Muller's ratchet — first-loss time t₀

A simulation study for the forthcoming manuscript "A semigroup approach towards the rate of Muller's ratchet" by C. S. Heinzel, P. Pfaffelhuber and A. Wakolbinger.

Each marker is one (ψ, δ) parameter set for the chosen N. Here ψ = N·s·e^−u/s is the key quantity for the ratchet's speed (clicks are frequent on a timescale of ψ generations when ψ ≪ 1, rare when ψ ≫ 1), and δ fixes the ratio u/s in units of log N: u/s = δ·log(N) (so larger δ means a larger u/s). Simulated y-values are computed per path, then averaged (mean ± SD over paths with finite t₀ > 0; only sets where 100% of paths clicked are shown). Dashed lines are theory curves (no averaging, drawn over all δ). Hover a point for ψ, δ, s, u, u/s, N·e^(−u/s).

The two update orders start from different initial conditions: each path begins at the stationary marginal of its order — Poisson(u/s) for selection → mutation, but Poisson((u/s)·(1−s)) for mutation → selection (the fittest class is, on average, slightly fuller when mutation acts first), so the two curves are not just a reordering of the same run.