Inferring Adaptive Landscapes from Phylogenetic Trees

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


A Story

Q}-< 04.09 == Q}-< | O}| L- f(x)dx ?

BM OU wtf == | O‘}|L-



==Q}-<


______

Q}-<

O}I

L-




O}

-<

Q}

-< f(x) dt



?Carl Boettiger, UC Davis Adaptive Landscapes 11/52

O}-<==

______


`}I

OL-

______






Felsenstein’s question

Is brain size evolutioncorrelated to

body size evolution?


Natural Selection or Shared Ancestry?


Natural Selection or Shared Ancestry?


Correcting for history: Correcting for branch length

Reasons species are similar:

1 Same function – natural selection2 Same ancestors – shared history



Reasons species are similar:1 Same function – natural selection

2 Same ancestors – shared history



Reasons species are similar:1 Same function – natural selection2 Same ancestors – shared history



Reasons species are similar:1 Same function – natural selection2 Same ancestors – shared history


Expected divergence: unbiased model

0

5

10

Time

TTHTTTTTTH =⇒ −6TTHTTHHHTT =⇒ −2TTHTTHHHTH =⇒ 0



0

5

10

Time




0

5

10

Time

TTHTTTTTTH =⇒ −6

TTHTTHHHTT =⇒ −2TTHTTHHHTH =⇒ 0



0

5

10

Time

TTHTTTTTTH =⇒ −6TTHTTHHHTT =⇒ −2

TTHTTHHHTH =⇒ 0



0

5

10

Time



Independent Contrasts

11,6 5,1 4,1 10,5 11,65,14,1 10,5


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



11,6 5,1 4,1 10,5

Tim e

6

5

0

8,3.5 7,3


11− 5√2


11 + 52

= 8


8− 7√1 + 2× 5



11,6 5,1 4,1 10,5

Tim e

6

5

0

8,3.5 7,3


11− 5√2


11 + 52

= 8


8− 7√1 + 2× 5



11,6 5,1 4,1 10,5

Tim e

6

5

0

8,3.5 7,3


11− 5√2


11 + 52

= 8


8− 7√1 + 2× 5


< Watch the focus shift from the data to the model. . . >


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



11,6 5,1 4,1 10,5

Tim e

6

5

0 (7.5,3.75) ?

(8, 3.5) (7, 3)







11,6 5,1 4,1 10,5

Tim e

6

5

0 (7.5,3.75) ?

(8, 3.5) (7, 3)







11,6 5,1 4,1 10,5

Tim e

6

5

0 (7.5,3.75) ?

(8, 3.5) (7, 3)






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?


< Are we taking the model too seriously? >


Differing rates between clades?

29 2111

O’Meara et. al. (2006)



29 2111




29 2111



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


























Wait wait, where’d the selection go?

The Adaptive Landscape of Brownian Motion:


Wait wait, where’d the selection go?

The Adaptive Landscape of Brownian Motion:


OU Model: some selection

Hansen (1997)Butler & King (2004)Harmon (2008)


Evolutionary questions thus far(BM & OU)





5 Strength of stablizing selection

6 Peak location of stablizing selection


















A closer look at data and model

11 10

Tim e

6

5

0

8 7

7.5

5 4


What’s wrong with this picture?

data

5 8 11predicted trait for most of tree


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



11 10

Tim e

6

5

0

8 7

7.5

5 4


OU = single peak




11 10

Tim e

6

5

0

8 7

7.5

5 4


OU = single peak



Problem: Models with funny sounding physicsnames aren’t very biological

Solution: Stop using silly physics models


Problem: Models with funny sounding physicsnames aren’t very biological

Solution: Stop using silly physics models






Anoles


Ecomorphs of Anoles

Williams (1969)


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


. . . 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


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


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


Nonlinear Models and the Forward Approach

How do we do this and why hasn’t it been done yet?


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?


Three loops

L(θ1, θ2|~x)


1 Simulate on tree many timesgenerate probability distribution ateach tipCompare to character trait data ofeach tip to generate a likelihoodscore for the parameters.





Three loops

L(θ1, θ2|~x)







Three loops

L(θ1, θ2|~x)







Three loops

L(θ1, θ2|~x)







Labrids


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)


Jaws! Suck or Crush?

Collar et. al. (2008)


morphology predicts niche?

How many peaks? Where? How wide or steep? How deep arevalleys? Transitions between peaks? Emergence of peaks?


_ __ __ _ _______(_)___ _/ /_ / /_______________ _____ ___ | | /| / / ___/ / __ `/ __ \/ __/ ___/ ___/ __ `/ __ \/ _ \| |/ |/ / / / / /_/ / / / / /_(__ ) /__/ /_/ / /_/ / __/|__/|__/_/ /_/\__, /_/ /_/\__/____/\___/\__,_/ .___/\___/ /____/ /_/

Test unique, biologically driven hypothesesOpen Source R package, interface with existing softwareand formatsLeadership computing: DOE Teragrid Lincoln (1536processors, 47.5 TF)


_ __ __ _ _______(_)___ _/ /_ / /_______________ _____ ___ | | /| / / ___/ / __ `/ __ \/ __/ ___/ ___/ __ `/ __ \/ _ \| |/ |/ / / / / /_/ / / / / /_(__ ) /__/ /_/ / /_/ / __/|__/|__/_/ /_/\__, /_/ /_/\__/____/\___/\__,_/ .___/\___/ /____/ /_/

Test unique, biologically driven hypothesesOpen Source R package, interface with existing softwareand formatsLeadership computing: DOE Teragrid Lincoln (1536processors, 47.5 TF)


< Extensions >


Bounded Evolution in Adaptive Radiations

Brownian Motion with soft boundaries – a Landscape view:


Species Interactions and Community Phylogenetics


Thanks!

O}-<

Q}-<


Inferring Adaptive Landscapes from Phylogenetic Trees

Education

sigma carl boettiger

clades carl boettiger

time carl boettiger

anoles carl boettiger

biological carl boettiger

tree carl boettiger

brownian motion carl

tim e carl boettiger