Walk through a nursery in almost any country and the boys and girls come out close to level: roughly 105 boys for every 100 girls, by one recent global estimate. In many other mammals, birds and insects the numbers also sit close to level. Yet a single male can father hundreds of offspring while a female is limited to far fewer. If all that matters is how many young a population produces, a herd with a few males and a great many females would do the job. So why does nature keep paying for so many sons?
The idea is usually credited to the statistician and geneticist R. A. Fisher, who set it out, tersely, in his 1930 book The Genetical Theory of Natural Selection. Darwin had made a similar argument in the first edition of The Descent of Man (1871) and then dropped it, and the German biologist Carl Düsing published one in 1883 and 1884. The logic is a piece of bookkeeping.
Every child has exactly one mother and one father. So, across the whole population, sons together get exactly as many children as daughters together get. Now suppose males are rare. Then each son is, on average, a parent of many more children than each daughter is. A mother who tilts her brood towards sons is buying the better ticket, and her genes, including whatever tilted her, spread. The reverse holds if males are common. The balance point, where a son and a daughter are worth the same, is an even split.
Below is a population of 300 mothers. Each carries a heritable trait: the fraction of her children that are sons. Every generation, a mother's number of grandchildren is her daughters plus her sons multiplied by whatever a son is currently worth (the number of females per male in the whole population). Mothers who leave more grandchildren are more likely to be the parents of the next generation, and each trait is nudged a little at random when it is passed on. This is a simplified model, with nothing in it but that bookkeeping.
Start it at 20% sons. At that point a son is worth four daughters, because every son shares the offspring that four times as many females produce. The line climbs steadily towards 50%, and as it does the price of a son falls towards one. Start it at 80% and it comes down instead. In both directions it slows to a stop in the same place, because only at an even split does neither choice beat the other.
Press the disaster button. In the model, 70% of adult males vanish for one generation, so the males that remain are suddenly worth far more than before. Mothers who happened to have more sons are rewarded, and the average rises above one half. A few generations later males are too common, sons lose their edge, the reward flips, and the line comes back. Fisher's equilibrium is a trap with a slope on every side. Any population drifting away from it is pushed home again.
Fisher actually put it in terms of cost: parents should spend equally on sons and daughters. When the two sexes cost the same to raise, that is an even count. If sons were far more expensive to rear than daughters, selection would favour producing fewer of them, so that the total spent on each sex came out equal. He also pointed out that boys die more often in infancy, which fits a slight excess of boys at birth, though the details of the human numbers are still argued over.
The argument assumes that a son competes for mates across the whole population. In 1967 W. D. Hamilton published a paper in Science called "Extraordinary sex ratios", about the cases where that fails. In some parasitic wasps, for instance, a mother lays eggs in a single host, and her sons mate with their sisters before anyone leaves. Her sons are really competing with one another for a handful of mates. One son is enough for a whole brood of daughters, and any more is a waste, so she makes mostly daughters. This is the same bookkeeping as before. Once the group of mates is small, the price of a son drops, and the equilibrium moves.
That is what makes the idea such a good one in biology. It makes a clear prediction, a ratio near one half, and it also tells you in advance where the prediction should break and in which direction.