A general model of continuous character evolution
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A general model of continuous character evolution

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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.

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.

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  • 1. A general model for continuous character evolution Carl Boettiger UC Davis June 20, 2011Carl Boettiger, UC Davis Release of Constraint 1/37
  • 2. A Key Innovation in Jaw Morphology?Carl Boettiger, UC Davis Release of Constraint 2/37
  • 3. A long time ago. . .Carl Boettiger, UC Davis Release of Constraint 3/37
  • 4. This fishCarl Boettiger, UC Davis Release of Constraint 4/37
  • 5. Got a good idea Westneat et. al. (2005)Carl Boettiger, UC Davis Release of Constraint 5/37
  • 6. and did this:Carl Boettiger, UC Davis Release of Constraint 6/37
  • 7. and did this:Carl Boettiger, UC Davis Release of Constraint 6/37
  • 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)Carl Boettiger, UC Davis Release of Constraint 7/37
  • 10. A Key Innovation* in Jaw Morphology? * With respect to the resulting diversity of morphology, rather than species diversityCarl Boettiger, UC Davis Release of Constraint 8/37
  • 11. One group remains under selective constraint One with innovation can diversify morphologyCarl Boettiger, UC Davis Release of Constraint 9/37
  • 12. This is a nice question for comparative phylogenetic models. . .Carl Boettiger, UC Davis Release of Constraint 10/37
  • 13. We don’t have that model.Carl Boettiger, UC Davis Release of Constraint 11/37
  • 14. I have that modelCarl Boettiger, UC Davis Release of Constraint 12/37
  • 15. Models for Continuous Character EvolutionCarl Boettiger, UC Davis Release of Constraint 13/37
  • 16. A Phylogeny of Phylogenetic Models BM Brownie ouch OU 2006 2004 1999 1997 1985Carl Boettiger, UC Davis Release of Constraint 14/37
  • 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
  • 18. Some comparative physiology: Brownie dX = σ × dBt trait change rate BrownianCarl Boettiger, UC Davis Release of Constraint 16/37
  • 19. Some comparative physiology: Brownie dX = σ × dBt trait change rate BrownianCarl Boettiger, UC Davis Release of Constraint 16/37
  • 20. Some comparative physiology: ouch dX = α( θ −X)dt + σdBt optimumCarl Boettiger, UC Davis Release of Constraint 17/37
  • 21. Some comparative physiology: ouch dX = α( θ −X)dt + σdBt optimumCarl Boettiger, UC Davis Release of Constraint 17/37
  • 22. How about: dX = α (θ − X)dt + σdBt selectionCarl Boettiger, UC Davis Release of Constraint 18/37
  • 23. How about: dX = α (θ − X)dt + σdBt selectionCarl Boettiger, UC Davis Release of Constraint 18/37
  • 24. Combine both: dX = α( θ −X)dt + σ dBt optimum divers. rateCarl Boettiger, UC Davis Release of Constraint 19/37
  • 25. Combine both: dX = α( θ −X)dt + σ dBt optimum divers. rateCarl Boettiger, UC Davis Release of Constraint 19/37
  • 26. Many other combinations: dX = α ( θ −X)dt + σdBt selection optimumCarl Boettiger, UC Davis Release of Constraint 20/37
  • 27. Many other combinations: dX = α ( θ −X)dt + σdBt selection optimumCarl Boettiger, UC Davis Release of Constraint 20/37
  • 28. One model to rule them all? dX = α ( θ −X)dt + σ dBt selection optimum divers. rateCarl Boettiger, UC Davis Release of Constraint 21/37
  • 29. One model to rule them all? dX = α ( θ −X)dt + σ dBt selection optimum divers. rateCarl Boettiger, UC Davis Release of Constraint 21/37
  • 30. But do you have the power to wield it?Carl Boettiger, UC Davis Release of Constraint 22/37
  • 31. But do you have the power to wield it? Do you have . . . the complete time-calibrated tree of life?Carl Boettiger, UC Davis Release of Constraint 22/37
  • 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?Carl Boettiger, UC Davis Release of Constraint 22/37
  • 33. A dangerous pathCarl Boettiger, UC Davis Release of Constraint 23/37
  • 34. A dangerous path Ridges so flat and long you may be stuck foreverCarl Boettiger, UC Davis Release of Constraint 23/37
  • 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 failCarl Boettiger, UC Davis Release of Constraint 23/37
  • 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 treacherousCarl Boettiger, UC Davis Release of Constraint 23/37
  • 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 treacherousCarl Boettiger, UC Davis Release of Constraint 23/37
  • 38. Likelihood ridges α ∝ σ 2 ridge-lineCarl Boettiger, UC Davis Release of Constraint 24/37
  • 39. Likelihood ridges α ∝ σ 2 ridge-line small or deeply branching phylogeniesCarl Boettiger, UC Davis Release of Constraint 24/37
  • 40. Likelihood ridges α ∝ σ 2 ridge-line small or deeply branching phylogenies Closely nested regime paintingsCarl Boettiger, UC Davis Release of Constraint 24/37
  • 41. Survival Strategieson rugged likelihood surfaces Sub-modelsCarl Boettiger, UC Davis Release of Constraint 25/37
  • 42. Survival Strategieson rugged likelihood surfaces Sub-models Simulated annealing (if max-likelihood)Carl Boettiger, UC Davis Release of Constraint 25/37
  • 43. Survival Strategieson rugged likelihood surfaces Sub-models Simulated annealing (if max-likelihood) MCMC → posterior distributions (in Bayesian mode)Carl Boettiger, UC Davis Release of Constraint 25/37
  • 44. Survival Strategieson rugged likelihood surfaces Sub-models Simulated annealing (if max-likelihood) MCMC → posterior distributions (in Bayesian mode) PMC for power estimates & model choice*Carl Boettiger, UC Davis Release of Constraint 25/37
  • 45. Survival Strategieson 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 reviewCarl Boettiger, UC Davis Release of Constraint 25/37
  • 46. Returning to our opening example. . .Carl Boettiger, UC Davis Release of Constraint 26/37
  • 47. Returning to our opening example. . .Carl Boettiger, UC Davis Release of Constraint 26/37
  • 48. Can a key innovation release selective constraint? Differing trait diversification Differing strengths of stabilizing rates, or selection?Carl Boettiger, UC Davis Release of Constraint 27/37
  • 49. Differing Trait Diversification Rate ModelCarl Boettiger, UC Davis Release of Constraint 28/37
  • 50. Differing Stabilizing Selection StrengthCarl Boettiger, UC Davis Release of Constraint 29/37
  • 51. So which is the better model? Differing Diversification Log Likelihood: -94 Parameters: 4 Differing Selection Log Likelihood: -92 Parameters: 4Carl Boettiger, UC Davis Release of Constraint 30/37
  • 52. So which is the better model? Differing Diversification Log Likelihood: -94 Parameters: 4 Differing Selection Log Likelihood: -92 Parameters: 4Carl Boettiger, UC Davis Release of Constraint 30/37
  • 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.Carl Boettiger, UC Davis Release of Constraint 30/37
  • 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. . .Carl Boettiger, UC Davis Release of Constraint 30/37
  • 55. A slightly simpler model comparison Differing trait diversification Differing strengths of stabilizing rates, or selection?Carl Boettiger, UC Davis Release of Constraint 31/37
  • 56. Differing Stabilizing Selection Strength Differing Trait Diversification RateCarl Boettiger, UC Davis Release of Constraint 32/37
  • 57. ComparisonCarl Boettiger, UC Davis Release of Constraint 33/37
  • 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
  • 59. Conclusions 1 A new phylogenetic methodCarl Boettiger, UC Davis Release of Constraint 35/37
  • 60. Conclusions 1 A new phylogenetic method 2 Complex models are dangerous with inadequate powerCarl Boettiger, UC Davis Release of Constraint 35/37
  • 61. Conclusions 1 A new phylogenetic method 2 Complex models are dangerous with inadequate power 3 Have methods to quantify power and uncertainty.Carl Boettiger, UC Davis Release of Constraint 35/37
  • 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 dataCarl Boettiger, UC Davis Release of Constraint 35/37
  • 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.comCarl Boettiger, UC Davis Release of Constraint 36/37
  • 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