Phylogenetic Trees - Parsimony Tutorial #13 © Ydo Wexler & Dan Geiger .

Phylogenetic Trees - Reminder phylogenetic tree: diagram showing evolutionary lineages of species/genes why construct trees? to understand lineage of various species to understand how various functions evolved to understand multiple alignments

Phylogenetic Trees - Methods There are several methods with which we estimate how good a tree describes the data (and thus the evolution process) Distance based methods Parsimony Likelihood

Phylogenetic Trees - Reminder leaves represent objects (genes, species) being compared internal nodes are hypothetical ancestral units in a rooted tree, path from root to a node represents an evolutionary path an unrooted tree specifies relationships among objects, but not evolutionary paths

Parsimony Based Approches given: character-based data do: find a tree that explains the data with a minimal number of changes

Parsimony Example there are various trees that could explain the phylogeny of the following sequences: AAG, AAA, GGA, AGA AAA AGA AAG GGA AAA AGA AAG GGA parsimony prefers the second tree because it requires less substitution events

Parsimony Based Approches usually these approaches involve two separate components: A search through the space of trees A procedure to find the minimum number of changes needed to explain the data (for a given tree topology)

Fitch’s Algorithm traverse tree from leaves to root determining set of possible states (e.g. nucleotides) for each internal node traverse tree from root to leaves picking ancestral states for internal nodes

Fitch’s Algorithm – Step 1 do a post-order (from leaves to root) traversal of tree Determine possible states Ri of internal node i with children j and k

Fitch’s Algorithm – Step 1 # of changes = # union operations T T AGT CT GT C T G T A T

Fitch’s Algorithm – Step 2 do a pre-order (from root to leaves) traversal of tree select state rj of internal node j with parent i

Fitch’s Algorithm – Step 2 CT C A G AGT GT T CT C A G AGT GT T CT C A G AGT GT T CT C A G AGT GT T CT C A G AGT GT T CT C A G AGT GT

Weighted Version of Fitch’s Algorithm instead of assuming all state changes are equally likely, use different costs S(a,b) for different changes 1st step of algorithm is to propagate costs up through tree

Weighted Version of Fitch’s Algorithm want to determine min. cost Ri(a) of assigning character a to node i for leaves:

Weighted Version of Fitch’s Algorithm want to determine min. cost Ri(a) of assigning character a to node i for internal nodes: a i j k b

Weighted Version of Fitch’s Algorithm – Step 2 do a pre-order (from root to leaves) traversal of tree select minimal cost character for root For each internal node j, select character that produced minimal cost at parent i

Exploring the Space of Trees we’ve considered how to find the minimum number of changes for a given tree topology need some search procedure for exploring the space of tree topologies Given n sequences there are Possible rooted trees

Exploring the Space of Trees taxa (n) # trees 4 15 5 105 6 945 8 135,135 10 30,405,375

Limitations of Sequence Based Phylogenetic trees Sequences must be Orthologues, NOT Paralogues to draw evolutionary inferences. Will not work with Recombinational DNA transfer between genomes (common in viruses and Prokaryotes). Does not apply to larger DNA sequences involving DNA crossovers (“Family Trees”).