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Juan Daza UCF Fall 2008 Juan Daza UCF Fall 2008 Estimating divergence times from molecular data

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Reconstructing the evolutionary process History of Life on earth

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Reconstructing the evolutionary process History of Life on earth

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Evolutionary process implies TIME We are interested in determine How, Where, Why, WHEN evolution occurs or has occurred Genetic data Molecular evolution theory Molecular dating

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The general procedure of molecular dating PhylogramUltrametric tree

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The evolution of molecular dating Hemoglobin example The term is introduced Neutral theory Statistical properties of clocks Fitchs test

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Autocorrelation of rates Local clocks The evolution of molecular dating branch pruning NPRSBayesian Penalized likelihood Uncorrelated rates

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The evolution of molecular dating

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Amino acids Nucleotides Pruning branches Local clocks (PAML, Pathd8 packages) Relaxed clocks Correlated rates (r8s, Multidivtime) Uncorrelated rates (Beast)

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Applications Species divergence Explosive radiations Gene evolution Rates estimation Virus epidemiology Historical demography bursts Time Log (# lineages)

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The molecular clock hypothesis The hypothesis of the molecular clock proposes that molecular evolution occurs at rates that persist through time and across lineages Constant Burst The discovery of the molecular clock stands out as the most significant result of research in molecular evolution. Wilson et al., 1977

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Emile Zuckerland and Linus Pauling …It is possible to evaluate very roughly and tentatively the time that has elapsed since any of the hemoglobin chains present in a given species and controlled by non-allelic genes diverged from a common chain ancestor.... From paleontological evidence it may be estimated that the common ancestor of man and horse lived in the Cretaceous or possibly the Jurassic period, say between 100 and 160 million years ago.... The presence of 18 differences between human and horse -chains would indicate that each chain had 9 evolutionary effective mutations in 100 to 160 millions of years. This yields a figure of 11 to 18 million years per amino acid substitution in a chain of about 150 amino acids, with a medium [sic] figure of 14.5 million years… Constant Burst Zuckerland and Pauling, 1962

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Emile Zuckerland and Linus Pauling Constant Burst

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The molecular clock hypothesis Constant Burst rate = number of substitutions per site per year number of substitutions per site Divergence time between species i and j Confidence interval

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The molecular clock hypothesis Increasing of genetic data Quantification of rates Molecular evolution understanding Constant Framework for hypothesis testing

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The molecular clock hypothesis Constant Differences in generation times Differences in population size Natural selection and its intensity Some biological attributes might be responsible:

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Null hypothesis: the phylogeny is rooted and the branch lengths are constrained such that all of the tips can be drawn at a single time plane. Alternative hypothesis: each branch is allowed to vary independently. Chi-square distribution with 3 d.f. Log Likelihood ratio test

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Amount of evolution BL = R*T What to do if the clock is rejected? Branch lengths

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Error in topology Error in branch lengths Error in rates optimization Error in calibration PhylogramUltrametric tree What to do if the clock is rejected?

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…Go simple Eliminate branches (lineages) that are causing the clock to be rejected What to do if the clock is rejected?

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Objective functions need to be developed to reduce dimensionality

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Global clock to Local clocks Assign specific rates to specific parts of the tree and calculate divergence times Packages: PAML Pathd8 r1r1 r2r2

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…what if still doesnt work? We need to find the function that explain the data better. Relaxed clock methods Maximum Likelihood and Bayesian Inference Uncorrelated relaxed clocks Correlated relaxed clocks

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Penalized Likelihood Method (Sanderson, 2002) A likelihood method to generate an ultrametric chronogram from a non-ultrametric tree Finds the best fitting model of rate evolution considering both: 1.how well modeled changes explain the branch lengths 2.The amount of rate changes across the tree (less change = better) Rates correlation

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Penalized Likelihood Method (Sanderson, 2002) A topology with branch lengths is required. Absolute or relative dates can be obtained. Bootstrap method is used for confidence intervals (time consuming!!!) Fossil cross validation

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Penalized Likelihood Method (Sanderson, 2002) Maximizes the sequence data (X) on a combination of average rates (R) and time (T) with a penalty function to discourage rate change. Likelihood Penalty function

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Number of pseudoreplicates Mean date for the same node from all bootstrap pseudoreplicates Estimate of time for a single node from single bootstrap pseudoreplicate Standard error of a bootstrap distribution Confidence intervals for Penalized Likelihood (Burbrink and Pyron, 2008)

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)( )()(),()( ),,,( CXp vpCTpvTRpBXp CXvRTp Posterior Likelihood Prior marginal p of the data agestreeparameters constraints Bayesian Inference (Thorne and Kishino, 2000; Drummond et al., 2006) Uses the bayes rule to estimate rates and dates

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Bayesian Inference (Thorne and Kishino, 2000; Drummond et al., 2006) BL=0.065 subs/site BL=R*T

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Bayesian Inference (Thorne and Kishino, 2000; Drummond et al., 2006) r=0.1 t=0.65

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Bayesian Inference (Thorne and Kishino, 2000; Drummond et al., 2006) BL=0.065 subs/site

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Bayesian Inference (Thorne and Kishino, 2000; Drummond et al., 2006) Prior BL=0.065 subs/site

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Bayesian Inference (Thorne and Kishino, 2000; Drummond et al., 2006) Prior Posterior BL=0.065 subs/site

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Thorne and Kishino, 1998 BL=0.065 subs/site A topology is required. Branch lengths are estimated using the F84 model Variance-covariance matrix of the branch lengths are also estimated Several priors (e.g., time constraints, rates) can be included MCMC methods are implemented to sample from the posterior

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Drummond et al., 2006 BL=0.065 subs/site A topology is not required. Phylogeny and dates are estimated simultaneously. More complex models can be applied. Several priors (e.g., time constraints, rates) can be included. Distributions do not need to be normal. MCMC methods are implemented to sample from the posterior

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Coalescent theory and molecular dating Coalescent A stochastic process that describes how population genetic processes determine the shape of the genealogy of sampled gene sequences. + Molecular dating Test hypotheses about historical demography

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Coalescent theory and molecular dating Coalescent A stochastic process that describes how population genetic processes determine the shape of the genealogy of sampled gene sequences. + Molecular dating Test hypotheses about historical demography E O

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Coalescent theory and molecular dating Coalescent A stochastic process that describes how population genetic processes determine the shape of the genealogy of sampled gene sequences. + Molecular dating Test hypotheses about historical demography HCV Bison

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The methods seems to be more realistic but… Are they more accurate in the real world? How do we know if a method is appropiate??

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Uncertainty of phylogenetic relationships. Rates of evolution are unknown for many organisms. Rate heterogeneity no molecular clock. Lack of calibration points (fossils, biogeographic events). BL = R*T There are many factors that can affect divergence times

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Gene tree vs. species tree Coalescent times Divergence times Time of cladogenetic event = TMRCA

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0.54 0.66 0.91 0.74 0.84 New World Crotalinae

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Fossil quality Calibration Error includes several components: Fossil misidentified (belongs elsewhere and calibrates a different node) Fossil mis-dated (uncertainty in determining absolute age of fossil) Non-preservation (fossil never gives true origin - impossible to avoid)

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Fossil cross-validation (Near et al., 2005) Test the effect of each fossil on the time estimates We left one fossil and re- estimated dates of remaining fossils using r8s Consistent Inconsistent Fossil quality

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Parameters: Average difference between molecular ages and fossil ages Sumsquares of differences Standard deviation Effect of removing inconsistent fossils Fossils inconsistency Fossil quality

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Number of fossils removed s Inconsistency 1 2 3 4 5 Fossil calibration Fossil 1 Overestimation underestimation Best ? Fossil quality

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Use of all fossils Different values of (parameter that relaxes the molecular clock using Penalized Likelihood). 0.01 0.1 1 10 100 1000 10000 Estimation of divergence time using r8s Rate heterogeneity

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Cross-validation score Substitution rate ratio Log ( ) Clock behavior Rate heterogeneity

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5 different outgroups depending of its distance to the ingroup (number of internal branches) Optimization of branch lenghts using likelihood and the GTR+ +I model Estimation of divergence time using the Mean Path Length method Pathd8 ingroup outgroup 1 outgroup 2 outgroup 3 Outgroup choice

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Node Estimated age Outgroup choice

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The saturation problem 2 nd codon position 3 rd codon position GTR dist Uncorrected dist

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Target Calibration Calibration BELOW the target OVERESTIMATION The saturation problem

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Target Calibration Calibration ABOVE the target UNDERESTIMATION The saturation problem

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Parameters required to derive posterior densities Phylogenetics topology, node support DTE credibility intervals of dates Implemented in the Multidistribute package (baseml, estbranches, multidivtime) We tested: Time expected rttm, rttmsd Rate expected rtrate,rtratesd Bigtime brownmean minab Fossils Model priors

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rttm 15 18 25 rttmsd 0.1 0.3 0.5 Model priors 15 18 25

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bigtime 24 30 50 rtrate 0.05 0.14 0.2 Model priors

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brownmean 0.56 0.83 1.1 minab 0.5 1.0 1.5 Model priors

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fossils with without w w/o Model priors

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mean Locus

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717 bp 669 bp 417 bp503 bp SD Locus

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M SD LowerUpper Partitioned vs unpartitioned Locus

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DateUpper MCMC

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The final result…you hope is the best estimate!!!!

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MY final remarks Hedges is always wrong!! Graur and Martin were wrong!!! Ok, to some extent! Time estimation using molecular data is a very useful tool in the advance of evolutionary theory Divergence time estimation procedures should to take into account factors different than violations of molecular clock assumptions in order to avoid spurious results.

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Ln(7.9*10 -14 ) –ln(6.2*10 -12 ) is 2 – distributed with (n-2) degrees of freedom Output from Likelihood Method. Likelihood: 6.2*10 -12 = 0.34.

Ln(7.9*10 -14 ) –ln(6.2*10 -12 ) is 2 – distributed with (n-2) degrees of freedom Output from Likelihood Method. Likelihood: 6.2*10 -12 = 0.34.

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