Equal Input Model (Gamma)

In real data, amino acid frequencies usually vary among the different kinds of amino acids and substitution rates are not uniform among sites. In this case, the correction based on the equal input model gives a better estimate of the number of amino acidsubstitutions than the Poisson correction distance.  The rate variation among sites is modeled using the Gamma distribution; for computing this distance you will need to provide a gamma parameterRH_Gamma_parameter (a).

MEGA provides facilities for computing the following quantities:

Formulas used are:

Distance

where p is the proportion of different amino acid sites, 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., g_i is the frequency of amino acid i,and

Variance