1. Building Phylogenies Maximum Likelihood

2. Methods Distance-based Parsimony Maximum likelihood

3. Methods Distance-based Parsimony Maximum likelihood

4. ML is based on a Markov model of evolution Observed: The species labeling the leaves Hidden: The ancestral states Transition probabilities: The mutation probabilities Assumptions: –Only mutations are allowed –Sites are independent

5. Models of evolution at a site Transition probability matrix: M = [m ij ], i, j  {A, C, T, G} where m ij = Prob(i  j mutation in 1 time unit) Branches may have different lengths

6. The probability of an assignment AGCT Probability = m TG · m GA · m GG · m TT · m TC · m TT G T T

7. Ancestral reconstruction: most likely assignment AGCT L* = max X,Y,Z {m XY · m YA · m YG · m XZ · m ZC · m ZT } Y X Z Compute using Viterbi algorithm

8. Likelihood of a tree AGCT L* =  X,Y,Z {m XY · m YA · m YG · m XZ · m ZC · m ZT } Y X Z Compute using forward algorithm

9. Analyzing a site

10. Analysis for site j

11. Analysis for all sites Use enumeration (exhaustive, branch and bound, branch swapping, etc.) to find ML tree

12. Comments ML is robust ML converges to correct answer as more data is added Can put in a Bayesian statistical framework, to obtain a distribution of possible phylogenies ML can be slow

13. Complicating factors

14. Issues Complicating factors: –Gene duplication –Horizontal gene transfer: Exchange of genetic material between species –Chimeric genes Evolution may not be described by a tree, but by a network

15. Gene Duplication 11 22  human  -globin 5’3’

16. Homology, orthology, and paralogy Homology: Similarity attributed to descent from a common ancestor. Orthologous sequences: Homologous sequences in different species that arose from a common ancestral gene during speciation –May or may not be responsible for a similar function Paralogous sequences: Homologous sequences within a single species that arose by gene duplication.

17. Orthology and Paralogy http://www.ncbi.nlm.nih.gov/Education/BLASTinfo/Orthology.html

18. Conflicts between genes y species? AB CAC B SpeciesGenes

19. Resolving the conflict AB CA B C AB C   Problem: Resolve conflicts using the minimum number of duplications