NJML+: an extension of the NJML method to handle protein sequence data and computer software implementation

While the maximum-likelihood (ML) method of tree reconstruction is statistically rigorous, it is extremely time-consuming for reconstructing large trees. We previously developed a hybrid method (NJML) that combines the neighbor-joining (NJ) and ML methods and thus is much faster than the ML method and improves the performance of NJ. However, we considered only nucleotide sequence data, so NJML is not suitable for handling amino acid sequence data, which requires even more computer time. NJML+ is an implementation of a further improved method for practical data analyses (including protein sequence data). Our extensive simulations using nucleotide and amino acid sequences showed that NJML+ gave good results in tree reconstruction. Indeed, NJML+ showed substantial improvements over existing methods in terms of both computational times and efficiencies, especially for amino acid sequence data. We also developed a "user-friendly" interface for the NJML+ program, including a simple tree viewer.