A continuous-time model to correct for selection in mutation accumulation experiments

Mutation accumulation (MA) experiments are crucial for understanding evolution. In microbial populations, these experiments typically involve periods of population growth, where a single individual forms a visible colony, followed by severe bottlenecks. Studies on the effects of positive and negative selection in MA experiments have shown that, even with as few as ten generations of growth between bottlenecks, beneficial mutations will be substantially over-represented (Wahl and Agashe, 2022); this effect is known as "selection bias". In previous work, we developed a discrete-time model and demonstrated that when stochastic offspring distributions are considered, selection bias is even stronger than previously predicted (Ezadian and Wahl, 2025). Since bacterial division is unlikely to remain synchronized over 15 or more generations, this study extends the discrete-time model to a continuous-time framework. Since lineages that start reproducing early accrue a compounded advantage, a continuous-time model offers an even more accurate correction for selection in MA experiments. In addition, we develop techniques for estimating the selection bias when only colonies above a fixed threshold size (e.g. visible colonies) are selected at the bottleneck, an experimental protocol that further exacerbates selection bias. We develop and describe computationally efficient techniques for correcting experimental MA data whether all colonies or only visible colonies are considered.