Botany 940 Review 1 Parsimony Likelihood Principle Ingredients of molecular evolution models Substitution rate matrix Distribution of rates Bootstrap Divergence times Next week Bayesian methods Testing monophyly Parsimony a b c d TAATAATTAAAA TATTTTTTATAA TAAATAATTTTT TAATAAATTAAT ab cd ac bd ad bc L 11 L 14 L 12 a c b d Bootstrap with Parsimony 12 volunteers choose a number between 1 and 12 Get a new alignment and a new MP tree Repeat a c a 69 b b a 31 d d b 0 c c d Likelihood principle Probability model can be used to make predictions c a many b d Data probability model A T A A A A T A and few likelihood probability of the data under the model measures the fit of the model to the data T A A A A A A T Maximum Likelihood ML tree find the tree and parameters that maximize the likelihood Tree score log likelihood ab cd ac bd ad bc 30 34 31 02 31 02 parameters a 0 b 55 35 c 55 d 0 a 0 c 7 9 0 b 55 d 35 a 0 d 35 27 b 27 c 7 6 Bootstrap with Maximum Likelihood 12 volunteers choose a number between 1 and 12 Get a new alignment and a new ML tree Repeat a c a 80 b b a 15 d d b 5 c c d Ingredients of molecular evolution models Topology Branch lengths in number of substitutions per site Usually unconstrained no clock Substitution rate matrix A 1 33 33 33 C 33 1 33 33 G 33 33 1 33 T 33 33 33 1 1 20 60 20 85 40 35 10 20 1 20 60 60 20 1 20 20 60 20 1 15 60 35 10 15 40 65 10 15 40 35 90 JC K80 k 3 F81 unequal base freq Ingredients of molecular evolution models Common models reversible The root doesn t matter Base freq ti tv ratio param JC equal 1 0 K80 equal free 1 F81 free 1 3 HKY85 free free 4 F84 free free 4 TN93 free two ti tv ratios are free 5 GTR free All rate ratios are free 8 Ingredients of molecular evolution models Distribution of rates across sites Some sites are slow some are fast Model each site chooses a rate r at random from some distribution r 0 2 r 1 r 1 2 r 0 8 Ingredients of molecular evolution models Distribution of rates across sites Model Gamma distribution of rates continuous and discretized for calculations Ingredients of molecular evolution models Distribution of rates across lineages Covarion models hidden on off process for absence presence of constraint 1 3 parameters Ingredients of molecular evolution models Partitions in the data 1st 2nd and 3rd codon positions several genes are available or several exons and introns or nuclear mt DNA Allow blocks to have their own models and or parameters Estimation of Divergence Times Times and rates are counfounded Sites can evolve for 1 million years at 5 10 7 subst year site or for 10 000 years at 5 10 5 subst year site the alignement will look the same 0 5 subst site on average Difficult problem fossil calibrations usually few and uncertain rates vary a lot
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