Neighbor Joining

Jay MehtaCSC 6520

Instructor :- Dr. Alex Zelikovsky

Distance Matrix Methods ?• These are methods which are used for building phylogenetic trees.• These methods rely on genetic distances to form a tree.• Neighbor Joining method is one of the Distance Matrix methods.

Some examples of Phylogenetic/

Evolutionary Trees

Example:-

One More Example:-

Last Example:-

Uses:-The neighbor-joining method allows scientists to calculate when different species, or variations within a species, diverged by analyzing differences on a molecular level.

The Neighbor Joining Algorithm

Input Output• Species represented as Points.

• Distance Matrix.

• Evolutionary Tree which can also be called a Resolved Tree.

Additive MetricThe algorithm is based on the assumption that we are dealing with additive trees. An additive tree means a tree where

the distance between nodes 1 and 2 =

the distance between node 1 and node X +

the distance between node 2 and node X

Least Square Objective (NP-complete)

• Real world observed distances between the species.• Calculated Distance over the phylogenetic tree.• Objective Minimizing

Our objective is to find a tree and branch lengths minimizing the least squares residual. This is definitely a NP-complete problem.

𝑆=∑𝑖𝑗

(𝐷𝑖𝑗−𝑇 𝑖𝑗 )2

Step 1:-• Modify the input distance matrix using this equation.

Next Steps:-• Find the pair of points (taxa) for which has lowest value.• Connect the two nodes using a new node. Give it a new label.• Calculate distances from the new node to existing taxa.• Distance of the new node from the pair nodes.

• Distance of outside taxa from the new node.

Next Steps…

+ =

Using the formulas mentioned in the previous slide calculate the distances and the new matrix.

Repeat the steps.

Algorithm Analysis:-

𝑂 (𝑛3)

Implementations• RapidNJ• NINJA• BIONJ• Weighbor

Thank You