The Score of Reproduction: Why Species Give Birth at Certain Ages

Original: "Evolutionary Entropy Shapes Reproductive Lifespan in Age-Structured Populations"
arXiv:2606.22001 · 2026-06-20 · CC BY 4.0 · 1 min
Reproductive windows in animals are arranged to maximize evolutionary entropy, a measure of how widely reproduction is spread across ages.

An orchestra plays a score in which every note is the birth of offspring at a particular age. In some species the notes cluster into a short phrase; in others they stretch across an entire lifetime. The rhythm of that distribution can be calculated from life tables.

Scientists took tables that list, for each age, the chances of surviving and the number of offspring born. From these tables they derived a quantity: evolutionary entropy. It measures how evenly reproduction is spread across ages. If a species gives birth at one and the same age, entropy is low; if its reproductive effort is smeared over decades, entropy is high. It turned out that entropy does not depend on how fecund a species is or how long it lives, only on the shape of the distribution.

If survival declines too slowly compared with the rate of population growth, entropy grows without bound, and no optimal age exists. If survival declines quickly, the maximum is finite and points to a specific age.

A test on 130 animal species showed strong agreement: in 85.8% of species, the predicted and observed reproductive medians matched to within two age classes. This means that the score of reproduction in most species is tuned to maximum entropy. Now, from demographic tables alone, one can assess a species' reproductive strategy without spending years on field observations.

Among the species analyzed was the beluga sturgeon (Huso huso), one of the longest-lived fish, whose predicted reproductive median deviated by 23 age classes, the largest spread in the sample.

The idea that the distribution of reproductive contributions can be described by entropy echoes the concept of "demographic pressure" in Ursula K. Le Guin's novel The Dispossessed, where a society deliberately regulates reproduction to maintain equilibrium.

H = -\frac{\sum_{j} p_j \log p_j}{T}
Entropy measures the temporal variance of reproductive contribution, normalized to the mean age of reproduction
q^A + q - 1 = 0
Defines the boundary between a finite entropy maximum and an asymptotic regime
H_n = \frac{-\log q \left( \frac{q}{1-q} - \frac{n q^n}{1-q^n} \right) + \log\left( \frac{1-q^n}{1-q} \right)}{A + \frac{q}{1-q} - \frac{n q^n}{1-q^n}}
Explicit entropy formula for a truncated geometric distribution with parameter q and window length n
Concepts
Cope's rule evolution Price equation reproduction embryonic development lifespan epigenetic aging principle of maximum entropy epigenetic clock epidemic model Wright–Fisher model species Hardy–Weinberg principle phylogenetic network Fisher's fundamental theorem of natural selection ecological pyramid rule genetic algorithm