Every species has its own life clock, but the hand pointing to the peak of reproduction always stops at the same mark: 37% of the way. In the beech, the cod, and the human, the maximum effort to continue the lineage falls at the moment when a little more than a third of the maximum lifespan has been lived. This is not a coincidence but a mathematical rule that works as reliably as gravity.
An organism that reproduces too early does not have time to grow and accumulate strength. One that waits too long risks dying without leaving offspring. The optimal moment is when enough resources have been accumulated, but the chance of surviving to the next season is still high. Mathematics specifies: this moment arrives when 37% of all opportunities that life can offer have passed. For a uniform stream of chances, this is exactly 37% of the maximum lifespan.
Scientists tested this on 2197 species: in 96% of them, maturation occurs no later than this mark. In 967 fish species, the age when growth slows falls at 0.367 of the maximum age. Fifteen detailed studies, from trees to humans, give the peak of reproduction in the window 0.32–0.42. Even survival to the maximum age is predicted by the same model: about 1% of individuals live to the end, which matches observations.
The life clock that measures out 37% before the main decision ticks in all species. The mathematics of optimal stopping explains why the hand stops exactly here: it is the best compromise between preparation and risk. Nature does not calculate in its head, but evolution for millions of years selected those who happened to hit this point. Now we know what number stands behind this choice.
The number 1/e (about 0.37) is known as the "37% rule" in the fussy suitor problem: to maximize your chance of picking the best partner, you should reject the first 37% of candidates, then choose the first one better than all previous ones. In biology, the same number governs the timing of the reproductive peak.
In Stanisław Lem's novel Solaris, the planet's ocean displays behavior reminiscent of optimal stopping on the scale of geological epochs, but there is no direct analogy to the 1/e law in well-known science fiction.
Not published on arXiv. Here are its page, the PDF and the formalization: you can check it yourself, not only read our account.