1. Branch and Bound Optimization In an exhaustive search, all possible trees in a search space are generated for comparison At each node, if the tree is optimal we retain it As the number of taxa becomes large, this approach becomes intractable Thus, there is a need for an approach that can effectively prune the search space so that finding solution may become more feasible One such approach is the branch-and-bound method

2. Exhaustive Search Search for optimal trees by evaluating every possible tree Feasible only for <=11 taxa, as processing costs rapidly increase after that Figure shows exhaustive search for a 5-taxa tree

3. Branch and Bound Focuses on pruning the search space by ignoring families of trees that can not possible produce a better answer than the best one already found Traverse a search tree in a depth-first sequence Trees that have longer tree length than the previously examined ones are ignored MP (Maximum Parsimony tree, i.e. the topology with the minimum tree length) is determined by evaluating tree lengths for a group of trees that have potentially shorter length Faster than an exhaustive search, but still impractical for large numbers of taxa

4. Branch and Bound Methodology When a node is encountered that has a higher tree-length than the minimum tree length, all the subsequent expansions for the tree are pruned away This corresponds to taking a subset of m taxa, where m<n (n = current minimum found) and computing tree length If this tree length is larger than the tree length we have for any n taxa configuration, the m tree topology and all its children are aborted from further consideration