Stochastic modelling and analysis of neutral tumor evolution. - Can neutral tumor evolution be inferred from real data?

We develop a branching process with accumulating mutations to model neutral tumor evolution. Furthermore, by using this model, it will be shown in details which approximations and simplifications that are necessary in order to deduce the same expression as in Willams et. al (2016)[1] characterizing a neutral tumor evolution. Stochastic simulations of the branching process will actively be used in order to validate approximations with respect to accuracy. The model will then take DNA sequencing into account, and a measure for showing the inaccuracies of observed variant allele frequencies will be developed. Lastly, in terms of inaccuracies from both the power-law distribution deduced and after sequencing, it will be argued that there are yet too much uncertainties in order to infer, using statistical hypothesis tests, whether a neutral tumor evolution actually is a good description of evolution for certain tumors. [1] Williams, M. J., Werner, B., P. Barnes, C., Graham, T. A. & Sottoriva, A. (2016), Identification ofneutral tumor evolution across cancer types ,Nature Genetics48(3), 238 244