Post on 11-May-2015
description
Inferring Adaptive Landscapesfrom Phylogenetic Trees
Carl Boettiger
UC Davis
June 8, 2010
Carl Boettiger, UC Davis Adaptive Landscapes 1/52
Introduction: a Story of C. Boettiger and C. Martin
Background of Comparative Methods
Wrightscape: a nonlinear, forward approach
Carl Boettiger, UC Davis Adaptive Landscapes 2/52
A Story
Q}-< 04.09 == Q}-< | O}| L- f(x)dx ?
BM OU wtf == | O‘}|L-
Carl Boettiger, UC Davis Adaptive Landscapes 3/52
Carl Boettiger, UC Davis Adaptive Landscapes 4/52
==Q}-<
Carl Boettiger, UC Davis Adaptive Landscapes 5/52
______
Q}-<
O}I
L-
Carl Boettiger, UC Davis Adaptive Landscapes 6/52
Carl Boettiger, UC Davis Adaptive Landscapes 7/52
Carl Boettiger, UC Davis Adaptive Landscapes 8/52
O}
-<
Q}
-< f(x) dt
Carl Boettiger, UC Davis Adaptive Landscapes 9/52
Carl Boettiger, UC Davis Adaptive Landscapes 10/52
?Carl Boettiger, UC Davis Adaptive Landscapes 11/52
O}-<==
______
Carl Boettiger, UC Davis Adaptive Landscapes 12/52
`}I
OL-
______
Carl Boettiger, UC Davis Adaptive Landscapes 13/52
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
Felsenstein’s question
Is brain size evolutioncorrelated to
body size evolution?
Carl Boettiger, UC Davis Adaptive Landscapes 15/52
Natural Selection or Shared Ancestry?
Carl Boettiger, UC Davis Adaptive Landscapes 16/52
Natural Selection or Shared Ancestry?
Carl Boettiger, UC Davis Adaptive Landscapes 16/52
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
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
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
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
Expected divergence: unbiased model
0
5
10
Time
TTHTTTTTTH =⇒ −6TTHTTHHHTT =⇒ −2TTHTTHHHTH =⇒ 0
Carl Boettiger, UC Davis Adaptive Landscapes 18/52
Expected divergence: unbiased model
0
5
10
Time
TTHTTTTTTH =⇒ −6TTHTTHHHTT =⇒ −2TTHTTHHHTH =⇒ 0
Carl Boettiger, UC Davis Adaptive Landscapes 18/52
Expected divergence: unbiased model
0
5
10
Time
TTHTTTTTTH =⇒ −6
TTHTTHHHTT =⇒ −2TTHTTHHHTH =⇒ 0
Carl Boettiger, UC Davis Adaptive Landscapes 18/52
Expected divergence: unbiased model
0
5
10
Time
TTHTTTTTTH =⇒ −6TTHTTHHHTT =⇒ −2
TTHTTHHHTH =⇒ 0
Carl Boettiger, UC Davis Adaptive Landscapes 18/52
Expected divergence: unbiased model
0
5
10
Time
TTHTTTTTTH =⇒ −6TTHTTHHHTT =⇒ −2TTHTTHHHTH =⇒ 0
Carl Boettiger, UC Davis Adaptive Landscapes 18/52
Independent Contrasts
11,6 5,1 4,1 10,5 11,65,14,1 10,5
Carl Boettiger, UC Davis Adaptive Landscapes 19/52
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
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
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
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
< Watch the focus shift from the data to the model. . . >
Carl Boettiger, UC Davis Adaptive Landscapes 21/52
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
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
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
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
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?
Carl Boettiger, UC Davis Adaptive Landscapes 23/52
< Are we taking the model too seriously? >
Carl Boettiger, UC Davis Adaptive Landscapes 24/52
Differing rates between clades?
29 2111
O’Meara et. al. (2006)
Carl Boettiger, UC Davis Adaptive Landscapes 25/52
Differing rates between clades?
29 2111
O’Meara et. al. (2006)
Carl Boettiger, UC Davis Adaptive Landscapes 26/52
Differing rates between clades?
29 2111
O’Meara et. al. (2006)
Carl Boettiger, UC Davis Adaptive Landscapes 27/52
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
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
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
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
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
Wait wait, where’d the selection go?
The Adaptive Landscape of Brownian Motion:
Carl Boettiger, UC Davis Adaptive Landscapes 29/52
Wait wait, where’d the selection go?
The Adaptive Landscape of Brownian Motion:
Carl Boettiger, UC Davis Adaptive Landscapes 29/52
OU Model: some selection
Hansen (1997)Butler & King (2004)Harmon (2008)
Carl Boettiger, UC Davis Adaptive Landscapes 30/52
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
Carl Boettiger, UC Davis Adaptive Landscapes 31/52
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
Carl Boettiger, UC Davis Adaptive Landscapes 31/52
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
Carl Boettiger, UC Davis Adaptive Landscapes 31/52
A closer look at data and model
11 10
Tim e
6
5
0
8 7
7.5
5 4
Carl Boettiger, UC Davis Adaptive Landscapes 32/52
What’s wrong with this picture?
data
5 8 11predicted trait for most of tree
Carl Boettiger, UC Davis Adaptive Landscapes 33/52
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
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
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
Problem: Models with funny sounding physicsnames aren’t very biological
Solution: Stop using silly physics models
Carl Boettiger, UC Davis Adaptive Landscapes 35/52
Problem: Models with funny sounding physicsnames aren’t very biological
Solution: Stop using silly physics models
Carl Boettiger, UC Davis Adaptive Landscapes 35/52
Introduction: a Story of C. Boettiger and C. Martin
Background of Comparative Methods
Wrightscape: a nonlinear, forward approach
Carl Boettiger, UC Davis Adaptive Landscapes 36/52
Anoles
Carl Boettiger, UC Davis Adaptive Landscapes 37/52
Ecomorphs of Anoles
Williams (1969)
Carl Boettiger, UC Davis Adaptive Landscapes 38/52
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
Carl Boettiger, UC Davis Adaptive Landscapes 39/52
. . . 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
Carl Boettiger, UC Davis Adaptive Landscapes 40/52
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
Carl Boettiger, UC Davis Adaptive Landscapes 41/52
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
Carl Boettiger, UC Davis Adaptive Landscapes 41/52
Nonlinear Models and the Forward Approach
How do we do this and why hasn’t it been done yet?
Carl Boettiger, UC Davis Adaptive Landscapes 42/52
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?
Carl Boettiger, UC Davis Adaptive Landscapes 43/52
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?
Carl Boettiger, UC Davis Adaptive Landscapes 43/52
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?
Carl Boettiger, UC Davis Adaptive Landscapes 43/52
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?
Carl Boettiger, UC Davis Adaptive Landscapes 43/52
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?
Carl Boettiger, UC Davis Adaptive Landscapes 43/52
Labrids
Carl Boettiger, UC Davis Adaptive Landscapes 44/52
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)
Carl Boettiger, UC Davis Adaptive Landscapes 45/52
Jaws! Suck or Crush?
Collar et. al. (2008)
Carl Boettiger, UC Davis Adaptive Landscapes 46/52
morphology predicts niche?
How many peaks? Where? How wide or steep? How deep arevalleys? Transitions between peaks? Emergence of peaks?
Carl Boettiger, UC Davis Adaptive Landscapes 47/52
_ __ __ _ _______(_)___ _/ /_ / /_______________ _____ ___ | | /| / / ___/ / __ `/ __ \/ __/ ___/ ___/ __ `/ __ \/ _ \| |/ |/ / / / / /_/ / / / / /_(__ ) /__/ /_/ / /_/ / __/|__/|__/_/ /_/\__, /_/ /_/\__/____/\___/\__,_/ .___/\___/ /____/ /_/
Test unique, biologically driven hypothesesOpen Source R package, interface with existing softwareand formatsLeadership computing: DOE Teragrid Lincoln (1536processors, 47.5 TF)
Carl Boettiger, UC Davis Adaptive Landscapes 48/52
_ __ __ _ _______(_)___ _/ /_ / /_______________ _____ ___ | | /| / / ___/ / __ `/ __ \/ __/ ___/ ___/ __ `/ __ \/ _ \| |/ |/ / / / / /_/ / / / / /_(__ ) /__/ /_/ / /_/ / __/|__/|__/_/ /_/\__, /_/ /_/\__/____/\___/\__,_/ .___/\___/ /____/ /_/
Test unique, biologically driven hypothesesOpen Source R package, interface with existing softwareand formatsLeadership computing: DOE Teragrid Lincoln (1536processors, 47.5 TF)
Carl Boettiger, UC Davis Adaptive Landscapes 48/52
< Extensions >
Carl Boettiger, UC Davis Adaptive Landscapes 49/52
Bounded Evolution in Adaptive Radiations
Brownian Motion with soft boundaries – a Landscape view:
Carl Boettiger, UC Davis Adaptive Landscapes 50/52
Species Interactions and Community Phylogenetics
Carl Boettiger, UC Davis Adaptive Landscapes 51/52
Thanks!
O}-<
Q}-<
Carl Boettiger, UC Davis Adaptive Landscapes 52/52