Molecular Evolution Day 02 Lewis + Swafford + Zwicki - integrated with Eric terms / concepts, so details may be highly inaccurate. Comments and error-detection greatly appreciated :) - AND - multiply probabilities for events that happen simultaneously - OR - add probabilities for events that are mutually exclusive - Phylogenetic probabilities: 1) multiply probabilities for observed states and a single set/combination of possible ancestral states. 2) Add probabilities for different possible sets/combinations of ancestral states to explore unobserved ancestral states/nodes - Likelihood probability: Probability of observations as computed by a given model. - Likelihood criterion: The model with the largest (maximum) likelihood probability is the least surprising, and so the model with the largest maximum likelihood is the most likely of the tested models to explain the observed data. - Likelihood probabilities (x) can be really really small, so people prefer to use the log likelihood ( log(x) or ln(x) ). - Probabilities are always between 0 and 1, which means the log of probabilities will always be negative, i.e., log likelihoods are always negative. - a tree bipartition or split is written as AB|CDE or **--- - number of substitutions = rate x time v = { r } t - there are a number of different nucleotide substitution models for determining the substitution rate (r): JC69, F81, K80, F84, HKY85, GTR - the likelihood of a tree is the product of likelihoods for each site of paired aligned sequences of each branch of the tree: L = ( L site 1 ) ( L site 2 )...( Lsite n ) - GG_________AG arbitrarily root on GG Tree likelihood L = ( L site 1 ) ( L site 2 ) Lsite1 = Pr(G) x Pr(G|G for a given product of ( substitution rate alpha )( time t ) ) Lsite2 = Pr(G) x Pr(A|G for a given product of ( substitution rate alpha )( time t ) ) You can now plot log likelihood as a function of (alpha) x (t) to determine the maximum log likelihood. I still dont quite understand this... - It is necessary to explore all possible ancestral states when computing the maximum likelihood of a given tree. - Pruning allows a calculation to be made once and then reused, providing a much more efficient exploration and likelihood calculation for all possible ancestral states on a tree. - Because rate and time are confounded in the number of substitutions, it is convienent to standardize things by setting the rate to a value such that one substitution occurs in one unit time. Thus, time or branch lengths is measured in evolutionary distance - expected number of substitutions per site. - JC69: All nucleotide base frequencies are equal and have equal rates of nucleotide substitution. 1 parameter model - Jukes-Cantor transition probability is the probability that a site starting with nucleotide X will end in nucleotide Y after t amount of time, assuming equal substitution rates alpha. - ACHNyons vs substitutions - any base can appear for ACHNyons, substitution a differnent base appears. - substitutions + identical replacement + nothing are incorporated into a model for Jukes-Cantor transition probablities - equilibrium frequency under JC69 is 0.25 per nucleotide, as all are equal - The JC69 rate matrix has one parameter, alpha, which doesn’t differentiation nucleotide substitution transtitions from transversions. - K80 or K2P: nucletotide base frequencies are equal but nucleotide substitution rates are not equal. 2 parameter model - K80 separates nucleotide substitution transitions from transversions - K80 rate matrix has two parameters kappa and beta. kappa = alpha / beta. alpha = transition rate. beta = transversion rate. - F81: nucleotide base frequencies are not equal but nucleotide substitution reates are equal. A four parameter model. - F81 parameters are: mew is ? some factor for base frequencies. PieA, PieC, PieG are the nucleotide base frequencies. PieT is calculate from the other three and is not included as a parameter in the model. - HKY85: Nucleotide base frequencies and nucleotide substitution rates are unequal. A five parameter model.
Posted on: Wed, 30 Jul 2014 10:58:38 +0000
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