Genealogies in Growing Solid Tumors

Over the past two decades, the theory of tumor evolution has largely focused on the selective sweeps model. According to this theory, tumors evolve by a succession of clonal expansions that are initiated by driver mutations that have a fitness advantage over the resident types. A 2015 study of colon cancer [44] has suggested an alternative theory of tumor evolution, the so-called Big Bang model, in which all of the necessary driver mutations are acquired before expansion began, and the evolutionary dynamics within the expanding population are predominantly neutral. In this paper, we will describe a simple mathematical model inspired by work of Hallatschek and Nelson [25] that makes quantitative predictions about spatial patterns of genetic variability. While this model has some success in matching observed patterns in two dimensions, it fails miserably in three dimensions. Despite this failure, we think the model analyzed here will be a useful first step in building an accurate model.