1. PrIME Probabilistic Integrated Models of Evolution
Bengt Sennblad,
Dept. Plant and Env. Sciences, GU
and Stockholm Bioinformatics Center (SBC)

2. Outline PrIME models GEM SRT GSR HGM Gene Evolution Model
Sequence evolution with Rates and Times
GSR
Gene Sequence evolution with iid Rates
HGM
Gene evolution in hybrid networks

3. Outline
What?
Why?
When?
How?
So?

4. GEM The Gene Evolution Model
Lars Arvestad, KTH
Ann-Charlotte Berggren, UU
Jens Lagergren, KTH
Bengt Sennblad

5. What? Gene (loci) tree evolution
GEM – gene loci (Coalescence – gene alleles)
Gene duplication and loss process
Models duplications/losses that are fixed in population

6. What? – genetic mechanism
Recombination errors
Unequal crossing-over
Tandem repeats
Segmental duplication
Retrotransoposition
mRNA ® cDNA ® insertion
Loss of intron, regulatory regions
Chromosome/genome duplication

7. What? – the process Gene tree evolves inside species tree Speciation÷
Speciation
Duplication
Loss
This is a scenario that shows how a gene tree in blue has evolved with respect to a species tree in black
So this is the root of the species tree and this is the root of the gene tree
Three types of gene effectiong events are shown...
For instance ...
Losses are important, but in some cases, as for orthology analyses, they are not needed
For this reason we use reconcilations to show the evolution of a gene tree,

8. Why? Ohno, S. 1970, Evolution by gene duplication, Springer,
NEOFUNCTIONALIZATION
SUBFUNCTIONALIZATION
ADAPTIVE EVOLUTION

9. Fitch’s Definition of Orthology 
mouse
chicken
frog
Speciation shown as
Duplication shown as
Fitch 1970
Orthologs - LCA speciation
Paralogs - LCA duplication
Orthologs - more likely to share function
Paralogs - more likely to have different function

10. Mushegian et al. 1998. Genome Res
Why?
INCONGRUENCE!
Biological causes
Duplication-loss
Lateral gene transfer
Allele sorting
Methodological
Systematic
Stochastic
Mushegian et al Genome Res

11. Reconciling given species and gene tree
Species tree A B C D E F G H A B C D E F G H
Gene tree

12. Reconciliation  Þ Reconciled tree (G,g)
Gene tree vertex on species tree edge is a duplication
Gene tree vertex on species tree vertex is a speciation
This is a scenario that shows how a gene tree in blue has evolved with respect to a species tree in black
So this is the root of the species tree and this is the root of the gene tree
Three types of gene effectiong events are shown...
For instance ...
Losses are important, but in some cases, as for orthology analyses, they are not needed
For this reason we use reconcilations to show the evolution of a gene tree, ÷

13. When? Parsimony Reconciliation (MPR)
Goodman et al. 1979, Page and co-workers sev. papers, Guigo 1996, Hallett & Lagergren 2000

14. Most parsimonious reconciliation
Speciation shown as
Duplication shown as
Goodman et al 1979
This is a scenario that shows how a gene tree in blue has evolved with respect to a species tree in black
So this is the root of the species tree and this is the root of the gene tree
Three types of gene effectiong events are shown...
For instance ...
Losses are important, but in some cases, as for orthology analyses, they are not needed
For this reason we use reconcilations to show the evolution of a gene tree, A B C A B C

15. Most parsimonious reconciliation
Speciation shown as
Duplication shown as
Goodman et al 1979
This is a scenario that shows how a gene tree in blue has evolved with respect to a species tree in black
So this is the root of the species tree and this is the root of the gene tree
Three types of gene effectiong events are shown...
For instance ...
Losses are important, but in some cases, as for orthology analyses, they are not needed
For this reason we use reconcilations to show the evolution of a gene tree,

16. Most parsimonious reconciliation
Speciation shown as
Duplication shown as
Goodman et al 1979
This is a scenario that shows how a gene tree in blue has evolved with respect to a species tree in black
So this is the root of the species tree and this is the root of the gene tree
Three types of gene effectiong events are shown...
For instance ...
Losses are important, but in some cases, as for orthology analyses, they are not needed
For this reason we use reconcilations to show the evolution of a gene tree,

17. Most parsimonious reconciliation
Speciation shown as
Duplication shown as
Goodman et al 1979
This is a scenario that shows how a gene tree in blue has evolved with respect to a species tree in black
So this is the root of the species tree and this is the root of the gene tree
Three types of gene effectiong events are shown...
For instance ...
Losses are important, but in some cases, as for orthology analyses, they are not needed
For this reason we use reconcilations to show the evolution of a gene tree,

18. Most parsimonious reconciliation
Speciation shown as
Duplication shown as
Goodman et al 1979
This is a scenario that shows how a gene tree in blue has evolved with respect to a species tree in black
So this is the root of the species tree and this is the root of the gene tree
Three types of gene effectiong events are shown...
For instance ...
Losses are important, but in some cases, as for orthology analyses, they are not needed
For this reason we use reconcilations to show the evolution of a gene tree,

19. Most parsimonious reconciliation
Speciation shown as
Duplication shown as
Goodman et al 1979
This is a scenario that shows how a gene tree in blue has evolved with respect to a species tree in black
So this is the root of the species tree and this is the root of the gene tree
Three types of gene effectiong events are shown...
For instance ...
Losses are important, but in some cases, as for orthology analyses, they are not needed
For this reason we use reconcilations to show the evolution of a gene tree,

20. Most parsimonious reconciliation
Speciation shown as
Duplication shown as
Goodman et al 1979
This is a scenario that shows how a gene tree in blue has evolved with respect to a species tree in black
So this is the root of the species tree and this is the root of the gene tree
Three types of gene effectiong events are shown...
For instance ...
Losses are important, but in some cases, as for orthology analyses, they are not needed
For this reason we use reconcilations to show the evolution of a gene tree,

21. When? Parsimony Reconciliation (MPR) Bootstrapped MPR
Goodman et al. 1979, Page and co-workers sev. papers, Guigo 1996, Hallett & Lagergren 2000
Bootstrapped MPR
Storm & Sonnhammer 2002, Zmasek & Eddy 2002

22. Why only MPR? Speciation shown as Duplication shown as
This is a scenario that shows how a gene tree in blue has evolved with respect to a species tree in black
So this is the root of the species tree and this is the root of the gene tree
Three types of gene effectiong events are shown...
For instance ...
Losses are important, but in some cases, as for orthology analyses, they are not needed
For this reason we use reconcilations to show the evolution of a gene tree, 22

23. Why only MPR? Speciation shown as Duplication shown as
This is a scenario that shows how a gene tree in blue has evolved with respect to a species tree in black
So this is the root of the species tree and this is the root of the gene tree
Three types of gene effectiong events are shown...
For instance ...
Losses are important, but in some cases, as for orthology analyses, they are not needed
For this reason we use reconcilations to show the evolution of a gene tree, 23

24. Why only MPR? ® Probabilistic reconciliation Speciation shown as
Duplication shown as
Intuition: Depending on gene family, we might believe more in some reconciliations than in others
® Probabilistic reconciliation
This is a scenario that shows how a gene tree in blue has evolved with respect to a species tree in black
So this is the root of the species tree and this is the root of the gene tree
Three types of gene effectiong events are shown...
For instance ...
Losses are important, but in some cases, as for orthology analyses, they are not needed
For this reason we use reconcilations to show the evolution of a gene tree, 24

25. When? Parsimony Reconciliation (MPR) Bootstrapped 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

26. The Gene Evolution Model
How?

27. 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’

28. Birth-death process gives trees1 28

29. Birth-death process gives trees1 29

30. Birth-death process gives trees1 30

31. Birth-death process gives trees1 31

32. Birth-death process gives trees1 32

33. Birth-death process gives trees1 33

34. Birth-death process gives trees1 34

35. 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’

36. Extinct lineages 1 36

37. Extinct lineages 1 37

38. Isomorphisms

39. Gene evolution model
Gene effecting events: losses, duplications, and speciation
The model contains three gene effecting events, namely the ones we have seen before
Duplications
Speciations; and
Losses
In the model a gene tree evolves inside a species tree according to the following rules
Start
Edge, canonical
Speciation, reaches, (leaf)
Finally, losses are pruned, so a rec is obtained
Nei et al have considered a similar model, without formalizing it mathematically, and concluded that it is biologically sound
Matematically sound and almost canonical and biologically sound

40. Gene evolution model
Gene effecting events: losses, duplications, and speciation
A gene tree evolves inside the species tree
The model contains three gene effecting events, namely the ones we have seen before
Duplications
Speciations; and
Losses
In the model a gene tree evolves inside a species tree according to the following rules
Start
Edge, canonical
Speciation, reaches, (leaf)
Finally, losses are pruned, so a rec is obtained
Nei et al have considered a similar model, without formalizing it mathematically, and concluded that it is biologically sound
Matematically sound and almost canonical and biologically sound

41. Gene evolution model
Gene effecting events: losses, duplications, and speciation
A gene tree evolves inside the species tree
A gene starts at time t before the root
The model contains three gene effecting events, namely the ones we have seen before
Duplications
Speciations; and
Losses
In the model a gene tree evolves inside a species tree according to the following rules
Start
Edge, canonical
Speciation, reaches, (leaf)
Finally, losses are pruned, so a rec is obtained
Nei et al have considered a similar model, without formalizing it mathematically, and concluded that it is biologically sound
Matematically sound and almost canonical and biologically sound

42. Gene evolution model
Gene effecting events: losses, duplications, and speciation
A gene tree evolves inside the species tree
A gene starts at time t before the root
Along an edge linear birth death process
The model contains three gene effecting events, namely the ones we have seen before
Duplications
Speciations; and
Losses
In the model a gene tree evolves inside a species tree according to the following rules
Start
Edge, canonical
Speciation, reaches, (leaf)
Finally, losses are pruned, so a rec is obtained
Nei et al have considered a similar model, without formalizing it mathematically, and concluded that it is biologically sound
Matematically sound and almost canonical and biologically sound

43. Gene evolution model
Gene effecting events: losses, duplications, and speciation
A gene tree evolves inside the species tree
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
The model contains three gene effecting events, namely the ones we have seen before
Duplications
Speciations; and
Losses
In the model a gene tree evolves inside a species tree according to the following rules
Start
Edge, canonical
Speciation, reaches, (leaf)
Finally, losses are pruned, so a rec is obtained
Nei et al have considered a similar model, without formalizing it mathematically, and concluded that it is biologically sound
Matematically sound and almost canonical and biologically sound

44. Gene evolution model
Gene effecting events: losses, duplications, and speciation
A gene tree evolves inside the species tree
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
The model contains three gene effecting events, namely the ones we have seen before
Duplications
Speciations; and
Losses
In the model a gene tree evolves inside a species tree according to the following rules
Start
Edge, canonical
Speciation, reaches, (leaf)
Finally, losses are pruned, so a rec is obtained
Nei et al have considered a similar model, without formalizing it mathematically, and concluded that it is biologically sound
Matematically sound and almost canonical and biologically sound

45. Gene evolution model
Gene effecting events: losses, duplications, and speciation
A gene tree evolves inside the species tree
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
The model contains three gene effecting events, namely the ones we have seen before
Duplications
Speciations; and
Losses
In the model a gene tree evolves inside a species tree according to the following rules
Start
Edge, canonical
Speciation, reaches, (leaf)
Finally, losses are pruned, so a rec is obtained
Nei et al have considered a similar model, without formalizing it mathematically, and concluded that it is biologically sound
Matematically sound and almost canonical and biologically sound

46. Generating a scenario Speciation Duplication Loss
This is a scenario that shows how a gene tree in blue has evolved with respect to a species tree in black
So this is the root of the species tree and this is the root of the gene tree
Three types of gene effectiong events are shown...
For instance ...
Losses are important, but in some cases, as for orthology analyses, they are not needed
For this reason we use reconcilations to show the evolution of a gene tree,

47. Generating a scenario Speciation Duplication Loss
This is a scenario that shows how a gene tree in blue has evolved with respect to a species tree in black
So this is the root of the species tree and this is the root of the gene tree
Three types of gene effectiong events are shown...
For instance ...
Losses are important, but in some cases, as for orthology analyses, they are not needed
For this reason we use reconcilations to show the evolution of a gene tree,

48. Generating a scenario Speciation Duplication Loss
This is a scenario that shows how a gene tree in blue has evolved with respect to a species tree in black
So this is the root of the species tree and this is the root of the gene tree
Three types of gene effectiong events are shown...
For instance ...
Losses are important, but in some cases, as for orthology analyses, they are not needed
For this reason we use reconcilations to show the evolution of a gene tree,

49. Generating a scenario Speciation Duplication Loss
This is a scenario that shows how a gene tree in blue has evolved with respect to a species tree in black
So this is the root of the species tree and this is the root of the gene tree
Three types of gene effectiong events are shown...
For instance ...
Losses are important, but in some cases, as for orthology analyses, they are not needed
For this reason we use reconcilations to show the evolution of a gene tree,

50. Generating a scenario Speciation Duplication Loss
This is a scenario that shows how a gene tree in blue has evolved with respect to a species tree in black
So this is the root of the species tree and this is the root of the gene tree
Three types of gene effectiong events are shown...
For instance ...
Losses are important, but in some cases, as for orthology analyses, they are not needed
For this reason we use reconcilations to show the evolution of a gene tree,

51. Generating a scenario Speciation Duplication Loss
This is a scenario that shows how a gene tree in blue has evolved with respect to a species tree in black
So this is the root of the species tree and this is the root of the gene tree
Three types of gene effectiong events are shown...
For instance ...
Losses are important, but in some cases, as for orthology analyses, they are not needed
For this reason we use reconcilations to show the evolution of a gene tree,

52. Generating a scenario Speciation Duplication Loss
This is a scenario that shows how a gene tree in blue has evolved with respect to a species tree in black
So this is the root of the species tree and this is the root of the gene tree
Three types of gene effectiong events are shown...
For instance ...
Losses are important, but in some cases, as for orthology analyses, they are not needed
For this reason we use reconcilations to show the evolution of a gene tree,

53. Reconciliation – losses have been pruned
Reconciled tree (G, )
Reconciliation – losses have been pruned ÷
So the end result of this process is a gene tree and a reconciliation of it and the species tree
Probabilities
Generation probability
Posterior probability of a reconciliation given a gene tree

54. Reconstruction Reconstruction Pr[G,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
So the end result of this process is a gene tree and a reconciliation of it and the species tree
Probabilities
Generation probability
Posterior probability of a reconciliation given a gene tree 54

55. GEM Generation relatively simple Probability of reconciled tree
Probability of gene tree:
Posterior of reconciliation:
Max likelihood reconciliation:

56. Example application: Probabilistic orthology analysis
Sennblad, Lagergren submitted

57. MHC example: MPR orthology
Most parsimonious reconciled trees (\mpr{}) for the MHC data set. (a) \mpr{} for the full four primates data set.
(b) \mpr{} for the reduced data set simulating that the human genome
has not been sampled. The species tree is scaled to the time scale on
the left, which is given in million years ago. Gene annotation
follows \cite{Nei1997}. The blue integer numbers in (b) indicate
potential speciation vertices; in (a) the blue zero indicates the
vertex corresponding to vertex zero in (b) (i.e., the least common
ancestor to the \textit{Pongo}, \textit{Gorilla} and all
\textit{Saguinus} genes except \textit{Saguinus-3}). All
illustrations of reconciled trees were made with \texttt{primetv}
\cite{Sennblad2007a}. 57

58. MHC example: MPR orthology
1(b)
Most parsimonious reconciled trees (\mpr{}) for the MHC data set. (a) \mpr{} for the full four primates data set.
(b) \mpr{} for the reduced data set simulating that the human genome
has not been sampled. The species tree is scaled to the time scale on
the left, which is given in million years ago. Gene annotation
follows \cite{Nei1997}. The blue integer numbers in (b) indicate
potential speciation vertices; in (a) the blue zero indicates the
vertex corresponding to vertex zero in (b) (i.e., the least common
ancestor to the \textit{Pongo}, \textit{Gorilla} and all
\textit{Saguinus} genes except \textit{Saguinus-3}). All
illustrations of reconciled trees were made with \texttt{primetv}
\cite{Sennblad2007a}.
28 orthology predictions 58

59. Three other reconciliations
Out of 210 in total 59

60. Reconciliation probabilities2
1(b) 60

61. Posterior & posterior mean
Modification of DP for Pr[G|S,l,m]
MCMC 61

62. Speciation probabilities62

63. ABCA 63

64. Speciation probabilities64

65. MHC birth-death parameter posterior65

66. When is MP-reconciliation incorrect?
1000 (G,) per square
Histogram from simulations study of the frequency of cases where \mpr{} makes false orthology predictions. For combinations of birth and death rates 1000 random reconciled trees were generated. The bars indicate the frequency of cases for which \mpr{} make false orthology predictions. 66

67. Performance of probabilistic orthology analysis
Draw from posterior distribution
Biological realism
Generate synthetic (G,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)

68. ROC for MHC-like data
Speciation? Y sensitivity, X specificity 68

69. ROC for ABCA-like data
Speciation? Y sensitivity, X specificity 69

70. Programs primeGEM; xprimeGEM xprimeGEM-max xprimeGEM-enum
Probability of gene tree:
Orthology analysis:
xprimeGEM
Probability of reconciled tree
Posterior of reconciliation:
xprimeGEM-max
Max likelihood reconciliation:
xprimeGEM-enum
Enumerates all g with Prob.

72. ’Comparison’ Coalesence -- Allele evolution
Alleles evolve by random sampling from parental population
Underlying pure birth process
Gene duplication and loss -- gene family evolution
Gene copies are created by duplication events
Gene copies are lost by loss events
Underlying birth-death process

73. Later similar work -- gene copy number

74. Later similar work -- coalescence

75. Later similar work -- coalescence