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.
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A general model of continuous character evolution
- 1. A general model for continuous character evolution Carl Boettiger UC Davis June 20, 2011 Carl 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 fish Carl 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 diversity Carl Boettiger, UC Davis Release of Constraint 8/37
- 11. One group remains under selective constraint One with innovation can diversify morphology Carl 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 model Carl Boettiger, UC Davis Release of Constraint 12/37
- 15. Models for Continuous Character Evolution Carl Boettiger, UC Davis Release of Constraint 13/37
- 16. A Phylogeny of Phylogenetic Models BM Brownie ouch OU 2006 2004 1999 1997 1985 Carl 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 Brownian Carl Boettiger, UC Davis Release of Constraint 16/37
- 19. Some comparative physiology: Brownie dX = σ × dBt trait change rate Brownian Carl Boettiger, UC Davis Release of Constraint 16/37
- 20. Some comparative physiology: ouch dX = α( θ −X)dt + σdBt optimum Carl Boettiger, UC Davis Release of Constraint 17/37
- 21. Some comparative physiology: ouch dX = α( θ −X)dt + σdBt optimum Carl Boettiger, UC Davis Release of Constraint 17/37
- 22. How about: dX = α (θ − X)dt + σdBt selection Carl Boettiger, UC Davis Release of Constraint 18/37
- 23. How about: dX = α (θ − X)dt + σdBt selection Carl Boettiger, UC Davis Release of Constraint 18/37
- 24. Combine both: dX = α( θ −X)dt + σ dBt optimum divers. rate Carl Boettiger, UC Davis Release of Constraint 19/37
- 25. Combine both: dX = α( θ −X)dt + σ dBt optimum divers. rate Carl Boettiger, UC Davis Release of Constraint 19/37
- 26. Many other combinations: dX = α ( θ −X)dt + σdBt selection optimum Carl Boettiger, UC Davis Release of Constraint 20/37
- 27. Many other combinations: dX = α ( θ −X)dt + σdBt selection optimum Carl 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. rate Carl 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. rate Carl 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 path Carl Boettiger, UC Davis Release of Constraint 23/37
- 34. A dangerous path Ridges so flat and long you may be stuck forever Carl 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 fail Carl 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 treacherous Carl 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 treacherous Carl Boettiger, UC Davis Release of Constraint 23/37
- 38. Likelihood ridges α ∝ σ 2 ridge-line Carl Boettiger, UC Davis Release of Constraint 24/37
- 39. Likelihood ridges α ∝ σ 2 ridge-line small or deeply branching phylogenies Carl Boettiger, UC Davis Release of Constraint 24/37
- 40. Likelihood ridges α ∝ σ 2 ridge-line small or deeply branching phylogenies Closely nested regime paintings Carl Boettiger, UC Davis Release of Constraint 24/37
- 41. Survival Strategies on rugged likelihood surfaces Sub-models Carl Boettiger, UC Davis Release of Constraint 25/37
- 42. Survival Strategies on rugged likelihood surfaces Sub-models Simulated annealing (if max-likelihood) Carl Boettiger, UC Davis Release of Constraint 25/37
- 43. Survival Strategies on 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 Strategies on 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 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 Carl 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 Model Carl Boettiger, UC Davis Release of Constraint 28/37
- 50. Differing Stabilizing Selection Strength Carl 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: 4 Carl 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: 4 Carl 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 Rate Carl Boettiger, UC Davis Release of Constraint 32/37
- 57. Comparison Carl 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 method Carl Boettiger, UC Davis Release of Constraint 35/37
- 60. Conclusions 1 A new phylogenetic method 2 Complex models are dangerous with inadequate power Carl 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 data Carl 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.com Carl 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