. The additive tree reconstruction technique starts with this tree. And then adds one more species each time, based on the distance matrix combined with the property mentioned above. If we consider for example an additive matrix and 5 species and . First we form an additive tree for two species and . Then we chose a third one, let's say and attach it to a point on the edge between and . The edge weights are computed with the property above. Next we add the fourth species to any of the edges. If we apply the property then we identify that should be attached to only one specific edge. Finally, we add following the same procedure as before. UPGMA The basic principle of UPGMA(Unweighted Pair Group Method with Arithmetic Mean) is that similar species should be closer in the phylogenetic tree. Hence, it builds the tree by clustering similar sequences iteratively. The method works by building the phylogenetic tree bottom up from its leaves. Initially, we have leaves (or singleton trees), each representing a species in . Those leaves are referred as clusters. Then, we perform iterations. In each iteration, we identify two clusters and with the smallest average distance and merge them to form a bigger cluster . If we suppose is ultrametric, for any cluster created by the UPGMA algorithm, is a valid ultrametric tree. Neighbor joining Neighbor is a bottom-up clustering method. It takes a distance matrix specifying the distance between each pair of sequences. The algorithm starts with a completely unresolved tree, whose topology corresponds to that of a star network, and iterates over the following steps until the tree is completely resolved and all branch lengths are known: Based on the current distance matrix calculate the matrix (defined below). Find the pair of distinct taxa i and j (i.e. with ) for which has its lowest value. These taxa are joined to a newly created node, which is connected to the central node. In the figure at right, f and g are joined to the new node u. Calculate the distance from each of the taxa in the pair to this new node. Calculate the distance from each of the taxa outside of this pair to the new node. Start the algorithm again, replacing the pair of joined neighbors with the new node and using the distances calculated in the previous step. Fitch-Margoliash The