Maximum Composite Likelihood (Gamma Rates and Heterogeneous Patterns)

The Tamura-Nei (1993)Tamura_and_Nei_1993 distance estimated by the composite likelihood methodHC_MCL (Tamura et al. 2004Tamura_et_al_2004) with the gamma model corrects for multiple hits, taking into account the rate substitution differences between nucleotides and the inequality of nucleotide frequencies.  In this distance, evolutionary rates among sites are modeled using the gamma distribution.  You will need to provide a gamma parameter According to the gamma distribution, the substitution rate often varies from site to site within a sequence. The shape of this distribution is determined by a value known as the gamma parameter, which is also known as the shape parameter.RH_Gamma_parameter for computing this distance. When the nucleotide frequencies between the sequences are different, the expected proportions of observed differences (P1, P2, and Q) in the computation of the composite likelihoodMaximum_Composite_Likelihood can be obtained by the modified formulas according to Tamura and Kumar (2002)Tamura_and_Kumar_2002 to relax the assumption of the substitution pattern homogeneity.