Large Scale Phylogenetic Inference

1
Large Scale Phylogenetic Inference Mark Pagel
and Andrew Meade Reading University m.pagel_at_rdg.a
c.uk
2
Large-Scale Phylogenetic Inference Approaches
and Problems Availability of data Inference
from aligned gene sequences traversing the
universe MCMC and MCMCMC inference (assessing
the potential for large-scale inference) A model
of pattern-heterogeneity suitable for
concatenated sequences
A Tree of Life n 4000 species David Hills
3
The accumulation of gene sequence data

• Year No. of Sequences
• 1994 215,273
• 2001 14,976,310
• 70X growth over 7 years
• Compare 20 per annum 3.6X
• growth over 7 years

4
Numbers of gene sequences for metazoan phyla
5
Source GenBank All nucleotide sequences
6
Large-Scale Phylogenetic Inference Approaches
and Problems Availability of data Inference
from aligned gene sequences traversing the
universe MCMC and MCMCMC inference (assessing
the potential for large-scale inference) A model
of pattern-heterogeneity suitable for
concatenated sequences
7
Number of Possible Phylogenetic Trees
Species Unrooted Rooted
No. rooted 275292135328356515452597297515244
30639300973035816196098326553772152587890625 No.
unrooted 283806325080779912837729172696128150920
628587998105114415737667754150390625
N50
8
Sampling the Universe of Phylogenetic Trees

• Markov-Chain Monte Carlo (MCMC) Methods
• Generate a large number of phylogenetic trees
  from a Markov Chain
• at equilibrium randomly sample from universe of
  trees

sampling mechanism The Metropolis-Hastings
Algorithm
Accept new tree with p1.0 if L(Tn1) gt
L(Tn) otherwise accept with probability ?
L(Tn1)/ L(Tn)
9
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10
Long Interspersed Nuclear Elements --
LINEs --autonomously replicating retrotransposons
endonuclease
reverse transcriptase
3
5
6000 bases
-- as old as mammals (at least) --20-40 active
elements --500,000-1,000,000 fossil
fragments --account for 20 of nucleotide
content of human genome
11
Phylogenetic tree of LINEs in the Human genome
n500 Sampled from Markov Chain
12
Convergence of a Markov chainsampling
phylogenetic tree of n500 tips using
an alignment of n4400 nucleotides
log-likelihood
Iteration number
NB 99 of increase in likelihood in first 2.8
of run. 0.07 change in final 2 million
iterations
13
Frequency histogram of log-likelihoods for
phylogenetic trees of n500 LINEs in Human
genome (alignment 4000 bp). Note unconverged
chain.
n 1000 trees
Mean -700299.7 Std. Dev. 15.91 n1000
log-likelihood
14
Metropolis-Coupled Markov Chain Monte Carlo
(MCMCMC)
Given m simultaneous Markov chains, swap states
each iteration among a randomly chosen pair i
and j according to
xi xj
xk
likelihood ratio chain i likelihood ratio
chain j
yi yj
yk
15
Temperatures of heated chains
cold chain
t0.2
1/(1t(i-1)
t0.5
1/i
number of chains, i
16
Swapping behaviour of an MCMCMC analysis
17
Phylogeny of Human LINE-1 elements (92 elements,
4kb sequences)
10-15
millions of years ago
90
120
18
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19
LINEs data Log-likelihoods of trees from cold
chain (converged chain)
Log-likelihoods
pre-swap trees
post-swap trees
20
Large-Scale Phylogenetic Inference Approaches
and Problems Availability of data Inference
from aligned gene sequences traversing the
universe MCMC and MCMCMC inference (assessing
the potential for large-scale inference) A model
of pattern-heterogeneity suitable for
concatenated sequences
21
Pattern-Heterogeneity Model of Gene-Sequence
Evolution Allow for different genes in a single
concatenated alignment or different regions of
the same gene to evolve in qualitatively
different ways Contrast rate heterogeneity can
only detect difference in rates Implement
pattern-heterogeneity without partitioning
data P-H will always equal or better the
performance of gamma rate heterogeneity model.
Normally yields substantial improvements (100s
of log-units) Applications Detecting regions
of genes that evolve differently Large-scale
inference suitable for concatenated gene
sequences (e.g. recent phylogeny of the mammals
was based upon 16,000 nucleotides and 16 genes),
or supermatrix alignments
22
Applications of pattern-heterogeneity model
Single gene alignment
species 1 species n
pattern 2
pattern 1
pattern 3
23
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10
24
Testing the Pattern Heterogeneity Model two
different rate matrices
Generate data on a known tree according to these
two matrices and form a concatenated alignment.
gene 1 600 bases gene 2 400 bases
25
log-likelihoods obtained from three models
applied to simulated pattern-heterogeneity data
26
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27
log-likelihoods by site in the simulated
pattern-heterogeneity data
28
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29
Pattern-heterogeneity model Simulated and
obtained values of the rate parameters
30
log-likelihoods for combined LSU/SSU nrRNA data
set 54 species n800 sites
31
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32
log-likelihoods by site in the LSU/SSU combined
data set
The divide between the two genes
33
Log-likelihoods for cytochrome-b data set. N433
sites of which 300 are fixed for a single
nucleotide
34
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35
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36
Metropolis-Hastings Algorithm Accept new tree
according to
Likelihood ratio prior ratio
proposal ratio
Xdata (e.g., gene sequences) Ttree
(topology, branches, parameters)