The Molecular Clock and Divergence Dating

From substitutions to time

The molecular clock hypothesis says that substitutions accumulate at a roughly steady rate over time, so a branch length measured in substitutions per site is simply that rate multiplied by the elapsed time. If you know the rate you can divide branch lengths by it to recover durations, and if instead you know the age of some nodes or tips you can solve for the rate. Dating is what turns an ordinary phylogram, whose branches are in substitution units, into a time-tree whose node heights are ages.

Strict versus relaxed clocks

A strict clock assumes one substitution rate across every branch, which is easy to estimate but breaks down when lineages differ in generation time, metabolism, or repair efficiency. A relaxed clock lets each branch carry its own rate, most often by drawing branch rates independently from a lognormal distribution in the uncorrelated relaxed clock. Because branch length equals rate times time, letting the rate vary is precisely what allows one observed branch length to map onto different possible durations.

On its own a clock only gives relative ages, so you need calibrations to pin down absolute time. For organisms sampled across years, such as RNA viruses, the tip sampling dates supply the calibration directly, an approach called tip dating. For deep splits you instead constrain internal nodes with fossil ages, usually written as bounded intervals in a plain date file that LSD2, the least-squares dating engine built into IQ-TREE 2, can read. Each line names the most recent common ancestor by listing its descendant taxa comma-separated with no spaces, then the constraint.

Homo_sapiens,Pan_troglodytes b(-10,-6)
Homo_sapiens,Macaca_mulatta b(-34,-24)
Homo_sapiens,Callithrix_jacchus b(-48,-38)

iqtree2 -s primates.fasta -m GTR+G \
  --date dates.txt --date-tip 0 --date-ci 100 \
  -o Callithrix_jacchus -B 1000 -T AUTO

--- START PHYLOGENETIC DATING (LSD2) ---
Reading date file dates.txt ... 3 ancestral constraints found
Tree rooted using outgroup: Callithrix_jacchus
Number of samples for CI: 100

Root age:  -43.58 Myr  [95% CI: -47.12 ; -39.86]
Rate:      1.18e-03 subst/site/Myr  [95% CI: 1.02e-03 ; 1.37e-03]

Dated tree and summary written to:
  primates.fasta.timetree.nex
  primates.fasta.timetree.nwk
  primates.fasta.timetree.lsd

For a fully Bayesian time-tree, BEAST2 co-estimates the topology, the relaxed clock rates, and every node age while propagating uncertainty from all of them into the result. In BEAUti you set a site model, pick the optimised or uncorrelated lognormal relaxed clock, and add each fossil as an MRCA prior with a lognormal age distribution before exporting the XML. You then run the MCMC and summarize the posterior into a single annotated tree carrying interval estimates.

beast -threads 4 -seed 12345 primates_ucln.xml

treeannotator -burnin 10 -heights median \
  primates_ucln.trees primates_mcc.tree