Consecutive seeding and transfer of genetic diversity in metastasis

The transfer of genetic diversity between spatially separated growing populations is relevant to a wide range of biological applications, including clonal diversity in cancer metastasis, clonal hematopoiesis in stem cell biology, and species diversity in ecology. We study a multitype branching process of population growth that originates from a single individual but over time receives additional migrants. We derive a surprisingly simple expression for the fraction of genetic diversity transferred between populations as a function of the immigration rates that connect them. Additionally, we calculate statistics for the fixation index FST between populations. Using this model framework, we analyze single-cell sequencing data from ovarian, breast, and colorectal cancer samples collected from 15 patients. For these genetically diverse cell populations, we find an average seeding rate of 1-10 migrant cells per cellular generation time. Under typical metastasis growth conditions, this estimate suggests that 16-130 cells seeded each metastasis and left surviving lineages. Since primary tumors are often surgically removed, the genetic diversity of these metastases determines the probability for treatment efficacy.