interpreting ‘tree space’ in the context of very large empirical datasets
TRANSCRIPT
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.)
€
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
€
L = Pr(D | T) = Pr D i( ) | T( )i=1
m
∏
Independence of sites (1) Independence of branches (2)
€
L = Pr(D | T) = Pr D i( ) | T( )i=1
m
∏
€
= 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
€
∆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