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

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.