Molecular Clocks

Prediction of time from molecular divergence

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

Molecular Clock

• Molecular divergence is ROUGHLY correlated with divergence of time

Evidence for Rate Constancyin Hemoglobin

from Zuckerkandl and Pauling (1965)

• Given – a phylogenetic tree – branch lengths– a time estimate for

one (or more) node(s) C HD R M

110 MYA

• Can we date other nodes in the tree?

• Yes... if the rate of molecular change is constant across all branches

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)

Page & Holmes p240

Rate Constancy?

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

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

Rate Heterogeneity among lineages

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)

Cause Reason

Population size changes

Genetic drift more likely to fix neutral alleles in small population

Strength of selection changes over time

1. new role/environment

2. gene duplication

3. change in another gene

Rate Changes within a Lineage

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

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

Relative Rates TestsSarich & 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

Relative Rates TestsSarich & Wilson 1973, Wu and Li 1985

Taxon 2

Taxon 3 Outgroup

0

Taxon 1

Taxon 2

Taxon 3 Outgroup

Taxon 1

Relative Rates TestsSarich & Wilson 1973, Wu and Li 1985

Taxon 2

Taxon 3 Outgroup

K01

K02

K03

0

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

Taxon 1

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)

Measuring Evolutionary time with a molecular clock

1. Estimate genetic distance d = number amino acid replacements

2. Use paleontological data to determine date of common ancestor

T = time since divergence

3. Estimate calibration rate (number of genetic changes expected per unit time)

r = d / 2T

4. Calculate time of divergence for novel sequences

Tij = dij / 2r

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

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

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

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

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 valuesMolecular Systematics p536

Molecular DatingSources 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

Working Around Rate Heterogeneity

1. Identify lineages that deviate and remove them

2. 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

3. Explicitly model rate variation (relaxed clocks)

Relaxing the Molecular ClockRutschmann 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)

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

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

General ReferencesReviews/Critiques1. Bromham and Penny. The modern molecular clock, Nature

Genetics, 2003.2. Graur and Martin. Reading the entrails of chickens...the illusion of

precision. Trends in Genetics, 2004.3. Rutschmann.2006 Molecular dating of phylogenetic trees: A brief

review of current methods that estimate divergence times. Diversity and Distributions

Textbooks:1. Molecular Systematics. 2nd edition. Edited by Hillis, Moritz, and

Mable.2. Inferring Phylogenies. Felsenstein.3. Molecular Evolution, a phylogenetic approach. Page and Holmes.4. Chapter 11 textbook “The Phylogenetic Handbook”

Dealing with Rate Heterogeneity1. Yang and Yoder. Comparison of likelihood and bayesian methods for

estimating divergence times. Syst. Biol, 2003.2. Kishino, Thorne, and Bruno. Performance of a divergence time

estimation method under a probabilistic model of rate evolution. Mol. Biol. Evol, 2001.

3. Huelsenbeck, Larget, and Swofford. A compound poisson process for relaxing the molecular clock. Genetics, 2000.

Testing for Rate heterogeneity1. Takezaki, Rzhetsky and Nei. Phylogenetic test of the molecular clock

and linearized trees. Mol. Bio. Evol., 1995.2. Bromham, Penny, Rambaut, and Hendy. The power of relative rates

test depends on the data. J Mol Evol, 2000.3. Wilcox, T. P., F. J. Garcia de Leon, D. A. Hendrickson, and D. M.

Hillis. 2004. Convergence among cave catfishes: long-branch attraction and a Bayesian relative rates test. Mol. Phylogenet. Evol. 31:1101-1113.

Rate Heterogeneity References