A new molecular evolution model for limited insertion independent of substitution

We recently introduced a new molecular evolution model called the IDIS model for Insertion Deletion Independent of Substitution  and . In the IDIS model, the three independent processes of substitution, insertion and deletion of residues have constant rates. In order to control the genome expansion during evolution, we generalize here the IDIS   model by introducing an insertion rate which decreases when the sequence grows and tends to 0 for a maximum sequence length _nmax$n_{\max }$.