Phylogenetic analysis is to analyze the evolutionary of species according to the characteristics of biological sequences The analytical results are generally represented by phylogenetic trees NJ (Neighbor-Joining) is a frequently used algorithm for constructing phylogenetic trees, which is based on distances between taxa, because of its few assumptions, fast operation and high accuracy It is known that NJ usually constructs different phylogenetic trees for the same dataset with different input orders, known as “tied trees” This paper proposes an improved method of NJ, called as ENJ (Extended Neighbor-Joining) ENJ can join several (currently limited to three) nodes with the same minimum distance into a new node rather than joining two nodes in one iteration, so it may construct triple phylogenetic trees We have inferred the formulas for updating the distance values and calculating the branch lengths in ENJ algorithm We have test ENJ with simulated data and real data The experimental results show that compared with other methods, the trees constructed by ENJ are more similar to the initial trees, and its speed is much faster than the NJ algorithm Moreover, we have constructed a phylogenetic tree for the novel coronavirus (2019-nCoV) and related coronaviruses by ENJ, which shows that 2019-nCoV and SARS-CoV are closer than other coronaviruses Because it is different from the existing phylogenetic trees for those coronavirus, we construct a phylogenetic network for them The network shows those species have a reticulate evolution
ENJ algorithm can construct triple phylogenetic trees