Genetic evidence for natural selection in humans in the contemporary United States

Significance

I leverage recent advances in molecular genetics to test directly whether genetic variants associated with a number of phenotypes have been under natural selection in the contemporary United States. My finding that natural selection has been slowly occurring for genetic variants associated with educational attainment and (suggestively, in females) for variants associated with age at menarche provides additional evidence that humans are still evolving—albeit slowly and at a rate that cannot account for more than a small fraction of the large changes that have occurred over the past few generations.

Abstract

Recent findings from molecular genetics now make it possible to test directly for natural selection by analyzing whether genetic variants associated with various phenotypes have been under selection. I leverage these findings to construct polygenic scores that use individuals’ genotypes to predict their body mass index, educational attainment (EA), glucose concentration, height, schizophrenia, total cholesterol, and (in females) age at menarche. I then examine associations between these scores and fitness to test whether natural selection has been occurring. My study sample includes individuals of European ancestry born between 1931 and 1953 who participated in the Health and Retirement Study, a representative study of the US population. My results imply that natural selection has been slowly favoring lower EA in both females and males, and are suggestive that natural selection may have favored a higher age at menarche in females. For EA, my estimates imply a rate of selection of about −1.5 mo of education per generation (which pales in comparison with the increases in EA observed in contemporary times). Although they cannot be projected over more than one generation, my results provide additional evidence that humans are still evolving—albeit slowly, especially compared with the rapid changes that have occurred over the past few generations due to cultural and environmental factors.

Whether natural selection has been operating and still operates in modern humans—and at what rate—has been the subject of much debate. Until recently, it was often held that human evolution had come to an end about 40,000–50,000 y ago (see, e.g., ref. 1). However, new evidence that has been accumulating over the last decade suggests that natural selection has been operating in humans over the past few thousand years (2–4) and that a number of adaptations—such as lactase persistence (5), resistance to malaria (6), and adaptation to high altitude (7)—have occurred relatively recently. It has also been shown that height (HGT) and body mass index (BMI) have been under selection in Europeans (8).

In parallel, a number of recent studies have sought to examine the association between lifetime reproductive success (LRS)—the number of children an individual ever gave birth to or fathered—and various phenotypes in contemporary human populations. [In modern populations with low mortality, fitness can be reasonably approximated by LRS (9, 10), notwithstanding some caveats summarized in Discussion.] These studies have typically found that natural selection has been operating in contemporary humans (9, 11–14). It has also been shown that there was significant variance in relative fitness in a preindustrial human population, such that there was much potential for natural selection (15).

However, this literature has analyzed the relationship between phenotypes and LRS, and natural selection occurs only when genotypes that are associated with the phenotypes covary with reproductive success. This literature’s conclusions regarding ongoing natural selection are thus particularly sensitive to assumptions that are needed to estimate the relationship between genotypes and phenotypes and to the inclusion in the analysis of all correlated phenotypes with causal effects on fitness (16, 17). Some of those assumptions have been criticized and debated (e.g., ref. 18), and it has proven challenging to include all relevant correlated phenotypes in analyses of selection in natural populations (17). (The latter point matters because if, for example, phenotypes 1 and 2 are phenotypically but not genetically correlated and if only phenotype 2 is under selection, an analysis based on phenotypic data that does not include phenotype 2 or that fails to account for the lack of genetic correlation may erroneously conclude that phenotype 1 is also under selection.)

Recent advances in molecular genetics now make it possible to look directly at the relationship between LRS and genetic variants associated with various phenotypes, thus eliminating those potential confounds. Here, I examine the association between relative LRS (rLRS)—the ratio of LRS to the mean LRS of individuals of the same gender born in the same years—and genetic variants associated with various phenotypes, for a sample of females and males in the Health and Retirement Study (HRS). Using rLRS instead of LRS as the measure of fitness helps control for the effects of time trends in LRS and makes it possible to interpret my estimates as rates of natural selection (9, 16). (My results are robust to using LRS instead of rLRS as the measure of fitness.)

The phenotypes I analyze are BMI, educational attainment (EA), fasting glucose concentration (GLU), HGT, schizophrenia (SCZ), plasma concentrations of total cholesterol (TC), and age at menarche (AAM; in females). These phenotypes were selected on the basis of previous evidence showing that selection acts on some of them (see, e.g., ref. 9) and because summary statistics [i.e., the estimated effects of the single-nucleotide polymorphisms (SNPs) on the phenotypes] from previous large-scale genome-wide association studies (GWAS) are available for them (19–25).

The HRS is a representative longitudinal panel study of ∼20,000 Americans shortly before and during retirement. It is well suited for this study for several reasons. First, the HRS was designed to be representative of the US population over the age of 50 y (26), which makes it possible to generalize my results to the entire US population of European ancestry born in the years of my study sample. In addition, individuals in the study are in the later stages of their lives, when they have typically completed their lifetime reproduction. Nonetheless, as I explain in Discussion, selection bias due to incomplete genotyping of the study participants and differential survival remains a concern, although genotyped individuals do not appear to differ markedly from nongenotyped individuals in my study sample.

To mitigate the risks of confounding by population stratification, my analyses focus on unrelated individuals of European ancestry and control for the top 20 principal components of the genetic relatedness matrix [which capture the main dimensions along which the ancestry of the individuals in the dataset vary (27)]. To mitigate the risk of selection bias due to differential mortality, and to ensure that the LRS variable is a good proxy for completed fertility, I limit my analyses to individuals born between 1931 and 1953 who were at least 45 y old (for females) or 50 y old (for males) when asked the number of children they ever gave birth to or fathered. I refer to the resulting sample as the “study sample.” I performed my main analyses separately for females and males, as different selection gradients can operate across genders.

In a recent paper, Tropf et al. (28) used genetic data to study the relationship between LRS and age at first birth in a sample of females, and found that the two phenotypes are negatively genetically correlated. My analyses complement theirs in several important ways: My analyses cover both females and males and seven different phenotypes; they include childless individuals (who can have an important impact on the gene pool by foregoing reproduction); they translate selected estimates into interpretable measures of the rate at which natural selection has been operating; and they indirectly leverage the statistical power of previous large-scale GWAS to estimate the relationship between rLRS and genetic variants associated with the phenotypes, thus increasing the precision of my estimates for some phenotypes. [An alternative to my score regression approach (described in Genetic Evidence for Natural Selection) is the bivariate GREML method (29) (used by Tropf et al.), but it is not well suited for the present study. It has very low power and yields imprecise estimates of the genetic correlation in samples of moderate size like the HRS, given the low SNP heritability of rLRS (28), according to the GCTA-GREML Power Calculator (30). It also requires a dataset with phenotypic data for every studied phenotype and assumes normally distributed phenotypes (which is not realistic for rLRS).]

Phenotypic Evidence for Natural Selection

I begin by looking at the phenotypic evidence for natural selection in the HRS. The HRS contains phenotypic variables for four of the seven phenotypes I study: BMI, EA, HGT, and TC. (The phenotypic variable for TC is an indicator for a self-reported health problem with high cholesterol, and not plasma concentrations of TC as in the GWAS of TC.) Table S1 reports summary statistics for these and for the other phenotypic variables I use, both for all individuals in the study sample and for the genotyped individuals in the study sample. As can be seen, the two samples look remarkably similar. Table 1 reports estimates from separate regressions of rLRS on each of these phenotypic variables (and on control variables) for the sample of all individuals (genotyped and not genotyped) in the study sample. Stouter females and males, less educated females and males, and smaller females have significantly higher rLRS (P < 0.001 in all cases). The estimates for the sample of genotyped individuals are very similar (Table S2), thus suggesting that the two samples are similar in terms of the selection gradients that were operating on the various phenotypes.

Table S1.

Summary statistics for the phenotypic variables

Phenotype	Comment	Unit	All individuals (genotyped and not genotyped)			Genotyped individuals only
			N	Mean	SD	N	Mean	SD
Females
Birth year	—	Year	6,414	1,941.21	6.41	3,416	1,941.35	6.40
LRS	Number of children ever given birth to	Children	6,414	2.57	1.63	3,416	2.58	1.58
BMI	Mean across waves of female BMI residualized on birth year dummies, plus mean female BMI across all waves and females	BMI points	6,396	27.01	5.73	3,413	27.18	5.56
EA	—	Years of education	6,403	12.98	2.38	3,410	13.12	2.33
HGT	Mean across waves of female HGT residualized on birth year dummies, plus mean female HGT across all waves and females	Centimeters	6,411	162.95	6.36	3,416	163.14	6.25
TC	Indicator variable for a self-reported health problem with high cholesterol in 1992	1 = yes	4,152	0.25	0.43	2,217	0.25	0.44
Childlessness	Indicator variable for a childless individual (LRS = 0)	1 = childless	6,414	0.10	0.31	3,416	0.10	0.31
Males
Birth year	—	Year	5,436	1,940.83	6.50	2,571	1,941.07	6.50
LRS	Number of children ever fathered	Children	5,435	2.45	1.60	2,571	2.47	1.57
BMI	Mean across waves of male BMI residualized on birth year dummies, plus mean male BMI across all waves and males	BMI points	5,432	27.81	4.53	2,571	27.79	4.49
EA	—	Years of education	5,420	13.27	2.82	2,566	13.49	2.70
HGT	Mean across waves of male HGT residualized on birth year dummies, plus mean male HGT across all waves and males	Centimeters	5,436	178.07	6.63	2,571	178.18	6.48
TC	Indicator variable for a self-reported health problem with high cholesterol in 1992	1 = yes	3,078	0.24	0.42	1,441	0.27	0.44
Childlessness	Indicator variable for a childless individual (LRS = 0)	1 = childless	5,435	0.12	0.32	2,571	0.11	0.31

This table shows the summary statistics for the study sample. For the main analyses, I use rLRS, not LRS. The phenotypic variable for TC is an indicator for a self-reported health problem with high cholesterol, and not plasma concentrations of TC as in the GWAS of TC. The HRS does not contain phenotypic variables for GLU, AAM, and SCZ.

Table 1.

Estimates from separate regressions of rLRS on each phenotypic variable, for all individuals

Variable	Females		Males
	Coefficient estimate	N	Coefficient estimate	N
BMI	0.008*** (0.001)	6,396	0.006*** (0.002)	5,431
EA	−0.057*** (0.003)	6,403	−0.022*** (0.003)	5,419
HGT	−0.006*** (0.001)	6,411	−0.001 (0.001)	5,435
TC	0.000 (0.021)	4,152	−0.027 (0.026)	3,078

This table shows estimates of the coefficients on the phenotypic variables and their SEs (in parentheses) from separate regressions of rLRS on each phenotypic variable and on control variables, for all individuals (genotyped and not genotyped) in the study sample. (***P < 0.01.)

Table S2.

Estimates from separate regressions of rLRS on each phenotypic variable and on the polygenic score of each phenotype

Variable	Regressions of rLRS on the phenotypic variables								Regressions of rLRS on the scores, genotyped individuals only
	All individuals (genotyped and not genotyped)				Genotyped individuals only
	$\widehat{\beta }$	SE	P	N	β	SE	P	N	Score	$\widehat{\beta }$	SE	P	N
Females
BMI	0.008	0.001	<0.001	6,396	0.010	0.002	<0.001	3,413	Score of BMI	0.006	0.010	0.58	3,416
EA	−0.057	0.003	<0.001	6,403	−0.055	0.004	<0.001	3,410	Score of EA	−0.033	0.010	0.002	3,416
									Score of GLU	0.009	0.010	0.40	3,416
HGT	−0.006	0.001	<0.001	6,411	−0.009	0.002	<0.001	3,416	Score of HGT	−0.011	0.014	0.44	3,416
									Score of SCZ	−0.001	0.011	0.96	3,416
TC	0.000	0.021	0.99	4,152	−0.002	0.028	0.95	2,217	Score of TC	−0.012	0.011	0.27	3,416
									Score of AAM	0.018	0.011	0.08	3,416
Males
BMI	0.006	0.002	<0.001	5,431	0.010	0.003	<0.001	2,571	Score of BMI	0.016	0.013	0.23	2,571
EA	−0.022	0.003	<0.001	5,419	−0.020	0.005	<0.001	2,566	Score of EA	−0.031	0.012	0.013	2,571
									Score of GLU	−0.013	0.013	0.31	2,571
HGT	−0.001	0.001	0.58	5,435	−0.001	0.002	0.60	2,571	Score of HGT	−0.005	0.018	0.78	2,571
									Score of SCZ	0.009	0.013	0.53	2,571
TC	−0.027	0.026	0.290	3,078	−0.020	0.036	0.58	1,441	Score of TC	−0.003	0.013	0.80	2,571

“Regression of rLRS on the phenotypic variables” mirrors Table 1 but shows the results both for all individuals (genotyped and not genotyped) and for the genotyped individuals only, and it also reports the P values. (The results for all individuals are the same as those reported in Table 1 but with the P values.) It shows estimates of the coefficients on the phenotypic variables (and their SEs and P values) from separate regressions of rLRS on each phenotypic variable. Each estimate comes from a different regression, and every regression includes birth year dummies and HRS-defined cohort dummies. The HRS does not contain phenotypic variables for GLU, AAM, and SCZ. “Regression of rLRS on the scores” shows the same results as Table 2 but also reports the P values. It shows estimates of the coefficients on the polygenic scores (and their SEs and P values) from separate regressions of rLRS on the polygenic score of each phenotype. Each estimate comes from a different regression. All regressions included birth year dummies, HRS-defined cohort dummies, and the top 20 principal components of the genetic relatedness matrix. The coefficients can be interpreted as directional selection differentials of the scores, expressed in Haldanes—i.e., each coefficient equals the implied change in the score that will occur due to natural selection in one generation, expressed in SDs of the score.

As mentioned, without assumptions to estimate the relationship between genotypes and phenotypes and without considering all correlated phenotypes with possible causal effects on fitness, it is not possible to translate these estimates into estimates of evolutionary change—even over a single generation. Previous research, however, has established that these phenotypes are all moderately to highly heritable (31); notwithstanding the possible effects of correlated phenotypes, this is suggestive that genotypes associated with BMI, EA, and HGT covary with fitness and that natural selection has been operating on these phenotypes.

Genetic Evidence for Natural Selection

To test directly whether natural selection has been operating on the genetic variants associated with BMI, EA, GLU, HGT, SCZ, TC, and AAM, the summary statistics from the latest GWAS of these phenotypes were used to construct polygenic scores that partially predict the genotyped individuals’ phenotypes based on their genotyped SNPs. To avoid overfitting (32), the GWAS summary statistics used are all based on meta-analyses that exclude the HRS. For the main analyses, LDpred (33) was used to construct the scores. LDpred uses a prior on the SNPs’ effect sizes and adjusts summary statistics for linkage disequilibrium (LD) between SNPs to produce scores that have higher predictive power than the alternatives. (My results are robust to using scores constructed with PLINK (34), which does not adjust the summary statistics for LD between SNPs.) The scores were standardized to have mean zero and an SD of 1. Additional details on the construction of the scores are provided in Materials and Methods and in SI Materials and Methods.

Fig. 1 shows the highest previously reported R² of the scores from the articles reporting the GWAS whose summary statistics were used to construct the scores, as well as the incremental R² of the scores of BMI, EA, HGT, and TC (for which there are phenotypic variables in the HRS) in the study sample. (The incremental R² of the score of a phenotype is defined as the difference between the R² of the regression of the phenotype on controls for sex and birth year, the top 20 principal components of the genetic relatedness matrix, and the score, and the R² of the same regression but without the score.) The incremental R² estimates range from 0.012 (for TC) to 0.174 (for HGT) and are all significantly larger than zero; nonetheless, they are all much smaller than estimates of the phenotypes’ heritability in the existing literature (31), implying that the scores are very imperfect proxies for the individuals’ true genetic scores (defined as the sum of the true average causal effects of all their alleles) for the various phenotypes. [The R² of the polygenic score of a phenotype is bounded by the phenotype’s heritability (32) and depends, in part, on the precision with which the effects of the individual genetic variants were estimated in the GWAS of that phenotype, which, in turn, depends on the GWAS sample size. Future, larger GWAS should allow more precise estimation of the effects of the genetic variants and the construction of more precise scores.]

Fig. 1.

Predictive power (R²) of polygenic scores of the various phenotypes. “Previously reported” denotes the highest previously reported R² of scores from prediction analyses from the articles reporting the GWAS whose summary statistics were used to construct the scores of BMI (19), EA (20), HGT (22), and SCZ (23) (the R² of the score was not reported for GLU, AAM, and TC). The previously reported R² for SCZ is the R² on the liability scale. “Estimated in HRS” denotes estimates of the incremental R² of the LDpred scores used in this article and for which there are phenotypic variables in the HRS, with percentile confidence intervals estimated with the nonparametric bootstrap with 1,000 bootstrap samples.

Table 2 reports estimates from separate regressions of rLRS on the polygenic scores of the various phenotypes [and on control variables, which include the top 20 principal components of the genetic relatedness matrix (27)]. The score of EA is significantly negatively associated with rLRS for both females (P = 0.002) and males (P = 0.013). The association remains significant after Bonferroni correction for 13 tests (the number of estimates reported in Table 2) for females, but not for males (Bonferroni-corrected P = 0.022 for females, = 0.174 for males). The estimates for females and males are similar, and the association is also significant in the sample of females and males together (Table S3; P = 1.2 × 10⁻⁵) and remains significant after Bonferroni correction for seven tests (the number of phenotypes) (Bonferroni-corrected P = 8.3 × 10⁻⁵). Fig. 2 shows the mean polygenic score of EA as a function of LRS, by sex. Both females and males who had no children have a significantly higher mean score of EA than those who had one or more children (P < 0.005 in both cases, unpaired t tests). Thus, the negative association between rLRS and the score of EA appears to be driven primarily by score differences between individuals with and without children.

Table 2.

Estimates from separate regressions of rLRS on the polygenic score of each phenotype

Score	Females	Males
Score of BMI	0.006 (0.010)	0.016 (0.013)
Score of EA	−0.033*** (0.010)	−0.031** (0.012)
Score of GLU	0.009 (0.010)	−0.013 (0.013)
Score of HGT	−0.011 (0.014)	−0.005 (0.018)
Score of SCZ	−0.001 (0.011)	0.009 (0.013)
Score of TC	−0.012 (0.011)	−0.003 (0.013)
Score of AAM	0.018* (0.011)	—
N	3,416	2,571

This table shows estimates of the coefficients on the polygenic scores and their SEs (in parentheses) from separate regressions of rLRS on the polygenic score of each phenotype and on control variables, for the study sample. All regressions for each sex had the same number of observations. (*P < 0.10; **P < 0.05; ***P < 0.01.)

Table S3.

Estimates from separate regressions of rLRS on the polygenic score of each phenotype, for the study sample and for each cohort separately, and by sex and for females and males together

Score	Study sample (born 1931–1953)	HRS1 cohort (born 1931–1941)	HRS2 cohort (born 1942–1947)	HRS3 cohort (born 1948–1953)
Females
Score of BMI	0.006 (0.010)	0.017 (0.014)	0.004 (0.020)	−0.034 (0.025)
Score of EA	−0.033*** (0.010)	−0.038*** (0.014)	−0.044** (0.020)	−0.001 (0.025)
Score of GLU	0.009 (0.010)	0.002 (0.014)	0.029 (0.021)	0.004 (0.024)
Score of HGT	−0.011 (0.014)	−0.025 (0.019)	0.024 (0.028)	−0.019 (0.033)
Score of SCZ	−0.001 (0.011)	−0.012 (0.015)	0.053** (0.022)	−0.035 (0.025)
Score of TC	−0.012 (0.011)	−0.022 (0.014)	−0.005 (0.021)	0.010 (0.025)
Score of AAM	0.018* (0.011)	0.008 (0.014)	0.021 (0.021)	0.037 (0.024)
N	3,416	1,840	811	765
Males
Score of BMI	0.016 (0.013)	0.015 (0.016)	−0.025 (0.029)	0.049 (0.032)
Score of EA	−0.031** (0.012)	−0.050*** (0.015)	−0.010 (0.028)	0.012 (0.031)
Score of GLU	−0.013 (0.013)	0.009 (0.016)	−0.023 (0.028)	−0.051* (0.031)
Score of HGT	−0.005 (0.018)	0.016 (0.022)	−0.043 (0.040)	−0.024 (0.042)
Score of SCZ	0.009 (0.013)	0.033** (0.016)	−0.033 (0.032)	−0.009 (0.033)
Score of TC	−0.003 (0.013)	−0.010 (0.016)	0.010 (0.030)	0.022 (0.033)
N	2,571	1,493	506	572
Females and males together (one person per household)
Score of BMI	0.018* (0.010)	0.025** (0.012)	0.013 (0.018)	−0.014 (0.022)
Score of EA	−0.041*** (0.009)	−0.047*** (0.012)	−0.039** (0.018)	−0.008 (0.021)
Score of GLU	−0.003 (0.009)	0.011 (0.012)	0.006 (0.018)	−0.037* (0.021)
Score of HGT	−0.015 (0.013)	−0.008 (0.016)	0.001 (0.026)	−0.011 (0.028)
Score of SCZ	0.011 (0.010)	0.011 (0.013)	−0.016 (0.020)	−0.004 (0.022)
Score of TC	−0.008 (0.010)	−0.012 (0.012)	−0.005 (0.019)	0.007 (0.022)
N	4,361	2,647	1,135	1,121

This table mirrors Table 2 but also shows the results for each cohort separately as well as for females and males together (the results for the study sample for females and for males separately are the same as those shown in Table 2). The table shows estimates of the coefficients on the polygenic scores and their SEs (in parentheses) from separate regressions of rLRS on the polygenic score of each phenotype. Each estimate comes from a different regression. All regressions included birth year dummies, HRS-defined cohort dummies, and the top 20 principal components of the genetic relatedness matrix, and all regressions for a cohort and sex had the same number of observations. The regressions for females and males together also included a sex dummy and only included the respondent with the lowest PN in each household. (The results for the score of EA are robust to alternative ways of selecting one respondent per household, but the significant estimates for the score of BMI are not.) The coefficients can be interpreted as directional selection differentials of the scores, expressed in Haldanes—i.e., each coefficient equals the implied change in the score that will occur due to natural selection in one generation, expressed in SDs of the score. (*P < 0.10; **P < 0.05; ***P < 0.01.)

Fig. 2.

Mean polygenic score of EA as a function of LRS, for females and males in the study sample.

The polygenic score of AAM is also significantly and positively associated with rLRS for females at the 10% level (P = 0.080), but this association does not remain significant after Bonferroni correction for 13 tests. I therefore interpret it as being weakly suggestive that genetic variants associated with higher AAM may have been selected for. The polygenic scores of the other phenotypes (BMI, GLU, HGT, SCZ, and TC) are not robustly significantly associated with rLRS. Although these estimates are small in magnitude and insignificant, this could be due to lack of statistical power and because my polygenic scores are imperfect proxies for the true genetic scores, and does not prove that natural selection has not been operating on genetic variants associated with those phenotypes.

According to the Robertson−Price identity (35, 36), the directional selection differential of a “character” is equal to the genetic covariance between the character and relative fitness. (A character is an observable feature of an organism, and its directional selection differential is the change in its mean value due to natural selection in one generation.) As I show in SI Materials and Methods, if we define the polygenic scores as the characters of interest, it follows that the coefficients on the scores reported in Table 2 can be interpreted as the directional selection differentials of the scores themselves, expressed in Haldanes—i.e., each coefficient equals the implied change in the score that will occur due to natural selection in one generation, expressed in SDs of the score per generation. Hence, the estimates from Table 2 imply that natural selection has been operating on the score of EA at a rate of −0.033 Haldanes among females and of −0.031 Haldanes among males in the study sample. (Even if the mechanism that underlies the negative association between rLRS and the score of EA is that more educated people choose to have fewer children, it would still be the case that natural selection has been operating.)

I rescaled these estimates of the directional selection differential of the score of EA to express them in years of education per generation rather than in Haldanes (SI Materials and Methods). My rescaled estimates imply that natural selection has been operating on the score of EA at rates of −0.022 [95% confidence interval (CI): −0.036 to −0.009] and −0.022 (95% CI: −0.040 to −0.004) years of education per generation for females and males—or about −1 wk of education per generation for both sexes.

I also obtained estimates of the directional selection differential of EA (or, equivalently, of the true genetic score of EA), which is equal (under some assumptions) to the directional selection differential of the polygenic score of EA multiplied by the ratio of the heritability of EA to the R² of the score of EA (SI Materials and Methods). [I assume the heritability of EA to be 0.40, based on a recent meta-analysis of existing heritability estimates of EA (37).] Generalizing my results from the study sample to the general population, my estimates imply that natural selection has been operating on EA at rates of −1.30 (95% CI: −2.12 to −0.54) and −1.53 (95% CI: −2.85 to −0.31) months of education per generation among US females and males of European ancestry born between 1931 and 1953. As I discuss in Discussion, these rates are small relative to the increases in EA that have been observed over the past few generations.

I performed a number of checks to verify the robustness of my results. First, I repeated the analyses with LRS instead of rLRS. Second, I used polygenic scores constructed with PLINK (34) instead of LDpred. Third, I only included individuals aged no more than 70 y in 2008 (the last year in which individuals were genotyped) and at least 50 y old (for females) or 55 y old (for males) when asked their number of children—to mitigate the risk of selection bias due to differential mortality and to ensure that almost every individual had completed fertility when asked his or her number of children. Fourth, I included the HRS0 cohort of individuals born between 1924 and 1930 together with the study sample. (As detailed in Materials and Methods, I define cohorts based on the individuals’ birth years; the study sample includes the HRS1, HRS2, and HRS3 cohorts, but excludes the HRS0 cohort because of possible selection bias based on mortality.) Table S4 presents the results of those checks. In all cases, the results for EA are robust. Further, for the score of EA for both females and males and for the score of AAM (for females), the estimates are not significantly different from one another at the 5% level across the HRS1, HRS2, and HRS3 cohorts (Table S3 and t tests of the interactions between the coefficients on the scores and cohort dummies).

Table S4.

Robustness checks for the regressions reported in Table 2

Score	LRS (instead of rLRS) as the dependent variable	PLINK (instead of LDpred) polygenic scores	Females aged 50–70 y and males aged 55–70 y only	Study sample together with the HRS0 cohort
Females
Score of BMI	0.020 (0.027)	0.002 (0.011)	−0.007 (0.014)	0.002 (0.009)
Score of EA	−0.085*** (0.027)	−0.028*** (0.011)	−0.030** (0.014)	−0.021** (0.009)
Score of GLU	0.019 (0.026)	−0.003 (0.010)	0.014 (0.013)	0.000 (0.009)
Score of HGT	−0.030 (0.036)	−0.011 (0.013)	−0.007 (0.018)	−0.016 (0.013)
Score of SCZ	−0.001 (0.028)	−0.010 (0.012)	0.001 (0.014)	0.001 (0.010)
Score of TC	−0.036 (0.027)	−0.001 (0.010)	−0.009 (0.014)	−0.005 (0.010)
Score of AAM	0.045* (0.027)	0.022** (0.010)	0.021 (0.014)	0.013 (0.010)
N	3,416	3,416	2,065	4,182
Males
Score of BMI	0.047 (0.031)	0.021 (0.013)	0.003 (0.021)	0.013 (0.011)
Score of EA	−0.079** (0.031)	−0.031** (0.013)	−0.074*** (0.020)	−0.021* (0.011)
Score of GLU	−0.030 (0.030)	−0.014 (0.013)	−0.019 (0.020)	−0.003 (0.011)
Score of HGT	0.007 (0.040)	0.001 (0.017)	−0.026 (0.029)	0.007 (0.016)
Score of SCZ	0.022 (0.036)	0.004 (0.015)	0.018 (0.022)	0.015 (0.012)
Score of TC	−0.009 (0.031)	−0.001 (0.013)	−0.016 (0.021)	−0.008 (0.012)
N	2,571	2,571	959	3,173

This table mirrors Table 2 but shows the results for alternative specifications and samples. Column 2 shows the estimates and SEs (in parentheses) from separate regressions of LRS (instead of rLRS) on the polygenic score of each phenotype for the study sample; column 3 shows the estimates and SEs from separate regressions of rLRS on the polygenic score of each phenotype constructed with PLINK (instead of LDpred) for the study sample; column 4 shows estimates and SEs from separate regressions of rLRS on the polygenic score of each phenotype, but only for individuals in the study sample who were aged no more than 70 y in 2008 (the last year for genotyping) and at least 50 y old when asked the number of children they ever gave birth to (for females) or at least 55 y old when asked the number of children they ever fathered (for males); column 5 shows estimates and SEs from separate regressions of rLRS on the polygenic score of each phenotype, but for the study sample and the HRS0 cohort together. All regressions included birth year dummies, HRS-defined cohort dummies, and the top 20 principal components of the genetic relatedness matrix, and all regressions for each specification and sex had the same number of observations. The coefficients in column 2 can be interpreted as the effects of 1-SD increases in the scores on the number of children ever given birth to (for females) or the number of children ever fathered (for males). The coefficients in columns 3–5 can be interpreted as directional selection differentials of the scores, expressed in Haldanes—i.e., each coefficient equals the implied change in the score that will occur due to natural selection in one generation, expressed in SDs of the score. (*P < 0.10; **P < 0.05; ***P < 0.01.)

Following Lande and Arnold (16), I also estimated quadratic regressions of rLRS on all of the polygenic scores and their squares and interactions together and on control variables, to test for nonlinear selection (Table S5 and SI Materials and Methods). I found no convincing evidence that nonlinear selection has been operating on the genetic variants associated with the various phenotypes.

Table S5.

Estimates from the quadratic regression from Lande and Arnold (16) of rLRS on all of the polygenic scores of the different phenotypes, all of the squared polygenic scores, and all their interactions

Score	Females	Males
Score of BMI	0.003 (0.011)	0.012 (0.013)
Score of EA	−0.035*** (0.011)	−0.029** (0.013)
Score of GLU	0.010 (0.010)	−0.012 (0.013)
Score of HGT	−0.008 (0.014)	0.004 (0.018)
Score of SCZ	−0.001 (0.011)	0.006 (0.014)
Score of TC	−0.013 (0.011)	−0.004 (0.013)
Score of AAM	0.022** (0.011)	—
Squared score of BMI	−0.006 (0.008)	−0.001 (0.010)
Squared score of EA	−0.012 (0.008)	−0.004 (0.009)
Squared score of GLU	−0.007 (0.007)	−0.002 (0.009)
Squared score of HGT	−0.009 (0.007)	0.000 (0.009)
Squared score of SCZ	0.010 (0.007)	0.022** (0.009)
Squared score of TC	−0.007 (0.007)	0.000 (0.009)
Squared score of AAM	−0.004 (0.008)	—
Score of BMI × score of EA	0.005 (0.011)	0.004 (0.013)
Score of BMI × score of GLU	0.002 (0.011)	−0.011 (0.013)
Score of BMI × score of HGT	−0.008 (0.012)	−0.015 (0.013)
Score of BMI × score of SCZ	0.017 (0.011)	0.015 (0.013)
Score of BMI × score of TC	0.009 (0.011)	0.016 (0.014)
Score of BMI × score of AAM	−0.012 (0.011)	—
Score of EA × score of GLU	−0.006 (0.011)	0.017 (0.012)
Score of EA × score of HGT	−0.003 (0.011)	0.001 (0.013)
Score of EA × score of SCZ	0.001 (0.011)	−0.032** (0.013)
Score of EA × score of TC	−0.010 (0.011)	0.000 (0.013)
Score of EA × score of AAM	0.003 (0.011)	—
Score of GLU × score of HGT	−0.020* (0.011)	−0.002 (0.013)
Score of GLU × score of SCZ	−0.008 (0.011)	0.008 (0.013)
Score of GLU × score of TC	−0.007 (0.010)	0.013 (0.013)
Score of GLU × score of AAM	−0.015 (0.011)	—
Score of HGT × score of SCZ	0.004 (0.011)	0.022 (0.014)
Score of HGT × score of TC	0.000 (0.011)	−0.010 (0.013)
Score of HGT × score of AAM	0.003 (0.012)	—
Score of SCZ × score of TC	−0.028*** (0.010)	−0.004 (0.013)
Score of SCZ × score of AAM	−0.019* (0.011)	—
Score of TC × score of AAM	0.002 (0.011)	—
N	3,416	2,571

This table shows estimates (and their SEs, in parentheses) from the quadratic regression from Lande and Arnold (16) of rLRS on all of the polygenic scores of the different phenotypes, all of the squared polygenic scores, and all their interactions, for the study sample. (I thus treat the scores themselves—as opposed to the phenotypes, as is usual—as the characters of interest in Lande and Arnold’s quadratic framework.) The estimates for females come from one single regression, and the estimates for males come from another single regression. Each regression included birth year dummies, HRS-defined cohort dummies, and the top 20 principal components of the genetic relatedness matrix. (*P < 0.10; **P < 0.05; ***P < 0.01.)

SI Materials and Methods

The Study Sample and the Cohorts.

The HRS is a longitudinal panel study for which a representative sample of ∼20,000 Americans have been surveyed every 2 y since 1992 (the HRS oversamples certain minority groups, but this does not affect the current study, which only uses data on individuals of European ancestry.) All individuals were born between 1900 and 1992, with more than 95% of the individuals who have been successfully genotyped born in 1953 or earlier. All primary respondents were over the age of 50 y when enrolled; spouses of the primary respondents were also interviewed, regardless of age. DNA samples have been collected for a subsample of the HRS participants between 2006 and 2008.

My main analyses focus on individuals born between 1931 and 1953. To reduce the risks of confounding by population stratification, I restrict the analyses to unrelated individuals of European ancestry (i.e., non-Hispanic White individuals; some of those unrelated individuals are spouses). To ensure that the LRS variable is a good proxy for completed fertility, I only include females who were at least 45 y old when asked the number of children they ever gave birth to and males who were at least 50 y old when asked the number of children they ever fathered. (Although the HRS contains variables on self-reported age at menopause, I do not use those variables to exclude females who had not completed menopause when asked the number of children they ever gave birth to, because this could induce a selection bias and because those variables are imprecisely measured.) Further, to ensure that the sample of individuals who have been successfully genotyped is comparable to the sample of individuals who have not, I only include individuals who were enrolled in the HRS and asked the number of children they ever gave birth to or fathered in 2008 or earlier (all but two individuals who have been successfully genotyped were enrolled in the HRS and asked this question in 2008 or earlier, but a large number of individuals who have not been successfully genotyped were enrolled later). This left 6,414 females and 5,436 males with phenotypic data and 3,416 unrelated females and 2,571 unrelated males who have been successfully genotyped and who passed the quality control filters described below (and for whom I could thus construct polygenic scores). I refer to the resulting sample as the “study sample.”

For some specifications, I divided the study sample into cohorts based on the individuals’ birth years. The HRS1 cohort contains individuals born from 1931 to 1941; the HRS2 cohort contains individuals born from 1942 to 1947; and the HRS3 cohort contains individuals born from 1948 to 1953. Table S6 provides more details on these cohorts and on the HRS0 cohort of individuals born from 1924 to 1930. My definition of the cohorts closely resembles the HRS's, except for the fact that the HRS assigns the primary respondents' spouses or partners to the primary respondents' cohorts regardless of the spouses’ years of birth; hence, except for the spouses of a few primary respondents, my HRS0, HRS1, HRS2, and HRS3 cohorts are identical to the HRS’s Children of the Depression, Initial HRS, War Baby, and Early Baby Boomer cohorts. The HRS cohorts were added to the HRS at different times, and dividing the study sample into cohorts allowed me to test the robustness of my results across cohorts.

Table S6.

Description of cohorts

Descriptive variable	HRS0	HRS1	HRS2	HRS3
Included in the study sample?	No	Yes	Yes	Yes
Year of birth	1924–1930	1931–1941	1942–1947	1948–1953
Females
N (genotyped and not genotyped)	1,736	3,505	1,528	1,381
Age asked no. of children, first–99th percentiles, y	65–77	55–73	49–66	45–62
Age when genotyped (in 2006–2008), y	76–84	65–77	59–66	53–60
Fraction survived to 2008	0.69	0.82	0.90	0.96
Fraction asked to be genotyped (in 2006–2008)	0.59	0.70	0.74	0.73
Fraction consented to be genotyped (in 2006–2008)	0.51	0.61	0.62	0.63
Fraction in sample of genotyped individuals	0.44	0.52	0.53	0.55
Males
N (genotyped plus not genotyped)	1,562	3,231	1,068	1,137
Age asked no. of children, first–99th percentiles, y	66–80	55–75	50–68	50–62
Age when genotyped (in 2006–2008), y	76–84	65–77	59–66	53–60
Fraction survived to 2008	0.60	0.76	0.86	0.97
Fraction asked to be genotyped (in 2006–2008)	0.52	0.63	0.65	0.70
Fraction consented to be genotyped (in 2006–2008)	0.47	0.54	0.55	0.58
Fraction in sample of genotyped individuals	0.39	0.46	0.47	0.50

For each cohort, I include all individuals of European ancestry born in the cohort's years of birth, who were enrolled in the HRS and asked the number of children they ever gave birth to or fathered in 2008 or earlier, and who were at least 45 y old when asked the number of children they ever gave birth to (for females) or at least 50 y old when asked the number of children they ever fathered (for males). “Fraction in sample of genotyped individuals” indicates the fraction of individuals who are in the sample of unrelated genotyped individuals who passed the quality control filters described in SI Materials and Methods (the sample used in the analyses with the genotyped individuals). The HRS0 cohort is not included in the study sample because of the high mortality among its members by 2008 (the last year when individuals were genotyped) and because of evidence of selection bias for the genotyped individuals in that cohort. The main results are robust to the inclusion of that cohort.

To mitigate the risk of selection bias based on mortality, I excluded the HRS0 cohort from the study sample, but my main results are robust to the inclusion of that cohort (Table S4). As shown in Table S6, only 69% of females and 60% of males in the HRS0 cohort survived to 2008, the last year when individuals were genotyped. Also, for the study sample, the estimates from the regressions of rLRS on the phenotypic variables are very similar between the sample of genotyped individuals and the sample of all individuals (Table 1 and Table S2). By contrast, as can be seen in Table S7, for the HRS0 cohort, the coefficient on phenotypic EA is negative and significant in the sample of all females (P = 0.031), but the corresponding coefficient in the sample of genotyped females is positive. That latter coefficient is significantly different from the coefficient in the sample of females who have not been genotyped (P = 0.009, t test of the interaction between the coefficient on EA and a dummy for genotyped individuals), suggesting that sample selection bias is at play for the HRS0 cohort. Also to mitigate the risk of selection bias based on mortality, I excluded individuals born before 1924 from the study sample. I also excluded individuals born after 1953 from the study sample, as very few of them have been genotyped.

Table S7.

Estimates from separate regressions of rLRS on each phenotypic variable and on the polygenic score of each phenotype, for the HRS0 cohort (born 1924–1930)

Variable	Regressions of rLRS on the phenotypic variables				Regressions of rLRS on the scores, genotyped individuals only
	All individuals (genotyped and not genotyped)		Genotyped individuals only
	Coefficient estimate	N	Coefficient estimate	N	Score	Coefficient estimate	N
Females
BMI	0.015*** (0.003)	1,731	0.008* (0.005)	766	Score of BMI	−0.020 (0.023)	766
EA	−0.013** (0.006)	1,736	0.008 (0.009)	766	Score of EA	0.031 (0.023)	766
					Score of GLU	−0.044* (0.023)	766
HGT	−0.000 (0.003)	1,735	−0.001 (0.004)	766	Score of HGT	−0.046 (0.031)	766
					Score of SCZ	0.006 (0.025)	766
TC	−0.024 (0.122)	93	—	—	Score of TC	0.020 (0.023)	766
					Score of AAM	−0.010 (0.024)	766
Males
BMI	0.003 (0.004)	1,562	0.007 (0.006)	602	Score of BMI	0.002 (0.026)	602
EA	−0.003 (0.005)	1,561	−0.001 (0.008)	602	Score of EA	0.029 (0.026)	602
					Score of GLU	0.044* (0.026)	602
HGT	−0.003 (0.002)	1,562	−0.004 (0.004)	602	Score of HGT	0.054 (0.034)	602
					Score of SCZ	0.037 (0.026)	602
TC	−0.067 (0.059)	590	−0.102 (0.091)	220	Score of TC	−0.026 (0.025)	602

This table mirrors Table S2, but shows results for the HRS0 cohort. “Regression of rLRS on the phenotypic variables” shows estimates of the coefficients on the phenotypic variables and their SEs (in parentheses) from separate regressions of rLRS on each phenotypic variable. Each estimate comes from a different regression, and every regression included birth year dummies and HRS-defined cohort dummies. The HRS does not contain phenotypic variables for GLU, AAM, and SCZ; the results are not reported for TC for genotyped females because there are only 36 genotyped females with TC data in the HRS0 cohort. “Regression of rLRS on the scores” shows estimates of the coefficients on the polygenic scores and their SEs (in parentheses) from separate regressions of rLRS on the polygenic score of each phenotype. Each estimate comes from a different regression. All regressions include birth year dummies, HRS-defined cohort dummies, and the top 20 principal components of the genetic relatedness matrix. The coefficients can be interpreted as directional selection differentials of the scores, expressed in Haldanes—i.e., each coefficient equals the implied change in the score that will occur due to natural selection in one generation, expressed in SDs of the score. (*P < 0.10; **P < 0.05; ***P < 0.01.)

Phenotypic Variables.

For my baseline analyses, I operationalize relative fitness with the rLRS variable. Using rLRS instead of LRS as the measure of fitness helps control for the effects of time trends in LRS and makes it possible to interpret my estimates as rates of natural selection (1, 21). (My results are robust to using LRS instead of rLRS as the measure of fitness.) The LRS variable is the number of children females ever gave birth to or the number of children males ever fathered. Most individuals were asked this question in their first HRS interview. As Fig. S1 shows, LRS for females and males declined gradually between 1931 and 1953, from around three children in the early 1930s to two children around 1950. To construct the rLRS variable, I proceeded as follows: For any given birth year, I first calculated the mean LRS for all females born in the preceding, the given, and the following birth years; I then obtained rLRS for females born in the given birth year by dividing their LRS by this mean LRS. I proceeded analogously for males.

Fig. S1.

Three-year rolling average of LRS by birth year, for females and males in the study sample. The rolling average for each year was calculated using the year's data together with data from the previous and following years.

The HRS contains phenotypic variables for BMI, EA, HGT, and TC. The TC phenotypic variable is an indicator variable for a self-reported health problem with high cholesterol in 1992, and not plasma concentrations of TC as in the GWAS of TC. BMI was measured in each wave of the HRS, and the BMI phenotypic variable for females is the mean across waves of female BMI residualized on birth year dummies, plus the mean female BMI across all waves. The BMI phenotypic variable for males is defined analogously. HGT was also measured in each wave of the HRS, and the HGT phenotypic variable is also defined analogously for both sexes. The EA variable is from the RAND HRS data. Table S1 presents summary statistics for these phenotypic variables and for birth year, LRS, and childlessness (a dummy that is equal to 1 if an individual is childless). The HRS does not contain phenotypic variables for GLU, SCZ, and AAM (in females).

Quality Control of the Genotypic Data and Polygenic Scores.

Following ref. 33, the individuals’ genotyped (as opposed to imputed) SNPs were used to compute the polygenic scores. The HRS-provided binary PLINK-format data files that exclude chromosome anomalies greater than 10 MB (among other things) were used. Following the HRS recommendations regarding the use of the genotypic data (58), only individuals in the HRS-provided “hwe_eur_keep.txt” file were used; this effectively only kept a set of unrelated individuals of European ancestry, with missing call rate of less than 2%, who self-identified as White, and falling within 1 SD of all self-identified non-Hispanic Whites on the first two principal components of the genetic relatedness matrix of all unrelated individuals. Also following the HRS recommendations, only SNPs in the HRS-provided “SNP_qual_maf_filter_extract.txt” file were used; among other things, this effectively removed SNPs with minor allele frequency (MAF) less than 1%, with P value less than 1 × 10⁻⁴ on the test for Hardy–Weinberg equilibrium, and with missing call rate greater than 2%. In addition, the following filters were applied to the resulting sample, which only includes the “hwe_eur_keep.txt” individuals and the “SNP_qual_maf_filter_extract.txt” SNPs: SNPs with MAF less than 1%, with P value less than 1 × 10⁻⁴ on the test for Hardy–Weinberg equilibrium, and (following ref. 33) with missing call rate greater than 1%, were excluded; 1,411,964 SNPs passed these quality control filters. For each set of GWAS summary statistics, SNPs with MAF less than 1% in the summary statistics were also dropped.

The individuals’ genotyped SNPs that passed the above quality control filters and that were present in the phenotype’s summary statistics files were used to construct the polygenic scores. Depending on the phenotype, there were between 505,254 and 544,493 such overlapping SNPs (except for GLU, for which there were only 22,895 such overlapping SNPs, because the GLU GWAS was conducted with only ∼66,000 SNPs). The average sample sizes across the SNPs in the summary statistics used to construct the polygenic scores are ${\overline{N}}_{BMI}=\mathrm{232,186}$, ${\overline{N}}_{EA}=\mathrm{386,098}$, ${\overline{N}}_{HGT}=\mathrm{243,630}$, and ${\overline{N}}_{TC}=\mathrm{92,793}$ individuals. The summary statistics for GLU, SCZ, and MEN did not contain sample size information, but the reported samples sizes for the main GWAS of these phenotypes are $N_{GLU}=\mathrm{133,010}$, $N_{SCZ}\approx \mathrm{80,000}$, and $N_{MEN}=\mathrm{132,989}$ individuals. To avoid overfitting, I ensured that the GWAS summary statistics used to construct the polygenic scores for each phenotype are based on meta-analyses that exclude the HRS dataset (32). The HRS was not included in the GWAS of BMI, GLU, HGT, SZC, TC, and AAM. For EA, whose GWAS included the HRS (20), summary statistics based on a meta-analysis that excludes the HRS were used to construct the scores.

For the main analysis, I used LDpred (33) to construct the polygenic scores; for a robustness check, I also constructed a set of polygenic scores with PLINK (34). (For EA, polygenic scores were constructed and directly provided to me by SSGAC, following the procedure described here and which I used to construct the other scores.) For a given phenotype and a given individual $i$, both the LDpred and PLINK scores are calculated as the weighted sums of individual i’s SNPs,

$${\text{PGS}}_i={\displaystyle \sum }_{j=1}^m{\widehat{\beta }}_j{g}_{ji},$$

where ${\text{PGS}}_i$ is individual i’s polygenic score, ${\widehat{\beta }}_j$ is an estimate of SNP j’s effect size (i.e., the effect of having one more copy of the reference allele at SNP j), and $g_{ij}$ is the genotype of individual i at SNP j (coded as having zero, one, or two copies of the reference allele at SNP j). For the PLINK scores, the ${\widehat{\beta }}_j$ for a given SNP j is simply the GWAS estimate for SNP j. Because nearby SNPs tend to be in LD (i.e., correlated), that GWAS estimate captures the causal effects both of SNP j and of SNPs that are in LD with SNP j. As a result, PLINK polygenic scores effectively count the causal effects of SNPs that are in LD with other SNPs multiple times. To correct for this multiple counting problem, LDpred uses information on LD between SNPs from a reference panel together with a prior on the SNPs’ effect sizes, and adjusts the GWAS estimate for SNP j to obtain an estimate of the causal effect of SNP j independent of the effects of other SNPs. LDpred then uses that estimate as the ${\widehat{\beta }}_j$ for SNP j in the above formula. The resulting LDpred score for individual i is therefore the sum of i’s genotype across all SNPs, weighted by the LDpred estimates of the SNPs’ causal effects; it is an unbiased predictor of the true genetic score (and of the phenotype itself) for individual i, conditional on the model assumptions and the data (33).

For the LDpred scores, the study sample individuals’ genotyped SNPs that passed the above quality control filters were used as the reference panel to calculate the LD between the SNPs. (LDpred requires that the reference panel be from a population that is similar to that in which the GWAS summary statistics were estimated (33); here, the study sample individuals and almost all of the individuals in the various GWAS whose summary statistics are used are of European ancestry.) The LDpred prior on the SNPs’ effect sizes depends on an assumed Gaussian mixture weight, which corresponds to the assumed fraction of causal markers. For each phenotype, LDpred scores were constructed for each of the following Gaussian mixture weights: 0.0001, 0.0003, 0.001, 0.003, 0.01, 0.03, 0.1, 0.3, and 1. For BMI, EA, HGT, and TC—for which there are phenotypic variables in the HRS—I selected the weights that maximize the incremental R² of each score in an OLS regression of the phenotypic variable on the score and on variables for sex, birth year, birth year squared, and the top 20 principal components of the genetic relatedness matrix. For each of GLU, SCZ, and AAM—for which there are no phenotypic variables in the HRS—I selected the weights that maximize the correlations between the score and known correlates of the phenotype, controlling for sex, birth year, birth year squared, and the top 20 principal components. For GLU, I selected the weight that maximizes the correlation with a variable indicating if an individual ever had diabetes or high blood sugar; for SCZ, I selected the weight that maximizes the correlations with neuroticism (60) and cognitive ability (61); for AAM, I selected the weight that maximizes the correlations with HGT and BMI (62). For each phenotype, I verified that the correlation between the score and the phenotype or the known correlates has the expected direction. Table S8 shows the parameters used to construct the scores and the sources for each phenotype’s summary statistics. The scores were standardized to have mean zero and an SD of 1.

Table S8.

Summary information on the polygenic scores of the different phenotypes

Score	Optimal Gaussian mixture weight for LDpred	LDpred window size (no. of SNPs)	No. of SNPs used	Assumed GWAS sample size	GWAS article	Source for GWAS summary statistics	R2, previously reported	Incremental R2 (SE), estimated in HRS
Score of BMI	0.1	170	505,254	232,186	(19)	www.broadinstitute.org/collaboration/giant/index.php/GIANT_consortium_data_files#GWAS_Anthropometric_2015_BMI	0.06	0.089*** (0.007)
Score of EA	0.1	180	544,493	386,098	(20)	SSGAC (Summary statistics from a meta-analysis excluding the HRS were used)	0.039	0.074*** (0.006)
Score of GLU	0.03	10	22,894	120,000	(21)	www.magicinvestigators.org/downloads/	—	—
Score of HGT	1	170	510,411	243,630	(22)	www.broadinstitute.org/collaboration/giant/index.php/GIANT_consortium_data_files#GWAS_Anthropometric_2014_Height	0.17	0.174*** (0.009)
Score of SCZ	0.3	180	544,225	75,000	(23)	www.med.unc.edu/pgc/files/resultfiles	0.070	—
Score of TC	0.3	175	530,012	92,793	(24)	www.broadinstitute.org/mpg/pubs/lipids2010/	—	0.012*** (0.004)
Score of AAM	0.3	170	506,120	120,000	(25)	www.reprogen.org/data_download.html	—	—

For every phenotype, the polygenic score was constructed using LDpred (33), using the individuals' genotyped SNPs that passed quality control filters and overlapped with the SNPs in the phenotype's summary statistics file. The optimal Gaussian mixture weights (the assumed fractions of causal markers) were selected to maximize each score's R² with respect to the corresponding phenotype or to maximize the correlations between each score and known correlates of the corresponding phenotype. As recommended, LDpred windows approximately equal to the number of used SNPs divided by 3,000 were used. The assumed GWAS sample sizes are the assumed sample sizes for LDpred, based on mean sample sizes across the used SNPs (when SNP-level sample sizes are reported) or based on the reported GWAS sample sizes (slightly reduced to account for missing observations). The previously reported R² and the incremental R² estimated in the HRS are the numerical values of the results presented in Fig. 1 (with SEs instead of 95% CI). The incremental R² estimated in the HRS for the score of EA is substantially higher than the previously reported R² because the score I used in the HRS is based on summary statistics from a meta-analysis that includes one additional large cohort (the UK Biobank). (***P < 0.01.)

To construct the PLINK scores, the PLINK’s “score” command was used with the default options; I then standardized the resulting scores so that they have mean zero and an SD of 1.

Association Analyses.

For each of BMI, EA, HGT, and TC—for which there are phenotypic variables in the HRS—I regressed rLRS on the corresponding phenotypic variable, separately for males and females; these regressions included birth year dummies and HRS-defined cohort dummies, and were estimated by OLS. For all phenotypes, I also regressed rLRS on the polygenic score of the phenotype in various samples; the regressions included birth year dummies, HRS-defined cohort dummies, and the top 20 principal components of the genetic relatedness matrix, and were also estimated by OLS. (The top principal components of the genetic relatedness matrix capture the main dimensions along which the ancestry of the individuals in the dataset vary and are commonly used to control for population stratification (27); section 5 of the supplemental material of ref. 59 demonstrates how controlling for the top principal components can eliminate some spurious associations. I did not control for the top 20 principal components in the regressions of rLRS on the phenotypic variables because it is not possible to compute these for the individuals who have not been successfully genotyped.) For the regressions in the sample of females and males together, I also controlled for sex and only included the respondent with the lowest PN in each household, as spouses very often have the same number of children, which induces a complex correlation structure between the error terms (the results for the score of EA are robust to alternative ways of selecting one respondent per household).

In most results tables, I report the coefficient estimates and SEs, with stars to indicate statistical significance; P values for the results shown in Tables 1 and 2 are reported in Table S2, and other P values are included in log files available upon request. As Lande and Arnold (16) note, the estimates and SEs from these OLS regressions are unbiased; however, rLRS is not a continuous variable, and the error terms from these regressions are not normally distributed, so the P values based on the OLS t statistics are only asymptotically valid. Here, given the large sample sizes, the P values should be informative. To verify, I used the nonparametric bootstrap method to bootstrap the t statistics of the coefficients whose estimates are reported in Tables 1 and 2, using 10,000 bootstrap samples. Specifically, for each coefficient $\widehat{\beta }$ reported in Tables 1 and 2, I obtained the bootstrapped distribution of the t statistic $\widehat{t}=\widehat{\beta }/SE\left(\widehat{\beta }\right)$ by calculating the t statistic $\widehat{t_b}$ for each bootstrap sample b [where $\widehat{t_b}=({\widehat{\beta }}_b-\widehat{\beta })/S{E}^{\ast }\left({\widehat{\beta }}_b\right)$, ${\widehat{\beta }}_b$ is the estimate for bootstrap sample b, and $S{E}^{\ast }$ is the bootstrap SE; I subtracted $\widehat{\beta }$ from the numerator to make the distribution of $\widehat{t_b}$ consistent with the null hypothesis (63)]. I then calculated the percentile of the actual t statistic $\widehat{t}$ relative to the distribution of $\widehat{t_b}$ to obtain the bootstrapped P value. The bootstrapped P values were very similar to the P values implied by the asterisks in Tables 1 and 2.

I also note that the SEs and P values of my estimates from regressions of rLRS on the LDpred scores do not account for the uncertainty stemming from the selection of the Gaussian mixture weights for the LDpred scores. However, all my results are robust to the use of the PLINK scores instead of the selected LDpred scores; my results for EA are robust to the use of the alternative weights of 0.3 and 1 instead of 0.1 (for lower weights, the scores of EA have much lower incremental R²); my results for AAM are actually much stronger and more robust with the alternative weight of 1 instead of 0.3; and my insignificant results for the other phenotypes remain insignificant with different weights. All of this implies that my main results are not driven by the weight selection procedure.

Directional Selection Differentials.

The directional selection differential of a character is the change in its mean value due to natural selection in one generation. The Robertson−Price identity (35, 36) equates the directional selection differential of a character to the genetic covariance between the character and relative fitness,

$$\mathrm{\Delta }\overline{z}=\overline{z^{\ast }}-\overline{z}={\text{Cov}}_a\left(w,z\right),$$

where $z$ is the character of interest before selection, $z^{\ast }$ is the character of interest after one generation of selection, $w$ is relative fitness, and ${\text{Cov}}_a\left(\hspace{0.17em}.\right)$ is the genetic covariance.

If we define the polygenic score of EA (as opposed to EA, as would be usual) as the character of interest, then

$$\begin{array}{c}\mathrm{\Delta }{\overline{z}}_{\text{PGS}\hspace{0.17em}\text{of}\hspace{0.17em}\text{EA}}={\text{Cov}}_a\left(\text{rLRS},\text{PGS}\hspace{0.17em}\text{of}\hspace{0.17em}\text{EA}\right)=\text{Cov}\left(\text{rLRS},\text{PGS}\hspace{0.17em}\text{of}\hspace{0.17em}\text{EA}\right)\\ =\frac{\text{Cov}\left(\text{rLRS},\text{PGS}\hspace{0.17em}\text{of}\hspace{0.17em}\text{EA}\right)}{\text{Var}\left(\text{PGS}\hspace{0.17em}\text{of}\hspace{0.17em}\text{EA}\right)}={\beta }_{\text{rLRS}\hspace{0.17em}\text{on}\hspace{0.17em}\text{PGS}\hspace{0.17em}\text{of}\hspace{0.17em}\text{EA}},\end{array}$$

where “PGS of EA” is the polygenic score of EA. The second equality follows because the nongenetic component of rLRS is independent of the genetic component of EA (by definition) and thus of PGS of EA, the third equality follows from the fact that the score of EA has been standardized to have unit variance, and the last equality holds if the other covariates in the regression of rLRS on PGS of EA are uncorrelated with PGS of EA (which is a reasonable approximation). [This can also be derived from the framework of Lande and Arnold (16), in which the directional selection differential $\mathrm{\Delta }\overline{z}$ is given by $\mathrm{\Delta }\overline{z}=\overline{z^{\ast }}-\overline{z}=\mathit{G}\cdot {\mathit{P}}^{-1}\cdot \text{Cov}\left(w,z\right)$, where $\mathit{G}$ and $\mathit{P}$ are the genotypic and phenotypic variance−covariance matrices. If we treat the score of EA as the single character of interest—as opposed to the phenotype, as would be usual—then $\mathit{G}=\mathit{P}$ and $\text{Cov}\left(w,z\right)={\text{Cov}}_a(w,z)$, and the Robertson−Price identity follows.)

Hence, the directional selection differential of the score of EA is equal to the coefficient on the score of EA in the regression of rLRS on the score of EA. In other words, my estimates of the coefficients on the score of EA in Table 2 can be interpreted as directional selection differentials, or as the implied changes in the mean values of the score of EA that will occur in one generation as a result of natural selection. Furthermore, because the score of EA has an SD of 1, these implied changes are expressed in Haldanes (1 Haldane is 1 SD per generation). This also applies to the scores of BMI, GLU, HGT, SCZ, TC, and AAM.

To express the estimates of the directional selection differential for the score of EA in years of education per generation instead of in Haldanes, I first rescale the score of EA in years of education and calculate its SD in years of education. If we let $\widetilde{\text{PGS}\hspace{0.17em}\text{of}\hspace{0.17em}\text{EA}}$ denote the rescaled polygenic score of EA, then $\text{EA}=\widetilde{\text{PGS}\hspace{0.17em}\text{of}\hspace{0.17em}\text{EA}}+{\epsilon }_{PGS}$ and $R_{\widetilde{\text{PGS}\hspace{0.17em}\text{of}\hspace{0.17em}\text{EA}}}^2=\text{Var}\left(\widetilde{\text{PGS}\hspace{0.17em}\text{of}\hspace{0.17em}\text{EA}}\right)/\text{Var}\left(\text{EA}\right)$, and it follows that ${\sigma }_{\widetilde{\text{PGS}\hspace{0.17em}\text{of}\hspace{0.17em}\text{EA}}}={\sigma }_{\text{EA}}\cdot \sqrt{R_{\widetilde{\text{PGS}\hspace{0.17em}\text{of}\hspace{0.17em}\text{EA}}}^2}$. We can then express the directional selection differential for the score of EA in years of education per generation by multiplying the estimates of $\mathrm{\Delta }{\overline{z}}_{\text{PGS}\hspace{0.17em}\text{of}\hspace{0.17em}\text{EA}}={\widehat{\beta }}_{\text{rLRS}\hspace{0.17em}\text{on}\hspace{0.17em}\text{PGS}\hspace{0.17em}\text{of}\hspace{0.17em}\text{EA}}$ (expressed in Haldanes) by $\widetilde{{\sigma }_{\text{PGS}\hspace{0.17em}\text{of}\hspace{0.17em}\text{EA}}}$,

$$\widetilde{\mathrm{\Delta }{\overline{z}}_{\text{PGS}\hspace{0.17em}\text{of}\hspace{0.17em}\text{EA}}}\equiv \mathrm{\Delta }{\overline{z}}_{\text{PGS}\hspace{0.17em}\text{of}\hspace{0.17em}\text{EA}}\cdot \widetilde{{\sigma }_{\text{PGS}\hspace{0.17em}\text{of}\hspace{0.17em}\text{EA}}}.$$

Using this formula and using the nonparametric bootstrap method with 1,000 bootstrap samples to estimate percentile confidence intervals, I obtain estimates of the rescaled directional selection differential for the score of EA of $\widetilde{\mathrm{\Delta }{\overline{z}}_{\text{PGS}\hspace{0.17em}\text{of}\hspace{0.17em}\text{EA}}}=-0.022$ (95% CI: −0.036 to −0.009) and $\widetilde{\mathrm{\Delta }{\overline{z}}_{\text{PGS}\hspace{0.17em}\text{of}\hspace{0.17em}\text{EA}}}=-0.022$ (95% CI: −0.040 to −0.004) years of education per generation for females and for males, or about −1 wk of education per generation for both sexes. (These calculations can, in principle, also apply to the other phenotypes but are not performed here because I do not have an estimate of $R_{\widetilde{\text{PGS}\hspace{0.17em}\text{of}\hspace{0.17em}\text{AAM}}}^2$ and because my estimates for the scores of BMI, GLU, HGT, SCZ, and TC are not significant.)

For a given phenotype, LDpred calculates the posterior mean of the true genetic score of the phenotype; the result is an unbiased predictor of the true genetic score of the phenotype (and of the phenotype itself), conditional on the model assumptions and the data (33). (Here, the scores are rescaled unbiased predictors of the true genetic scores, but this does not affect the present derivations.) Thus, if we focus on EA, we can write

$$\widetilde{g_{\text{EA}}}=\hspace{0.17em}\widetilde{\text{PGS}\hspace{0.17em}\text{of}\hspace{0.17em}\text{EA}}+\tilde{U},$$

where $\widetilde{g_{\text{EA}}}$ is the true genetic score of EA, $\tilde{U}$ is orthogonal to $\widetilde{\text{PGS}\hspace{0.17em}\text{of}\hspace{0.17em}\text{EA}}$, and $\widetilde{g_{\text{EA}}}$, $\widetilde{\text{PGS}\hspace{0.17em}\text{of}\hspace{0.17em}\text{EA}}$, and $\tilde{U}$ are expressed in years of education.

To obtain an estimate of the directional selection differential of EA (or, equivalently, of the true genetic score of EA—rather than of the score of EA) expressed in years of education per generation, observe that

$$\begin{array}{c}\widetilde{\mathrm{\Delta }{\overline{z}}_{\text{EA}}}\equiv {\text{Cov}}_a\left(\text{rLRS},\text{EA}\right)=\text{Cov}\left(\text{rLRS},\widetilde{g_{\text{EA}}}\right)\\ =\frac{\text{Cov}\left(\text{rLRS},\widetilde{g_{\text{EA}}}\right)}{\text{Var}\left(\widetilde{g_{\text{EA}}}\right)}\cdot \frac{\text{Var}\left(\widetilde{g_{\text{EA}}}\right)}{\text{Var}\left(\text{EA}\right)}\cdot \frac{\text{Var}\left(\text{EA}\right)}{\text{Var}\left(\widetilde{\text{PGS}\hspace{0.17em}\text{of}\hspace{0.17em}\text{EA}}\right)}\cdot \text{Var}\left(\widetilde{\text{PGS}\hspace{0.17em}\text{of}\hspace{0.17em}\text{EA}}\right)\\ =\frac{\text{Cov}\left(\text{rLRS},\widetilde{g_{\text{EA}}}\right)}{\text{Var}\left(\widetilde{g_{\text{EA}}}\right)}\cdot h_{\text{EA}}^2/R_{\widetilde{\text{PGS}\hspace{0.17em}\text{of}\hspace{0.17em}\text{EA}}}^2\cdot \text{Var}\left(\widetilde{\text{PGS}\hspace{0.17em}\text{of}\hspace{0.17em}\text{EA}}\right)\\ ={\widehat{\beta }}_{\text{rLRS}\hspace{0.17em}\text{on}\hspace{0.17em}\widetilde{g_{\text{EA}}}}\cdot h_{\text{EA}}^2/R_{\widetilde{\text{PGS}\hspace{0.17em}\text{of}\hspace{0.17em}\text{EA}}}^2\cdot \text{Var}\left(\widetilde{\text{PGS}\hspace{0.17em}\text{of}\hspace{0.17em}\text{EA}}\right),\end{array}$$

where $h_{\text{EA}}^2$ is the heritability of EA and $R_{\widetilde{\text{PGS}\hspace{0.17em}\text{of}\hspace{0.17em}\text{EA}}}^2$ is the R² of the score. The second equality follows because the nongenetic component of rLRS is independent of the genetic component of EA (by definition).

Under the assumption that $\text{E}\left[\text{rLRS}|\widetilde{\text{PGS}\hspace{0.17em}\text{of}\hspace{0.17em}\text{EA}},\tilde{U}\right]=\beta \cdot \widetilde{\text{PGS}\hspace{0.17em}\text{of}\hspace{0.17em}\text{EA}}+\beta \cdot \tilde{U}=\beta \cdot \widetilde{g_{\text{EA}}}$ (or, equivalently, that ${\beta }_{\text{rLRS}\hspace{0.17em}\text{on}\hspace{0.17em}\widetilde{g_{\text{EA}}}}={\beta }_{\text{rLRS}\hspace{0.17em}\text{on}\hspace{0.17em}\widetilde{\text{PGS}\hspace{0.17em}\text{of}\hspace{0.17em}\text{EA}}}$), the following holds: ${\beta }_{\text{rLRS}\hspace{0.17em}\text{on}\hspace{0.17em}\widetilde{g_{\text{EA}}}}={\beta }_{\text{rLRS}\hspace{0.17em}\text{on}\hspace{0.17em}\widetilde{\text{PGS}\hspace{0.17em}\text{of}\hspace{0.17em}\text{EA}}}={\beta }_{\text{rLRS}\hspace{0.17em}\text{on}\hspace{0.17em}\text{PGS}\hspace{0.17em}\text{of}\hspace{0.17em}\text{EA}}/\widetilde{{\sigma }_{\text{PGS}\hspace{0.17em}\text{of}\hspace{0.17em}\text{EA}}}=\mathrm{\Delta }{\overline{z}}_{\text{PGS}\hspace{0.17em}\text{of}\hspace{0.17em}\text{EA}}/\widetilde{{\sigma }_{\text{PGS}\hspace{0.17em}\text{of}\hspace{0.17em}\text{EA}}}.$ It follows that

$$\begin{array}{c}\widetilde{\mathrm{\Delta }{\overline{z}}_{\text{EA}}}=\mathrm{\Delta }{\overline{z}}_{\text{PGS}\hspace{0.17em}\text{of}\hspace{0.17em}\text{EA}}/\widetilde{{\sigma }_{\text{PGS}\hspace{0.17em}\text{of}\hspace{0.17em}\text{EA}}}\cdot h_{\text{EA}}^2/R_{\widetilde{\text{PGS}\hspace{0.17em}\text{of}\hspace{0.17em}\text{EA}}}^2\cdot \text{Var}\left(\widetilde{\text{PGS}\hspace{0.17em}\text{of}\hspace{0.17em}\text{EA}}\right)\\ =\mathrm{\Delta }{\overline{z}}_{\text{PGS}\hspace{0.17em}\text{of}\hspace{0.17em}\text{EA}}\cdot \widetilde{{\sigma }_{\text{PGS}\hspace{0.17em}\text{of}\hspace{0.17em}\text{EA}}}\cdot h_{\text{EA}}^2/R_{\widetilde{\text{PGS}\hspace{0.17em}\text{of}\hspace{0.17em}\text{EA}}}^2\\ =\widetilde{\mathrm{\Delta }{\overline{z}}_{\text{PGS}\hspace{0.17em}\text{of}\hspace{0.17em}\text{EA}}}\cdot h_{\text{EA}}^2/R_{\widetilde{\text{PGS}\hspace{0.17em}\text{of}\hspace{0.17em}\text{EA}}}^2.\end{array}$$

In other words, under the assumption that the coefficient on the score of EA in a regression of rLRS on the score is equal to the coefficient on the true genetic score of EA in a regression of rLRS on the true genetic score, it follows that the directional selection differential of EA is equal to the directional selection differential of the score multiplied by the ratio of the heritability of EA to the R² of the score of EA.

Estimates of the heritability of EA vary substantially across studies and countries, but a recent meta-analysis of existing heritability estimates of EA obtained a mean of ∼0.40 (37). Assuming that $h_{\text{EA}}^2=0.40$, using my earlier estimates of $R_{\text{PGS}\hspace{0.17em}\text{of}\hspace{0.17em}\text{EA}}^2$ and $\widetilde{\mathrm{\Delta }{\overline{z}}_{\text{PGS}\hspace{0.17em}\text{of}\hspace{0.17em}\text{EA}}}$, and using the nonparametric bootstrap method with 1,000 bootstrap samples to estimate percentile confidence intervals, I obtain estimates of the directional selection differential of EA of $\widetilde{\mathrm{\Delta }{\overline{z}}_{\text{EA}}}=-0.108$ (95% CI: −0.177 to −0.045) and $\widetilde{\mathrm{\Delta }{\overline{z}}_{\text{EA}}}=-0.128$ (95% CI: −0.237 to −0.025) years of education per generation for females and for males, respectively—which is equivalent to −1.30 (95% CI: −2.12 to −0.54) and −1.53 (95% CI: −2.85 to −0.31) months of education per generation for females and males, respectively. (These estimates of the confidence intervals do not account for the uncertainty in the value of the heritability of EA, nor for the uncertainty stemming from the selection of the Gaussian mixture weights for the LDpred scores.)

Testing for Nonlinear Selection.

Lande and Arnold (16) show that, under the assumption that the characters have a multivariate normal distribution before selection, the estimates from a quadratic regression of relative fitness on all of the characters and their squares and interactions together can inform whether the characters are under any of the three types of nonlinear selection: stabilizing, disruptive, or correlational selection. In that framework, the coefficients on the characters capture the forces of directional selection; the coefficients on the squared characters capture the forces of stabilizing and disruptive selection acting directly on the variances of the characters and will be positive for the characters that are under disruptive selection and negative for the characters that are under stabilizing selection; and the coefficients on the interacted characters capture the forces of correlational selection (9) as well as the impact of selection on the covariance between the characters. All of these coefficients are needed to project evolutionary changes over more than one generation.

I treat the polygenic scores themselves (as opposed to the phenotypes, as is usual) as the characters of interest and estimate the quadratic regression of rLRS on all of the scores and their squares and interactions together, along with birth year dummies, HRS-defined cohort dummies, and the top 20 principal components of the genetic relatedness matrix, separately for females and males in the study sample, by OLS.

Table S5 reports the results. For both females and males, few of the coefficients on the squared and interacted scores are significant at the 5% level. The most significant estimate is that of the coefficient on the interaction of the scores of SCZ and TC in females (P = 0.007), but it is not significant after Bonferroni correction (it is not significant after Bonferroni correction for more than seven tests; coefficients on 28 squared or interacted scores are tested for females, and 21 are tested for males, so 49 tests are conducted in total). There is thus no solid evidence that stabilizing, disruptive, or correlational selection has been operating on the genetic variants associated with the various phenotypes. Comparing Table S5 to Table 2, the coefficient estimates on the scores from the quadratic regressions are very similar to those from the regressions of rLRS on each score individually. This is not surprising, because the correlations between most scores are low and the coefficients on the squared and interacted scores are small. I emphasize that these null results could be attributable to lack of statistical power and to the polygenic scores being imperfect proxies for the true genetic scores; they do not prove that there has been no stabilizing, disruptive, or correlational selection of the genetic variants associated with the various phenotypes.

Discussion

My results suggest that natural selection has been operating on the genetic variants associated with EA, and possibly with AAM. Although I find no evidence that natural selection has been operating on the genetic variants associated with the other phenotypes or that nonlinear selection has been operating, I emphasize that this could be because my polygenic scores are imperfect proxies for the true genetic scores, which limits the statistical power of my analyses.

My estimates of the negative associations between rLRS and both phenotypic EA and the polygenic score of EA are consistent with previous findings of negative associations between LRS and phenotypic EA in samples of females (38–41), males (38, 41), and females and males together (42) in contemporary Western populations, although positive phenotypic associations have also been reported for males (39). My estimates are also consistent with concurrent findings of a negative phenotypic association for females and males together and of a negative correlation between LRS and a score of EA (constructed with the summary statistics from an earlier, smaller GWAS of EA) (43). To my knowledge, few articles have investigated the relationship between phenotypic AAM and LRS in contemporary Western populations. Kirk et al. (44) find a quadratic relationship that is suggestive of stabilizing selection, but they find no genetic covariation (using behavioral genetic techniques in a sample of twins). Consistent with the results of my regressions of rLRS on phenotypic BMI and HGT (Table 1), there is previous phenotypic evidence of positive selection for weight and negative selection for HGT in females (9, 45). Previous studies have also documented a positive (9) and an inverted-U (45) relationship between LRS and phenotypic HGT in males, and have found evidence of negative selection for TC and of stabilizing selection for GLU in females (11), in contemporary Western human populations.

Consistent with the results from previous studies with phenotypic data (e.g., ref. 9), my results suggest that natural selection has been operating slowly relative to the rapid changes that have occurred over the past few generations, presumably due to cultural and environmental factors. For instance, my estimate of a directional selection differential of EA of about −1.5 mo of education per generation pales in comparison with the increase of 6.2 y in the mean level of EA that took place for native-born Americans born between 1876 and 1951 (46) (which is equivalent to about 2 y of education per generation). Moreover, although I find suggestive evidence that genetic variants associated with higher AAM may have been selected for, AAM has substantially decreased in contemporary Western populations (47). Also, although I find no evidence of selection for the genetic variants associated with BMI and HGT, both phenotypes have markedly increased over the past century (48). Thus, although natural selection is still operating, the environment appears to have achieved an “evolutionary override” (28) on the measurable phenotypes I study.

As shown in Okbay et al. (20), the association between the score of EA and EA is not likely to be driven by the effects of culture, the environment, or population stratification, and is likely to reflect the true causal effects of multiple genetic variants. For instance, in cohorts that are independent of those used in the GWAS of EA, the score remains significant in regressions of EA on the score when family fixed effects are also included. Moreover, estimates from an LD score regression (49)—which disentangles the signal due to the genetic variants’ causal effects from the signal due to confounding biases—suggest that stratification is not a major source of bias in the GWAS summary statistics of EA. Okbay et al. also analyzed the summary statistics of EA and obtained sizeable and significant estimates of the genetic correlation between EA and several neuropsychiatric and cognitive phenotypes, as well as of the genetic variance of EA accounted for by SNPs annotated to the central nervous system relative to other SNPs. Thus, although it is not possible to rule out with certainty that my results are (at least partly) confounded by stratification, stratification is unlikely to be an important concern.

Several additional caveats should be kept in mind when interpreting my results. First, rLRS is not a perfect proxy for long-term genetic contribution. Among other possible reasons for this, a tradeoff between the quantity and quality of children has been documented in preindustrial human societies and may still exist in modern societies (50). In the presence of such a tradeoff, the number of grandchildren or third-generation descendants is a better measure of fitness—although most datasets (including the HRS) lack such data, and it has been shown that LRS and number of grandoffspring were perfectly genetically correlated in a postindustrial human population (10). Also, in growing populations, individuals who successfully reproduce earlier in life tend to have higher fitness (51), but rLRS does not account for fertility timing. In the case of EA, individuals with high EA typically have children at a more advanced age, which may further reduce their fitness. Alternative measures of fitness—such as the intrinsic rate of increase (the exponentiated Lotka’s r)—account for fertility timing, but they require data on the age at birth of every offspring and do not always perform better in natural populations (52). A second caveat is that it is not possible to translate my estimates into projected evolutionary changes over more than one generation, because my results do not account for the effects of all phenotypes that correlate genetically with the phenotypes I study and that also have causal effects on fitness (16). (Selection on phenotypes that are genetically correlated with the phenotypes of interest impacts their genetic covariance, which, in turn, impacts the selection gradients on the phenotypes of interest in future generations.) Furthermore, because the cultural environment changes through time, the selection gradients that existed from 1931 to 1953 may not apply to earlier and subsequent periods, which makes long-term projections problematic. For instance, it has been shown that the demographic transition has significantly changed the selective forces in some populations (41, 53–55).

Lastly, there are several reasons why my results in the study sample of genotyped individuals might not be fully generalizable to the entire US population of European ancestry born between 1931 and 1953. First, the HRS only targets individuals who survived until age 50 y, and about 10% of female and 15% of male Americans born in 1940 died before reaching age 50 y, based on data from the US Social Security Administration (56). Second, in the study sample, only 85% of the participants were still alive in 2008 (the last year when they could be genotyped), 69% were asked to be genotyped, and 59% consented to be genotyped. That being said, a comparison of the summary statistics for all individuals in the study sample and for the genotyped individuals in the study sample (Table S1) suggests that there are no important differences between the two samples, and the results of the phenotypic regressions are very similar across the two samples (Table 1 and Table S2).

In sum, and keeping those limitations in mind, my results strongly suggest that genetic variants associated with EA have slowly been selected against among both female and male Americans of European ancestry born between 1931 and 1953, and that natural selection has thus been occurring in that population—albeit at a rate that pales in comparison with the rapid changes that have occurred in recent generations. My results also suggest that genetic variants positively associated with AAM may have been positively selected for among females in that population. As larger GWAS are conducted and better estimates of genetic variants’ effects on various phenotypes become available, polygenic scores will become more precise. The eventual completion of a GWAS of LRS will also make it possible to use other methods, such as LD score regressions (57), to estimate the genetic covariance between LRS and other phenotypes. Future studies that address the above-mentioned limitations will be able to leverage these developments to replicate my results and to obtain more precise estimates of the rate at which natural selection has been and is occurring in humans.

Materials and Methods

The Study Sample and the Cohorts.

The HRS is a longitudinal panel study for which a representative sample of ∼20,000 Americans have been surveyed every 2 y since 1992. My main analyses focus on individuals born between 1931 and 1953. To reduce the risks of confounding by population stratification, I restrict the analyses to unrelated individuals of European ancestry (i.e., non-Hispanic White individuals). To ensure that the LRS variable is a good proxy for completed fertility, I only include females who were at least 45 y old and males who were at least 50 y old when asked the number of children they ever gave birth to or fathered. Further, to ensure that the sample of individuals who have been successfully genotyped (whose DNA samples were collected between 2006 and 2008) is comparable to the sample of individuals who have not, I only include individuals who were enrolled in the HRS and asked the number of children they ever gave birth to or fathered in 2008 or earlier. This left 6,414 females and 5,436 males with phenotypic data and 3,416 unrelated females and 2,571 unrelated males who have been successfully genotyped and who passed the quality control filters described in SI Materials and Methods (and for whom I could thus construct polygenic scores). I refer to the resulting sample as the “study sample.”

For some specifications, I divided the study sample into three nonoverlapping cohorts based on the individuals’ birth years. This allowed me to test the robustness of my results across cohorts (my definition of the cohorts resembles the definition used by the HRS, which recruited its different cohorts at different times). Table S6 summarizes the three cohorts—which I label HRS1 (birth years 1931–1941), HRS2 (birth years 1942–1947), and HRS3 (birth years 1948–1953)—as well as the HRS0 cohort of individuals born between 1924 and 1930. To mitigate the risk of selection bias based on mortality, I excluded the HRS0 cohort of individuals born between 1924 and 1930 from the study sample (Table S6 and SI Materials and Methods), but my main results are robust to the inclusion of that cohort (Table S4). (Table S7 reports results for the HRS0 cohort.) For the same reason, I excluded individuals born before 1924 from the study sample. I also excluded individuals born after 1953 from the study sample, as very few of them have been genotyped.

Phenotypic Variables.

For my baseline analyses, I operationalize relative fitness with the rLRS variable. As Fig. S1 shows, LRS for females and males declined gradually between 1931 and 1953, from around three children in the early 1930s to two children around 1950. Table S1 presents summary statistics for birth year, LRS, and childlessness, as well as for the phenotypic variables for BMI, EA, HGT, and TC. SI Materials and Methods provide details on the construction of these variables. The HRS does not contain phenotypic variables for GLU, SCZ, and AAM (in females).

Quality Control of the Genotypic Data and Polygenic Scores.

I followed the HRS recommendations regarding the use of the genotypic data (58). The individuals’ genotyped SNPs that passed the quality control filters and that were present in the phenotypes’ GWAS summary statistics files were used to construct the polygenic scores. Depending on the phenotype, there were between 505,254 and 544,493 such overlapping SNPs (except for GLU, for which there were only 22,895 such overlapping SNPs). The average sample sizes across the SNPs used to construct the scores are ${\overline{N}}_{BMI}=\mathrm{232,186}$, ${\overline{N}}_{EA}=\mathrm{386,098}$, ${\overline{N}}_{HGT}=\mathrm{243,630}$, and ${\overline{N}}_{TC}=\mathrm{92,793}$ individuals; the summary statistics for GLU, SCZ, and MEN did not contain sample size information, but the reported samples sizes for the main GWAS of these phenotypes are $N_{GLU}=\mathrm{133,010}$, $N_{SCZ}\approx \mathrm{80,000}$, and $N_{MEN}=\mathrm{132,989}$ individuals. The GWAS summary statistics used to construct the scores are all based on meta-analyses that exclude the HRS.

For the main analysis, I used LDpred (33) to construct the polygenic scores; for a robustness check, I also constructed polygenic scores with PLINK (34). [The polygenic scores of EA were constructed and provided to me by the Social Science Genetic Association Consortium (SSGAC), following the procedure described here and which I used to construct the other scores.] Both the LDpred and the PLINK scores for an individual are weighted sums of the individual’s genotype across all SNPs. For the PLINK scores, the weight for each SNP is the GWAS estimate of the SNP’s effect, which captures the causal effects of both the SNP and of SNPs that are in LD; for the LDpred scores, the weight for each SNP is the LDpred estimate of the SNP’s causal effect, which LDpred calculates by adjusting the SNPs’ GWAS estimates with a prior on the SNPs’ effect sizes and information on the LD between the SNPs from a reference panel. The LDpred prior on the SNPs’ effect sizes depends on an assumed Gaussian mixture weight. For each phenotype, LDpred scores were constructed for a range of Gaussian mixture weights, and I selected the score with the weight that maximizes the incremental R² of the score or the correlations between the score and known correlates of the phenotype. Both the LDpred and PLINK scores were standardized to have mean zero and an SD of 1. SI Materials and Methods provide more information on the quality control steps and the construction of the polygenic scores, and Table S8 shows the parameters used to construct the scores and the sources for each phenotype’s summary statistics.

Association Analyses.

For each of BMI, EA, HGT, and TC—for which phenotypic variables are available in the HRS—I regressed rLRS on the corresponding phenotypic variable, separately for females and males; those regressions included birth year dummies and HRS-defined cohort dummies and were estimated by ordinary least squares (OLS). For all phenotypes, I also regressed rLRS on the polygenic score of the phenotype in various samples; the regressions also included birth year dummies, HRS-defined cohort dummies, and the top 20 principal components of the genetic relatedness matrix [to control for population stratification (27); see also section 5 of the supplemental material of ref. 59)], and were also estimated by OLS. For the regressions in the sample of females and males together, I also controlled for sex and only included the respondent with the lowest person number (PN, an HRS identifier) in each household, as spouses very often have the same number of children, which induces a complex correlation structure between the error terms (the results for the score of EA are robust to alternative ways of selecting one respondent per household). In most results tables, I report the coefficient estimates and SEs, with asterisks to indicate statistical significance; P values for the main results are reported in Table S2. The SEs and P values of my estimates from regressions of rLRS on the LDpred scores do not account for the uncertainty stemming from the selection of the Gaussian mixture weights for the LDpred scores; however, the fact that my main results are robust to the use of the PLINK scores instead of the selected LDpred scores implies that my results are not driven by this weight selection procedure.

Directional Selection Differentials.

Based on the Robertson−Price identity (35, 36), the directional selection differential of a character is equal to its genetic covariance with relative fitness. As I show in SI Materials and Methods, it follows that the estimates of the coefficients on the polygenic scores reported in Table 2 can be interpreted as directional selection differentials of the scores, expressed in Haldanes (1 Haldane is 1 SD per generation). SI Materials and Methods also show how to rescale the estimates of the directional selection differential for the score of EA to express them in years of education per generation instead of in Haldanes, and shows how to obtain estimates of the directional selection differential of EA (or, equivalently, of the true genetic score of EA—rather than of the polygenic score of EA) expressed in years of education per generation (under some assumptions). I used the nonparametric bootstrap method with 1,000 bootstrap samples to obtain percentile confidence intervals for the estimates of the directional selection differentials.

Institutional Review of this Project.

This project was reviewed and approved by the National Bureau of Economic Research (NBER) Institutional Review Board. The Harvard University Committee on the Use of Human Subjects also reviewed the protocol for this project and determined that it is not human subjects research.