Developed in 2001 by Simon Wheelan and Nick Goldman, the WAG (WhelanWheelan And Goldman) matrix is calculated using a [[maximum likelihood]] estimating procedure. The use of maximum likelihood makes it less prone to systematic errors than are the matrices based simply on comparing closely related homologs, such as PAM. The substitution scores are calculated based on the likelihood of a change considering multiple tree topologies derived using [[neighbor-joining]]. The scores correspond to an [[substitution model]] which includes also amino-acid stationary frequencies and a scaling factor in the similarity scoring. There are two versions of the matrix: WAG matrix based on the assumption of the same amino-acid stationary frequencies across all the compared protein and WAG* matrix with different frequencies for each of included [[protein family|protein families]].<ref name="WAG original paper">{{cite journal |last1=Whelan |first1=Simon |last2=Goldman |first2=Nick |title=A General Empirical Model of Protein Evolution Derived from Multiple Protein Families Using a Maximum-Likelihood Approach |journal=Molecular Biology and Evolution |date=1 May 2001 |volume=18 |issue=5 |pages=691–699 |doi=10.1093/oxfordjournals.molbev.a003851 |url=https://doi.org/10.1093/oxfordjournals.molbev.a003851 |issn=0737-4038}}</ref>
== Specialized substitution matrices and their extensions ==
