Abstract
The ratio of males to females among an individual's offspring at birth (offspring sex ratio) has long been of great interest to evolutionary biologists. The human offspring sex ratio is around 1 : 1 and is understood primarily in terms of Fisher's principle (R. A. Fisher, The genetical theory of natural selection, 1930), which is based on the insight that in a population with an unequal sex ratio, each individual of the rarer sex will on average have greater reproductive value than each individual of the more common sex. Accordingly, individuals genetically predisposed to produce the rarer sex will tend to have greater fitness and thus genes predisposing to bearing that sex will increase in frequency until the population sex ratio approaches 1 : 1. An assumption of this perspective is that individuals' offspring sex ratio is heritable. However, the heritability in humans remains remarkably uncertain, with inconsistent findings and important power limitations of existing studies. To address this persistent uncertainty, we used data from the entire Swedish-born population born 1932 or later, including 3 543 243 individuals and their 4 753 269 children. To investigate whether offspring sex ratio is influenced by genetic variation, we tested the association between individuals' offspring's sex and their siblings' offspring's sex (n pairs = 14 015 421). We estimated that the heritability for offspring sex ratio was zero, with an upper 95% confidence interval of 0.002, rendering Fisher's principle and several other existing hypotheses untenable as frameworks for understanding human offspring sex ratio.
Keywords: familial aggregation, negative frequency-dependent selection, Trivers–Willard, steroid hormones, sex allocation
1. Introduction
The ratio of males to females among an individual's offspring at birth (offspring sex ratio) and has been of great interest to evolutionary biologists for more than a century. ‘Fisher's principle' [1], which can be traced to Darwin (1871; see [2]), explains offspring sex ratio using the concept of negative frequency-dependent selection and has been described as ‘probably the most celebrated argument in evolutionary biology' [2]. Briefly, it is argued that––all else being equal––in a population with an unequal sex ratio, each individual of the rarer sex will on average have greater reproductive value than each individual of the more common sex, because each sex must contribute exactly half the ancestry of future generations. In this scenario, individuals genetically predisposed to produce the rarer sex will tend to have greater fitness (more grandchildren) and thus genes predisposing to bearing that sex will increase in frequency until the population sex ratio approaches 1 : 1 and the advantage of those genes dissipates. In this way, the theory goes, offspring sex ratio is maintained in the population at around 1 : 1––the equilibrium ratio, or evolutionarily stable strategy.
The human offspring sex ratio is around 1 : 1 and is understood primarily in terms of Fisher's principle [3]. Fisher's principle does not necessarily predict an even offspring sex ratio, but it will do so if parental investment after birth is equal for the average female and male. Sex determination in humans depends on whether an offspring inherits an X or Y chromosome from the father, so an even sex ratio would also be predicted by random Mendelian segregation of sex chromosomes, in the absence of a Fisherian or other adaptive process [4].
An assumption of Fisher's principle is that offspring sex ratio is heritable (i.e. its between-individual variation is influenced by genetic variation), because heritability is necessary for Fisher's principle to operate [1,5]: without heritable variation, the offspring sex ratio cannot respond to selection. Indeed, beyond Fisher's principle, much of the theory pertaining to human offspring sex ratio, including variations of the Trivers–Willard hypothesis [6–11], also predicts heritable variation––a point we return to in the discussion.
For such a clear, falsifiable assumption that is central to much of the theory on which the field is based, the heritability of offspring sex ratio in humans remains remarkably uncertain. In Science in 1951, Bernstein [12] wrote that researchers had ‘shown conclusively that the tendency in a family to produce offspring of one sex only or primarily one sex is hereditary', but subsequent reviews and major studies did not reach such definitive conclusions (e.g. [13,14]). In 2001 alone, one study involving genotyped families found that human offspring sex ratio was significantly influenced by paternal genetic factors [15], while another involving twins concluded that it was not heritable at all [16]. In a still more recent study, a genealogical database compiled by amateur and professional family tree researchers was used to test parent–offspring correlations in offspring sex ratio and estimated a significant heritability (0.057 ± 0.002) in males, which the author proposed to be caused by a yet-to-be-identified polymorphic autosomal gene [17].
A limitation of all of these studies, and a potential cause of the inconsistency in their findings, is insufficient statistical power due to sample sizes used. Though the overall samples in the studies were sometimes large (e.g. 556 387 individuals in [17]), the samples directly used for testing for heritability were always relatively modest is size (e.g. 1224 parent–offspring pairs in [17]). The studies consistently indicate that any heritability in human offspring sex ratio must be fairly small, so larger samples with sufficient power for very precise estimates are required to reliably establish its presence or absence.
To address this persistent uncertainty regarding the heritability of offspring sex ratio in humans, we conducted a familial aggregation analysis of offspring sex, using data from the entire Swedish-born population born 1932 or later. The sample included 3 543 243 Swedish individuals and their 4 753 269 children. Specifically, to investigate whether offspring sex ratio has genetic variation, we tested the association between individuals' offspring's sex and their siblings' offspring's sex (n pairs = 14 015 421). We also estimated heritability and its upper bound. The data used in this study are of a much larger scale than previous research, yielding essentially 100% power to detect a heritability of 0.057, as estimated by Gellatly [17], or even an order of magnitude smaller than that. Further, the data are essentially complete and unbiased, being based on prospectively collected government registry records [18–20].
2. Methods
(a). Study population
Using the unique personal identification number given to each Swedish citizen at birth or immigration [19], we linked two administrative population registers in Sweden: the Total Population Register (TPR); [18] and the Multi-Generation Register (MGR), as of 31 December 2013 [20]. Details on each register will be provided below. We included all Swedes born in 1932 or later who had identified biological parents, had at least one biological child born before 2014, and were not born from a multiple birth. In this sample, we identified all parental siblings (index generation) and all pairs of their offspring, i.e. cousins (in total, 14 015 421 pairs). In total, 3 543 243 individuals were identified. We then identified all their offspring, yielding 4 753 269 individuals. Offspring from multiple births (n = 107 006) were excluded from analyses because they might bias our estimates, for example, due the heritability of twinning and issues with statistical dependence within pairs.
The TPR was established in 1967, but covers individuals alive in Sweden in 1947 and later (gathered from previous registers; [19]); the coverage is essentially complete [18]. The MGR includes all registered parents of individuals born 1932 and onwards, who were alive in 1961 and later [20]. The proportion of known parents of individuals is high and has increased over time to 100% for mothers and 98% for fathers, born 1961 and later [20].
(b). Study variables
The analysed variable was sex, as registered in the TPR. Since 1972 sex may be changed in the register, but this is very uncommon [19]. From 1973, all pregnancies with delivery in week 28 or later, regardless of whether it was a stillbirth or not, were registered, and a sex was assigned. In July 2008, this threshold was moved to week 22 of the pregnancy [21]. Prior to 1973, information about the occurrence and sex of stillbirths was not documented as accurately.
(c). Statistical analyses
We performed analyses of familial aggregation of offspring sex using logistic regression within a generalized estimating equation framework (with cluster–robust standard errors to account for familial relatedness [22–25]). The independent variable was the sex of an individual's offspring and the dependent variable was the sex of the individual's sibling's offspring (sex was coded 0 for male and 1 for female). Results are presented as odds ratios (OR) with 95% confidence intervals (CIs), i.e. the odds of siblings' offspring being of the same sex as opposed to opposite sex (with an OR above 1 indicating a higher likelihood the offspring are of the same sex and an OR below 1 indicating a higher likelihood the offspring are of the opposite sex). We analysed all possible pairs of offspring for all full sibling parents (i.e. all pairs of cousins); individuals can therefore appear more than once in the analyses, but the cluster–robust estimator appropriately accounted for dependencies between pairs in calculating the standard errors and CIs. We also ran analyses separately for offspring of all full sisters, all full brothers, all maternal half-siblings and all paternal half-siblings. To avoid potential effects of parents stopping their childbearing depending on the sex composition of their offspring, we also performed the analyses on first-born offspring only (as compared to all offspring).
To assess the upper limit of the heritability of offspring sex ratio, we estimated tetrachoric correlations (used to measure agreement of binary data) of offspring sex among all full siblings. Since full siblings on average share 50% of their co-segregating alleles, the upper bound of the (narrow sense) heritability can be computed as twice the tetrachoric correlation between full siblings. Thus, we calculated the 95% CIs for the tetrachoric correlations and identified the upper 95% CI of the heritability as two times the upper 95% CI of the tetrachoric correlation. For this analysis, the CIs were calculated using a non-parametric bootstrap approach with 2000 resamplings. We performed this analysis on all pairs of offspring as well as on only first-born offspring.
One way associations in offspring sex ratio could arise is if parents tended to stop their reproduction once a desired sex composition of offspring had been reached. To address whether deviations from randomness in sex of offspring were present, we performed two additional analyses within-nuclear families (i.e. offspring of index parents). First, we analysed the association between the sexes of offspring in families conditioned on final family size; we determined the association between offspring's sex separately for families of different sizes (with 2 to 10 children). That is, we identified all families of a specific final attained family size, such as all families with three offspring. Similar to our main analyses on parental siblings, where all pairs of offspring to parental siblings were identified, in this sub-population, we identified all pairs of offspring siblings within each family; in the case of final family size of three the pairs were 1&2, 1&3 and 2&3. We analysed the data similarly as for parental sibling pairs, using logistic regression with each offspring acting as exposure and outcome separately in each pair, while accounting for dependency between rows using cluster-robust standard errors.
Second, we performed an analysis per birth order, regardless of final family size. In this latter analysis, the sex of the nth child was predicted based on the sex of each of the older siblings (e.g. we predicted the sex of the third-born child based on the sex of the first- and second-born child). In contrast with the previous analysis, this analysis is not affected by potential bias from a tendency to stop having children after desired sex composition is attained. Together, these two analyses tested potential reproductive stopping effects which could produce biased heritability estimates.
To assess potential issues with sub-optimal coverage of registries, which varied over time (with increasing quality), we re-analysed the association of offspring sex between siblings using data on parental full siblings in nine different (overlapping) birth cohorts––those with earliest year of birth of parents limited to 1932, 1947 or 1961, and latest year of birth limited to 1973, 1985 or 2000.
To test whether the exclusion of multiple births (twins, triplets, etc.) affected the results, we re-performed the familial aggregation analyses including multiple births in full siblings, female full siblings, male full siblings, and maternal- and paternal half-siblings. This re-analysis was done both using all offspring and using only first-born offspring.
To ensure our estimates of heritability were robust with respect to different modelling approaches, we compared our results using sibling regressions (as above) to estimates from the ‘animal model' [26,27], which incorporates pedigree information and hence models all known relationships in our data. We used families with index generation individuals born between 1932 and 1973 to ensure good coverage through their reproductive age (the youngest were 40 by the end of follow-up), excluded twin births, and ran the model using identity link. In total 3 869 556 offspring sex outcomes were included (83.3% of the total 4 646 263, excluding the twin births), total number of founders was 2 181 396 (males plus females), and 1 443 205 mothers and 1 434 946 fathers were identified to 2 651 143 individuals who had at least one offspring. The maximum depth of pedigrees was four generations (where the youngest generation was included only as outcome measure). We ran sensitivity checks with the index generation individuals born between 1932 and 1973: (i) using a probit link function––to model the heritability on the liability scale [28]; (ii) using a logit link function; (iii) using only females in index generation and an identity link function; and (iv) using only males in index generation and an identity link function.
Analyses were performed in the statistical software R [29], using the packages drgee [30], polycor [31] and pedigreemm.
3. Results
Table 1 and figure 1 show descriptive information about the parents and offspring in our sample. The sample included more mothers than fathers (ratio = 51.9 : 48.1) and more male than female offspring (ratio = 51.4 : 48.6) (both p < 0.001 by exact binomial test). The mean number of offspring was 2.189 (2.185 in females, and 2.193 in males); the range was 1 to 17 offspring in both males and females, although less than 0.02% had 10 or more offspring (distribution up to five offspring displayed in table 1).
Table 1.
Descriptive information on index (parent) and offspring generation.
| Index generation | ||||
|---|---|---|---|---|
| number (%) | no. males (%) | no. females (%) | p-value, males versus femalesa | |
| individuals | 3 543 243 (100.0) | 1 703 093 (48.1) | 1 840 150 (51.9) | <0.001 |
| birth year | <0.001 | |||
| 1932–1939 | 393 240 (11.1) | 193 562 (11.4) | 199 678 (10.9) | |
| 1940–1949 | 817 672 (23.1) | 402 484 (23.6) | 415 188 (22.6) | |
| 1950–1959 | 717 630 (20.3) | 351 116 (20.6) | 366 514 (19.9) | |
| 1960–1969 | 757 448 (21.4) | 368 664 (21.6) | 388 784 (21.1) | |
| 1970–1979 | 615 801 (17.4) | 291 326 (17.1) | 324 475 (17.6) | |
| 1980–1989 | 231 730 (6.5) | 93 240 (5.5) | 138 490 (7.5) | |
| 1990–1999 | 9722 (0.3) | 2701 (0.2) | 7021 (0.4) | |
| number of offspring | <0.001 | |||
| 1 | 756 283 (21.3) | 377 753 (22.2) | 378 530 (20.6) | |
| 2 | 1 743 847 (49.2) | 825 331 (48.5) | 918 516 (49.9) | |
| 3 | 768 758 (21.7) | 363 458 (21.3) | 405 300 (22.0) | |
| 4 | 200 823 (5.7) | 98 797 (5.8) | 102 026 (5.5) | |
| 5 | 51 160 (1.4) | 26 264 (1.5) | 24 896 (1.4) | |
| >5 | 22 372 (0.6) | 11 490 (0.7) | 10 882 (0.6) | |
| ever multiple birth | <0.001 | |||
| no | 3 456 774 (97.6) | 1 660 948 (97.5) | 1 795 826 (97.6) | |
| yes | 86 469 (2.4) | 42 145 (2.5) | 44 324 (2.4) | |
|
offspring generation | ||||
| n (%) | male offspring (%) | female offspring (%) | ||
| individuals | 4 753 269 (100.0) | 2 444 030 (51.4) | 2 309 239 (48.6) | <0.001 |
| birth year | 0.785 | |||
| <1960 | 189 242 (4.0) | 97 162 (4.0) | 92 080 (4.0) | |
| 1960–1969 | 787 591 (16.6) | 405 354 (16.6) | 382 237 (16.6) | |
| 1970–1979 | 901 497 (19.0) | 463 472 (19.0) | 438 025 (19.0) | |
| 1980–1989 | 913 010 (19.2) | 469 412 (19.2) | 443 598 (19.2) | |
| 1990–1999 | 870 598 (18.3) | 447 200 (18.3) | 423 398 (18.3) | |
| 2000–2013 | 1 091 331 (23.0) | 561 430 (23.0) | 529 901 (22.9) | |
| birth orderb | 0.778 | |||
| 1 | 2 059 372 (43.3) | 1 058 701 (43.3) | 1 000 671 (43.3) | |
| 2 | 1 699 793 (35.8) | 874 369 (35.8) | 825 424 (35.7) | |
| 3 | 700 240 (14.7) | 360 147 (14.7) | 340 093 (14.7) | |
| 4 | 206 140 (4.3) | 105 857 (4.3) | 100 283 (4.3) | |
| 5 | 58 976 (1.2) | 30 167 (1.2) | 28 809 (1.2) | |
| >5 | 28 748 (0.6) | 14 789 (0.6) | 13 959 (0.6) | |
| from multiple birth | <0.001 | |||
| no | 4 646 263 (97.7) | 2 389 914 (97.8) | 2 256 349 (97.7) | |
| yes | 107 006 (2.3) | 54 116 (2.2) | 52 890 (2.3) | |
ap-values are calculated by exact binomial test or Pearson chi-square test.
bIf the child's birth order is different for the mother and the father, the latter order is presented.
Figure 1.
Panel (a) presents the sex ratio in offspring by birth years of the index generation and panel (b) presents the sex ratio in offspring by birth year of the offspring. Estimates presented for years with 2000 or more observations. Since later born in index generation have had shorter time to have children, fewer observations exist in these years; hence, CIs are wider for later birth years of index generation (a). since index generation were born 1932 or later, there are fewer offspring born to them in earlier years; hence, CIs are wider for earlier birth years of offspring generation (b).
Table 2 presents the results of the main analyses, i.e. the OR representing the odds of an individual's offspring's sex being the same as their sibling's offspring's sex, divided by the odds of an individual's offspring's sex being different from their sibling's offspring's sex. Thus, ORs above 1 indicates higher likelihood of same sex, and ORs below 1 higher likelihood of opposite sex. Results are also shown separately for full sisters, full brothers, as well as maternal half-siblings, and paternal half-siblings.
Table 2.
Association between sex of an individual's offspring and sex of their sibling's offspring. Odds ratios above 1 indicate a higher likelihood of siblings' offspring having the same sex, odds ratios below 1 a higher likelihood of opposite sex.
| index generation, biological relation | pairs of offspring analysis |
only first-born offspring analysis |
||||
|---|---|---|---|---|---|---|
| no. pairsa | odds ratio (95% confidence interval) | p-value | no. pairs | odds ratio (95% confidence interval) | p-value | |
| full siblings | 11 958 896 | 1.001 (0.998, 1.003) | 0.523 | 2 246 883 | 0.997 (0.995, 1.002) | 0.246 |
| full siblings–females | 3 200 160 | 1.002 (0.997, 1.006) | 0.407 | 596 622 | 0.995 (0.985, 1.005) | 0.298 |
| full siblings–males | 2 840 847 | 1.001 (0.996, 1.006) | 0.719 | 534 693 | 0.998 (0.987, 1.009) | 0.712 |
| maternal half-siblings | 912 648 | 0.999 (0.991, 1.008) | 0.898 | 182 802 | 0.999 (0.981, 1.018) | 0.939 |
| paternal half-siblings | 1 143 877 | 1.006 (0.999, 1.014) | 0.106 | 235 495 | 1.002 (0.986, 1.019) | 0.767 |
Note: Analyses performed with generalized estimating equations with logit link and standard errors clustered on parental sibling clusters. Offspring from multiple births (twins, triplets and higher) have been excluded from analyses.
aBecause nuclear families were considered as a unit, each pair could only contribute to one family. However, individuals can be part of more than one pair as each offspring may be part of cousin pairs both on her/his mother's and father's side and because each offspring can be part of multiple pairs on mother's and/or father's side. Therefore, the numbers of pairs here do not match numbers of offspring presented in table 1.
None of the odds ratios were statistically significantly different from 1, indicating that there were no significant associations between an individual's offspring's sex and the sex of their sibling's offspring. Results were similar when only looking at the first-born offspring; all ORs were non-significant and close to 1. Because of the enormous sample sizes, the estimates are extremely precise with very narrow CIs. For example, for the whole sample of full sibling pairs, we found an OR of 1.001 with 95% CIs of 0.998, 1.003.
The observed tetrachoric correlation between full siblings was 0.00029 (95% CI: −0.00038, 0.00098) and for first-born offspring −0.00120 (95% CI: −0.00284, 0.00027). Thus, the estimate was not significantly different from zero and the upper 95% confidence bound of the heritability (twice the upper CI of the sibling correlation [32]) was 0.0020 (or 0.0005 for first-born offspring). Using the animal model, with an identity link function, similarly yielded a null heritability estimate (0.0004; 95% CI: 0.0000–0.0010). The same analysis using a probit link function yielded a heritability estimate of 0.0005, and with logit link function an estimate of 0.0004 (we could not obtain CIs for these analyses). For women, the estimated heritability, using an identity link function, was 0.0005 (95% CI: 0.0000–0.0015) and for men, 0.0004 (95% CI: 0.0000–0.0014).
Table 3 shows the results of the within-family analyses. In the left part is the association between the sexes of the offspring within families of certain size (for families with 2 to 10 children). In families with a final number of two children, the offspring were more likely to be opposite sex than expected by chance (OR = 0.854; 95% CI: 0.847, 0.860). For families with 3 to 7 children, there was a significant effect (p < 0.001) in the opposite direction, with a higher likelihood of an excess of same-sex offspring (OR estimates range between 1.049 and 1.077). However, when predicting the sex of the nth child based on the sex of the older siblings but irrespective of final family size, the associations were statistically non-significant (table 3, right side). Thus, the sex distribution within-nuclear families deviated from what is expected by chance, with two-child families having children of opposite sex more often than expected. However, removing the conditioning of final family size (i.e. not restricting the birth-order-specific analyses depending on final family size, but including all offspring available, regardless of whether the parents had more offspring in the future) made associations null, indicating that the associations were driven by parents selectively stopping reproduction, rather than by biological differences in sex determination of offspring related to parity.
Table 3.
Within-family offspring sex associations. Left, the within-nuclear-family sex associations for families of different sizes (final number of children 2 to 10). Right, prediction (OR) of the sex of the nth child based on the sex of each older sibling, regardless of final family size. Odds ratios above 1 indicate a higher likelihood individuals' offspring having the same sex, odds ratios below 1 a higher likelihood of opposite sex. NA, not applicable. Analyses performed with generalized estimating equations with logit link and standard errors clustered on parental sibling clusters.
| final family size (no. of children) |
final family size analysis |
birth order analysis |
|||||
|---|---|---|---|---|---|---|---|
| no. of pairsa | odds ratio (95% confidence intervals) | p-value | nth born child | no. of pairsa | odds ratio (95% confidence intervals)b | p-value | |
| 1 | NA | NA | NA | 1 | NA | NA | NA |
| 2 | 1 085 061 | 0.854 (0.847, 0.860) | <0.001 | 2 | 1 748 196 | 0.997 (0.991, 1.003) | 0.363 |
| 3 | 1 461 533 | 1.049 (1.042, 1.056) | <0.001 | 3 | 1 349 407 | 1.005 (0.998, 1.012) | 0.148 |
| 4 | 803 803 | 1.077 (1.068, 1.087) | <0.001 | 4 | 559 402 | 0.999 (0.989, 1.010) | 0.916 |
| 5 | 354 620 | 1.073 (1.058, 1.088) | <0.001 | 5 | 206 348 | 1.003 (0.985, 1.021) | 0.772 |
| 6 | 156 337 | 1.073 (1.051, 1.095) | <0.001 | 6 | 79 373 | 0.993 (0.965, 1.023) | 0.660 |
| 7 | 69 366 | 1.071 (1.037, 1.106) | <0.001 | 7 | 32 318 | 1.008 (0.963, 1.055) | 0.747 |
| 8 | 34 331 | 1.043 (0.997, 1.090) | 0.065 | 8 | 14 593 | 1.057 (0.988, 1.131) | 0.106 |
| 9 | 16 540 | 1.064 (0.996, 1.137) | 0.064 | 9 | 6978 | 0.982 (0.890, 1.084) | 0.724 |
| 10 | 10 779 | 1.091 (1.003, 1.186) | 0.042 | 10 | 3706 | 0.969 (0.847, 1.109) | 0.651 |
aBecause nuclear families were considered as a unit, each pair could only contribute to one family. However, individuals can be part of more than one pair as each first-born offspring may be part of cousin pairs both on her/his mother's and father's side and because each first-born offspring can be part of multiple pairs on mother's and/or father's side. Therefore, the numbers of pairs here do not match numbers of offspring presented in table 1.
bOR of the sex of the nth child based on the sex of each older sibling; e.g. for the fourth-born child, the dependent variable is the sex of child 4, and independent variable is from siblings born first, second and third.
We also split the sample into different birth cohorts; we did not find any significant association between the sex of individuals' offspring and sex of their siblings' offspring, either when considering all pairs of offspring or when only considering first-born offspring (table 4). Finally, when including multiple births the results were essentially unchanged (results not shown).
Table 4.
Association between sex of an individual's offspring and sex of their sibling's offspring, restricted by birth year of parents. Odds ratios above 1 indicate a higher likelihood of siblings' offspring having the same sex, odds ratios below 1 a higher likelihood of opposite sex. Note: Analyses performed with generalized estimating equations with logit link and standard errors clustered on parental sibling clusters.
| birth year restrictionsa | all pairs of offspring |
only first-born offspring |
||||
|---|---|---|---|---|---|---|
| no. pairs | odds ratio (95% confidence interval) | p-value | no. pairs | odds ratio (95% confidence interval) | p-value | |
| from 1932 to 2000 | 11 958 896 | 1.001 (0.998,1.003) | 0.523 | 2 246 883 | 0.997 (0.992,1.002) | 0.246 |
| from 1932 to 1985 | 11 842 051 | 1.001 (0.998,1.003) | 0.640 | 2 203 557 | 0.997 (0.992,1.002) | 0.234 |
| from 1932 to 1973 | 10 456 786 | 1.001 (0.998, 1.003) | 0.674 | 1 879 161 | 0.997 (0.992,1.003) | 0.338 |
| from 1947 to 2000 | 7 160 659 | 1.000 (0.997,1.003) | 0.978 | 1 393 138 | 0.995 (0.988,1.001) | 0.120 |
| from 1947 to 1985 | 7 043 814 | 1.000 (0.997,1.003) | 0.842 | 1 349 812 | 0.994 (0.988,1.001) | 0.108 |
| from 1947 to 1973 | 5 658 558 | 0.999 (0.996,1.003) | 0.745 | 1 025 418 | 0.995 (0.987,1.002) | 0.164 |
| from 1961 to 2000 | 3 057 004 | 1.001 (0.997,1.006) | 0.521 | 667 896 | 0.998 (0.989,1.008) | 0.711 |
| from 1961 to 1985 | 2 940 194 | 1.001 (0.996,1.005) | 0.760 | 624 579 | 0.998 (0.988,1.008) | 0.678 |
| from 1961 to 1973 | 1 583 439 | 1.001 (0.995,1.007) | 0.786 | 304 960 | 1.001 (0.987,1.015) | 0.911 |
a‘From' and ‘to' refers to between which birth years the index generation individuals are born. The 1932–2000 analysis is the full analyses (as in table 1).
4. Discussion
In a sample comprising 4 753 269 offspring of 3 543 243 Swedes, we detected no significant genetic influence on offspring sex ratio. In fact, our heritability estimate was zero, with an upper 95% CI of 0.0020 (i.e. two-tenths of one per cent), rendering Fisher's principle untenable as a framework for understanding human offspring sex ratio.
Our results also rule out the possibility that offspring sex ratios are adaptively calibrated to individuals' heritable traits. Certain interpretations of the Trivers–Willard effect [6] propose that parents who possess any heritable trait that disproportionately benefits the fitness of one sex will bias their offspring sex ratio towards that sex [8]. A number of studies have reported evidence of such effects––e.g. male-biased offspring sex ratio in bigger, taller [8], wealthier [11], higher status [7] and less sociosexually restricted [10] parents, and a female-biased offspring sex ratio in more physically attractive parents [9]. Several of these findings, though, have been questioned on statistical grounds [33–35], and other studies have not supported the hypothesis (including very large birth cohort studies, e.g. [8,36,37]). Our findings are incompatible with the basic effect: if offspring sex ratio was calibrated to heritable traits, then it would necessarily be heritable to some degree as well.
According to the same principle, our results also rule out a hypothesis [38,39] that offspring sex ratio in humans (and in other mammals) is influenced by steroid hormone levels in parents at the time of conception. As James [40] notes, if the hypothesis was true, then offspring sex ratio would be heritable to some degree because steroid hormone levels are themselves heritable [41,42]. Therefore, given our finding of zero heritability, the hormone-level hypothesis is untenable.
Another proposal is that the environment experienced by mothers during early life may affect their subsequent offspring sex ratio [43]. Because the vast majority of siblings in our study would have grown up together and thus shared many aspects of their early environment, the lack of any sibling similarity in offspring sex ratio further limits the possibility of adaptive variation in relation to these shared environmental factors. Moreover, any environmental effect––or any factor that is at all stable––should cause correlation within-individuals regarding the sex of different offspring (e.g. a woman whose first child is a boy is more likely to have subsequent boys compared to girls); we did not see any such auto-correlation in offspring sex, indicating that there are no stable factors of persons or their environments that influence their offspring sex ratio.
If human offspring sex ratio is not heritable and/or under adaptive control in calibration to heritable or environmental factors, what causes its variance between individuals? One possible explanation is that some parents stop their reproduction dependent on sex composition attained in the family. This behaviour would produce deviations from expected distributions of sexes in families, but the sex determination at conception could still be entirely random. We have indirect evidence on this question: conditioning on final family size produced statistically significant association between sexes within a family. However, when not conditioning on the final family size, but predicting the sex of the nth child based on the sex of their older siblings regardless of final family size, the associations were statistically non-significant. In sum, all of our results are consistent with the simple explanation that variation in offspring sex ratio in humans is due to unbiased Mendelian segregation of sex chromosomes during spermatogenesis and unbiased fertilization. The slight excess of male births is likely to be due to a general difference in survival of male and female embryos in the womb, the reasons for which are not yet understood [4].
This is by far the largest study of the heritability of offspring sex ratio in humans, but to our knowledge it is also the largest such study in any animal. Our findings do not preclude heritable offspring sex ratio in other species with similar sex determination systems, but there is little compelling evidence for such genetic variation (e.g. [44,45]). Moreover, if offspring sex ratio in other such species were heritable, it would raise perplexing questions as to how heritability could have been lost in the human lineage. Under Fisher's principle, offspring sex ratio is subject to negligible selection when the population is near equilibrium [1,5], which it normally is; even in the hypothetical case of large variance in local sex ratios, selection favours equal investment (e.g. alternating male and female offspring) [46], not random Mendelian sex determination, where uneven investment is likely for individual parents. How and why would such weak selection have eliminated all genetic variation in offspring sex ratio while substantial genetic variation has been maintained in virtually every other human variable that has been studied [47], including fitness itself [48]?
Although the study has a large and largely unbiased sample, it is not perfect, and there are some limitations to consider. First, the register's coverage on parental identity, while very good, is not 100% (particularly for fathers), which could introduce slight bias towards the null. Non-paternity (i.e. the assumed biological father is not the biological father) is rare (approx. 1–2%) in human populations [49,50], so this could not explain a zero heritability estimate. Further, sensitivity analysis with birth years restricted to the highest quality data also showed the null association. Another consideration is that, although stillbirths are registered, we do not know the sex of spontaneous or selectively aborted fetuses early in pregnancy. But we have no reason to believe that the spontaneous abortions would bias the observed association to precisely null. Last, our approach did not include estimation of non-additive genetic, common environmental or parental effects. Not accounting for these factors could lead to an overestimation of the heritability of sex ratio, but given that we found near-zero heritability, this limitation cannot have meaningfully biased our results.
In conclusion, we found in a large and well-characterized sample that there is no heritable, familial or stable between-individual variance in human offspring sex ratio, ruling out various theories on which much of the scientific understanding of the trait had been based. Our findings suggest a rethink of sex ratio theory is necessary, at least as it applies to humans.
Supplementary Material
Acknowledgements
B.P.Z. received funding from The Australian Research Council (grant no. FT160100298). K.J.H.V. is supported by the Foundation Volksbond Rotterdam.
Ethics
The study was approved by the Regional Ethics Review Board in Stockholm (Dnr 2013/862–31/5). Informed consent was not required since it was a registry study, so no individual was contacted.
Data accessibility
Data used for this manuscript cannot be shared publicly due to the Swedish Secrecy Act. Data from the Total Population Register and the Multi-Generation Register were used for this study and made available by ethical approval. Researchers may apply for access through the Swedish Research Ethics Boards (www.etikprovningsmyndigheten.se) and from the primary data owner Statistics Sweden (www.scb.se), in accordance with Swedish law.
Authors' contributions
B.P.Z., K.J.H.V. and R.K.-H. designed the study and wrote the paper. P.L., H.W., and R.K.-H. obtained and organized the data. R.K.-H. analysed the data.
Competing interests
The authors declare no competing interests.
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Associated Data
This section collects any data citations, data availability statements, or supplementary materials included in this article.
Supplementary Materials
Data Availability Statement
Data used for this manuscript cannot be shared publicly due to the Swedish Secrecy Act. Data from the Total Population Register and the Multi-Generation Register were used for this study and made available by ethical approval. Researchers may apply for access through the Swedish Research Ethics Boards (www.etikprovningsmyndigheten.se) and from the primary data owner Statistics Sweden (www.scb.se), in accordance with Swedish law.