Inferring mutation rates from evolutionary histories with path integral methods

Living things evolve to increase their chances of survival within their environment. The same process also occurs for pathogens such as viruses or bacteria within a host. Better understanding the evolution of antibiotic resistance or how pathogens escape from immune responses may inform the design of better treatment techniques and vaccines. Evolutionary models such as the Wright-Fisher model can simulate such processes. However, these models depend on knowing detailed properties of a pathogen, such as its mutation rate and how mutations affect its fitness. Here we study how such properties can be inferred from data, in particular, genetic sequences collected over time from a population. Recent work applied techniques from statistical physics to models from population genetics to derive a path integral that efficiently quantifies the probability of an evolutionary history of a population. This allowed for the estimation of the fitness effects of mutations from data, assuming that the underlying mutation rates were known. Here, we consider the opposite case: how can mutation rates be estimated from data, assuming that the underlying fitness effects of mutations are given. We derive an approximate expression to estimate mutation rates from data in this scenario and show its performance in example simulations.