchers actually recognize it?

Use the simplified calculation from essay eleven: if time bins are independent and share a detection probability, the chance of missing every bin is the single-bin miss probability raised to the number of bins. With an eighty-percent chance of detection per million years, a long absence becomes hard to explain. Low or variable detection, or correlated gaps, defeats that simple multiplication. An equally long blank may then supply no reliable upper bound.

Here is the crucial point: a maximum-age calibration brings in not just a date, but assumptions about the completeness of the fossil record. Expressing them as a prior does not make them untestable, or mean researchers have hidden them. Can the reader see what has been assumed? How much does another reasonable prior change the result? What happens when a new fossil turns up?

Here the difference between hard and soft bounds comes into view as well. A soft maximum permits a small amount of prior probability beyond the boundary. It says: if this group had existed that early, we would probably have seen it, but the chance of missing it is still not zero.

Simulations and real examples show that hard and soft bounds can give very similar results when fossils and sequences agree. Once they conflict, however, a soft bound allows other information to outweigh a bad calibration. A hard bound forces the answer to obey an erroneous constraint and may produce an excessively narrow credible interval. Placental mammals offer a practical version of this logic, and neither side is playing games.

Those arguing for a younger crown group point to the relatively rich Late Cretaceous mammal localities of North America and Eurasia. If several major branches of living placentals were already widespread, there should be some probability of finding recognizable members.

The other side points out that the records for the same period in Africa, Antarctica, Madagascar, India, and other regions are far poorer. Moreover, early crown-group members may have been intrinsically difficult to distinguish morphologically from the stem group.

The dispute is therefore not simply “found or not found.” It is whether the detection probability is high enough to support that maximum age. And the probability is estimated, not measured, with orders-of-magnitude differences between continents. This is the practical form of Essay Eleven’s equation: the strength of negative evidence is not determined by the zero alone.

The shape of the calibration prior belongs to the same family of problems. Uniform, exponential, and lognormal distributions are not harmless mathematical packaging. A uniform distribution gives no age between its upper and lower bounds any extra preference.

An exponential distribution places the greatest probability near the minimum bound and tapers into the past. A lognormal distribution can form a skewed peak beyond the fossil minimum while retaining a long tail.

In effect, each encodes a different hypothesis about how far the oldest fossil usually lies from the true divergence. So when the molecular information at a node is weak, changing the shape of the prior changes the posterior. Flowering plants provide the best current example.

Historical molecular estimates span roughly 140–270 million years ago. A set of node-dating and fossilized birth–death analyses in 2025 mainly returned crown-group ages of 255–202 million years, largely Triassic but reaching into the Late Permian at the older end. A 2026 study that integrated a fossil-occurrence model and molecular dating in sequence brought the origin forward to the Late Jurassic, on the order of 150 million years ago.

On the fossil side, the earliest generally accepted angiosperm pollen and macrofossil evidence is concentrated in the Early Cretaceous, around 133–125 million years ago.

For the 2025 results, then, the gap is 70–120 million years. For the 2026 results, it shrinks to roughly 15–25 million years. Smaller, but not zero.

The studies appeared a year apart, yet their dates are far apart. This is not simply a story of sequencing more genes. Fossil incorporation, calibration, and sampling models all matter. But these studies are not a controlled comparison with only the calibrations changed, so their whole difference cannot be assigned to one factor. When a review says “recent molecular evidence supports this date,” ask not only which papers it cites, but which assumptions those papers make.

One final, symmetrical warning: an unreasonably old maximum bound systematically leaves deep nodes too much “room toward the past.” A hard bound drawn too tightly, on the other hand, manufactures false precision. Deep nodes are especially dangerous because sequences may have become saturated over such long time scales. Absolute time then depends more on calibrations and rate priors than on the sequences themselves.

VII Accounts That Do Not Balance, and a Table of Which Way Errors Run

Now for the actual accounts. Placental mammals first. On the molecular side, many multigene and genome-wide analyses in the twenty-first century place the origin of crown placentals and many interordinal splits in the Cretaceous, with basal nodes often around 100–110 million years old. Different calibrations and rate models can shift the root age anywhere from 70 million to more than 120 million years.

On the fossil side, the strict morphological “explosive model” places unequivocal crown placentals mainly after 66 million years ago. A 2023 study that directly modeled large numbers of fossil-occurrence records supported the presence of crown placentals in the Late Cretaceous, close to the boundary, but later origins for most order-level crown groups.

The traditional gap of 30–45 million years thus contracts to anything from a few million to something over ten million years. It still does not bring all the order-level nodes into agreement.

Three models are often confused here. They should be defined by which nodes cross the end-Cretaceous boundary, not named after the people who support them. In the explosive model, the great majority, or even all, of the major branches between and within crown-placental orders lie close to or after 66 million years ago.

In the long-fuse model, crown placentals had already originated and most interordinal splits had already occurred in the Cretaceous, but most crown groups within orders expanded later. In the short-fuse model, diversification between orders and some diversification within orders had already taken place well back in the Cretaceous.

These are not “the fossil model,” “the molecular model,” and “the compromise model.” The most direct support for the explosive model comes from a strict reading of the crown-group fossil record and morphological systematics.

The long-fuse pattern is most often recovered by multigene relaxed clocks. The short-fuse pattern and various intermediate forms can result from different rate filters, fossil calibrations, and fossil-occurrence models. Change the calibrations, and the same large molecular matrix can move between these patterns.

Placental mammals also illustrate a point that keeps recurring in this essay: error within a method can be much smaller than the distance between methods. In a particular molecular analysis, a single basal node may have a 95% interval only a few million to a little over ten million years wide.

Yet a strict fossil first appearance and some molecular central estimates can sit 30 or 40 million years apart. When calibration and rate uncertainty have been resampled together, the total interval for the placental root has stretched from 70 million all the way to 130 million years ago, far wider than the internal error obtained by conditioning on a single model.

Birds. Molecular time trees have long placed the root of modern birds and some of their major lineages in the Cretaceous. Different analyses often return basal ages of 80–100 million years, or older still. A 2024 study using twenty fossil calibrations again found that modern birds began diversifying in the Late Cretaceous and continued branching across the boundary.

On the fossil side, the most secure crown-bird fossils had been clustered around 67 million years ago. New Antarctic material has strengthened the evidence that crown-bird lineages were present by 69 million years ago. It has not pushed reliable fossils of every major living branch deeper into the Cretaceous.

How this case has been handled is instructive. The 2024 study soon drew public criticism of its choice of fossil calibrations; the original authors responded that their Cretaceous time scale was robust. In practice, the response has been to change calibrations and reexamine node posteriors, not to average a fossil first appearance with a molecular central estimate.

The deep split between marsupials and placentals. A 2012 phylogenomic analysis dated it to about 168–178 million years ago. In 2011, a fossil about 160 million years old had been interpreted as a eutherian, briefly bringing the fossil lower bound almost up to the molecular clock.

Its phylogenetic placement was subsequently challenged. If only the more secure Early Cretaceous record is accepted, the lower bound lies around 125–110 million years ago.

So if the specimen really is about 160 million years old and belongs on the eutherian branch, the gap described above is only eight to eighteen million years; remove that anchor and it may return to forty to sixty million. Placement is not the only dispute: provenance and age have also been questioned. Morphological tip dating has suggested a younger age, but that is not a direct redating of the rock. Both premises behind this calibration need to be visible.

This also explains why these cases count as “competition” rather than a “division of labor.” A large total-evidence analysis incorporating morphology in 2013 strengthened the case for a young placental root. Subsequent molecular time-tree work explicitly challenged that age. The two sides were not arguing about when an ecological role became established. They were arguing about when the common ancestor of crown placentals existed: the same node, the same historical event, two nonoverlapping intervals.

Two comparisons are equally useful. One involves shelled marine sister groups on opposite sides of the Isthmus of Panama. Tests of trans-isthmian sister-species pairs using fossil calibrations have returned molecular divergence dates close to the period of isthmus formation for some lineages with reliable shell records. The gap between methods is on the scale of a million years, not tens of millions.

Hard-shell preservation combined with a shallower time scale yields a highly sensitive record. But not every species pair split at the same time, so the closure of the isthmus cannot be treated as a single clock time shared by every lineage.

The other is a counterexample, and it matters more than the favorable comparison: sea urchins. Sea urchins have mineralized skeletons that preserve extremely well, and a fossil record far better than that of a typical soft-bodied deep stem group.

Even so, modern phylogenomic dating can still put some crown nodes tens of millions of years before their known fossils. Mineralized hard parts improve detection probability; they do not guarantee agreement between molecules and fossils. Set out the mechanisms behind these accounts, and we get a table showing which way each one pushes. The shape of that table is itself the conclusion.

Some mechanisms have a fixed direction, pushing the discrepancy toward “molecules older.” The lag before first appearance makes the known fossil first appearance too young. Late development or poor recognition of crown-group diagnostic traits makes the recognizable first appearance too young.

Ancestral polymorphism and incomplete lineage sorting make single-gene coalescence older than the species split. An actual acceleration on the target branch that the model fails to recognize often pushes the molecular date older.

Mechanisms acting in the opposite direction are real too. Mistaking a stem group for a crown group makes the fossil minimum too old. Later gene flow and introgression make coalescence in the affected genes younger.

An actual slowdown on the target branch that the model fails to recognize often pushes the molecular date younger. Inadequate correction for saturation has a first-order tendency to compress deep dates toward the present. A hard maximum set too young forces the node to be too young.

Another class has no fixed direction at all: long-branch attraction, compositional bias, and complex site heterogeneity. They damage the topology first and change the ages indirectly. Which node represents which historical split changes; calibration placements and branch lengths change with it. The result can be older or younger.

“Molecules older than fossils” is therefore especially common in the literature because at least four mechanisms pile up in that direction, not because it is mathematically inevitable. Finding that one direction predominates cannot, in reverse, prove that there is only one cause.

VIII The Remainder Lies in Independence

This final section will begin with attempts at integration, then ask what remains after integration.

One approach tries to stop “turning a fossil into a node bound and then throwing the fossil itself away.” Total-evidence dating brings the molecular sequences of living groups, the morphological characters of living and fossil groups, and the geological ages of fossils into a single phylogenetic inference. Fossils enter as sampled tips on the tree. Their placement is determined by the morphological matrix, rather than by a researcher deciding in advance, “This fossil calibrates this node.”

The fossilized birth–death process goes a step further: it also models why a fossil should turn up where it does. Lineages originate and go extinct at certain rates while entering the fossil record at another rate. Living and fossil species are treated as different samples from the same macroevolutionary process, rather than one being the real tree and the other merely an external calibration.

This does solve a substantive problem. In standard node dating, whether a 100-million-year-old fossil makes the node most likely to be 102, 110, or 140 million years old depends on a distribution specified by the researcher. This approach instead tries to generate the distribution of node times from the fossil-sampling process itself.

But it also adds more things that must be estimated or stipulated: speciation rate, extinction rate, fossil-sampling rate, and the proportion of living groups sampled. Fewer of the old node-calibration priors are needed, in exchange for an explicit set of macroevolutionary and sampling assumptions. Essay Eleven’s discipline is especially direct here: a model can correct only for absences it has parameterized.

If the model contains only “an average fossil-sampling rate per million years,” it can correct for random sampling failures. It cannot automatically know that an entire continent lacks exposed sedimentary rocks for a whole period, that a particular body structure is never preserved, that a research tradition never collects tiny specimens, or that every fossil of a lineage has been misclassified. These are not random absences already identified within that sampling rate. They will not disappear because the algorithm has been given a different name.

Tests have confirmed this: such methods are sensitive to which fossils you feed them. Subsampling fossil-occurrence records indiscriminately, without controlling for the fossils’ phylogenetic affinities, can yield ages for groups that are incompatible with the known fossil evidence.

Nor did a large simulation with known answers conclude that the truth could always be recovered. Overall, the method recovered relationships among living groups fairly well, but the correct placement of fossils proved harder to recover. For node times, the number of fossils and the age of the oldest fossil often mattered more than the degree of rate heterogeneity between branches or the number of morphological characters.

The model of morphological evolution adds another dependency. A total-evidence analysis usually has to specify a model for discrete morphological characters and decide whether rates are equal across characters, whether the morphological clock is strict, and whether partitioning and directional change are allowed. Teeth, skulls, limbs, and soft-tissue characters plainly need not behave like independent “letter positions,” all with the same rate and the same transition probabilities.

Combining them does not automatically produce a third, better ruler. It puts two rulers into one probability system. With suitable assumptions, that can improve estimates and consistently propagate modeled uncertainty. Absences, misidentifications, and preservation biases left out of the model do not disappear merely because the analysis is “joint.” We can now return to the title: competition, or a division of labor?

The accurate answer holds on three levels at once. At the level of direct observation, there is a division of labor. Fossils give direct observations of preserved individual organisms, their morphology, and their stratigraphic position; molecular methods give direct observations of substitution differences in living sequences.

At the level of hidden nodes, there is competition. The two sometimes assign probability estimates to the same node that cannot be observed directly, and their intervals can fail to overlap at all. At the level of the inference system, there is coupling. Molecular clocks use fossil calibrations; joint models go further and write both into the same generative process. Call any one of these levels alone “the true relationship,” and you lose the other two.

An experiment makes the coupling particularly vivid: the pseudoextinction experiment. Researchers first use molecular data to build a strongly supported backbone for the living orders. They then deliberately remove all the molecular and soft-tissue characters from one living group, treat it as “an extinct group known only from hard tissues that could fossilize,” and place it back into the morphological tree.

The result is that most order-level groups move to different extents, and only a few stay where they were. Modern molecular trees can therefore tell paleontologists, in return, which phylogenetic placements are most vulnerable to convergence and missing data when only the preservable part of morphology is available.

While we are here, let us correct a common exaggeration. These are not two scholarly nation-states that never speak to one another. The authors developing new methods overlap extensively, paleontologists themselves develop probabilistic fossil-sampling models, and joint models are a product of that convergence.

The real asymmetry lies elsewhere. Molecular trees often change the phylogenetic identification of fossils. Molecular clocks almost never change the numerical age of the rock itself. A reliably dated ash bed does not become younger because a clock gives a different age for a node. This essay therefore adds a twelfth entry to our list of remainders: the remainder lies in independence.

The two rulers appear to offer independent tests of each other, yet one has the other built into its inputs. Their disagreement can therefore be read neither as “one of them must be wrong” nor as “two independent lines of evidence have failed to cross-validate.”

This differs from Essay Fourteen’s “remainder in a ruler that does not exist.” There, the ruler was missing. Here, both rulers exist, both work, and both give us numbers. The remainder lies in the assumption that they are independent.

There is another rule worth taking away, one that will outlast the particular subject of this essay. A narrow posterior interval within a model does not show that systematic error between models is small. In the grass-tree case, the model that gave the narrower interval was precisely the one that failed to cover the truth.

The implication is that, when reporting a date, we should report at least two things separately: the interval within the model, and the spread obtained by changing models. Hide the latter, and the precision the reader sees is false. Finally, the question with no universal answer: what should we do when the two rulers give vastly different ages for one node?

In actual practice there is no single automatic rule of adjudication, and our three cases took three different paths. For placentals, the response has been to set competing models side by side. Explosive, soft-explosive, trans-boundary, long-fuse, and short-fuse models continue to be explicitly named and compared. Researchers ask what rates, fossil placements, and numbers of ghost or zombie lineages each would require. For birds, the response has been to rerun analyses with different calibrations and argue in public. For flowering plants, it has been to report sensitivity ranges and declare the dependence on models.

Nobody averages 66 million and 100 million years into 83 million. That fact itself has a shape we keep encountering in this series. When disagreement comes from models rather than noise, taking the midpoint is not a compromise. It combines two different hypotheses into a third that neither side ever proposed.

Taking the union of the intervals makes sense in a conservative review, but it cannot be interpreted as a new 95% probability interval: the different models are not sampling from the same probability space. Choosing one is defensible only when there are additional model tests. In the grass-tree case, the marginal likelihood strongly favored the random local clock, giving the authors reason to accept the older set of dates. Not because older dates are inherently more credible, but because the same data supplied additional evidence that discriminated between the rate models.

And “declaring the matter unresolved” is not a failure of method. When systematic error exceeds the internal error on either side, it is the only honest state of affairs.

This statement has a testable form. First ask how large each side’s internal error is. Then ask how far the central estimate moves when the clock model, the calibrations, or the shape of the prior is changed. If the second number is clearly larger than the first, then however narrow an interval either side reports, a range is all we can honestly claim for now.

The placental root is just such a case. An individual analysis may have an internal interval spanning only a little over ten million years. Allow calibration and rate uncertainty to vary together, and the range stretches from 70 million to 130 million years ago. The two spans differ severalfold, and it is usually the first that gets quoted.

Here, there is no change of level to adjudicate. What we are left with is something else: the stretch that still fails to coincide after two constructs have become inputs to each other. It lies in neither ruler. It lies between them, in an assumption that has never been measured and has always been taken as a premise.

We still need both rulers. When a neat date appears, pause to see what is holding their ends in place.