Estimation of divergence times

Center for Evolutionary Medicine and Informatics

MPAWEstimation of divergence times

Fabia U. Battistuzzi

[email protected]


Two dimensions of evolution Staphylococcaceae

Lactobacillaceae

Mycoplasmataceae1

Symbiobacterium

Thermoanaerobacteriaceae1

Dehalococcoides

Synechococcaceae2

Merismopediaceae

Frankiaceae

Nocardiaceae

Bifidobacteriaceae

Francisellaceae

Enterobacteriaceae

Colwelliaceae

Pseudomonadaceae

Legionellaceae

Piscirickettsiaceae

Rhodocyclaceae

Alcaligenaceae

Erythrobacteraceae

Bradyrhizobiaceae

Bartonellaceae

Acetobacteraceae

Rickettsiaceae

Myxococcaceae

Geobacteraceae

Chlamydiaceae

Bacteroidaceae

Spirochaetaceae

050010001500200025003000

Lineage Relations

Time frame

Evolutionary Rate


Molecular clocks – brief overview

Time

Se

que

nce

Cha

nge

X

Kumar, Nature Reviews Genetics (2005)

1962 1968

19721976

1984 1989

19972006

1st protein clock




1962 1968

19721976

1984 1989

19972006

1st protein clock

Neutral theory

Rate tests




1962 1968

19721976

1984 1989

19972006

1st protein clock

Neutral theory

Deut.-Prot. divergenceRate tests

Rate Autocorrelation

Ancestor

Descendant

slower faster




1962 1968

19721976

1984 1989

19972006

1st protein clock

Neutral theory



Local rates

slower faster




1962 1968

19721976

1984 1989

19972006

1st protein clock

Neutral theory



Local rates

Autocorrelated clocks

Uncorrelated clocks


What can we do with molecular clocks?

• Species divergence• Phylogeography• Epidemiology• Rate estimations

Eastern fox squirrel (Sciurus niger) lacks phylogeographic structure: recent range expansion and phenotypic differentiation


Molecular clock packages available

• BEAST – Drummond & Rambaut– Uncorrelated rates

• MCMCTree – Yang– Uncorrelated and autocorrelated rates

• MultiDivTime – Thorne & Kishino– Autocorrelated rates between ancestor-descendant

• Pathd8 – Britton et al.– Autocorrelation between sister groups

• Phylobayes – Lartillot et al.– Uncorrelated and autocorrelated rates

• R8s – Sanderson– Strict, local, relaxed clock


Molecular clock packages available

• BEAST – uncorrelated rates• MCMCTree – uncorrelated & autocorrelated rates• MultiDivTime – autocorrelated rates

Basic functionality

1. bayesian methods: based on priors and data, estimate posteriors (divergence times and credibility intervals)

2. analyze partitioned data (codon positions, genes)

3. calibration points

4. estimate phylogeny and/or branch lengths


Calibration priors

Minimum only Maximum only Minimum-Maximum

time

lognormal

: 95% probability

uniformtime

exponentialtime

normaltime


Calibration priors

Minimum only Maximum only Minimum-Maximum

time

: 95% probability

time

exponentialtime

normaltime

Hedges and Kumar, Trends in Genetics (2004)


BEAUTI & BEAST

• nexus file • xml file


Phylogeny specification

<newick id="startingTree">(((((Ssc:0.65,Bta:0.65):0.16,((Cfa:0.46,Fca:0.46):0.28,Eca:0.74):0.07):0.11,

(((Rno:0.20,Mmu:0.20):0.65,Ocu:0.85):0.05,(((Hsa:0.05,Ptr:0.05):0.05,Ppy:0.10):0.13,Mml:0.23):0.67):0.02):0.81,Tvu1:1.73):1.37,Gga:3.10);</newick>


Strict clock & Relaxed clock

Priors


Operators

• remove “Tree” operator for fixed phylogeny


Generations

• Convergence & ESS values


Beast running…


A fuzzy caterpillar


MCMCTree

seqfile = exampleseqs.phy treefile = example.tre outfile = exampleseqs_3.out

(((((Ssc,Bta),((Cfa,Fca)'B(0.45,0.47)',Eca)),(((Rno,Mmu),Ocu),(((Hsa,Ptr),Ppy)'B(0.09,0.11)',Mml))),Tvu1),Gga);


MCMCTree


(((((Ssc,Bta),((Cfa,Fca)‘L(0.35,0.1,0.5,0.025)',Eca)),(((Rno,Mmu),Ocu),(((Hsa,Ptr),Ppy),Mml))),Tvu1),Gga);

ppLL

ppLLttLL pp cc


MCMCTree


ndata = 1 usedata = 3 * 0: no data; 1:seq like; 2:use in.BV; 3: out.BV clock = 3 * 1: global clock; 2: independent rates; 3: correlated rates RootAge = < 3.0 * safe constraint on root age, used if no fossil for root.

Ancestor

Descendant

slower fasterslower faster

Ancestor

Descendant

uncorrelated autocorrelated


MCMCTree

( , )F c TL

model = 4 * 0:JC69, 1:K80, 2:F81, 3:F84, 4:HKY85alpha = 0 * alpha for gamma rates at sitesncatG = 5 * No. categories in discrete gamma

cleandata = 0 * remove sites with ambiguity data (1:yes, 0:no)?

BDparas = 2 2 0.1 * birth, death, samplingkappa_gamma = 6 2 * gamma prior for kappaalpha_gamma = 1 1 * gamma prior for alpha

rgene_gamma = 1 7.13 * gamma prior for overall rates for genessigma2_gamma = 1 1.15 * gamma prior for sigma^2 (for clock=2 or 3)

rgene: prior on rate parameter;

Sigma2: prior on rate heterogeneity;

( , )F BL TL


TimeTrees

300 250 200 150 100 50 0

Time (millions of years)


TimeTrees

Ssc Bta Cfa Fca Eca Rno Mmu Ocu Hsa Ptr Ppy Mml Tvu1 Gga

050100150200


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0 20 40 60 80 100

true time

est

ima

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tim

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Model Match

Model Violation


TimeTrees

Ssc Bta Cfa Fca Eca Rno Mmu Ocu Hsa Ptr Ppy Mml Tvu1 Gga

050100150200


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true time

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Model Match

Model Violation

Model ViolationBEAST


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-45 -35 -25 -15 -5 5 15 25 35 45 55 65

% difference from true time

freq

uenc

y

ModelMatch

ModelViolationBEAST


MCMCTree

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-45 -35 -25 -15 -5 5 15 25 35 45 55 65


fre

que

ncy

ModelMatch

ModelViolation autocorrelation

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-45 -35 -25 -15 -5 5 15 25 35 45 55 65


fre

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ModelMatch

ModelViolation uncorrelation


MultiDivTime

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-45 -35 -25 -15 -5 5 15 25 35 45 55 65


fre

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Model Violation


16%

84%

95% Credibility intervals

6%

94%

4%

96%

12%

88%

TT

TT

Success

Failure

Model Match

Model Violation


Things to remember

• Check priors for calibrations, substitution rate, rate model, etc.• Repeat every analyses at least twice to check for convergence• Look for the “fuzzy caterpillar” for all parameters• Test assumptions’ effects using multiple methods and priors (bayes factors)• Credibility intervals are a conservative estimate of divergences

Questions ?

Technology

Estimation of divergence times