Presentation to the Center for Population Biology, November 2010

1. Inferring Adaptive Landscapes
from Phylogenetic Trees
Carl Boettiger
UC Davis
June 8, 2010
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2. Introduction: a Story of C. Boettiger and C. Martin
Background of Comparative Methods
Wrightscape: a nonlinear, forward approach
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3. A Story
Q}-< 04.09 == Q}-< | O}| L- f(x)dx ?
BM OU wtf == | O‘}|L-
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4. Carl Boettiger, UC Davis Adaptive Landscapes 4/52

5. Q}-<
==
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6. ______
Q}-<
O}I
L-
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7. Carl Boettiger, UC Davis Adaptive Landscapes 7/52

8. Carl Boettiger, UC Davis Adaptive Landscapes 8/52

9. O}-<
Q}-<
f(x) dt
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10. Carl Boettiger, UC Davis Adaptive Landscapes 10/52

11. ?
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12. ______
O}-<
==
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13. ______
OL-
`}I
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14. Introduction: a Story of C. Boettiger and C. Martin
Background of Comparative Methods
Wrightscape: a nonlinear, forward approach
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15. Felsenstein’s question
Is brain size evolution
correlated to
body size evolution?
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16. Natural Selection or Shared Ancestry?
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17. Natural Selection or Shared Ancestry?
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18. Correcting for history: Correcting for branch length
Reasons species are similar:
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19. Correcting for history: Correcting for branch length
Reasons species are similar:
1
Same function – natural selection
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20. Correcting for history: Correcting for branch length
Reasons species are similar:
1
Same function – natural selection
2
Same ancestors – shared history
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21. Correcting for history: Correcting for branch length
Reasons species are similar:
1
Same function – natural selection
2
Same ancestors – shared history
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22. Expected divergence: unbiased model
10
5
0
Time
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23. Expected divergence: unbiased model
10
5
0
Time
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24. Expected divergence: unbiased model
10
5
TTHTTTTTTH =⇒ −6
0
Time
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25. Expected divergence: unbiased model
10
5
TTHTTTTTTH =⇒ −6
TTHTTHHHTT =⇒ −2
0
Time
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26. Expected divergence: unbiased model
10
5
TTHTTTTTTH =⇒ −6
TTHTTHHHTT =⇒ −2
TTHTTHHHTH =⇒ 0
0
Time
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27. Independent Contrasts
11,6 5,1 4,1 10,5 4,1 5,1 11,6 10,5
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28. Contrasts are differences in independent branches
11,6 5,1 4,1 10,5
6
5 8,3.5 7,3
0
Tim e
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29. Contrasts are differences in independent branches
Sister taxa = easy contrasts:
11,6 5,1 4,1 10,5
6 11 − 5
√
2
5 8,3.5 7,3
0
Tim e
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30. Contrasts are differences in independent branches
Sister taxa = easy contrasts:
11,6 5,1 4,1 10,5
6 11 − 5
√
2
5 8,3.5 7,3
Interior node estimates:
11 + 5
=8
2
0
Tim e
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31. Contrasts are differences in independent branches
Sister taxa = easy contrasts:
11,6 5,1 4,1 10,5
6 11 − 5
√
2
5 8,3.5 7,3
Interior node estimates:
11 + 5
=8
2
0 Another set of contrasts:
Tim e
8−7
√
1+2×5
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32. < Watch the focus shift from the data to the model. . . >
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33. Estimating ancestral states and rates of change
11,6 5,1 4,1 10,5
6
5 (8, 3.5) (7, 3)
0 (7.5,3.75) ?
Tim e
Schluter et. al. (1997)
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34. Estimating ancestral states and rates of change
11,6 5,1 4,1 10,5
6 Expected ancestral states:
5 (8, 3.5) (7, 3) intermediate trait values
0 (7.5,3.75) ?
Tim e
Schluter et. al. (1997)
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35. Estimating ancestral states and rates of change
11,6 5,1 4,1 10,5
6 Expected ancestral states:
5 (8, 3.5) (7, 3) intermediate trait values
Expected rate of change:
0
matching the toss rate
Tim e
(7.5,3.75) ?
Schluter et. al. (1997)
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36. Estimating ancestral states and rates of change
11,6 5,1 4,1 10,5
6 Expected ancestral states:
5 (8, 3.5) (7, 3) intermediate trait values
Expected rate of change:
0
matching the toss rate
Tim e
(7.5,3.75) ?
Also estimates uncertainty
Schluter et. al. (1997)
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37. Changing Rates and Adaptive Radiations?
11,6 5,1 4,1 10,5
6
5 (8, 3.5) (7, 3)
Evidence that the
rates of evolution
are accelerating?
0 (7.5,3.75) ?
Tim e
Freckleton & Harvey (2006)
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38. < Are we taking the model too seriously? >
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39. Differing rates between clades?
9 11 2 21
O’Meara et. al. (2006)
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40. Differing rates between clades?
9 11 2 21
O’Meara et. al. (2006)
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41. Differing rates between clades?
9 11 2 21
O’Meara et. al. (2006)
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42. Evolutionary questions thus far
(Brownian Motion)
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43. Evolutionary questions thus far
(Brownian Motion)
1 Correlated trait evolution
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44. Evolutionary questions thus far
(Brownian Motion)
1 Correlated trait evolution
2 Rate of trait evolution over time
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45. Evolutionary questions thus far
(Brownian Motion)
1 Correlated trait evolution
2 Rate of trait evolution over time
3 Changes in the rate of evolution over time
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46. Evolutionary questions thus far
(Brownian Motion)
1 Correlated trait evolution
2 Rate of trait evolution over time
3 Changes in the rate of evolution over time
4 Differing rates between clades
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47. Wait wait, where’d the selection go?
The Adaptive Landscape of Brownian Motion:
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48. Wait wait, where’d the selection go?
The Adaptive Landscape of Brownian Motion:
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49. OU Model: some selection
Hansen (1997)
Butler & King (2004)
Harmon (2008)
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50. Evolutionary questions thus far
(BM & OU)
1 Correlated trait evolution
2 Rate of trait evolution over time
3 Changes in the rate of evolution over time
4 Differing rates between clades
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51. Evolutionary questions thus far
(BM & OU)
1 Correlated trait evolution
2 Rate of trait evolution over time
3 Changes in the rate of evolution over time
4 Differing rates between clades
5 Strength of stablizing selection
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52. Evolutionary questions thus far
(BM & OU)
1 Correlated trait evolution
2 Rate of trait evolution over time
3 Changes in the rate of evolution over time
4 Differing rates between clades
5 Strength of stablizing selection
6 Peak location of stablizing selection
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53. A closer look at data and model
11 5 4 10
6
5 8 7
0 7.5
Tim e
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54. What’s wrong with this picture?
data
5 8 11
predicted trait
for most of tree
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55. Multiple adaptive peaks: the need for nonlinear models
BM fails to explain clustering
11 5 4 10
6
5 8 7
0 7.5
Tim e
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56. Multiple adaptive peaks: the need for nonlinear models
BM fails to explain clustering
11 5 4 10
6
5 8 7
OU = single peak
0 7.5
Tim e
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57. Multiple adaptive peaks: the need for nonlinear models
BM fails to explain clustering
11 5 4 10
6
5 8 7
OU = single peak
0 7.5
Tim e
Nonlinear selection gradients
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58. Problem: Models with funny sounding physics
names aren’t very biological
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59. Problem: Models with funny sounding physics
names aren’t very biological
Solution: Stop using silly physics models
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60. Introduction: a Story of C. Boettiger and C. Martin
Background of Comparative Methods
Wrightscape: a nonlinear, forward approach
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61. Anoles
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62. Ecomorphs of Anoles
Williams (1969)
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63. Distribution of hind limb sizes of Anoles . . .
22.3
28.4
21.5
21.3
18.7
19.9
18.9
0.06
21.1
18.3
19.7
19.6
18.8
Density
0.04
28.8
28.6
23.6
27.9
27.1
0.02
13.5
14.9
14.5
14.3
14.2
0.00
14.3
10 15 20 25 30 35
N = 23 Bandwidth = 2.278
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64. . . . on the phylogenetic tree
22.3
28.4
21.5
21.3
18.7
19.9
18.9
21.1
18.3
19.7
19.6
18.8
28.8
28.6
23.6
27.9
27.1
13.5
14.9
14.5
14.3
14.2
14.3
0 10 20 30 40
time
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65. exp(-(log(x) - k1)^2/(2 * sigma)) + exp(-(log(x) - k2)^2/(2 *
sigma)) + exp(-(log(x) - k3)^2/(2 * sigma))
Carl Boettiger, UC Davis
0.7 0.8 0.9 1.0
12
15
18
20
x
24 25
Adaptive Landscapes
Inferred landscape: multiple peaks
30
35
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66. Inferred landscape: multiple peaks
exp(-(log(x) - k1)^2/(2 * sigma)) + exp(-(log(x) - k2)^2/(2 *
sigma)) + exp(-(log(x) - k3)^2/(2 * sigma))
0.7 0.8 0.9 1.0
12 15 18 20 24 25 30 35
x
Tree reveals three-peaked adaptive landscape hidden in raw
data
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67. Nonlinear Models and the Forward Approach
How do we do this and why hasn’t it been done yet?
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68. Three loops
1 Simulate on tree many times
L(θ1 , θ2 |x)
BM, OU, peaks,
dXt = f (Xt )dt + g(Xt )dBt
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69. Three loops
1 Simulate on tree many times
generate probability distribution at
each tip
Compare to character trait data of
each tip to generate a likelihood
score for the parameters.
L(θ1 , θ2 |x)
BM, OU, peaks,
dXt = f (Xt )dt + g(Xt )dBt
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70. Three loops
1 Simulate on tree many times
generate probability distribution at
each tip
Compare to character trait data of
each tip to generate a likelihood
score for the parameters.
2 Search over parameters by
simulated annealing with MCMC
L(θ1 , θ2 |x)
BM, OU, peaks,
dXt = f (Xt )dt + g(Xt )dBt
Carl Boettiger, UC Davis Adaptive Landscapes 43/52

71. Three loops
1 Simulate on tree many times
generate probability distribution at
each tip
Compare to character trait data of
each tip to generate a likelihood
score for the parameters.
2 Search over parameters by
simulated annealing with MCMC
L(θ1 , θ2 |x)
3 Search over models: information
criteria
BM, OU, peaks,
dXt = f (Xt )dt + g(Xt )dBt
Carl Boettiger, UC Davis Adaptive Landscapes 43/52

72. Three loops
1 Simulate on tree many times
generate probability distribution at
each tip
Compare to character trait data of
each tip to generate a likelihood
score for the parameters.
2 Search over parameters by
simulated annealing with MCMC
L(θ1 , θ2 |x)
3 Search over models: information
criteria
BM, OU, peaks,
dXt = f (Xt )dt + g(Xt )dBt Computationally demanding?
Carl Boettiger, UC Davis Adaptive Landscapes 43/52

73. Labrids
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74. Fly or Paddle? Fin morphology predicts niche
High aspect ratio: fast
Low aspect ratio: fast turns
sustained swimming
122 species phylogenetic tree with fin aspect ratio and fin angle.
Collar et. al. (2008)
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75. Jaws! Suck or Crush?
Collar et. al. (2008)
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76. morphology predicts niche?
How many peaks? Where? How wide or steep? How deep are
valleys? Transitions between peaks? Emergence of peaks?
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77. _ __ __
_ _______(_)___ _/ /_ / /_______________ _____ ___
| | /| / / ___/ / __ `/ __ / __/ ___/ ___/ __ `/ __ / _
| |/ |/ / / / / /_/ / / / / /_(__ ) /__/ /_/ / /_/ / __/
|__/|__/_/ /_/__, /_/ /_/__/____/___/__,_/ .___/___/
/____/ /_/
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78. _ __ __
_ _______(_)___ _/ /_ / /_______________ _____ ___
| | /| / / ___/ / __ `/ __ / __/ ___/ ___/ __ `/ __ / _
| |/ |/ / / / / /_/ / / / / /_(__ ) /__/ /_/ / /_/ / __/
|__/|__/_/ /_/__, /_/ /_/__/____/___/__,_/ .___/___/
/____/ /_/
Test unique, biologically driven hypotheses
Open Source R package, interface with existing software
and formats
Leadership computing: DOE Teragrid Lincoln (1536
processors, 47.5 TF)
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79. < Extensions >
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80. Bounded Evolution in Adaptive Radiations
Brownian Motion with soft boundaries – a Landscape view:
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81. Species Interactions and Community Phylogenetics
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82. Thanks!
O}-<
Q}-<
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