The Fossilized Birth-Death Process -- Evolution 2013

T F B-D P:A C M F

C B DT E

Tracy A. Heath

John P. HuelsenbeckTanja Stadler

Evolution 2013, Snowbird, Utah USA

A A T-S M

Dating species divergence times

• What was the spacialand climaticenvironment ofancient angiosperms?

• Did the uplift of thePatagonian Andesdrive the diversity ofPeruvian lilies?

• Was thediversification of beescorrelated with theorigin of floweringplants?

(Cardinal & Danforth. PRSB. 2013)(Antonelli & Sanmartin. Syst. Biol. 2011)

Correlated evolutionHistorical biogeography

Understanding Evolutionary Processes

Fossils (or other data) are necessary to estimate absolutenode ages

There is no information inmolecular sequence data forabsolute time

Uncertainty in theplacement of fossils

10%10%

10%200 My

400 My

Combining extant and fossilspecies

ta © AntWeb.org

OrthopteraParaneoptera

NeuropteraRaphidiopteraColeo PolyphagaColeoptera AdephagaLepidopteraMecoptera

XyelaMacroxyela

RunariaParemphytus

Blasticotoma

TenthredoAglaostigmaDolerus

SelandriaStrongylogasterMonophadnoidesMetallus

Athalia

Taxonus

HoplocampaNematinusNematusCladiusMonoctenusGilpiniaDiprion

CimbicinaeAbiaCorynis

ArgeSterictiphoraPergaPhylacteophagaLophyrotoma

AcorduleceraDecameria

Neurotoma

OnycholydaPamphiliusCephalciaAcantholyda

Megalodontes cephalotesMegalodontes skorniakowii

CephusCalameutaHartigiaSyntexisSirexXerisUrocerusTremexXiphydria

Orussus

Stephanidae AStephanidae B

Megalyridae

Trigonalidae

Chalcidoidea

Evanioidea

Ichneumonidae

Cynipoidea

Apoidea AApoidea BApoidea CVespidae

Grimmaratavites

Ghilarella

AulidontesProtosirexAuliscaKaratavitesSepulca

Onokhoius

TrematothoraxThoracotremaProsyntexis

FerganolydaRudisiriciusSogutia

XyelulaBrigittepterus

MesolydaBrachysyntexis

DahuratomaPseudoxyelocerus

PalaeathaliaAnaxyela

SyntexyelaKulbastavia

Undatoma

Abrotoxyela

Mesoxyela mesozoicaSpathoxyela

TriassoxyelaLeioxyela

NigrimonticolaChaetoxyelaAnagaridyela

EoxyelaLiadoxyela

Xyelotoma

Pamphiliidae undescribed

Turgidontes

PraeoryssusParoryssus

Mesorussus

SymphytopterusCleistogasterLeptephialtitesStephanogaster

100100

350 300 250 200 150 100 50 0 million years before present

% of morphological

characters scored

for each terminal

(Ronquist, Klopfstein, et al. Syst. Biol. 2012. doi: 10.1093/sysbio/sys058)

In the absence ofmorphological data for bothfossil and extant taxa,molecular phylogenies aredated using calibrationdensities on internal nodes

Bayesian inference is well suited to accommodatinguncertainty in the age of the calibration node

Divergence times arecalibrated by placingparametric densities oninternal nodes offset by ageestimates from the fossilrecord

200 My

P D C N

Common practice in Bayesian divergence-time estimation:

Parametric distributions areoffset by the age of theoldest fossil assigned to aclade

Uniform (min, max)

Exponential (λ)

Gamma (α, β)

Log Normal (µ, σ2)

Time (My)Minimum age

Calibration Density Approach

P D C N

Common practice in Bayesian divergence-time estimation:

Estimates of absolute nodeages are driven primarily bythe calibration density

Specifying appropriatedensities is a challenge formost molecular biologists

Uniform (min, max)

Exponential (λ)

Gamma (α, β)

Log Normal (µ, σ2)

Time (My)Minimum age

Calibration Density Approach

We would prefer toeliminate the need forad hoc calibrationprior densities

Calibration densitiesdo not account fordiversification of fossils

Gray wolf

Spotted seal

Giant panda

Spectacled bear

Sun bear

Am. black bear

Asian black bear

Brown bear

Polar bear

Sloth bear

Zaragocyon daamsi

Ballusia elmensis

Ursavus brevihinus

Ailurarctos lufengensis

Ursavus primaevus

Agriarctos spp.

Kretzoiarctos beatrix

Indarctos vireti

Indarctos arctoides

Indarctos punjabiensis

Giant short-faced bear

Cave bear

Fossil and Extant Bears (Krause et al. BMC Evol. Biol. 2008; Abella et al. PLoS ONE 2012)

We want to use allof the available fossils

Example: Bears12 fossils are reducedto 4 calibration ageswith calibration densitymethods

Gray wolf

Spotted seal

Giant panda

Spectacled bear

Sun bear

Am. black bear

Asian black bear

Brown bear

Polar bear

Sloth bear

Zaragocyon daamsi

Ballusia elmensis

Ursavus brevihinus

Ursavus primaevus

Agriarctos spp.

Indarctos vireti

Indarctos arctoides

Cave bear

Because fossils arepart of thediversification process,we can combine fossilcalibration withbirth-death models

Gray wolf

Spotted seal

Giant panda

Spectacled bear

Sun bear

Am. black bear

Asian black bear

Brown bear

Polar bear

Sloth bear

Zaragocyon daamsi

Ballusia elmensis

Ursavus brevihinus

Ursavus primaevus

Agriarctos spp.

Indarctos vireti

Indarctos arctoides

Cave bear

This relies on abranching model thataccounts forspeciation, extinction,and rates offossilization,preservation, andrecovery

Gray wolf

Spotted seal

Giant panda

Spectacled bear

Sun bear

Am. black bear

Asian black bear

Brown bear

Polar bear

Sloth bear

Zaragocyon daamsi

Ballusia elmensis

Ursavus brevihinus

Ursavus primaevus

Agriarctos spp.

Indarctos vireti

Indarctos arctoides

Cave bear

T F B-D P (FBD)

Lineage-based speciation &extinction model thatcombines fossil calibrationand the model ofdiversification

0175 255075100125150

Recovered

fossil

Combining Calibration with the Birth-Death Model (Heath, Huelsenbeck, Stadler in prep.)

T F B-D P (FBD)

Eliminates specification ofcalibration prior densities

All available fossils areuseful for calibration

0175 255075100125150

Recovered

fossil

T F B-D P (FBD)

Recovered fossil specimensprovide historicalobservations of thediversification process thatgenerated the tree ofextant species

0175 255075100125150

T F B-D P (FBD)

The probability of the treeand fossil observationsunder a birth-death modelwith rate parameters:

S = speciation

E = extinction

F = fossilization/recovery 0175 255075100125150

T F B-D P (FBD)

Because we typically donot know the exactphylogenetic placement ofmost calibration fossils, weuse MCMC to samplerealizations of thediversification process 0175 255075100125150

T F B-D P (FBD)

We assume that the fossilis a descendant of aspecified calibrated node

The time of the fossil: Aindicates an observation ofthe birth-death process afterthe age of the node N

0250 50100150200

Time (My)

T F B-D P (FBD)

The fossil must attach tothe tree at some time: ⋆

0250 50100150200

Time (My)

T F B-D P (FBD)

If it is the descendant ofan unobserved lineage, thenthere is a speciation eventat time ⋆ on one of the 2branches

0250 50100150200

Time (My)

T F B-D P (FBD)

If it is the descendant ofan unobserved lineage, thenthere is a speciation eventat time ⋆ on one of the 2branches

0250 50100150200

Time (My)

T F B-D P (FBD)

If ⋆ = A, the fossil is anobservation of a lineageancestral to the extantspecies

0250 50100150200

Time (My)

T F B-D P (FBD)

If ⋆ = A, the fossil is anobservation of a lineageancestral to the extantspecies

0250 50100150200

Time (My)

T F B-D P (FBD)

The probability of thisrealization of thediversification process isconditional on:

S , E , and F

0250 50100150200

Time (My)

T F B-D P (FBD)

Using MCMC, we cansample the age of thecalibrated node • whileconditioning on

S , E , and F

other node agesA and ⋆

0250 50100150200

Time (My)

T F B-D P (FBD)

MCMC allows us toconsider all possible valuesof ⋆ (marginalization)

0250 50100150200

Time (My)

T F B-D P (FBD)

0250 50100150200

Time (My)

T F B-D P (FBD)

0250 50100150200

Time (My)

T F B-D P (FBD)

0250 50100150200

Time (My)

T F B-D P (FBD)

The posterior samples ofthe calibrated node age areinformed by the fossilattachment times

0250 50100150200

Time (My)

T F B-D P (FBD)

The FBD model allowsmultiple fossils to calibratea single node

0250 50100150200

Time (My)

T F B-D P (FBD)

Given ⋆ and A, the newfossil can attach to the treevia speciation along eitherbranch in the extant tree

0250 50100150200

Time (My)

T F B-D P (FBD)

0250 50100150200

Time (My)

T F B-D P (FBD)

0250 50100150200

Time (My)

T F B-D P (FBD)

Or the unobserved branchleading to the othercalibrating fossil

0250 50100150200

Time (My)

T F B-D P (FBD)

If ⋆ = A, then the newfossil lies directly on abranch in the extant tree

0250 50100150200

Time (My)

T F B-D P (FBD)

If ⋆ = A, then the newfossil lies directly on abranch in the extant tree

0250 50100150200

Time (My)

T F B-D P (FBD)

Or it is an ancestor of theother calibrating fossil

0250 50100150200

Time (My)

T F B-D P (FBD)

The probability of thisrealization of thediversification process isconditional on:

S , E , and F

0250 50100150200

Time (My)

T F B-D P (FBD)

Using MCMC, we cansample the age of thecalibrated node whileconditioning on

S , E , and F

other node agesA and ⋆

A and ⋆N

0250 50100150200

Time (My)

T F B-D P (FBD)

0250 50100150200

Time (My)

B I U FBD

Implemented in DPPDiv

0250 50100150200

Time (My)

Soon to be available at: https://github.com/trayc7/FDPPDIV

http://phylo.bio.ku.edu/content/tracy-heath-dppdiv

FBD Implementation (Heath, Huelsenbeck, Stadler in prep.)

FBD: P S D

Simulated Trees:

S= 0.5

S − E = 0.01

100 replicate trees, eachwith 20 extant tips

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Simulations: Methods

FBD: P S D

Fossilization Events:generated under a Poissonprocess at rate ψ

ψ = 0.1

0175 255075100125150

FBD: P S D

Fossil Sampling:random sampling of fossilsto generate 4 different setsof fossils

FBD: P S D

Calibration Fossils:A set of calibration fossilsgenerated from the 10%random sample

a calibration fossil is theoldest fossil assignable to agiven node

Calibration

fossils

keep only oldest fossils

for a given node

in extant tree

FBD: P S D

FBD Model:Analyses of simulated datasets using 5 different sets offossils

Calibration

fossils

10%50% 5%25%

(simulated sequence data under GTR+Γ)

Simulations: Analysis

FBD: P S DCalibration Densities• Hyperprior on each calibration density(Heath. Syst. Biol. 2012)

• Fixed exponential with mean equal totrue node age

• Fixed exponential with arbitrary scaledmean (0.2 × fossil age)

Calibration

fossils

3520806040

Node Age

Hyperprior

3520806040

Node Age

Fixed–True

3520806040

Node Age

Fixed–Scaled

Simulations: Analysis

B A S D

Node Age

95% CI

True Age

Coverage Probability:

The proportion of the time the95% credible interval (CI)contains the true value is ameasure of accuracy

Precision:

Large 90% CI widths indicatelow precision

Evaluating Accuracy and Precision

A: FBD N-A ENode-age estimates across 100 replicates were moreaccurate under the FBD model compared with estimatesunder the most reliable calibration density approaches(for 10% sampled fossils)

Analysis CoverageModel probabilityFBD ModelFBD – ALL available fossils 0.966FBD – Calibration fossils only 0.953

Calibration Density(calibration fossils only)Hyperprior 0.930Fixed – True 0.904Fixed – Scaled 0.680

*Accuracy: proportion of time the 95% credible interval covers the true node age

Simulations: Results (Heath, Huelsenbeck, Stadler in prep.)

A: FBD N-A E

0.1 1 10 100 1000

10% sampled fossils

FBD Model

all fossilsonly calibration fossils

Calibration Density

HyperpriorFixed-TrueFixed-Scaled

True node age (log scale)

P: FBD N-A E

0.1 1 10 100 1000

10% sampled fossils

FBD Model

all fossilsonly calibration fossils

Calibration Density

HyperpriorFixed-TrueFixed-Scaled

I N F C

Decreasing the number of calibrating fossils does not have alarge, negative impact on the coverage probability

Node-age estimates under the FBD are robust to thenumber of sampled fossils

Pct. of total Median # of fossils Coveragefossils sampled [min, max] probability50% 86 [50, 231] 0.91825% 43 [25, 116] 0.96010% 17 [10, 46] 0.9665% 9 [5, 23] 0.944

*Accuracy: proportion of time the 95% credible interval covers the true node age

*Median total # fossils across replicates: 173 [101, 462]

I N F C

0.1 1 10 100 1000

FBD Model

Pct. total fossils

I N F C

0.1 1 10 100 1000

FBD ModelPct. total fossils

The FBD model provides anestimate of the number oflineages over time

050100150200

Time (My)

50100150 0200

Time (My)

of lin

Lineage diversity over time with fossils

MCMC samples thetimes of lineages inthe reconstructed treeand the times of thefossil lineages

(for 1 simulation replicate with 10% random sample of fossils)

Visualize extant andsampled fossil lineagediversification whenusing all availablefossils (21 total)

Choosing only theoldest (calibration)fossils reduced the setof sampled fossilsfrom 21 to 12,giving less informationabout diversificationover time

B: D T

Sequence data for extantspecies:

• 8 Ursidae• 1 Canidae (gray wolf)• 1 Phocidae (spotted seal)

Fossil ages:

• 12 Ursidae• 5 Canidae• 5 Pinnipedimorpha

DPP relaxed clock model(Heath, Holder, Huelsenbeck MBE 2012)

Fixed tree topology

Phylogenetic Relationships

Fossil Data

fossil canids

fossil pinnepeds

stem fossil ursids

fossil Ailuropodinae

giant short-faced bear

cave bear

Empirical Analysis (Wang 1994, 1999; Krause et al. 2008; Fulton & Strobeck 2010; Abella et al. 2012)

B: D TGray wolf

Spotted seal

Giant panda

Spectacled bear

Sun bear

Am. black bear

Asian black bear

Brown bear

Polar bear

Sloth bear

1. fossil canids

2. fossil pinnepeds

2. stem fossil ursids

3. fossil Ailuropodinae

4. giant short-faced bear

5. cave bear

Empirical Analysis (Heath, Huelsenbeck, Stadler in prep.; silhouette images: http://phylopic.org/)

B: D T

Gray wolf

Spotted seal

Giant panda

Spectacled bear

Sun bear

Am. black bear

Asian black bear

Brown bear

Polar bear

Sloth bear

95% CI

Eocene Oligocene Miocene

Time (My)

01020304050

B: D TGray wolf

Spotted seal

Giant panda

Spectacled bear

Sun bear

Am. black bear

Asian black bear

Brown bear

Polar bear

Sloth bear

fossil canids

fossil pinnipeds

stem fossil ursids

cave bear

Time (My)

01020304050

B: L T T

Improved sampling of extant and fossil caniform species(across ingroup & outgroup) would improve estimates oflineage diversification

Empirical Analysis (Heath, Huelsenbeck, Stadler in prep.)

T F B-D P (FBD)

Improved statistical inference of absolute node ages

Biologically motivatedmodels can bettercapture statisticaluncertainty

Gray wolf

Spotted seal

Giant panda

Spectacled bear

Sun bear

Am. black bear

Asian black bear

Brown bear

Polar bear

Sloth bear

fossil canids

fossil pinnipeds

stem fossil ursids

cave bear

Time (My)

01020304050

Modeling Diversification Processes (Heath, Huelsenbeck, Stadler in prep.)

T F B-D P (FBD)

Use all available fossils

Eliminates arbitrarychoice of calibrationpriors

Gray wolf

Spotted seal

Giant panda

Spectacled bear

Sun bear

Am. black bear

Asian black bear

Brown bear

Polar bear

Sloth bear

fossil canids

fossil pinnipeds

stem fossil ursids

cave bear

Time (My)

01020304050

T F B-D P (FBD)

Extensions of the FBDcan account forstratigraphic samplingof fossils and shifts inrates of speciationand extinction

Gray wolf

Spotted seal

Giant panda

Spectacled bear

Sun bear

Am. black bear

Asian black bear

Brown bear

Polar bear

Sloth bear

fossil canids

fossil pinnipeds

stem fossil ursids

cave bear

Time (My)

01020304050

T F B-D P (FBD)

Extensions of the FBDcan account forstratigraphic samplingof fossils and shifts inrates of speciationand extinction

0175 255075100125150

0.2 1.05

Preservation Rate

ATrilogenetics: Likelihood Methods for Phylogenetics ofFossil Taxa: http://phylo.bio.ku.edu/fossil/

Thanks to:

• Paul Lewis• Bastien Boussau• Michael Landis• Brian Moore• UCB CTEG group

Collaborators:

• Mark Holder• Bruce Lieberman• Alexis Stamatakis• Tomáš Flouri• Diego Darriba

Funding:

• NSF DEB-1256993 (to Holder & Lieberman)• NIH GM-069801 & GM-086887 (to J. Huelsenbeck)• ETH Zürich Fellowship (to T. Stadler)

Twitter: @trayc7 Slides: www.slideshare.net/trayc7

Thanks! DPPDiv: http://phylo.bio.ku.edu/content/tracy-heath-dppdiv

The Fossilized Birth-Death Process -- Evolution 2013

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