Describe the form of a substitution matrix One of the unique strengths of Hy-Phy is its ability to implement any special case of a general time reversible model, regardless of the dimensions of the character set. We will devote an entire chapter to model specification (see ???). To accomplish this feat, we decompose the evolutionary model into two components: the character frequencies, and the substitution parameters. We rely on the fact that any special case of the general reversible model can be written in a form where entries in the substitution matrix are products of substitution parameters and character frequencies (see ???). In F81.bf we see one of the very simplest model specifications. The line F81RateMatrix = {{* ,mu,mu,mu} {mu,* ,mu,mu} {mu,mu,* ,mu} {mu,mu,mu,* }}; in conjuction with a frequency vesctor such as obsFreqs, is sufficient to define the F81 model. Note that the syntax of the matrix definition consists simply of the rows of a matrix. For the F81 model, the instantaneous rate matrix is traditionally denoted $$\bordermatrix{\ & A & C & G & T \cr A &-\mu(1-\pi_A)& \mu \pi_C &... ...(1-\pi_G)& \mu \pi_T \cr T & \mu \pi_A & \mu \pi_C & \mu \pi_G &-\mu(1-\pi_T) }$$ Observe the similarity between this matrix and the Hy-Phy syntax. The Hy-Phy operator * is defined as "the negative of the sum of all non-diagonal entries on the row". (Rate matrices have the property of row elements summing to zero.)
Sergei L. Kosakovsky Pond and Spencer V. Muse, 1997-2002