Accommodating clustered divergences in phylogenetic inference

transcript

Accommodatingclustered divergences inphylogenetic inference

Jamie R. Oaks1,2

1Department of Biology, University ofWashington

2Department of Biological Sciences,Auburn University

October 21, 2015

Clustered diversification Jamie Oaks – phyletica.org 1/27

I Phylogenetics is rapidlyprogressing as an endeavorof statistical inference

I “Big data” present excitingpossibilities andcomputational challenges

I Exciting opportunities todevelop new ways to studybiology in the light ofphylogeny

Current state of phylogenetics

I Assumption: Divergences are independent across the tree

I We know this assumptionis frequently violated

I Why account for thisnon-independence?

1. Improve inference

2. Provide a frameworkfor studying processesof co-diversification

I This is a model-choiceproblem

Divergence model choice

τ2 τ1

τ1τ2

τ3 τ1τ2

Inferring co-diversification

m1 m2 m3 m4 m5

τ2 τ1

τ1τ2

τ3 τ1τ2

J. R. Oaks et al. (2013). Evolution 67: 991–1010, J. R. Oaks (2014). BMC Evolutionary Biology 14: 150

m1 m2 m3 m4 m5

τ2 τ1

τ1τ2

τ3 τ1τ2

We want to infer m and T given DNA sequence alignments X

p(m1 |X) p(m2 |X) p(m3 |X) p(m4 |X) p(m5 |X)τ1

τ2 τ1

τ1τ2

τ3 τ1τ2

τ2 τ1

τ1τ2

τ3 τ1τ2

p(mi |X) ∝ p(X |mi )p(mi )

τ2 τ1

τ1τ2

τ3 τ1τ2

p(X |mi ) =

∫θp(X | θ,mi )p(θ |mi )dθ

τ2 τ1

τ1τ2

τ3 τ1τ2

p(X |mi ) =

∫θp(X | θ,mi )p(θ |mi )dθ

I Divergence times

I Gene trees

I Substitution parameters

I Demographic parameters

τ2 τ1

τ1τ2

τ3 τ1τ2

Challenges:

1. Cannot solve all the integrals analytically

I Numerical approximation via approximate-likelihood Bayesiancomputation (ABC)

2. Sampling over all possible models

I 5 taxa = 52 modelsI 10 taxa = 115,975 modelsI 20 taxa = 51,724,158,235,372 models!!I A “diffuse” Dirichlet process prior (DPP)

τ2 τ1

τ1τ2

τ3 τ1τ2

Challenges:

1. Cannot solve all the integrals analytically

I Numerical approximation via approximate-likelihood Bayesiancomputation (ABC)

τ2 τ1

τ1τ2

τ3 τ1τ2

Challenges:

1. Cannot solve all the integrals analyticallyI Numerical approximation via approximate-likelihood Bayesian

computation (ABC)

τ2 τ1

τ1τ2

τ3 τ1τ2

Challenges:

computation (ABC)

τ2 τ1

τ1τ2

τ3 τ1τ2

Challenges:

computation (ABC)

2. Sampling over all possible modelsI 5 taxa = 52 models

I 10 taxa = 115,975 modelsI 20 taxa = 51,724,158,235,372 models!!I A “diffuse” Dirichlet process prior (DPP)

τ2 τ1

τ1τ2

τ3 τ1τ2

Challenges:

computation (ABC)

2. Sampling over all possible modelsI 5 taxa = 52 modelsI 10 taxa = 115,975 models

I 20 taxa = 51,724,158,235,372 models!!I A “diffuse” Dirichlet process prior (DPP)

τ2 τ1

τ1τ2

τ3 τ1τ2

Challenges:

computation (ABC)

2. Sampling over all possible modelsI 5 taxa = 52 modelsI 10 taxa = 115,975 modelsI 20 taxa = 51,724,158,235,372 models!!

I A “diffuse” Dirichlet process prior (DPP)

τ2 τ1

τ1τ2

τ3 τ1τ2

Challenges:

computation (ABC)

2. Sampling over all possible modelsI 5 taxa = 52 modelsI 10 taxa = 115,975 modelsI 20 taxa = 51,724,158,235,372 models!!I A “diffuse” Dirichlet process prior (DPP)

“Easy” as ABC

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“Easy” as ABC

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“Easy” as ABC

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“Easy” as ABC

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“Easy” as ABC

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0.81.0 0.0

“Easy” as ABC

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0.81.0 0.0

“Easy” as ABC

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“Easy” as ABC

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“Easy” as ABC

0.00.2

0.40.6

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τ2 τ1

τ1τ2

τ3 τ1τ2

Challenges:

computation (ABC)

2. Sampling over all possible modelsI 5 taxa = 52 modelsI 10 taxa = 115,975 modelsI 20 taxa = 51,724,158,235,372 models!!I A “diffuse” Dirichlet process prior (DPP)

Sampling divergence models—a novel approach

I The divergence models are ways of assigning our taxa toevents

I A Dirichlet process prior (DPP) model is a convenient andflexible solution

I Common Bayesian approach to assigning variables to anunknown number of categories

I Controlled by “concentration” parameter: α

Peter Dirichlet

(αα+1

)(αα+2

= 0.758

αα+2

(αα+1

= 0.076

(αα+1

= 0.076

αα+1

)(αα+2

= 0.076

αα+2

= 0.015

(αα+1

)(αα+2

= 0.758

αα+2

(αα+1

= 0.076

(αα+1

= 0.076

αα+1

)(αα+2

= 0.076

αα+2

= 0.015

(αα+1

)(αα+2

= 0.758

αα+2

(αα+1

= 0.076

(αα+1

= 0.076

αα+1

)(αα+2

= 0.076

αα+2

= 0.015

(αα+1

)(αα+2

= 0.758

αα+2

(αα+1

= 0.076

(αα+1

= 0.076

αα+1

)(αα+2

= 0.076

αα+2

= 0.015

(αα+1

)(αα+2

= 0.758

αα+2

(αα+1

= 0.076

(αα+1

= 0.076

αα+1

)(αα+2

= 0.076

αα+2

= 0.015

α = 0.5

(αα+1

)(αα+2

)= 0.067

= 0.758

αα+2

(αα+1

)= 0.133

= 0.076

(αα+1

)= 0.133

= 0.076

αα+1

)(αα+2

)= 0.133

= 0.076

αα+2

)= 0.533

= 0.015

α = 10.0

(αα+1

)(αα+2

)= 0.758

αα+2

(αα+1

)= 0.076

(αα+1

)= 0.076

αα+1

)(αα+2

)= 0.076

αα+2

)= 0.0152

New method: dpp-msbayes

I Flexible Dirichlet-process prior (DPP) over all possibledivergence models

I Flexible priors on parameters to avoid strongly weightedposteriors

I Multi-processing to accommodate genomic datasets

J. R. Oaks (2014). BMC Evolutionary Biology 14: 150Clustered diversification Jamie Oaks – phyletica.org 12/27

dpp-msbayes: Simulation-based assessment

Validation:

I Simulate 50,000 datasets and analyze each under the samemodel

Robustness:

I Simulate datasets that violate model assumptions and analyzeeach of them

dpp-msbayes: Simulation-based assessment

Validation:

I Simulate 50,000 datasets and analyze each under the samemodel

Robustness:

I Simulate datasets that violate model assumptions and analyzeeach of them

dpp-msbayes: Validation results

0.0 0.2 0.4 0.6 0.8 1.00.0

Posterior probability of one divergence

dpp-msbayes: Robustness results

0.0 0.2 0.4 0.6 0.8 1.00.0

0.0 0.2 0.4 0.6 0.8 1.0

Posterior probability of one divergence

dpp-msbayes: Performance

I New method for estimating shared evolutionary history shows:

1. Model-choice accuracy2. Robustness to model violations3. Power to detect variation in divergence times4. It’s fast!

I A new tool for biologists to leverage comparativegenomic data to explore processes of co-diversification

dpp-msbayes: Performance

I New method for estimating shared evolutionary history shows:

1. Model-choice accuracy2. Robustness to model violations3. Power to detect variation in divergence times4. It’s fast!

I A new tool for biologists to leverage comparativegenomic data to explore processes of co-diversification

Empirical applications

Did repeatedfragmentation of islandsduring inter-glacial risesin sea level promotediversification?

Empirical applications

Did repeatedfragmentation of islandsduring inter-glacial risesin sea level promotediversification?

Climate-driven diversification

Results

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

Results

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

0100200300400500Time (kya)

Sea le

vel (m

More data!

I Collecting genomic data from taxa co-distributed acrossSoutheast Asian Islands and Mainland

I Preliminary results for 1000 loci from 5 pairs of Gekkomindorensis populations

More data!

I Collecting genomic data from taxa co-distributed acrossSoutheast Asian Islands and Mainland

I Preliminary results for 1000 loci from 5 pairs of Gekkomindorensis populations

1 2 3 4 5Number of divergence events, j¿j

Diversification across African rainforests

I Did climate cycles drivediversification andcommunity assembly acrossrainforest taxa?

I Preliminary results with 300loci from 3 taxa

Diversification across African rainforests

I Did climate cycles drivediversification andcommunity assembly acrossrainforest taxa?

I Preliminary results with 300loci from 3 taxa

1 2 3Number of divergence events, j¿j

Conclusions

I New method for estimating shared evolutionary historyI Shows good “frequentist” behaviorI Relatively robust to model violations

I Finding support for temporally clustered divergences inmultiple systems

I However, there is a lot of uncertainty!

Conclusions

Current work: More power

I Full-likelihood Bayesian implementation

I Uses all the information in the dataI Applicable to deeper timescales

I Analytically integrate over gene trees 1

I Very efficient numerical approximation of posteriorI Applicable to NGS datasets

1D. Bryant et al. (2012). Molecular Biology And Evolution 29: 1917–1932

I Full-likelihood Bayesian implementationI Uses all the information in the dataI Applicable to deeper timescales

Next step: A general framework

I Develop a framework for inferringshared divergences acrossphylogenies

I Generalize Bayesian phylogeneticsto incorporate shared divergences

I Sample models numerically viareversible-jump Markov chainMonte Carlo

Benefits:

I Improve phylogenetic inference

I Framework for studying processesof co-diversification

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Benefits:

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Benefits:

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Everything is on GitHub. . .

Software:

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

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

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

Open-Science Notebook:

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

Acknowledgments

Ideas and feedback:

I Leache Lab

I Minin Lab

I Holder Lab

I Brown Lab/KU Herpetology

Computation:

Funding:

Photo credits:

I Rafe Brown, Cam Siler, JesseGrismer, & Jake Esselstyn

I FMNH Philippine MammalWebsite:

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

I PhyloPic!

Questions?

joaks@auburn.edu