Rare Events Analysis and Computation for Stochastic Evolution of Bacterial Populations

TL;DR

This paper introduces a gradient descent computational method to efficiently identify the most likely trajectories of rare genetic events in bacterial populations, based on large deviations theory for Markov chains.

Contribution

It presents a novel gradient descent algorithm for fast, accurate computation of rare event trajectories in stochastic bacterial evolution models.

Findings

The algorithm outperforms existing methods in speed and accuracy.

Numerical simulations validate the computational efficiency and robustness.

The approach effectively captures rare genotype emergence in large populations.

Abstract

In this paper, we develop a computational approach for computing most likely trajectories describing rare events that correspond to the emergence of non-dominant genotypes. This work is based on the large deviations approach for discrete Markov chains describing the genetic evolution of large bacterial populations. We demonstrate that a gradient descent algorithm developed in this paper results in the fast and accurate computation of most-likely trajectories for a large number of bacterial genotypes. We supplement our analysis with extensive numerical simulations demonstrating the computational advantage of the designed gradient descent algorithm over other, more simplified, approaches.