Weini Huang

All life organisms accumulate genetic errors during cell reproduction. Such errors named as mutations are the source of evolution, but also can lead to severe diseases such as different types of cancer. While it is often hard to measure dynamic properties of many biological systems e.g. the growth history of tumours in patients, the pattern of mutations accumulated in tissues can be used as a footprint to quantify those dynamic traits. Here we focus on two types of mutation patterns, Site frequency spectra (SFS) and mutation burden distribution (MBD), where SFS measuring the probability density distribution of all mutations across cells in a population and mutation burden distribution referring to number of mutations accumulated in single cells. Analytical solution of SFS both in growing (cancer) and constant (healthy) populations are continuous with power-law shapes. Mutation frequencies exceeding the expected average are often considered a signal of positive selection, where given mutations drive the out-control growth of cells. However, in single evolutionary trajectories, the SFS is non-continuous and many especially high frequencies are entirely void of mutations. We observed in our stochastic simulations that mutations can jointly move towards high frequencies and fixation. This  lead to an effectively bi-modal process in single evolutionary repeats. While all real data from patients correspond to single evolutionary processes, a SFS exceeding the expected average by large margins is not necessarily an aberration in need of an explanation, but instead can be a regular occurrence even in the absence of selection. In addition, the SFS and MBD can be united in a natural way by a general framework based on recurrence relations. Using public available data, we showed that integrating the SFS from the population level and MBD from the single cell level data can bring more precise predictions than standard evolutionary models where only one of the information are considered.