QMix: An Efficient Program to Automatically Estimate Multi-Matrix Mixture Models for Amino Acid Substitution Process.

The single-matrix amino acid (AA) substitution models are widely used in phylogenetic analyses; however, they are unable to properly model the heterogeneity of AA substitution rates among sites. The multi-matrix mixture models can handle the site rate heterogeneity and outperform the single-matrix models. Estimating multi-matrix mixture models is a complex process and no computer program is available for this task. In this study, we implemented a computer program of the so-called QMix based on the algorithm of LG4X and LG4M with several enhancements to automatically estimate multi-matrix mixture models from large datasets. QMix employs QMaker algorithm instead of XRATE algorithm to accurately and rapidly estimate the parameters of models. It is able to estimate mixture models with different number of matrices and supports multi-threading computing to efficiently estimate models from thousands of genes. We re-estimate mixture models LG4X and LG4M from 1471 HSSP alignments. The re-estimated models (HP4X and HP4M) are slightly better than LG4X and LG4M in building maximum likelihood trees from HSSP and TreeBASE datasets. QMix program required about 10 hours on a computer with 18 cores to estimate a mixture model with four matrices from 200 HSSP alignments. It is easy to use and freely available for researchers.