Statistical inference of phylogenetic networks

Claudia Solís-Lemus 1

Joint work with Cécile Ané 1 2

1Department of Statistics, UW-Madison

2Department of Botany, UW-Madison

October 28, 2015

Motivation: Tree of life

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Data

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Phylogenetic tree

(a) Rooted (b) Unrooted

Figure: Binary phylogenetic tree

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Estimated tree

Alligator

Emu

Kiwi

Ostrich

Swan

Goose

Chicken

Falcon

Finch

Osprey

Woodpecker

Ibis

Stork

Vulture

Penguin

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Gene tree reconstruction

Human

Chimpanzee

Gorilla

Orangutan

Markov model for

sequence evolution

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Markov model for sequence evolution: A,C,G,T

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Markov model for sequence evolution: A,C,G,T

L =∑w

∑y

∑x

π(w)Pt6(w , y)Pt5(w ,G)Pt3(y , x)Pt4(y ,C)

Pt2(x ,C)Pt1(x ,A)

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Markov model for sequence evolution: A,C,G,T

L =∑w

∑y

∑x

π(w)Pt6(w , y)Pt5(w ,G)Pt3(y , x)Pt4(y ,C)

Pt2(x ,C)Pt1(x ,A)

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Gene tree reconstruction

Numerical optimization for branch lengths: tHeuristic optimization for tree topology

Available software: MrBayes (Huelsenbeck and Ronquist, 2001)RAxML (Stamatakis, 2014)

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Challenge: big space of trees

# Species # Unrooted trees # Rooted trees1 1 12 1 13 1 34 3 155 15 1056 105 9457 945 103958 10,395 135,1359 135,135 2,027,02510 2,027,025 34,459,42511 34,459,425 654,729,07512 654,729,075 13,749,310,57513 13,749,310,575 316,234,143,225...

......

52 > # atoms in universe

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Challenge: gene tree discordance

76% Human

Chimpanzee

Gorilla

Orangutan

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Challenge: gene tree discordance

76% Human

Chimpanzee

Gorilla

Orangutan

12% Human

Gorilla

12% Human

Orangutan

Species tree and gene trees can be different!

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Species tree vs Gene tree

Human Chimpanzee Gorilla

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From gene trees to species tree

?

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Multiple reasons for gene tree discordance

1 gene tree reconstruction error2 horizontal gene transfer (HGT)3 incomplete lineage sorting (ILS)

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2. Horizontal Gene Transfer (HGT)

Psst! Hey kid! Wanna be a Superbug...?

Stick some of this into your genome...

Even penicillin won't be able to harm you...

www.nearingzero.net

www.quora.net

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2. Horizontal Gene Transfer (HGT)

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2. HGT => Phylogenetic network

(c) Rooted (d) Unrooted

Figure: Binary phylogenetic network

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3. Incomplete lineage sorting (ILS)

Gene trees differ inside a species tree

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3. Incomplete lineage sorting (ILS)

Gene trees differ inside a species tree

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3. Incomplete lineage sorting (ILS)

Gene trees differ inside a species tree

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3. Incomplete lineage sorting (ILS)

Gene trees differ inside a species tree

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3. Incomplete lineage sorting (ILS)

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Multispecies coalescent model on a network (ILS+HGT)

P(gene tree | species network,t, γ)

Meng & Kubatko (2009), Yu Degnan & Nakhleh (2012)

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Maximum likelihood estimationModel:

Data: multiple gene alignments −→ multiple gene trees

L(network, t, γ) =∏g

P(g |network, t, γ)

Numerical optimization for t, γ

Heuristic optimization for network topology

PhyloNet Maximum LikelihoodYu, Dong, Liu & Nakhleh (2014)

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Challenge: huge space of networks

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Challenge: expensive computation of likelihood

Gene tree: ((a, c), (b1, b2))

Figure: Yu, Dong, Liu, Nakhleh (2014)

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Maximum pseudolikelihood estimation

Quartet-based inference:

L̃(network, t, γ) ∝∏

q∈Q(network)

Likelihood(q, t, γ)

Numerical optimization for t, γ

Heuristic optimization for network topology

SNaQ Maximum PseudolikelihoodS.-L., Ané (2015)

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SNaQ (S.-L., Ané, 2015)

Maximum pseudolikelihoodestimation of unrooted networksquartet-based inferenceInput: unrooted gene treesFast, scalable,easy pseudolikelihood computation

www.github.com/crsl4/PhyloNetworks

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SNaQ (S.-L., Ané, 2015)

0

20

40

60

80

100

10 30 100 300 1k 3k

PhyloNetSNaQ

n=6, h=1

Tim

e (

min

ute

s)

10 30 100 300 1k 3k

n=6, h=2

0

50

100

150

200

number of genes

10 30 100 300 1k 3k

n=10, h=2

Tim

e (

hours

)

number of genes

10 30 100 300 1k 3k

n=15, h=3

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Identifiability issues: flat pseudolikelihood

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Xiphophorus fish data (Cui et al., 2013)

1183 genes, 24 swordtails and platyfish, 5 hybridizations

XalvareziXmayaeXhelleriiXsignumXclemenciae_F2XmonticolusXmultilineatusXnigrensisXpygmaeusXcontinensXcorteziXnezahuacoyotlXmontezumaeXmalinche_CHIC2Xbirchmanni_GARCXmilleriXevelynaeXvariatusXcouchianusXgordoniXmeyeriXxiphidiumXandersiXmaculatus

X.alvarezi

X.mayae

X.hellerii

X.signum

X.clemenciae

X.monticolus

X.multilineatus

X.nigrensis

X.pygmaeus

X.continens

X.cortezi

X.nezahualcoyotl

X.montezumae

X.malinche

X.birchmanni

X.milleri

X.evelynae

X.variatus

X.couchianus

X.gordoni

X.meyeri

X.xiphidium

X.andersi

X.macalatus

SS

NS

NP

SP

� Loss of sword• Loss of ability to produce sword

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Many challenges

Huge space of networks- How to search efficiently?

No clear idea on the shape of pseudolikelihood function- Flatness => Identifiability issues:

· Identify hybrid node in cycle?- Many local maxima

Properties for pseudolikelihood estimator

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Final remark

(SNaQ uses NLopt)

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Acknowledgements

Joint work with Cécile Ané

Thanks:Doug BatesNoah Stenz

Sarah Friedrich (for cool SNaQ logo)

DEB 0949121

DEB 1354793www.github.com/crsl4/PhyloNetworks

claudia@stat.wisc.edu

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