a new phylogenetic comparative method: detecting niches and transitions with continuous characters
DESCRIPTION
Talk given at the annual Evolution meeting in Portland, Oregon, June 26thTRANSCRIPT
A new phylogenetic comparative method:detecting niches and transitions with
continuous characters.
Carl Boettiger
UC Davis
June 26, 2010
Carl Boettiger, UC Davis Niches & Transitions 1/35
Size in Lesser Antilles Anoles
Log Body Size
Fre
quen
cy
2.6 2.8 3.0 3.2 3.4
01
23
45
67
Carl Boettiger, UC Davis Niches & Transitions 2/35
3.073.062.992.942.933.353.12.982.932.982.913.053.363.353.333.33.162.72.672.652.662.662.6
Carl Boettiger, UC Davis Niches & Transitions 3/35
Goals
1 Demonstrate selecting models byinformation criteria is inadequate
2 I’ll propose a more robust framework
Carl Boettiger, UC Davis Niches & Transitions 4/35
Goals
1 Demonstrate selecting models byinformation criteria is inadequate
2 I’ll propose a more robust framework
Carl Boettiger, UC Davis Niches & Transitions 4/35
Goals
1 Demonstrate selecting models byinformation criteria is inadequate
2 I’ll propose a more robust framework
Carl Boettiger, UC Davis Niches & Transitions 4/35
Types of models
Carl Boettiger, UC Davis Niches & Transitions 5/35
Comparing Models
t2
t1
md
mgli
fe
oc
gm
gagb
sa
nula
lb
bc
bn
be
wawb
sn
sc
se
po
t2
t1
md
mgli
fe
oc
gm
gagb
sa
nula
lb
bc
bn
be
wawb
sn
sc
se
po
t2
t1
md
mgli
fe
oc
gm
gagb
sa
nula
lb
bc
bn
be
wawb
sn
sc
se
po
Carl Boettiger, UC Davis Niches & Transitions 6/35
Comparing Models
−70 −60 −50 −40 −30 −20
−2 Log Likelihood
BM OU.1OU.2OU.3
( Better Scores)Carl Boettiger, UC Davis Niches & Transitions 7/35
Comparing Models: AIC
−70 −60 −50 −40 −30 −20
AIC
BM OU.1OU.2OU.3
( Better Scores)Carl Boettiger, UC Davis Niches & Transitions 8/35
Comparing Models: Estimating Uncertainty
−70 −60 −50 −40 −30 −20
AIC
BM OU.1OU.2OU.3
( Better Scores)Carl Boettiger, UC Davis Niches & Transitions 9/35
Comparing Models: Uncertainty dominates
−70 −60 −50 −40 −30 −20
AIC
BM OU.1OU.2OU.3
( Better Scores)Carl Boettiger, UC Davis Niches & Transitions 10/35
Sources of this uncertainty
Small datasetsUninformative topologyModel details (i.e. high rates)
−70 −60 −50 −40 −30 −20
AIC
BM OU.1OU.2OU.3
Carl Boettiger, UC Davis Niches & Transitions 11/35
Information criteria alone may be misleading
Carl Boettiger, UC Davis Niches & Transitions 12/35
A Better Way: Comparing Models Directly
Likelihood Ratio
Fre
quen
cy
−10 0 10 20 30 40 50
050
100
150
200
250
300
−2 logL(BM)
L(OU.2)
−70 −60 −50 −40 −30 −20
−2 Log Likelihood
BM OU.2
Carl Boettiger, UC Davis Niches & Transitions 13/35
Method
Likelihood Ratio
Fre
quen
cy
−10 0 10 20 30 40 50
050
100
150
200
250
300
−70 −60 −50 −40 −30 −20
−2 Log Likelihood
BM OU.2
1 Simulate many datasetsunder model A
2 Re-fit both A & B to eachsimulated dataset
3 Write log Likelihood(A) -log Likelihood(B)
Carl Boettiger, UC Davis Niches & Transitions 14/35
Method
Likelihood Ratio
Fre
quen
cy
−10 0 10 20 30 40 50
050
100
150
200
250
300
−70 −60 −50 −40 −30 −20
−2 Log Likelihood
BM OU.2
1 Simulate many datasetsunder model A
2 Re-fit both A & B to eachsimulated dataset
3 Write log Likelihood(A) -log Likelihood(B)
Carl Boettiger, UC Davis Niches & Transitions 14/35
Method
Likelihood Ratio
Fre
quen
cy
−10 0 10 20 30 40 50
050
100
150
200
250
300
−70 −60 −50 −40 −30 −20
−2 Log Likelihood
BM OU.2
1 Simulate many datasetsunder model A
2 Re-fit both A & B to eachsimulated dataset
3 Write log Likelihood(A) -log Likelihood(B)
Carl Boettiger, UC Davis Niches & Transitions 14/35
BM vs OU.2
Likelihood Ratio
Fre
quen
cy
−10 0 10 20 30 40 50
050
100
150
200
250
300
p = 0.002
−70 −60 −50 −40 −30 −20
−2 Log Likelihood
BM OU.2
Carl Boettiger, UC Davis Niches & Transitions 15/35
OU.2 vs BM: Simulating under OU.2
Likelihood Ratio
Fre
quen
cy
−80 −60 −40 −20
050
100
150
p = 0.237
−70 −60 −50 −40 −30 −20
−2 Log Likelihood
BM OU.2
Carl Boettiger, UC Davis Niches & Transitions 16/35
Model A rejects Model B.Model B doesn’t reject Model A.
Carl Boettiger, UC Davis Niches & Transitions 17/35
How about two very similar models? BM vs OU.1
Likelihood Ratio
Fre
quen
cy
0 10 20 30
010
020
030
040
0
p = 0.778
−70 −60 −50 −40 −30 −20
−2 Log Likelihood
BM OU.1
Carl Boettiger, UC Davis Niches & Transitions 18/35
How would AIC rule compare?
Likelihood Ratio
Fre
quen
cy
0 10 20 30
010
020
030
040
0AIC
p = 0.779−70 −60 −50 −40 −30 −20
−2 Log Likelihood
BM OU.1
Carl Boettiger, UC Davis Niches & Transitions 19/35
When data is insufficient to distinguish,method can say “I don’t know”
Carl Boettiger, UC Davis Niches & Transitions 20/35
Can we distinguish between OU.2 and OU.3?
Likelihood Ratio
Fre
quen
cy
−80 −60 −40 −20 0 20
050
100
150
200
250
−70 −60 −50 −40 −30 −20
−2 Log Likelihood
OU.2OU.3
Carl Boettiger, UC Davis Niches & Transitions 21/35
Simulate under OU.2 and compare to OU.3 . . .
Likelihood Ratio
Fre
quen
cy
−80 −60 −40 −20 0 20
050
100
150
200
250
p = 0.051
−70 −60 −50 −40 −30 −20
−2 Log Likelihood
OU.2OU.3
Carl Boettiger, UC Davis Niches & Transitions 22/35
OU.3 vs OU.2: Now we’re preferring OU.2!
Likelihood Ratio
Fre
quen
cy
−60 −40 −20 0 20
050
100
150
200
250
300
350
p = 0.003
−70 −60 −50 −40 −30 −20
−2 Log Likelihood
OU.2OU.3
Carl Boettiger, UC Davis Niches & Transitions 23/35
Model A rejects Model B.Model B rejects Model A.
Carl Boettiger, UC Davis Niches & Transitions 24/35
Non-nested models
t2t1mdmglifeocgmgagbsanulalbbcbnbewawbsnscsepo
t2t1mdmglifeocgmgagbsanulalbbcbnbewawbsnscsepo
Carl Boettiger, UC Davis Niches & Transitions 25/35
Replacing paintings with a transition model
Carl Boettiger, UC Davis Niches & Transitions 26/35
All models are nestedEstimate number of nichesAlso estimate rates of transitions
Carl Boettiger, UC Davis Niches & Transitions 27/35
A hard problem in two easy pieces
P( | ) = P( | )P( | )
Carl Boettiger, UC Davis Niches & Transitions 28/35
Summary
1 Quantifiable, robust model choiceLikelihood Ratio
Fre
quen
cy
−10 0 10 20 30 40 50
050
100
150
200
250
300
p = 0.002
2 Identify when data is insufficientLikelihood Ratio
Fre
quen
cy
0 10 20 30
010
020
030
040
0
p = 0.778
3 New framework avoids painting &non-nested comparison
Carl Boettiger, UC Davis Niches & Transitions 29/35
Thanks!
Chris MartinPeter WainwrightSamantha PriceRoi Holzman
Graham CoopPeter RalphAlan HastingsDoE CSGF
Carl Boettiger, UC Davis Niches & Transitions 30/35
Time
Sta
te
Carl Boettiger, UC Davis Niches & Transitions 31/35
Time
Sta
te
Carl Boettiger, UC Davis Niches & Transitions 32/35
Time
Sta
te
Carl Boettiger, UC Davis Niches & Transitions 33/35
Comparing Models
t2
t1
md
mgli
fe
oc
gm
gagb
sa
nula
lb
bc
bn
be
wawb
sn
sc
se
po
t2
t1
md
mgli
fe
oc
gm
gagb
sa
nula
lb
bc
bn
be
wawb
sn
sc
se
po
t2
t1
md
mgli
fe
oc
gm
gagb
sa
nula
lb
bc
bn
be
wawb
sn
sc
se
po
Carl Boettiger, UC Davis Niches & Transitions 34/35
OU.3 vs OU.4: Why you should mistrust painting trees
Likelihood Ratio
Fre
quen
cy
−50 0 50 100
050
100
150
200
250
300
350
p = 0
−120 −100 −80 −60 −40 −20
−2 Log Likelihood
OU.3OU.4
Carl Boettiger, UC Davis Niches & Transitions 35/35