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

Reproductive success requires allocating effort across lifespan in a manner that balances the risk of early mortality against the benefit of higher fecundity or parental expertise that increase with body size or age. Here we report a cross-taxonomic analysis of reproductive schedules in plants, animals, and humans, showing that peak reproductive effort consistently occurs at approximately 1/e (~37%) of species-specific maximum lifespan. The pattern is robust across major phylogenetic groups and independent of absolute lifespan. This convergence is both logically and numerically consistent with the optimal stopping fraction (1/e) of the 1/e-law of best choice (Bruss 1984), which maximizes the probability of selecting a superior option under uncertainty by delaying commitment until 1/e of the available options have been examined. By integrating population dynamics and empirical data with this formal decision-theoretic model, our results document a striking, previously unrecognized quantitative regularity linking lifespan and reproductive timing, and show that it is explained from first principles by the 1/e-law. These findings offer an organizing quantitative account of a core life-history schedule and suggest that biological reproductive timing is governed by probabilistic optimal-stopping principles.