A new phylogenetic comparative method: detecting niches and transitions with continuous characters
Nature Precedings (2010)
- ISSN: 17560357
- DOI: 10.1038/npre.2010.4615
Available from
Carl Boettiger's profile on Mendeley.
or
Available from
Carl Boettiger's profile on Mendeley.
Page 1
A new phylogenetic comparative method: detecting niches and transitions with continuous characters
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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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
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2.6 2.8 3.0 3.2 3.4
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Log Body Size
Fre
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2.6 2.8 3.0 3.2 3.4
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Goals
1 Demonstrate selecting models by
information criteria is inadequate
2 I’ll propose a more robust framework
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1 Demonstrate selecting models by
information 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 by
information criteria is inadequate
2 I’ll propose a more robust framework
Carl Boettiger, UC Davis Niches & Transitions 4/35
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1 Demonstrate selecting models by
information 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 by
information criteria is inadequate
2 I’ll propose a more robust framework
Carl Boettiger, UC Davis Niches & Transitions 4/35
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1 Demonstrate selecting models by
information 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
t2t1
md
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t2t1
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gmga
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lalb
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bewa
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t2t1
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gmga
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t2t1
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gmga
gbsa
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bewa
wbsn
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t2t1
md
mgli
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gmga
gbsa
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lalb
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bewa
wbsn
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t2t1
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gmga
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Comparing Models
−70 −60 −50 −40 −30 −20
−2 Log Likelihood
BM OU.1OU.2OU.3
( Better Scores)
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−2 Log Likelihood
BM OU.1OU.2OU.3
( Better Scores)
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Comparing Models: AIC
−70 −60 −50 −40 −30 −20AIC
BM OU.1OU.2OU.3
( Better Scores)
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−70 −60 −50 −40 −30 −20AIC
BM OU.1OU.2OU.3
( Better Scores)
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Comparing Models: Estimating Uncertainty
−70 −60 −50 −40 −30 −20AIC
BM OU.1OU.2OU.3
( Better Scores)
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BM OU.1OU.2OU.3
( Better Scores)
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Comparing Models: Uncertainty dominates
−70 −60 −50 −40 −30 −20AIC
BM OU.1OU.2OU.3
( Better Scores)
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( Better Scores)
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Sources of this uncertainty
Small datasets
Uninformative topology
Model details (i.e. high rates)
−70 −60 −50 −40 −30 −20AIC
BM OU.1OU.2OU.3
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Small datasets
Uninformative topology
Model details (i.e. high rates)
−70 −60 −50 −40 −30 −20AIC
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
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Method
Likelihood Ratio
Fre
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50
100
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−70 −60 −50 −40 −30 −20
−2 Log Likelihood
BM OU.2
1 Simulate many datasets
under model A
2 Re-fit both A & B to each
simulated dataset
3 Write log Likelihood(A) -
log Likelihood(B)
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Fre
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−70 −60 −50 −40 −30 −20
−2 Log Likelihood
BM OU.2
1 Simulate many datasets
under model A
2 Re-fit both A & B to each
simulated 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
0
50
100
150
200
250
300
−70 −60 −50 −40 −30 −20
−2 Log Likelihood
BM OU.2
1 Simulate many datasets
under model A
2 Re-fit both A & B to each
simulated dataset
3 Write log Likelihood(A) -
log Likelihood(B)
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Likelihood Ratio
Fre
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−10 0 10 20 30 40 50
0
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100
150
200
250
300
−70 −60 −50 −40 −30 −20
−2 Log Likelihood
BM OU.2
1 Simulate many datasets
under model A
2 Re-fit both A & B to each
simulated 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
0
50
100
150
200
250
300
−70 −60 −50 −40 −30 −20
−2 Log Likelihood
BM OU.2
1 Simulate many datasets
under model A
2 Re-fit both A & B to each
simulated dataset
3 Write log Likelihood(A) -
log Likelihood(B)
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Likelihood Ratio
Fre
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−10 0 10 20 30 40 50
0
50
100
150
200
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−70 −60 −50 −40 −30 −20
−2 Log Likelihood
BM OU.2
1 Simulate many datasets
under model A
2 Re-fit both A & B to each
simulated 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
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50
100
150
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p = 0.002
−70 −60 −50 −40 −30 −20
−2 Log Likelihood
BM OU.2
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Likelihood Ratio
Fre
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−10 0 10 20 30 40 50
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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
0
50
100
150
p = 0.237
−70 −60 −50 −40 −30 −20
−2 Log Likelihood
BM OU.2
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Likelihood Ratio
Fre
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0
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100
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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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Model B doesn’t reject Model A.
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How about two very similar models? BM vs OU.1
Likelihood Ratio
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0 10 20 30
0
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p = 0.778
−70 −60 −50 −40 −30 −20
−2 Log Likelihood
BM OU.1
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0 10 20 30
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p = 0.778
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−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
0
100
200
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400
AIC
p = 0.779
−70 −60 −50 −40 −30 −20
−2 Log Likelihood
BM OU.1
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Likelihood Ratio
Fre
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0 10 20 30
0
100
200
300
400
AIC
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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method can say “I don’t know”
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Can we distinguish between OU.2 and OU.3?
Likelihood Ratio
Fre
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−80 −60 −40 −20 0 20
0
50
100
150
200
250
−70 −60 −50 −40 −30 −20
−2 Log Likelihood
OU.2OU.3
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Fre
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−80 −60 −40 −20 0 20
0
50
100
150
200
250
−70 −60 −50 −40 −30 −20
−2 Log Likelihood
OU.2OU.3
Carl Boettiger, UC Davis Niches & Transitions 21/35
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Simulate under OU.2 and compare to OU.3 . . .
Likelihood Ratio
Fre
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ncy
−80 −60 −40 −20 0 20
0
50
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
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Fre
que
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−80 −60 −40 −20 0 20
0
50
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
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OU.3 vs OU.2: Now we’re preferring OU.2!
Likelihood Ratio
Fre
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ncy
−60 −40 −20 0 20
0
50
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
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Fre
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ncy
−60 −40 −20 0 20
0
50
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
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Model A rejects Model B.
Model B rejects Model A.
Carl Boettiger, UC Davis Niches & Transitions 24/35
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Model B rejects Model A.
Carl Boettiger, UC Davis Niches & Transitions 24/35
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Page 29
Non-nested models
t2t1
mdmg
life
ocgm
gagb
sanu
lalb
bcbn
bewa
wbsn
scse
po
t2t1
mdmg
life
ocgm
gagb
sanu
lalb
bcbn
bewa
wbsn
scse
po
Carl Boettiger, UC Davis Niches & Transitions 25/35
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t2t1
mdmg
life
ocgm
gagb
sanu
lalb
bcbn
bewa
wbsn
scse
po
t2t1
mdmg
life
ocgm
gagb
sanu
lalb
bcbn
bewa
wbsn
scse
po
Carl Boettiger, UC Davis Niches & Transitions 25/35
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Replacing paintings with a transition model
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All models are nested
Estimate number of niches
Also estimate rates of transitions
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Estimate number of niches
Also estimate rates of transitions
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A hard problem in two easy piecesP( | ) = P( | )P( | )
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Summary
1 Quantifiable, robust model choice Likelihood Ratio
Frequency
−10 0 10 20 30 40 50050
1001502
0025030
0
p = 0.002
2 Identify when data is insufficient
Likelihood Ratio
Frequency
0 10 20 30010
0200
300400 p = 0.778
3 New framework avoids painting &
non-nested comparison
Carl Boettiger, UC Davis Niches & Transitions 29/35
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1 Quantifiable, robust model choice Likelihood Ratio
Frequency
−10 0 10 20 30 40 50050
1001502
0025030
0
p = 0.002
2 Identify when data is insufficient
Likelihood Ratio
Frequency
0 10 20 30010
0200
300400 p = 0.778
3 New framework avoids painting &
non-nested comparison
Carl Boettiger, UC Davis Niches & Transitions 29/35
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Page 34
Thanks!
Chris Martin
Peter Wainwright
Samantha Price
Roi Holzman
Graham Coop
Peter Ralph
Alan Hastings
DoE CSGF
Carl Boettiger, UC Davis Niches & Transitions 30/35
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Chris Martin
Peter Wainwright
Samantha Price
Roi Holzman
Graham Coop
Peter Ralph
Alan Hastings
DoE CSGF
Carl Boettiger, UC Davis Niches & Transitions 30/35
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Time
Stat
e
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Stat
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Time
Stat
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Time
Stat
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Page 38
Comparing Models
t2
t1
md
mgli
fe
oc
gmga
gbsa
nu
lalb
bcbn
be
wa
wb
sn
sc
se
po
t2
t1
md
mgli
fe
oc
gmga
gbsa
nu
lalb
bcbn
be
wa
wb
sn
sc
se
po
t2
t1
md
mgli
fe
oc
gmga
gbsa
nu
lalb
bcbn
be
wa
wb
sn
sc
se
po
Carl Boettiger, UC Davis Niches & Transitions 34/35
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t2
t1
md
mgli
fe
oc
gmga
gbsa
nu
lalb
bcbn
be
wa
wb
sn
sc
se
po
t2
t1
md
mgli
fe
oc
gmga
gbsa
nu
lalb
bcbn
be
wa
wb
sn
sc
se
po
t2
t1
md
mgli
fe
oc
gmga
gbsa
nu
lalb
bcbn
be
wa
wb
sn
sc
se
po
Carl Boettiger, UC Davis Niches & Transitions 34/35
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Page 39
OU.3 vs OU.4: Why you should mistrust painting trees
Likelihood Ratio
Fre
que
ncy
−50 0 50 100
0
50
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
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Likelihood Ratio
Fre
que
ncy
−50 0 50 100
0
50
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
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