Slide 1Today’s ObjectivesSlide 3Basic ProbabilityBasic ProbabilityBasic ProbabilitySlide 7a. Long Branch AttractionHow Can We Test Phylogenetic Methods?b. ExampleThe Example TreeThe Tree (with specific taxa)Supportive vs. Misleading Characters“Simulate” Many TimesSlide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21Slide 22Slide 23Slide 24Slide 25Slide 26Slide 27Slide 28Slide 29Slide 30Slide 31Slide 32Slide 33Slide 34Slide 35Slide 36Slide 37Slide 38Slide 39Slide 40Slide 41Slide 42For Example:For Example:For Example:Another Example:Another Example:f. Graph P versus QGraph P versus QGraph P versus QTry Web SimulationSignificance of LBASlide 53Slide 54Slide 55Slide 56Slide 57Slide 58Maximum Likelihood for PhylogeniesExampleC. Specify/Assume ModelD. Compare Different Possible TreesExample (For now, consider 2 of 3 trees to save time)e. Calculate probability for all different character historiese. 1. Maximum Likelihood ReconstructionRemember ModelSlide 67Probability of Possibility #1Probability of Possibility #1Likelihood of Possibility #1Likelihood of Possibility #1Likelihood of Possibility #1Likelihood of Possibility #2Likelihood of Possibility #2Likelihood of Possibility #2Likelihood of Possibility #2Likelihood of Possibility #2Likelihood of Possibility #3Likelihood of Possibility #4Likelihood of TreeACompare to TreeBf. Choose Best TreeMaximum Likelihood versus ParsimonyToday’s TopicsDistance Methods vs. Parsimony and MLTake Home MessageSlide 87Lecture 5Felsenstein Zone, Long Branch Attraction, and Maximum Likelihood in phylogeneticsToday’s Objectives•Understand that there are challenges to correct phylogeny reconstruction–(Derive Long Branch Attraction Example)•Example of Model-Based Method–Understand how to use Maximum Likelihood to reconstruct simple phylogeniesI. Review Basic ProbabilityBasic ProbabilityP(heads)=0.5 P(tails)=0.5Basic ProbabilityProbability of flipping HEADS AND THEN TAILS:0.5 * 0.5 = 0.25Basic ProbabilityProbability of flipping HEADS OR TAILS: 0.5 + 0.5 = 1.0Concerns with Phylogenies:Long Branch Attraction andThe Felsenstein Zonea. Long Branch Attraction•Parsimony proven under certain conditions to be “positively misleading”•Felsenstein (1978)•Later named “Felsenstein Zone”•Other methods also susceptible to varying degreesHow Can We Test Phylogenetic Methods?•Congruence – (Do different datasets, procedures agree?)•Known Phylogenies – (Well supported or experimentally generated)•Simulation – (Generate data with a computer)b. Example•Imagine characters have two states, present (1) and absent (0)•Imagine a rooted tree with 3 species•Ancestral State is 0 and it can evolve to 1, but not reverse•There are 4 branches, 2 are long (high chance changes in trait) 2 are short (low chance for changes in trait)The Example Tree0????“P branches”Probability ofChange = P“Q branches”Probability of Change = QThe Tree(with specific taxa)0????“P branches”Probability ofChange = P“Q branches”Probability of Change = QSupportive vs. Misleading Characters01100101Supports Correct Tree Supports Incorrect Tree“Simulate” Many Times0110011001100110011001100110010101100110011001010101010101010101c. What is the probability that the “P” branches will have the same state?0101“P branches”Probability ofChange = P“Q branches”Probability of Change = QWhat is the probability that the “P” branches will have the same state?0101“P branches”Probability ofChange = P“Q branches”Probability of Change = QWhat state(s)at this node?What is the probability that the “P” branches will have the same state?0101“P branches”Probability ofChange = P“Q branches”Probability of Change = Q0What is the probability that the “P” branches will have the same state?0101“P branches”Probability ofChange = P“Q branches”Probability of Change = Q0What is theprobability ofchanging to 1?What is the probability that the “P” branches will have the same state?0101“P branches”Probability ofChange = P“Q branches”Probability of Change = Q0PPWhat is the probability that the “P” branches will have the same state?0101“P branches”Probability ofChange = P“Q branches”Probability of Change = Q0P PPPWhat is the probability that the “P” branches will have the same state?0101“P branches”Probability ofChange = P“Q branches”Probability of Change = Q0What is theprobability of startingand ending at 0?What is the probability that the “P” branches will have the same state?0101“P branches”Probability ofChange = P“Q branches”Probability of Change = Q0P * (1-Q) * P1-QWhat is the probability that the “P” branches will have the same state?0101“P branches”Probability ofChange = P“Q branches”Probability of Change = Q0P * (1-Q) * (1-Q) * P1-Q1-Qd. What is the probability that the first 2 branches will have the same state?0110?“P branches”Probability ofChange = P“Q branches”Probability of Change = QWhat is the probability that the first 2 branches will have the same state?0110?“P branches”Probability ofChange = P“Q branches”Probability of Change = QWhat state shouldbe here?What is the probability that the first 2 branches will have the same state?0110“P branches”Probability ofChange = P“Q branches”Probability of Change = Q101 or 0What is the probability that the first 2 branches will have the same state?0110(1-P) * [Q + (PQ) * (1-Q)]“P branches”Probability ofChange = P“Q branches”Probability of Change = Q1 or 0001101+What is the probability that the first 2 branches will have the same state?0110“P branches”Probability ofChange = P“Q branches”Probability of Change = Q1 or 0001101+What is the probabilityof not changing alongthis branch?What is the probability that the first 2 branches will have the same state?0110“P branches”Probability ofChange = P“Q branches”Probability of Change = Q001101+1- PWhat is the probability that the first 2 branches will have the same state?0110“P branches”Probability ofChange = P“Q branches”Probability of Change = Q001101+1- P1- PWhat is the probability that the first 2 branches will have the same state?0110“P branches”Probability ofChange = P“Q branches”Probability of Change = Q001101+What is the probabilityof NOT changing onthis branch?1- PWhat is the probability that the first 2 branches will have the same state?0110“P branches”Probability