Molecular clock

A molecular clock relates accumulated nucleotide substitutions to elapsed evolutionary time through an assumed rate. Two lineages evolving at the same constant rate $r$ for time $T$ have total expected substitution count $2rT$ per site before accounting for repeated changes obscured in endpoint sequences. Rate variation among sites or branches requires a more general clock model.

A molecular branch length is expected substitutions per site, the product of evolutionary rate and elapsed time. Without external calibration, simultaneous rescaling of rate and time preserves the sequence likelihood. Fossil or geological bounds, or informative sampling dates, supply time information; relaxed clocks allow rate variation. Calibration uncertainty, saturation and gene/species-tree discordance must be propagated rather than turned into an exact historical date.

Use of dated fossil evidence to constrain evolutionary times. Geological age, phylogenetic placement, stem versus crown assignment and uncertainty all affect the constraint.

A calibration constraint allowing a small nonzero probability outside its principal range. It represents uncertainty but still needs biologically defensible tail probabilities.

A calibration constraint assigning zero probability to ages beyond a specified limit. Sequence data cannot overcome an excluded age under that prior.

A model allowing evolutionary rates to vary among branches. The distribution and dependence of rates affect inferred times and must be distinguished from absolute-time calibration.

A model assigning the same evolutionary rate to the relevant branches. Expected branch length is rate multiplied by duration; scaling times and inverse-scaling the rate preserves the sequence likelihood.