Tamura-Nei distance (Gamma rates and Heterogeneous patterns)

The Tamura-Nei (1993Tamura_and_Nei_1993) distance 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 modified formula (Tamura and Kumar 2002Tamura_and_Kumar_2002) relaxes the assumption of the substitution pattern homogeneity.

The Tamura-Nei model

MEGA provides facilities for computing the following quantities for this method:

The formulas for computing these quantities are as follows:

Distances

where P₁ and P₂ are the proportions of transitional differences between nucleotides A and G, and between T and C, respectively, Q is the proportion of transversional differences, g_XA, g_XC, g_XG, g_XT, are the respective frequencies of A, C, G and T of sequence X, g_XR = g_XA + g_XG and g_XY = g_XT + g_XC, g_A, g_C, g_G, g_T, g_R, and g_Y are the average frequencies of the pair of sequences, a is the 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. and

The variances can be estimated by the bootstrap method.