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

Juan DazaUCF

Fall 2008

Reconstructing the evolutionary process

Reconstructing the evolutionary process

Evolutionary process implies TIME

We are interested in determineHow,Where,Why,WHEN evolution occursor has occurred

Genetic data

Molecular evolution

theory

Molecular dating

The general procedure of molecular dating

Phylogram Ultrametric tree

The evolution of molecular datingHemoglobin

example

The term is introduced

Neutral theory

Statisticalproperties of

clocks

Fitch’s test

Autocorrelation of rates

Local clocks

The evolution of molecular datingbranch pruning

NPRS Bayesian

Penalized likelihood

Uncorrelated rates

The evolution of molecular dating

The evolution of molecular dating

• Amino acids• Nucleotides• Pruning branches• Local clocks (PAML, Pathd8 packages)• Relaxed clocks

Correlated rates (r8s, Multidivtime)

Uncorrelated rates (Beast)

Applications

Species divergence

Explosive radiations

Gene evolution

Rates estimation

Virus epidemiology

Historical demography

0

5

10

15

20

25

30

35

40

45

50

0 5 10 15 20 25 30 35 40

bursts

TimeLo

g (#

line

ages

)

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

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 BurstZuckerland and Pauling, 1962

Emile Zuckerland and Linus Pauling

Constant Burst

The molecular clock hypothesis

Constant Burst

)(2

)()(

vE

KETE ijij

v

K

v

KTT

2,

2],[ 2121

rate = number of substitutions per site per year

number of substitutions

per siteDivergence time

between species i

and j

Confidence interval

The molecular clock hypothesis

Increasing of genetic dataQuantification of ratesMolecular evolution understanding

Constant

Framework for hypothesis testing

The molecular clock hypothesis

Constant

• Differences in generation times

• Differences in population size

• Natural selection and its intensity

Some biological attributes might be responsible:

LLclocknonclock

loglog2

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

Amount of evolution BL = R*T

What to do if the clock is rejected?

Branch lengths

Error in topologyError in branch lengths

Error in rates optimizationError in calibration

Phylogram Ultrametric tree

What to do if the clock is rejected?

…Go simple

Eliminate branches (lineages) that are causing the clock to be rejected

What to do if the clock is rejected?

What to do if the clock is rejected?

Objective functions need to be developed to reduce dimensionality

Global clock to Local clocks

Assign specific rates to specific parts of the tree and calculate divergence times

Packages:

PAMLPathd8

r1

r2

…what if still doesn’t 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

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 lengths2. The amount of rate changes across the tree (less

change = better)

Rates correlation

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

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.

RTRXp ,log

Likelihood Penalty function

Number of pseudoreplicates

Mean date for the same node from all

bootstrap pseudoreplicates

Estimate of time for a single node from single bootstrap pseudoreplicate

1

)(1

2

n

n

i BBi

B

Standard error of a bootstrap

distribution

Confidence intervals for Penalized Likelihood(Burbrink and Pyron, 2008)

)(

)()(),()(),,,(

CXp

vpCTpvTRpBXpCXvRTp

Posterior Likelihood Prior

marginal p of the data

ages tree parameters

constraints

Bayesian Inference(Thorne and Kishino, 2000; Drummond et al., 2006)

Uses the bayes’ rule to estimate rates and dates

Bayesian Inference(Thorne and Kishino, 2000; Drummond et al., 2006)

BL=0.065 subs/site

BL=R*T

Bayesian Inference(Thorne and Kishino, 2000; Drummond et al., 2006)

r=0.1

t=0.65

Bayesian Inference(Thorne and Kishino, 2000; Drummond et al., 2006)

BL=0.065 subs/site

Bayesian Inference(Thorne and Kishino, 2000; Drummond et al., 2006)

Prior

BL=0.065 subs/site

Bayesian Inference(Thorne and Kishino, 2000; Drummond et al., 2006)

Prior

Posterior

BL=0.065 subs/site

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

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

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

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

EO

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

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??

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

Gene tree vs. species tree

Coalescent times

Divergence times

Time of cladogenetic

event≠=

TMRCA

0.1

Deinagkistrodon acutusOvophis chaseni B306

Hypnale hypnaleCalloselasma rhodostoma

Ermia B300Protobothrops flavoviridisProtobothrops tokarensis

Proto cornutus B350Protobothrops jerdonii

Protobothrops elegansProtobothrops mucrosquamatus B106Protobothrops mucrosquamatus

Ovophis monticolajbsOvophis monticola rom

Ovophis monticola A87Ovophis montmakGloydius strauchi

Gloydius ussuriensisGloydius halysGloydius shedaoensis

Trimeresurus gracilis A86Trimeresurus gracilis ntub

Ovophis okinavensiscpOvophis okinavensisfk

Lachesis stenophrysLachesis muta

Ophryacus undulatusOphryacus melanurus

Agkistrodon contortrixAgkistrodon piscivorusAgkistrodon bilineatush

Agkistrodon tayloriSistrurus catenatus

Sistrurus miliarusCrotalus cerastes

Crotalus polystictusSistrurus ravus

Crotalus pusillusCrotalus triseriatusXoCrotalus triseriatusTo

Crotalus lepidusCrotalus aquilusCrotalus triseriatusLG

Crotalus horridusARCrotalus horridusNY

Crotalus priceiCrotalus intermedius

Crotalus transversusCrotalus enyo

Crotalus willardiROMCrotalus willardi2575Crotalus willardi413

Crotalus adamanteusCrotalus tigris

Crotalus mitchelliCrotalus scutulatus

Crotalus viridisCrotalus molossus

Crotalus basiliscusCrotalus unicolor

Crotalus durissusCrotalus vegrandis

Crotalus atroxCrotalus tortugensisCrotalus catalinensisCrotalus exsul

Crotalus ruberBothriechis supercilliarisBothriechis schlegelii

Bothriechis nigroviridisBothriechis lateralisBothriechis thalassinus

Bothriechis marchiBothriechis bicolor

Bothriechis auriferBothriechis rowleyi

Bothrocophias hyoproraBothrocophias microphthalmus2

Bothrops ammodytoidesBothrops cotiara

Bothrops alternatusBothrops insularis

Bothrops erythromelasBothrops neuwiedi

Bothriopsis bilineataBothriopsis taeniata

Bothriopsis oligolepis4Bothrops jararacussu

Bothrops atroxBothrops asper

A picadoi Alajuella CRAtropoides picadoiA picadoi SanJose2 CRA picadoi SanJose CR

Atropoides Honduras AnH1A n occiduus Solola GUATA n occiduus Sonsonate ELSALVA n occiduus1 Guatemala GUATAtropoides occiduus2 Escuintla GUATA n occiduus2 Escuintla GUATA olmec Chiapas1 MEXA olmec Chiapas2 MEXAtropoides olmecA olmec1 Veracruz MEXA olmec Chiapas3 MEXA olmec BVerapaz GUATA olmec2 Veracruz MEXA olmec Oaxaca MEXA n nummifer Hidalgo MEX

A n nummifer Veracruz3 MEXA n nummifer Veracruz2 MEXA n nummifer Veracruz1 MEXAtropoides nummifer Puebla MEXA n nummifer Puebla MEXAtropoides mexicanusclpA n mexicanus SanJose CRA n mexicanus Puntar CRA n mexicanus Cartago2 CRA n mexicanus Cartago1 CRA n mexicanus Huehet GUATA n mexicanus Quiche GUAT

A n mexicanus Izabal GUATA n mexicanus AVerpaz GUATA n mexicanus BVerpaz GUATA n mexicanus Peten GUAT

P dunni Pd4Porthidium dunniPorthidium dunni Oaxaca1 MEX

P ophryomegas Zacapa GUATP ophryomegas Hond ND4 PSPHPorthidium ophryomegasPorthidium ophryomegas Guanacaste CR

P yucatanicum PY1Porthidium nasutumPorthidium nasutum CR CLPP nasutum Alajuela CRP nasutum AVerapaz GUATP nasutum CR1P nasutum CR4P lansbergi MargIs VENP lansbergi PANAMA

AF191580 WW P nasutum EcuadorPorthidium arcosePorthidium arcosae ECUADOR CLP

P porrasi Punt5 CRP porrasi Punt4 CRP porrasi Punt3 CRPorthidium porrasi Punt2 CRP porrasi Punt2 CR

Cerrophidion petlacalensisC tzotzliroum Chiapas1 MEXC tzotzliroum Chiapas2 CR

C godmani SantaAna ESC godmani Ocotepeque2 HNDC godmani Ocotepeque1 HNDC godmani Honduras CgH2C godmani Honduras CgH3

C godmani SanJose4 CRCerrophidion godmaniC godmani SanJose5 CRC godmani SanJose6 CRC godmani SanJose1 CRC godmani SanJose2 CRC godmani SanJose3 CRC godmani SanJose CR

C godmani Quetzal GUATC godmani Guat GuatC godmani Guat3 GUATC godmani Guat2 GUATC godmani Oaxaca2 MexC godmani Oaxaca MEX

C godmani Huehuet GUATC godmani Quiche GUATC godmani Bverapaz2 GUATC godmani SanMarcos GUATC godmani BVerapaz GUATCerrophidion godmani GUATC godmani GUAT

0.1

Deinagkistrodon acutusOvophis chaseni B306

Hypnale hypnaleCalloselasma rhodostoma

Ermia B300Protobothrops flavoviridisProtobothrops tokarensis

Proto cornutus B350Protobothrops jerdonii

Protobothrops elegansProtobothrops mucrosquamatus B106Protobothrops mucrosquamatus

Ovophis monticolajbsOvophis monticola rom

Ovophis monticola A87Ovophis montmakGloydius strauchi

Gloydius ussuriensisGloydius halysGloydius shedaoensis

Trimeresurus gracilis A86Trimeresurus gracilis ntub

Ovophis okinavensiscpOvophis okinavensisfk

Lachesis stenophrysLachesis muta

Ophryacus undulatusOphryacus melanurus

Agkistrodon contortrixAgkistrodon piscivorusAgkistrodon bilineatush

Agkistrodon tayloriSistrurus catenatus

Sistrurus miliarusCrotalus cerastes

Crotalus polystictusSistrurus ravus

Crotalus pusillusCrotalus triseriatusXoCrotalus triseriatusTo

Crotalus lepidusCrotalus aquilusCrotalus triseriatusLG

Crotalus horridusARCrotalus horridusNY

Crotalus priceiCrotalus intermedius

Crotalus transversusCrotalus enyo

Crotalus willardiROMCrotalus willardi2575Crotalus willardi413

Crotalus adamanteusCrotalus tigris

Crotalus mitchelliCrotalus scutulatus

Crotalus viridisCrotalus molossus

Crotalus basiliscusCrotalus unicolor

Crotalus durissusCrotalus vegrandis

Crotalus atroxCrotalus tortugensisCrotalus catalinensisCrotalus exsul

Crotalus ruberBothriechis supercilliarisBothriechis schlegelii

Bothriechis nigroviridisBothriechis lateralisBothriechis thalassinus

Bothriechis marchiBothriechis bicolor

Bothriechis auriferBothriechis rowleyi

Bothrocophias hyoproraBothrocophias microphthalmus2

Bothrops ammodytoidesBothrops cotiara

Bothrops alternatusBothrops insularis

Bothrops erythromelasBothrops neuwiedi

Bothriopsis bilineataBothriopsis taeniata

Bothriopsis oligolepis4Bothrops jararacussu

Bothrops atroxBothrops asper

A picadoi Alajuella CRAtropoides picadoiA picadoi SanJose2 CRA picadoi SanJose CR

Atropoides Honduras AnH1A n occiduus Solola GUATA n occiduus Sonsonate ELSALVA n occiduus1 Guatemala GUATAtropoides occiduus2 Escuintla GUATA n occiduus2 Escuintla GUATA olmec Chiapas1 MEXA olmec Chiapas2 MEXAtropoides olmecA olmec1 Veracruz MEXA olmec Chiapas3 MEXA olmec BVerapaz GUATA olmec2 Veracruz MEXA olmec Oaxaca MEXA n nummifer Hidalgo MEX

A n nummifer Veracruz3 MEXA n nummifer Veracruz2 MEXA n nummifer Veracruz1 MEXAtropoides nummifer Puebla MEXA n nummifer Puebla MEXAtropoides mexicanusclpA n mexicanus SanJose CRA n mexicanus Puntar CRA n mexicanus Cartago2 CRA n mexicanus Cartago1 CRA n mexicanus Huehet GUATA n mexicanus Quiche GUAT

A n mexicanus Izabal GUATA n mexicanus AVerpaz GUATA n mexicanus BVerpaz GUATA n mexicanus Peten GUAT

P dunni Pd4Porthidium dunniPorthidium dunni Oaxaca1 MEX

P ophryomegas Zacapa GUATP ophryomegas Hond ND4 PSPHPorthidium ophryomegasPorthidium ophryomegas Guanacaste CR

P yucatanicum PY1Porthidium nasutumPorthidium nasutum CR CLPP nasutum Alajuela CRP nasutum AVerapaz GUATP nasutum CR1P nasutum CR4P lansbergi MargIs VENP lansbergi PANAMA

AF191580 WW P nasutum EcuadorPorthidium arcosePorthidium arcosae ECUADOR CLP

P porrasi Punt5 CRP porrasi Punt4 CRP porrasi Punt3 CRPorthidium porrasi Punt2 CRP porrasi Punt2 CR

Cerrophidion petlacalensisC tzotzliroum Chiapas1 MEXC tzotzliroum Chiapas2 CR

C godmani SantaAna ESC godmani Ocotepeque2 HNDC godmani Ocotepeque1 HNDC godmani Honduras CgH2C godmani Honduras CgH3

C godmani SanJose4 CRCerrophidion godmaniC godmani SanJose5 CRC godmani SanJose6 CRC godmani SanJose1 CRC godmani SanJose2 CRC godmani SanJose3 CRC godmani SanJose CR

C godmani Quetzal GUATC godmani Guat GuatC godmani Guat3 GUATC godmani Guat2 GUATC godmani Oaxaca2 MexC godmani Oaxaca MEX

C godmani Huehuet GUATC godmani Quiche GUATC godmani Bverapaz2 GUATC godmani SanMarcos GUATC godmani BVerapaz GUATCerrophidion godmani GUATC godmani GUAT

0.54

0.66

0.91

0.74

0.84

NewWorld

Crotalinae

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)

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

Parameters:

1

n

DD xi

i

x

xi

ix DSS 2

)1(

2

1

nn

Ds xi

i

n

x

Average difference between molecular ages and fossil ages

Sumsquares of differences

Standard deviation

Effect of removing inconsistent fossils

Fossils inconsistency

-6

-4

-2

0

2

4

6

8

1 2 3 4 5

Fossil calibration

Fossil 1

Ove

resti

mati

onun

dere

stim

ation

Best ?

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

4.2

4.4

4.6

4.8

5

5.2

5.4

5.6

5.8

6

-2 -1 0 1 2 3 4

0

10

20

30

40

50

60

-2 -1 0 1 2 3 4

Cros

s-va

lidati

on s

core

Subs

tituti

on ra

te ra

tio

Log () Log ()

Clock behavior

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

0

4

8

12

16

20

1 2 3 4 5 6

Gloydius

Ovophis_jbs

Proto

Ermia

Calloselasma

Gloydius 41T

Node

Est

imate

d a

ge

2nd codon

position

3rd codon position

GTR dist

GTR dist

Unco

rrect

ed

dis

t

Unco

rrect

ed

dis

t

Target

Calibration

Calibration BELOW the target OVERESTIMATION

Target

Calibration

Calibration ABOVE the target UNDERESTIMATION

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 expectedrttm, rttmsd

Rate expectedrtrate,rtratesd

Bigtime

brownmean

minab

Fossils

0

5

10

15

20

25

48 48 48 79 79 79 57 57 57 89 89 89

Node

MY

A

02

468

10

121416

1820

48 48 48 79 79 79 57 57 57 89 89 89

Node

MY

A

rttm

15

18

25

rttmsd

0.1

0.3

0.5

15 18 25

0

2

46

8

10

12

1416

18

20

48 48 48 79 79 79 57 57 57 89 89 89

Node

MY

A

0

24

6

810

12

14

1618

20

48 48 48 79 79 79 57 57 57 89 89 89

Node

MY

A

bigtime

24

30

50

rtrate

0.05

0.14

0.2

0

24

68

10

1214

1618

20

48 48 48 79 79 79 57 57 57 89 89 89

Node

MY

A

02

46

81012

1416

1820

48 48 48 79 79 79 57 57 57 89 89 89

Node

MY

A

brownmean

0.56

0.83

1.1

minab

0.5

1.0

1.5

0

2

4

6

810

12

14

16

18

20

48 48 79 79 57 57 89 89

Node

MY

A

fossils

with

without

w w/o

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

18.0

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0

4X

Cyt

b

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

18.0

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0

4X

ND

4

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

18.0

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0

4X

12S

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

18.0

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0

4X

16S

mean

0.0

0.4

0.8

1.2

1.6

2.0

2.4

2.8

3.2

3.6

0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6

4X

Cyt

b

0.0

0.4

0.8

1.2

1.6

2.0

2.4

2.8

3.2

3.6

0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6

4X

ND

4

0.0

0.4

0.8

1.2

1.6

2.0

2.4

2.8

3.2

3.6

0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6

4X

12S

0.0

0.4

0.8

1.2

1.6

2.0

2.4

2.8

3.2

3.6

0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6

4X

16S

717 bp 669 bp

417 bp 503 bp

SD

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

18.0

20.0

22.0

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0 22.0

4X

mD

NA

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0

4X

mD

NA

0.0

0.4

0.8

1.2

1.6

2.0

2.4

2.8

3.2

3.6

0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6

4X

mD

NA

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

18.0

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0

4X

mD

NA

M SD

Lower Upper

Partitioned vs unpartitioned

0

2

4

6

8

10

12

14

16

18

20

0 2 4 6 8 10 12 14 16 18 20

8 million

1 m

illio

n

0

2

4

6

8

10

12

14

16

18

0 2 4 6 8 10 12 14 16 18

8 million

1 m

illio

n

Date Upper

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

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.