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Generalizing phylogenetics to infer shared evolutionary events

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Slides for seminar given to the Louisiana State University Department of Biological Sciences on 6 November 2017.

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Generalizing phylogenetics to infer shared evolutionary events

  1. 1. Generalizing phylogenetics to infer shared evolutionary events Jamie R. Oaks1 1Department of Biological Sciences, Auburn University November 6, 2017 c 2007 Boris Kulikov boris-kulikov.blogspot.com Shared divergences Jamie Oaks – phyletica.org 1/33
  2. 2. Shared divergences Jamie Oaks – phyletica.org 2/33
  3. 3. Shared ancestry is a fundamental property of life Shared divergences Jamie Oaks – phyletica.org 2/33
  4. 4. Shared ancestry is a fundamental property of life Phylogenetics is rapidly progressing as the statistical foundation of comparatve biology Shared divergences Jamie Oaks – phyletica.org 2/33
  5. 5. Shared ancestry is a fundamental property of life Phylogenetics is rapidly progressing as the statistical foundation of comparatve biology “Big data” present exciting possibilities and computational challenges Shared divergences Jamie Oaks – phyletica.org 2/33
  6. 6. Shared ancestry is a fundamental property of life Phylogenetics is rapidly progressing as the statistical foundation of comparatve biology “Big data” present exciting possibilities and computational challenges Exciting opportunities to develop new ways to study biology in the light of phylogeny Shared divergences Jamie Oaks – phyletica.org 2/33
  7. 7. Shared divergences Jamie Oaks – phyletica.org 3/33
  8. 8. Assumption: All processes of diversification affect each lineage independently and only cause bifurcating divergences. Shared divergences Jamie Oaks – phyletica.org 3/33
  9. 9. Shared divergences Jamie Oaks – phyletica.org 4/33
  10. 10. Shared divergences Jamie Oaks – phyletica.org 4/33
  11. 11. Shared divergences Jamie Oaks – phyletica.org 4/33
  12. 12. Shared divergences Jamie Oaks – phyletica.org 4/33
  13. 13. Biogeography Environmental changes that affect whole communities of species Shared divergences Jamie Oaks – phyletica.org 5/33
  14. 14. Biogeography Environmental changes that affect whole communities of species Gene family evolution Chromosomal duplications Shared divergences Jamie Oaks – phyletica.org 5/33
  15. 15. Biogeography Environmental changes that affect whole communities of species Gene family evolution Chromosomal duplications Epidemiology Disease spread via co-infected individuals Transmission at social gatherings Shared divergences Jamie Oaks – phyletica.org 5/33
  16. 16. Biogeography Environmental changes that affect whole communities of species Gene family evolution Chromosomal duplications Epidemiology Disease spread via co-infected individuals Transmission at social gatherings Endosymbiont evolution (e.g., parasites, microbiome) Speciation of the host Co-colonization of new host species Shared divergences Jamie Oaks – phyletica.org 5/33
  17. 17. Why account for shared divergences? Shared divergences Jamie Oaks – phyletica.org 6/33
  18. 18. Why account for shared divergences? 1. Improve inference Shared divergences Jamie Oaks – phyletica.org 6/33
  19. 19. True history τ1τ2τ3 Current tree model τ1 τ2 τ3τ4 τ5 τ6 τ7 τ8 Shared divergences Jamie Oaks – phyletica.org 6/33
  20. 20. Why account for shared divergences? 1. Improve inference Shared divergences Jamie Oaks – phyletica.org 7/33
  21. 21. Why account for shared divergences? 1. Improve inference 2. Provide a framework for studying processes of co-diversification Shared divergences Jamie Oaks – phyletica.org 7/33
  22. 22. Biogeography Environmental changes that affect whole communities of species Gene family evolution Chromosomal duplications Epidemiology Disease spread via co-infected individuals Transmission at social gatherings Endosymbiont evolution (e.g., parasites, microbiome) Speciation of the host Co-colonization of new host species Shared divergences Jamie Oaks – phyletica.org 8/33
  23. 23. τ1 Shared divergences Jamie Oaks – phyletica.org 9/33
  24. 24. τ1 Shared divergences Jamie Oaks – phyletica.org 9/33
  25. 25. τ1 Shared divergences Jamie Oaks – phyletica.org 9/33
  26. 26. τ2 τ1 Shared divergences Jamie Oaks – phyletica.org 9/33
  27. 27. τ1τ2 Shared divergences Jamie Oaks – phyletica.org 9/33
  28. 28. τ1τ2 Shared divergences Jamie Oaks – phyletica.org 9/33
  29. 29. τ3 τ1τ2 Shared divergences Jamie Oaks – phyletica.org 9/33
  30. 30. m1 m2 m3 m4 m5 τ1 τ2 τ1 τ1τ2 τ1τ2 τ3 τ1τ2 J. R. Oaks et al. (2013). Evolution 67: 991–1010, J. R. Oaks (2014). BMC Evolutionary Biology 14: 150 Shared divergences Jamie Oaks – phyletica.org 10/33
  31. 31. m1 m2 m3 m4 m5 τ1 τ2 τ1 τ1τ2 τ1τ2 τ3 τ1τ2 We want to infer the model and divergence times given DNA alignments J. R. Oaks et al. (2013). Evolution 67: 991–1010, J. R. Oaks (2014). BMC Evolutionary Biology 14: 150 Shared divergences Jamie Oaks – phyletica.org 10/33
  32. 32. p(m1 | X) p(m2 | X) p(m3 | X) p(m4 | X) p(m5 | X) τ1 τ2 τ1 τ1τ2 τ1τ2 τ3 τ1τ2 We want to infer the model and divergence times given DNA alignments J. R. Oaks et al. (2013). Evolution 67: 991–1010, J. R. Oaks (2014). BMC Evolutionary Biology 14: 150 Shared divergences Jamie Oaks – phyletica.org 10/33
  33. 33. p(m1 | X) p(m2 | X) p(m3 | X) p(m4 | X) p(m5 | X) τ1 τ2 τ1 τ1τ2 τ1τ2 τ3 τ1τ2 We want to infer the model and divergence times given DNA alignments p(mi | X) ∝ p(X | mi )p(mi ) J. R. Oaks et al. (2013). Evolution 67: 991–1010, J. R. Oaks (2014). BMC Evolutionary Biology 14: 150 Shared divergences Jamie Oaks – phyletica.org 10/33
  34. 34. p(m1 | X) p(m2 | X) p(m3 | X) p(m4 | X) p(m5 | X) τ1 τ2 τ1 τ1τ2 τ1τ2 τ3 τ1τ2 We want to infer the model and divergence times given DNA alignments p(mi | X) ∝ p(X | mi )p(mi ) p(X | mi ) = θ p(X | θ, mi )p(θ | mi )dθ J. R. Oaks et al. (2013). Evolution 67: 991–1010, J. R. Oaks (2014). BMC Evolutionary Biology 14: 150 Shared divergences Jamie Oaks – phyletica.org 10/33
  35. 35. p(m1 | X) p(m2 | X) p(m3 | X) p(m4 | X) p(m5 | X) τ1 τ2 τ1 τ1τ2 τ1τ2 τ3 τ1τ2 We want to infer the model and divergence times given DNA alignments p(mi | X) ∝ p(X | mi )p(mi ) p(X | mi ) = θ p(X | θ, mi )p(θ | mi )dθ Divergence times Gene trees Substitution parameters Demographic parameters J. R. Oaks et al. (2013). Evolution 67: 991–1010, J. R. Oaks (2014). BMC Evolutionary Biology 14: 150 Shared divergences Jamie Oaks – phyletica.org 10/33
  36. 36. p(m1 | X) p(m2 | X) p(m3 | X) p(m4 | X) p(m5 | X) τ1 τ2 τ1 τ1τ2 τ1τ2 τ3 τ1τ2 Challenges: J. R. Oaks et al. (2013). Evolution 67: 991–1010, J. R. Oaks (2014). BMC Evolutionary Biology 14: 150 Shared divergences Jamie Oaks – phyletica.org 10/33
  37. 37. p(m1 | X) p(m2 | X) p(m3 | X) p(m4 | X) p(m5 | X) τ1 τ2 τ1 τ1τ2 τ1τ2 τ3 τ1τ2 Challenges: 1. Likelihood is tractable, but difficult J. R. Oaks et al. (2013). Evolution 67: 991–1010, J. R. Oaks (2014). BMC Evolutionary Biology 14: 150 Shared divergences Jamie Oaks – phyletica.org 10/33
  38. 38. p(m1 | X) p(m2 | X) p(m3 | X) p(m4 | X) p(m5 | X) τ1 τ2 τ1 τ1τ2 τ1τ2 τ3 τ1τ2 Challenges: 1. Likelihood is tractable, but difficult 2. Sampling over all possible models J. R. Oaks et al. (2013). Evolution 67: 991–1010, J. R. Oaks (2014). BMC Evolutionary Biology 14: 150 Shared divergences Jamie Oaks – phyletica.org 10/33
  39. 39. p(m1 | X) p(m2 | X) p(m3 | X) p(m4 | X) p(m5 | X) τ1 τ2 τ1 τ1τ2 τ1τ2 τ3 τ1τ2 Challenges: 1. Likelihood is tractable, but difficult 2. Sampling over all possible models 5 taxa = 52 models J. R. Oaks et al. (2013). Evolution 67: 991–1010, J. R. Oaks (2014). BMC Evolutionary Biology 14: 150 Shared divergences Jamie Oaks – phyletica.org 10/33
  40. 40. p(m1 | X) p(m2 | X) p(m3 | X) p(m4 | X) p(m5 | X) τ1 τ2 τ1 τ1τ2 τ1τ2 τ3 τ1τ2 Challenges: 1. Likelihood is tractable, but difficult 2. Sampling over all possible models 5 taxa = 52 models 10 taxa = 115,975 models J. R. Oaks et al. (2013). Evolution 67: 991–1010, J. R. Oaks (2014). BMC Evolutionary Biology 14: 150 Shared divergences Jamie Oaks – phyletica.org 10/33
  41. 41. p(m1 | X) p(m2 | X) p(m3 | X) p(m4 | X) p(m5 | X) τ1 τ2 τ1 τ1τ2 τ1τ2 τ3 τ1τ2 Challenges: 1. Likelihood is tractable, but difficult 2. Sampling over all possible models 5 taxa = 52 models 10 taxa = 115,975 models 20 taxa = 51,724,158,235,372 models!! J. R. Oaks et al. (2013). Evolution 67: 991–1010, J. R. Oaks (2014). BMC Evolutionary Biology 14: 150 Shared divergences Jamie Oaks – phyletica.org 10/33
  42. 42. Shared divergences Jamie Oaks – phyletica.org 11/33
  43. 43. Shared divergences Jamie Oaks – phyletica.org 12/33
  44. 44. Did repeated fragmentation of islands during inter-glacial rises in sea level promote diversification? Shared divergences Jamie Oaks – phyletica.org 12/33
  45. 45. Shared divergences Jamie Oaks – phyletica.org 13/33
  46. 46. Shared divergences Jamie Oaks – phyletica.org 13/33
  47. 47. Shared divergences Jamie Oaks – phyletica.org 13/33
  48. 48. Approach #1 Challenges: 1. Likelihood is tractable, but difficult 2. Sampling over all possible models Shared divergences Jamie Oaks – phyletica.org 14/33
  49. 49. Approach #1 Challenges: 1. Likelihood is tractable, but difficult Use an existing method! 2. Sampling over all possible models Use an existing method! Shared divergences Jamie Oaks – phyletica.org 14/33
  50. 50. 0.00 0.25 0.50 0.75 1.00 1 2 3 4 5 6 7 8 9 Number of events Probability J. R. Oaks et al. (2013). Evolution 67: 991–1010 Shared divergences Jamie Oaks – phyletica.org 15/33
  51. 51. Approach #2 Challenges: 1. Likelihood is tractable, but difficult 2. Sampling over all possible models Shared divergences Jamie Oaks – phyletica.org 16/33
  52. 52. Approach #2 Challenges: 1. Likelihood is tractable, but difficult Numerical approximation via approximate-likelihood Bayesian computation (ABC) 2. Sampling over all possible models Shared divergences Jamie Oaks – phyletica.org 16/33
  53. 53. Approach #2 Challenges: 1. Likelihood is tractable, but difficult Numerical approximation via approximate-likelihood Bayesian computation (ABC) 2. Sampling over all possible models Shared divergences Jamie Oaks – phyletica.org 18/33
  54. 54. Approach #2 Challenges: 1. Likelihood is tractable, but difficult Numerical approximation via approximate-likelihood Bayesian computation (ABC) 2. Sampling over all possible models A “diffuse” Dirichlet process prior (DPP) Shared divergences Jamie Oaks – phyletica.org 18/33
  55. 55. α 1 1 α α 2 1 Shared divergences Jamie Oaks – phyletica.org 19/33
  56. 56. α 1 1 α α 2 1 Shared divergences Jamie Oaks – phyletica.org 19/33
  57. 57. α 1 1 α α 2 1 Shared divergences Jamie Oaks – phyletica.org 19/33
  58. 58. α 1 1 α α 2 1 Shared divergences Jamie Oaks – phyletica.org 19/33
  59. 59. α α+1 α α+2 α α α+1 1 α+2 1 α α+1 1 α+2 1 α 1 α+1 α α+2 α 1 α+1 2 α+22 1 Shared divergences Jamie Oaks – phyletica.org 19/33
  60. 60. α = 0.5 α α+1 α α+2 = 0.067 α α α+1 1 α+2 = 0.133 1 α α+1 1 α+2 = 0.133 1 α 1 α+1 α α+2 = 0.133 α 1 α+1 2 α+2 = 0.5332 1 Shared divergences Jamie Oaks – phyletica.org 19/33
  61. 61. α = 10.0 α α+1 α α+2 = 0.758 α α α+1 1 α+2 = 0.076 1 α α+1 1 α+2 = 0.076 1 α 1 α+1 α α+2 = 0.076 α 1 α+1 2 α+2 = 0.0152 1 Shared divergences Jamie Oaks – phyletica.org 19/33
  62. 62. New method: dpp-msbayes Approximate-likelihood Bayesian approach to inferring models of shared divergences J. R. Oaks (2014). BMC Evolutionary Biology 14: 150 Shared divergences Jamie Oaks – phyletica.org 20/33
  63. 63. New method: dpp-msbayes Approximate-likelihood Bayesian approach to inferring models of shared divergences Flexible Dirichlet-process prior (DPP) over all possible divergence models J. R. Oaks (2014). BMC Evolutionary Biology 14: 150 Shared divergences Jamie Oaks – phyletica.org 20/33
  64. 64. New method: dpp-msbayes Approximate-likelihood Bayesian approach to inferring models of shared divergences Flexible Dirichlet-process prior (DPP) over all possible divergence models Flexible priors on parameters to avoid strongly weighted posteriors J. R. Oaks (2014). BMC Evolutionary Biology 14: 150 Shared divergences Jamie Oaks – phyletica.org 20/33
  65. 65. New method: dpp-msbayes Approximate-likelihood Bayesian approach to inferring models of shared divergences Flexible Dirichlet-process prior (DPP) over all possible divergence models Flexible priors on parameters to avoid strongly weighted posteriors Multi-processing to accommodate genomic datasets J. R. Oaks (2014). BMC Evolutionary Biology 14: 150 Shared divergences Jamie Oaks – phyletica.org 20/33
  66. 66. 0.00 0.05 0.10 0.15 0.20 1 2 3 4 5 6 7 8 9 Number of events Probability J. R. Oaks et al. (2013). Evolution 67: 991–1010 Shared divergences Jamie Oaks – phyletica.org 21/33
  67. 67. Insulasaurus Ptenochirus Macroglossus Haplonycteris Gekko Dendrolaphis Cyrtodactylus Cynopterus Crocidura 0 5 10 15 Time Comparison J. R. Oaks et al. (2013). Evolution 67: 991–1010 Shared divergences Jamie Oaks – phyletica.org 21/33
  68. 68. Approach #3 Challenges: 1. Likelihood is tractable, but difficult 2. Sampling over all possible models A “diffuse” Dirichlet process prior (DPP) Shared divergences Jamie Oaks – phyletica.org 22/33
  69. 69. Approach #3 Challenges: 1. Likelihood is tractable, but difficult Challenge accepted 2. Sampling over all possible models A “diffuse” Dirichlet process prior (DPP) Shared divergences Jamie Oaks – phyletica.org 22/33
  70. 70. Ecoevolity: Estimating evolutionary coevality 1 R. M. Neal (2000). Journal of Computational and Graphical Statistics 9: 249–265 2 D. Bryant et al. (2012). Molecular Biology and Evolution 29: 1917–1932 Shared divergences Jamie Oaks – phyletica.org 23/33
  71. 71. Ecoevolity: Estimating evolutionary coevality CTMC model of characters evolving along genealogies Coalescent model of genealogies branching within populations Dirichlet-process prior across divergence models Gibbs sampling1 to numerically sample models Analytically integrate over genealogies2 1 R. M. Neal (2000). Journal of Computational and Graphical Statistics 9: 249–265 2 D. Bryant et al. (2012). Molecular Biology and Evolution 29: 1917–1932 Shared divergences Jamie Oaks – phyletica.org 23/33
  72. 72. Ecoevolity: Estimating evolutionary coevality CTMC model of characters evolving along genealogies Coalescent model of genealogies branching within populations Dirichlet-process prior across divergence models Gibbs sampling1 to numerically sample models Analytically integrate over genealogies2 Goal: Fast, full-likelihood Bayesian method to infer patterns of co-diversification from genome-scale data 1 R. M. Neal (2000). Journal of Computational and Graphical Statistics 9: 249–265 2 D. Bryant et al. (2012). Molecular Biology and Evolution 29: 1917–1932 Shared divergences Jamie Oaks – phyletica.org 23/33
  73. 73. Does it work? Shared divergences Jamie Oaks – phyletica.org 24/33
  74. 74. Ecoevolity: Simulation-based assessment 0.00 0.02 0.04 0.06 True divergence time (τ) 0.00 0.01 0.02 0.03 0.04 0.05 0.06Estimateddivergencetime(ˆτ) p(τ ∈ CI) = 0.946 RMSE = 1.02e-04 Shared divergences Jamie Oaks – phyletica.org 25/33
  75. 75. Ecoevolity: Simulation-based assessment True number of events (k) Estimatednumberofevents(ˆk) 105 5 0 1 266 7 0 2 114 p(ˆk = k) = 0.970 p(k) = 0.980 1 1 2 2 3 3 Shared divergences Jamie Oaks – phyletica.org 25/33
  76. 76. Ecoevolity: Simulation-based assessment 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Trueprobability 14884 101 151 492 4872 Posterior probability of one divergence All sites 12414 1391 2650 3193 852 Variable only Shared divergences Jamie Oaks – phyletica.org 25/33
  77. 77. Ecoevolity: “Bake off” 0.00 0.05 0.10 0.15 0.20 0.00 0.05 0.10 0.15 0.20 ecoevolity p(τ ∈ CI) = 0.915 RMSE = 9.14e-04 dpp-msbayes p(τ ∈ CI) = 0.989 RMSE = 3.88e-03 msbayes p(τ ∈ CI) = 0.973 RMSE = 1.25e-02 True divergence time (τ) Estimateddivergencetime(¯τ) Shared divergences Jamie Oaks – phyletica.org 26/33
  78. 78. Ecoevolity: “Bake off” 0.000 0.002 0.004 0.006 0.000 0.001 0.002 0.003 0.004 0.005 0.006 ecoevolity p(Ne µ ∈ CI) = 0.936 RMSE = 2.11e-04 dpp-msbayes p(Ne µ ∈ CI) = 0.945 RMSE = 9.04e-04 msbayes p(Ne µ ∈ CI) = 0.751 RMSE = 1.48e-03 True root population size (Neµ) Estimatedrootpopulationsize(¯Neµ) Shared divergences Jamie Oaks – phyletica.org 26/33
  79. 79. Ecoevolity: “Bake off” 105 18 0 3 250 19 0 9 96 p(k ∈ 95%CS) = 0.992 p(ˆk = k) = 0.902 pp(k) = 0.942 ecoevolity 1 1 2 2 3 3 125 42 2 0 218 77 0 0 36 p(k ∈ 95%CS) = 0.996 p(ˆk = k) = 0.758 pp(k) = 0.789 dpp-msbayes 165 58 18 0 111 120 0 2 26 p(k ∈ 95%CS) = 0.964 p(ˆk = k) = 0.604 pp(k) = 0.699 msbayes True number of events (k) Estimatednumberofevents(ˆk) Shared divergences Jamie Oaks – phyletica.org 26/33
  80. 80. Ecoevolity: “Bake off” 105 18 0 3 250 19 0 9 96 p(k ∈ 95%CS) = 0.992 p(ˆk = k) = 0.902 pp(k) = 0.942 ecoevolity 1 1 2 2 3 3 125 42 2 0 218 77 0 0 36 p(k ∈ 95%CS) = 0.996 p(ˆk = k) = 0.758 pp(k) = 0.789 dpp-msbayes 165 58 18 0 111 120 0 2 26 p(k ∈ 95%CS) = 0.964 p(ˆk = k) = 0.604 pp(k) = 0.699 msbayes True number of events (k) Estimatednumberofevents(ˆk) Average run time: 33.4 minutes 4.4 days Shared divergences Jamie Oaks – phyletica.org 26/33
  81. 81. More data! RADseq: 400k–2million bases for 8 pairs of populations Shared divergences Jamie Oaks – phyletica.org 27/33
  82. 82. Ecoevolity: Results 0.0 0.2 0.4 0.6 1 2 3 4 5 6 7 8 Number of events Probability Shared divergences Jamie Oaks – phyletica.org 28/33
  83. 83. Ecoevolity: Results Sibuyan | Tablas Panay | Negros Polillo | Luzon 3 Luzon 2 | Camiguin Norte Luzon 1 | Babuyan Claro Samar | Leyte Palawan | Kinabalu Bohol | Camiguin Sur 0.0000 0.0025 0.0050 0.0075 0.0100 Time Comparison Shared divergences Jamie Oaks – phyletica.org 28/33
  84. 84. Our journey 0.00 0.25 0.50 0.75 1.00 1 2 3 4 5 6 7 8 9 Number of events Probability Shared divergences Jamie Oaks – phyletica.org 29/33
  85. 85. Our journey 0.00 0.25 0.50 0.75 1.00 1 2 3 4 5 6 7 8 9 Number of events Probability 0.00 0.05 0.10 0.15 0.20 1 2 3 4 5 6 7 8 9 Number of events Probability Shared divergences Jamie Oaks – phyletica.org 29/33
  86. 86. Our journey 0.00 0.25 0.50 0.75 1.00 1 2 3 4 5 6 7 8 9 Number of events Probability 0.00 0.05 0.10 0.15 0.20 1 2 3 4 5 6 7 8 9 Number of events Probability 0.0 0.2 0.4 0.6 1 2 3 4 5 6 7 8 Number of events Probability Shared divergences Jamie Oaks – phyletica.org 29/33
  87. 87. Our journey 0.00 0.25 0.50 0.75 1.00 1 2 3 4 5 6 7 8 9 Number of events Probability 0.00 0.05 0.10 0.15 0.20 1 2 3 4 5 6 7 8 9 Number of events Probability 0.0 0.2 0.4 0.6 1 2 3 4 5 6 7 8 Number of events Probability Conclusions? Shared divergences Jamie Oaks – phyletica.org 29/33
  88. 88. Next step: A general framework Develop a framework for inferring shared divergences across phylogenies τ1τ2 Shared divergences Jamie Oaks – phyletica.org 30/33
  89. 89. Next step: A general framework Develop a framework for inferring shared divergences across phylogenies τ1τ2 Shared divergences Jamie Oaks – phyletica.org 30/33
  90. 90. Next step: A general framework Develop a framework for inferring shared divergences across phylogenies Generalize Bayesian phylogenetics to incorporate shared divergences τ1τ2 Shared divergences Jamie Oaks – phyletica.org 30/33
  91. 91. Next step: A general framework Develop a framework for inferring shared divergences across phylogenies Generalize Bayesian phylogenetics to incorporate shared divergences Sample models numerically via reversible-jump Markov chain Monte Carlo τ1τ2 Shared divergences Jamie Oaks – phyletica.org 30/33
  92. 92. Next step: A general framework Develop a framework for inferring shared divergences across phylogenies Generalize Bayesian phylogenetics to incorporate shared divergences Sample models numerically via reversible-jump Markov chain Monte Carlo Benefits: Improve phylogenetic inference Framework for studying processes of co-diversification τ1τ2 Shared divergences Jamie Oaks – phyletica.org 30/33
  93. 93. Everything is on GitHub. . . Software: Ecoevolity: https://github.com/phyletica/ecoevolity PyMsBayes: https://joaks1.github.io/PyMsBayes dpp-msbayes: https://github.com/joaks1/dpp-msbayes ABACUS: Approximate BAyesian C UtilitieS. https://github.com/joaks1/abacus Open-Science Notebook: Ecoevolity experiments: https://github.com/phyletica/ecoevolity-experiments msBayes experiments: https://github.com/joaks1/msbayes-experiments Shared divergences Jamie Oaks – phyletica.org 31/33
  94. 94. Acknowledgments Ideas and feedback: Leach´e Lab Minin Lab Mark Holder Tracy Heath Michael Landis Computation: Funding: Photo credits: Rafe Brown, Cam Siler, Jesse Grismer, & Jake Esselstyn FMNH Philippine Mammal Website: D.S. Balete, M.R.M. Duya, & J. Holden PhyloPic! Shared divergences Jamie Oaks – phyletica.org 32/33
  95. 95. Questions? joaks@auburn.edu c 2007 Boris Kulikov boris-kulikov.blogspot.com Shared divergences Jamie Oaks – phyletica.org 33/33

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