A general model of continuous character evolution
Nature Precedings (2011)
- ISSN: 17560357
- DOI: 10.1038/npre.2011.6080.1
Available from
Carl Boettiger's profile on Mendeley.
or
Available from
Carl Boettiger's profile on Mendeley.
Page 1
A general model of continuous character evolution
A general model for continuous character
evolution
Carl Boettiger
UC Davis
June 20, 2011
Carl Boettiger, UC Davis Release of Constraint 1/37
evolution
Carl Boettiger
UC Davis
June 20, 2011
Carl Boettiger, UC Davis Release of Constraint 1/37
Page 2
A Key Innovation in Jaw Morphology?
Carl Boettiger, UC Davis Release of Constraint 2/37
Carl Boettiger, UC Davis Release of Constraint 2/37
Page 3
A long time ago. . .
Carl Boettiger, UC Davis Release of Constraint 3/37
Carl Boettiger, UC Davis Release of Constraint 3/37
Page 4
This fish
Carl Boettiger, UC Davis Release of Constraint 4/37
Carl Boettiger, UC Davis Release of Constraint 4/37
Page 5
Got a good idea
Westneat et. al. (2005)
Carl Boettiger, UC Davis Release of Constraint 5/37
Westneat et. al. (2005)
Carl Boettiger, UC Davis Release of Constraint 5/37
Page 6
and did this:
Carl Boettiger, UC Davis Release of Constraint 6/37
Carl Boettiger, UC Davis Release of Constraint 6/37
Page 7
and did this:
Carl Boettiger, UC Davis Release of Constraint 6/37
Carl Boettiger, UC Davis Release of Constraint 6/37
Page 8
Parrotfish with the intramandibular joint:
have over 6 times greater disparity
in their jaw opening lever ratio
have over 3 times greater disparity
in their closing lever ratio
comparable variation in protrusion
and they are a younger clade
relative to other parrotfish
(corrected for body mass)
Price et. al. (2010)
Carl Boettiger, UC Davis Release of Constraint 7/37
have over 6 times greater disparity
in their jaw opening lever ratio
have over 3 times greater disparity
in their closing lever ratio
comparable variation in protrusion
and they are a younger clade
relative to other parrotfish
(corrected for body mass)
Price et. al. (2010)
Carl Boettiger, UC Davis Release of Constraint 7/37
Page 9
Parrotfish with the intramandibular joint:
have over 6 times greater disparity
in their jaw opening lever ratio
have over 3 times greater disparity
in their closing lever ratio
comparable variation in protrusion
and they are a younger clade
relative to other parrotfish
(corrected for body mass)
Price et. al. (2010)
Carl Boettiger, UC Davis Release of Constraint 7/37
have over 6 times greater disparity
in their jaw opening lever ratio
have over 3 times greater disparity
in their closing lever ratio
comparable variation in protrusion
and they are a younger clade
relative to other parrotfish
(corrected for body mass)
Price et. al. (2010)
Carl Boettiger, UC Davis Release of Constraint 7/37
Page 10
A Key Innovation* in Jaw Morphology?
* With respect to the resulting diversity of morphology,
rather than species diversity
Carl Boettiger, UC Davis Release of Constraint 8/37
* With respect to the resulting diversity of morphology,
rather than species diversity
Carl Boettiger, UC Davis Release of Constraint 8/37
Page 11
One group remains under
selective constraint
One with innovation can
diversify morphology
Carl Boettiger, UC Davis Release of Constraint 9/37
selective constraint
One with innovation can
diversify morphology
Carl Boettiger, UC Davis Release of Constraint 9/37
Page 12
This is a nice question for comparative
phylogenetic models. . .
Carl Boettiger, UC Davis Release of Constraint 10/37
phylogenetic models. . .
Carl Boettiger, UC Davis Release of Constraint 10/37
Page 13
We don’t have that model.
Carl Boettiger, UC Davis Release of Constraint 11/37
Carl Boettiger, UC Davis Release of Constraint 11/37
Page 14
I have that model
Carl Boettiger, UC Davis Release of Constraint 12/37
Carl Boettiger, UC Davis Release of Constraint 12/37
Page 15
Models for Continuous Character
Evolution
Carl Boettiger, UC Davis Release of Constraint 13/37
Evolution
Carl Boettiger, UC Davis Release of Constraint 13/37
Page 16
A Phylogeny of Phylogenetic ModelsBM Brownie ouch OU
1985
1997
1999
2006
2004
Carl Boettiger, UC Davis Release of Constraint 14/37
1985
1997
1999
2006
2004
Carl Boettiger, UC Davis Release of Constraint 14/37
Page 17
Something is missing
Brownie:
Differing rates of diversification ouch:
Differing selective optima
Where’s the link? Can it be both?
Carl Boettiger, UC Davis Release of Constraint 15/37
Brownie:
Differing rates of diversification ouch:
Differing selective optima
Where’s the link? Can it be both?
Carl Boettiger, UC Davis Release of Constraint 15/37
Page 18
Some comparative physiology: Brownie
dX︸︷︷︸
trait change
= σ︸︷︷︸
rate
× dBt︸ ︷︷ ︸
Brownian
Carl Boettiger, UC Davis Release of Constraint 16/37
dX︸︷︷︸
trait change
= σ︸︷︷︸
rate
× dBt︸ ︷︷ ︸
Brownian
Carl Boettiger, UC Davis Release of Constraint 16/37
Page 19
Some comparative physiology: Brownie
dX︸︷︷︸
trait change
= σ︸︷︷︸
rate
× dBt︸ ︷︷ ︸
Brownian
Carl Boettiger, UC Davis Release of Constraint 16/37
dX︸︷︷︸
trait change
= σ︸︷︷︸
rate
× dBt︸ ︷︷ ︸
Brownian
Carl Boettiger, UC Davis Release of Constraint 16/37
Page 20
Some comparative physiology: ouch
dX = α( θ︸︷︷︸
optimum
−X)dt+ σdBt
Carl Boettiger, UC Davis Release of Constraint 17/37
dX = α( θ︸︷︷︸
optimum
−X)dt+ σdBt
Carl Boettiger, UC Davis Release of Constraint 17/37
Page 22
How about:
dX = α︸︷︷︸
selection
(θ −X)dt+ σdBt
Carl Boettiger, UC Davis Release of Constraint 18/37
dX = α︸︷︷︸
selection
(θ −X)dt+ σdBt
Carl Boettiger, UC Davis Release of Constraint 18/37
Page 23
How about:
dX = α︸︷︷︸
selection
(θ −X)dt+ σdBt
Carl Boettiger, UC Davis Release of Constraint 18/37
dX = α︸︷︷︸
selection
(θ −X)dt+ σdBt
Carl Boettiger, UC Davis Release of Constraint 18/37
Page 24
Combine both:
dX = α( θ︸︷︷︸
optimum
−X)dt+ σ︸︷︷︸
divers. rate
dBt
Carl Boettiger, UC Davis Release of Constraint 19/37
dX = α( θ︸︷︷︸
optimum
−X)dt+ σ︸︷︷︸
divers. rate
dBt
Carl Boettiger, UC Davis Release of Constraint 19/37
Page 25
Combine both:
dX = α( θ︸︷︷︸
optimum
−X)dt+ σ︸︷︷︸
divers. rate
dBt
Carl Boettiger, UC Davis Release of Constraint 19/37
dX = α( θ︸︷︷︸
optimum
−X)dt+ σ︸︷︷︸
divers. rate
dBt
Carl Boettiger, UC Davis Release of Constraint 19/37
Page 27
Many other combinations:
dX = α︸︷︷︸
selection
( θ︸︷︷︸
optimum
−X)dt+ σdBt
Carl Boettiger, UC Davis Release of Constraint 20/37
dX = α︸︷︷︸
selection
( θ︸︷︷︸
optimum
−X)dt+ σdBt
Carl Boettiger, UC Davis Release of Constraint 20/37
Page 28
One model to rule them all?
dX = α︸︷︷︸
selection
( θ︸︷︷︸
optimum
−X)dt+ σ︸︷︷︸
divers. rate
dBt
Carl Boettiger, UC Davis Release of Constraint 21/37
dX = α︸︷︷︸
selection
( θ︸︷︷︸
optimum
−X)dt+ σ︸︷︷︸
divers. rate
dBt
Carl Boettiger, UC Davis Release of Constraint 21/37
Page 29
One model to rule them all?
dX = α︸︷︷︸
selection
( θ︸︷︷︸
optimum
−X)dt+ σ︸︷︷︸
divers. rate
dBt
Carl Boettiger, UC Davis Release of Constraint 21/37
dX = α︸︷︷︸
selection
( θ︸︷︷︸
optimum
−X)dt+ σ︸︷︷︸
divers. rate
dBt
Carl Boettiger, UC Davis Release of Constraint 21/37
Page 33
A dangerous path
Ridges so flat and long you may
be stuck forever
Rugged likelihood surfaces such that
common ML algorithms (Nelder-Mead,
L-BFGS-B), will fail
AIC, familiar guide to model choice,
is slimy and treacherous
Carl Boettiger, UC Davis Release of Constraint 23/37
Ridges so flat and long you may
be stuck forever
Rugged likelihood surfaces such that
common ML algorithms (Nelder-Mead,
L-BFGS-B), will fail
AIC, familiar guide to model choice,
is slimy and treacherous
Carl Boettiger, UC Davis Release of Constraint 23/37
Page 34
A dangerous path
Ridges so flat and long you may
be stuck forever
Rugged likelihood surfaces such that
common ML algorithms (Nelder-Mead,
L-BFGS-B), will fail
AIC, familiar guide to model choice,
is slimy and treacherous
Carl Boettiger, UC Davis Release of Constraint 23/37
Ridges so flat and long you may
be stuck forever
Rugged likelihood surfaces such that
common ML algorithms (Nelder-Mead,
L-BFGS-B), will fail
AIC, familiar guide to model choice,
is slimy and treacherous
Carl Boettiger, UC Davis Release of Constraint 23/37
Page 36
A dangerous path
Ridges so flat and long you may
be stuck forever
Rugged likelihood surfaces such that
common ML algorithms (Nelder-Mead,
L-BFGS-B), will fail
AIC, familiar guide to model choice,
is slimy and treacherous
Carl Boettiger, UC Davis Release of Constraint 23/37
Ridges so flat and long you may
be stuck forever
Rugged likelihood surfaces such that
common ML algorithms (Nelder-Mead,
L-BFGS-B), will fail
AIC, familiar guide to model choice,
is slimy and treacherous
Carl Boettiger, UC Davis Release of Constraint 23/37
Page 37
A dangerous path
Ridges so flat and long you may
be stuck forever
Rugged likelihood surfaces such that
common ML algorithms (Nelder-Mead,
L-BFGS-B), will fail
AIC, familiar guide to model choice,
is slimy and treacherous
Carl Boettiger, UC Davis Release of Constraint 23/37
Ridges so flat and long you may
be stuck forever
Rugged likelihood surfaces such that
common ML algorithms (Nelder-Mead,
L-BFGS-B), will fail
AIC, familiar guide to model choice,
is slimy and treacherous
Carl Boettiger, UC Davis Release of Constraint 23/37
Page 38
Likelihood ridges
α ∝ σ2 ridge-line
small or deeply branching
phylogenies
Closely nested regime paintings
Carl Boettiger, UC Davis Release of Constraint 24/37
α ∝ σ2 ridge-line
small or deeply branching
phylogenies
Closely nested regime paintings
Carl Boettiger, UC Davis Release of Constraint 24/37
Page 39
Likelihood ridges
α ∝ σ2 ridge-line
small or deeply branching
phylogenies
Closely nested regime paintings
Carl Boettiger, UC Davis Release of Constraint 24/37
α ∝ σ2 ridge-line
small or deeply branching
phylogenies
Closely nested regime paintings
Carl Boettiger, UC Davis Release of Constraint 24/37
Page 40
Likelihood ridges
α ∝ σ2 ridge-line
small or deeply branching
phylogenies
Closely nested regime paintings
Carl Boettiger, UC Davis Release of Constraint 24/37
α ∝ σ2 ridge-line
small or deeply branching
phylogenies
Closely nested regime paintings
Carl Boettiger, UC Davis Release of Constraint 24/37
Page 41
Survival Strategies
on rugged likelihood surfaces
Sub-models
Simulated annealing (if max-likelihood)
MCMC→ posterior distributions (in
Bayesian mode)
PMC for power estimates & model choice*
(“A simulation analysis in a box” for your study)
* Boettiger et al. 2011 in review
Carl Boettiger, UC Davis Release of Constraint 25/37
on rugged likelihood surfaces
Sub-models
Simulated annealing (if max-likelihood)
MCMC→ posterior distributions (in
Bayesian mode)
PMC for power estimates & model choice*
(“A simulation analysis in a box” for your study)
* Boettiger et al. 2011 in review
Carl Boettiger, UC Davis Release of Constraint 25/37
Page 43
Survival Strategies
on rugged likelihood surfaces
Sub-models
Simulated annealing (if max-likelihood)
MCMC→ posterior distributions (in
Bayesian mode)
PMC for power estimates & model choice*
(“A simulation analysis in a box” for your study)
* Boettiger et al. 2011 in review
Carl Boettiger, UC Davis Release of Constraint 25/37
on rugged likelihood surfaces
Sub-models
Simulated annealing (if max-likelihood)
MCMC→ posterior distributions (in
Bayesian mode)
PMC for power estimates & model choice*
(“A simulation analysis in a box” for your study)
* Boettiger et al. 2011 in review
Carl Boettiger, UC Davis Release of Constraint 25/37
Page 44
Survival Strategies
on rugged likelihood surfaces
Sub-models
Simulated annealing (if max-likelihood)
MCMC→ posterior distributions (in
Bayesian mode)
PMC for power estimates & model choice*
(“A simulation analysis in a box” for your study)
* Boettiger et al. 2011 in review
Carl Boettiger, UC Davis Release of Constraint 25/37
on rugged likelihood surfaces
Sub-models
Simulated annealing (if max-likelihood)
MCMC→ posterior distributions (in
Bayesian mode)
PMC for power estimates & model choice*
(“A simulation analysis in a box” for your study)
* Boettiger et al. 2011 in review
Carl Boettiger, UC Davis Release of Constraint 25/37
Page 45
Survival Strategies
on rugged likelihood surfaces
Sub-models
Simulated annealing (if max-likelihood)
MCMC→ posterior distributions (in
Bayesian mode)
PMC for power estimates & model choice*
(“A simulation analysis in a box” for your study)
* Boettiger et al. 2011 in review
Carl Boettiger, UC Davis Release of Constraint 25/37
on rugged likelihood surfaces
Sub-models
Simulated annealing (if max-likelihood)
MCMC→ posterior distributions (in
Bayesian mode)
PMC for power estimates & model choice*
(“A simulation analysis in a box” for your study)
* Boettiger et al. 2011 in review
Carl Boettiger, UC Davis Release of Constraint 25/37
Page 47
Returning to our opening example. . .
Carl Boettiger, UC Davis Release of Constraint 26/37
Carl Boettiger, UC Davis Release of Constraint 26/37
Page 48
Can a key innovation release selective constraint?
Differing trait diversification
rates, or
Differing strengths of stabilizing
selection?
Carl Boettiger, UC Davis Release of Constraint 27/37
Differing trait diversification
rates, or
Differing strengths of stabilizing
selection?
Carl Boettiger, UC Davis Release of Constraint 27/37
Page 49
Differing Trait Diversification Rate Model
Carl Boettiger, UC Davis Release of Constraint 28/37
Carl Boettiger, UC Davis Release of Constraint 28/37
Page 52
So which is the better model?
Differing Diversification
Log Likelihood: -94
Parameters: 4
Differing Selection Log
Likelihood: -92
Parameters: 4
Not enough power for this comparison in this trait.
. . . must try harder. . .
Carl Boettiger, UC Davis Release of Constraint 30/37
Differing Diversification
Log Likelihood: -94
Parameters: 4
Differing Selection Log
Likelihood: -92
Parameters: 4
Not enough power for this comparison in this trait.
. . . must try harder. . .
Carl Boettiger, UC Davis Release of Constraint 30/37
Page 53
So which is the better model?
Differing Diversification
Log Likelihood: -94
Parameters: 4
Differing Selection Log
Likelihood: -92
Parameters: 4
Not enough power for this comparison in this trait.
. . . must try harder. . .
Carl Boettiger, UC Davis Release of Constraint 30/37
Differing Diversification
Log Likelihood: -94
Parameters: 4
Differing Selection Log
Likelihood: -92
Parameters: 4
Not enough power for this comparison in this trait.
. . . must try harder. . .
Carl Boettiger, UC Davis Release of Constraint 30/37
Page 55
A slightly simpler model comparison
Differing trait diversification
rates, or
Differing strengths of stabilizing
selection?
Carl Boettiger, UC Davis Release of Constraint 31/37
Differing trait diversification
rates, or
Differing strengths of stabilizing
selection?
Carl Boettiger, UC Davis Release of Constraint 31/37
Page 57
Comparison
Carl Boettiger, UC Davis Release of Constraint 33/37
Carl Boettiger, UC Davis Release of Constraint 33/37
Page 58
If we prefer to be Bayesian: MCMC
These are posteriors, not likelihood bootstraps. Requires
priors, etc.
But, looks pretty much the same.
Carl Boettiger, UC Davis Release of Constraint 34/37
These are posteriors, not likelihood bootstraps. Requires
priors, etc.
But, looks pretty much the same.
Carl Boettiger, UC Davis Release of Constraint 34/37
Page 60
Conclusions
1 A new phylogenetic method
2 Complex models are dangerous with inadequate power
3 Have methods to quantify power and uncertainty.
4 Hobbit-sized swords: Smaller sub-models for smaller data
Carl Boettiger, UC Davis Release of Constraint 35/37
1 A new phylogenetic method
2 Complex models are dangerous with inadequate power
3 Have methods to quantify power and uncertainty.
4 Hobbit-sized swords: Smaller sub-models for smaller data
Carl Boettiger, UC Davis Release of Constraint 35/37
Page 61
Conclusions
1 A new phylogenetic method
2 Complex models are dangerous with inadequate power
3 Have methods to quantify power and uncertainty.
4 Hobbit-sized swords: Smaller sub-models for smaller data
Carl Boettiger, UC Davis Release of Constraint 35/37
1 A new phylogenetic method
2 Complex models are dangerous with inadequate power
3 Have methods to quantify power and uncertainty.
4 Hobbit-sized swords: Smaller sub-models for smaller data
Carl Boettiger, UC Davis Release of Constraint 35/37
Page 63
Acknowledgements
Peter Wainwright
Wainwright Lab
Graham Coop
Peter Ralph
Funding:
Download the development version now:
https://github.com/cboettig/wrightscape
Slides and more our on new Lab Blog:
http://wainwrightlab.wordpress.com
Carl Boettiger, UC Davis Release of Constraint 36/37
Peter Wainwright
Wainwright Lab
Graham Coop
Peter Ralph
Funding:
Download the development version now:
https://github.com/cboettig/wrightscape
Slides and more our on new Lab Blog:
http://wainwrightlab.wordpress.com
Carl Boettiger, UC Davis Release of Constraint 36/37
Page 64
An Addendum on Reproducible Research
Slides on http://wainwrightlab.wordpress.com
See meta-data, script, version of code, data, recent
changes. . .
Carl Boettiger, UC Davis Release of Constraint 37/37
Slides on http://wainwrightlab.wordpress.com
See meta-data, script, version of code, data, recent
changes. . .
Carl Boettiger, UC Davis Release of Constraint 37/37
Sign up today - FREE
Mendeley saves you time finding and organizing research. Learn more
- All your research in one place
- Add and import papers easily
- Access it anywhere, anytime
Start using Mendeley in seconds!
Readership Statistics
1 Reader on Mendeley
by Discipline
100% Biological Sciences
by Academic Status
100% Ph.D. Student
by Country
100% United States