Download - A new phylogenetic comparative method: detecting niches and transitions with continuous characters
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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
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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
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3.073.062.992.942.933.353.12.982.932.982.913.053.363.353.333.33.162.72.672.652.662.662.6
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Goals
1 Demonstrate selecting models byinformation criteria is inadequate
2 I’ll propose a more robust framework
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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
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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
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Types of models
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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
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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
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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
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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
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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
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Sources of this uncertainty
Small datasetsUninformative topologyModel details (i.e. high rates)
−70 −60 −50 −40 −30 −20
AIC
BM OU.1OU.2OU.3
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Information criteria alone may be misleading
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A Better Way: Comparing Models Directly
Likelihood Ratio
Fre
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−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
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Method
Likelihood Ratio
Fre
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−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)
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Method
Likelihood Ratio
Fre
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−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)
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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)
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BM vs OU.2
Likelihood Ratio
Fre
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−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
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OU.2 vs BM: Simulating under OU.2
Likelihood Ratio
Fre
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−80 −60 −40 −20
050
100
150
p = 0.237
−70 −60 −50 −40 −30 −20
−2 Log Likelihood
BM OU.2
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Model A rejects Model B.Model B doesn’t reject Model A.
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How about two very similar models? BM vs OU.1
Likelihood Ratio
Fre
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0 10 20 30
010
020
030
040
0
p = 0.778
−70 −60 −50 −40 −30 −20
−2 Log Likelihood
BM OU.1
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How would AIC rule compare?
Likelihood Ratio
Fre
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0 10 20 30
010
020
030
040
0AIC
p = 0.779−70 −60 −50 −40 −30 −20
−2 Log Likelihood
BM OU.1
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When data is insufficient to distinguish,method can say “I don’t know”
Carl Boettiger, UC Davis Niches & Transitions 20/35
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Can we distinguish between OU.2 and OU.3?
Likelihood Ratio
Fre
quen
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−80 −60 −40 −20 0 20
050
100
150
200
250
−70 −60 −50 −40 −30 −20
−2 Log Likelihood
OU.2OU.3
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Simulate under OU.2 and compare to OU.3 . . .
Likelihood Ratio
Fre
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−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
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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
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Model A rejects Model B.Model B rejects Model A.
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Non-nested models
t2t1mdmglifeocgmgagbsanulalbbcbnbewawbsnscsepo
t2t1mdmglifeocgmgagbsanulalbbcbnbewawbsnscsepo
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Replacing paintings with a transition model
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All models are nestedEstimate number of nichesAlso estimate rates of transitions
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A hard problem in two easy pieces
P( | ) = P( | )P( | )
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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
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Thanks!
Chris MartinPeter WainwrightSamantha PriceRoi Holzman
Graham CoopPeter RalphAlan HastingsDoE CSGF
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Time
Sta
te
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Time
Sta
te
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Time
Sta
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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
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OU.3 vs OU.4: Why you should mistrust painting trees
Likelihood Ratio
Fre
quen
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−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