Phylogenetic Prediction Lecture II by Clarke S. Arnold March 19, 2002

1. Phylogenetic Prediction Lecture IIby Clarke S. ArnoldMarch 19, 2002

2. Outline • Comments about Trees • UPGMA (Unweighted Pair Group Method with Arithmetic Mean) analysis • Other uses of phylogenetic trees • Conversion of Alignment Scores to distances • Maximum Likelihood Approach • Comments on Neighbor Joining Algorithm • Conclusion

3. Comments on Trees • Trees give insights into underlying data • Identical trees can appear differently depending upon the method of display • Information maybe lost when creating the tree. The tree is not the underlying data.

4. UPGMA (Unweighted Pair Group Method with Arithmetic Mean) Algorithm • Create distance matrix • Build internal representation of Tree • Find two closest members • Combine members • Calculate new distances for combined node • Repeat until only one node is left (root node) • Draw Tree • If node Draw Node and Exit • Else Find Short and Tall Trees • Recursive Call DrawTree(Tall_Tree) • Recursive Call DrawTree(Short_Tree) • DrawConnection(Tall_Tree, Short_Tree) • Exit • Calculate loss of information (Cophenetic Correlation Coefficient) • Number between –1 and 1. • 1 Perfect Correlation • 0 No Correlation • -1 Perfect Reverse Correlation

5. Distance Matrix of 16s rna gene • Global alignments were done between 6 species of bacteria • Sequences were 500 base pair sequences from MIDI LABS. • Mismatches were used as the data points for the distance matrix. • sequences.txt http://genome.cs.mtu.edu/align/align.html alignments.txt

6. UPGMA Analysis • UPGMA Spread Sheet UPGMAfinal.xls

7. Other uses of phylogenetic trees • Verification of Taxonomy • Organisms have been classified into various groups before gene sequencing. • Is there a relationship between genetic differences and existing taxonomy? • bacpseu.txt http://clustalw.genome.ad.jp/ CLUSTALW.doc • bacpseustaph.txtTaxonomy.doc • Identification of Unknowns • Unknown is placed in the tree along with known samples • The relationship between the known and unknown sample allows for identification • unknown_id.txtUnknown_Results.doc • Non genetic analysis (Fatty Acids) • FattyAcid_PseuBaci.rtf

8. Conversion of Alignment Scores to Distances • Alignment scores are large for similar sequences. • Distance methods require that the distances between similar sequences are smaller than the distances between less similar sequences. • Large alignment scores need to be mapped to small distances and vice versa.

9. Maximum Likelihood Analysis • Same as Maximum Parsimony except rates of nucleic acids substitutions are not considered to have equal probability. • All possible unrooted trees are evaluated. (Same for Parsimony) • Each column of the alignment is processed. (Same for Parsimony) • The transition of A -> T will have a different probability than the transition from G -> C • Start with a frequency distribution table that specifies the probability of one base being substituted for another base. • See probabilities of nucleotide substitution. (Table 6.5 pg 275) • Probability that unrooted tree predicts each column of the alignment is calculated. • Probabilities for each column are summed together for each tree. • The unrooted tree with the highest probability is chosen.

10. Maximum Likelihood Example • Four sequences are compared (w, x, y and z) • All unrooted trees are shown • In this example we will examine the first unrooted tree.

11. Maximum Likelihood Example Continued • L(Tree x) = L0 * L1 * L2 * L3 * L4 * L5 * L6 • L0 base probability of nucleotide at 0 (0.25) • L1 probability of nucleotide changing from value at 0 to value at 1. • L2 probability of nucleotide changing from value at 0 to value at 1. • L3 probability of nucleotide changing from value at 1 to value at 3 (T). • L4, L5, L6 probability of nucleotide changing to value at leaf.

12. Maximum Likelihood Example Continued • There are 64 likelihood trees to evaluate. (number of internal nodes) ^ (number of bases) or 3^4. • We will show evaluation TTG against the first unrooted tree for column TTAG • Determine values for L0, … L6. Values are determined by looking up probabilities in transition probability table. • Probability of L2 is T->G • Probability of L5 is G -> A • Probability of L3 is T->T • Determine combined probability L0 * L1 * L2 * … * L6

13. Maximum Likelihood Example Continued • Determine probability for combination TGG • Determine probability for the other 62 combinations. • Sum all the trees together. L(Tree) = (LTree1) + L(Tree2) + … + L(Tree64) • Move to next column and repeat the same procedure. • Once all columns are complete sum all the probabilities. This is the likelihood of the first unrooted tree. • Continue this process for the other unrooted trees. • Pick the unrooted tree with the highest probability. This is the most likely unrooted tree.

14. Comments on Neighbor Joining compared with Fitch • Not nearest neighbor (objective is to create the smallest tree). • Nearest Neighbor is almost identical to Fitch except for the evaluation function. • Start with star • Evaluate all possibilities by combine any two nodes and run Fitch. • Evaluate size of tree by summing lengths of branchesPick smallest and continue. • Evaluation of Fitch is done by calculating the predicted distance between each pair of sequences for each tree to find the tree that best fits the original data. • Question? Is summing the braches faster that calculating predicted distance?

15. Conclusion • Phylogenetic Prediction can be used for more than Evolutionary Distance • Verification of Taxonomy • Identification of unknown • Techniques work for genetic and non genetic data (Fatty Acid). • Use multiple methods for verification • Pick at least two different types of methods from Parsimony, Distance and Likelihood. • If the analysis is in agreement there is a higher level of confidence that the analysis is correct.