Balancing the Last Birth: A Game-Theoretical Resolution to the Human Sex Ratio Puzzle

TL;DR

This paper presents a game-theoretical model explaining the persistent slight male bias in human birth sex ratios, showing that stable ratios can differ from 1:1 while last-born children tend to be evenly balanced.

Contribution

It introduces a new model linking sex-specific mortality and parental strategies to stable sex ratios, extending Fisher's principle to last-born children.

Findings

Stable sex ratios can differ from 1:1 due to parental continuation probabilities.

Last-born children have an equilibrium sex ratio of 1:1, proven to be evolutionarily stable.

The model explains the persistent male bias in human births through reproductive strategies.

Abstract

We study the evolution of offspring sex ratios using a game-theoretical model in which the decision to have another child depends on the sex of the previous child. Motivated by higher male infant mortality and the tendency to try again after a child's death, our model allows different continuation probabilities after sons and daughters. We find that a stable sex ratio at birth (SRB) differing from 1:1 can arise when these continuation probabilities differ. However, the sex ratio among last-born children (SRLB) always converges to 1:1. We mathematically prove that this 1:1 SRLB is an evolutionarily stable strategy under a new fitness measure based on the number of offspring in successful mating pairs, rather than the number of descendants in the whole population. Our results generalize Fisher's principle by showing that equilibrium is maintained at the level of last births even when the overall SRB is biased. This offers a potential explanation for the persistent slight male bias in human births, linking it to sex-specific child mortality and parental reproductive strategies in historical populations.