A phylogenetic tree model on tree $T$ has outcomes that are described by assigning each leaf of the tree any label from a particular set (typically the label set is the set of DNA bases, \{A,T,C,G\}). The probability of a certain assignment of labels depends on transition probabilities between each ordered pair of labels. These transition probabilities are the parameters of the model.
In a group based model, the label set is a group $G$ (typically $\mathbb{Z}/2$ or $(\mathbb{Z}/2)^2$), and the transition probability for a pair $(g,h)$ depends only on $hg$. This reduces the number of parameters from $G^2$ to $G$. Depending on the model, further identifications of parameters are imposed.
An object of class Model stores the information about a groupbased model required to compute phylogenetic invariants. This information includes the elements of the group, how those elements are partitioned, and a set of automorphisms of the group that preserve the partitions.
There are four builtin models: CavenderFarrisNeyman or binary model (CFNmodel); JukesCantor model (JCmodel); Kimura 2parameter model (K2Pmodel); and Kimura 3parameter model (K3Pmodel). Other models can be constructed with model.


