The Coupon Collection Behavior in Human Reproduction.

There is evidence in humans for genetic influences on the probability (Pboy) that a birth yields a boy instead of a girl [1-6], suggesting a potential variation of Pboy among families. To quantify this variation, we analyze the survey data from over 300,000 UK Biobank participants primarily born between 1940 and 1970 [7]. Surprisingly, the proportion of male children in a family, or sex ratio (SR), has a significantly smaller among-family variation than expected under a uniform Pboy. We propose that this phenomenon results from reproductive behaviors reflecting a preference for having children of both sexes, much like the coupon collector's problem in probability theory where collecting a complete set of distinct coupons is considered a win. We find that the observed deficit in SR variation is explainable by 3.3% of "coupon-collecting" families. Consistently, significantly more families than expected have all children of the same sex except for the child born last. This trend is more pronounced in the late than the early half of the families in the data, suggesting an increasing popularity of this behavior. Analysis of a Dutch genealogical dataset spanning the past 4 centuries reveals higher-than-expected SR variations over much of the history; only after 1940 did the SR variation drop below the expectation. We conclude that a significant fraction of couples now exhibit the coupon collection behavior in reproduction such that SR is more homogeneous among families than expected by chance.