Title: Griffiths-Tavare versus Lambert coalescents: Application in modeling of cancer evolution
Authors: Marek Kimmel - Rice University (United States) [presenting]
Abstract: Recent years brought a large amount of work concerning retrospective reconstruction of cancer growth and mutation sometimes called the genetic archaeology of tumors. Most of this work has been based on the mathematical framework of Moran model or Kingman coalescent. However, neither of these approaches assumes an underlying model of proliferation, which would reflect cell divisions, frequently inefficient, of cells in tumors. One way of taking this latter into account is to base the coalescent trees on branching processes, with the simplest nontrivial scenario being the binary fission Markov age-dependent branching process aka birth and death process. This approach has been developed mostly by previously. We derive an explicit expression for the expectation of the site frequency spectrum (SFS) in Lambert model, and develop a simple and efficient simulation scheme based on the iid rv representation. We also examine how the SFS based on birth-and-death process differ from those based on Griffiths-Tavare model. This includes a discussion of the singleton estimation problem as well as the self-renewal fraction versus proliferation rate controversy.