Mixed models are sometimes called "site models".
Mixed models combine substitution models with respective probabilities. We call submodels all the models that are mixed in the mixture. A Mixed model is either the mixture of several predefined models, or based on a "simple" model in which some parameters follow given distributions.
During the likelihood computation process, all the submodels of the mixture are successively applied on the branches, and the mean (see below) of all the likelihoods is computed.
A site can follow given paths all along the tree, with given probabilities.
In homogeneous reconstruction, a path corresponds to a same submodel on all the branches, in a stationary condition. The probability of a path is the probability of its submodel. Given a site follows a path, a likelihood can be computed; and the overall likelihood on this site is the mean of these likelihoods (given the probabilities of the paths). This means that the root distribution is a mixture of the equilibrium distributions of the submodels.
With nonhomogeneous reconstruction, several models are applied on the tree, some models are mixed, some are not. A path is a vector which size is the number of mixed models (see below for more details and the declaration of paths).
Since the attribution of a submodel from a mixed model to a given site is a unique random variable, affecting the same mixed model to a set of branches S means that the attribution to this site is the same on all the branches of S. If model M=(Ma,Mb,Mc) is defined on a set of branches S, a site in constrained to follow either Ma on all S, or Mb on all S, or Ms on all S. If we want that two branches of S are independant, two similar mixed models must be defined. Moreover, it is possible to define paths that define dependencies between submodels of different mixtures (see below).
MixedModel(model={model description})Mixture model from a given model in which some parameters follow a probabilistic distribution. Any discrete distribution available can be used See Discrete distributions. The description of the parameters distributions is described below.
model=MixedModel(model=TN93(kappa1=Gamma(n=4,alpha=3,beta=1),\
kappa2=Exponential(lambda=2),\
theta=0.5,theta1=0.2,theta2=0.1))
has parameters TN93.kappa1_Gamma.alpha, TN93.kappa1_Gamma.beta, TN93.kappa2_Exponential.lamba, TN93.theta, MixedModel.TN93.theta1, TN93.theta2.
See the Bio++ description.
Mixture(model1={model description},..., modeln={model description} [, relrate1={1>real>0},..., relrate{n-1}={1>real>0}, relproba1={1>real>0}, ..., relproba{n-1}={1>real>0}, "equilibrium frequencies"])Mixture model built from several models: each model has its own probability and rate.
Arguments relproba{i} stands for the relative probability and relrate{i} stands for the relative rate of each model (in the order the models are given). Default: relproba{i}=1/{n-i+1}, such that the probabilty of each site is 1/n, and relrate{i}=1/{n-i+1} such that the rate of each site is 1.
model=Mixture(model1=GY94(), model2=YN98(), relrate1=0.1)
has parametersMixture.relrate1, Mixture.relproba1, Mixture.1_GY94.kappa, Mixture.1_GY94.V, Mixture.2_YN98.kappa, Mixture.2_YN98.omega.
See the Bio++ description.