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EVOLUTION individuals are increasingly accessible to many researchers. survival to postreproductive age and may not be completed rLRS Another advantage comes from the ability to control for possi- for males. Despite the weak signal, we find that 23 female traits ble cultural transmission of traits, which is generally confounded and 21 male traits have significant nonzero directional selection with genetics in observational studies because parents pass both gradients (βˆ) at a family-wise error rate (FWER) ≤ 0.05. How- on to their offspring (11). This issue can be partially mitigated by ever, many of these traits are highly correlated (SI Appendix, accounting for population structure (28) and geography in sam- Figs. S4 and S5) and should not be viewed as separable axes of ples of unrelated individuals. selection. In the first attempt to use SNP-array data to study contem- The βˆ estimates for traits with a significant estimate in at least porary natural selection on complex traits, Tropf et al. (19) one sex are shown in Fig. 1A. Overall, the βˆ estimates were found a negative genetic correlation between relative lifetime not highly correlated between sexes. This implies that there is reproductive success (rLRS)—the individual lifetime reproduc- some sex-specific selection acting on these phenotypes, consis- tive success divided by the mean—and age at first birth, using tent with recent work on the genetic and phenotypic correlates a bivariate linear mixed-modeling approach (26, 29). How- of viability (45). In many instances, the difference between sexes ever, Beauchamp (25) noted that the bivariate analyses are is driven by a large difference in the magnitude, not the sign, of βˆ. underpowered with modest sample sizes and chose to analyze For example, the estimate for educational attainment in females genetic predictors derived from the results of independent large ˆ −172 genome-wide association studies (GWAS). Significant negative is βEA,F = −0.0612 ± 0.0022 (P < 10 ) while the estimate ˆ −2.3 correlations between polygenic prediction scores for female edu- in males is βEA,M = −0.0086 ± 0.003 (P ≈ 10 ). Conversely, cational attainment and rLRS have been found in the popula- the estimate for birth weight in males, βˆBW ,M = 0.021 ± tions of the contemporary United States (25) and Iceland (27). 0.0038 (P < 10−7), is much larger than the estimate in females But reliance on external GWAS summary statistics limits analy- of βˆBW ,F = 0.0047 ± 0.0027 (P = 0.084). Height is the only trait ses to traits that have already been thoroughly characterized at we studied for which the data indicate sexually antagonistic selec- the genetic level. −39 tion. In females βˆHT,F = −0.028 ± 0.0021 (P < 10 ), while in Here, we analyze the phenotypic and genetic correlates of ˆ −18 rLRS in the UK Biobank (UKB). The UKB is a large population- males βHT,M = 0.022 ± 0.0025 (P < 10 ). Fig. 2 further illus- based prospective study of the genetic and environmental deter- trates that the predicted phenotypic optimum is above and below minants of aging-related disease (30). The dataset consists of the population mean height for males and females, respectively, over 500,000 individuals from the United Kingdom who have consistent with multiple previous studies showing a difference in been genotyped at common SNPs and clinically phenotyped contemporary selection pressures on height between males and for many different traits. These data provide paired genotype females (13). Further, the empirical relationship between LRS and phenotype samples large enough to accurately measure and height, illustrated in SI Appendix, Fig. S2, is very similar additive genetic correlation between many heritable complex to that predicted by a Gaussian stabilizing selection model (SI traits (31). Appendix, Fig. S3). First, we apply the Lande and Arnold (10) framework through In contrast to a recent study (25), 12 traits in females and 14 regression analyses of the relationship between a suite of phe- traits in males have a significant nonlinear selection gradient esti- γˆ notypes and a proxy for fitness, rLRS, in 217,728 females and mate ( ). It is important to note that the sample size available in ref. 25 was nearly two orders of magnitude smaller than that of 158,638 males. Then, the genetic data available from 157,807 the present study. The histogram of γˆ values in SI Appendix, Fig. female and 115,902 male unrelated samples are used to estimate S1B shows a skew toward negative values. Specifically, 47 of the genetic correlations between the phenotypes and rLRS through 64 sex–trait combinations examined show a negative quadratic linkage disequilibrium (LD)-score regression analysis (32, 33). selection gradient (median γˆ = −0.0059), of which 26 were sig- This analysis was supported by the observation that rLRS had a ˆ low, but measurable heritability. Our analyses replicate the main nificant. Twenty-four sex–trait pairs had a nonzero β and a sig- results of other recent studies (19, 25, 27) and uncover a host of nificant negative γˆ, which is indicative of the simultaneous action other significant genetic correlations with rLRS. We also report of directional and stabilizing selection. estimates of quadratic relationships with rLRS, which may be Fig. 1B shows that, unlike many of the βˆ estimates, the esti- interpreted as evidence consistent with stabilizing or disruptive mates of γˆ were quite similar in both sexes. For example, the −37 selection, informing efforts to model the processes that maintain estimates for height are γˆHT,F = −0.0189 ± 0.0014 (P < 10 ) −17 heritable variation in human complex traits (34–43). Our obser- in females and γˆHT,M = −0.015 ± 0.0017 (P < 10 ) in males, vations are consistent with the action of weak directional and respectively. Fig. 1B shows that among traits with significant γˆ in stabilizing selection and limited disruptive selection in the UK both sexes the male estimate tends to be farther from zero (with Biobank population. height being an exception). We find no traits with significant γˆ in both sexes with opposite signs. Fig. 1B shows that age at menopause, fluid intelligence score, Phenotypic Observations and age at first birth (AFB) all have a positive γˆ in females. We estimate linear (β) and quadratic (γ) selection gradients In addition, the γˆ for educational attainment is positive in both by regressing rLRS onto phenotypes and squared phenotypes sexes. A positive value of γ can be interpreted as evidence of (10). Because of possible heterogeneity in selection pressures disruptive selection. However, our results for AFB are more and rLRS measurement precision—documented number of live indicative of a plateauing of directional selection toward the births in females vs. self-reported number of children fathered upper phenotypic extreme rather than true disruptive selection in males—all analyses were performed on a sex-specific basis. In (SI Appendix, Fig. S6). The situation is somewhat less clear for total, we analyzed 37 traits in females and 33 traits in males; the the other phenotypes with a significant positive γˆ (SI Appendix, traits and results are listed in Dataset S1. The histogram of βˆ (SI Figs. S7, S9, and S10) and these results should be followed up Appendix, Fig. S1A) shows that the observed signals of directional more closely in future work. selection are weaker than what has been found in other species A multiple-regression analysis provided a more conservative (44). Such weak selection gradients are unlikely to lead to large perspective on the phenotypic correlates of rLRS. Due to mul- changes in phenotypic distributions over clinically or socially rel- ticollinearity (SI Appendix, Figs. S4 and S5) and nonoverlap- evant timescales (25, 27). However, it is important to note that ping missing data, we had to choose only a subset of traits for the measured rLRS may be biased because it is conditional on the multiple regression. The full multiple-regression results are

2 of 6 | www.pnas.org/cgi/doi/10.1073/pnas.1707227114 Sanjak et al. ajke al. et Sanjak three all model, reduced the EA, In with interaction. model their multiple-regression and reduced a AFB, fitted we rLRS that appears (46) selection it apparent EA. the Rather, relation- on drive AFB, rLRS. linear regression as increased such simple separate factors, and a correlated the EA from to between away contrast set- points ship multiple-regression strongly sharp the and in in results stands EA positive between This is association females ting. the in pressure, of rLRS multiple-regression blood direction and the the in systolic However, significant density, model. are ratio mineral waist-to-hip bone and menarche, females, at In of of models. direction estimates regression their the single-trait retain the and from regression association multiple sig- the are pressure in blood systolic nificant and (BMI), index body-mass rate, AFB, S1 on data that in Note included blood (WT). zero. systolic to weight set (PWRI), and were index (WHR), values reflection regression ratio their pulse-wave waist-to-hip and (WC), (PWP), flow males expiratory circumference time for peak available waist peak-to-peak (NS), not estimate, score pulse-wave are (FVC), neuroticism (SRT) (PWA), AAM capacity (MTM), and threshold vital index AMP, matches reception forced identify stiffness weight (FIS), correctly speech arterial birth to score (SBP), (BMR), pulse-wave time intelligence pressure rate birth mean (PR), fluid metabolic first (HT), (FEV), rate basal height at volume pulse (BMI), (HGS), age expiratory strength index (AAM), (PEF), forced grip body-mass menarche (EA), hand (BMD), at attainment (HC), density age circumference educational mineral descriptions: hip (DBP), bone trait pressure (BFP), abbreviated blood percentage following diastolic body-fat the (BW), (AMP), with menopause labeled (FWER at are significant age Points being (AFB), traits. of basis across the consistency on and selected interpretation were Traits males. and females 1. Fig. AB ofrhrepoeterltosi ewe F,E,and EA, AFB, between relationship the explore further To nmls h siae of estimates the males, In . ( A and DtstS1 Dataset B ctepo hwn h antd f( of magnitude the showing Scatterplot ) β o dctoa tanet(A,AB age AFB, (EA), attainment educational for adaesmaie in summarized are and β o adgi tegh pulse strength, hand-grip for IAppendix SI A ierslcingradients selection linear ) Table , ≤ il ersincmae ihtesprt ersin.For regressions. of separate estimates the the with females, compared regression children tiple popu- fewer Icelandic the have in to work the prior tend (27). despite with EA lation is consistent higher is This and with children. with overall more individuals people have those among that to life, that fact tend in suggest will later results EA children higher these have terms who AFB simpler females between In association rLRS. negative strong and be the that can by and model explained EA-alone increases the fully AFB of in as coefficient effect regression positive the negative more the that becomes is rLRS observation on EA this reduced with consistent the hypothesis in is AFB ( positive and EA positive is between strongly term EA interaction the for addition, In association significant model. of highly direction were the interaction) one and ( linear (two terms IAppendix SI 0 h siae of estimates The . 5 na es n e.Etmtsaeo the on are Estimates sex. one least at in 05) β ˆ n ( and B al S1 Table , udai eeto gradients selection quadratic ) β AFB adsd.Tehrzna ahdln niae a indicates 1. line of fitness dashed predicted right- horizontal relative the The on (gray) side. axis an male hand with and overlaid (red) are female phenotypes (male) of black black Histograms dashed and dashed lines. (female) red and by solid indicated (female) vertical are means population red The lines. solid (male) and predicted by are across shown range values phenotypic fitness Gaus- observed relative the parameterized function, the fitness sian Using gradi- Gaussian function. a selection of fitness parameters quadratic into converted and were ents Linear height. of 2. Fig. γ ˆ : eemc essgicn ntemul- the in significant less much were .A nteiiilmlil regression, multiple initial the in As ). EA 0 = γ rdce eaiefins safunction a as fitness relative Predicted . 03 o g tfis iebrhand birth live first at age for ± 0 . 06( 0016 γ ˆ z NSEryEdition Early PNAS soesaefrtheoretical for scale -score o eeto ftat in traits of selection a for P < 10 − 112 ) .One ). | f6 of 3

EVOLUTION BMI were significant—with the BMI estimate reversing direc- our study-wise significance threshold, the results are consistent tion to be positive. In males, the estimates of γ for EA and with the hypothesis that contemporary selection on reproduction BMI were significant—with both retaining their direction of favors higher BMI in males and support exploration of the same association. hypothesis in females. The genetic correlation estimate for AFB in females was the Genetic Correlations with rLRS strongest observed in our study. We estimate that the rˆg,rLRS The phenotypic results are consistent with the action of natu- for AFB is −0.593 ± 0.035 (P < 10−16). This result is con- ral selection, but for adaptation to occur there must be effects sistent both with our phenotypic observations and with prior on the genetic level. To this end, we analyzed genetic data pedigree-based results (17). EA is also strongly negatively corre- from 157,807 female and 115,902 male unrelated samples. Esti- lated with rLRS; we estimate the rˆg,rLRS for EA to be −0.316 ± mates of the genetic correlations between several traits and 0.037 (P < 10−16) in females and −0.2539 ± 0.052 (P < 10−5) rLRS, rg,rLRS , were obtained from the data, using LD-score in males. However, the most likely explanation for these genetic regression (32, 33). LD-score regression uses the regression of results is something very similar to what we observed on the cross-products of z statistics onto a measure of LD in a the phenotypic level for these two traits, which would agree genomic window (the LD score), assuming a polygenic architec- with work on contemporary selection in an Icelandic popu- ture, to estimate genetic covariance components from GWAS lation (27). results. We also analyzed the UKB interim data release, using Another interesting aspect of the observed negative direc- a linear mixed-modeling (LMM) approach. This approach was tional selection on AFB is that it would suggest selection for not computationally feasible on the full dataset; we report the increased female reproductive lifespan. However, the evidence results on the full dataset using LD-score regression in the main is less clear when we compare the results on AFB to other text, but see SI Appendix for a discussion of the LMM results. female reproductive life-history traits such as the age at menar- All genetic variance and covariance estimates are contained in che (AAM) and age at menopause (AMP). In fact, we esti- Dataset S2. mate that the genetic correlation with rLRS is positive for AAM −4.4 Theory predicts that traits highly correlated with fitness will (rˆg,rLRS = 0.133 ± 0.032 (P < 10 )) and negative for AMP −3.7 have low heritability (47). As expected, rLRS has a low but sig- (rˆg,rLRS = −0.168 ± 0.045 (P < 10 )). The genetic result for nificant SNP heritability in the UKB dataset, which means that AMP is particularly unexpected because it is inconsistent with we have power to detect strong genetic correlations. Specifically, both our phenotypic result (even though the phenotypic corre- 2 the LD-score regression estimates of hSNP,rLRS were 0.056 and lation is very small, 0.02) and a prior result obtained in a pedi- 0.033 in females and males, respectively, with respective stan- gree study (17). Further, we estimate that the genetic correla- dard errors of 0.0046 and 0.0054. Fig. 3 shows rˆg,rLRS for the tion between AAM and AFB is strongly positive despite the subset of traits for which an estimate was marginally significant fact that signs of the rˆg,rLRS estimates for the two traits are (P ≤ 10−3) in at least one sex. opposite. We intuitively expect a positive relationship between The estimated genetic correlation with rLRS was significant AAM and AFB because the latter requires the former. However, for several anthropometric traits. For example, the estimates of the positive genetic correlation between rLRS and AAM is less −5 rˆg,rLRS for height are −0.1278 ± 0.0274 (P < 10 ) in females explicable. and −0.0074 ± 0.0412 (P = 0.18) in males. Recall that we esti- Estimation of the genetic evidence of nonlinear selection was mated a significant negative selection gradient in females with not performed because of lack of statistical power. Theory pre- a small but significant positive selection gradient in males. The dicts that the additive genetic variance for a squared pheno- phenotypic results are in agreement with prior studies in Western type is likely to be very small and, when present, is confounded populations (13), suggesting that selection on reproductive suc- with genetic control of phenotypic variability. In addition, the cess favors shorter females and taller males. However, because empirical heritability estimates for squared phenotypes are small we see no evidence for a genetic correlation between height and (SI Appendix, Fig. S19). Despite the lack of power, a poly- rLRS in males, we do not predict that the observed phenotypic genic predictor for height, constructed from a meta-analysis of selection in males would induce a response to selection (in a sin- the Genetic Investigation of Anthropometric Traits (GIANT)– gle generation). UKB joint dataset, did show a marginally significant negative BMI provides another important example of evidence for quadratic regression coefficient in females (see SI Appendix for directional selection on an anthropometric trait. We estimate details). −2.6 that the rˆg,rLRS for BMI is 0.104 ± 0.0344 (P = 10 ) in females and 0.31 ± 0.046 (P < 10−10) in males. These results Discussion are qualitatively similar to our phenotypic results which indicated Estimates of linear and quadratic selection gradients were positive directional selection in both sexes with a larger estimate obtained via simple linear regression of a broad set of pheno- in males. Although the genetic result for females did not pass types onto a proxy for fitness. The results suggest that many traits

Fig. 3. Bar plots showing genetic correlations Females Males between a selection of traits and rLRS for females AFB * EA * (red) and males (blue). Traits were selected on the EA * FIS basis of being marginally significant (P ≤ 0.001) FIS * in at least one sex and were sorted in ascending AMP * HT order of the estimate for each sex. Data are dis- HT * BFP * BMR played as the correlation estimate plus or minus the HC * WT SE (∼ P ≤ 0.001, *FWER ≤ 0.05). Bars are labeled BMR HC * with the following abbreviated trait descriptions: WC WHR * age at menarche (AAM), age at first birth (AFB), age at menopause (AMP), body-fat percentage BMI WC * WHR (BFP), body-mass index (BMI), basal metabolic rate WT * BFP (BMR), educational attainment (EA), fluid intelli- AAM * BMI * gence score (FIS), hip circumference (HC), height −0.50 −0.25 0.00 0.25 −0.2 0.0 0.2 0.4 (HT), waist circumference (WC), waist-to-hip ratio Genetic correlation with rLRS Genetic correlation with rLRS (WHR), and weight (WT).

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Any Research supported R01-GM115564 and 1321846. Graduate work Grant 1078037 (NSF) upon NIH dation (Grants based by is supported Council material was Research work Medical This National Australian and the Australian and Health the 160103860) by Project supported (Discovery are P.M.V. Council and Research M.R.R., J.S., 12505. Project under ACKNOWLEDGMENTS. UKB the in the of participants see descriptions Methods analyses, all detailed Research and For Multicentre and preparation consent. data Northwest informed study The written the provided 0.05. study approved of rate Committee anal- 33. error Ethics all ref. family-wise in in a Bonferroni-corrected developed used LD- using at protocol using were determined the was calculated men to significance were Statistical for according using correlations software y Genetic performed regression (57). 50 were score R analyses and in Phenotypic females regression noted. over linear for otherwise ancestry y white-British unless 45 be self-reported yses, of may of and ages samples Sys- UKB from the Management Access data the UKB the Only from from tem. researchers obtained fide bona were all by data accessed genetic and Phenotypic Methods and Materials architecture genetic the shaped trait. that the ones evolutionary of the contemporary from research how differ further understand forces better not, to are com- needed they is are If con- gradients. traits their selection know by complex parameterized temporary not models of do equilibrium we architectures with mensurate Presently, genetic humans. the evo- in the whether traits for complex model moving-optimum of supports dynamic work lution a Our of (11). the study evolution study further human to of phenotyping dynamics extensive ongoing with data genetic molecular like sample population a in UKB. variation the genetic on interro- stabilizing acting of observe selection directly methods to and/or genetic variance genetic sizes the nonadditive sample gating at larger stabilizing require of will effects level the of characterization ough tblzn eeto per ob h oecmo form common more the be to appears selection Stabilizing ehv hw h oe fcmiighigh-throughput combining of power the shown have We 65 hc ol ecniee ek u otiili the- a in nontrivial but weak, considered be would which , V V . 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