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Maximum likelihood testing model

Maximum likelihood testing model. Definition. Method for the inference of phylogeny Method that searches for the tree with the highest probability or likelihood. Advantages of Maximum likelihood. Lower variance than other methods Least affected by sampling error

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Maximum likelihood testing model

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  1. Maximum likelihood testing model

  2. Definition • Method for the inference of phylogeny • Method that searches for the tree with the highest probability or likelihood.

  3. Advantages of Maximum likelihood • Lower variance than other methods • Least affected by sampling error • Robust to many violations of the assumptions of the evolutionary model, even with very short sequences, they outperform other methods). • Are less error prone. • Statistically well founded. • Evaluate different tree topologies.

  4. Disadvantages of Maximum likelihood • CPU intensive and may take a long time to complete an evaluation • The result is dependent on the model of evolution used.

  5. Example going through the Maximum likelihood model • Assume that we have the aligned nucleotide sequences for four taxa: (1) A G G C U C C A A ....A (2) A G G U U C G A A ....A (3) A G C C C A G A A.... A • A U U U C G G A A.... C Evaluate the likelihood of the uprooted tree represented by the nucleotides of site j in the sequence http://www.icp.ucl.ac.be/~opperd/private/max_likeli.html

  6. Since the likelihood of the tree is independent of the position of the root, we can display the figure as shown in Figure B. • Assume that the nucleotides evolve independently (the Markovian model of evolution) • Calculate the likelihood for each site separately and combine the likelihood into a total value towards the end. • . To calculate the likelihood for site j, we have to consider all the possible scenarios by which the nucleotides present at the tips of the tree could have evolved. • Therefore the likelihood for a particular site is the summation of the probabilities of every possible reconstruction of ancestral states, given some model of base substitution. http://www.icp.ucl.ac.be/~opperd/private/max_likeli.html

  7. So in this specific case all possible nucleotides A, G, C, and T occupying nodes (5) and (6), or 4 x 4 = 16 possibilities: • Protein sequences each site may occupy 20 states (that of the 20 amino acids) • 20x20 thus 400 possibilities have to be considered. • Since any one of these scenarios could have led to the nucleotide configuration at the tip of the tree, we must calculate the probability of each and sum them to obtain the total probability for each site j. http://www.icp.ucl.ac.be/~opperd/private/max_likeli.html

  8. The likelihood for the full tree then is product of the likelihood at each site. • Since the individual likelihoods are extremely small numbers it is convenient to sum the log likelihoods at each site and report the likelihood of the entire tree as the log likelihood.

  9. This above procedure is then repeated for all possible topologies (for all possible trees). • The tree with the highest probability is the tree with the highest maximum likelihood.

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