A general model for continuous characterevolution

Carl Boettiger

UC Davis

June 20, 2011

Carl Boettiger, UC Davis Release of Constraint 1/37

A Key Innovation in Jaw Morphology?

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A long time ago. . .

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This fish

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Got a good idea

Westneat et. al. (2005)

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and did this:

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and did this:

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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

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One group remains underselective constraintOne with innovation candiversify morphology

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This is a nice question for comparativephylogenetic models. . .

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We don’t have that model.

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I have that model

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Models for Continuous CharacterEvolution

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A Phylogeny of Phylogenetic Models

BM Brownie ouch OU

1985

1997

1999

2006

2004

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Something is missing

Brownie:Differing rates of diversification ouch:

Differing selective optima

Where’s the link? Can it be both?

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Some comparative physiology: Brownie

dX︸︷︷︸trait change

= σ︸︷︷︸rate× dBt︸ ︷︷ ︸

Brownian

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Some comparative physiology: Brownie

dX︸︷︷︸trait change

= σ︸︷︷︸rate× dBt︸ ︷︷ ︸

Brownian

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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

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How about:

dX = α︸︷︷︸selection

(θ −X)dt+ σdBt

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How about:

dX = α︸︷︷︸selection

(θ −X)dt+ σdBt

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Combine both:

dX = α( θ︸︷︷︸optimum

−X)dt+ σ︸︷︷︸divers. rate

dBt

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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

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Likelihood ridges

α ∝ σ2 ridge-linesmall or deeply branchingphylogenies

Closely nested regime paintings

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Likelihood ridges

α ∝ σ2 ridge-linesmall or deeply branchingphylogeniesClosely nested regime paintings

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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

Returning to our opening example. . .

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Returning to our opening example. . .

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Can a key innovation release selective constraint?

Differing trait diversificationrates, or

Differing strengths of stabilizingselection?

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Differing Trait Diversification Rate Model

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Differing Stabilizing Selection Strength

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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?

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Differing Stabilizing Selection Strength

Differing Trait Diversification Rate

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Comparison

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If we prefer to be Bayesian: MCMC

These are posteriors, not likelihood bootstraps. Requirespriors, etc.But, looks pretty much the same.

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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

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An Addendum on Reproducible ResearchSlides on http://wainwrightlab.wordpress.comSee meta-data, script, version of code, data, recentchanges. . .

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