1. Molecular Clocks
Prediction of time from molecular divergence

2. Outline What is the molecular clock hypothesis?
How do you detect deviations of the molecular clock hypothesis?
Assuming a perfect molecular clock, what are the potential pitfalls in using it for dating?
Dating with “relaxed” clocks
Cautionary notes

3. Molecular Clock
Molecular divergence is ROUGHLY correlated with divergence of time

4. Evidence for Rate Constancy in Hemoglobin
from Zuckerkandl and Pauling (1965)

5. Given Can we date other nodes in the tree?M
Given
a phylogenetic tree
branch lengths
a time estimate for one (or more) node(s)
110 MYA
Can we date other nodes in the tree?
Yes... if the rate of molecular change is constant across all branches

6. The Molecular Clock Hypothesis
Amount of genetic difference between sequences is a function of time since separation
Rate of molecular change is constant (enough) to predict times of divergence (within the bounds of particular genes and taxa)

7. Rate Constancy?
Page & Holmes p240

8. Rate Heterogeneity Rate of molecular evolution can differ between
nucleotide positions
genes
genomic regions
genomes within species (nuclear vs organelle)
species
over time
If not considered, introduces bias into time estimates

9. Rate Heterogeneity among lineages
Cause
Reason
Repair mechanisms
e.g. RNA viruses have
error-prone polymerases
Metabolic rate
More free radicals
Generation time
Copies DNA more frequently
Population size
Effects mutation fixation rate

10. Local Clocks?
Closely related species often share similar properties, likely to have similar rates
For example
murid rodents on average 2-6 times faster than apes and humans (Graur & Li p150)
mouse and rat rates are nearly equal (Graur & Li p146)

11. Rate Changes within a Lineage
Cause
Reason
Population size changes
Genetic drift more likely to fix neutral alleles in small population
Strength of selection changes over time
new role/environment
gene duplication
change in another gene

12. Identifying rate heterogeneity
Tests of molecular clock:
Likelihood ratio test
identifies deviance from clock but not the deviant sequences
Relative rates tests
compares rates of sister nodes using an outgroup
Tajima test
Number of sites in which character shared by outgroup and only one of two ingroups should be equal for both ingroups
Branch length test
deviation of distance from root to leaf compared to average distance

13. Likelihood Ratio Test
estimate a phylogeny under molecular clock and without it
e.g. root-to-tip distances must be equal
difference in likelihood ~ 2*Chi^2 with n-2 degrees of freedom (n = # taxa in tree)
asymptotically
when models are nested

14. Relative Rates Tests Sarich & Wilson 1973, Wu and Li 1985
Tests whether distance between two taxa and an outgroup are equal (or average rate of two clades vs an outgroup)
need to compute expected variance
many triples to consider, and not independent (although modifications such as Li & Bousquet 1992 correct for this)
Lacks power, esp
short sequences
low rates of change
Given length and number of variable sites in typical sequences used for dating, (Bromham et al 2000) says:
unlikely to detect moderate variation between lineages (1.5-4x)
likely to result in substantial error in date estimates

15. Relative Rates Tests Sarich & Wilson 1973, Wu and Li 1985
Taxon 1
Taxon 1
Taxon 2
Taxon 2
Taxon 3 Outgroup
Taxon 3 Outgroup

16. Relative Rates Tests Sarich & Wilson 1973, Wu and Li 1985
H0: K01 = K02 or K01 - K02 = 0
K13 = K01 + K03 (1)
K23 = K02 + K03 (2)
K12 = K01 + K02 (3)
K01 = (K13 + K12 – K23 )/2 (4)
K02 = (K12 + K23 – K13 )/2 (5)
K03 = (K13 + K23 – K12 )/2 (6)
K01 – K02 = K13 - K23
Variance z = K13 - K23 \ [var (K13 - K23)] 1/2
Compare to normal distribution
K01
Taxon 1
K02
Taxon 2
K03
Taxon 3 Outgroup

17. Bayesian Relative Rates test (Wilcox et al. 2004)
MrBayes in conjunction with Cadence; variation is estimated from the posterior distribution
Cadence summarizes for all tree samples, the distance between specific taxa and the most recent common ancestor (MRCA)

18. Measuring Evolutionary time with a molecular clock
Estimate genetic distance
d = number amino acid replacements
Use paleontological data to determine date of common ancestor
T = time since divergence
Estimate calibration rate (number of genetic changes expected per unit time)
r = d / 2T
Calculate time of divergence for novel sequences
Tij = dij / 2r

19. Perfect Molecular Clock
Change linear function time (substitutions ~ Poisson) (variation is only due to stochastic error)
Rates constant (positions/lineages)
Tree perfect
Molecular distance estimated perfectly
Calibration dates without error
Regression (time vs substitutions) without error

20. Poisson Variance (Assuming A Perfect Molecular Clock)
If mutation every MY
Poisson variance
95% lineages 15 MYA old have 8-22 substitutions
8 substitutions also could be 5 MYA
Molecular Systematics p532

21. Estimating Substitution Rate
Calculate separate rate for each data set (species/genes) using known date of divergence (from fossil, biogeography)
One calibration point
Rate = d/2T
More than one calibration point
use regression

22. Calibration Complexities
Cannot date fossils perfectly
Fossils usually not direct ancestors
branched off tree before (after?) splitting event.
Impossible to pinpoint the age of last common ancestor of a group of living species

23. Linear Regression Fix intercept at (0,0)
Fit line between divergence estimates and calibration times
Calculate regression and prediction confidence limits
A = regression line
B1-B2 = 95% CI of regression line
C1-C2 = 95% CI for predicted time values
Molecular Systematics p536

24. Molecular Dating Sources of Error (assuming constant rates)
Both X and Y values only estimates
substitution model could be incorrect
tree could be incorrect
errors in orthology assignment
Poisson variance is large
Pairwise divergences correlated (Molec Systematics p534)
inflates correlation between divergence & time
Sometimes calibrations correlated
if using derived calibration points
Error in inferring slope
Confidence interval for predictions much larger than confidence interval for slope

25. Working Around Rate Heterogeneity
Identify lineages that deviate and remove them
Quantify degree of rate variation to put limits on possible divergence dates
requires several calibration dates, not always available
gives very conservative estimates of molecular dates
Explicitly model rate variation (relaxed clocks)

26. Relaxing the Molecular Clock Rutschmann 2006 (review)
Likelihood analysis
Assign each branch a rate parameter
explosion of parameters, not realistic
User can partition branches based on domain knowledge
Rates of partitions are independent
Nonparametric methods smooth rates along tree and penalized likelihood (program r8s)
Bayesian approach
stochastic model of evolutionary change
prior distribution of rates:
Autocorrelation: BEAST and Multidivtime
Non-autocorrelation: BEAST (can also incorporate uncertainty in topology)

27. Multiple Gene Loci
“Trying to estimate time of divergence from one protein is like trying to estimate the average height of humans by measuring one human”
--Molecular Systematics p539
Ideally:
use multiple genes
use multiple calibration points

28. Even so, be Very cautious about divergence time inferences
Point estimates are absurd
Sample errors often based only on the difference between estimates in the same study
Even estimates with confidence intervals unlikely to really capture all sources of variance

29. General References Reviews/Critiques
Bromham and Penny. The modern molecular clock, Nature Genetics, 2003.
Graur and Martin. Reading the entrails of chickens...the illusion of precision. Trends in Genetics, 2004.
Rutschmann.2006 Molecular dating of phylogenetic trees: A brief review of current methods that estimate divergence times. Diversity and Distributions
Textbooks:
Molecular Systematics. 2nd edition. Edited by Hillis, Moritz, and Mable.
Inferring Phylogenies. Felsenstein.
Molecular Evolution, a phylogenetic approach. Page and Holmes.
Chapter 11 textbook “The Phylogenetic Handbook”

30. Rate Heterogeneity References
Dealing with Rate Heterogeneity
Yang and Yoder. Comparison of likelihood and bayesian methods for estimating divergence times. Syst. Biol, 2003.
Kishino, Thorne, and Bruno. Performance of a divergence time estimation method under a probabilistic model of rate evolution. Mol. Biol. Evol, 2001.
Huelsenbeck, Larget, and Swofford. A compound poisson process for relaxing the molecular clock. Genetics, 2000.
Testing for Rate heterogeneity
Takezaki, Rzhetsky and Nei. Phylogenetic test of the molecular clock and linearized trees. Mol. Bio. Evol., 1995.
Bromham, Penny, Rambaut, and Hendy. The power of relative rates test depends on the data. J Mol Evol, 2000.
Wilcox, T. P., F. J. Garcia de Leon, D. A. Hendrickson, and D. M. Hillis Convergence among cave catfishes: long-branch attraction and a Bayesian relative rates test. Mol. Phylogenet. Evol. 31: