Deterministic Modeling of Muller’s Ratchet Effect in Populations Evolving in an Environment of Finite Capacity

We study how small harmful mutations spread in populations that reproduce asexually. This process is known as Muller’s ratchet—it means that even though these mutations are damaging, they can still build up over generations. To explore this, we use a mathematical model that describes how such mutations move through a population living in an environment with limited resources. We model Muller’s ratchet deterministically using differential equations, incorporating modifications that account for extinction risk of small mutation classes. We analyze two modifications: a published cutoff modification and a more flexible exponential modification. We show that the exponential modification better matches stochastic simulations over specific parameter ranges.