Generalizing phylogenetics to infer patterns of shared evolutionary events

Generalizing
phylogenetics to infer
patterns of shared
evolutionary events
Jamie R. Oaks
Department of Biological Sciences &
Museum of Natural History, Auburn
University
August 23, 2018
c 2007 Boris Kulikov boris-kulikov.blogspot.com
Shared divergences Jamie Oaks – phyletica.org 1/35

Shared ancestry is a fundamental
property of life

property of life
Phylogenetics is rapidly
progressing as the statistical
foundation of comparatve biology

property of life
“Big data” present exciting
possibilities and computational
challenges

property of life
“Big data” present exciting
possibilities and computational
challenges
Exciting opportunities to develop
new ways to study biology in the
light of phylogeny

Assumption: All processes of
diversiﬁcation aﬀect each lineage
independently and only cause
bifurcating divergences.

Violating independent divergences

Biogeography
Environmental changes that
aﬀect whole communities of
species

Biogeography
species
Gene family evolution
Chromosomal duplications

Biogeography
species
Epidemiology
Disease spread via co-infected
individuals
Transmission at social
gatherings

Biogeography
species
Epidemiology
individuals
gatherings
Endosymbiont evolution (e.g.,
parasites, microbiome)
Speciation of the host
Co-colonization of new host
species

Why account for shared divergences?

1. Improve inference

True history
τ1τ2τ3
Current tree model
τ1 τ2 τ3τ4 τ5 τ6 τ7 τ8

2. Provide a framework for studying processes of co-diversiﬁcation

Biogeography
species
Epidemiology
individuals
gatherings
Endosymbiont evolution (e.g.,
parasites, microbiome)
Speciation of the host
Co-colonization of new host
species

τ1

τ2 τ1

τ1τ2

τ3 τ1τ2

m1 m2 m3 m4 m5
τ1 τ2 τ1 τ1τ2 τ1τ2 τ3 τ1τ2
J. R. Oaks et al. (2013). Evolution 67: 991–1010, J. R. Oaks (2014). BMC Evolutionary Biology 14: 150

m1 m2 m3 m4 m5
τ1 τ2 τ1 τ1τ2 τ1τ2 τ3 τ1τ2
We want to infer the model and divergence times given DNA alignments

p(m1 | X) p(m2 | X) p(m3 | X) p(m4 | X) p(m5 | X)
τ1 τ2 τ1 τ1τ2 τ1τ2 τ3 τ1τ2

τ1 τ2 τ1 τ1τ2 τ1τ2 τ3 τ1τ2
p(mi | X) ∝ p(X | mi )p(mi )

τ1 τ2 τ1 τ1τ2 τ1τ2 τ3 τ1τ2
Challenges:

τ1 τ2 τ1 τ1τ2 τ1τ2 τ3 τ1τ2
Challenges:
1. Likelihood is tractable, but gene trees are a pain

τ1 τ2 τ1 τ1τ2 τ1τ2 τ3 τ1τ2
Challenges:
2. Sampling over all possible models

τ1 τ2 τ1 τ1τ2 τ1τ2 τ3 τ1τ2
Challenges:
5 taxa = 52 models

τ1 τ2 τ1 τ1τ2 τ1τ2 τ3 τ1τ2
Challenges:
5 taxa = 52 models
10 taxa = 115,975 models

τ1 τ2 τ1 τ1τ2 τ1τ2 τ3 τ1τ2
Challenges:
5 taxa = 52 models
10 taxa = 115,975 models
20 taxa = 51,724,158,235,372 models!!

Did repeated
fragmentation of islands
during inter-glacial rises in
sea level promote
diversiﬁcation?

Approach #1
Challenges:
1. Likelihood is tractable, but gene trees are diﬃcult
1
M. J. Hickerson et al. (2006). Evolution 60: 2435–2453
2
W. Huang et al. (2011). BMC Bioinformatics 12: 1

Approach #1
Challenges:
Use an existing method1,2
Use an existing method1,2
1
M. J. Hickerson et al. (2006). Evolution 60: 2435–2453
2
W. Huang et al. (2011). BMC Bioinformatics 12: 1

0.00
0.25
0.50
0.75
1.00
1 2 3 4 5 6 7 8 9
Number of events
Probability
J. R. Oaks et al. (2013). Evolution 67: 991–1010

Approach #2
Challenges:

Approach #2
Challenges:
Numerical approximation via approximate-likelihood Bayesian
computation (ABC)

Approach #2
Challenges:
computation (ABC)

Approach #2
Challenges:
computation (ABC)
A “diﬀuse” Dirichlet process prior (DPP)

α
1
1
α
α
2
1

α
α+1
α
α+2
α
α
α+1
1
α+2
1
α
α+1
1
α+2
1
α
1
α+1
α
α+2
α
1
α+1
2
α+22
1

α = 0.5
α
α+1
α
α+2 = 0.067
α
α
α+1
1
α+2 = 0.133
1
α
α+1
1
α+2 = 0.133
1
α
1
α+1
α
α+2 = 0.133
α
1
α+1
2
α+2 = 0.5332
1

α = 10.0
α
α+1
α
α+2 = 0.758
α
α
α+1
1
α+2 = 0.076
1
α
α+1
1
α+2 = 0.076
1
α
1
α+1
α
α+2 = 0.076
α
1
α+1
2
α+2 = 0.0152
1

New method: dpp-msbayes
Approximate-likelihood Bayesian approach to inferring models of
shared divergences
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

0.00
0.05
0.10
0.15
0.20
1 2 3 4 5 6 7 8 9
Number of events
Probability

Insulasaurus
Ptenochirus
Macroglossus
Haplonycteris
Gekko
Dendrolaphis
Cyrtodactylus
Cynopterus
Crocidura
0 5 10 15
Time
Comparison

Approach #3
Challenges:
1
D. Bryant et al. (2012). Molecular Biology and Evolution 29: 1917–1932

Approach #3
Challenges:
Bryant et al.1
introduced a way to integrate over them analytically
1

Ecoevolity: Estimating evolutionary coevality1
1
J. R. Oaks (2018). bioRxiv doi:10.1101/324525
2
R. M. Neal (2000). Journal of Computational and Graphical Statistics 9: 249–265
3

CTMC model of characters evolving along genealogies
Coalescent model of genealogies branching within populations
Dirichlet-process prior across divergence models
Gibbs sampling2 to numerically sample models
Analytically integrate over genealogies3
1
2
3

CTMC model of characters evolving along genealogies
Coalescent model of genealogies branching within populations
Dirichlet-process prior across divergence models
Gibbs sampling2 to numerically sample models
Analytically integrate over genealogies3
Goal: Fast, full-likelihood Bayesian method to infer patterns of
co-diversiﬁcation from genome-scale data
1
2
3

Does it work?

0.00 0.02 0.04 0.06
True divergence time (τ)
0.00
0.01
0.02
0.03
0.04
0.05
0.06
Estimateddivergencetime(ˆτ)
p(τ ∈ CI) = 0.946 RMSE = 1.02e-04

True number of events (k)
Estimatednumberofevents(ˆk)
105 5 0
1 266 7
0 2 114
p(ˆk = k) = 0.970 p(k) = 0.980
1
1
2
2
3
3

“Bake oﬀ”
0.00 0.05 0.10 0.15 0.20
0.00
0.05
0.10
0.15
0.20
ecoevolity
p(τ ∈ CI) = 0.915
RMSE = 9.14e-04
dpp-msbayes
p(τ ∈ CI) = 0.989
RMSE = 3.88e-03
msbayes
p(τ ∈ CI) = 0.973
RMSE = 1.25e-02
True divergence time (τ)
Estimateddivergencetime(¯τ)

“Bake oﬀ”
0.000 0.002 0.004 0.006
0.000
0.001
0.002
0.003
0.004
0.005
0.006
ecoevolity
p(Ne µ ∈ CI) = 0.936
RMSE = 2.11e-04
dpp-msbayes
p(Ne µ ∈ CI) = 0.945
RMSE = 9.04e-04
msbayes
p(Ne µ ∈ CI) = 0.751
RMSE = 1.48e-03
True root population size (Neµ)
Estimatedrootpopulationsize(¯Neµ)

“Bake oﬀ”
105 18 0
3 250 19
0 9 96
p(k ∈ 95%CS) = 0.992
p(ˆk = k) = 0.902 pp(k) = 0.942
ecoevolity
1
1
2
2
3
3
125 42 2
0 218 77
0 0 36
p(k ∈ 95%CS) = 0.996
p(ˆk = k) = 0.758 pp(k) = 0.789
dpp-msbayes
165 58 18
0 111 120
0 2 26
p(k ∈ 95%CS) = 0.964
p(ˆk = k) = 0.604 pp(k) = 0.699
msbayes

“Bake oﬀ”
105 18 0
3 250 19
0 9 96
p(k ∈ 95%CS) = 0.992
p(ˆk = k) = 0.902 pp(k) = 0.942
ecoevolity
1
1
2
2
3
3
125 42 2
0 218 77
0 0 36
p(k ∈ 95%CS) = 0.996
p(ˆk = k) = 0.758 pp(k) = 0.789
dpp-msbayes
165 58 18
0 111 120
0 2 26
p(k ∈ 95%CS) = 0.964
p(ˆk = k) = 0.604 pp(k) = 0.699
msbayes
Average run time:
33.4 minutes 4.4 days

More data!
RADseq: 400k–2million bases for 8
pairs of populations
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
Bohol
Palawan
Samar
Luzon 1
Luzon 2
Polillo
Panay
Sibuyan
Camiguin Sur
Borneo
Leyte
Babuyan Claro
Camiguin Norte
Luzon 3
Negros
Tablas
Connected?
Yes
Maybe
No
10
15
20
118 120 122 124 126

Ecoevolity: Results
0.0
0.2
0.4
0.6
1 2 3 4 5 6 7 8
Number of events
Probability
J. R. Oaks et al. (2018). bioRxiv doi:10.1101/395434

Ecoevolity: Results
The results are very diﬀerent
than the ABC methods

Ecoevolity: Results
But, these are diﬀerent data

Ecoevolity: Results
But, these are diﬀerent data
For a direct comparison, we
applied full-likelihood and ABC
methods to random subset of
RADseq data
200 loci from 3 pairs of gecko
populations

A B
<0.000624
0.00533
553
0.0
0.3
0.6
0.9
1 2 3
Number of events
Probability
Camiguin Norte | Dalupiri
Maestre De Campo | Masbate
Babuyan Claro | Calayan
0.000 0.003 0.006 0.009 0.012
Divergence time
Ecoevolity
C D
18.9
0.151
0.0119
0.00
0.25
0.50
0.75
1 2 3
Number of events
Probability
Camiguin Norte | Dalupiri
Maestre De Campo | Masbate
Babuyan Claro | Calayan
0.000 0.003 0.006 0.009 0.012
Divergence time
dpp-msbayes

Our journey
0.00
0.25
0.50
0.75
1.00
1 2 3 4 5 6 7 8 9
Number of events
Probability

Our journey
0.00
0.25
0.50
0.75
1.00
1 2 3 4 5 6 7 8 9
Number of events
Probability
0.00
0.05
0.10
0.15
0.20
1 2 3 4 5 6 7 8 9
Number of events
Probability

Our journey
0.00
0.25
0.50
0.75
1.00
1 2 3 4 5 6 7 8 9
Number of events
Probability
0.00
0.05
0.10
0.15
0.20
1 2 3 4 5 6 7 8 9
Number of events
Probability
0.0
0.2
0.4
0.6
1 2 3 4 5 6 7 8
Number of events
Probability

Our journey
0.00
0.25
0.50
0.75
1.00
1 2 3 4 5 6 7 8 9
Number of events
Probability
0.00
0.05
0.10
0.15
0.20
1 2 3 4 5 6 7 8 9
Number of events
Probability
0.0
0.2
0.4
0.6
1 2 3 4 5 6 7 8
Number of events
Probability
Conclusions?

Next step: A general framework
Develop a framework for
inferring shared divergences
across phylogenies τ1τ2

across phylogenies
Generalize Bayesian
phylogenetics to incorporate
shared divergences
τ1τ2

across phylogenies
Generalize Bayesian
shared divergences
Sample models numerically via
reversible-jump Markov chain
Monte Carlo
τ1τ2

across phylogenies
Generalize Bayesian
shared divergences
Sample models numerically via
reversible-jump Markov chain
Monte Carlo
Beneﬁts:
Improve phylogenetic inference
Framework for studying
processes of co-diversiﬁcation
τ1τ2

Everything is on GitHub. . .
Software:
Ecoevolity: https://github.com/phyletica/ecoevolity
PyMsBayes: https://joaks1.github.io/PyMsBayes
dpp-msbayes: https://github.com/joaks1/dpp-msbayes
ABACUS: Approximate BAyesian C UtilitieS.
https://github.com/joaks1/abacus
Open-Science Notebooks:
Ecoevolity experiments:
https://github.com/phyletica/ecoevolity-experiments
msBayes experiments:
https://github.com/joaks1/msbayes-experiments
Gecko RADseq: https://github.com/phyletica/gekgo

Acknowledgments
Ideas and feedback:
Phyletica Lab (the Phyleticians)
Mark Holder
Leach´e Lab
Minin Lab
Tracy Heath
Michael Landis
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!

Questions?
joaks@auburn.edu
phyletica.org
c 2007 Boris Kulikov boris-kulikov.blogspot.com

Generalizing phylogenetics to infer patterns of shared evolutionary events

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