  Most human tumors result from the accumulation of multiple genetic and
epigenetic alterations in a single cell. Mutations that confer a fitness
advantage to the cell are known as driver mutations and are causally related to
tumorigenesis. Other mutations, however, do not change the phenotype of the
cell or even decrease cellular fitness. While much experimental effort is being
devoted to the identification of the different functional effects of individual
mutations, mathematical modeling of tumor progression generally considers
constant fitness increments as mutations are accumulated. In this paper we
study a mathematical model of tumor progression with random fitness increments.
We analyze a multi-type branching process in which cells accumulate mutations
whose fitness effects are chosen from a distribution. We determine the effect
of the fitness distribution on the growth kinetics of the tumor. This work
contributes to a quantitative understanding of the accumulation of mutations
leading to cancer phenotypes.
