Molecular Clocks

1
Molecular Clocks
Prediction of time from molecular divergence
2
Molecular Clock

• Molecular divergence is ROUGHLY correlated with
  divergence of time

3
Evidence for Rate Constancyin Hemoglobin
from Zuckerkandl and Pauling (1965)
4

• 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

5
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)

6
Rate Constancy?
Page Holmes p240
7
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

8
Rate Heterogeneity among lineages
9
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)

10
Rate Changes within a Lineage
11
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

12
Likelihood Ratio Test

• estimate a phylogeny under molecular clock and
  without it
• e.g. root-to-tip distances must be equal
• difference in likelihood 2Chi2 with n-2
  degrees of freedom (n taxa in tree)
• asymptotically
• when models are nested

13
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

14
Relative Rates TestsSarich Wilson 1973, Wu and
Li 1985
Taxon 1
Taxon 1
0
Taxon 2
Taxon 2
Taxon 3 Outgroup
Taxon 3 Outgroup
15
Relative Rates TestsSarich 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
0
K02
Taxon 2
K03
Taxon 3 Outgroup
16
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

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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

18
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

19
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

20
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

21
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

22
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

23
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)

24
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
• Bayesian approach
• stochastic model of evolutionary change
• prior distribution of rates
• Bayes theorem
• MCMC

25
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

26
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

27
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.

28
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.