Evidence for the 1/e-law predicting optimal timing of reproduction across taxa
Froese, T.; Froese, R.; Bruss, T.
Show abstract
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.
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