Model -- a group-based model

Description

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 $h-g$. 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 group-based 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 built-in models: Cavender-Farris-Neyman or binary model (CFNmodel); Jukes-Cantor model (JCmodel); Kimura 2-parameter model (K2Pmodel); and Kimura 3-parameter model (K3Pmodel). Other models can be constructed with model.

i1 : M = CFNmodel

o1 = Model{AList => HashTable{0 => {1, 0}}}
                              1 => {0, 1}
           Automorphisms => HashTable{}
           Buckets => {{0}, {1}}
           Group => {0, 1}

o1 : Model

i2 : T = leafTree(3,{})

o2 = {{0, 1, 2}, {set {0}, set {1}, set {2}}}

o2 : LeafTree

i3 : phyloToricAMatrix(T,M)

o3 = | 1 1 0 0 |
     | 0 0 1 1 |
     | 1 0 1 0 |
     | 0 1 0 1 |
     | 1 0 0 1 |
     | 0 1 1 0 |

              6       4
o3 : Matrix ZZ  <-- ZZ

Methods that use an object of class Model :

buckets(Model) -- see buckets -- the equivalence classes of group elements of a Model
fourierToProbability(Ring,Ring,ZZ,Model) -- see fourierToProbability -- map from Fourier coordinates to probability coordinates
group(Model) -- see group -- the group of a Model
leafColorings(LeafTree,Model) -- see leafColorings -- list the consistent colorings of a tree
leafColorings(ZZ,Model) -- see leafColorings -- list the consistent colorings of a tree
phyloToric42(Graph,Model) -- see phyloToric42 -- compute the invariants of a group-based phylogenetic model with 4ti2
phyloToric42(LeafTree,Model) -- see phyloToric42 -- compute the invariants of a group-based phylogenetic model with 4ti2
phyloToric42(ZZ,List,Model) -- see phyloToric42 -- compute the invariants of a group-based phylogenetic model with 4ti2
phyloToricAMatrix(Graph,Model) -- see phyloToricAMatrix -- construct the design matrix of a group-based phylogenetic model
phyloToricAMatrix(LeafTree,Model) -- see phyloToricAMatrix -- construct the design matrix of a group-based phylogenetic model
phyloToricAMatrix(ZZ,List,Model) -- see phyloToricAMatrix -- construct the design matrix of a group-based phylogenetic model
phyloToricFP(LeafTree,Model) -- see phyloToricFP -- compute the invariants of a group-based phylogenetic model with toric fiber products
phyloToricFP(ZZ,List,Model) -- see phyloToricFP -- compute the invariants of a group-based phylogenetic model with toric fiber products
phyloToricLinears(LeafTree,Model) -- see phyloToricLinears -- compute the linear invariants of a group-based phylogenetic model
phyloToricLinears(ZZ,List,Model) -- see phyloToricLinears -- compute the linear invariants of a group-based phylogenetic model
phyloToricQuads(LeafTree,Model) -- see phyloToricQuads -- compute the quadratic invariants of a group-based phylogenetic model
phyloToricQuads(ZZ,List,Model) -- see phyloToricQuads -- compute the quadratic invariants of a group-based phylogenetic model
phyloToricRandom(LeafTree,Model) -- see phyloToricRandom -- compute a random invariant of a group-based phylogenetic model
phyloToricRandom(ZZ,List,Model) -- see phyloToricRandom -- compute a random invariant of a group-based phylogenetic model
pRing(LeafTree,Model) -- see pRing -- construct the ring of probability coordinates
pRing(ZZ,Model) -- see pRing -- construct the ring of probability coordinates
qRing(LeafTree,Model) -- see qRing -- construct the ring of Fourier coordinates
qRing(ZZ,Model) -- see qRing -- construct the ring of Fourier coordinates

Fixed objects of class Model :

CFNmodel -- the model corresponding to the Cavender-Farris-Neyman model or binary Jukes Cantor
JCmodel -- the model corresponding to the Jukes Cantor model
K2Pmodel -- the model corresponding to the Kimura 2-parameter model
K3Pmodel -- the model corresponding to the Kimura 3-parameter model

For the programmer

The object Model is a type, with ancestor classes HashTable < Thing.

Model -- a group-based model

Description

See also

Methods that use an object of class Model :

Fixed objects of class Model :

For the programmer