Islands and Integrals

Islands and IntegralsProcesses of Diversification in an Island Archipelago and

Bayesian Methods of Comparative Phylogeographical ModelChoice

Jamie R. Oaks1

1Department of Ecology and Evolutionary Biology, University of Kansas

October 16, 2013

Islands and Integrals J. Oaks, University of Kansas 1/53

Southeast Asia


Southeast Asia


Philippine Archipelago


Philippine Archipelago


Climate-driven diversification model

I Repeated coalescence andfragmentation of islandcomplexes

I Prominent paradigm forexplaining Philippinebiodiversity

I Proposed as model ofdiversification












Testing climate-driven diversification

Did repeated fragmentation ofislands during inter-glacialrises in sea level promotediversification?

Model has testable prediction:

I Temporally clustereddivergences among taxaco-distributed acrossfragmented islands




Model has testable prediction:

I Temporally clustereddivergences among taxaco-distributed acrossfragmented islands


Climate-driven model: Prediction

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T2

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T5

τ2 τ1

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T4

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Divergence model choice

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T = (T1,T2,T3,T4,T5)

τ = {τ1, τ2}

|τ| = 2

T2

T3

T5

τ2 τ1

T1

T4

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T = (330, 330, 125, 125, 125)

τ = {125, 330}

|τ| = 2

T2

T3

T5

τ2 τ1

T1

T4

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T = (330, 330, 125, 330, 125)

τ = {125, 330}

|τ| = 2

T2

T3

T5

τ2 τ1

T1

T4

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T = (375, 330, 125, 330, 125)

τ = {125, 330, 375}

|τ| = 3

T2

T3

T5

τ2 τ1

T1

τ3

T4

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T = (T1,T2,T3,T4,T5)

τ = {τ1, τ2, τ3}

|τ| = 3

T2

T3

T5

τ2 τ1

T1

τ3

T4

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T = (T1,T2, . . . ,TY)

τ = {τ1, . . . , τ|τ|}

|τ|

T2

T3

T5

τ2 τ1

T1

τ3

T4

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T = (T1,T2, . . . ,TY)

τ = {τ1, . . . , τ|τ|}

|τ|

I We want to infer T given DNAsequence alignments X

I

p(T |X) =p(X |T)p(T)

p(X)

I This approach implemented inmsBayes

I Not that simple



T = (T1,T2, . . . ,TY)

τ = {τ1, . . . , τ|τ|}

|τ|


I


p(X)


I Not that simple



T = (T1,T2, . . . ,TY)

τ = {τ1, . . . , τ|τ|}

|τ|


I


p(X)


I Not that simple



T = (T1,T2, . . . ,TY)

τ = {τ1, . . . , τ|τ|}

|τ|


I


p(X)


I Not that simple


The msBayes model

T2

T3

T5

τ2 τ1

T1

T4

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The msBayes model

T1

T2

τ2

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The msBayes model

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The msBayes model

X Sequence alignments

G Gene trees

T Divergence times

Θ Demographicparameters

T1

T2

τ2

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The msBayes model


G Gene trees

T Divergence times

Θ Demographicparameters

T1

T2

τ2

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The msBayes model

Full Model:

p(G,T,Θ |X) =p(X |G,T,Θ)p(G,T,Θ)

p(X)


G Gene trees

T Divergence times

Θ Demographic parameters


The msBayes model

Full Model:


p(X)


G Gene trees

T Divergence times

Θ Demographic parameters


The msBayes model

Full Model:


p(X)

p(G,T, θA, θD1, θD2, τB, ζD1, ζD2,m, α,υ | X,φ,ρ, ν)

=1

p(X)p(T)f (α)

[ Y∏i=1

p(θA,i )p(θD1,i , θD2,i )p(τB,i )p(ζD1,i )f (ζD2,i )p(mi )

ki∏j=1

p(Xi,j | Gi,j , φi,j )p(Gi,j | Ti , θA,i , θD1,i , θD2,i , ρi,j , νi,j , υj , τB,i , ζD1,i , ζD2,i ,mi )

][K∏

j=1

f (υj |α)]


The msBayes model

Full Model:


p(X)

Approximate Bayesian computation (ABC)

X → S∗ → Bε(S∗)


The msBayes model

Full Model:


p(X)

Approximate Bayesian computation (ABC)

X → S∗ → Bε(S∗)

Approximate Model:

p(G,T,Θ |Bε(S∗)) =p(X |G,T,Θ)p(G,T,Θ)

p(Bε(S∗))


The msBayes model

Full Model:


p(X)

T Vector of divergence times across pairs of populations

|τ| Number of divergence parameters

DT The variance of T


Species n1 n2

MammalsCrocidura beatus 12 11Crocidura negrina-panayensis 12 6Hipposideros obscurus 19 9Hipposideros pygmaeus 3 12Cynopterus brachyotis 20 8Cynopterus brachyotis 8 14Haplonycteris fischeri 29 8Haplonycteris fischeri 9 21Macroglossus minimus 19 4Macroglossus minimus 8 10Ptenochirus jagori 4 7Ptenochirus jagori 8 8Ptenochirus minor 30 9SquamatesCyrtodactylus gubaot-sumuroi 29 6Cyrtodactylus annulatus 14 3Cyrtodactylus philippinicus 6 14Gekko mindorensis 8 11Insulasaurus arborens 22 10Pinoyscincus jagori 8 8Dendrelaphis marenae 6 6AnuransLimnonectes leytensis 4 2Limnonectes magnus 2 3


Species n1 n2



Species n1 n2



Species n1 n2



Species n1 n2



Species n1 n2



Species n1 n2



Empirical results

Strong support forsimultaneous divergence ofall 22 taxon pairs

pp > 0.96

∼100,000–250,000 years ago


Simulation-based power analyses

What is “simultaneous”?

I Simulate datasets in which all 22 divergence times are random

I τ ∼ U(0, 0.5MGA)

I τ ∼ U(0, 1.5MGA)

I τ ∼ U(0, 2.5MGA)

I τ ∼ U(0, 5.0MGA)

I MGA = Millions of Generations Ago

I Simulate 1000 datasets for each τ distribution

I Analyze all 4000 datasets as we did the empirical data



What is “simultaneous”?I Simulate datasets in which all 22 divergence times are random

I τ ∼ U(0, 0.5MGA)

I τ ∼ U(0, 1.5MGA)

I τ ∼ U(0, 2.5MGA)

I τ ∼ U(0, 5.0MGA)







I τ ∼ U(0, 0.5MGA)

I τ ∼ U(0, 1.5MGA)

I τ ∼ U(0, 2.5MGA)

I τ ∼ U(0, 5.0MGA)







I τ ∼ U(0, 0.5MGA)

I τ ∼ U(0, 1.5MGA)

I τ ∼ U(0, 2.5MGA)

I τ ∼ U(0, 5.0MGA)





Simulation-based power analyses: Results

1 3 5 7 9 11 13 15 17 19 210.0

0.2

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0.8

1.0p( ˆ|τ|=1) =1.0

τ∼U(0, 0.5 MGA)

1 3 5 7 9 11 13 15 17 19 210.0

0.2

0.4

0.6

0.8

1.0p( ˆ|τ|=1) =1.0

τ∼U(0, 1.5 MGA)

1 3 5 7 9 11 13 15 17 19 210.0

0.2

0.4

0.6

0.8

1.0p( ˆ|τ|=1) =1.0

τ∼U(0, 2.5 MGA)

1 3 5 7 9 11 13 15 17 19 210.0

0.2

0.4

0.6

0.8

1.0p( ˆ|τ|=1) =1.0

τ∼U(0, 5.0 MGA)

Estimated number of divergence events (mode)

Dens

ity



1 3 5 7 9 11 13 15 17 19 210.0

0.2

0.4

0.6

0.8

1.0p( ˆ|τ|=1) =1.0

τ∼U(0, 0.5 MGA)

1 3 5 7 9 11 13 15 17 19 210.0

0.2

0.4

0.6

0.8

1.0p( ˆ|τ|=1) =1.0

τ∼U(0, 1.5 MGA)

1 3 5 7 9 11 13 15 17 19 210.0

0.2

0.4

0.6

0.8

1.0p( ˆ|τ|=1) =1.0

τ∼U(0, 2.5 MGA)

1 3 5 7 9 11 13 15 17 19 210.0

0.2

0.4

0.6

0.8

1.0p( ˆ|τ|=1) =1.0

τ∼U(0, 5.0 MGA)


Dens

ity

0.05 0.25 0.45 0.65 0.850

5

10

15

20

0.05 0.25 0.45 0.65 0.850

5

10

15

20

0.05 0.25 0.45 0.65 0.850

2

4

6

8

10

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0.05 0.25 0.45 0.65 0.850

2

4

6

8

10

Posterior probability of one divergence

Dens

ity



Strong support for highly clustered divergences when divergencetimes are random over 5 million generations

Our empirical results are likely spurious


Why the bias?

Potential causes of the bias:

1. The prior on divergence models

2. Broad uniform priors on many of the model’s parameters,including divergence times


Causes of bias: Prior on divergence models

T = (375, 330, 125, 330, 125)

τ = {125, 330, 375}

|τ| = 3

T2

T3

T5

τ2 τ1

T1

τ3

T4

0100200300400500Time (kya)

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Causes of bias: Prior on divergence models

I msBayes uses a discrete uniform prior on the number ofdivergence events, |τ|

# of

div

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mod

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A

p(M

|τ|,i)

0.00

0.01

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0.04

1 3 5 7 9 11 13 15 17 19 21

B

# of divergence events, |τ|


Causes of bias: Broad priors

I msBayes uses uniform priors on most model parameters,including divergence times

I This requires the use of broad priors

I Models with more divergence-time parameters have muchgreater parameter space, much of it with low likelihood

I This vast space can cause problems with Bayesian modelchoice

I Reduced marginal likelihoods























Causes of bias: Marginal likelihoods

p(X ) =

∫θ

p(X | θ)p(θ)dθ



p(X ) =

∫θ

p(X | θ)p(θ)dθ

0.0 0.2 0.4 0.6 0.8 1.0θ

0

5

10

15

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25

30

Dens

ity

p(X | θ)



p(X ) =

∫θ

p(X | θ)p(θ)dθ

0.0 0.2 0.4 0.6 0.8 1.0θ

0

5

10

15

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25

30

Dens

ity

p(X | θ)

p(θ)









p(θ |X ) =p(X | θ)p(θ)

p(X )

p(X ) =

∫θ

p(X | θ)p(θ)dθ



p(θ1 |X ,M1) =p(X | θ1,M1)p(θ1 |M1)

p(X |M1)

p(X |M1) =

∫θ1

p(X | θ1,M1)p(θ |M1)dθ1



p(θ1 |X ,M1) =p(X | θ1,M1)p(θ1 |M1)

p(X |M1)

p(X |M1) =

∫θ1

p(X | θ1,M1)p(θ |M1)dθ1

p(M1 |X ) =p(X |M1)p(M1)

p(X |M1)p(M1) + p(X |M2)p(M2)



Predictions:

I Posterior estimates should be sensitive to priors

I As prior converges to distribution underlying the data, thebias should disappear

Testing prior sensitivity:

1. Analyze empirical data under several different prior settings

I Results are very sensitive

2. Use simulations to assess behavior when priors are correct



Predictions:




1. Analyze empirical data under several different prior settings

I Results are very sensitive




Predictions:




1. Analyze empirical data under several different prior settingsI Results are very sensitive




Predictions:







Simulation results: Performance when priors are correct

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0


True

prob

abili

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one

dive

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msBayes performs well when all assumptions are met



Predictions:






3. Use simulations to assess behavior under “ideal” real-worldpriors



Predictions:






3. Use simulations to assess behavior under “ideal” real-worldpriors


Simulation results: Power with informed priors

1 3 5 7 9 11 13 15 17 19 210.0

0.2

0.4

0.6

0.8

1.0p( ˆ|τ|=1) =1.0

τ∼U(0, 0.5 MGA)

1 3 5 7 9 11 13 15 17 19 210.0

0.2

0.4

0.6

0.8

1.0p( ˆ|τ|=1) =1.0

τ∼U(0, 1.5 MGA)

1 3 5 7 9 11 13 15 17 19 210.0

0.2

0.4

0.6

0.8

1.0p( ˆ|τ|=1) =1.0

τ∼U(0, 2.5 MGA)

1 3 5 7 9 11 13 15 17 19 210.0

0.2

0.4

0.6

0.8

1.0p( ˆ|τ|=1) =1.0

τ∼U(0, 5.0 MGA)


Dens

ity

1 3 5 7 9 11 13 15 17 19 210.0

0.2

0.4

0.6

0.8

1.0p( ˆ|τ|=1) =1.0

1 3 5 7 9 11 13 15 17 19 210.0

0.2

0.4

0.6

0.8

1.0p( ˆ|τ|=1) =1.0

1 3 5 7 9 11 13 15 17 19 210.0

0.2

0.4

0.6

0.8

1.0p( ˆ|τ|=1) =0.997

1 3 5 7 9 11 13 15 17 19 210.0

0.1

0.2

0.3

0.4

0.5

0.6p( ˆ|τ|=1) =0.473


Dens

ity


Simulation results: Power with informed priors

0.05 0.25 0.45 0.65 0.850

5

10

15

20

τ∼U(0, 0.5 MGA)

0.05 0.25 0.45 0.65 0.850

5

10

15

20

τ∼U(0, 1.5 MGA)

0.05 0.25 0.45 0.65 0.850

2

4

6

8

10

12

τ∼U(0, 2.5 MGA)

0.05 0.25 0.45 0.65 0.850

2

4

6

8

10

τ∼U(0, 5.0 MGA)


Dens

ity

0.05 0.25 0.45 0.65 0.8502

468

1012

14

0.05 0.25 0.45 0.65 0.850123456789

0.05 0.25 0.45 0.65 0.850

1

2

3

4

5

6

0.05 0.25 0.45 0.65 0.850.0

0.5

1.0

1.5

2.0


Dens

ity


Causes of bias: Simulation results

Broad uniform priors are reducing marginal likelihoods of modelswith more divergence events

Even when uniform priors are informed by the data the bias remains

Potential solution:

More flexible priors


Causes of bias: Simulation results

Broad uniform priors are reducing marginal likelihoods of modelswith more divergence events

Even when uniform priors are informed by the data the bias remains

Potential solution:



Mitigating the bias

Potential solution:


0.0 0.2 0.4 0.6 0.8 1.0θ

0

5

10

15

20

25

30De

nsity

p(X | θ)

p(θ)

Potential solution:

Alternative prior over divergence models (e.g., uniform or Dirichletprocess)


Mitigating the bias

Potential solution:


0.0 0.2 0.4 0.6 0.8 1.0θ

0

5

10

15

20

25

30De

nsity

p(X | θ)

p(θ)

Potential solution:



Mitigating the bias

Potential solution:


# of

div

erge

nce

mod

els

020

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8010

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0

1 3 5 7 9 11 13 15 17 19 21

A

p(M

|τ|,i)

0.00

0.01

0.02

0.03

0.04

1 3 5 7 9 11 13 15 17 19 21

B

# of divergence events, |τ|

Potential solution:



Mitigating the bias

Potential solution:


Potential solution:



New method: dpp-msbayes

I Reparameterized the model implemented in msBayes

I Replaced uniform priors on continuous parameters withgamma and beta distributions

I Dirichlet process prior (DPP) over all possible discretedivergence models

I Uniform prior over divergence models




















dpp-msbayes: Simulation-based assessment

Simulate 50,000 datasets under four models

MmsBayes I U-shaped prior on divergence modelsI Uniform priors on continuous parameters

MUshaped I U-shaped prior on divergence modelsI Gamma priors on continuous parameters

MUniform I Uniform prior on divergence modelsI Gamma priors on continuous parameters

MDPP I DPP prior on divergence modelsI Gamma priors on continuous parameters

Analyze all datasets under each of the models


dpp-msbayes: Simulation-based assessment

Assess power

I Simulate datasets in which all 22 divergence times are random

I τ ∼ U(0, 0.5MGA)

I τ ∼ U(0, 1.5MGA)

I τ ∼ U(0, 2.5MGA)

I τ ∼ U(0, 5.0MGA)





dpp-msbayes: Simulation results

0.0

0.2

0.4

0.6

0.8

1.0

MmsBayes MDPPM

msBayes

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0

MDPP


True

prob

abili

tyof

one

dive

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ce Analysis

modelData model



0.0

0.2

0.4

0.6

0.8

1.0

MmsBayes MDPP MUniform MUshaped

MmsBayes

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

MDPP


True

prob

abili

tyof

one

dive

rgen

ce Analysis

model

Data model



1 3 5 7 9 11 13 15 17 19 210.0

0.2

0.4

0.6

0.8

1.0p( ˆ|τ|=1) =1.0

τ∼U(0, 0.5 MGA)

1 3 5 7 9 11 13 15 17 19 210.0

0.2

0.4

0.6

0.8

1.0p( ˆ|τ|=1) =1.0

τ∼U(0, 1.5 MGA)

1 3 5 7 9 11 13 15 17 19 210.0

0.2

0.4

0.6

0.8

1.0p( ˆ|τ|=1) =0.999

τ∼U(0, 2.5 MGA)

1 3 5 7 9 11 13 15 17 19 210.00.10.20.30.40.50.60.70.80.9

p( ˆ|τ|=1) =0.83

τ∼U(0, 5.0 MGA)

MmsBayes


Dens

ity

1 3 5 7 9 11 13 15 17 19 210.0

0.2

0.4

0.6

0.8

1.0p( ˆ|τ|=1) =0.926

1 3 5 7 9 11 13 15 17 19 210.00.10.20.30.40.50.60.7

p( ˆ|τ|=1) =0.605

1 3 5 7 9 11 13 15 17 19 210.000.050.100.150.200.250.300.350.400.45

p( ˆ|τ|=1) =0.187

1 3 5 7 9 11 13 15 17 19 210.000.020.040.060.080.100.120.14

p( ˆ|τ|=1) =0.003

MDPP


Dens

ity



0.05 0.25 0.45 0.65 0.8502468

10121416

τ∼U(0, 0.5 MGA)

0.05 0.25 0.45 0.65 0.850123456789

τ∼U(0, 1.5 MGA)

0.05 0.25 0.45 0.65 0.85012

34

567

τ∼U(0, 2.5 MGA)

0.05 0.25 0.45 0.65 0.850.0

0.5

1.0

1.5

2.0

2.5

3.0

τ∼U(0, 5.0 MGA)

MmsBayes


Dens

ity

0.05 0.25 0.45 0.65 0.85012

34

567

0.05 0.25 0.45 0.65 0.850.00.51.01.52.02.53.03.54.0

0.05 0.25 0.45 0.65 0.850

1

2

3

4

5

0.05 0.25 0.45 0.65 0.850

5

10

15

20

MDPP


Dens

ity



0.0 0.02 0.04 0.06 0.08 0.1 0.120

50

100

150

200p(D̂T <0.01) =1.0

τ∼U(0, 0.5 MGA)

0.0 0.02 0.04 0.06 0.08 0.1 0.120

50

100

150

200p(D̂T <0.01) =0.999

τ∼U(0, 1.5 MGA)

0.0 0.02 0.04 0.06 0.08 0.1 0.120

50

100

150

200p(D̂T <0.01) =0.996

τ∼U(0, 2.5 MGA)

0.0 0.02 0.04 0.06 0.08 0.1 0.12020406080

100120140160180

p(D̂T <0.01) =0.637

τ∼U(0, 5.0 MGA)

MmsBayes

Estimated variance in divergence times (median)

Dens

ity

0.0 0.1 0.2 0.3 0.4 0.50

2

4

6

8

10p(D̂T <0.01) =0.002

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.40.00.51.01.52.02.53.03.54.04.5

p(D̂T <0.01) =0.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.40.0

0.5

1.0

1.5

2.0

2.5p(D̂T <0.01) =0.0

0.0 0.4 0.8 1.2 1.60.0

0.5

1.0

1.5

2.0

2.5

3.0p(D̂T <0.01) =0.0

MDPP


Dens

ity



0.0 0.02 0.04 0.06 0.08 0.1 0.120

50

100

150

200p(D̂T <0.01) =1.0

τ∼U(0, 0.5 MGA)

0.0 0.02 0.04 0.06 0.08 0.1 0.120

50

100

150

200p(D̂T <0.01) =0.999

τ∼U(0, 1.5 MGA)

0.0 0.02 0.04 0.06 0.08 0.1 0.120

50

100

150

200p(D̂T <0.01) =0.996

τ∼U(0, 2.5 MGA)

0.0 0.02 0.04 0.06 0.08 0.1 0.12020406080

100120140160180

p(D̂T <0.01) =0.637

τ∼U(0, 5.0 MGA)M

msBayes


Dens

ity

0.0 0.05 0.1 0.15 0.2 0.25 0.3 0.35010203040506070

p(D̂T <0.01) =0.914

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

5

10

15

20

25p(D̂T <0.01) =0.626

0.0 0.2 0.4 0.6 0.80123456789

p(D̂T <0.01) =0.235

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.40.0

0.5

1.0

1.5

2.0

2.5p(D̂T <0.01) =0.004

MUshaped


Dens

ity

0.0 0.1 0.2 0.3 0.4 0.50

2

4

6

8

10p(D̂T <0.01) =0.002

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.40.00.51.01.52.02.53.03.54.04.5

p(D̂T <0.01) =0.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.40.0

0.5

1.0

1.5

2.0

2.5p(D̂T <0.01) =0.0

0.0 0.4 0.8 1.2 1.60.0

0.5

1.0

1.5

2.0

2.5

3.0p(D̂T <0.01) =0.0

MDPP


Dens

ity



I Results confirm the bias of msBayes was caused by

1. Broad uniform priors2. U-shaped prior on divergence models

I The new model shows improved model-choice accuracy,power, and robustness





Species n1 n2



dpp-msbayes: Philippine diversification

1 3 5 7 9 11 13 15 17 19 21Number of divergence events

0.0

0.1

0.2

0.3

0.4

0.5

Post

erio

r pro

babi

lity

msBayes


dpp-msbayes


dpp-msbayes: Philippine diversification


0.00

0.02

0.04

0.06

0.08

0.10

0.12

Prob

abili

ty

Prior


Posterior

0100200300400500Time (kya)

0

-50

-100

Sea le

vel (m

)


Conclusions

I Our new approximate-Bayesian method of phylogeographicalmodel choice shows improved behavior

I Improved accuracy, robustness, and powerI More “honest” estimates regarding uncertainty

I Philippine climate-driven diversification model?

I Results consistent with prediction of clustered divergencesI Results suggest multiple co-divergencesI However, there is a lot of uncertainty


Conclusions

I Our new approximate-Bayesian method of phylogeographicalmodel choice shows improved behavior

I Improved accuracy, robustness, and powerI More “honest” estimates regarding uncertainty

I Philippine climate-driven diversification model?I Results consistent with prediction of clustered divergencesI Results suggest multiple co-divergencesI However, there is a lot of uncertainty


Future directions: Full-Bayesian phylogenetic framework

T2

T3

T5

τ2 τ1

T1

τ3

T4

0100200300400500Time (kya)

0

-50

-100

Sea le

vel (m

)


Future directions: Full-Bayesian phylogenetic framework

0100200300400500Time (kya)

0

-50

-100

Sea le

vel (m

)


Software

Everything is on GitHub. . .

I dpp-msbayes: https://github.com/joaks1/dpp-msbayes

I PyMsBayes: https://github.com/joaks1/PyMsBayes

I ABACUS: Approximate BAyesian C UtilitieS.https://github.com/joaks1/abacus


https://github.com/joaks1/dpp-msbayes

https://github.com/joaks1/PyMsBayes

https://github.com/joaks1/abacus

Open Notebook Science

Everything is on GitHub. . .

I msbayes-experiments:https://github.com/joaks1/msbayes-experiments

I [email protected]


https://github.com/joaks1/msbayes-experiments

Acknowledgments

Ideas and feedback:

I KU Herpetology

I Holder Lab

I Melissa Callahan

I Mike Hickerson

I Laura Kubatko

I My committee

Computation:

I KU ITTC

I KU Computing Center

I iPlant

Funding:

I NSF

I KU Grad Studies, EEB & BI

I SSB

I Sigma Xi

Photo credits:

I Rafe Brown, Cam Siler, &Jake Esselstyn

I FMNH Philippine MammalWebsite:

I D.S. Balete, M.R.M. Duya,& J. Holden


Acknowledgments

Friends & Family


Acknowledgments

Friends & Family


Questions?


Gene tree divergences

Age (mybp)

Split

(Tax

on: I

slan

d 1−

Isla

nd 2

)

Crocidura beatus: Leyte−Samar

Crocidura negrina−panayensis: Negros−Panay

Cynopterus brachyotis: Biliran−Mindanao

Cynopterus brachyotis: Negros−Panay

Cyrtodactylus annulatus: Bohol−Mindanao

Cyrtodactylus gubaot−sumuroi: Leyte−Samar

Cyrtodactylus philippinicus: Negros−Panay

Dendrelaphis marenae: Negros−Panay

Gekko mindorensis: Negros−Panay

Haplonycteris fischeri: Biliran−Mindanao

Haplonycteris fischeri: Negros−Panay

Hipposideros obscurus: Leyte−Mindanao

Hipposideros pygmaeus: Bohol−Mindanao

Limnonectes leytensis: Bohol−Mindanao

Limnonectes magnus: Bohol−Mindanao

Macroglossus minimus: Biliran−Mindanao

Macroglossus minimus: Negros−Panay

Ptenochirus jagori: Leyte−Mindanao

Ptenochirus jagori: Negros−Panay

Ptenochirus minor: Biliran−Mindanao

Insulasaurus arborens: Negros−Panay

Pinoyscincus jagori: Mindanao−Samar

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

0.5 1.0 1.5 2.0 2.5 3.0


Causes of bias: Insufficient sampling

I Models with more parameter space are less densely sampled

I Could explain bias toward small models in extreme casesI Predicts large variance in posterior estimates

I We explored empirical and simulation-based analyses with 2, 5,and 10 million prior samples, and estimates were very similar

0.0 0.2 0.4 0.6 0.8 1.01e8

0.0

0.2

0.4

0.6

0.8

1.0

1.2

95%

HPD

DT

UnadjustedA

0.0 0.2 0.4 0.6 0.8 1.01e8

0.00.10.20.30.40.50.60.70.8 GLM-adjustedB

Number of prior samples


Geological history
