Brian O ’ Meara http:// www.brianomeara.info

1. Brian O’Meara • http://www.brianomeara.info http://www.youtube.com/watch?v=9R8hpPY_9kY Get out laptop, fire up R

2. install.packages("ctv") library(ctv) install.views("Phylogenetics") install.packages("corHMM")

3. Model selection

5. Likelihood ratio test test statistic = 2(ln L1 - ln L0)

6. Likelihood ratio test

7. Likelihood ratio test Posada and Crandal 1998

8. Akaike information criterion AICi = -2 ln Li + ki AIC is estimator as distance between truth and approximating model “Truth drops out as a constant”-- Burnham and Anderson 2004

9. Bayes Factors

10. Reversible jump MCMC Model 1 Model 1 Model 2 Model 2

11. Organize by: Question Method • Continuous time Markov Chain • Birth death process • Multivariate normal • BiSSE and friends • Tree stretching • Correlation of herbivory with group living • Crepuscular foraging being intermediate between nocturnal and diurnal • Biogeography • Causes of diversification • Rate of trait evolution • What limits the number of species

12. Flour, sugar, egg, butter, leavening, liquid

13. Continuous time Markov chain finite state space A, T, G, C woody, herbaceous susceptible, infected, recovered herbivorous, omnivorous, carnivorous 0, 2, 4, 6, 8, ..., 100 legs

14. Per day: What is probability of it leaving the store that day? If it leaves, what is the probability it was paid for? What is the probability it stays in the store ≥ two days?

15. Per ∆t:

16. Per ∆t:

17. Per ∆t:

18. Per ∆t:

19. Per ∆t:

20. Does the store ever get Twinkies back? [Do people return Twinkies for a refund?] H0: r*-store = 0 H1: r*-store > 0

21. Do adults give to kids at the same rate kids give to adults? H0: rchild-adult = radult-child H1: rchild-adult ≠ radult-child

22. From this basic model: • Hypotheses about rates for a single character (are some equal? are some zero?) • Hypotheses about correlation between characters • Tree inference • Ancestral state inference

23. Continuous time Markov chain finite state space

24. Currie et al. 2010 Nature

25. Currie et al. 2010 Nature

26. Currie et al. 2010 Nature

27. Currie et al. 2010 Nature

28. 0 0 0 0 0 0 0 0 0 Currie et al. 2010 Nature

29. 0 0 0 0 0 0 Currie et al. 2010 Nature

30. Currie et al. 2010 Nature

31. Currie et al. 2010 Nature

32. Currie et al. 2010 Nature

33. Currie et al. 2010 Nature

34. 0 A 1 A 0 B 1 B No social play No sex play No social play Yes sex play No sex play Yes social play Yes sex play Yes social play

36. 0 0 0 0

37. 0 A 1 A 0 B 1 B No social play No sex play No social play Yes sex play No sex play Yes social play Yes sex play Yes social play

38. No social play No sex play 0 A No social play Yes sex play No sex play Yes social play 1 A 0 B 1 B Yes sex play Yes social play

39. Pagel 1994

41. Barker & Pagel 2005

42. 0 1 1 1 0 0 1 0

43. Barker & Pagel 2005

44. Barker & Pagel 2005

46. ... ... up to maximum number of genes ... ... where a, b, etc. are just f(i, j, birthdeath rate)

47. Ree & Smith 2008

48. Ree & Smith 2008

49. Courtesy Nicolas Salamin

50. Joint: Choose values for x, y, z, w that together maximize likelihood