interpreting ‘tree space’ in the context of very large empirical datasets

Interpreting ‘tree space’ in the context of very large empirical

datasetsJoe Parker

School of Biological and Chemical Sciences

Queen Mary University of London

Topics

• What evolutionary biology is– And what we do in the lab

• Introducing phylogenies (trees / digraphs)• Molecular evolution• Tests involving phylogeny comparison• Problems in phylogeny comparison• Conclusion / thanks / questions

Introduction to our work (1/5)

A Tale of Bats and Whales

The Prestin gene & high-frequency hearing

Evolution

Prestin evolutionHuman NDLTRNRFFENPALWELLFH… SIHDAVLGSQLREALAEQEASAPPSQ

Rat NDLTSNRFFENPALKELLFH… SIHDAVLGSQVREAMAEQETTVLPPQ

Dog NDLTQNRFFENPALKELLFH… SIHDAVLGSQLREALAEQEASALPPQ

Dolphin SDLTRNQFFENPALLDLLFH… SIHDAVLGSLVREALAEKEAAAATPQ

Horseshoe Bat SDLTRNRFFENPALLDLLFH… SIHDAVLGSLVREALEEKEAAAATPQ

Introduction to phylogenies (2/5)

Phylogenies

• Phylogenies are directed graphs that show evolutionary relations between taxa

• Or our hypotheses about them

Comparative approaches

Tree space

• Phylogeneticists often talk about tree space - the set of all possible trees

• Within tree space two graphs are said to be adjacent if they differ at e.g. one internal node

• Trees are said to be ‘near’ if they are similar e.g. only a few rearrangements

• It is not actually a well-defined concept however

Introduction to molecular evolution (3/5)

Molecular evolution

• Molecular evolution is the study of the processes by which DNA sequences change over time

• Stochastic changes dominate over short time-scales but over longer ones directional natural selection is apparent

• Normally modelled as stochastic process

• Unlike classical physical phenomena largely understood as a statistical not mechanical phenomenon

Simple model: Jukes-Cantor 69

• Letters {A,C,G,T} • Equal frequencies at equilibrium• Transition probabilities u / 3 in time t• e.g. A C:

More generally:

Felsenstein (2004) Inferring Phylogenies. Springer, NY

(Following model figures and formulae: ibid.)

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Pr(C | A • u • t) =1

41−e

−4

3ut ⎛

⎝ ⎜

⎞

⎠ ⎟

Maximum likelihood

• One of the most popular frameworks for understanding and modelling molecular evolution and phylogenies

• Likelihood of data given model, phylogeny:

• Likelihood-maximisation gives a way to parametize model and/or phylogeny

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L = Pr(D | T) = Pr D i( ) | T( )i=1

m

∏

Independence of sites (1) Independence of branches (2)

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L = Pr(D | T) = Pr D i( ) | T( )i=1

m

∏

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= Pr A,C,C,C,G, x,y,z,w,T( )w

∑z

∑y

∑x

∑

Phylogenomics

• Advances mean data sets several orders of magnitude larger

• Shift in emphasis from ML on specific phylogenies to statistics of all

spectrum.ieee.orgIllumina.comflickr/stephenjjohnson

Phylogenomics

• Stochastic property of molecular evolution becomes apparent in large datasets

• Goodness-of-fit varies by site / gene for a single phylogeny / model

• Corollary: goodness-of-fit varies amongst models for a single genome

Hypothesis-comparison tests using multiple phylogenies (4/5)

Convergence detection by ∆SSLS - Parker e t al. (2013)

• De novo genomes:– four taxa– 2,321 protein-coding loci– 801,301 codons

• Published:– 18 genomes

• ~69,000 simulated datasets• ~3,500 cluster cores

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∆SSLSi = ln Li, H0− ln Li, Ha

Our pipeline for detecting genome-wide convergence

mean = 0.05

mean = 0.05 mean = -0.01 mean = -0.08

Continuous distributions

• Output approximates a continuous distribution• Comparing alternative hypotheses it is apparent that selection of tree gives largely

determines location skew etc (perhaps as expected)• But given that distribution tails are considered significant meaning of values in

these tails problematic / comparable

Significance by simulation

• Very common technique in evolutionary biology – simulate a large dataset under the null model, compare w/empirical

• in this context simulate data get unexpectedness U:

U = 1 – cdf ( ∆SSLSH0-Ha | j )

Problems in multiple-hypothesis phylogeny comparisons (5/5)

Multiple hypotheses

• Alternative hypotheses drawn from tree space• Same dataset different Ha, different U• What U expected for Ha?• More simulation – multiple draws from tree

space:

Uc,= U – mean Uc

Tree space

• In the context of ML tree space can be thought of as the distance in lnL units (or any other related statistic*) between two trees with otherwise identical models / data

• In our previous results this appeared continuous.

• This may be misleading; in reality tree space, or derived statistics, can be highly discontinuous.

Multiple comparisons

• However…. We recall that distance in tree space, or shape of tree space, not well determined.

• How to sample effectively to control U (as Uc)?• How to compare Uc for Ha?• Sample every point (tree)?• Sample lots?• Sample systematically? Inverse-distance? Etc

Tree space

• Previously with small empirical datasets assume a single phylogeny a good descriptor of most/many sites

• With large datasets this may not be true– Both small adjustments better fit for many sites– And also some large rearrangements

• Perhaps a better definition of tree space• Considering two Ha equidistant from H0

Tree distance properties

• Scalar distances informative• Triagonality• Proportional to L for a given model(?)• Vectors informative (?)

Tree distance candidates

• Statistic or model-based measures:– Parsimony, ML or amino-acid/nucleotide distance– ∆lnL

• Topology-based measures:– Number / type of rearrangement moves, e.g. • Nearest-neighbour interchange• Subtree prune-and-regraft• Tree bisection-and-reconnection

• Algorithm-based measures:– # Of algorithm move steps– Wall clock time

Acknowledgements

• School of Biological and Chemical Sciences, Queen Mary, University of London – Rossiter Group– Prof. Steve Rossiter (PI)– Drs Kalina Davies, Georgia Tsagkogeorga, Michael McGowen, Mao

Xiuguang– Seb Bailey, Kim Warren

• Others:– Profs Richard Nichols, Andrew Leitch (SBCS)– Drs Yannick Wurm, Richard Buggs, Chris Faulkes, Steve Le Comber (SBCS)– Drs Chris Walker & Rob Horton (GridPP HTC)

• Sanger Centre – Dr James Cotton

(L-R): Joe Parker; GeorgiaTsagkogeorga; Kalina Davies; Steve Rossiter; Xiuguang Mao; Seb Bailey