Is sex at birth a biological coin toss? Insights from a longitudinal and GWAS analysis

Abstract

Some families consistently have offspring of only one sex, raising questions about whether sex at birth is truly random. This study investigated whether offspring sex follows a simple binomial distribution within families and identified maternal factors associated with unisexual sibships. We analyzed 58,007 US women with two or more singleton live births (146,064 pregnancies, 1956-2015). Offspring sex followed a beta-binomial rather than a simple binomial distribution, indicating that each family may have a unique probability of male or female births, akin to a weighted coin toss. Deviations from simple binomial distribution were more pronounced when we excluded each woman's last birth to reduce the influence of sex-based stopping behavior. After excluding the last birth, older maternal age at first birth was associated with higher odds of having offspring of only one sex. A genome-wide association study identified maternal SNPs linked to having female-only (NSUN6) and male-only (TSHZ1) offspring. Our findings suggest maternal factors influence offspring sex distributions.

Fig. 1.. Distribution of offspring sex sequencing by sibship size (range: 2 to 5), in descending order by number and percentage of mothers within each sibship size.

Fig. 2.. Relative deviation of offspring sex distribution from binomial expectation by sibship size (range: 2 to 5).

Note that expected distribution was calculated as a simple binomial distribution with a probability of having a male offspring = 0.519 at any single birth, according to the male/female ratio in the study population. Relative deviation = (observed counts − expected counts)/expected counts. All chi-square tests P < 0.001.

Fig. 3.. Manhattan plot showing results of GWAS of having offspring of only one sex (versus having offspring of both sexes), excluding the last birth of all women.

Note that GWAS analysis was only conducted among NHSII participants with genome information. (A) Having offspring of only one sex (versus having offspring of both sexes), N = 2933. (B) Having offspring of only females (versus having offspring of both sexes), N = 2015. (C) Having offspring of only males (versus having offspring of both sexes), N = 2135. Multivariable models adjusted for sibship, ethnicity, and top four principal components.

Fig. 4.. Conditional probability of the sex of the next birth in families with offspring of only one sex.

Note that conditional probability was calculated on the basis of the fitted beta-binomial distribution after excluding the last birth from all women. For example, the conditional probability of the next birth being a boy for a beta-binomial distribution is given by $(\text{the} n+1 \text{birth is} \mathrm{a} \text{boy})=\frac{\mathrm{\alpha }+k}{\mathrm{\alpha }+\mathrm{\beta }+n}$ , where n is the current sibship size, and k is the current number of boys in the family.