The Fittest Cannot Breed True

Herbert Spencer's phrase, which Darwin adopted, sounds like a law and reads like a tautology: the fittest survive, and we know they're the fittest because they survived. Buried in it is a quiet assumption — that "fittest" names a type of organism that selection can, given time, make the population be. Usually it can. Here is the clean, well-documented case where it provably cannot.

The gene is HbS, one letter changed in the recipe for the β chain of haemoglobin. You carry two copies of the β-globin gene, so there are three kinds of person: AA (two normal copies), AS (one of each — a "carrier," almost always healthy), and SS (two sickle copies — sickle-cell disease, historically often fatal before adulthood). By itself HbS is a lethal recessive: it should have been scoured out of every population long ago. In much of equatorial Africa, the Mediterranean, and South Asia it wasn't — it sits at a stubborn, stable frequency. In 1949 J. B. S. Haldane guessed why, and in 1954 A. C. Allison showed it: the carriers AS resist falciparum malaria. Where malaria is holoendemic — a near-constant childhood threat — the heterozygote is the fittest of the three. AA dies of malaria; SS dies of anaemia; AS survives both.

And that is the trap. A heterozygote cannot breed true. Mate two carriers and Mendel guarantees the outcome: on average a quarter AA, half AS, a quarter SS. The one genotype selection prefers is the one genotype that, by the arithmetic of two-copy inheritance, it can never get a breeding population of. Every generation, random mating takes the winners and shatters them back into losers.

The balance you can set yourself

Below is the standard one-locus model of viability selection (the same Wright–Fisher ground as genetic drift, but with the fitnesses switched on). Fix the carrier's fitness at 1. Let malaria dock a fraction s from AA, and anaemia dock a fraction t from SS. Turn the two dials and watch where the population settles.

Leave the dials at the sickle-cell setting and the population parks itself at HbS ≈ 0.12 — right inside the band actually measured across holoendemic-malaria populations. About one person in five is a protected carrier. And the price of that protection never stops being paid: roughly one birth in 67 is SS, a child with sickle-cell disease, produced not by mutation but by the ordinary reshuffling of two healthy carriers. The population is at its fitness peak — and the peak still spends those lives, every generation, forever. Geneticists call the gap the segregation load: the distance between the fitness a population would have if it could be all-heterozygote and the best it can actually reach. Here it is 10.5%, and it is structural. There is no allele frequency that removes it.

Why selection is stuck: it cannot breed the winner true

Take the fittest genotype and try to build a population from it. Cross AS with AS — the best with the best:

The verdict was never about the gene

Press Turn malaria off on the instrument and the whole picture inverts. With s = 0 the carrier's advantage evaporates — AA and AS are now equally fit — and HbS is once again nothing but a recessive killer. Selection purges it: the equilibrium slides to zero and the gene drains away. The same allele, unchanged, goes from "maintained at 12%" to "removed" — the only thing that moved was the environment. This is the honest content of "fitness": not a property an allele has, but a number that only exists for a gene in a world. Change the world and you change the sign.

One more true thing the model shows, because it cuts against a tidy ending. When malaria lifts, HbS does not vanish quickly. It halves in about ten generations — then the descent stalls. A rare recessive allele hides where selection cannot see it: almost every copy sits in a healthy AS carrier, paying no cost, and selection only ever "reads" the allele in the vanishing fraction of SS births. So the tail is long — reaching 1% takes ~108 generations, 0.1% takes over a thousand. The population keeps producing children with the disease for millennia after the reason for the gene is gone. Removal, like maintenance, is something the arithmetic does slowly and never cleanly.

The mirror case, and the honest edges

Overdominance — heterozygote best — has an exact mirror: underdominance, heterozygote worst (as when two chromosome arrangements each work but their hybrid misfires). The very same equation still has an interior equilibrium, but now it repels instead of attracts: the population falls to whichever allele it started closer to, and the outcome is a matter of history, not fitness. The verifier checks this too — the same machine, one sign flipped, gives the opposite verdict. It is a standing reminder that "there is an equilibrium" and "the population goes there" are different claims.