Download speciation - Stockholm Bioinformatics Center

PrIME
Probabilistic Integrated Models of
Evolution
Bengt Sennblad,
Dept. Plant and Env. Sciences, GU
and Stockholm Bioinformatics Center (SBC)
Outline
• PrIME models
– GEM
• Gene Evolution Model
– SRT
• Sequence evolution with Rates and Times
– GSR
• Gene Sequence evolution with iid Rates
– HGM
• Gene evolution in hybrid networks
Outline
•
•
•
•
•
What?
Why?
When?
How?
So?
GEM
The Gene Evolution Model
Lars Arvestad, KTH
Ann-Charlotte Berggren, UU
Jens Lagergren, KTH
Bengt Sennblad
What?
• Gene (loci) tree evolution
– GEM – gene loci
(Coalescence – gene alleles)
– Gene duplication and loss process
• Models duplications/losses that are fixed in population
What?
– genetic mechanism
• Recombination errors
– Unequal crossing-over
– Tandem repeats
– Segmental duplication
• Retrotransoposition
– mRNA  cDNA  insertion
– Loss of intron, regulatory regions
• Chromosome/genome duplication
What?
– the process
• Gene tree evolves inside species tree
Speciation
Duplication
Loss
÷
Why?
Ohno, S. 1970, Evolution by gene duplication, Springer,
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Fitch’s Definition of Orthology

 
mouse

 
chicken
•
•
Speciation shown as
Duplication shown as
•
Fitch 1970
• Orthologs - LCA speciation
• Paralogs - LCA duplication
 
frog
Orthologs - more likely to
share function
Paralogs - more likely to
have different function
Why?
• Biological causes
– Duplication-loss
– Lateral gene transfer
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– Allele sorting
• Methodological
– Systematic
– Stochastic
Mushegian et al. 1998. Genome Res
Reconciling given species and gene
tree
Species tree
A
B
C
D
E
F
G
H
Gene tree
A
B
C
A
B
C
D
E
E
F
F
G
H
H
Reconciliation   Reconciled tree (G,)
Gene tree vertex on species tree edge is a duplication
Gene tree vertex on species tree vertex is a speciation
÷
When?
• Parsimony Reconciliation (MPR)
– Goodman et al. 1979, Page and co-workers sev.
papers, Guigo 1996, Hallett & Lagergren 2000
Most parsimonious reconciliation
•
•
Speciation shown as
Duplication shown as
•
Goodman et al 1979
A
A
B
C
B
C
Most parsimonious reconciliation
•
•
Speciation shown as
Duplication shown as
•
Goodman et al 1979
Most parsimonious reconciliation
•
•
Speciation shown as
Duplication shown as
•
Goodman et al 1979
Most parsimonious reconciliation
•
•
Speciation shown as
Duplication shown as
•
Goodman et al 1979
Most parsimonious reconciliation
•
•
Speciation shown as
Duplication shown as
•
Goodman et al 1979
Most parsimonious reconciliation
•
•
Speciation shown as
Duplication shown as
•
Goodman et al 1979
Most parsimonious reconciliation
•
•
Speciation shown as
Duplication shown as
•
Goodman et al 1979
When?
• Parsimony Reconciliation (MPR)
– Goodman et al. 1979, Page and co-workers sev. papers,
Guigo 1996, Hallett & Lagergren 2000
• Bootstrapped MPR
– Storm & Sonnhammer 2002, Zmasek & Eddy 2002
Why only MPR?
•
•
Speciation shown as
Duplication shown as
Why only MPR?
•
•
Speciation shown as
Duplication shown as
Why only MPR?
•
•
Speciation shown as
Duplication shown as
Intuition: Depending on gene
family, we might believe more in
some reconciliations than in others
 Probabilistic reconciliation
When?
• Parsimony Reconciliation (MPR)
– Goodman et al. 1979, Page and co-workers sev. papers,
Guigo 1996, Hallett & Lagergren 2000
• Bootstrapped MPR
– Storm & Sonnhammer 2002, Zmasek & Eddy 2002
• Probabilistic models
– Full reconciliation model, Arvestad et al. 2003, 2004,
– Gene copy number, Hahn 2005, Csürös & Miklós2006
The Gene Evolution Model
How?
Generation vs reconstruction
– the Birth-Death model
• Generation of data from model
– Example: BD(l,m)  tree T
– Repeated generation  distribution
– Statistical tests, e.g., ’parametric bootstrapping’
Birth-death process gives trees
0
1
Birth-death process gives trees
0
1
Birth-death process gives trees
0
1
Birth-death process gives trees
0
1
Birth-death process gives trees
0
1
Birth-death process gives trees
0
1
Birth-death process gives trees
0
1
Generation vs reconstruction
the birth-death model
• Generation of data from model
– Example: BD(l,m)  tree T
– Repeated generation  distribution
– Statistical tests, e.g., ’parametric bootstrapping’
• Reconstruction – Probability of given data
– Example: given T  Pr[T|l, m] under BD
– Compare different trees  ’reconstruction’
Extinct lineages
0
1
Extinct lineages
0
1
Isomorphisms
Gene evolution model
•
Gene effecting events: losses, duplications,
and speciation
Gene evolution model
•
Gene effecting events: losses, duplications,
and speciation
•
A gene tree evolves inside the species tree
Gene evolution model
•
Gene effecting events: losses, duplications,
and speciation
•
A gene tree evolves inside the species tree
1. A gene starts at time t before the root
Gene evolution model
•
Gene effecting events: losses, duplications,
and speciation
•
A gene tree evolves inside the species tree
1. A gene starts at time t before the root
2. Along an edge linear birth death process
Gene evolution model
•
Gene effecting events: losses, duplications,
and speciation
•
A gene tree evolves inside the species tree
1. A gene starts at time t before the root
2. Along an edge linear birth death process
3. At a speciation each gene linage splits into two
Gene evolution model
•
Gene effecting events: losses, duplications,
and speciation
•
A gene tree evolves inside the species tree
1.
2.
3.
4.
A gene starts at time t before the root
Along an edge linear birth death process
At a speciation each gene linage splits into two
Finally, losses are pruned
Gene evolution model
•
Gene effecting events: losses, duplications,
and speciation
•
A gene tree evolves inside the species tree
1.
2.
3.
4.
•
A gene starts at time t before the root
Along an edge linear birth death process
At a speciation each gene linage splits into two
Finally, losses are pruned
Biologically sound Nei et al., 1997
Generating a scenario
Speciation
Duplication
Loss
Generating a scenario
Speciation
Duplication
Loss
Generating a scenario
Speciation
Duplication
Loss
Generating a scenario
Speciation
Duplication
Loss
Generating a scenario
Speciation
Duplication
Loss
Generating a scenario
Speciation
Duplication
Loss
Generating a scenario
Speciation
Duplication
Loss
Reconciled tree (G, )
Reconciliation – losses have been pruned
÷
Reconstruction
• Reconstruction Pr[G,|S, l, m, t]
non-trivial
–
–
–
–
BD over edges
Ghosts
Isomorphisms
Sum over scenarios
• No. scenarios is exponential in
tree size
– Dynamic programming (DP)
– Efficient algorithm
GEM
• Generation relatively simple
• Probability of reconciled tree
• Probability of gene tree:
• Posterior of reconciliation:
• Max likelihood reconciliation:
Example application:
Probabilistic orthology analysis
Sennblad, Lagergren submitted
MHC example: MPR orthology
MHC example: MPR orthology
1(b)
Three other reconciliations
Reconciliation probabilities
2
1(b)
Posterior & posterior mean
Modification of DP for Pr[G|S,l,m]
MCMC
Speciation probabilities
ABCA
Speciation probabilities
MHC birth-death parameter posterior
When is MP-reconciliation incorrect?
• 1000 (G,) per square
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Performance of probabilistic orthology analysis
•
Draw from posterior distribution
– Biological realism
•
Generate synthetic (G,)
– Speciations are positives
•
Analyze
– classify genes as duplication/speciation based on probability
and threshold
•
ROC-curves
– Sensitivity = TP/(TP+FN)
– Specificity = TN/(TN+FP)
ROC for MHC-like data
• Speciation? Y sensitivity, X specificity
ROC for ABCA-like data
• Speciation? Y sensitivity, X specificity
Programs
• primeGEM;
– Probability of gene tree:
– Orthology analysis:
• xprimeGEM
– Probability of reconciled tree
– Posterior of reconciliation:
• xprimeGEM-max
– Max likelihood reconciliation:
• xprimeGEM-enum
– Enumerates all  with Prob.
’Comparison’
• Coalesence -- Allele
evolution
– Alleles evolve by random
sampling from parental
population
• Gene duplication and loss
-- gene family evolution
– Gene copies are created by
duplication events
– Gene copies are lost by loss
events
– Underlying pure birth
process
– Underlying birth-death
process
Later similar work -- gene copy number
Later similar work -- coalescence
Later similar work -- coalescence