  We present a comprehensive new framework for handling biologically accurate
models of molecular evolution. This model provides a systematic framework for
studying models of molecular evolution that implement heterogeneous rates,
conservation of reading frame, differing rates of insertion and deletion,
customizable parametrization of the probabilities and types of substitutions,
insertions, and deletions, as well as neighboring dependencies. We have stated
the model in terms of an infinite state Markov chain in order to maximize the
number of applicable theorems useful in the analysis of the model. We use such
theorems to develop an alignment-free parameter estimation technique. This
alignment-free technique circumvents many of the nuanced issues related to
alignment-dependent estimation. We then apply an implementation of our model to
reproduce (in a completely alignment-free fashion) some observed results of
Zhang and Gerstein (2003) regarding indel length distribution in human
ribosomal protein pseudogenes.
