Using coalescent theory to analyze genetic data from growing populations

Suppose we randomly sample individuals from a population and follow their ancestral lines backwards in time. The ancestral lines will merge, until eventually the entire sample is traced back to one common ancestor. Because the shape of the resulting genealogical tree affects how many mutations are inherited by the sampled individuals, the theory of coalescent processes can provide insight into what we should expect to observe in genetic data collected from the sample. When the size of the population stays approximately constant, the genealogy of the sample can be described by a well-studied coalescent process known as Kingman’s coalescent, in which each pair of lineages merges at rate one. However, some populations, such as populations of tumor cells, grow rapidly, and the classical theory based on Kingman’s coalescent does not apply. Recent results of Lambert (2018), and Harris, Johnston, and Roberts (2020) allow us to to construct the exact genealogy of a sample from a birth and death process.  We will use this construction to establish some new asymptotic results for the number of mutations that will be inherited by individuals sampled from an exponentially growing population. We will then apply these results to some data from blood cancer to estimate the rate at which the cancer is spreading. We will also present related results in a model in which the growth of the population is limited by spatial constraints.  The results for the birth and death process are based on joint work with Kit Curtius, Brian Johnson, and Yubo Shuai.  The results for spatial models are based on joint work with Shirshendu Ganguly and Yubo Shuai.

Bio
https://math.ucsd.edu/people/profiles/jason-schweinsberg