 Unlike many maximum likelihood calculations, the relative values for formula_115, formula_108, and formula_105 can vary across branches and the Hadamard transform can even provide evidence that the data do not fit a tree.The Hadamard transform can also be combined with a wide variety of methods to accommodate among-sites rate heterogeneity, using continuous distributions rather than the discrete approximations typically used in maximum likelihood phylogenetics (although one must sacrifice the invertibility of the Hadamard transform to use certain among-sites rate heterogeneity distributions).F81, the Felsenstein's 1981 model, is an extension of the JC69 model in which base frequencies are allowed to vary from 0.25 (formula_118)

Rate matrix