detecting evolutionary regime shifts with comparative phylogenetics

Introduction Parrotfish: a story A new method Challenges Opportunities

Detecting evolutionaryregime shifts with

comparativephylogenetics

@cboettig

Carl Boettiger, UC Davis Detecting Evolutionary Regime Shifts 1/61


Once upon a time. . .



Phylogeny was a nuisance.

something we “corrected for”



Then we turned our attention to the parameters

σ2

α

θ

λ

κ

δ

Diversification

Stabilizing selection

Adaptive Optimum

phylogenetic signal

speciational change

accelerating / decelerating rates



The parameters were allowed to change,

we became interestedin where the changes occur.



The parameters were allowed to change, we became interestedin where the changes occur.



Regime

Shifts



The (Updated) Phylogeny of Phylogenetic Models



Outline

1 A Method:

Detecting a release of constraint2 Challenges: The edge of identifiability3 Opportunities: Large, synthetic data sets



Outline

1 A Method: Detecting a release of constraint

2 Challenges: The edge of identifiability3 Opportunities: Large, synthetic data sets



Outline

1 A Method: Detecting a release of constraint2 Challenges:

The edge of identifiability3 Opportunities: Large, synthetic data sets



Outline

1 A Method: Detecting a release of constraint2 Challenges: The edge of identifiability

3 Opportunities: Large, synthetic data sets



Outline

1 A Method: Detecting a release of constraint2 Challenges: The edge of identifiability3 Opportunities:

Large, synthetic data sets



Outline

1 A Method: Detecting a release of constraint2 Challenges: The edge of identifiability3 Opportunities: Large, synthetic data sets



A key innovation?

This guy These fish



A key innovation?

This guy

These fish



A key innovation?

This guy These fish



Fish Suck



These fish don’t suck



Did this innovationrelease the constraints

of suction feeding?



. . . and release a burst of jaw evolution?

Wrasses

IntramandibularJoint

Pharyngeal Jaw

Parrotfish



An evolutionary regime shift?

a large change in the model parameters

In which parameters?



An evolutionary regime shift?

a large change in the model parametersIn which parameters?



Candidate models



Unconstrained Evolution



Constrained Evolution



Release of constraint



Accelerating rates



-2

-1

0

1

2

0 20 40 60 80 100time

trai

t va

lue

Brownian Motion

-2

-1

0

1

2

0 20 40 60 80 100time

trai

t va

lue

Ornstein-Uhlenbeck

-2

-1

0

1

2

0 20 40 60 80 100time

trai

t va

lue

Accelerated Evolution

-2

-1

0

1

2

0 20 40 60 80 100time

trai

t va

lue

Release of Constraint



XT1 = X0︸︷︷︸where you start

e−α1T1+

θ1(1 − e−α1T1

)︸︷︷︸Where you are going

+

∫ T1

0σ1e

α1(s−T1)dWs︸︷︷︸Random shocks along the way



XT2 = X1︸︷︷︸where you were

e−α2T2+

θ2(1 − e−α2T2

)︸︷︷︸

possibly new optimum

+

∫ T2

T1σ2e

α2(s−T2)dWs︸︷︷︸possibly new shocks

γi = −n∑

j=i+1αjtj



Generalized OU model

XN =n∑i=0

eγi

[θi(1 − eαiti

)+

∫ ti

0σie

αi(s−ti)dW is

]



Some Mathematical Conveniences

Gaussian process! Need onlyE(Xi) and Cov(Xi, Xj)Evolution on different branches isindependent




Gaussian process!

Need onlyE(Xi) and Cov(Xi, Xj)Evolution on different branches isindependent




Gaussian process! Need onlyE(Xi) and Cov(Xi, Xj)

Evolution on different branches isindependent




Gaussian process! Need onlyE(Xi) and Cov(Xi, Xj)Evolution on different branches isindependent



Averaging removes the random shocks

E(Xi) =n∑i=0

eγi

[θi(1 − eαiti

) ]

Itô Isometry makes stochastic integrals intoregular integrals!

E(∫f(Xi)dWi ×

∫f(Xj)dWj)

Cov(Xi, Xj) =n∑i=1

[eγi

∫ ti

0σie

αi(u−ti)dW iu

]×

m∑j=1

[eγ

′j

∫ sj

0σ′je

α′j(v−sj)dW j

v

]



Averaging removes the random shocks

E(Xi) =n∑i=0

eγi

[θi(1 − eαiti

) ]

Itô Isometry makes stochastic integrals intoregular integrals!

E(∫f(Xi)dWi ×

∫f(Xj)dWj)

Cov(Xi, Xj) =n∑i=1

[eγi

∫ ti

0σie

αi(u−ti)dW iu

]×

m∑j=1

[eγ

′j

∫ sj

0σ′je

α′j(v−sj)dW j

v

]Carl Boettiger, UC Davis Detecting Evolutionary Regime Shifts 34/61


Covariance matrix determines the likelihood

Cov(Xi, Xj) =k∑s=0

[eγs+γ′

sσ2s

2αs

(1 − e−2αsts

)]



OUwie

Beaulieu et al. 2012, Evolution



Challenges



Where the sidewalk ends

Generalizing models any further,we will not have analytic likelihoods



Limits of Identifiability?



Can our data support so many parameters?



How do we choose between multiple complex models?

Before we can ask which is the right model,

we must ask if we have enough data to tell.

Information citeria don’t address this.



How do we choose between multiple complex models?

Before we can ask which is the right model,we must ask if we have enough data to tell.

Information citeria don’t address this.



AIC scores for four model comparisons

0 10 20 30 40 50

0.00

0.04

0.08

(a) BM vs. OU.3

δ

Den

sity

-10 0 10 20 30

0.00

0.05

0.10

0.15

(b) OU.3 vs. OU.4

δ

Den

sity

0 50 100 150

0.00

0.01

0.02

0.03

0.04

(c) OU.3 vs. OU.15

δ

Den

sity

-5 0 5 10 15

0.00

0.05

0.10

0.15

0.20

(d) BM vs. OU.1

δ

Den

sity



AIC scores for four model comparisons

0 10 20 30 40 50

0.00

0.04

0.08

(a) BM vs. OU.3

δ

Den

sity

False Pos (37%)False Neg (0%)

-10 0 10 20 30

0.00

0.05

0.10

0.15

(b) OU.3 vs. OU.4

δ

Den

sity

False Pos (43.75%)False Neg (8.25%)

0 50 100 150

0.00

0.01

0.02

0.03

0.04

(c) OU.3 vs. OU.15

δ

Den

sity

False Pos (47.75%)False Neg (0%)

-5 0 5 10 15

0.00

0.05

0.10

0.15

0.20

(d) BM vs. OU.1

δ

Den

sity

False Pos (19.95%)False Neg (76.65%)



Phylogenetic Monte Carlo

Simulate from

simple model →




← Fits both models

to this data

Simulate from

simple model →





to this data

LogLik(simple)LogLik(complex)

Simulate from

simple model →





to this data


Simulate from

simple model →

Likelihood ratio

frequency





to this data


Simulate from

simple model →complex

model →

Likelihood ratio

frequency





to this data


Simulate from

simple model →complex

model →

Likelihood ratio

frequency

Boettiger et al. 2012, Evolution, pmc R package



Software has madecomparative methodsubiquitous. . .

So how about data?



Programmatic Access to data



Programmatic access for everyone

Building tools, building communityFollow @ropensci for more




Building tools, building community

Follow @ropensci for more




Building tools, building communityFollow @ropensci for more



A wealth of repositories



and what about the Parrotfish?Was it a release of constraint after all?

Of course!



Conclusions

1 Can distinguish mechanisms such as release ofconstraint.

2 Pushing the limits of analytic solutions,3 and more worryingly, the limits of our data4 New and diverse data sources would alleviate, but not

solve these issues5 Continue to foster a community of data sharing and code

sharing



Conclusions


2 Pushing the limits of analytic solutions,

3 and more worryingly, the limits of our data4 New and diverse data sources would alleviate, but not


sharing



Conclusions


2 Pushing the limits of analytic solutions,3 and more worryingly, the limits of our data

4 New and diverse data sources would alleviate, but notsolve these issues

5 Continue to foster a community of data sharing and codesharing



Conclusions



solve these issues

5 Continue to foster a community of data sharing and codesharing



Conclusions




sharing



Acknowledgments

Jeremy BeaulieuPeter WainwrightGraham CoopPeter RalphBrian O’MearaDuncan TempleLangand many more Slides, source code, and more

http://carlboettiger.info


carlboettiger.info

detecting evolutionary regime shifts with comparative phylogenetics

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