Abstract
Recent years have produced a large amount of work on inference about cancer evolution from mutations identified in cancer samples. Much of the modeling work has been based on classical models of population genetics, generalized to accommodate time-varying cell population size. Reverse-time genealogical views of such models, commonly known as coalescents, have been used to infer aspects of the past of growing populations. Another approach is to use branching processes, the simplest scenario being the linear birth-death process (lbdp), a binary fission Markov age-dependent branching process. A genealogical view of such models is also available. The two approaches lead to similar but not identical results. Inference from evolutionary models of DNA often exploits summary statistics of the sequence data, a common one being the so-called Site Frequency Spectrum (SFS). In a sequencing experiment with a known number of sequences, we can estimate for each site at which a novel somatic mutation has arisen, the number of cells that carry that mutation. These numbers are then grouped into sites which have the same number of copies of the mutant. SFS can be computed from the statistics of mutations in a sample of cells, in which DNA has been sequenced. In this paper, examine how the SFS based on birth-death processes differ from those based on the coalescent model. This may stem from the different sampling mechanisms in the two approaches. However, we also show mathematically and computationally that despite this, they can be made quantitatively comparable at least for the range of parameters typical for tumor cell populations. We also present a model of tumor evolution with selective sweeps, based on coalescence, and demonstrate how it may help in understanding the past history of tumor as well the influence of data pre-processing. We illustrate the theory with applications to several examples of The Cancer Genome Atlas tumors.
