the fossilized birth-death process -- evolution 2013
DESCRIPTION
Slides from Tracy Heath's Evolution 2013 presentation on the fossilized birth-death process, a model for calibrating Bayesian estimates of species divergence times.TRANSCRIPT
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
C D T
Fossils (or other data) are necessary to estimate absolutenode ages
There is no information inmolecular sequence data forabsolute time
Uncertainty in theplacement of fossils
N
A B C
20%
10%10%
10%200 My
400 My
F T D
Combining extant and fossilspecies
Fo
ssil
Ag
e D
ata
Se
qu
en
ce
Da
ta
© AntWeb.org
Mo
rph
olo
gic
al
Da
ta © AntWeb.org
0%
20%
40%
60%
80%
100%
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
97
100
100
100100
100100
100
100
100100
100
100100
100
100100
100
100100
100
100
100100
100
100
100
100
100
100
97
68
55
77
75
91
84
6157
62
9896
71
71
85
93
52
95
64
80
64
99
77
99
98
97
82
52
58
9490
60
70
57
8361
7060
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)
N CF
ossil
Ag
e D
ata
Se
qu
en
ce
Da
ta
© AntWeb.org
In the absence ofmorphological data for bothfossil and extant taxa,molecular phylogenies aredated using calibrationdensities on internal nodes
C D
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
N
A B C
200 My
De
nsity
Age
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
I F C
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)
I F C
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
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)
I F C
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
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)
I F C
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
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)
T F B-D P (FBD)
Lineage-based speciation &extinction model thatcombines fossil calibrationand the model ofdiversification
0175 255075100125150
Time
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
Time
Recovered
fossil
Combining Calibration with the Birth-Death Model (Heath, Huelsenbeck, Stadler in prep.)
T F B-D P (FBD)
Recovered fossil specimensprovide historicalobservations of thediversification process thatgenerated the tree ofextant species
0175 255075100125150
Time
Combining Calibration with the Birth-Death Model (Heath, Huelsenbeck, Stadler in prep.)
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
Time
Combining Calibration with the Birth-Death Model (Heath, Huelsenbeck, Stadler in prep.)
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
Time
Combining Calibration with the Birth-Death Model (Heath, Huelsenbeck, Stadler in prep.)
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)
Combining Calibration with the Birth-Death Model (Heath, Huelsenbeck, Stadler in prep.)
T F B-D P (FBD)
The fossil must attach tothe tree at some time: ⋆
0250 50100150200
Time (My)
N
Combining Calibration with the Birth-Death Model (Heath, Huelsenbeck, Stadler in prep.)
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)
N
Combining Calibration with the Birth-Death Model (Heath, Huelsenbeck, Stadler in prep.)
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)
N
Combining Calibration with the Birth-Death Model (Heath, Huelsenbeck, Stadler in prep.)
T F B-D P (FBD)
If ⋆ = A, the fossil is anobservation of a lineageancestral to the extantspecies
0250 50100150200
Time (My)
N
Combining Calibration with the Birth-Death Model (Heath, Huelsenbeck, Stadler in prep.)
T F B-D P (FBD)
If ⋆ = A, the fossil is anobservation of a lineageancestral to the extantspecies
0250 50100150200
Time (My)
N
Combining Calibration with the Birth-Death Model (Heath, Huelsenbeck, Stadler in prep.)
T F B-D P (FBD)
The probability of thisrealization of thediversification process isconditional on:
S , E , and F
0250 50100150200
Time (My)
N
Combining Calibration with the Birth-Death Model (Heath, Huelsenbeck, Stadler in prep.)
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)
N
Combining Calibration with the Birth-Death Model (Heath, Huelsenbeck, Stadler in prep.)
T F B-D P (FBD)
MCMC allows us toconsider all possible valuesof ⋆ (marginalization)
0250 50100150200
Time (My)
N
Combining Calibration with the Birth-Death Model (Heath, Huelsenbeck, Stadler in prep.)
T F B-D P (FBD)
MCMC allows us toconsider all possible valuesof ⋆ (marginalization)
0250 50100150200
Time (My)
N
Combining Calibration with the Birth-Death Model (Heath, Huelsenbeck, Stadler in prep.)
T F B-D P (FBD)
MCMC allows us toconsider all possible valuesof ⋆ (marginalization)
0250 50100150200
Time (My)
N
Combining Calibration with the Birth-Death Model (Heath, Huelsenbeck, Stadler in prep.)
T F B-D P (FBD)
MCMC allows us toconsider all possible valuesof ⋆ (marginalization)
0250 50100150200
Time (My)
Combining Calibration with the Birth-Death Model (Heath, Huelsenbeck, Stadler in prep.)
T F B-D P (FBD)
The posterior samples ofthe calibrated node age areinformed by the fossilattachment times
0250 50100150200
Time (My)
Combining Calibration with the Birth-Death Model (Heath, Huelsenbeck, Stadler in prep.)
T F B-D P (FBD)
The FBD model allowsmultiple fossils to calibratea single node
N
0250 50100150200
Time (My)
N
Combining Calibration with the Birth-Death Model (Heath, Huelsenbeck, Stadler in prep.)
T F B-D P (FBD)
Given ⋆ and A, the newfossil can attach to the treevia speciation along eitherbranch in the extant tree
N
0250 50100150200
Time (My)
N
Combining Calibration with the Birth-Death Model (Heath, Huelsenbeck, Stadler in prep.)
T F B-D P (FBD)
Given ⋆ and A, the newfossil can attach to the treevia speciation along eitherbranch in the extant tree
N
0250 50100150200
Time (My)
N
Combining Calibration with the Birth-Death Model (Heath, Huelsenbeck, Stadler in prep.)
T F B-D P (FBD)
Given ⋆ and A, the newfossil can attach to the treevia speciation along eitherbranch in the extant tree
N
0250 50100150200
Time (My)
N
Combining Calibration with the Birth-Death Model (Heath, Huelsenbeck, Stadler in prep.)
T F B-D P (FBD)
Or the unobserved branchleading to the othercalibrating fossil
N
0250 50100150200
Time (My)
N
Combining Calibration with the Birth-Death Model (Heath, Huelsenbeck, Stadler in prep.)
T F B-D P (FBD)
If ⋆ = A, then the newfossil lies directly on abranch in the extant tree
N
0250 50100150200
Time (My)
N
Combining Calibration with the Birth-Death Model (Heath, Huelsenbeck, Stadler in prep.)
T F B-D P (FBD)
If ⋆ = A, then the newfossil lies directly on abranch in the extant tree
N
0250 50100150200
Time (My)
N
Combining Calibration with the Birth-Death Model (Heath, Huelsenbeck, Stadler in prep.)
T F B-D P (FBD)
Or it is an ancestor of theother calibrating fossil
N
0250 50100150200
Time (My)
N
Combining Calibration with the Birth-Death Model (Heath, Huelsenbeck, Stadler in prep.)
T F B-D P (FBD)
The probability of thisrealization of thediversification process isconditional on:
S , E , and F
N
0250 50100150200
Time (My)
N
Combining Calibration with the Birth-Death Model (Heath, Huelsenbeck, Stadler in prep.)
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)
N
Combining Calibration with the Birth-Death Model (Heath, Huelsenbeck, Stadler in prep.)
T F B-D P (FBD)
MCMC allows us toconsider all possible valuesof ⋆ (marginalization)
0250 50100150200
Time (My)
Combining Calibration with the Birth-Death Model (Heath, Huelsenbeck, Stadler in prep.)
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:
E
S= 0.5
S − E = 0.01
100 replicate trees, eachwith 20 extant tips
0175 255075100125150
Time
Simulations: Methods
FBD: P S D
Fossilization Events:generated under a Poissonprocess at rate ψ
ψ = 0.1
0175 255075100125150
Time
Simulations: Methods
FBD: P S D
Fossil Sampling:random sampling of fossilsto generate 4 different setsof fossils
50%
5%
10%
25%
Simulations: Methods
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
10%
Calibration
fossils
keep only oldest fossils
for a given node
in extant tree
Simulations: Methods
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
De
nsity
Node Age
Hyperprior
3520806040
De
nsity
Node Age
Fixed–True
3520806040
De
nsity
Node Age
Fixed–Scaled
Tru
e
Fo
ssil
Tru
e
Fo
ssil
Tru
e
Fo
ssil
Simulations: Analysis
B A S D
Node Age
De
nsity
Node Age
De
nsity
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
0.2
0.4
0.6
0.8
1
0.1 1 10 100 1000
10% sampled fossils
FBD Model
all fossilsonly calibration fossils
Calibration Density
HyperpriorFixed-TrueFixed-Scaled
Cov
erag
e pr
obab
ility
True node age (log scale)
Simulations: Results (Heath, Huelsenbeck, Stadler in prep.)
P: FBD N-A E
0
20
40
60
80
100
120
0.1 1 10 100 1000
10% sampled fossils
FBD Model
all fossilsonly calibration fossils
Calibration Density
HyperpriorFixed-TrueFixed-Scaled
Cre
dibl
e in
terv
al w
idth
True node age (log scale)
Simulations: Results (Heath, Huelsenbeck, Stadler in prep.)
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]
Simulations: Results (Heath, Huelsenbeck, Stadler in prep.)
I N F C
0
0.2
0.4
0.6
0.8
1
0.1 1 10 100 1000
FBD Model
Pct. total fossils
50%
25%
10%
5%
Cov
erag
e pr
obab
ility
True node age (log scale)
Simulations: Results (Heath, Huelsenbeck, Stadler in prep.)
I N F C
0
10
20
30
40
50
60
70
80
90
0.1 1 10 100 1000
FBD ModelPct. total fossils
50%
25%
10%
5%
Cre
dibl
e in
terv
al w
idth
True node age (log scale)
Simulations: Results (Heath, Huelsenbeck, Stadler in prep.)
L T T
The FBD model provides anestimate of the number oflineages over time
050100150200
Time (My)
3.0
2.0
1.0
1.0
50100150 0200
Time (My)
Nu
mb
er
of lin
ea
ge
s
L T T
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)
Simulations: Results (Heath, Huelsenbeck, Stadler in prep.)
L T T
Lineage diversity over time with fossils
Visualize extant andsampled fossil lineagediversification whenusing all availablefossils (21 total)
(for 1 simulation replicate with 10% random sample of fossils)
Simulations: Results (Heath, Huelsenbeck, Stadler in prep.)
L T T
Lineage diversity over time with fossils
Choosing only theoldest (calibration)fossils reduced the setof sampled fossilsfrom 21 to 12,giving less informationabout diversificationover time
(for 1 simulation replicate with 10% random sample of fossils)
Simulations: Results (Heath, Huelsenbeck, Stadler in prep.)
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
Se
qu
en
ce
Da
ta
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
1
3
2
4
5
Empirical Analysis (Heath, Huelsenbeck, Stadler in prep.; silhouette images: http://phylopic.org/)
B: D T
Urs
ida
e
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
Plio
Ple
is
Time (My)
01020304050
Empirical Analysis (Heath, Huelsenbeck, Stadler in prep.; silhouette images: http://phylopic.org/)
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
fossil Ailuropodinae
giant short-faced bear
cave bear
Urs
ida
e
Eocene Oligocene Miocene
Plio
Ple
is
Time (My)
01020304050
Empirical Analysis (Heath, Huelsenbeck, Stadler in prep.; silhouette images: http://phylopic.org/)
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
fossil Ailuropodinae
giant short-faced bear
cave bear
Urs
ida
e
Eocene Oligocene Miocene
Plio
Ple
is
Time (My)
01020304050
Modeling Diversification Processes (Heath, Huelsenbeck, Stadler in prep.)
T F B-D P (FBD)
Improved statistical inference of absolute node ages
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
fossil Ailuropodinae
giant short-faced bear
cave bear
Urs
ida
e
Eocene Oligocene Miocene
Plio
Ple
is
Time (My)
01020304050
Modeling Diversification Processes (Heath, Huelsenbeck, Stadler in prep.)
T F B-D P (FBD)
Improved statistical inference of absolute node ages
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
fossil Ailuropodinae
giant short-faced bear
cave bear
Urs
ida
e
Eocene Oligocene Miocene
Plio
Ple
is
Time (My)
01020304050
Modeling Diversification Processes (Heath, Huelsenbeck, Stadler in prep.)
T F B-D P (FBD)
Improved statistical inference of absolute node ages
Extensions of the FBDcan account forstratigraphic samplingof fossils and shifts inrates of speciationand extinction
0175 255075100125150
Time
0.2 1.05
Preservation Rate
Modeling Diversification Processes (Heath, Huelsenbeck, Stadler in prep.)
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