Algorithm for statistical alignment of two sequences derived from a Poisson sequence length distribution

The statistical approach to DNA sequence evolution involves the stochastic modelling of the substitution, insertion and deletion processes. Substitution has been modelled by finite Markov-process for more than three decades. Modelling the insertion and deletion process is in its new-age, and the recent model has a serious drawback: it assumes geometric sequence length equilibrium distribution, which contradicts biological knowledge. An algorithm is presented that computes the joint probability of two sequences evolved on a non-reversible way from a Poisson sequence length distribution.