Artificial Wasteland · a portal in the Life seam · three layers, one engine
What Selection Cannot Do
Three layers in this archive get read as one lesson: evolution does not optimise. That reading is wrong, and it is wrong in a way you can operate. They are three mechanically different reasons the fittest fails to take over, and the third one is not a failure of selection at all.
The slogan is doing too much work. Put the three cases side by side and they disagree about which force fails. In the drift, the fittest does not win because nobody is pushing: switch selection off entirely and pure sampling noise still grinds one allele to fixation. In Muller's ratchet, selection is pushing hard and cannot reach: the least-loaded class is the rarest, and once it is gone, nothing without recombination can rebuild it. Those two are genuine failures of optimisation.
The third is not. In heterozygote advantage, selection is working exactly as advertised, the population sits at its selective optimum, and the fittest genotype still never takes over. The obstruction is Mendelian segregation, which has nothing to do with selection. Keeping that third case inside the slogan is how the slogan survives, and it is why the slogan is worth breaking.
The ten-second version
Here is a population of forty individuals, every one of them the fittest genotype there is: the carrier AS, which survives both malaria and anaemia. Nothing will be selected against. Nothing will mutate. Nobody will die of anything. Breed them with each other and press once.
Instrument 1 · the fittest, bred with the fittest
Generation 0. All 40 are AS, the fittest genotype.
Half of them are gone in one step, and no force removed them. The AS genotype cannot be transmitted: each parent passes one allele, not a genotype, so a quarter of the children get two As and a quarter get two Ss. Press it repeatedly and the running mean settles on exactly 1/2, which is the ceiling in the next section.
One engine, three regimes
The three layers are usually met as three separate pages, which makes them look like three opinions. They are not. Every one of them is the same reproduction rule, and this page runs exactly one copy of it:
Three knobs. W is the genotype fitness vector, r is recombination on or off, U is the deleterious mutation rate. Set W flat and you are in the drift. Set r = 0 with U > 0 and the ratchet clicks. Set the heterozygote above both homozygotes and the population settles at a polymorphism. Same code, three settings. Pick one.
Instrument 2 · the shared Wright-Fisher engine
knobs: W = [1, 1, 1] · r = on · U = 0
Ready.
Selection is switched off: all three genotypes have fitness 1. The frequency wanders because 2N gene copies are redrawn each generation, and nothing else.
The separating measurement
Each regime has one number that no other regime produces. Run the replicates and read them off. These are seeded, so they are reproducible, and the tolerance is stated with the answer.
Instrument 3 · replicate runs, same engine
Not yet run.
Drift terminates, always: with no force either way, the probability that a given allele is the one that fixes equals its starting frequency, exactly.
The sophisticated objection
Here is where a careful reader stops the portal. Fine, the three mechanisms differ in the details. But you have still shown three cases where the fittest does not take over. That just is "evolution does not optimise". You have won a vocabulary argument, not a real one.
The objection is fair and the answer is a further result, not a rebuttal. If the third case were a failure of optimisation, then weakening the obstruction would have to involve selection: more selection, or longer, or in a bigger population. It does not. Hold the fitnesses fixed, hold the population size fixed, hold the starting composition fixed, and change exactly one thing that is not a property of selection: whether inheritance goes through meiosis. The fittest genotype goes from unreachable to reachable.
And this is not a simulation result with error bars. For a finite population the genotype counts (nAA, nAS, nSS) form a finite Markov chain, so the question has an exact answer: enumerate the chain and look at which states are absorbing. Your browser does that below, by Gaussian elimination on the transient states, for the N you choose.
The segregation switch
Instrument 4 · the exact chain, solved live
start: 20% carriers, the rest AA · fitness W = [0.880, 1, 0.140] · identical on both sides
Left: inheritance through meiosis
0
P(the AS genotype fixes)
Right: inheritance by cloning
·
P(the AS genotype fixes)
Solving.
·
The left column is not a small number. It is not a number that shrinks as the population grows, or as you wait longer, or as you sharpen the fitness difference. It is zero, structurally, and the reason is one line: the only states this chain cannot leave are the ones where a single allele remains, and a population with a single allele has no heterozygotes in it. The all-carrier state is not a destination. It is a place the population passes through and leaves in one step, which is exactly what the first instrument on this page shows you by hand.
There is a related ceiling worth having in your pocket. Under random mating the heterozygote frequency is 2pq, and 2pq is maximised at p = q = 1/2, where it equals exactly one half. So even the momentary best a randomly-mating population can do is that half the population are carriers. Selection can push the allele frequency anywhere it likes; it cannot push past a ceiling that belongs to arithmetic.
Change the transmission rule and every one of those sentences stops being true, with the fitnesses untouched. This is not a thought experiment: it is why potatoes are grown from tubers and prized apple and citrus cultivars are grafted rather than grown from their own seed, because a heterozygous cultivar does not survive being crossed. (Dessert bananas are clonally propagated too, but for a different reason: they are sterile triploids that set no viable seed at all, so segregation never gets the chance.) The same holds for hybrid-origin clonal lineages, such as the all-female Amazon molly and apomictic dandelions, which retain the fixed heterozygosity of their hybrid ancestry precisely because they do not segregate. Cloning does not make selection stronger. It removes segregation, and the winner stays won.
The three, kept separate
| layer | selection | what fails | separating number | failure of optimisation? |
|---|---|---|---|---|
| Drift | absent | nobody is pushing | P(fix) = p₀, exactly | yes |
| Ratchet | present, blocked | selection cannot reach what recombination cannot rebuild | kmin monotone, forever | yes |
| Overdominance | present, at its optimum | the winner is not heritable as such | P(AS fixes) = 0, at every N | no |
The last column is the point of the portal. Two of these are evolution failing to climb. The third is evolution standing on the summit, paying a toll it can never stop paying, for a reason that lives in meiosis rather than in fitness.
The check
Every number above is computed in your browser, from the equations, at read time. The offline verifier recomputes all of them from scratch and re-runs the three member verifiers alongside its own: node research/what-selection-cannot-do/verify-what-selection-cannot-do.mjs, 57/57 (plus the drift's 31/31, the ratchet's 20/20 and heterozygote advantage's 15/15, spawned and required to exit 0).
What is exact, and what is Monte Carlo
Exact (no sampling, no tolerance): the absorbing set of the genotype-count chain and both fixation probabilities in instrument 4, solved by Gaussian elimination on the transient states; the equilibrium q* = s/(s+t) and its stability; the segregation load L = st/(s+t); the ceiling max 2pq = 1/2; and the Punnett law (1/4, 1/2, 1/4) out of the all-carrier state, which also gives P(all-AS survives one generation) = 2⁻ᴺ.
Monte Carlo (seeded, tolerance stated): instruments 1, 2 and 3. The replicate panel names its replicate count and reports agreement as a multiple of the standard error √(p(1−p)/R); the verifier uses 600 replicates at seed 20260720 and requires agreement within 4 SE.
The free choices, named
- s = 0.12 and t = 0.86. Round textbook-scale estimates of the fitness costs under holoendemic falciparum malaria, of the kind summarised in standard population-genetics texts. We have not traced this exact pair to a primary field study, and we do not claim it is one. They are also not constants of nature: malaria pressure varies enormously by region and era, and every equilibrium number here is a function of that choice. Both sliders are live, so move them and watch the numbers move. What does not move with them is the zero.
- N, the seed, and the starting composition. Instrument 4 starts from 20% carriers so that the comparison across N holds the starting frequency fixed rather than the starting count; with a fixed count instead, the clonal probability falls with N for a boring reason (the start gets rarer) and the comparison would mislead.
- The ratchet's regime. N = 200, U = 0.4, sd = 0.06 puts Haigh's least-loaded class at n₀ = N·e^(−U/s) ≈ 0.26, deep in the fast-clicking regime. That formula is Haigh's 1978 approximation, valid when the least-loaded class is small and the population is at mutation-selection balance; it is not an exact law, and the click rate depends on the whole (N, U, s) regime.
The idealisations of the engine, named
Wright-Fisher assumes non-overlapping generations, constant N, and random mating with no population structure or migration. This page adds: viability selection only, constant genotype fitnesses, a single focal locus with no mutation at it, and a deleterious background tracked as a per-individual count with multiplicative fitness and infinite sites. Free recombination of that background is modelled haploid-equivalently, as each parent passing Binomial(k, 1/2); that approximation is used only to show that recombination halts the ratchet, never to quote a rate. All of these are idealisations, and each one is a place where a real population differs.
What we are not claiming
Nothing here is new mathematics. Wright and Fisher gave the sampling model in 1930 and 1931, Haldane proposed the malaria hypothesis in 1949 and Allison gave the sickle-cell case in 1954, Muller described the ratchet in 1964, Felsenstein named it in 1974, and Haigh made it exact in 1978. The portal's only contribution is the separation: putting the three under one engine so that the third can be shown to be categorically unlike the other two. We also do not claim heterozygote advantage is common. Sickle cell is the textbook case because clear-cut single-locus overdominance in nature is uncommon, and how much standing genetic variation balancing selection maintains is genuinely disputed. The claim here is about one mechanism's structure, not its prevalence.
The repair this portal owed, and a correction to our own record
This slot was assigned partly to fix a suspected gap: that The Fittest Cannot Breed True shipped with no verifier and no check panel. On inspection that was half wrong, and the honest thing is to say so rather than claim a repair we did not need to make. That page does have a check panel, and its verifier does exist and passes 15/15. What it did not have was a research directory matching its own slug, which is how the gap was misread. This portal adds research/the-fittest-cannot-breed-true/ as a signpost to the verifier's real location, and re-runs that verifier inside its own.
The genuine gap the portal found was in this file's first draft, not in that page: the engine's initial population was seeded as all homozygotes, which is not Hardy-Weinberg, so the first generation could not match any random-mating model. The verifier caught it on its first run. Seeding now shuffles the 2N gene copies into individuals at random, and the agreement check that failed at |Δp| = 0.24 now passes at 0.019.
Where each member goes further than this portal does
The Drift carries the exact absorbing Markov chain on 2N+1 states, the heterozygosity decay H₀(1−1/2N)^t, and the honest frontier where drift and selection meet at s ~ 1/(2N), with Kimura's 1962 fixation formula checked against simulation. This portal uses only its null.
Muller's Ratchet proves the mutation-selection balance is exactly Poisson(U/s) by machine-precision arithmetic, gives the Haldane-Muller principle that mean fitness at balance is e^(−U) independent of s, and runs an explicit loci model so recombination is honest rather than approximated. This portal uses the count model only.
The Fittest Cannot Breed True has the deterministic side in full: the recursion, global stability, the recessive tail that takes over a thousand generations to clear after malaria lifts, and the underdominance mirror where the same equation's interior root repels instead of attracting. This portal adds the finite-population exactness and the clonal counterfactual it did not have.