Genome evolution by transformation, expansion and contraction (GETEC).

We propose here the GETEC (Genome Evolution by Transformation, Expansion and Contraction) model of gene evolution based on substitution, insertion and deletion of genetic motifs. The GETEC model unifies two classes of evolution models: models of substitution, insertion and deletion of nucleotides as function of time (Lèbre and Michel, 2010) and sequence length (Lèbre and Michel, 2012), and models of symmetric substitution of genetic motifs as function of time (Benard and Michel, 2011). Evolution of genetic motifs based on substitution, insertion and deletion is modeled by a differential equation whose analytical solutions give an expression of the genetic motif occurrence probabilities as a function of time or sequence length, as well as in direct time direction (past-present) or inverse time direction (present-past). Evolution models with "substitution only", i.e. without insertion and deletion, and with "insertion and deletion only", i.e. without substitution, are particular cases of the GETEC model. We have also developed a research software for computing the analytical solutions of the GETEC model. It is freely accessible at http://icube-bioinfo.u-strasbg.fr/webMathematica/GETEC/ or via the web site http://dpt-info.u-strasbg.fr/∼michel/.