INTERACTIVE COMPANION · EVOLUTION IN SILICO · POPULATION GENETICS

The Ratchet Bench

A live model accompanying “Why Sex Exists”

Two benches below. The first runs a single asexual population and draws its mutation load as a live histogram, with the least-loaded class picked out in solid colour. Watch that leftmost bar. When it empties, it is gone for good, the whole histogram slides one step to the right, and the ratchet has clicked. The second bench puts recombination back and lets you raise it until the clicking stops.

Both benches run the same two engines as the analysis script, at smaller scale so they fit in a browser tab. Nothing here was observed in an organism. The computation is the experiment.

Model 1. Watch the bottom rung go

A haploid population of N individuals. Each carries some number of deleterious mutations; each mutation costs a fraction s of fitness, and each offspring picks up a Poisson number of new ones with mean U. The population is carried exactly as a histogram over load classes, which is what makes it fast enough to animate.

The number to keep your eye on is n₀ = N e^−U/s, the size the least-loaded class should sit at in an infinite population. On the defaults that is 500 × e⁻⁴ = 9.158, so about nine individuals out of five hundred are carrying no mutations at all. Nine is not many. That is the whole problem.

Population size N 500 The article's worked arithmetic uses N = 500. Drag down to 100 and the ratchet speeds up visibly; drag up to 2000 and it nearly stops, because n₀ grows in proportion to N while the chance of losing the class falls much faster than that. Mutation rate U 0.20 Set it to exactly 0 first. The ratchet must never click and mean fitness must stay at 1, which is the null check the analysis script runs before anything else. Then put it back up. U enters only through λ = U/s, so doubling U is the same as halving s. Selection coefficient s 0.050 The interesting trick: hold n₀ fixed by moving N and s together and the rate still changes. Stronger selection makes the ratchet turn faster, not slower, which is why n₀ on its own cannot predict the rate. Generations per frame 4 Slow it to 1 to see individual clicks land. Push it to 40 to accumulate enough generations for the measured rate to settle near the article's value.

n₀ predicted: – λ = U/s: – k_min: – clicks: – measured rate: – mean load: –

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Model 2. How much sex does it take?

Recombination cannot be simulated honestly in load-class space, because whether two parents' mutations can be separated depends on whether they sit at the same sites. So this bench carries real genomes: 1024 sites per individual, packed into 32-bit words. A fraction R of each generation's offspring are made by recombining two fitness-weighted parents site by site; the rest are clones of one parent.

Two populations run side by side from the same starting point: the one you are controlling, and an asexual control pinned at R = 0. The plot is log mean fitness against generation for both. Start at R = 0 and confirm the two lines sit on top of each other, then raise R.

Recombination rate R 0.000 The article's thresholds, measured over 200 replicates: R = 0.027 halves the drift, R = 0.084 cuts it to a tenth, and R = 0.152 cuts it to a hundredth. Creep up through those three values and watch the gap between your line and the control open, then stop opening. Mutation rate U 0.30 0.30 is the article's base cell, chosen to be nasty: with s = 0.05 it gives λ = 6 and n₀ = 0.496, meaning half an individual in the population carries a clean genome. Raise U and even generous recombination starts to lose. Selection coefficient s 0.050 Raising s at fixed U lowers λ and lifts n₀ sharply, so the asexual control slows down and the rescue threshold drops. The equilibrium mean load should settle near λ = U/s whenever the ratchet is stalled; check it in the readout.

generation: – n₀ predicted: – mean load, yours: – control: – k_min drift, yours: – control: –

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What this bench is not

Every mutation costs exactly s, so there is no distribution of fitness effects. Fitness is multiplicative, so there is no epistasis. There is no back mutation, no beneficial mutation and no compensatory mutation, which is why fitness here falls forever with no floor under it. Recombination is free, every site assorting independently, which is stronger than any real chromosome manages, so the R you find here is a lower bound on what a genome with real linkage would need. Population size is pinned, so the mutational meltdown, where falling fitness shrinks the population and the shrinking speeds the ratchet, cannot happen. And with 1024 sites, a small fraction of mutations land where a mutation already sits and are lost.