Islands and Integrals

Islands and Integrals
Processes of Diversiﬁcation in an Island Archipelago and
Bayesian Methods of Comparative Phylogeographical Model
Choice
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

Philippine Archipelago

Climate-driven diversiﬁcation model
Repeated coalescence and
fragmentation of island
complexes

complexes
Prominent paradigm for
explaining Philippine
biodiversity

complexes
Prominent paradigm for
explaining Philippine
biodiversity
Proposed as model of
diversiﬁcation

Testing climate-driven diversiﬁcation
Did repeated fragmentation of
islands during inter-glacial
rises in sea level promote
diversiﬁcation?

diversiﬁcation?
Model has testable prediction:
Temporally clustered
divergences among taxa
co-distributed across
fragmented islands

Climate-driven model: Prediction
0100200300400500
Time (kya)
0
-50
-100
Sealevel(m)

Climate-driven model: Prediction
T2
T3
T5
τ2 τ1
T1
T4
0100200300400500
Time (kya)
0
-50
-100
Sealevel(m)

Divergence model choice
T2
T3
T5
τ2 τ1
T1
T4
0100200300400500
Time (kya)
0
-50
-100
Sealevel(m)

T = (T1, T2, T3, T4, T5)
τ = {τ1, τ2}
|τ| = 2
T2
T3
T5
τ2 τ1
T1
T4
0100200300400500
Time (kya)
0
-50
-100
Sealevel(m)

T = (330, 330, 125, 125, 125)
τ = {125, 330}
|τ| = 2
T2
T3
T5
τ2 τ1
T1
T4
0100200300400500
Time (kya)
0
-50
-100
Sealevel(m)

T = (330, 330, 125, 330, 125)
τ = {125, 330}
|τ| = 2
T2
T3
T5
τ2 τ1
T1
T4
0100200300400500
Time (kya)
0
-50
-100
Sealevel(m)

T = (375, 330, 125, 330, 125)
τ = {125, 330, 375}
|τ| = 3
T2
T3
T5
τ2 τ1
T1
τ3
T4
0100200300400500
Time (kya)
0
-50
-100
Sealevel(m)

T = (T1, T2, T3, T4, T5)
τ = {τ1, τ2, τ3}
|τ| = 3
T2
T3
T5
τ2 τ1
T1
τ3
T4
0100200300400500
Time (kya)
0
-50
-100
Sealevel(m)

T = (T1, T2, . . . , TY)
τ = {τ1, . . . , τ|τ|}
|τ|
T2
T3
T5
τ2 τ1
T1
τ3
T4
0100200300400500
Time (kya)
0
-50
-100
Sealevel(m)

T = (T1, T2, . . . , TY)
τ = {τ1, . . . , τ|τ|}
|τ|
We want to infer T given DNA
sequence alignments X

T = (T1, T2, . . . , TY)
τ = {τ1, . . . , τ|τ|}
|τ|
p(T | X) =
p(X | T)p(T)
p(X)

T = (T1, T2, . . . , TY)
τ = {τ1, . . . , τ|τ|}
|τ|
p(T | X) =
p(X | T)p(T)
p(X)
This approach implemented in
msBayes

T = (T1, T2, . . . , TY)
τ = {τ1, . . . , τ|τ|}
|τ|
p(T | X) =
p(X | T)p(T)
p(X)
This approach implemented in
msBayes
Not that simple

The msBayes model
T2
T3
T5
τ2 τ1
T1
T4
0100200300400500
Time (kya)
0
-50
-100
Sealevel(m)

The msBayes model
T1
T2
τ2
0100200300400500
Time (kya)
0
-50
-100
Sealevel(m)

The msBayes model
X Sequence alignments
G Gene trees
T Divergence times
Θ Demographic
parameters
T1
T2
τ2
0100200300400500
Time (kya)
0
-50
-100
Sealevel(m)

The msBayes model
G Gene trees
T Divergence times
Θ Demographic parameters

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(G, T, Θ | X) =
p(X | G, T, Θ)p(G, T, Θ)
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(G, T, Θ | X) =
p(X | G, T, Θ)p(G, T, Θ)
p(X)
Approximate Bayesian computation (ABC)
X → S∗
→ B (S∗
)

The msBayes model
Full Model:
p(G, T, Θ | X) =
p(X | G, T, Θ)p(G, T, Θ)
p(X)
Approximate Bayesian computation (ABC)
X → S∗
→ B (S∗
)
Approximate Model:
p(G, T, Θ | B (S∗
)) =
p(X | G, T, Θ)p(G, T, Θ)
p(B (S∗
))

The msBayes model
Full Model:
p(G, T, Θ | X) =
p(X | G, T, Θ)p(G, T, Θ)
p(X)
T Vector of divergence times across pairs of populations
|τ| Number of divergence parameters
DT The variance of T

Species n1 n2
Mammals
Crocidura beatus 12 11
Crocidura negrina-panayensis 12 6
Hipposideros obscurus 19 9
Hipposideros pygmaeus 3 12
Cynopterus brachyotis 20 8
Haplonycteris ﬁscheri 29 8
Macroglossus minimus 19 4
Ptenochirus jagori 4 7
Ptenochirus minor 30 9
Squamates
Cyrtodactylus gubaot-sumuroi 29 6
Cyrtodactylus annulatus 14 3
Cyrtodactylus philippinicus 6 14
Gekko mindorensis 8 11
Insulasaurus arborens 22 10
Pinoyscincus jagori 8 8
Dendrelaphis marenae 6 6
Anurans
Limnonectes leytensis 4 2
Limnonectes magnus 2 3

Species n1 n2
Mammals
Squamates
Anurans

Empirical results
Strong support for
simultaneous divergence of
all 22 taxon pairs
pp > 0.96
∼100,000–250,000 years ago

Simulation-based power analyses
What is “simultaneous”?

Simulate datasets in which all 22 divergence times are random

τ ∼ U(0, 0.5 MGA)
τ ∼ U(0, 1.5 MGA)
τ ∼ U(0, 2.5 MGA)
τ ∼ U(0, 5.0 MGA)
MGA = Millions of Generations Ago

τ ∼ U(0, 0.5 MGA)
τ ∼ U(0, 1.5 MGA)
τ ∼ U(0, 2.5 MGA)
τ ∼ U(0, 5.0 MGA)
Simulate 1000 datasets for each τ distribution
Analyze all 4000 datasets as we did the empirical data

Simulation-based power analyses: Results
1 3 5 7 9 11 13 15 17 19 210.0
0.2
0.4
0.6
0.8
1.0
p( 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
1.0
p( 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
1.0
p( 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
1.0
p( ˆ|τ| =1)=1.0
τ∼U(0, 5.0 MGA)
Estimated number of divergence events (mode)
Density

1 3 5 7 9 11 13 15 17 19 210.0
0.2
0.4
0.6
0.8
1.0
p( 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
1.0
p( 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
1.0
p( 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
1.0
p( ˆ|τ| =1)=1.0
τ∼U(0, 5.0 MGA)
Density
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
12
0.05 0.25 0.45 0.65 0.850
2
4
6
8
10
Posterior probability of one divergence
Density

Strong support for highly clustered divergences when divergence
times 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
0100200300400500
Time (kya)
0
-50
-100
Sealevel(m)

Causes of bias: Prior on divergence models
msBayes uses a discrete uniform prior on the number of
divergence events, |τ|
#ofdivergencemodels
020406080100120
1 3 5 7 9 11 13 15 17 19 21
A
p(M|τ|,i)
0.000.010.020.030.04
1 3 5 7 9 11 13 15 17 19 21
B
# of divergence events, |τ|

Causes of bias: Broad priors
msBayes uses uniform priors on most model parameters,

This requires the use of broad priors

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

Models with more divergence-time parameters have much
greater parameter space, much of it with low likelihood
This vast space can cause problems with Bayesian model
choice
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 1.0
θ
0
5
10
15
20
25
30
Density
p(X| θ)

p(X) =
θ
p(X | θ)p(θ)dθ
0.0 0.2 0.4 0.6 0.8 1.0
θ
0
5
10
15
20
25
30
Density
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:
Posterior estimates should be sensitive to priors
As prior converges to distribution underlying the data, the
bias should disappear

Predictions:
Testing prior sensitivity:

Predictions:
1. Analyze empirical data under several diﬀerent prior settings
Results are very sensitive

Predictions:
2. Use simulations to assess behavior when priors are correct

Simulation results: Performance when priors are correct
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
Trueprobabilityofonedivergence
msBayes performs well when all assumptions are met

Predictions:

Predictions:
3. Use simulations to assess behavior under “ideal” real-world
priors

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
1.0
p( 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
1.0
p( 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
1.0
p( 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
1.0
p( ˆ|τ| =1)=1.0
τ∼U(0, 5.0 MGA)
Density
1 3 5 7 9 11 13 15 17 19 210.0
0.2
0.4
0.6
0.8
1.0
p( 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
1.0
p( 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
1.0
p( 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
0.6
p( ˆ|τ| =1)=0.473
Density

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)
Density
0.05 0.25 0.45 0.65 0.850
2
4
6
8
10
12
14
0.05 0.25 0.45 0.65 0.850
1
2
3
4
5
6
7
8
9
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
Density

Causes of bias: Simulation results
Broad uniform priors are reducing marginal likelihoods of models
with more divergence events
Even when uniform priors are informed by the data the bias remains

Causes of bias: Simulation results
Broad uniform priors are reducing marginal likelihoods of models
with more divergence events
Even when uniform priors are informed by the data the bias remains
Potential solution:
More ﬂexible priors

Mitigating the bias
Potential solution:
0.0 0.2 0.4 0.6 0.8 1.0
θ
0
5
10
15
20
25
30
Density
p(X| θ)
p(θ)

Mitigating the bias
Potential solution:
#ofdivergencemodels
020406080100120
1 3 5 7 9 11 13 15 17 19 21
A
p(M|τ|,i)
0.000.010.020.030.04 1 3 5 7 9 11 13 15 17 19 21
B
# of divergence events, |τ|

Mitigating the bias
Potential solution:
Potential solution:
Alternative prior over divergence models (e.g., uniform or Dirichlet
process)

New method: dpp-msbayes
Reparameterized the model implemented in msBayes

Replaced uniform priors on continuous parameters with
gamma and beta distributions

Dirichlet process prior (DPP) over all possible discrete
divergence models

Dirichlet process prior (DPP) over all possible discrete
divergence models
Uniform prior over divergence models

dpp-msbayes: Simulation-based assessment
Simulate 50,000 datasets under four models
MmsBayes U-shaped prior on divergence models
Uniform priors on continuous parameters
MUshaped U-shaped prior on divergence models
Gamma priors on continuous parameters
MUniform Uniform prior on divergence models
MDPP DPP prior on divergence models
Analyze all datasets under each of the models

dpp-msbayes: Simulation-based assessment
Assess power
τ ∼ U(0, 0.5 MGA)
τ ∼ U(0, 1.5 MGA)
τ ∼ U(0, 2.5 MGA)
τ ∼ U(0, 5.0 MGA)
Simulate 1000 datasets for each τ distribution
Analyze all 4000 datasets as we did the empirical data

dpp-msbayes: Simulation results
0.0
0.2
0.4
0.6
0.8
1.0
MmsBayes MDPP
MmsBayes
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
Analysismodel
Data 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 1.0
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 0.0 0.2 0.4 0.6 0.8 1.0
MDPP
Analysismodel
Data model

1 3 5 7 9 11 13 15 17 19 210.0
0.2
0.4
0.6
0.8
1.0
p( 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
1.0
p( 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
1.0
p( ˆ|τ| =1)=0.999
τ∼U(0, 2.5 MGA)
1 3 5 7 9 11 13 15 17 19 210.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
p( ˆ|τ| =1)=0.83
τ∼U(0, 5.0 MGA)
MmsBayes
Density
1 3 5 7 9 11 13 15 17 19 210.0
0.2
0.4
0.6
0.8
1.0
p( ˆ|τ| =1)=0.926
1 3 5 7 9 11 13 15 17 19 210.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
p( ˆ|τ| =1)=0.605
1 3 5 7 9 11 13 15 17 19 210.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
p( ˆ|τ| =1)=0.187
1 3 5 7 9 11 13 15 17 19 210.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
p( ˆ|τ| =1)=0.003
MDPP
Density

0.05 0.25 0.45 0.65 0.850
2
4
6
8
10
12
14
16
τ∼U(0, 0.5 MGA)
0.05 0.25 0.45 0.65 0.850
1
2
3
4
5
6
7
8
9
τ∼U(0, 1.5 MGA)
0.05 0.25 0.45 0.65 0.850
1
2
3
4
5
6
7
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
Density
0.05 0.25 0.45 0.65 0.850
1
2
3
4
5
6
7
0.05 0.25 0.45 0.65 0.850.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
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
Density

0.0 0.02 0.04 0.06 0.08 0.1 0.120
50
100
150
200
p( ˆDT <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
200
p( ˆDT <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
200
p( ˆDT <0.01)=0.996
τ∼U(0, 2.5 MGA)
0.0 0.02 0.04 0.06 0.08 0.1 0.120
20
40
60
80
100
120
140
160
180
p( ˆDT <0.01)=0.637
τ∼U(0, 5.0 MGA)
MmsBayes
Estimated variance in divergence times (median)
Density
0.0 0.1 0.2 0.3 0.4 0.50
2
4
6
8
10
p( ˆDT <0.01)=0.002
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
2.5
3.0
3.5
4.0
4.5
p( ˆDT <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
2.5
p( ˆDT <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
3.0
p( ˆDT <0.01)=0.0
MDPP
Density

0.0 0.02 0.04 0.06 0.08 0.1 0.120
50
100
150
200
p( ˆDT <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
200
p( ˆDT <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
200
p( ˆDT <0.01)=0.996
τ∼U(0, 2.5 MGA)
0.0 0.02 0.04 0.06 0.08 0.1 0.120
20
40
60
80
100
120
140
160
180
p( ˆDT <0.01)=0.637
τ∼U(0, 5.0 MGA)
MmsBayes
Density
0.0 0.05 0.1 0.15 0.2 0.25 0.3 0.350
10
20
30
40
50
60
70
p( ˆDT <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
25
p( ˆDT <0.01)=0.626
0.0 0.2 0.4 0.6 0.80
1
2
3
4
5
6
7
8
9
p( ˆDT <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
2.5
p( ˆDT <0.01)=0.004
MUshaped
Density
0.0 0.1 0.2 0.3 0.4 0.50
2
4
6
8
10
p( ˆDT <0.01)=0.002
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
2.5
3.0
3.5
4.0
4.5
p( ˆDT <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
2.5
p( ˆDT <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
3.0
p( ˆDT <0.01)=0.0
MDPP
Density

Results conﬁrm the bias of msBayes was caused by
1. Broad uniform priors
2. U-shaped prior on divergence models
The new model shows improved model-choice accuracy,
power, and robustness

diversiﬁcation?

Species n1 n2
Mammals
Squamates
Anurans

dpp-msbayes: Philippine diversiﬁcation
1 3 5 7 9 11 13 15 17 19 21
Number of divergence events
0.0
0.1
0.2
0.3
0.4
0.5
Posteriorprobability
msBayes
1 3 5 7 9 11 13 15 17 19 21
dpp-msbayes

dpp-msbayes: Philippine diversiﬁcation
1 3 5 7 9 11 13 15 17 19 21
0.00
0.02
0.04
0.06
0.08
0.10
0.12
Probability
Prior
1 3 5 7 9 11 13 15 17 19 21
Posterior
0100200300400500
Time (kya)
0
-50
-100
Sealevel(m)

Conclusions
Our new approximate-Bayesian method of phylogeographical
model choice shows improved behavior
Improved accuracy, robustness, and power
More “honest” estimates regarding uncertainty

Conclusions
Our new approximate-Bayesian method of phylogeographical
model choice shows improved behavior
Improved accuracy, robustness, and power
More “honest” estimates regarding uncertainty
Philippine climate-driven diversiﬁcation model?
Results consistent with prediction of clustered divergences
Results suggest multiple co-divergences
However, there is a lot of uncertainty

Future directions: Full-Bayesian phylogenetic framework
T2
T3
T5
τ2 τ1
T1
τ3
T4
0100200300400500
Time (kya)
0
-50
-100 Sealevel(m)

Future directions: Full-Bayesian phylogenetic framework
0100200300400500
Time (kya)
0
-50
-100
Sealevel(m)

Software
Everything is on GitHub. . .
dpp-msbayes: https://github.com/joaks1/dpp-msbayes
PyMsBayes: https://github.com/joaks1/PyMsBayes
ABACUS: Approximate BAyesian C UtilitieS.
https://github.com/joaks1/abacus

Open Notebook Science
Everything is on GitHub. . .
msbayes-experiments:
https://github.com/joaks1/msbayes-experiments
joaks1@gmail.com

Acknowledgments
Ideas and feedback:
KU Herpetology
Holder Lab
Melissa Callahan
Mike Hickerson
Laura Kubatko
My committee
Computation:
KU ITTC
KU Computing Center
iPlant
Funding:
NSF
KU Grad Studies, EEB & BI
SSB
Sigma Xi
Photo credits:
Rafe Brown, Cam Siler, &
Jake Esselstyn
FMNH Philippine Mammal
Website:
D.S. Balete, M.R.M. Duya,
& J. Holden

Acknowledgments
Friends & Family

Questions?

Gene tree divergences
Age (mybp)
Split(Taxon:Island1−Island2)
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
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0.5 1.0 1.5 2.0 2.5 3.0

Causes of bias: Insuﬃcient sampling
Models with more parameter space are less densely sampled
Could explain bias toward small models in extreme cases
Predicts large variance in posterior estimates
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 1.0
1e8
0.0
0.2
0.4
0.6
0.8
1.0
1.2
95%HPDDT
UnadjustedA
0.0 0.2 0.4 0.6 0.8 1.0
1e8
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8 GLM-adjustedB
Number of prior samples

Geological history

Islands and Integrals

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