models of DNA evolution was proposed Jukes and Cantor in 1969. The Jukes-Cantor (JC or JC69) model assumes equal transition rates as well as equal equilibrium frequencies for all bases and it is the simplest sub-model of the GTR model. In 1980, Motoo Kimura introduced a model with two parameters (K2P or K80): one for the transition and one for the transversion rate. A year later, Kimura introduced a second model (K3ST, K3P, or K81) with three substitution types: one for the transition rate, one for the rate of transversions that conserve the strong/weak properties of nucleotides ( and , designated by Kimura), and one for rate of transversions that conserve the amino/keto properties of nucleotides ( and , designated by Kimura). An 1981, Joseph Felsenstein proposed a four-parameter model (F81) in which the substitution rate corresponds to the equilibrium frequency of the target nucleotide. Hasegawa, Kishino, and Yano unified the two last models to a five-parameter model (HKY). After these pioneering efforts, many additional sub-models of the GTR model were introduced into the literature (and common use) in the 1990s. Other models that move beyond the GTR model in specific ways were also developed and refined by several researchers. Almost all DNA substitution models are mechanistic models (as described above). The small number of parameters that one needs to estimate for these models makes it feasible to estimate those parameters from the data. It is also necessary because the patterns of DNA sequence evolution often differ among organisms and among genes within organisms. The later may reflect optimization by the action of selection for specific purposes (e.g. fast expression or messenger RNA stability) or it might reflect neutral variation in the patterns of substitution. Thus, depending on the organism and the type of gene, it is likely necessary to adjust the model to these circumstances. Two-state substitution models An alternative way to analyze DNA sequence data is to recode the nucleotides as purines (R) and pyrimidines (Y); this practice is often called RY-coding. Insertions and deletions in multiple sequence alignments can also be encoded as binary data and analyzed in using a two-state model. The simplest two-state model of sequence evolution is called the Cavender-Farris model or the Cavender-Farris-Neyman (CFN) model; the name of this model reflects the fact that it was described independently in several different publications. The CFN model is identical to the Jukes-Cantor model adapted to