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Inferring Adaptive Landscapesfrom Phylogenetic Trees
Carl Boettiger
UC Davis
June 8, 2010
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Introduction: a Story of C. Boettiger and C. Martin
Background of Comparative Methods
Wrightscape: a nonlinear, forward approach
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A Story
Q}-< 04.09 == Q}-< | O}| L- f(x)dx ?
BM OU wtf == | O‘}|L-
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==Q}-<
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______
Q}-<
O}I
L-
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O}
-<
Q}
-< f(x) dt
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O}-<==
______
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`}I
OL-
______
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Introduction: a Story of C. Boettiger and C. Martin
Background of Comparative Methods
Wrightscape: a nonlinear, forward approach
Carl Boettiger, UC Davis Adaptive Landscapes 14/52
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Felsenstein’s question
Is brain size evolutioncorrelated to
body size evolution?
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Natural Selection or Shared Ancestry?
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Natural Selection or Shared Ancestry?
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Correcting for history: Correcting for branch length
Reasons species are similar:
1 Same function – natural selection2 Same ancestors – shared history
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Correcting for history: Correcting for branch length
Reasons species are similar:1 Same function – natural selection
2 Same ancestors – shared history
Carl Boettiger, UC Davis Adaptive Landscapes 17/52
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Correcting for history: Correcting for branch length
Reasons species are similar:1 Same function – natural selection2 Same ancestors – shared history
Carl Boettiger, UC Davis Adaptive Landscapes 17/52
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Correcting for history: Correcting for branch length
Reasons species are similar:1 Same function – natural selection2 Same ancestors – shared history
Carl Boettiger, UC Davis Adaptive Landscapes 17/52
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Expected divergence: unbiased model
0
5
10
Time
TTHTTTTTTH =⇒ −6TTHTTHHHTT =⇒ −2TTHTTHHHTH =⇒ 0
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Expected divergence: unbiased model
0
5
10
Time
TTHTTTTTTH =⇒ −6TTHTTHHHTT =⇒ −2TTHTTHHHTH =⇒ 0
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Expected divergence: unbiased model
0
5
10
Time
TTHTTTTTTH =⇒ −6
TTHTTHHHTT =⇒ −2TTHTTHHHTH =⇒ 0
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Expected divergence: unbiased model
0
5
10
Time
TTHTTTTTTH =⇒ −6TTHTTHHHTT =⇒ −2
TTHTTHHHTH =⇒ 0
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Expected divergence: unbiased model
0
5
10
Time
TTHTTTTTTH =⇒ −6TTHTTHHHTT =⇒ −2TTHTTHHHTH =⇒ 0
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Independent Contrasts
11,6 5,1 4,1 10,5 11,65,14,1 10,5
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Contrasts are differences in independent branches
11,6 5,1 4,1 10,5
Tim e
6
5
0
8,3.5 7,3
Sister taxa = easy contrasts:
11− 5√2
Interior node estimates:
11 + 52
= 8
Another set of contrasts:
8− 7√1 + 2× 5
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Contrasts are differences in independent branches
11,6 5,1 4,1 10,5
Tim e
6
5
0
8,3.5 7,3
Sister taxa = easy contrasts:
11− 5√2
Interior node estimates:
11 + 52
= 8
Another set of contrasts:
8− 7√1 + 2× 5
Carl Boettiger, UC Davis Adaptive Landscapes 20/52
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Contrasts are differences in independent branches
11,6 5,1 4,1 10,5
Tim e
6
5
0
8,3.5 7,3
Sister taxa = easy contrasts:
11− 5√2
Interior node estimates:
11 + 52
= 8
Another set of contrasts:
8− 7√1 + 2× 5
Carl Boettiger, UC Davis Adaptive Landscapes 20/52
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Contrasts are differences in independent branches
11,6 5,1 4,1 10,5
Tim e
6
5
0
8,3.5 7,3
Sister taxa = easy contrasts:
11− 5√2
Interior node estimates:
11 + 52
= 8
Another set of contrasts:
8− 7√1 + 2× 5
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< Watch the focus shift from the data to the model. . . >
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Estimating ancestral states and rates of change
11,6 5,1 4,1 10,5
Tim e
6
5
0 (7.5,3.75) ?
(8, 3.5) (7, 3)
Schluter et. al. (1997)
Expected ancestral states:intermediate trait values
Expected rate of change:matching the toss rate
Also estimates uncertainty
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Estimating ancestral states and rates of change
11,6 5,1 4,1 10,5
Tim e
6
5
0 (7.5,3.75) ?
(8, 3.5) (7, 3)
Schluter et. al. (1997)
Expected ancestral states:intermediate trait values
Expected rate of change:matching the toss rate
Also estimates uncertainty
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Estimating ancestral states and rates of change
11,6 5,1 4,1 10,5
Tim e
6
5
0 (7.5,3.75) ?
(8, 3.5) (7, 3)
Schluter et. al. (1997)
Expected ancestral states:intermediate trait values
Expected rate of change:matching the toss rate
Also estimates uncertainty
Carl Boettiger, UC Davis Adaptive Landscapes 22/52
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Estimating ancestral states and rates of change
11,6 5,1 4,1 10,5
Tim e
6
5
0 (7.5,3.75) ?
(8, 3.5) (7, 3)
Schluter et. al. (1997)
Expected ancestral states:intermediate trait values
Expected rate of change:matching the toss rate
Also estimates uncertainty
Carl Boettiger, UC Davis Adaptive Landscapes 22/52
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Changing Rates and Adaptive Radiations?
11,6 5,1 4,1 10,5
Tim e
6
5
0 (7.5,3.75) ?
(8, 3.5) (7, 3)
Freckleton & Harvey (2006)
Evidence that therates of evolutionare accelerating?
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< Are we taking the model too seriously? >
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Differing rates between clades?
29 2111
O’Meara et. al. (2006)
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Differing rates between clades?
29 2111
O’Meara et. al. (2006)
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Differing rates between clades?
29 2111
O’Meara et. al. (2006)
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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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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
Carl Boettiger, UC Davis Adaptive Landscapes 28/52
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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
Carl Boettiger, UC Davis Adaptive Landscapes 28/52
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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
Carl Boettiger, UC Davis Adaptive Landscapes 28/52
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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
Carl Boettiger, UC Davis Adaptive Landscapes 28/52
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Wait wait, where’d the selection go?
The Adaptive Landscape of Brownian Motion:
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Wait wait, where’d the selection go?
The Adaptive Landscape of Brownian Motion:
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OU Model: some selection
Hansen (1997)Butler & King (2004)Harmon (2008)
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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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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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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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A closer look at data and model
11 10
Tim e
6
5
0
8 7
7.5
5 4
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What’s wrong with this picture?
data
5 8 11predicted trait for most of tree
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Multiple adaptive peaks: the need for nonlinear models
11 10
Tim e
6
5
0
8 7
7.5
5 4
BM fails to explain clustering
OU = single peak
Nonlinear selection gradients
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Multiple adaptive peaks: the need for nonlinear models
11 10
Tim e
6
5
0
8 7
7.5
5 4
BM fails to explain clustering
OU = single peak
Nonlinear selection gradients
Carl Boettiger, UC Davis Adaptive Landscapes 34/52
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Multiple adaptive peaks: the need for nonlinear models
11 10
Tim e
6
5
0
8 7
7.5
5 4
BM fails to explain clustering
OU = single peak
Nonlinear selection gradients
Carl Boettiger, UC Davis Adaptive Landscapes 34/52
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Problem: Models with funny sounding physicsnames aren’t very biological
Solution: Stop using silly physics models
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Problem: Models with funny sounding physicsnames aren’t very biological
Solution: Stop using silly physics models
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Introduction: a Story of C. Boettiger and C. Martin
Background of Comparative Methods
Wrightscape: a nonlinear, forward approach
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Anoles
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Ecomorphs of Anoles
Williams (1969)
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Distribution of hind limb sizes of Anoles . . .
10 15 20 25 30 35
0.0
00
.02
0.0
40
.06
N = 23 Bandwidth = 2.278
De
nsi
ty
10 15 20 25 30 35
13.5
14.3
14.3
14.2
14.514.9
23.6
27.1
27.9
28.628.8
21.118.319.7
18.8
19.6
22.328.4
18.7
18.9
19.9
21.3
21.5
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. . . on the phylogenetic tree
0 10 20 30 40
time
13.5
14.3
14.3
14.2
14.514.9
23.6
27.1
27.9
28.628.8
21.118.319.7
18.8
19.6
22.328.4
18.7
18.9
19.9
21.3
21.5
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Inferred landscape: multiple peaks
15 20 25 30 35
0.7
0.8
0.9
1.0
x
exp
(-(log(x
) -
k1)^
2/(
2 *
sig
ma))
+ e
xp(-
(log(x
) -
k2)^
2/(
2 *
si
gm
a))
+ e
xp(-
(log(x
) -
k3)^
2/(
2 *
sig
ma))
12 18 24 30
Tree reveals three-peaked adaptive landscape hidden in rawdata
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Inferred landscape: multiple peaks
15 20 25 30 35
0.7
0.8
0.9
1.0
x
exp
(-(log(x
) -
k1)^
2/(
2 *
sig
ma))
+ e
xp(-
(log(x
) -
k2)^
2/(
2 *
si
gm
a))
+ e
xp(-
(log(x
) -
k3)^
2/(
2 *
sig
ma))
12 18 24 30
Tree reveals three-peaked adaptive landscape hidden in rawdata
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Nonlinear Models and the Forward Approach
How do we do this and why hasn’t it been done yet?
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Three loops
L(θ1, θ2|~x)
BM, OU, peaks,dXt = f (Xt)dt + g(Xt)dBt
1 Simulate on tree many times
generate probability distribution ateach tipCompare to character trait data ofeach tip to generate a likelihoodscore for the parameters.
2 Search over parameters bysimulated annealing with MCMC
3 Search over models: informationcriteria
Computationally demanding?
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Three loops
L(θ1, θ2|~x)
BM, OU, peaks,dXt = f (Xt)dt + g(Xt)dBt
1 Simulate on tree many timesgenerate probability distribution ateach tipCompare to character trait data ofeach tip to generate a likelihoodscore for the parameters.
2 Search over parameters bysimulated annealing with MCMC
3 Search over models: informationcriteria
Computationally demanding?
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Three loops
L(θ1, θ2|~x)
BM, OU, peaks,dXt = f (Xt)dt + g(Xt)dBt
1 Simulate on tree many timesgenerate probability distribution ateach tipCompare to character trait data ofeach tip to generate a likelihoodscore for the parameters.
2 Search over parameters bysimulated annealing with MCMC
3 Search over models: informationcriteria
Computationally demanding?
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Three loops
L(θ1, θ2|~x)
BM, OU, peaks,dXt = f (Xt)dt + g(Xt)dBt
1 Simulate on tree many timesgenerate probability distribution ateach tipCompare to character trait data ofeach tip to generate a likelihoodscore for the parameters.
2 Search over parameters bysimulated annealing with MCMC
3 Search over models: informationcriteria
Computationally demanding?
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Three loops
L(θ1, θ2|~x)
BM, OU, peaks,dXt = f (Xt)dt + g(Xt)dBt
1 Simulate on tree many timesgenerate probability distribution ateach tipCompare to character trait data ofeach tip to generate a likelihoodscore for the parameters.
2 Search over parameters bysimulated annealing with MCMC
3 Search over models: informationcriteria
Computationally demanding?
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Labrids
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Fly or Paddle? Fin morphology predicts niche
Low aspect ratio: fast turnsHigh aspect ratio: fastsustained swimming
122 species phylogenetic tree with fin aspect ratio and fin angle.
Collar et. al. (2008)
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Jaws! Suck or Crush?
Collar et. al. (2008)
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morphology predicts niche?
How many peaks? Where? How wide or steep? How deep arevalleys? Transitions between peaks? Emergence of peaks?
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_ __ __ _ _______(_)___ _/ /_ / /_______________ _____ ___ | | /| / / ___/ / __ `/ __ \/ __/ ___/ ___/ __ `/ __ \/ _ \| |/ |/ / / / / /_/ / / / / /_(__ ) /__/ /_/ / /_/ / __/|__/|__/_/ /_/\__, /_/ /_/\__/____/\___/\__,_/ .___/\___/ /____/ /_/
Test unique, biologically driven hypothesesOpen Source R package, interface with existing softwareand formatsLeadership computing: DOE Teragrid Lincoln (1536processors, 47.5 TF)
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_ __ __ _ _______(_)___ _/ /_ / /_______________ _____ ___ | | /| / / ___/ / __ `/ __ \/ __/ ___/ ___/ __ `/ __ \/ _ \| |/ |/ / / / / /_/ / / / / /_(__ ) /__/ /_/ / /_/ / __/|__/|__/_/ /_/\__, /_/ /_/\__/____/\___/\__,_/ .___/\___/ /____/ /_/
Test unique, biologically driven hypothesesOpen Source R package, interface with existing softwareand formatsLeadership computing: DOE Teragrid Lincoln (1536processors, 47.5 TF)
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< Extensions >
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Bounded Evolution in Adaptive Radiations
Brownian Motion with soft boundaries – a Landscape view:
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Species Interactions and Community Phylogenetics
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Thanks!
O}-<
Q}-<
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