Genesis and growth of mutants is a central processus in evolutionary biology. The rate at which mutations randomly appear is a key parameter, determining the speed at which genetic diversity is generated. It is classically estimated through a classical experiment called the fluctuation test, where bacteria are growth in a non-selective medium and then exposed to a selective environment to count surviving mutants. Mutation rate is then inferred from the number of surviving mutants, using a now classical mathematical model which makes restrictive assumptions about the demographic processes involved.In this work, we are interested in more general cases not covered by this classical model (more complex demographics). We developed an efficient algorithm for stochastic simulation of this problem, and use it to perform simulation-based inference using approximate bayesian computing methods. We show that these methods can successfully infer one or several parameters of the model in arbitrarily complex growth models.
