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 ), 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 a formal decision-theoretic model, our results suggest a striking previously unrecognized quantitative regularity linking lifespan and reproductive timing. These findings provide a unifying perspective on life-history evolution and suggest that complex biological scheduling strategies are governed by probabilistic principles.