2. Comparative methods: Using trees to study evolution

3. Some uses for phylogenies Character evolution –Ancestral states –Trends and biases –Correlations among characters Molecular evolution –Evidence of selection “Key innovations” –Diversification rate

4. Why reconstruct character evolution? Can evaluate homology

5. How do we know that bat and bird wings are not homologous?

6. Why reconstruct character evolution? Can evaluate homology Can determine character-state polarity

8. Why reconstruct character evolution? Can evaluate homology Can determine character-state polarity Can evaluate the “selective regime” when a character evolved

9. Was the ancestor bird pollinated when red flowers evolved? Look at pollinators Bee to bird poll. Adaptation supported

10. Alternative result Bee to bird poll. Not an adaptation

11. A third possibility Bee to bird poll. Consistent with adaptation

12. Why reconstruct character evolution? Can evaluate homology Can determine character-state polarity Can evaluate the “selective regime” when a character evolved Can recreate ancestral genes/proteins

13. Dinosaur Rhodopsin Chang et al. (MBE 2002)

14. Character optimization using parsimony Pick the reconstruction that minimizes the “cost” What do you do if more than one most- parsimonious reconstruction –ACCTRAN/DELTRAN –Consider all What character-state weights should you use?

16. Cost-change graph (Ree and Donoghue 1998: Syst. Biol. 47:582-588)

17. Stability to gain:loss weights

18. What gain:loss weight to use? If you believe gains are more common (hence weighted less) you will find more gains (and vice versa) So how can you use a tree to establish if there is a gain:loss bias?

19. Wing loss and re-evolution? Whiting et al. (Nature 2003)

20. A likelihood approach Developed (in parallel) by Mark Pagel and Brent Milligan in 1994 Continuous time Markov model Select the rate of gains (0->1) and rate of losses (1->0) that maximizes the likelihood of the data given a sample tree (and branch lengths)

21. Transition rate matrix 01 01-q 1 q1q1 1q2q2 1-q 2 From To

22. Logic Calculate the likelihood of the data for a given value of q1 and q2 Modify q1 and q2 to find a pair of values that maximizes the probability of the data

23. Probabilities summed across all possible ancestral states 1101000110 0 0 0 0 0 0 0 0 0

24. How much of the likelihood contributed by each state at each node

26. Are gain and loss rates different? Likelihood ratio test –Model 1: gains and losses free to vary independently –Model 2: gains and losses equal How many degrees of freedom?

27. Ree and Donoghue, 1999

28. The likelihood method Provides a method for using the data to evaluate gain:loss bias Takes account of branch lengths Still sensitive to taxon sampling

29. 1101000110 Suppose this taxon contains 5000 species Suggests that the rate of losses is low

30. 1101000110 Suppose this taxon contains 5000 species Suggests that the rate of gains is low

31. After equalizing the number of species of each type

32. Correlated evolution Look at pairs of traits (where one trait can be an environment) –Body size and range size –Warning coloration and gregariousness –Fleshy fruit and dioecy Do these traits evolve non-independently?

33. Causes of non-independence Developmental “connectedness” Adaptation (Correlated evolution has been claimed to be the best evidence for evolution by natural selection)

34. Non-phylogenetic (“tip”) method Count species Do a chi-square test Green eyesBlue eyes Pale fur2100 Dark fur1502

35. Hypothetical tree Eyes g b g g b b Fur d d p p d p 150 100

36. Proposed solutions for discrete characters Do a chi-square test of changes rather than tip-states (various approaches) - Ridley; Sillen-Tullberg Use a Monte Carlo approach to ask if changes of the dependent variable are biased relative to expectations from changes placed on the tree at random - W. Maddison

37. Non-phylogenetic (“tip”) method FleshyDry One1034 Many2362

38. Maddison test Fleshy Branches Dry Branches One->Many37 Many.>One62 Probability that this pattern or a more extreme pattern could arise without fruit type affecting seed number is ca. 8%.

39. Problems with the Maddison test Requires one to define dependent and independent characters Does not take account of branch-length Very sensitive to inclusion/exclusion of species

40. Maximum likelihood approach (Pagel and Milligan) 0,00,11,01,1 0,0q12q130 0,1q210q24 1,0q310q34 1,10q42q43

41. Procedure Estimate the set of rates in the q-matrix that maximize the likelihood of the data and calculate that likelihood Constrain the matrix so that it represents independence (q12 = q34; q13 = q24; q21 = q43; q31 = q42) and repeat the calculation Use a likelihood ratio test to evaluate significance

42. Issues to consider Rejection of independence does not tell you what kind of non-independence you have You need reasonable branch lengths Sampling matters (if perhaps less than parsimony)