Inferring Adaptive Landscapes from Phylogenetic Trees

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Presentation to the Center for Population Biology, November 2010

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Inferring Adaptive Landscapes from Phylogenetic Trees

  1. 1. Inferring Adaptive Landscapes from Phylogenetic Trees Carl Boettiger UC Davis June 8, 2010 Carl Boettiger, UC Davis Adaptive Landscapes 1/52
  2. 2. Introduction: a Story of C. Boettiger and C. Martin Background of Comparative Methods Wrightscape: a nonlinear, forward approach Carl Boettiger, UC Davis Adaptive Landscapes 2/52
  3. 3. A Story Q}-< 04.09 == Q}-< | O}| L- f(x)dx ? BM OU wtf == | O‘}|L- Carl Boettiger, UC Davis Adaptive Landscapes 3/52
  4. 4. Carl Boettiger, UC Davis Adaptive Landscapes 4/52
  5. 5. Q}-< == Carl Boettiger, UC Davis Adaptive Landscapes 5/52
  6. 6. ______ Q}-< O}I L- Carl Boettiger, UC Davis Adaptive Landscapes 6/52
  7. 7. Carl Boettiger, UC Davis Adaptive Landscapes 7/52
  8. 8. Carl Boettiger, UC Davis Adaptive Landscapes 8/52
  9. 9. O}-< Q}-< f(x) dt Carl Boettiger, UC Davis Adaptive Landscapes 9/52
  10. 10. Carl Boettiger, UC Davis Adaptive Landscapes 10/52
  11. 11. ? Carl Boettiger, UC Davis Adaptive Landscapes 11/52
  12. 12. ______ O}-< == Carl Boettiger, UC Davis Adaptive Landscapes 12/52
  13. 13. ______ OL- `}I Carl Boettiger, UC Davis Adaptive Landscapes 13/52
  14. 14. Introduction: a Story of C. Boettiger and C. Martin Background of Comparative Methods Wrightscape: a nonlinear, forward approach Carl Boettiger, UC Davis Adaptive Landscapes 14/52
  15. 15. Felsenstein’s question Is brain size evolution correlated to body size evolution? Carl Boettiger, UC Davis Adaptive Landscapes 15/52
  16. 16. Natural Selection or Shared Ancestry? Carl Boettiger, UC Davis Adaptive Landscapes 16/52
  17. 17. Natural Selection or Shared Ancestry? Carl Boettiger, UC Davis Adaptive Landscapes 16/52
  18. 18. Correcting for history: Correcting for branch length Reasons species are similar: Carl Boettiger, UC Davis Adaptive Landscapes 17/52
  19. 19. Correcting for history: Correcting for branch length Reasons species are similar: 1 Same function – natural selection Carl Boettiger, UC Davis Adaptive Landscapes 17/52
  20. 20. Correcting for history: Correcting for branch length Reasons species are similar: 1 Same function – natural selection 2 Same ancestors – shared history Carl Boettiger, UC Davis Adaptive Landscapes 17/52
  21. 21. Correcting for history: Correcting for branch length Reasons species are similar: 1 Same function – natural selection 2 Same ancestors – shared history Carl Boettiger, UC Davis Adaptive Landscapes 17/52
  22. 22. Expected divergence: unbiased model 10 5 0 Time Carl Boettiger, UC Davis Adaptive Landscapes 18/52
  23. 23. Expected divergence: unbiased model 10 5 0 Time Carl Boettiger, UC Davis Adaptive Landscapes 18/52
  24. 24. Expected divergence: unbiased model 10 5 TTHTTTTTTH =⇒ −6 0 Time Carl Boettiger, UC Davis Adaptive Landscapes 18/52
  25. 25. Expected divergence: unbiased model 10 5 TTHTTTTTTH =⇒ −6 TTHTTHHHTT =⇒ −2 0 Time Carl Boettiger, UC Davis Adaptive Landscapes 18/52
  26. 26. Expected divergence: unbiased model 10 5 TTHTTTTTTH =⇒ −6 TTHTTHHHTT =⇒ −2 TTHTTHHHTH =⇒ 0 0 Time Carl Boettiger, UC Davis Adaptive Landscapes 18/52
  27. 27. Independent Contrasts 11,6 5,1 4,1 10,5 4,1 5,1 11,6 10,5 Carl Boettiger, UC Davis Adaptive Landscapes 19/52
  28. 28. Contrasts are differences in independent branches 11,6 5,1 4,1 10,5 6 5 8,3.5 7,3 0 Tim e Carl Boettiger, UC Davis Adaptive Landscapes 20/52
  29. 29. Contrasts are differences in independent branches Sister taxa = easy contrasts: 11,6 5,1 4,1 10,5 6 11 − 5 √ 2 5 8,3.5 7,3 0 Tim e Carl Boettiger, UC Davis Adaptive Landscapes 20/52
  30. 30. Contrasts are differences in independent branches Sister taxa = easy contrasts: 11,6 5,1 4,1 10,5 6 11 − 5 √ 2 5 8,3.5 7,3 Interior node estimates: 11 + 5 =8 2 0 Tim e Carl Boettiger, UC Davis Adaptive Landscapes 20/52
  31. 31. Contrasts are differences in independent branches Sister taxa = easy contrasts: 11,6 5,1 4,1 10,5 6 11 − 5 √ 2 5 8,3.5 7,3 Interior node estimates: 11 + 5 =8 2 0 Another set of contrasts: Tim e 8−7 √ 1+2×5 Carl Boettiger, UC Davis Adaptive Landscapes 20/52
  32. 32. < Watch the focus shift from the data to the model. . . > Carl Boettiger, UC Davis Adaptive Landscapes 21/52
  33. 33. Estimating ancestral states and rates of change 11,6 5,1 4,1 10,5 6 5 (8, 3.5)  (7, 3) 0 (7.5,3.75) ? Tim e Schluter et. al. (1997) Carl Boettiger, UC Davis Adaptive Landscapes 22/52
  34. 34. Estimating ancestral states and rates of change 11,6 5,1 4,1 10,5 6 Expected ancestral states: 5 (8, 3.5)  (7, 3) intermediate trait values 0 (7.5,3.75) ? Tim e Schluter et. al. (1997) Carl Boettiger, UC Davis Adaptive Landscapes 22/52
  35. 35. Estimating ancestral states and rates of change 11,6 5,1 4,1 10,5 6 Expected ancestral states: 5 (8, 3.5)  (7, 3) intermediate trait values Expected rate of change: 0 matching the toss rate Tim e (7.5,3.75) ? Schluter et. al. (1997) Carl Boettiger, UC Davis Adaptive Landscapes 22/52
  36. 36. Estimating ancestral states and rates of change 11,6 5,1 4,1 10,5 6 Expected ancestral states: 5 (8, 3.5)  (7, 3) intermediate trait values Expected rate of change: 0 matching the toss rate Tim e (7.5,3.75) ? Also estimates uncertainty Schluter et. al. (1997) Carl Boettiger, UC Davis Adaptive Landscapes 22/52
  37. 37. Changing Rates and Adaptive Radiations? 11,6 5,1 4,1 10,5 6 5 (8, 3.5)  (7, 3) Evidence that the rates of evolution are accelerating? 0 (7.5,3.75) ? Tim e Freckleton & Harvey (2006) Carl Boettiger, UC Davis Adaptive Landscapes 23/52
  38. 38. < Are we taking the model too seriously? > Carl Boettiger, UC Davis Adaptive Landscapes 24/52
  39. 39. Differing rates between clades? 9 11 2 21 O’Meara et. al. (2006) Carl Boettiger, UC Davis Adaptive Landscapes 25/52
  40. 40. Differing rates between clades? 9 11 2 21 O’Meara et. al. (2006) Carl Boettiger, UC Davis Adaptive Landscapes 26/52
  41. 41. Differing rates between clades? 9 11 2 21 O’Meara et. al. (2006) Carl Boettiger, UC Davis Adaptive Landscapes 27/52
  42. 42. Evolutionary questions thus far (Brownian Motion) Carl Boettiger, UC Davis Adaptive Landscapes 28/52
  43. 43. Evolutionary questions thus far (Brownian Motion) 1 Correlated trait evolution Carl Boettiger, UC Davis Adaptive Landscapes 28/52
  44. 44. Evolutionary questions thus far (Brownian Motion) 1 Correlated trait evolution 2 Rate of trait evolution over time Carl Boettiger, UC Davis Adaptive Landscapes 28/52
  45. 45. Evolutionary questions thus far (Brownian Motion) 1 Correlated trait evolution 2 Rate of trait evolution over time 3 Changes in the rate of evolution over time Carl Boettiger, UC Davis Adaptive Landscapes 28/52
  46. 46. Evolutionary questions thus far (Brownian Motion) 1 Correlated trait evolution 2 Rate of trait evolution over time 3 Changes in the rate of evolution over time 4 Differing rates between clades Carl Boettiger, UC Davis Adaptive Landscapes 28/52
  47. 47. Wait wait, where’d the selection go? The Adaptive Landscape of Brownian Motion: Carl Boettiger, UC Davis Adaptive Landscapes 29/52
  48. 48. Wait wait, where’d the selection go? The Adaptive Landscape of Brownian Motion: Carl Boettiger, UC Davis Adaptive Landscapes 29/52
  49. 49. OU Model: some selection Hansen (1997) Butler & King (2004) Harmon (2008) Carl Boettiger, UC Davis Adaptive Landscapes 30/52
  50. 50. Evolutionary questions thus far (BM & OU) 1 Correlated trait evolution 2 Rate of trait evolution over time 3 Changes in the rate of evolution over time 4 Differing rates between clades Carl Boettiger, UC Davis Adaptive Landscapes 31/52
  51. 51. Evolutionary questions thus far (BM & OU) 1 Correlated trait evolution 2 Rate of trait evolution over time 3 Changes in the rate of evolution over time 4 Differing rates between clades 5 Strength of stablizing selection Carl Boettiger, UC Davis Adaptive Landscapes 31/52
  52. 52. Evolutionary questions thus far (BM & OU) 1 Correlated trait evolution 2 Rate of trait evolution over time 3 Changes in the rate of evolution over time 4 Differing rates between clades 5 Strength of stablizing selection 6 Peak location of stablizing selection Carl Boettiger, UC Davis Adaptive Landscapes 31/52
  53. 53. A closer look at data and model 11 5 4 10 6 5 8 7 0 7.5 Tim e Carl Boettiger, UC Davis Adaptive Landscapes 32/52
  54. 54. What’s wrong with this picture? data 5 8 11 predicted trait for most of tree Carl Boettiger, UC Davis Adaptive Landscapes 33/52
  55. 55. Multiple adaptive peaks: the need for nonlinear models BM fails to explain clustering 11 5 4 10 6 5 8 7 0 7.5 Tim e Carl Boettiger, UC Davis Adaptive Landscapes 34/52
  56. 56. Multiple adaptive peaks: the need for nonlinear models BM fails to explain clustering 11 5 4 10 6 5 8 7 OU = single peak 0 7.5 Tim e Carl Boettiger, UC Davis Adaptive Landscapes 34/52
  57. 57. Multiple adaptive peaks: the need for nonlinear models BM fails to explain clustering 11 5 4 10 6 5 8 7 OU = single peak 0 7.5 Tim e Nonlinear selection gradients Carl Boettiger, UC Davis Adaptive Landscapes 34/52
  58. 58. Problem: Models with funny sounding physics names aren’t very biological Carl Boettiger, UC Davis Adaptive Landscapes 35/52
  59. 59. Problem: Models with funny sounding physics names aren’t very biological Solution: Stop using silly physics models Carl Boettiger, UC Davis Adaptive Landscapes 35/52
  60. 60. Introduction: a Story of C. Boettiger and C. Martin Background of Comparative Methods Wrightscape: a nonlinear, forward approach Carl Boettiger, UC Davis Adaptive Landscapes 36/52
  61. 61. Anoles Carl Boettiger, UC Davis Adaptive Landscapes 37/52
  62. 62. Ecomorphs of Anoles Williams (1969) Carl Boettiger, UC Davis Adaptive Landscapes 38/52
  63. 63. Distribution of hind limb sizes of Anoles . . .   22.3 28.4 21.5 21.3 18.7 19.9 18.9 0.06 21.1 18.3 19.7 19.6 18.8 Density 0.04 28.8 28.6 23.6 27.9 27.1 0.02 13.5 14.9 14.5 14.3 14.2 0.00 14.3 10 15 20 25 30 35 N = 23   Bandwidth = 2.278 Carl Boettiger, UC Davis Adaptive Landscapes 39/52
  64. 64. . . . on the phylogenetic tree 22.3 28.4 21.5 21.3 18.7 19.9 18.9 21.1 18.3 19.7 19.6 18.8 28.8 28.6 23.6 27.9 27.1 13.5 14.9 14.5 14.3 14.2 14.3 0 10 20 30 40 time Carl Boettiger, UC Davis Adaptive Landscapes 40/52
  65. 65. exp(-(log(x) - k1)^2/(2 * sigma)) + exp(-(log(x) - k2)^2/(2 *      sigma)) + exp(-(log(x) - k3)^2/(2 * sigma)) Carl Boettiger, UC Davis 0.7 0.8 0.9 1.0 12 15 18 20 x 24 25 Adaptive Landscapes Inferred landscape: multiple peaks 30 35 41/52
  66. 66. Inferred landscape: multiple peaks exp(-(log(x) - k1)^2/(2 * sigma)) + exp(-(log(x) - k2)^2/(2 *      sigma)) + exp(-(log(x) - k3)^2/(2 * sigma)) 0.7 0.8 0.9 1.0 12 15 18 20 24 25 30 35 x Tree reveals three-peaked adaptive landscape hidden in raw data Carl Boettiger, UC Davis Adaptive Landscapes 41/52
  67. 67. Nonlinear Models and the Forward Approach How do we do this and why hasn’t it been done yet? Carl Boettiger, UC Davis Adaptive Landscapes 42/52
  68. 68. Three loops 1 Simulate on tree many times L(θ1 , θ2 |x) BM, OU, peaks, dXt = f (Xt )dt + g(Xt )dBt Carl Boettiger, UC Davis Adaptive Landscapes 43/52
  69. 69. Three loops 1 Simulate on tree many times generate probability distribution at each tip Compare to character trait data of each tip to generate a likelihood score for the parameters. L(θ1 , θ2 |x) BM, OU, peaks, dXt = f (Xt )dt + g(Xt )dBt Carl Boettiger, UC Davis Adaptive Landscapes 43/52
  70. 70. Three loops 1 Simulate on tree many times generate probability distribution at each tip Compare to character trait data of each tip to generate a likelihood score for the parameters. 2 Search over parameters by simulated annealing with MCMC L(θ1 , θ2 |x) BM, OU, peaks, dXt = f (Xt )dt + g(Xt )dBt Carl Boettiger, UC Davis Adaptive Landscapes 43/52
  71. 71. Three loops 1 Simulate on tree many times generate probability distribution at each tip Compare to character trait data of each tip to generate a likelihood score for the parameters. 2 Search over parameters by simulated annealing with MCMC L(θ1 , θ2 |x) 3 Search over models: information criteria BM, OU, peaks, dXt = f (Xt )dt + g(Xt )dBt Carl Boettiger, UC Davis Adaptive Landscapes 43/52
  72. 72. Three loops 1 Simulate on tree many times generate probability distribution at each tip Compare to character trait data of each tip to generate a likelihood score for the parameters. 2 Search over parameters by simulated annealing with MCMC L(θ1 , θ2 |x) 3 Search over models: information criteria BM, OU, peaks, dXt = f (Xt )dt + g(Xt )dBt Computationally demanding? Carl Boettiger, UC Davis Adaptive Landscapes 43/52
  73. 73. Labrids Carl Boettiger, UC Davis Adaptive Landscapes 44/52
  74. 74. Fly or Paddle? Fin morphology predicts niche High aspect ratio: fast Low aspect ratio: fast turns sustained swimming 122 species phylogenetic tree with fin aspect ratio and fin angle. Collar et. al. (2008) Carl Boettiger, UC Davis Adaptive Landscapes 45/52
  75. 75. Jaws! Suck or Crush? Collar et. al. (2008) Carl Boettiger, UC Davis Adaptive Landscapes 46/52
  76. 76. morphology predicts niche? How many peaks? Where? How wide or steep? How deep are valleys? Transitions between peaks? Emergence of peaks? Carl Boettiger, UC Davis Adaptive Landscapes 47/52
  77. 77. _ __ __ _ _______(_)___ _/ /_ / /_______________ _____ ___ | | /| / / ___/ / __ `/ __ / __/ ___/ ___/ __ `/ __ / _ | |/ |/ / / / / /_/ / / / / /_(__ ) /__/ /_/ / /_/ / __/ |__/|__/_/ /_/__, /_/ /_/__/____/___/__,_/ .___/___/ /____/ /_/ Carl Boettiger, UC Davis Adaptive Landscapes 48/52
  78. 78. _ __ __ _ _______(_)___ _/ /_ / /_______________ _____ ___ | | /| / / ___/ / __ `/ __ / __/ ___/ ___/ __ `/ __ / _ | |/ |/ / / / / /_/ / / / / /_(__ ) /__/ /_/ / /_/ / __/ |__/|__/_/ /_/__, /_/ /_/__/____/___/__,_/ .___/___/ /____/ /_/ Test unique, biologically driven hypotheses Open Source R package, interface with existing software and formats Leadership computing: DOE Teragrid Lincoln (1536 processors, 47.5 TF) Carl Boettiger, UC Davis Adaptive Landscapes 48/52
  79. 79. < Extensions > Carl Boettiger, UC Davis Adaptive Landscapes 49/52
  80. 80. Bounded Evolution in Adaptive Radiations Brownian Motion with soft boundaries – a Landscape view: Carl Boettiger, UC Davis Adaptive Landscapes 50/52
  81. 81. Species Interactions and Community Phylogenetics Carl Boettiger, UC Davis Adaptive Landscapes 51/52
  82. 82. Thanks! O}-< Q}-< Carl Boettiger, UC Davis Adaptive Landscapes 52/52

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