Algorithm research project neighbor joining
- 1. Neighbor Joining Jay Mehta CSC 6520 Instructor :- Dr. Alex Zelikovsky
- 2. 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.
- 3. Some examples of Phylogenetic/ Evolutionary Trees
- 4. Example:-
- 7. 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.
- 9. Input Output • Species represented as Points. • Distance Matrix. • Evolutionary Tree which can also be called a Resolved Tree.
- 10. Additive Metric The 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
- 11. Least Square Objective (NP-complete) • 𝐷𝑖𝑗 − Real world observed distances between the species. • 𝑇𝑖𝑗 − Calculated Distance over the phylogenetic tree. • Objective Minimizing 𝑆 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 − 𝑇𝑖𝑗 2
- 12. Step 1:- • Modify the input distance matrix using this equation. 𝑄 𝑖, 𝑗 = 𝑛 − 2 ∗ 𝑑 𝑖, 𝑗 − 𝑘=1 𝑛 𝑑 𝑖, 𝑘 − 𝑘=1 𝑛 𝑑 𝑗, 𝑘 )
- 13. Next Steps:- • Find the pair of points (taxa) for which 𝑄 𝑖, 𝑗 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.
- 14. Next Steps… + = Using the formulas mentioned in the previous slide calculate the distances and the new matrix. Repeat the steps.
- 16. Implementations • RapidNJ • NINJA • BIONJ • Weighbor
- 17. Thank You