Theoretical foundation to estimate the relative efficiencies of the Jukes–Cantor+gamma model and the Jukes–Cantor model in obtaining the correct phylogenetic tree

This paper deals with the theoretical foundation to estimate the relative efficiency (probability of inferring the true tree) of different nucleotide substitution models. A novel theoretical approach has been developed to estimate the relative efficiency of nucleotide substitution models based on the neighbor-relation method. The theory was developed directly by using the four-point condition. Initially theoretical formulas for the Jukes–Cantor+gamma (JC+Γ) model and the Jukes–Cantor (JC) model were developed to estimate their relative efficiencies. Theoretical formulas were used on several model topologies for both models to obtain a true tree. Extensive simulations were performed on the same set of trees to test the strength of the theoretical approach. Simulation results demonstrated a good agreement with results obtained by the theoretical estimation. Overall the theoretical foundation for estimating model efficiencies is very accurate.