Abstract
A number of open questions in human evolutionary genetics would become tractable if we were able to directly measure evolutionary fitness. As a step towards this goal, we developed a method to test whether individual genetic variants, or sets of genetic variants, currently influence viability. The approach consists in testing whether the frequency of an allele varies across ages, accounting for variation in ancestry. We applied it to the Genetic Epidemiology Research on Aging (GERA) cohort and to the parents of participants in the UK Biobank. In the UK Biobank, variants that delay puberty timing are enriched in longer-lived parents (P~6×10−8 for fathers and P~1×10−4 for mothers), consistent with epidemiological studies. Similarly, in mothers, variants associated with later age at first birth are associated with a longer lifespan (P~6×10−4) and fewer children (P~3×10−9), pointing to an apparent trade-off between effects on fertility and longevity. Signals are also observed in fathers for variants influencing cholesterol level, heart disease risk, body mass index, and asthma, as well as for variants near CHRNA3 (P~ 4×10−8). In the GERA cohort, in contrast, only one signal is detected, for the APOE ε4 allele (P < 10−15). Results in the two cohorts suggest that even variants with late onset effects are kept at low frequency by purifying selection. In turn, the differences between these two cohorts point to gene-by-environment interactions influencing the genetic architecture of viability. Beyond these findings, our analysis serves as a proof of principle for how upcoming biomedical datasets can be used to learn about selection effects in contemporary humans.
Introduction
A number of central questions in evolutionary genetics remain open, in particular for humans. Which types of variants affect fitness? Which components of fitness do they affect? What is the relative importance of directional and balancing selection in shaping genetic variation? Part of the difficulty is that our understanding of selection pressures acting on the human genome is based either on experiments in fairly distantly related species or cell lines or on indirect statistical inferences from patterns of genetic variation [1–3].
The statistical inferences rely on patterns of genetic variation in present day samples (or very recently, in ancient samples [4]) to identify regions of the genome that appear to carry the footprint of positive selection [2]. For example, a commonly used class of methods asks whether rates of non-synonymous substitutions between humans and other species are higher than expected from putatively neutral sites, in order to detect recurrent changes to the same protein [5]. Another class instead relies on polymorphism data and looks for various footprints of adaptation involving single changes of large effect [6]. These approaches detect adaptation over different timescales and, likely as a result, suggest quite distinct pictures of human adaptation [1]. For example, approaches that are sensitive to selective pressures acting over millions of years have identified individual chemosensory and immune-related genes (e.g., [7]). In contrast, approaches that are most sensitive to selective pressures active over thousands or tens of thousands of years have revealed strong selective pressures on individual genes that influence human pigmentation (e.g., [8–10]), diet [11–13], as well as sets of variants that shape height [14–16]. Even more recent still, studies of contemporary populations have suggested that natural selection has influenced life history traits like age at first childbirth as well as educational attainment over the course of the last century [17–23].
Because these approaches are designed (either explicitly or implicitly) to be sensitive to a particular mode of adaptation, they provide a partial and potentially biased picture of what variants in the genome are under selection. In particular, most have much higher power to adaptations that involve strongly beneficial alleles that were rare in the population when first favored and will tend to miss selection on standing variation or adaptation involving many loci with small beneficial effects (e.g., [24–27]. Moreover, even where these methods identify a beneficial allele, they are not informative about the components of fitness that are affected or about possible fitness trade-offs between sexes or across ages.
In line with Lewontin's proposal to track age-specific mortality and fertility of hundreds of thousands of individuals for the study of natural selection [28], we introduce a more direct and, in principle, comprehensive way to study adaptation in humans, focusing on current viability selection. Similar to the approach that Alison took in comparing frequencies of the sickle cell allele in newborn and adults living in malarial environments [29], we aim to directly observe the effects of genotypes on survival, by taking advantage of the recent availability of genotypes from a large cohort of individuals of different ages. Specifically, we test for differences in the frequency of an allele across individuals of different ages, controlling for changes in ancestry and possible batch effects. This approach is similar in spirit to genome-wide association studies for longevity, yet does not focus on an endpoint (e.g. survival to an old age) but on any shift in allele frequencies with age. Thus it allows the identification of possible non-monotonic effects at different ages or sex differences. Any genetic variant that affects survival by definition has a fitness cost, even if the cost is too small to be effectively selected against (depending on the effective population size, the age structure of the population and the age at which the variant exerts its effects [30]). Of course a genetic variant can influence fitness without influencing survival, through effects on reproduction or inclusive fitness. Thus, our approach considers only one of the components of fitness that are likely important for human adaptation.
As a proof of principle, we applied our approach to two recent datasets: to 57,696 individuals of European ancestry from the Resource for Genetic Epidemiology Research on Aging (GERA) Cohort [31, 32] and, by proxy [33–35], to the parents of 95,513 individuals of European ancestry surveyed as part of the UK Biobank [36]. We did so for individual genetic variants, then jointly for sets of variants previously found to influence one of 42 polygenic traits [37–40].
Results
A method for testing for differences in allele frequencies across age bins
If a genetic variant does not influence viability, its frequency should be the same in individuals of all ages. We therefore test for changes in allele frequency across individuals of different ages, while accounting for systematic differences in the ancestry of individuals of different ages (for example, as a result of migration patterns over decades) and genotyping batch effects. We use a logistic regression model in which we regress each individual's genotype on their age bin, their ancestry as determined by principal component analysis (PCA) (Figure S1), and the batch in which they were genotyped (see Materials and Methods for details). In this model, we treat age bin as a categorical variable; this allows us to test for a relationship between age and the frequency of an allele regardless of the functional form of this relationship. We also test a model with an interaction between age and sex, to assess whether a variant affects survival differently in the two sexes.
We first evaluated the power of this method using simulations. We considered three possible trends in allele frequency with age: (i) a constant frequency up to a given age followed by a steady decrease, i.e., a variant that affects survival after a given age (e.g., variants contributing to late-onset disorders), (ii) a steady decrease across all ages for a variant with detrimental effect throughout life, and (iii) a U-shape pattern in which the allele frequency decreases to a given age but then increases, reflecting trade-offs in the effects at young and old ages, as hypothesized by the antagonistic pleiotropy theory of aging [41] or as may be seen if there are protective alleles that buffer the effect of risk alleles late in life [42] (Figure 1). In all simulations, we used sample sizes and age distributions that matched the GERA cohort (Figure S2). For simplicity, we also assumed no population structure or batch effects across age bins (Materials and Methods). For all trends, we set a maximum of 20% change in the allele frequency from the value in the first age bin (Figure 1).
Because of the age distribution of individuals in the GERA cohort (Figure S2), our power to detect the trend is greater when most of the change in allele frequency occurs at middle age (Figure 1). For example, for an allele with an initial allele frequency of 15% that begins to decrease in frequency among individuals at age 20, age 50, or age 70 years, there is around 20%, 90% and 60% power, respectively, to detect the trend at P < 5×10−8, the commonly-used criterion for genome-wide significance [43]. We also experimented with a version of the model where the age bin is treated as an ordinal variable; as expected, this model is more powerful if there is a linear relationship between age and allele frequency (Materials and Methods). Since in most cases, we do not know the functional form of the relationship between age and allele frequency a priori, we used the categorical model for all analyses, unless otherwise noted.
In the UK Biobank, all individuals were 45-69 years old at enrollment, so the age range of the participants is restricted and our method has low power. However, the UK Biobank participants reported the age at death of their parents; following recent studies [33–35], we therefore used these values (when reported) instead in our model. In this situation, we are testing for correlations between an allele frequency and the age at which the father or mother died. This approach obviously comes with the caveat that children inherit only 50% of their genome from each parent and so power is reduced (e.g., [44]. Further, the patterns expected when considering individuals who have died differ subtly from those generated among surviving individuals. Notably, when an allele begins to decline in frequency starting at a given age (Figure 1A), there should be an increase in the allele frequency among individuals who died at that age, followed by a decline in frequency, rather than the steady decrease expected among surviving individuals (Figure S3, see Materials and Methods for details).
We also adapted this model to allow us to test for changes in frequency at sets of genetic variants. Many phenotypes of interest, from complex disease risk to anthropomorphic traits such as age of menarche, are polygenic [45, 46]. If a polygenic trait has an effect on fitness, either directly or indirectly (i.e., through pleiotropic effects), the individual loci that influence the trait may be too subtle in their survival effects to be detectable with current sample sizes. We therefore investigated whether there is a shift across ages in sets of genetic variants that were identified as influencing a trait in genome-wide association studies (GWAS) (Table S1). Specifically, for a given trait, we calculated a polygenic score for each individual based on trait effect sizes of single variants previously estimated in GWAS and then test whether the scores vary significantly across 5-year age bins (see Materials and Methods for details). These scores are calculated under an additive model, which appears to provide a good fit to GWAS data [47]. If a polygenic trait is under stabilizing selection (e.g., human birth weight [48]), i.e., an intermediate polygenic score is optimal, no change in the mean value of polygenic score across different ages is expected. However, if extreme values of a trait are associated with lower chance of survival, the spread of the polygenic scores should decrease with age. To consider this possibility, we tested whether the squared difference of the polygenic scores from the population mean varies significantly across age bins (see Materials and Methods for details).
Testing for changes in allele frequency at individual genetic variants
We first applied the method to the GERA cohort, using 9,010,280 filtered genotyped and imputed autosomal biallelic single-nucleotide polymorphisms (SNPs) and indels. We focused on a subset of filtered 57,696 individuals confirmed to be of European ancestry by PCA (see Materials and Methods, Figures S4 and S5). The ages of these individuals were reported in bins of 5 year intervals (distribution shown in Figure S2). We tested for significant changes in allele frequencies across these bins. For each variant, we obtained a P value comparing a model in which the allele frequency changes with age to a null model (quantile-quantile plot shown in Figure S6A). All variants that reached genome-wide significance (P < 5×10−8) reside on chromosome 19 near the APOE gene (Figure 2A and Figure S7). This locus has previously been associated with longevity in multiple studies [49, 50]. The ε4 allele of the APOE gene is known to increase the risk of late-onset Alzheimer's disease (AD) as well as of cardiovascular diseases [51, 52]. We observed a monotonic decrease in the frequency of the T allele of the ε4 tag SNP rs6857 (C, protective allele; T, risk allele) beyond the age of 70 years old (Figure 2B). This trend is observed for both the heterozygous and homozygous risk variants (Figure S8), and for both males and females (Figure S9). No variant reached genome-wide significance testing for age by sex interactions (quantile-quantile plot shown in Figure S6B).
We further investigated the trends in frequency with age for the other two major APOE alleles defined by rs7412 and rs429358 SNPs: ε2 (rs7412-T, rs429358-T) and ε3 (rs7412-C, rs429358-T), while ε4 is (rs7412-C, rs429358-C) [53]. Unlike the ε4 allele, ε2 carriers are suggested to be at lower risk of Alzheimer's disease, cardiovascular disease, and mortality relative to the ε3 carriers [49, 53]. We focused on a subset of 38,703 individuals with unambiguous counts of each APOE allele. There is a significant change in the frequency of the ε4 allele with age in this subset (P~6×10−12), similar to the trend observed for the tag SNP rs6857 (Figure S10). The ε3 allele shows the reverse trend, with a significant, monotonic increase in frequency beyond age of 70 years old (P~2×10−8) (Figure S10). The enrichment of the ε3 allele in elderly individuals can be explained by the corresponding depletion of the ε4 allele, however, so does not necessarily imply an independent, protective effect of ε3. The frequency of the ε2 allele does not change significantly with age (P~0.2), possibly reflecting low power given its allele frequency of ~0.06 (Figure S10).
We considered the possibility that some unobserved confounding variable was driving the strength of this signal at APOE. Since there are two genotyped SNPs with signals similar to rs6857 within the locus, genotyping error seems unlikely to be driving the pattern (Figure S7). Another concern might be a form of ascertainment bias, in which individuals with Alzheimer's disease are underrepresented in the Kaiser Permanente Medical Care Plan. However, there is no correlation in these data between the amount of time that an individual has been enrolled in this insurance plan and the individual's APOE genotype (Figure S11). These observations, along with previously reported associations at this locus, argue that the allele frequency trends in Figure 2B are driven by effects of APOE genotype on mortality (or severe disability). Moreover, the effects that we identified are concordant with epidemiological data on the peak age of onset of Alzheimer's disease given 0 to 2 copies of APOE ε4 [51]. This case illustrates how our approach provides resolution about age effects of deleterious variants.
We estimated that we have ~93% power to detect the trend in allele frequency with age as observed for rs6857 (at a genome-wide significance level; see Materials and Methods). Using both versions of the model treating age bin as either a categorical or an ordinal variable, we have similar power to detect other potential trends considered in Figure 1, for variants as common as rs6857 and with similar magnitude of effect on survival. Yet across the genome, only APOE variants show a significant change in allele frequency with age for both versions of the model (Figure 2 and Figure S12). Thus, our finding only APOE ε4 suggests that there are few or no other common variants in the genome with an effect on survival as strong as seen in APOE region.
We then turned to the UK Biobank data. We applied our method to individuals of European ancestry whose data passed our filters; of these, 88,595 had death information available for their father and 71,783 for their mother. We analyzed 590,437 genotyped autosomal variants, applying similar quality control measures as with the GERA dataset (see Materials and Methods). We tested for significant changes in allele frequencies with father's age at death and mother's age at death stratified in eight 5-year interval bins (quantile-quantile plots shown in Figure S13).
Consistent with recent studies [33, 34], the variants showing a genome-wide significant change in allele frequency with father's age at death (P < 5×10−8) reside within a locus containing the nicotine receptor gene CHRNA3 (Figure 3A). The A allele of the CHRNA3 SNP rs1051730 (G, major allele; A, minor allele) has been shown to be associated with increased smoking quantity among individuals who smoke [54]. We observed a linear decrease in the frequency of the A allele of rs1051730 throughout almost all age ranges (Figure 3B). This allele did not show a significant trend with age in GERA (P~0.45, Figure S14).
For mother's age at death, a SNP in a locus containing the MEOX2 gene reached genome-wide significance (Figure 3C). The C allele of rs4721453 (T, major allele; C, minor allele) increases in frequency in the age bin centered at 76 years old (Figure S15), i.e., there is an enrichment among individuals that died at 74 to 78 years of age, which corresponds to a deleterious effect of the C allele in this period. The trend is similar and nominally significant for other genotyped common SNPs in moderate linkage disequilibrium with rs4721453 (Figure S15). Also, the signal for rs4721453 remains nominally significant when using subsets of individuals genotyped on the same genotyping array: 44,552 individuals on the UK Biobank Axiom array (P~7×10−5) and 25,231 individuals on the UK BiLEVE Axiom array (P~10−4). These observations suggest that the result is not due to genotyping errors, but it is not reproduced in GERA (P~0.17, Figure S16) and so it remains to be replicated. APOE variants were among the top nominally significant variants (P~10−7) (Figure 3C). At the APOE SNP rs769449 (G, major allele; A, minor allele), there is an increase in the frequency of A allele at around 70 years old before subsequent decrease (Figure 3D). This pattern is consistent with our finding in GERA (of a monotonic decrease beyond 70 years of age), considering the difference in patterns expected between allele frequency trends with age among survivors versus individuals who died (Figure S3).
We note that by considering parental age at death of the UK Biobank participants –– as done also in [33–35] — we introduce a bias towards older participants (who are more likely to have deceased parents, Figure S17A). We confirmed that our top signals are not significantly affected by such potential bias, observing similar trends in allele frequency with parental age at death when conditioning on age of the participants (Figure 17B).
We further tested for trends in allele frequency with parental age at death that differ between fathers and mothers focusing on 62,719 individuals with age at death information for both parents. No variant reached genome-wide significance level (Figure 18A). The rs4721453 near the MEOX2 gene and APOE variant rs769449 show nominally significant sex effects (P~7×10−8 and P~2 × 10−3, respectively), with stronger effects in females (Figure 18B). Variants near the CHRNA3 locus are nominally significant when using the model with parental age at deaths treated as ordinal variables (rs11858836, P~6× 10−4), with stronger effects in males (Figure 18B).
Testing for changes in allele frequency at trait-associated variants
We next applied our model to polygenic traits, rather than individual genetic variants. We focused on 42 polygenic traits, including disease risk and anthropomorphic traits of evolutionary importance such as age at menarche (AAM), for which a large number of common variants have been mapped in GWAS (see Table S1 for the list of traits and number of loci) [37–40]. For each individual and each trait, we calculated a polygenic score, and then tested whether this polygenic score, or its squared difference from the mean in the case of stabilizing selection, differs among individuals in different age bins.
In the GERA cohort, no trait reaches statistical significance, after accounting for multiple tests (Figure 4A). The strongest signal is an increase in the polygenic score for age at menarche (AAM) in older ages (P~7×10−3, without correction for multiple testing; Figure 4B), consistent with epidemiological studies suggesting early puberty timing to be associated with various adverse health outcomes [55]. We did not exclude males for analysis of AAM, because of the strong genetic correlation between the timing of puberty in males and females [56].
For disease traits potentially decreasing the chance of survival with increasing age, a monotonic decrease in polygenic score with age is plausible. Therefore, we also applied our version of the model with age treated as an ordinal variable, for which Alzheimer's disease (AD) (excluding the APOE locus) shows the strongest signal (P~5×10−3, see Figure 4C), indicative of a decrease in chance of survival with increased genetic risk of AD (Figure 4D). No trait shows significant age by sex effect (Figure S19), or significant change in the squared difference of polygenic score from the mean with age (Figure S20).
In the UK Biobank, using the model with parental age at deaths treated as ordinal variables, several disease risk traits show significant change in polygenic score with father's age at death (Figure 5A): total cholesterol (TC, P~5×10−10), coronary artery disease (CAD, P~2×10−8), low-density lipoproteins (LDL, P~6×10−8), triglycerides (TG, P~3×10−4), and body mass index (BMI, P~7×10−7), consistent with two recent studies [34, 35]. In addition, we uncovered significant changes in polygenic score with father's age at death for asthma (ATH, P~5×10−5) and puberty timing (P~6×10−8) (using AAM associated variants to proximate puberty timing scores in males). With the exception of lipid traits (Figure S21), the trends for one trait remain significant after accounting for changes in polygenic score of another trait (see Materials and Methods), this is specifically important for BMI and AAM where there is substantial genetic overlap [38]. Of particular interest, the score for puberty timing increased linearly with father's age at death (Figure 5B), indicating variants that delay puberty timing to be associated with a higher chance of survival, consistent with GERA and epidemiological studies. All other traits with significant signal showed a monotonic decline in score with age (Figure 5C-F).
For mothers, AAM and age at first birth (AFB) showed significant changes in polygenic score with age at death (P~10−4 and P~6 × 10−4, respectively, Figure 6A). Although there is some genetic correlation between AAM and AFB [39], the two signals seem to be distinct (Figure S21). Higher polygenic scores for AAM were enriched among longer-lived mothers (Figure 6B), as seen for fathers. Similarly, the score for AFB increased with mother's age at death (Figure 6C), indicating an association between variants that delay AFB and longer lifespan. Previous studies suggest that there is a genetic correlation between AFB and the number of children ever born [21], and genetic predictions of later AFB were associated with lower chance of reproduction [39]. In line with these reports, we found an inverse correlation between higher polygenic score for AFB and lower number of children for deceased mothers of the UK Biobank participants (P~3×10−9, Figure 6D). These findings point to an apparent trade-off between effects on fertility and longevity for variants underlying AFB, consistent with epidemiological studies [57]. No additional age effects were revealed when parental age at deaths were treated as categorical variables (Figure S22). We emphasize, however, that detecting an effect of age on AFB and AAM (or other traits) does not imply that these are the phenotypes under viability selection, as the variants that contribute likely have pleiotropic effects on other traits.
Testing for age by sex interaction, total cholesterol showed stronger effects in males (P~7×10−4, Figures S23). Using the model with parental age at deaths treated as categorical variables high-density lipoproteins (HDL) showed the strongest age by sex effect, with seemingly distinct trends in males and females (P~3×10−4, Figures S23). No trait showed significant change in the squared difference of polygenic score from the mean with father's or mother's age at death (Figure S24).
Discussion
We introduced a new approach to identify genetic variants that affect survival to a given age and thus to directly observe viability selection ongoing in humans. Attractive features of the approach include that we do not need to make a decision a priori about which loci or traits matter to viability and focus not on an endpoint (e.g., survival to an old age) but on any shift in allele frequencies with age, thereby learning about the ages at which effects are manifest and possible differences between sexes.
To illustrate the potential of our approach, we performed a scan for genetic variants that impact age-specific mortality in the GERA and the UK Biobank cohorts. We only found a few variants, the majority of which were identified in previous studies. This result is in some ways expected: available data only provide high power to detect effects of common variants (>15-20%) on survival (Figure 1), yet if these variants were under viability selection, we would not expect them to be common, short of strong balancing selection due to trade-offs between sexes, ages or environments. As sample sizes increase, however, the approach introduced here should provide a comprehensive picture of viability selection in humans. To illustrate this point, we repeated our power simulation with 500,000 samples, and found that we should have high power to detect the trends for alleles at a couple percent frequency (Figure S25).
Already, however, this application raises a number of interesting questions about the nature of viability selection in humans. Notably, we discovered only a few variants influencing viability in the two cohorts, all of which exert their effect late in life. On first thought, this finding may suggest such variants to be neutrally-evolving. We would argue that if anything, our findings of only a few common variants with effects on survival late in life suggest the opposite: that even variants with late onset effects have been weeded out by purifying selection. Indeed, unless the number of loci in the genome that could give rise to such variants (i.e., the mutational target size) is tiny, other variants such as APOE ε4 must often arise. That they are not observed when we have very high power to detect them suggests they are kept at lower frequency by purifying selection. Why might they be selected despite affecting survival only at old ages? Possible explanations include that they decrease the direct fitness of males sufficiently to be effectively selected (notably given the large, recent effective population size of humans [58]) or that they impact the inclusive fitness of males or females. If this explanation is correct, it raises the question of why APOE ε4 has not been weeded out. We speculate that the environment today has changed in such a way that has made this allele more deleterious recently. For example, it has been proposed that the evolution of this allele has been influenced by changes in physical activity [59] and parasite burden [60].
Also interesting is the fact that our results differ markedly between the GERA cohort of individuals from California and the parents of the individuals in the UK Biobank. We confirmed that our different findings between the GERA cohort and the UK Biobank are not driven by using slightly different sets of trait-associated variants (considering that the trait associated variants passing our filters were not identical), finding similar results when using variants that passed quality control steps in both datasets (Figure S26). The differences between cohorts are most notable at the CHRNA3 locus and the sets of polygenic traits; both show strong signals among fathers of the individuals in the UK Biobank but not in GERA. We cannot rule out that these differences are simply due to power, as comparisons between the two cohorts are complicated by a number of factors. In particular, changes in the age structure of a population can perturb the frequency trend of a selected allele, even if its effects on fecundity and survival are unchanged [30]. However, the analysis of mothers and fathers of individuals in the UK Biobank should have similar power and there too, we see marked differences. Together, these observations therefore point to strong gene-environment interactions of lifespan, such that the environments of males in the UK in the mid to late 1900s, females in this same period in the UK, and California in the late 1900s were different enough to change the genetic architecture of lifespan. In this regard, we note that the GERA participants are generally well-educated with above average incomes (dbGaP phs000674.v1.p1), and thus the different observations in GERA and UK Biobank may in part reflect an interaction of socioeconomic status and genetic effects.
The CHRNA3 locus, in which variants are associated with the amount of smoking among smokers, even suggests a salient environmental factor. Smoking prevalence has decreased significantly over the past few decades in both the UK and California, with men in the UK consistently smoking more than women or people in California: from 1970 to 2000, smoking prevalence decreased from around 70% to 36% in middle-aged men from UK, compared to from around 50% to 28% in middle-aged women from UK, and from around 40% to 20% in Californians [61, 62]. These epidemiological patterns are potentially consistent with our observation of more pronounced effect on male than female age at death among parents of UK Biobank participants, and the lack of significant pattern in either sex in GERA, particularly since GERA individuals are around a generation time younger than parents of UK Biobank participants. In any case, these results highlight the utility of cohorts with both genetic and environmental information.
While our method is designed to detect changes in allele frequencies (and in polygenic scores) caused by genetic effects on age-specific survival, such changes could in principle also arise from effects on other components of fitness. For example, if the frequency of a genetic variant in a population decreases over decades due to an effect on fertility, its frequency would increase with the age of surviving individuals sampled at a given time (as in the GERA cohort). This confounding is less of an issue when considering effects on the age at death (what we measured in the UK Biobank). Nonetheless, even in the UK Biobank, fertility effects may manifest as effects on age of death; for example, because when sampling a cohort of children, parents with later ages at death are possibly born earlier (Figure S27). Thus, some caution is required in interpreting trends with age as strictly reflecting viability effects. However, in the UK Biobank, our signals remain after we account for changes in allele frequencies with year of birth of the participants themselves (ideally we would want to condition on parents born at similar times, which we cannot do; instead, we used birth year of the participants as an estimator for birth year of the parents, Figures S17 and S28). Thus, we believe our results in the UK Biobank not to be confounded by fertility effects. Moreover, a number of our findings in this study are consistent with prior knowledge of effects on survival, such as those for disease risk variants like APOE ε4.
We caution further that possible trade-offs between different fitness components, particularly for life-history traits such as AFB [63], imply that considering effects on survival or on fertility alone is insufficient to infer whether the net effect of a variant or set of variants is beneficial. Instead, to convert effects on viability, such as those detected here, or effects on fertility reported elsewhere [22, 23] into an understanding of how natural selection acts on an allele requires a characterization of its effects on all components of fitness.
In any case, moving forward, application of our approach to the millions of samples in the pipeline (such as the UK Biobank [64], the Precision Medicine Initiative Cohort Program [65], and the Vanderbilt University biobank (BioVU)[66]), in which the viability effects of rare as well as common alleles can be examined, should provide a comprehensive answer to the question of which loci affect survival, helping to address long-standing open questions such as the relative importance of viability selection in shaping genetic variation and the extent to which genetic variation is maintained by fitness trade-offs between sexes or across ages.
Materials and Methods
1. Datasets
1.1. GERA cohort
We performed our analyses on the data for 62,318 participants of the Kaiser Permanente Northern California multi-ethnic Genetic Epidemiology Research on Adult Health and Aging (GERA) cohort, self-reported to be "White-European American", "South Asian", "Middle-Eastern" or "Ashkenazi" but no other ethnicities, among a list of 23 choices on the GERA survey, and genotyped on a custom array at 670,176 SNPs designed for Non-Hispanic White individuals [31, 32]. We determined the age of the participants and the number of years they were enrolled in the Kaiser Permanente Medical Insurance Plan at the time of the survey (year 2007).
2. Quality control (QC)
GERA cohort
We used PLINK v1.9 [68] to remove individuals with missing sex information or with a mismatch between genotype data and sex information, individuals with <96% call rate, and related individuals. We validated self-reported European ancestries using principal component analysis (PCA), see below, and removed individuals identified as non-European (Figures S4 and S5). In the end, 57,696 individuals remained.
Using PLINK, we removed SNPs with <1% minor allele frequency, SNPs with <95% call rate, and SNPs failing a Hardy-Weinberg equilibrium test with P < 10−8 (filtering based on HWE test could potentially exclude true signals of viability selection, if selection coefficients were very large [69], but this possibility is much less likely than genotyping error). We additionally tested for a correlation between age (or sex) and missingness, which can induce artificial change in the allele frequencies as a function of age (or sex). We thus removed SNPs showing a significant age-missingness or sex-missingness correlation, defined as a chi-squared test with P < 10−7. After these steps, 599,659 SNPs remained.
We imputed the genotypes of the filtered GERA individuals using post-QC SNPs, and using the 1000 Genomes phase 3 haplotypes as a reference panel [70]. We phased observed genotypes using EAGLE v1.0 software [71]. The inferred haplotypes were then passed to IMPUTE2 v2.3.2 software for imputation in chunks of 1Mb, using the default parameters of the software [72]. To gain computational speed, variants with <0.5% minor allele frequency in the 1000 Genomes European populations were removed from the reference panel. This step should not affect our analysis because our statistical model is not well powered for rare variants, given the GERA data sample size. We called imputed genotypes with posterior probability >0.9, and then filtered the imputed genotypes, removing variants with IMPUTE2 info score <0.5 and with minor allele frequency <1%. We also used imputation with leave-one-out approach [73] to impose a second stage of QC on genotyped SNPs, removing SNPs that were imputed back with high reported certainty (info score >0.5) and with <90% concordance between the imputed and the original genotypes. These yielded a total of 9,010,280 imputed and genotyped biallelic SNPs and indels.
For our analysis of the APOE alleles (ε2, ε3 and ε4) which are defined by rs7412 and rs429358 SNPs [53], given the lack of tag SNPs for all three alleles, we kept a subset of 38,703 individuals with no poorly-imputed genotypes for these two SNPs, for whom the count of each APOE allele could be determined unambiguously.
2.2. UK Biobank
In the UK Biobank, we obtained sets of genotype calls and the output of imputation as performed by the UK Biobank researchers [67, 74]. We first applied QC metrics to the autosomal genotyped SNPs. We used PLINK to remove SNPs with <1% minor allele frequency, SNPs with <95% call rate, and SNPs failing a Hardy-Weinberg equilibrium test with P < 10−8. These filters were applied separately to SNPs genotyped on the UK Biobank Axiom and the UK BiLEVE Axiom arrays. Then, we divided the genotyped SNPs into three sets (SNPs specific to either array and shared SNPs) and then performed additional QC on each set separately: we removed SNPs with significant allele frequency difference between genotyped and imputed calls (chi-squared test P < 10−5) and SNPs showing a significant correlation between missingness and age or sex of the participants, as well as with participants' father's or mother's age at death (chi-squared test P < 10−7). We then extracted this list of SNPs from the imputed genotype files available from the UK Biobank (we did not use the full set of imputed genotypes). From this set, we removed SNPs with <1% minor allele frequency, SNPs with <95% call rate, and SNPs failing a Hardy-Weinberg equilibrium test with P < 10−8, yielding 590,437 SNPs. For variants influencing quantitative traits, we first extracted them from imputed genotypes, and then imposed the same QC measures as above.
Each participant was asked to provide the age at death of their father and their mother (if applicable) on each assessment visit. For each participant that reported an age at death of father and/or mother, we averaged over the ages reported at recruitment and any subsequent repeat assessment visits, and used PLINK to exclude individuals with >5 year variation in their answers across visits (around 800 individuals). We also removed adopted individuals, as well as individuals with a mismatch between genotype data and sex information, resulting in 88,595 individuals with age at death information for their father, 71,783 individuals for their mother, and 62,719 individuals for both parents.
3. Principal Component Analysis
We performed PCA, using the EIGENSOFT v6.0.1 package with the fastpca algorithm [75, 76], for two purposes: (i) as a quality control on individuals to validate self-reported European ancestries, and (ii) to correct for population structure in our statistical model.
3.1. European ancestry validation
We used more stringent QC criteria specifically for the PCA, compared to the QC steps described above. We filtered a subset of 157,277 SNPs in GERA and 220,447 in the UK Biobank, retaining SNPs shared between the datasets and the 1000 Genomes phase 3 data, removing non-autosomal SNPs, SNPs with <1% minor allele frequency, SNPs with <99% call rate, and SNPs failing a Hardy-Weinberg equilibrium test with P < 10−6. We then performed LD-pruning using PLINK with pairwise r2 <0.2 in windows of 50 SNPs shifting every 10 SNP. We used these SNPs to infer principal components for the 1000 Genomes phase 3 data [70]. We then projected individuals onto these PCs. In GERA, we observed that the majority of individuals have European ancestry, and marked individuals with PCs deviating from the population mean, for any of the first six PCs, as non-European (Figures S4 and S5). In the UK Biobank, the European ancestry of all individuals was confirmed (not shown).
3.2. Control for population structure
After the main QC stage, additional QC steps (as in section 3.1) were implemented for PCA. In the UK Biobank, we also removed inversion variants on chromosome 8 which otherwise dominate the PC2 (not shown). A subset of 156,721 SNPs in GERA and 207,657 SNPs in the UK Biobank was then used to infer PCs for individuals passing QC (Figure S1). The first 10 PCs were used as covariates in our statistical model.
4. Quantitative Traits
We downloaded the list of variants contributing to 39 traits (all traits but age at menarche, age at first birth and age at natural menopause) and their effect sizes recently described in Pickrell et al. [37], from: https://github.com/PickrellLab/gwas-pw-paper/tree/master/all_single. For age at menarche, we used the variants and effect sizes recently identified by Day et. al [38]. We used variants associated with age at first birth from Barban et al., identified in either sex-specific analyses or analyses of both sexes and used the effect sizes estimated in the combined analysis [39]. We used age at natural menopause associated variants and their effect sizes from Day et al. [40]. For all traits, we used variants that were genotyped/imputed with high quality in our data (see Table S1).
5. Statistical Model
5.1. An individual variant
Using a logistic regression we predict the genotype of individual j (the counts of an arbitrarily selected reference allele, Gij= 0,1 or 2) at variant i, using the individual's ancestry, the batch at which the individual was genotyped, and individual's age (as well as sex, see below) as explanatory variables. Specifically, distribution of Gij is Bin(2, pij), where pij, the probability of observing the reference allele for individual j at variant i, is related to explanatory variables as: where βl is the effect of principal component l (to account for population structure), is the effect of being in batch γm (to account for potential systematic differences between genotyping packages), kn is the effect of being in age bin n, obtained by regression across individuals with non-missing genotypes at variant i, and I and J are indicator variables for the genotyping batch and age bin, respectively. In the version of the model in which we treat age as an ordinal variable, we replace J age bin variables with one age variable. In the GERA dataset, age binning is over the age of the participants in 14 categories, from age 19 onwards, in 5-year intervals, and for the UK Biobank, it is over 8 categories for the age at death of father or mother, from age 63 onwards, in 5-year intervals. In the UK Biobank, we included all ages at death below 63 in one age bin to minimize the potential noise caused by accidental deaths at young ages.
We tested for an effect of age categories by a likelihood ratio test with a null model using only the covariates (PCs and batch terms) (H0: kn = 0, for all n) and an alternative also including age terms as predictors (H.: Kn ≠ 0, for at least one n):
To test for age by sex effectts in GERA we included two sets of additional predictors. The first consists in two indicator variables for sex, Kmale and Kfemale, which are included to capture possible sex effects induced by potential genotyping errors or missmapping of sex chromosome linked alleles (we note that because of Hardy-Weinberg equilibrium, mean allele frequency difference between males and females are not expected). The second set of predictors consists in age by sex terms, J×K. We then compare a model with age and sex terms as predictors to a model also including age by sex terms. To test for sex effects in the UK Biobank, we compared a model with both father and mother age terms separately as predictors to a model with one set of age categories for average age at death of both parents, only for individuals reporting the age at death for both parents. In all models PCs and batch terms were incorporated as covariates.
5.2. Set of variants
As for the model described above for an individual variant, we investigated age and age by sex effects on quantitative traits for which large number of large common genetic variants have been identified in genome-wide association studies (GWAS). For a given trait, we used a linear regression with the same covariates and predictors as for the model for an individual variant, to predict the polygenic score for individual j, Sj, by summing the previously estimated effect of single variants assuming additivity and that the effect sizes are similar in the GWAS panels and the cohorts considered here:
Sj is calculated as ∑aiGij + ∑.2aiqi(standardized to mean 0), where the first sum is across variants with non-missing genotypes, ai is the effect size for the arbitrary selected reference allele at variant i, and the second sum is across the variants with missing genotypes estimating their contribution assuming Hardy-Weinberg equilibrium where qi is the frequency of the alternate allele. Likelihood ratio tests, as described above, were used to test for age and age by sex effects.
We performed additional tests in the UK Biobank: (i) To assess the interdependence of detected age effects (Figure S21), for each pair of traits [i,j], we tested for changes in the polygenic score for trait i with parental age at death as described above, but also used the polygenic score for trait j as a covariate in the null model (in addition to PCs and batch terms). (ii) To evaluate if our signals possibly reveal effects on fitness components other than survival (as described in Discussion, Figure S28), we used the birth year of the participants as a covariate in the null model (in addition to PCs and batch terms). The birth year was binned from year 1938 onwards, in 3-year intervals. (iii) To test for change in polygenic score of AFB with number of children of the deceased mothers of the UK Biobank participants (Figure 6D), the number of siblings of the participants were used in the described models, as an ordinal variable, instead of maternal age at death.
All Manhattan and quantile-quantile plots were generated using qqman [77] and GWASTools [78] packages.
6. Power simulations
We ran simulations to determine the power of our statistical model to detect deviation of allele Frequency trends with age across 14 age categories mimicking the GERA individuals (57,696 individuals with age distribution as in Figure S2) from a null model, which for simplicity was no change in frequency with age, i.e., no changes as a result of age-dependent variation in population structure and batch effects. For a given Trend in Frequency of an allele with age, we Generated 1000 simulated trends where the distribution of the number of the alleles in age bin i is Bin (2Ni,fi), where Ni and fi are the sample size and the sample allele frequency in bin i.we then estimated the power to detect the trend as the fraction of cases in which P < 5×10−8 by a chi-squared test.
7. Survival simulations
We ran simulations to investigate the relationship between allele frequency with age of the survived individuals and the age of the individuals who died in a cohort. We simulated 2×106 individuals going forward in time in 1 year increments. For each time step forward, we tuned the chance of survival of the individuals based on their count of a risk allele for a given variant such that the number of individuals dying in the increment complies with: (i) a normal distribution of ages at death with mean of 70 years and standard deviation of 13 years, roughly as is observed for parental age at deaths in the UK Biobank, and (ii) a given frequency of the risk allele among those who survive. Specifically, we modeled the survival rate of the population, S, as the weighted mean for 2 alleles carriers, S2, 1 allele carriers, S1, and non-carriers, S0: where f denotes the frequency of genotypes in the population and x denotes the age. Si and S are related: Si(x) = S(x) fi(x)/fi, where fi(x) is the genotype frequency among individuals survived up to age x. Given a trend in allele frequency with age, we calculated genotype frequencies with age assuming Hardy-Weinberg equilibrium, and then estimated genotype dependent chance of survival, Si(x), taking S(x) as the survival function for N(70,132).
Acknowledgments
We thank Guy Sella for helpful discussions. This research has used the UK Biobank Resource (application number 11138), and was funded in part by Columbia University (a Research Initiative in Science and Engineering grant to MP and JKP) and the National Institutes of Health (grant R01MH106842 to JKP and R01GM115889 to Guy Sella). These data analyses were approved by the Columbia University Institutional Review Board, protocols AAAQ2700 and AAAP0478.
Footnotes
↵* These authors co-supervised this project.
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