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bioRxiv · 10.64898/2026.06.30.733937

Evidence for the 1/e-law predicting optimal timing of reproduction across taxa

Froese, T.·Froese, R.·Bruss, T.
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Abstract

The timing of peak reproductive effort is a central problem in life-history theory, yet a simple first-principles target for that timing relative to lifespan has been missing. We propose that generation time is an optimal stopping time. Under the 1/e-law of best choice, the unique strategy that guarantees the highest minimum probability of selecting a superior option is to wait until a cumulative fraction 1/e of opportunities has passed. When reproductive opportunities arrive in an approximately time-homogeneous way over adult life, that threshold is 1/e (about 37%) of maximum lifespan. This fraction is confirmed by standard population dynamics for indeterminate growers, combining von Bertalanffy growth with constant mortality. A compilation of published reproductive schedules in plants, animals, and humans illustrates the predicted alignment across taxa and absolute timescales. The 1/e-law thus supplies an organizing quantitative account of a core life-history schedule.

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Froese, T., Froese, R., Bruss, T.. 2026-07-03. Evidence for the 1/e-law predicting optimal timing of reproduction across taxa. https://doi.org/10.64898/2026.06.30.733937

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