Rare Events Simulation In Bacterial Genetic Evolution Models

Rare events often disturb the dynamics of random systems dramatically, despite their low frequencies. It is crucial to study the possible paths leading to the happening of these rare events and the probabilities of these paths. We focus on rare events the frequencies of certain intermediate-strength genotypes become unusually large in the stochastic model of bacterial genetic evolution. Such rare events are called fixations. We introduce two numerical algorithms to estimate the probabilities of fixations. The first algorithm is based on the large deviations theory and the importance sampling method. The second algorithm is inspired by the genealogy method introduced by physicists.