because including the stop codons would mean that one is calculating the probability of finding sense codon after time given that the ancestral codon is would involve the possibility of passing through a state with a premature stop codon. An alternative (and commonly used) way to write the instantaneous rate matrix ( matrix) for the nucleotide GTR model is: The matrix is normalized so . This notation is easier to understand than the notation originally used by Tavaré, because all model parameters correspond either to "exchangeability" parameters ( through , which can also be written using the notation ) or to equilibrium nucleotide frequencies . Note that the nucleotides in the matrix have been written in alphabetical order. In other words, the transition probability matrix for the matrix above would be: Some publications write the nucleotides in a different order (e.g., some authors choose to group two purines together and the two pyrimidines together; see also models of DNA evolution). These difference in notation make it important to be clear regarding the order of the states when writing the matrix. The value of this notation is that instantaneous rate of change from nucleotide to nucleotide can always be written as , where is the exchangeability of nucleotides and and is the equilibrium frequency of the nucleotide. The matrix shown above uses the letters through for the exchangeability parameters in the interest of readability, but those parameters could also be to written in a systematic manner using the notation (e.g., , , and so forth). Note that the ordering of the nucleotide subscripts for exchangeability parameters is irrelevant (e.g., ) but the transition probability matrix values are not (i.e., is the probability of observing A in sequence 1 and C in sequence 2 when the evolutionary distance between those sequences is whereas is the probability of observing C in sequence 1 and A in sequence 2 at the same evolutionary distance). An arbitrarily chosen exchangeability parameters (e.g., ) is typically set to a value of 1 to increase the readability of the exchangeability parameter estimates (since it allows users to express those values relative to chosen exchangeability parameter). The practice of expressing the exchangeability parameters in relative terms is not problematic because the matrix is normalized. Normalization allows (time) in the matrix exponentiation to be expressed in units of expected substitutions per site (standard practice in molecular phylogenetics). This is the