Tajima Nei Distance (Gamma Rates and Heterogeneous patterns)

In real data, nucleotide frequencies often deviate substantially from 0.25. In this case the Tajima-Nei distance (Tajima and Nei 1984Tajima_and_Nei_1984) gives a better estimate of the number of nucleotide substitutions than the Jukes-Cantor distance. Note that this assumes an equality of substitution rates among sites and between transitionalRH_Transition and transversionalRH_Transversion substitutions.  The rate variation among sites is modeled using the gamma distribution, and 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 (a) for computing this distance.When the nucleotide frequencies are different between the sequences, the modified formula (Tamura and Kumar 2002Tamura_and_Kumar_2002) relaxes the assumption of substitution pattern homogeneity.

The Felsenstein-Tajima-Nei model

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

d: Transitions + Transversions: Number of nucleotide substitutions per site.

L: No of valid common sites: Number of sites compared.

The formulas for computing these quantities are as follows:

Distance

where p is the proportion of sites with different nucleotides, 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

where x_ij is the relative frequency of the nucleotide pair i and j,  g_i’s are the nucleotide frequencies.

Variance can be estimated by the bootstrap method.