This document discusses challenges in phylogenetic inference when divergences are not independent across the tree. It notes that current methods assume independence but divergences are often clustered. Accounting for clustering could improve inference and study co-diversification processes. However, inferring co-diversification is challenging due to inability to solve integrals analytically and needing to sample over an enormous number of possible divergence models as the number of taxa increases. Approximate Bayesian computation and using a diffuse Dirichlet process prior may help address some of these challenges.

1. Accommodating
clustered divergences in
phylogenetic inference
Jamie R. Oaks1,2
1Department of Biology, University of
Washington
2Department of Biological Sciences,
Auburn University
October 21, 2015
c 2007 Boris Kulikov boris-kulikov.blogspot.com
Clustered diversification Jamie Oaks – phyletica.org 1/27

2. Phylogenetics is rapidly
progressing as an endeavor
of statistical inference
c 2007 Boris Kulikov boris-kulikov.blogspot.com
Clustered diversification Jamie Oaks – phyletica.org 2/27

3. Phylogenetics is rapidly
progressing as an endeavor
of statistical inference
“Big data” present exciting
possibilities and
computational challenges
c 2007 Boris Kulikov boris-kulikov.blogspot.com
Clustered diversification Jamie Oaks – phyletica.org 2/27

4. Phylogenetics is rapidly
progressing as an endeavor
of statistical inference
“Big data” present exciting
possibilities and
computational challenges
Exciting opportunities to
develop new ways to study
biology in the light of
phylogeny
c 2007 Boris Kulikov boris-kulikov.blogspot.com
Clustered diversification Jamie Oaks – phyletica.org 2/27

5. Current state of phylogenetics
Clustered diversification Jamie Oaks – phyletica.org 3/27

6. Current state of phylogenetics
Assumption: Divergences are independent across the tree
Clustered diversification Jamie Oaks – phyletica.org 3/27

7. Current state of phylogenetics
Assumption: Divergences are independent across the tree
We know this assumption
is frequently violated
Clustered diversification Jamie Oaks – phyletica.org 3/27

8. Current state of phylogenetics
Assumption: Divergences are independent across the tree
We know this assumption
is frequently violated
Clustered diversification Jamie Oaks – phyletica.org 3/27

9. Current state of phylogenetics
Assumption: Divergences are independent across the tree
We know this assumption
is frequently violated
Why account for this
non-independence?
Clustered diversification Jamie Oaks – phyletica.org 3/27

10. Current state of phylogenetics
Assumption: Divergences are independent across the tree
We know this assumption
is frequently violated
Why account for this
non-independence?
1. Improve inference
Clustered diversification Jamie Oaks – phyletica.org 3/27

11. Current state of phylogenetics
Assumption: Divergences are independent across the tree
We know this assumption
is frequently violated
Why account for this
non-independence?
1. Improve inference
2. Provide a framework
for studying processes
of co-diversification
Clustered diversification Jamie Oaks – phyletica.org 3/27

12. Current state of phylogenetics
Assumption: Divergences are independent across the tree
We know this assumption
is frequently violated
Why account for this
non-independence?
1. Improve inference
2. Provide a framework
for studying processes
of co-diversification
This is a model-choice
problem
Clustered diversification Jamie Oaks – phyletica.org 3/27

13. Divergence model choice
τ1
T1
T2
T3
Clustered diversification Jamie Oaks – phyletica.org 4/27

14. Divergence model choice
τ1
T1
T2
T3
Clustered diversification Jamie Oaks – phyletica.org 4/27

15. Divergence model choice
τ2 τ1
T1
T2
T3
Clustered diversification Jamie Oaks – phyletica.org 4/27

16. Divergence model choice
τ1τ2
T1
T2
T3
Clustered diversification Jamie Oaks – phyletica.org 4/27

17. Divergence model choice
τ1τ2
T1
T2
T3
Clustered diversification Jamie Oaks – phyletica.org 4/27

18. Divergence model choice
τ3 τ1τ2
T1
T2
T3
Clustered diversification Jamie Oaks – phyletica.org 4/27

19. Inferring co-diversification
m1 m2 m3 m4 m5
τ1
T1
T2
T3
τ2 τ1
T1
T2
T3
τ1τ2
T1
T2
T3
τ1τ2
T1
T2
T3
τ3 τ1τ2
T1
T2
T3
J. R. Oaks et al. (2013). Evolution 67: 991–1010, J. R. Oaks (2014). BMC Evolutionary Biology 14: 150
Clustered diversification Jamie Oaks – phyletica.org 5/27

20. Inferring co-diversification
m1 m2 m3 m4 m5
τ1
T1
T2
T3
τ2 τ1
T1
T2
T3
τ1τ2
T1
T2
T3
τ1τ2
T1
T2
T3
τ3 τ1τ2
T1
T2
T3
We want to infer m and T given DNA sequence alignments X
J. R. Oaks et al. (2013). Evolution 67: 991–1010, J. R. Oaks (2014). BMC Evolutionary Biology 14: 150
Clustered diversification Jamie Oaks – phyletica.org 5/27

21. Inferring co-diversification
p(m1 | X) p(m2 | X) p(m3 | X) p(m4 | X) p(m5 | X)
τ1
T1
T2
T3
τ2 τ1
T1
T2
T3
τ1τ2
T1
T2
T3
τ1τ2
T1
T2
T3
τ3 τ1τ2
T1
T2
T3
We want to infer m and T given DNA sequence alignments X
J. R. Oaks et al. (2013). Evolution 67: 991–1010, J. R. Oaks (2014). BMC Evolutionary Biology 14: 150
Clustered diversification Jamie Oaks – phyletica.org 5/27

22. Inferring co-diversification
p(m1 | X) p(m2 | X) p(m3 | X) p(m4 | X) p(m5 | X)
τ1
T1
T2
T3
τ2 τ1
T1
T2
T3
τ1τ2
T1
T2
T3
τ1τ2
T1
T2
T3
τ3 τ1τ2
T1
T2
T3
We want to infer m and T given DNA sequence alignments X
p(mi | X) ∝ p(X | mi )p(mi )
J. R. Oaks et al. (2013). Evolution 67: 991–1010, J. R. Oaks (2014). BMC Evolutionary Biology 14: 150
Clustered diversification Jamie Oaks – phyletica.org 5/27

23. Inferring co-diversification
p(m1 | X) p(m2 | X) p(m3 | X) p(m4 | X) p(m5 | X)
τ1
T1
T2
T3
τ2 τ1
T1
T2
T3
τ1τ2
T1
T2
T3
τ1τ2
T1
T2
T3
τ3 τ1τ2
T1
T2
T3
We want to infer m and T given DNA sequence alignments X
p(mi | X) ∝ p(X | mi )p(mi )
p(X | mi ) =
θ
p(X | θ, mi )p(θ | mi )dθ
J. R. Oaks et al. (2013). Evolution 67: 991–1010, J. R. Oaks (2014). BMC Evolutionary Biology 14: 150
Clustered diversification Jamie Oaks – phyletica.org 5/27

24. Inferring co-diversification
p(m1 | X) p(m2 | X) p(m3 | X) p(m4 | X) p(m5 | X)
τ1
T1
T2
T3
τ2 τ1
T1
T2
T3
τ1τ2
T1
T2
T3
τ1τ2
T1
T2
T3
τ3 τ1τ2
T1
T2
T3
We want to infer m and T given DNA sequence alignments X
p(mi | X) ∝ p(X | mi )p(mi )
p(X | mi ) =
θ
p(X | θ, mi )p(θ | mi )dθ
Divergence times
Gene trees
Substitution parameters
Demographic parameters
J. R. Oaks et al. (2013). Evolution 67: 991–1010, J. R. Oaks (2014). BMC Evolutionary Biology 14: 150
Clustered diversification Jamie Oaks – phyletica.org 5/27

25. Inferring co-diversification
p(m1 | X) p(m2 | X) p(m3 | X) p(m4 | X) p(m5 | X)
τ1
T1
T2
T3
τ2 τ1
T1
T2
T3
τ1τ2
T1
T2
T3
τ1τ2
T1
T2
T3
τ3 τ1τ2
T1
T2
T3
Challenges:
J. R. Oaks et al. (2013). Evolution 67: 991–1010, J. R. Oaks (2014). BMC Evolutionary Biology 14: 150
Clustered diversification Jamie Oaks – phyletica.org 5/27

26. Inferring co-diversification
p(m1 | X) p(m2 | X) p(m3 | X) p(m4 | X) p(m5 | X)
τ1
T1
T2
T3
τ2 τ1
T1
T2
T3
τ1τ2
T1
T2
T3
τ1τ2
T1
T2
T3
τ3 τ1τ2
T1
T2
T3
Challenges:
1. Cannot solve all the integrals analytically
J. R. Oaks et al. (2013). Evolution 67: 991–1010, J. R. Oaks (2014). BMC Evolutionary Biology 14: 150
Clustered diversification Jamie Oaks – phyletica.org 5/27

27. Inferring co-diversification
p(m1 | X) p(m2 | X) p(m3 | X) p(m4 | X) p(m5 | X)
τ1
T1
T2
T3
τ2 τ1
T1
T2
T3
τ1τ2
T1
T2
T3
τ1τ2
T1
T2
T3
τ3 τ1τ2
T1
T2
T3
Challenges:
1. Cannot solve all the integrals analytically
Numerical approximation via approximate-likelihood Bayesian
computation (ABC)
J. R. Oaks et al. (2013). Evolution 67: 991–1010, J. R. Oaks (2014). BMC Evolutionary Biology 14: 150
Clustered diversification Jamie Oaks – phyletica.org 5/27

28. Inferring co-diversification
p(m1 | X) p(m2 | X) p(m3 | X) p(m4 | X) p(m5 | X)
τ1
T1
T2
T3
τ2 τ1
T1
T2
T3
τ1τ2
T1
T2
T3
τ1τ2
T1
T2
T3
τ3 τ1τ2
T1
T2
T3
Challenges:
1. Cannot solve all the integrals analytically
Numerical approximation via approximate-likelihood Bayesian
computation (ABC)
2. Sampling over all possible models
J. R. Oaks et al. (2013). Evolution 67: 991–1010, J. R. Oaks (2014). BMC Evolutionary Biology 14: 150
Clustered diversification Jamie Oaks – phyletica.org 5/27

29. Inferring co-diversification
p(m1 | X) p(m2 | X) p(m3 | X) p(m4 | X) p(m5 | X)
τ1
T1
T2
T3
τ2 τ1
T1
T2
T3
τ1τ2
T1
T2
T3
τ1τ2
T1
T2
T3
τ3 τ1τ2
T1
T2
T3
Challenges:
1. Cannot solve all the integrals analytically
Numerical approximation via approximate-likelihood Bayesian
computation (ABC)
2. Sampling over all possible models
5 taxa = 52 models
J. R. Oaks et al. (2013). Evolution 67: 991–1010, J. R. Oaks (2014). BMC Evolutionary Biology 14: 150
Clustered diversification Jamie Oaks – phyletica.org 5/27

30. Inferring co-diversification
p(m1 | X) p(m2 | X) p(m3 | X) p(m4 | X) p(m5 | X)
τ1
T1
T2
T3
τ2 τ1
T1
T2
T3
τ1τ2
T1
T2
T3
τ1τ2
T1
T2
T3
τ3 τ1τ2
T1
T2
T3
Challenges:
1. Cannot solve all the integrals analytically
Numerical approximation via approximate-likelihood Bayesian
computation (ABC)
2. Sampling over all possible models
5 taxa = 52 models
10 taxa = 115,975 models
J. R. Oaks et al. (2013). Evolution 67: 991–1010, J. R. Oaks (2014). BMC Evolutionary Biology 14: 150
Clustered diversification Jamie Oaks – phyletica.org 5/27

31. Inferring co-diversification
p(m1 | X) p(m2 | X) p(m3 | X) p(m4 | X) p(m5 | X)
τ1
T1
T2
T3
τ2 τ1
T1
T2
T3
τ1τ2
T1
T2
T3
τ1τ2
T1
T2
T3
τ3 τ1τ2
T1
T2
T3
Challenges:
1. Cannot solve all the integrals analytically
Numerical approximation via approximate-likelihood Bayesian
computation (ABC)
2. Sampling over all possible models
5 taxa = 52 models
10 taxa = 115,975 models
20 taxa = 51,724,158,235,372 models!!
J. R. Oaks et al. (2013). Evolution 67: 991–1010, J. R. Oaks (2014). BMC Evolutionary Biology 14: 150
Clustered diversification Jamie Oaks – phyletica.org 5/27

32. Inferring co-diversification
p(m1 | X) p(m2 | X) p(m3 | X) p(m4 | X) p(m5 | X)
τ1
T1
T2
T3
τ2 τ1
T1
T2
T3
τ1τ2
T1
T2
T3
τ1τ2
T1
T2
T3
τ3 τ1τ2
T1
T2
T3
Challenges:
1. Cannot solve all the integrals analytically
Numerical approximation via approximate-likelihood Bayesian
computation (ABC)
2. Sampling over all possible models
5 taxa = 52 models
10 taxa = 115,975 models
20 taxa = 51,724,158,235,372 models!!
A “diffuse” Dirichlet process prior (DPP)
J. R. Oaks et al. (2013). Evolution 67: 991–1010, J. R. Oaks (2014). BMC Evolutionary Biology 14: 150
Clustered diversification Jamie Oaks – phyletica.org 5/27

33. “Easy” as ABC
A
A
A
G
G
G
C
C
C
C
C
C
G
G
G
G
G
G
A
A
A
A
A
T
A
A
A
A
A
A
T
T
C
C
C
C
G
G
G
G
G
G
T
T
T
T
T
T
G
G
G
G
G
G
C
C
C
T
T
T
T
T
T
C
C
C
C
C
C
C
C
C
G
G
G
G
G
G
C
C
T
T
T
T
A
A
A
A
A
A
C
C
C
C
C
C
G
G
G
G
G
G
T
T
T
T
T
T
A
A
A
G
G
G
C
C
C
C
C
C
C
C
C
C
C
C
A
A
A
T
T
T
G
G
G
G
G
G
T
T
T
T
C
C
A
A
A
A
A
A
C
C
C
C
C
C
C
C
C
T
T
T
G
G
G
G
G
G
G
G
G
G
G
G
T
T
T
T
T
T
S1
S2
S3
Clustered diversification Jamie Oaks – phyletica.org 6/27

34. “Easy” as ABC
A
A
A
G
G
G
C
C
C
C
C
C
G
G
G
G
G
G
A
A
A
A
A
T
A
A
A
A
A
A
T
T
C
C
C
C
G
G
G
G
G
G
T
T
T
T
T
T
G
G
G
G
G
G
C
C
C
T
T
T
T
T
T
C
C
C
C
C
C
C
C
C
G
G
G
G
G
G
C
C
T
T
T
T
A
A
A
A
A
A
C
C
C
C
C
C
G
G
G
G
G
G
T
T
T
T
T
T
A
A
A
G
G
G
C
C
C
C
C
C
C
C
C
C
C
C
A
A
A
T
T
T
G
G
G
G
G
G
T
T
T
T
C
C
A
A
A
A
A
A
C
C
C
C
C
C
C
C
C
T
T
T
G
G
G
G
G
G
G
G
G
G
G
G
T
T
T
T
T
T
S1
S2
S3
Clustered diversification Jamie Oaks – phyletica.org 6/27

35. “Easy” as ABC
A
A
A
G
G
G
C
C
C
C
C
C
G
G
G
G
G
G
A
A
A
A
A
T
A
A
A
A
A
A
T
T
C
C
C
C
G
G
G
G
G
G
T
T
T
T
T
T
G
G
G
G
G
G
C
C
C
T
T
T
T
T
T
C
C
C
C
C
C
C
C
C
G
G
G
G
G
G
C
C
T
T
T
T
A
A
A
A
A
A
C
C
C
C
C
C
G
G
G
G
G
G
T
T
T
T
T
T
A
A
A
G
G
G
C
C
C
C
C
C
C
C
C
C
C
C
A
A
A
T
T
T
G
G
G
G
G
G
T
T
T
T
C
C
A
A
A
A
A
A
C
C
C
C
C
C
C
C
C
T
T
T
G
G
G
G
G
G
G
G
G
G
G
G
T
T
T
T
T
T
S1
S2
S3
Clustered diversification Jamie Oaks – phyletica.org 6/27

36. “Easy” as ABC
0.0
0.2
0.4
0.6
0.8
1.0 0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
1.0
S1
S2
S3
Clustered diversification Jamie Oaks – phyletica.org 7/27

37. “Easy” as ABC
0.0
0.2
0.4
0.6
0.8
1.0 0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
1.0
S1
S2
S3
Clustered diversification Jamie Oaks – phyletica.org 7/27

38. “Easy” as ABC
0.0
0.2
0.4
0.6
0.8
1.0 0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
1.0
S1
S2
S3
Clustered diversification Jamie Oaks – phyletica.org 7/27

39. “Easy” as ABC
0.0
0.2
0.4
0.6
0.8
1.0 0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
1.0
S1
S2
S3
Clustered diversification Jamie Oaks – phyletica.org 7/27

40. “Easy” as ABC
0.0
0.2
0.4
0.6
0.8
1.0 0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
1.0
S1
S2
S3
Clustered diversification Jamie Oaks – phyletica.org 7/27

41. “Easy” as ABC
0.0
0.2
0.4
0.6
0.8
1.0 0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
1.0
S1
S2
S3
Clustered diversification Jamie Oaks – phyletica.org 7/27

42. “Easy” as ABC
0.0
0.2
0.4
0.6
0.8
1.0 0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
1.0
S1
S2
S3
Clustered diversification Jamie Oaks – phyletica.org 7/27

43. “Easy” as ABC
0.0
0.2
0.4
0.6
0.8
1.0 0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
1.0
S1
S2
S3
Clustered diversification Jamie Oaks – phyletica.org 7/27

44. “Easy” as ABC
0.0
0.2
0.4
0.6
0.8
1.0 0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
1.0
S1
S2
S3
Clustered diversification Jamie Oaks – phyletica.org 7/27

46. Inferring co-diversification
p(m1 | X) p(m2 | X) p(m3 | X) p(m4 | X) p(m5 | X)
τ1
T1
T2
T3
τ2 τ1
T1
T2
T3
τ1τ2
T1
T2
T3
τ1τ2
T1
T2
T3
τ3 τ1τ2
T1
T2
T3
Challenges:
1. Cannot solve all the integrals analytically
Numerical approximation via approximate-likelihood Bayesian
computation (ABC)
2. Sampling over all possible models
5 taxa = 52 models
10 taxa = 115,975 models
20 taxa = 51,724,158,235,372 models!!
A “diffuse” Dirichlet process prior (DPP)
J. R. Oaks et al. (2013). Evolution 67: 991–1010, J. R. Oaks (2014). BMC Evolutionary Biology 14: 150
Clustered diversification Jamie Oaks – phyletica.org 9/27

47. Sampling divergence models—a novel approach
The divergence models are ways of assigning our taxa to
events
Clustered diversification Jamie Oaks – phyletica.org 10/27

48. Sampling divergence models—a novel approach
The divergence models are ways of assigning our taxa to
events
A Dirichlet process prior (DPP) model is a convenient and
flexible solution
Peter Dirichlet
Clustered diversification Jamie Oaks – phyletica.org 10/27

49. Sampling divergence models—a novel approach
The divergence models are ways of assigning our taxa to
events
A Dirichlet process prior (DPP) model is a convenient and
flexible solution
Common Bayesian approach to assigning variables to an
unknown number of categories
Peter Dirichlet
Clustered diversification Jamie Oaks – phyletica.org 10/27

50. Sampling divergence models—a novel approach
The divergence models are ways of assigning our taxa to
events
A Dirichlet process prior (DPP) model is a convenient and
flexible solution
Common Bayesian approach to assigning variables to an
unknown number of categories
Controlled by “concentration” parameter: α
Peter Dirichlet
Clustered diversification Jamie Oaks – phyletica.org 10/27

51. α
α+2
1
α+2
1
α+2
α
α+1
α
α+2
2
α+2
1
α+1
Clustered diversification Jamie Oaks – phyletica.org 11/27

52. α
α+2
1
α+2
1
α+2
α
α+1
α
α+2
2
α+2
1
α+1
Clustered diversification Jamie Oaks – phyletica.org 11/27

53. α
α+2
1
α+2
1
α+2
α
α+1
α
α+2
2
α+2
1
α+1
Clustered diversification Jamie Oaks – phyletica.org 11/27

54. α
α+2
1
α+2
1
α+2
α
α+1
α
α+2
2
α+2
1
α+1
Clustered diversification Jamie Oaks – phyletica.org 11/27

55. α
α+1
α
α+2
α
α+2
α
α+1
1
α+2
1
α+2
α
α+1
1
α+21
α+2
α
α+1
1
α+1
α
α+2
α
α+2
1
α+1
2
α+2
2
α+2
1
α+1
Clustered diversification Jamie Oaks – phyletica.org 11/27

56. α = 0.5
α
α+1
α
α+2 = 0.067
α
α+2
α
α+1
1
α+2 = 0.133
1
α+2
α
α+1
1
α+2 = 0.1331
α+2
α
α+1
1
α+1
α
α+2 = 0.133
α
α+2
1
α+1
2
α+2 = 0.5332
α+2
1
α+1
Clustered diversification Jamie Oaks – phyletica.org 11/27

57. α = 10.0
α
α+1
α
α+2 = 0.758
α
α+2
α
α+1
1
α+2 = 0.076
1
α+2
α
α+1
1
α+2 = 0.0761
α+2
α
α+1
1
α+1
α
α+2 = 0.076
α
α+2
1
α+1
2
α+2 = 0.0152
α+2
1
α+1
Clustered diversification Jamie Oaks – phyletica.org 11/27

58. New method: dpp-msbayes
Flexible Dirichlet-process prior (DPP) over all possible
divergence models
J. R. Oaks (2014). BMC Evolutionary Biology 14: 150
Clustered diversification Jamie Oaks – phyletica.org 12/27

59. New method: dpp-msbayes
Flexible Dirichlet-process prior (DPP) over all possible
divergence models
Flexible priors on parameters to avoid strongly weighted
posteriors
J. R. Oaks (2014). BMC Evolutionary Biology 14: 150
Clustered diversification Jamie Oaks – phyletica.org 12/27

60. New method: dpp-msbayes
Flexible Dirichlet-process prior (DPP) over all possible
divergence models
Flexible priors on parameters to avoid strongly weighted
posteriors
Multi-processing to accommodate genomic datasets
J. R. Oaks (2014). BMC Evolutionary Biology 14: 150
Clustered diversification Jamie Oaks – phyletica.org 12/27

61. dpp-msbayes: Simulation-based assessment
Validation:
Simulate 50,000 datasets and analyze each under the same
model
Clustered diversification Jamie Oaks – phyletica.org 13/27

62. dpp-msbayes: Simulation-based assessment
Validation:
Simulate 50,000 datasets and analyze each under the same
model
Robustness:
Simulate datasets that violate model assumptions and analyze
each of them
Clustered diversification Jamie Oaks – phyletica.org 13/27

63. dpp-msbayes: Validation results
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
Posterior probability of one divergence
Trueprobabilityofonedivergence
J. R. Oaks (2014). BMC Evolutionary Biology 14: 150
Clustered diversification Jamie Oaks – phyletica.org 14/27

64. dpp-msbayes: Robustness results
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
Posterior probability of one divergence
Trueprobabilityofonedivergence
J. R. Oaks (2014). BMC Evolutionary Biology 14: 150
Clustered diversification Jamie Oaks – phyletica.org 15/27

65. dpp-msbayes: Performance
New method for estimating shared evolutionary history shows:
1. Model-choice accuracy
2. Robustness to model violations
3. Power to detect variation in divergence times
4. It’s fast!
J. R. Oaks (2014). BMC Evolutionary Biology 14: 150
Clustered diversification Jamie Oaks – phyletica.org 16/27

66. dpp-msbayes: Performance
New method for estimating shared evolutionary history shows:
1. Model-choice accuracy
2. Robustness to model violations
3. Power to detect variation in divergence times
4. It’s fast!
A new tool for biologists to leverage comparative
genomic data to explore processes of co-diversification
J. R. Oaks (2014). BMC Evolutionary Biology 14: 150
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67. Empirical applications
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68. Empirical applications
Did repeated
fragmentation of islands
during inter-glacial rises
in sea level promote
diversification?
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69. Climate-driven diversification
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70. Climate-driven diversification
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71. Climate-driven diversification
Clustered diversification Jamie Oaks – phyletica.org 18/27

72. Results
1 3 5 7 9 11 13 15 17 19 21
Number of divergence events
0.00
0.02
0.04
0.06
0.08
0.10
Posteriorprobability
J. R. Oaks (2014). BMC Evolutionary Biology 14: 150
Clustered diversification Jamie Oaks – phyletica.org 19/27

73. Results
1 3 5 7 9 11 13 15 17 19 21
Number of divergence events
0.00
0.02
0.04
0.06
0.08
0.10
Posteriorprobability
0100200300400500
Time (kya)
0
-50
-100
Sealevel(m)
J. R. Oaks (2014). BMC Evolutionary Biology 14: 150
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74. More data!
Collecting genomic data from taxa co-distributed across
Southeast Asian Islands and Mainland
Clustered diversification Jamie Oaks – phyletica.org 20/27

75. More data!
Collecting genomic data from taxa co-distributed across
Southeast Asian Islands and Mainland
Preliminary results for 1000 loci from 5 pairs of Gekko
mindorensis populations
1 2 3 4 5
Number of divergence events, j¿j
-5.0
-4.0
-3.0
-2.0
-1.0
0.0
1.0
2.0
3.02ln(Bayesfactor)
Clustered diversification Jamie Oaks – phyletica.org 20/27

76. Diversification across African rainforests
Did climate cycles drive
diversification and
community assembly across
rainforest taxa?
Clustered diversification Jamie Oaks – phyletica.org 21/27

77. Diversification across African rainforests
Did climate cycles drive
diversification and
community assembly across
rainforest taxa?
Preliminary results with 300
loci from 3 taxa
1 2 3
Number of divergence events, j¿j
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2ln(Bayesfactor)
Clustered diversification Jamie Oaks – phyletica.org 21/27

78. Conclusions
New method for estimating shared evolutionary history
Shows good “frequentist” behavior
Relatively robust to model violations
Clustered diversification Jamie Oaks – phyletica.org 22/27

79. Conclusions
New method for estimating shared evolutionary history
Shows good “frequentist” behavior
Relatively robust to model violations
Finding support for temporally clustered divergences in
multiple systems
Clustered diversification Jamie Oaks – phyletica.org 22/27

80. Conclusions
New method for estimating shared evolutionary history
Shows good “frequentist” behavior
Relatively robust to model violations
Finding support for temporally clustered divergences in
multiple systems
However, there is a lot of uncertainty!
Clustered diversification Jamie Oaks – phyletica.org 22/27

81. Current work: More power
Full-likelihood Bayesian implementation
1
D. Bryant et al. (2012). Molecular Biology And Evolution 29: 1917–1932
Clustered diversification Jamie Oaks – phyletica.org 23/27

82. Current work: More power
Full-likelihood Bayesian implementation
Uses all the information in the data
Applicable to deeper timescales
1
D. Bryant et al. (2012). Molecular Biology And Evolution 29: 1917–1932
Clustered diversification Jamie Oaks – phyletica.org 23/27

83. Current work: More power
Full-likelihood Bayesian implementation
Uses all the information in the data
Applicable to deeper timescales
Analytically integrate over gene trees 1
1
D. Bryant et al. (2012). Molecular Biology And Evolution 29: 1917–1932
Clustered diversification Jamie Oaks – phyletica.org 23/27

84. Current work: More power
Full-likelihood Bayesian implementation
Uses all the information in the data
Applicable to deeper timescales
Analytically integrate over gene trees 1
Very efficient numerical approximation of posterior
Applicable to NGS datasets
1
D. Bryant et al. (2012). Molecular Biology And Evolution 29: 1917–1932
Clustered diversification Jamie Oaks – phyletica.org 23/27

85. Next step: A general framework
Develop a framework for inferring
shared divergences across
phylogenies
τ1τ2
T1
T2
T3
Clustered diversification Jamie Oaks – phyletica.org 24/27

86. Next step: A general framework
Develop a framework for inferring
shared divergences across
phylogenies
τ1τ2
T1
T2
T3
Clustered diversification Jamie Oaks – phyletica.org 24/27

87. Next step: A general framework
Develop a framework for inferring
shared divergences across
phylogenies
Generalize Bayesian phylogenetics
to incorporate shared divergences
τ1τ2
T1
T2
T3
Clustered diversification Jamie Oaks – phyletica.org 24/27

88. Next step: A general framework
Develop a framework for inferring
shared divergences across
phylogenies
Generalize Bayesian phylogenetics
to incorporate shared divergences
Sample models numerically via
reversible-jump Markov chain
Monte Carlo
τ1τ2
T1
T2
T3
Clustered diversification Jamie Oaks – phyletica.org 24/27

89. Next step: A general framework
Develop a framework for inferring
shared divergences across
phylogenies
Generalize Bayesian phylogenetics
to incorporate shared divergences
Sample models numerically via
reversible-jump Markov chain
Monte Carlo
Benefits:
Improve phylogenetic inference
Framework for studying processes
of co-diversification
τ1τ2
T1
T2
T3
Clustered diversification Jamie Oaks – phyletica.org 24/27

90. Everything is on GitHub. . .
Software:
dpp-msbayes: https://github.com/joaks1/dpp-msbayes
PyMsBayes: https://joaks1.github.io/PyMsBayes
ABACUS: Approximate BAyesian C UtilitieS.
https://github.com/joaks1/abacus
Open-Science Notebook:
msbayes-experiments:
https://github.com/joaks1/msbayes-experiments
Clustered diversification Jamie Oaks – phyletica.org 25/27

91. Acknowledgments
Ideas and feedback:
Leach´e Lab
Minin Lab
Holder Lab
Brown Lab/KU Herpetology
Computation:
Funding:
Photo credits:
Rafe Brown, Cam Siler, Jesse
Grismer, & Jake Esselstyn
FMNH Philippine Mammal
Website:
D.S. Balete, M.R.M. Duya,
& J. Holden
PhyloPic!
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92. Questions?
joaks@auburn.edu
c 2007 Boris Kulikov boris-kulikov.blogspot.com
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