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.
8. Parrotfish with the intramandibular joint:
Carl Boettiger, UC Davis Release of Constraint 7/37
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)
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10. A Key Innovation* in Jaw Morphology?
* With respect to the resulting diversity of morphology,
rather than species diversity
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11. One group remains under
selective constraint
One with innovation can
diversify morphology
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12. This is a nice question for comparative
phylogenetic models. . .
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13. We don’t have that model.
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14. I have that model
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15. Models for Continuous Character
Evolution
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16. A Phylogeny of Phylogenetic Models
BM Brownie ouch OU
2006
2004
1999
1997
1985
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17. Something is missing
Brownie:
Differing rates of diversification
ouch:
Differing selective optima
Where’s the link? Can it be both?
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18. Some comparative physiology: Brownie
dX = σ × dBt
trait change rate Brownian
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19. Some comparative physiology: Brownie
dX = σ × dBt
trait change rate Brownian
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20. Some comparative physiology: ouch
dX = α( θ −X)dt + σdBt
optimum
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21. Some comparative physiology: ouch
dX = α( θ −X)dt + σdBt
optimum
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22. How about:
dX = α (θ − X)dt + σdBt
selection
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23. How about:
dX = α (θ − X)dt + σdBt
selection
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24. Combine both:
dX = α( θ −X)dt + σ dBt
optimum divers. rate
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25. Combine both:
dX = α( θ −X)dt + σ dBt
optimum divers. rate
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26. Many other combinations:
dX = α ( θ −X)dt + σdBt
selection optimum
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27. Many other combinations:
dX = α ( θ −X)dt + σdBt
selection optimum
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28. One model to rule them all?
dX = α ( θ −X)dt + σ dBt
selection optimum divers. rate
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29. One model to rule them all?
dX = α ( θ −X)dt + σ dBt
selection optimum divers. rate
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30. But do you have the power to wield it?
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31. But do you have the power to wield it?
Do you have . . . the complete
time-calibrated tree of life?
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32. But do you have the power to wield it?
Do you have . . . the complete Or is your data a hobbit?
time-calibrated tree of life?
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34. A dangerous path
Ridges so flat and long you may
be stuck forever
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35. 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
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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
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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
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38. Likelihood ridges
α ∝ σ 2 ridge-line
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39. Likelihood ridges
α ∝ σ 2 ridge-line
small or deeply branching
phylogenies
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40. Likelihood ridges
α ∝ σ 2 ridge-line
small or deeply branching
phylogenies
Closely nested regime paintings
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42. Survival Strategies
on rugged likelihood surfaces
Sub-models
Simulated annealing (if max-likelihood)
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43. Survival Strategies
on rugged likelihood surfaces
Sub-models
Simulated annealing (if max-likelihood)
MCMC → posterior distributions (in
Bayesian mode)
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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*
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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
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46. Returning to our opening example. . .
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47. Returning to our opening example. . .
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48. Can a key innovation release selective constraint?
Differing trait diversification Differing strengths of stabilizing
rates, or selection?
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51. So which is the better model?
Differing Diversification
Log Likelihood: -94
Parameters: 4
Differing Selection Log
Likelihood: -92
Parameters: 4
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52. So which is the better model?
Differing Diversification
Log Likelihood: -94
Parameters: 4
Differing Selection Log
Likelihood: -92
Parameters: 4
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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.
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54. 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. . .
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55. A slightly simpler model comparison
Differing trait diversification Differing strengths of stabilizing
rates, or selection?
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56. Differing Stabilizing Selection Strength
Differing Trait Diversification Rate
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58. If we prefer to be Bayesian: MCMC
These are posteriors, not likelihood bootstraps. Requires
priors, etc.
But, looks pretty much the same.
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59. Conclusions
1 A new phylogenetic method
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60. Conclusions
1 A new phylogenetic method
2 Complex models are dangerous with inadequate power
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61. Conclusions
1 A new phylogenetic method
2 Complex models are dangerous with inadequate power
3 Have methods to quantify power and uncertainty.
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62. 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
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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
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64. An Addendum on Reproducible Research
Slides on http://wainwrightlab.wordpress.com
See meta-data, script, version of code, data, recent
changes. . .
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