1. Multiple Alignment and Phylogenetic Trees
Csc 487/687 Computing for Bioinformatics

2. Terms related to graphs
Graph ― an abstract structure containing nodes and edges
Path ― a consecutive set of edges
Tree ― a connected graph with exactly one path between every two nodes
Edge length ―a number assigned to each edge signifying in some sense the distance between the nodes connected by edge
Path length ― the sum of the lengths of the edges that comprise the path
We describe phylogenetic relationships as trees. Graph, path, connected graph. Root, leaf. Binary tree. Directed graph. Each edge has one direction. Phylogenetic tree, directed graph. Ancestor-descendent relationship. Maybe you assign numbers to each edge for signifying the distance between the nodes connected by edge.
In phylogenetic trees, edge lengths means some measure of dissimilarity between two species. The time since their separation.

3. Deriving phylogenetic trees
Phenetic approach
Measuring a set of distances between species, and generate the tree by a hierarchical clustering procedure.
Cladistic approach
Consider possible pathways of evolution
Infer the features of the ancestor at each node
Choose an optimal tree according to some model of evolutionary changes.
Genealogy
There are two approach. Makes no reference to any historical model of the relationships. Similarity, genealogy.

4. Phenetic (clustering) approach
a simple clustering procedure
Determine a measure of the similarity or difference for all pairs
Create a tree from the set of dissimilarity iteratively
First choose two closely-related species, and insert a node to represent their common ancestor.
Replace the two selected species by a set containing both
Replace the distances from the pair to the others by the average distance of the two selected species to the others.
It can be used to produce a tree even in the absence of evolutionary relationships. Departmental store has goods clustered into sections according the types of product. Given a set of species,
This could depend on the physical body trait such as the difference of the average heights of members of two species. The number of different bases. For DNA sequence.

5. Phenetic (clustering) approach
Example
UPGMA method (Unweighted pair group method with arithmetic mean)
The number of different bases as the measure of dissimilarity between each pair of species. Use a simple clustering procedure to derive the phylogenetic tree.
The distance matrix. Symmetric, half. Nonzero distance. The first cluster. External evidence

6. Cladistic methods
The goal is to select the correct tree by utilizing an explicit model of the evolutionary process.
Maximum parsimony
Maximum likelihood
They are specialized to sequence data, starting from a multiple sequence alignment
Anatomic. Postulate. Ancestry. Taxa

7. Maximum parsimony method
An optimal tree as the one that introduces the fewest mutations.
Several trees may postulate the same number of mutations
Not unique answer

8. Maximum likelihood method
Assign quantitative probabilities to mutational events
The optimal tree is the one with the highest likelihood of generating the observed data
Not just counting them

9. The problem of varying rates of evolution
Subject to the errors if the rates of evolutionary change vary along different branches of the tree
outgroup―a species more distantly related to all the species than any pair of them is to each other.
Suppose that the four species A, B, C, D have the phylogenetic tree. Consistent with the dissimilarity matrix. Change very fast. Phylogeny doesn’t change. Incorrect phylogenetic tree. Primate, non-primate mammal such as a cow

10. Computational Consideration
Cladistic methods―maximum parsimony and maximum likelihood―are more accurate than simpler clustering method
But require large amount of computer time
Approximate answers
Calculated phylogenies are often approximations