A general model for continuous character                            evolution                            Carl Boettiger   ...
A Key Innovation in Jaw Morphology?Carl Boettiger, UC Davis   Release of Constraint   2/37
A long time ago. . .Carl Boettiger, UC Davis            Release of Constraint   3/37
This fishCarl Boettiger, UC Davis      Release of Constraint   4/37
Got a good idea      Westneat et. al. (2005)Carl Boettiger, UC Davis               Release of Constraint   5/37
and did this:Carl Boettiger, UC Davis   Release of Constraint   6/37
and did this:Carl Boettiger, UC Davis   Release of Constraint   6/37
Parrotfish with the intramandibular joint:Carl Boettiger, UC Davis   Release of Constraint   7/37
Parrotfish with the intramandibular joint:              have over 6 times greater disparity              in their jaw openi...
A Key Innovation* in Jaw Morphology?                       * With respect to the resulting diversity of morphology,       ...
One group remains under              selective constraint              One with innovation can              diversify morp...
This is a nice question for comparative                phylogenetic models. . .Carl Boettiger, UC Davis   Release of Const...
We don’t have that model.Carl Boettiger, UC Davis               Release of Constraint   11/37
I have that modelCarl Boettiger, UC Davis           Release of Constraint   12/37
Models for Continuous Character                           EvolutionCarl Boettiger, UC Davis       Release of Constraint   ...
A Phylogeny of Phylogenetic Models     BM                Brownie                            ouch     OU                   ...
Something is missing                    Brownie:   Differing rates of diversification                                      ...
Some comparative physiology: Brownie                              dX          = σ × dBt                           trait ch...
Some comparative physiology: Brownie                              dX          = σ × dBt                           trait ch...
Some comparative physiology: ouch                           dX = α(   θ     −X)dt + σdBt                                 o...
Some comparative physiology: ouch                           dX = α(   θ     −X)dt + σdBt                                 o...
How about:                           dX =      α (θ − X)dt + σdBt                                  selectionCarl Boettiger...
How about:                           dX =      α (θ − X)dt + σdBt                                  selectionCarl Boettiger...
Combine both:                    dX = α(   θ      −X)dt +                  σ     dBt                           optimum    ...
Combine both:                    dX = α(   θ      −X)dt +                  σ     dBt                           optimum    ...
Many other combinations:                       dX =     α (       θ       −X)dt + σdBt                              select...
Many other combinations:                       dX =     α (       θ       −X)dt + σdBt                              select...
One model to rule them all?               dX =          α (       θ       −X)dt +                     σ          dBt      ...
One model to rule them all?               dX =          α (       θ       −X)dt +                     σ          dBt      ...
But do you have the power to wield it?Carl Boettiger, UC Davis   Release of Constraint   22/37
But do you have the power to wield it?     Do you have . . . the complete      time-calibrated tree of life?Carl Boettiger...
But do you have the power to wield it?     Do you have . . . the complete             Or is your data a hobbit?      time-...
A dangerous pathCarl Boettiger, UC Davis   Release of Constraint   23/37
A dangerous path     Ridges so flat and long you may     be stuck foreverCarl Boettiger, UC Davis   Release of Constraint  ...
A dangerous path     Ridges so flat and long you may     be stuck forever              Rugged likelihood surfaces such that...
A dangerous path     Ridges so flat and long you may     be stuck forever              Rugged likelihood surfaces such that...
A dangerous path     Ridges so flat and long you may     be stuck forever              Rugged likelihood surfaces such that...
Likelihood ridges              α ∝ σ 2 ridge-lineCarl Boettiger, UC Davis           Release of Constraint   24/37
Likelihood ridges              α ∝ σ 2 ridge-line              small or deeply branching              phylogeniesCarl Boet...
Likelihood ridges              α ∝ σ 2 ridge-line              small or deeply branching              phylogenies         ...
Survival Strategieson rugged likelihood surfaces              Sub-modelsCarl Boettiger, UC Davis   Release of Constraint  ...
Survival Strategieson rugged likelihood surfaces              Sub-models              Simulated annealing (if max-likeliho...
Survival Strategieson rugged likelihood surfaces              Sub-models              Simulated annealing (if max-likeliho...
Survival Strategieson rugged likelihood surfaces              Sub-models              Simulated annealing (if max-likeliho...
Survival Strategieson rugged likelihood surfaces              Sub-models              Simulated annealing (if max-likeliho...
Returning to our opening example. . .Carl Boettiger, UC Davis   Release of Constraint   26/37
Returning to our opening example. . .Carl Boettiger, UC Davis   Release of Constraint   26/37
Can a key innovation release selective constraint?  Differing trait diversification       Differing strengths of stabilizin...
Differing Trait Diversification Rate ModelCarl Boettiger, UC Davis   Release of Constraint   28/37
Differing Stabilizing Selection StrengthCarl Boettiger, UC Davis   Release of Constraint   29/37
So which is the better model?          Differing Diversification          Log Likelihood: -94          Parameters: 4       ...
So which is the better model?          Differing Diversification          Log Likelihood: -94          Parameters: 4       ...
So which is the better model?          Differing Diversification          Log Likelihood: -94          Parameters: 4       ...
So which is the better model?          Differing Diversification          Log Likelihood: -94          Parameters: 4       ...
A slightly simpler model comparison  Differing trait diversification       Differing strengths of stabilizing  rates, or   ...
Differing Stabilizing Selection Strength                             Differing Trait Diversification RateCarl Boettiger, UC...
ComparisonCarl Boettiger, UC Davis   Release of Constraint   33/37
If we prefer to be Bayesian: MCMC              These are posteriors, not likelihood bootstraps. Requires              prio...
Conclusions         1    A new phylogenetic methodCarl Boettiger, UC Davis             Release of Constraint   35/37
Conclusions         1    A new phylogenetic method         2    Complex models are dangerous with inadequate powerCarl Boe...
Conclusions         1    A new phylogenetic method         2    Complex models are dangerous with inadequate power        ...
Conclusions         1    A new phylogenetic method         2    Complex models are dangerous with inadequate power        ...
Acknowledgements      Peter Wainwright      Wainwright Lab      Graham Coop      Peter Ralph      Funding:                ...
An Addendum on Reproducible Research              Slides on http://wainwrightlab.wordpress.com              See meta-data,...
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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.

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A general model of continuous character evolution

  1. 1. A general model for continuous character evolution Carl Boettiger UC Davis June 20, 2011Carl Boettiger, UC Davis Release of Constraint 1/37
  2. 2. A Key Innovation in Jaw Morphology?Carl Boettiger, UC Davis Release of Constraint 2/37
  3. 3. A long time ago. . .Carl Boettiger, UC Davis Release of Constraint 3/37
  4. 4. This fishCarl Boettiger, UC Davis Release of Constraint 4/37
  5. 5. Got a good idea Westneat et. al. (2005)Carl Boettiger, UC Davis Release of Constraint 5/37
  6. 6. and did this:Carl Boettiger, UC Davis Release of Constraint 6/37
  7. 7. and did this:Carl Boettiger, UC Davis Release of Constraint 6/37
  8. 8. Parrotfish with the intramandibular joint:Carl Boettiger, UC Davis Release of Constraint 7/37
  9. 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. 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. 11. One group remains under selective constraint One with innovation can diversify morphologyCarl Boettiger, UC Davis Release of Constraint 9/37
  12. 12. This is a nice question for comparative phylogenetic models. . .Carl Boettiger, UC Davis Release of Constraint 10/37
  13. 13. We don’t have that model.Carl Boettiger, UC Davis Release of Constraint 11/37
  14. 14. I have that modelCarl Boettiger, UC Davis Release of Constraint 12/37
  15. 15. Models for Continuous Character EvolutionCarl Boettiger, UC Davis Release of Constraint 13/37
  16. 16. A Phylogeny of Phylogenetic Models BM Brownie ouch OU 2006 2004 1999 1997 1985Carl Boettiger, UC Davis Release of Constraint 14/37
  17. 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. 18. Some comparative physiology: Brownie dX = σ × dBt trait change rate BrownianCarl Boettiger, UC Davis Release of Constraint 16/37
  19. 19. Some comparative physiology: Brownie dX = σ × dBt trait change rate BrownianCarl Boettiger, UC Davis Release of Constraint 16/37
  20. 20. Some comparative physiology: ouch dX = α( θ −X)dt + σdBt optimumCarl Boettiger, UC Davis Release of Constraint 17/37
  21. 21. Some comparative physiology: ouch dX = α( θ −X)dt + σdBt optimumCarl Boettiger, UC Davis Release of Constraint 17/37
  22. 22. How about: dX = α (θ − X)dt + σdBt selectionCarl Boettiger, UC Davis Release of Constraint 18/37
  23. 23. How about: dX = α (θ − X)dt + σdBt selectionCarl Boettiger, UC Davis Release of Constraint 18/37
  24. 24. Combine both: dX = α( θ −X)dt + σ dBt optimum divers. rateCarl Boettiger, UC Davis Release of Constraint 19/37
  25. 25. Combine both: dX = α( θ −X)dt + σ dBt optimum divers. rateCarl Boettiger, UC Davis Release of Constraint 19/37
  26. 26. Many other combinations: dX = α ( θ −X)dt + σdBt selection optimumCarl Boettiger, UC Davis Release of Constraint 20/37
  27. 27. Many other combinations: dX = α ( θ −X)dt + σdBt selection optimumCarl Boettiger, UC Davis Release of Constraint 20/37
  28. 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. 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. 30. But do you have the power to wield it?Carl Boettiger, UC Davis Release of Constraint 22/37
  31. 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. 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. 33. A dangerous pathCarl Boettiger, UC Davis Release of Constraint 23/37
  34. 34. A dangerous path Ridges so flat and long you may be stuck foreverCarl Boettiger, UC Davis Release of Constraint 23/37
  35. 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. 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. 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. 38. Likelihood ridges α ∝ σ 2 ridge-lineCarl Boettiger, UC Davis Release of Constraint 24/37
  39. 39. Likelihood ridges α ∝ σ 2 ridge-line small or deeply branching phylogeniesCarl Boettiger, UC Davis Release of Constraint 24/37
  40. 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. 41. Survival Strategieson rugged likelihood surfaces Sub-modelsCarl Boettiger, UC Davis Release of Constraint 25/37
  42. 42. Survival Strategieson rugged likelihood surfaces Sub-models Simulated annealing (if max-likelihood)Carl Boettiger, UC Davis Release of Constraint 25/37
  43. 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. 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. 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. 46. Returning to our opening example. . .Carl Boettiger, UC Davis Release of Constraint 26/37
  47. 47. Returning to our opening example. . .Carl Boettiger, UC Davis Release of Constraint 26/37
  48. 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. 49. Differing Trait Diversification Rate ModelCarl Boettiger, UC Davis Release of Constraint 28/37
  50. 50. Differing Stabilizing Selection StrengthCarl Boettiger, UC Davis Release of Constraint 29/37
  51. 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. 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. 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. 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. 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. 56. Differing Stabilizing Selection Strength Differing Trait Diversification RateCarl Boettiger, UC Davis Release of Constraint 32/37
  57. 57. ComparisonCarl Boettiger, UC Davis Release of Constraint 33/37
  58. 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. 59. Conclusions 1 A new phylogenetic methodCarl Boettiger, UC Davis Release of Constraint 35/37
  60. 60. Conclusions 1 A new phylogenetic method 2 Complex models are dangerous with inadequate powerCarl Boettiger, UC Davis Release of Constraint 35/37
  61. 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. 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. 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. 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
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