Seminar

In recent years, there have been an increasing interest in modeling the evolution of cancer tumors through different stochastic models. Some of these models assume that there is no interaction among daughter cells with their progenitors (branching processes) and there are some others that indeed consider this interaction: Moran models. 

If recurrent mutations are allowed in wild-type cells, they will be eventually replaced by mutants. However, if the time to extinction is sufficiently long, the conditional distribution of surviving wild-type cells arises. If it is stationary given non-extinction, it is called the quasi-stationary distribution (QSD). In this talk, I will give a brief introduction to the Moran model and some of its variants. I will also show the analytical forms of the QSD for the case of birth and death rates being constant, for the neutral case and for the directionally selective Moran models.