a general model of continuous character evolution
DESCRIPTION
I present a model that generalizes common comparative methods. I highlight some of the dangers of more complex methods and outline ways of addressing these challenges.TRANSCRIPT
A general model for continuous characterevolution
Carl Boettiger
UC Davis
June 20, 2011
Carl Boettiger, UC Davis Release of Constraint 1/37
Parrotfish with the intramandibular joint:
have over 6 times greater disparityin their jaw opening lever ratiohave over 3 times greater disparityin their closing lever ratiocomparable variation in protrusionand they are a younger claderelative to other parrotfish
(corrected for body mass)
Price et. al. (2010)
Carl Boettiger, UC Davis Release of Constraint 7/37
Parrotfish with the intramandibular joint:have over 6 times greater disparityin their jaw opening lever ratiohave over 3 times greater disparityin their closing lever ratiocomparable variation in protrusionand they are a younger claderelative to other parrotfish
(corrected for body mass)
Price et. al. (2010)
Carl Boettiger, UC Davis Release of Constraint 7/37
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
One group remains underselective constraintOne with innovation candiversify morphology
Carl Boettiger, UC Davis Release of Constraint 9/37
This is a nice question for comparativephylogenetic models. . .
Carl Boettiger, UC Davis Release of Constraint 10/37
A Phylogeny of Phylogenetic Models
BM Brownie ouch OU
1985
1997
1999
2006
2004
Carl Boettiger, UC Davis Release of Constraint 14/37
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
Some comparative physiology: Brownie
dX︸︷︷︸trait change
= σ︸︷︷︸rate× dBt︸ ︷︷ ︸
Brownian
Carl Boettiger, UC Davis Release of Constraint 16/37
Some comparative physiology: Brownie
dX︸︷︷︸trait change
= σ︸︷︷︸rate× dBt︸ ︷︷ ︸
Brownian
Carl Boettiger, UC Davis Release of Constraint 16/37
Some comparative physiology: ouch
dX = α( θ︸︷︷︸optimum
−X)dt+ σdBt
Carl Boettiger, UC Davis Release of Constraint 17/37
Some comparative physiology: ouch
dX = α( θ︸︷︷︸optimum
−X)dt+ σdBt
Carl Boettiger, UC Davis Release of Constraint 17/37
Combine both:
dX = α( θ︸︷︷︸optimum
−X)dt+ σ︸︷︷︸divers. rate
dBt
Carl Boettiger, UC Davis Release of Constraint 19/37
Combine both:
dX = α( θ︸︷︷︸optimum
−X)dt+ σ︸︷︷︸divers. rate
dBt
Carl Boettiger, UC Davis Release of Constraint 19/37
Many other combinations:
dX = α︸︷︷︸selection
( θ︸︷︷︸optimum
−X)dt+ σdBt
Carl Boettiger, UC Davis Release of Constraint 20/37
Many other combinations:
dX = α︸︷︷︸selection
( θ︸︷︷︸optimum
−X)dt+ σdBt
Carl Boettiger, UC Davis Release of Constraint 20/37
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
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
But do you have the power to wield it?
Do you have . . . the completetime-calibrated tree of life?
Or is your data a hobbit?
Carl Boettiger, UC Davis Release of Constraint 22/37
But do you have the power to wield it?
Do you have . . . the completetime-calibrated tree of life?
Or is your data a hobbit?
Carl Boettiger, UC Davis Release of Constraint 22/37
But do you have the power to wield it?
Do you have . . . the completetime-calibrated tree of life?
Or is your data a hobbit?
Carl Boettiger, UC Davis Release of Constraint 22/37
A dangerous path
Ridges so flat and long you maybe stuck forever
Rugged likelihood surfaces such thatcommon 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
A dangerous pathRidges so flat and long you maybe stuck forever
Rugged likelihood surfaces such thatcommon 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
A dangerous pathRidges so flat and long you maybe stuck forever
Rugged likelihood surfaces such thatcommon 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
A dangerous pathRidges so flat and long you maybe stuck forever
Rugged likelihood surfaces such thatcommon 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
A dangerous pathRidges so flat and long you maybe stuck forever
Rugged likelihood surfaces such thatcommon 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
Likelihood ridges
α ∝ σ2 ridge-line
small or deeply branchingphylogeniesClosely nested regime paintings
Carl Boettiger, UC Davis Release of Constraint 24/37
Likelihood ridges
α ∝ σ2 ridge-linesmall or deeply branchingphylogenies
Closely nested regime paintings
Carl Boettiger, UC Davis Release of Constraint 24/37
Likelihood ridges
α ∝ σ2 ridge-linesmall or deeply branchingphylogeniesClosely nested regime paintings
Carl Boettiger, UC Davis Release of Constraint 24/37
Survival Strategieson rugged likelihood surfaces
Sub-models
Simulated annealing (if max-likelihood)MCMC→ posterior distributions (inBayesian 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
Survival Strategieson rugged likelihood surfaces
Sub-modelsSimulated annealing (if max-likelihood)
MCMC→ posterior distributions (inBayesian 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
Survival Strategieson rugged likelihood surfaces
Sub-modelsSimulated annealing (if max-likelihood)MCMC→ posterior distributions (inBayesian 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
Survival Strategieson rugged likelihood surfaces
Sub-modelsSimulated annealing (if max-likelihood)MCMC→ posterior distributions (inBayesian 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
Survival Strategieson rugged likelihood surfaces
Sub-modelsSimulated annealing (if max-likelihood)MCMC→ posterior distributions (inBayesian 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
Can a key innovation release selective constraint?
Differing trait diversificationrates, or
Differing strengths of stabilizingselection?
Carl Boettiger, UC Davis Release of Constraint 27/37
Differing Trait Diversification Rate Model
Carl Boettiger, UC Davis Release of Constraint 28/37
Differing Stabilizing Selection Strength
Carl Boettiger, UC Davis Release of Constraint 29/37
So which is the better model?
Differing DiversificationLog Likelihood: -94Parameters: 4Differing Selection LogLikelihood: -92Parameters: 4
Not enough power for this comparison in this trait.. . . must try harder. . .
Carl Boettiger, UC Davis Release of Constraint 30/37
So which is the better model?
Differing DiversificationLog Likelihood: -94Parameters: 4Differing Selection LogLikelihood: -92Parameters: 4
Not enough power for this comparison in this trait.. . . must try harder. . .
Carl Boettiger, UC Davis Release of Constraint 30/37
So which is the better model?
Differing DiversificationLog Likelihood: -94Parameters: 4Differing Selection LogLikelihood: -92Parameters: 4
Not enough power for this comparison in this trait.
. . . must try harder. . .
Carl Boettiger, UC Davis Release of Constraint 30/37
So which is the better model?
Differing DiversificationLog Likelihood: -94Parameters: 4Differing Selection LogLikelihood: -92Parameters: 4
Not enough power for this comparison in this trait.. . . must try harder. . .
Carl Boettiger, UC Davis Release of Constraint 30/37
A slightly simpler model comparison
Differing trait diversificationrates, or
Differing strengths of stabilizingselection?
Carl Boettiger, UC Davis Release of Constraint 31/37
Differing Stabilizing Selection Strength
Differing Trait Diversification Rate
Carl Boettiger, UC Davis Release of Constraint 32/37
Comparison
Carl Boettiger, UC Davis Release of Constraint 33/37
If we prefer to be Bayesian: MCMC
These are posteriors, not likelihood bootstraps. Requirespriors, etc.But, looks pretty much the same.
Carl Boettiger, UC Davis Release of Constraint 34/37
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
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
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
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
Acknowledgements
Peter WainwrightWainwright LabGraham CoopPeter RalphFunding:
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
An Addendum on Reproducible ResearchSlides on http://wainwrightlab.wordpress.comSee meta-data, script, version of code, data, recentchanges. . .
Carl Boettiger, UC Davis Release of Constraint 37/37