II.3 Molecular Clock Dating Bruce Rannala and Ziheng Yang OUTLINE Nonparametric Rate Smoothing Method. One of the first methods for modeling sequence substitution rate 1. The molecular evolutionary clock evolution among lineages (a relaxed molecular clock). 2. Molecular clock dating This early heuristic procedure penalizes changes in 3. Testing the molecular clock rate between ancestral and descendant branches while 4. Statistical methods for divergence time maximizing the probability of the data (i.e., the like- estimation lihood), this was referred to as a penalized likelihood. 5. Maximum likelihood estimation of divergence Molecular Clock. The hypothesis (or observation) that times DNA (or amino acid) sequences accumulate changes 6. Bayesian estimation of divergence times at a constant rate through time (and among species). 7. Fossil calibrations A “relaxed” clock model allows rates to vary across 8. Relaxed clocks and prior model of rate drift lineages in an orderly way; there may be a “local 9. Perspectives clock” with constant rates in subsets of species (in a likelihood analysis), or there may be lineage-specific This chapter reviews the history of the molecular clock, rates that are either independent observations from a its impact on molecular evolution, and the controversies common distribution or correlated between ancestral surrounding mechanisms of evolutionary rate variation and descendant species (in a Bayesian analysis). and the application of the clock to date species diver- gences. We review current molecular clock dating meth- ods, including maximum likelihood and Bayesian meth- 1. THE MOLECULAR EVOLUTIONARY CLOCK ods, with an emphasis on relaxing the clock and on incorporating uncertainties into fossil calibrations. In the early 1960s, it was observed that the amino acid differences between aligned hemoglobin or cytochrome c sequences from different species were roughly propor- GLOSSARY tional to the times of divergence between the species Fossil Calibrations. The use of the fossil record to specify (according to the fossil record). These observations led the ages of nodes (divergence events) on the phyloge- Emile Zuckerkandl and Linus Pauling to propose the netic tree. In the simplest case, an interior node on the hypothesis of a molecular evolutionary clock in 1965. tree is assigned a fixed age, and a molecular clock is The clock was envisaged as a stochastic one, with “ticks” then applied in an analysis of the sequence data to corresponding to nucleotide or amino acid substitutions, estimate the absolute ages of the remaining nodes. which occur at random time intervals. Although parti- More sophisticated calibration methods use Bayesian cular substitutions occur at random times, the rate at methodology to accommodate uncertainties in the which substitutions occur is assumed to be constant or fossil record, by specifying a distribution for a node age “clocklike” through time and across lineages. The pro- (instead of a fixed constant). cess is analogous to the way in which the random decay Fossil/sequence Information Plot. A regression-based me- of isotopes can be used to construct an atomic clock. thod for determining how much remaining uncertainty Furthermore, much the way that different isotopes have for node ages is due to uncertainties in fossil calibration a characteristic rate of radioactive decay, different pro- times (or lack thereof) and how much to insufficient teins can have different evolutionary rates, meaning that sequence data. their molecular clocks tick at different rates. 68 Phylogenetics and the History of Life The molecular clock hypothesis had an immediate that humans have lower rates than other apes and and profound impact on the emerging field of molecular monkeys—characterized as the primate slowdown and evolution, greatly expanding the role of molecular ana- hominoid slowdown, respectively. Two major factors lysis in studies of phylogeny and the timing of significant that could account for such between-species rate dif- evolutionary events; nonetheless, the molecular clock ferences are generation time (with a shorter generation hypothesis has been a focus of controversy throughout time causing more germ-line cell divisions per calendar the five decades of its history. The reliability of the clock year and a higher substitution rate) and DNA repair and its implications for the mechanism of molecular mechanism (with less reliable repair mechanisms asso- evolution were a focus of immediate controversy. The ciated with higher mutation [and substitution] rates). molecular clock hypothesis was proposed at a time when Perhaps because of the generation time effect or other the neo-Darwinian theory of evolution was generally correlated life history variables, for example metabolic accepted by evolutionary biologists, according to which rate, substitution rates tend to be negatively related to the evolutionary process is dominated by natural selec- body size, with high rates in rodents, intermediate rates tion. A constant rate of evolution among species as dif- in primates, and slow rates in whales. Species with small ferent as mice and monkeys was incompatible with that body sizes tend to have shorter generation times and theory. Species living in different habitats, with different higher metabolic rates. The negative correlation be- life histories, generation times, etc., must be under very tween substitution rate and body size has been supported different regimes of selection (and therefore should have in some studies but questioned in others. The disagree- different substitution rates). When the neutral theory of ments do not appear to have been resolved. molecular evolution was first proposed (by Motoo Ki- mura in 1968 and by Jack King and Thomas Jukes in 2. MOLECULAR CLOCK DATING 1969), the observed clocklike behavior of molecular evo- lution was considered major supporting evidence. The molecular clock hypothesis provides a simple yet The neutral theory emphasizes random fixation of powerful way of dating evolutionary events. Under the neutral or nearly neutral mutations (see chapter V.1). clock assumption, the expected distance between se- Under such a model, the rate of substitution is equal to quences increases linearly with time of divergence. the neutral mutation rate, independent of factors such as When external information about the geological ages of environmental change and population size variation. If one or more divergence events on a phylogeny is avail- the mutation rate is similar and the function of a protein able, based on the fossil record or certain geological remains the same across species (so that the same pro- events, the distances between sequences or the branch portion of mutations are neutral), a constant substitu- lengths on the tree can be converted into absolute geo- tion rate is expected. Rate differences among proteins logical times. This is known as molecular clock dating. are explained by the presupposition that different pro- The earliest application of the clock to estimate di- teins are under different functional constraints, with a vergence times was by Zuckerkandl and Pauling in 1962, different proportion of amino acids experiencing neutral who used an approximate clock to date duplication mutations. events among a, b, g,andd globins of the hemoglobin The neutral theory is not the only mechanism com- family. The molecular clock has since been used widely patible with clocklike evolution; neither does the neutral to date species divergences. The outcomes of molecular theory always predict a molecular clock. For example, clock analyses have often produced controversies, usu- the efficiency of DNA repair mechanisms may vary ally because the molecular dates are at odds with the among lineages leading to differences in the rate of ne- fossil record. One controversy concerns the origin of the utral mutations and a violation of the clock (but not of major animal forms. Fossil forms of metazoan phyla the neutral theory). Controversies also exist concerning appear as an “explosion” around 540 million years ago whether the neutral theory predicts rate constancy over in the early Cambrian, but most molecular estimates of generations or over calendar time, or whether the clock the ages of these divergence events have been much older, applies only to silent (synonymous) DNA changes, or sometimes twice as old. Another controversy surrounds instead to protein evolution as well. the origins and divergences of modern mammals and Since the 1980s, DNA sequences have accumulated birds following the demise of the dinosaurs about 65 rapidly, replacing the protein sequences predominantly million years ago at the Cretaceous-Tertiary boundary used in earlier studies. DNA sequences have now been (the KT boundary). Molecules again generated much used to conduct extensive tests of the clock and to esti- older dates than expected by paleontologists. mate evolutionary rates in different groups of organ- Part of the discrepancy between molecular and fossil isms. An interesting early observation was that primates data is due to the incompleteness of the fossil record. have lower rates of DNA substitution than rodents, and Fossils provide information concerning the date by which Molecular Clock Dating 69 a newly diverging lineage had developed diagnostic mor- A Clock B No clock phological characters. There may be a lag between the time that a lineage arose and the age of the first fossil with the derived traits of the descendants. Molecular dating, in b contrast, infers ages of nodes