Here the authors present a novel formalism for understand the emergence of mutations within a population, similar to the Moran process, but based on mutation rates pulled from Poisson distributions. This allows, per the author, for more exact (and simple) calculations for waiting times. I pulled this one out of the 'Probability' portion of the arXiv, and it is certainly Mathematical oncology (capital M, lower case o), but as so many folks in our field use the Moran process (and probability theory in general), I thought it would be of interest. Maybe +Dominik Wodarz would like to comment?
The waiting time for a second mutation: an alternative to the Moran model
(Submitted on 28 Jun 2013)
The appearance of cancer in a tissue is thought to be the result of two or more successive mutations. We propose a stochastic model that allows for an exact computation of the distribution of the waiting time for a second mutation. This models the time of appearance of the first cancerous cell in a tissue. Our model is an alternative to the Moran model with mutations.
link to arXiv: http://arxiv.org/abs/1306.6919