This study aimed to decompose and quantify additive genetic sources of variation to intelligence and personality in novel manners, using molecular genetic and pedigree data from the same large sample. In doing so, we sought to identify reasons for the gap between pedigree-based and SNP-based estimates of heritability in samples of unrelated individuals, a difference that might be due to genetic variants in poor LD with SNPs genotyped on current platforms. A number of novel findings speak to long-standing questions in behaviour genetics and evolutionary genetics of psychological differences [16, 32, 66].

Firstly, using GREML-KIN we could account for the entire heritability of general intelligence and education, as estimated in twin and family studies, by adding the G and K estimates we derived directly from genome-wide molecular genetic data [63, 67]. Secondly, using GREML-MS, we replicated this finding with imputed data on unrelated individuals. For general intelligence and education, a substantial and significant proportion of the phenotypic variance was found to be explained by pedigree-associated genetic effects (h2 kin ). The pedigree-associated genetic variants accounted for over half of the genetic effects in these phenotypes. Even though GREML-MS is expected to underestimate heritability for traits where the genetic architecture includes the contribution of CNVs, structural variants and very rare variants [64], we were nevertheless able to recover the majority of this heritability following imputation to the Haplotype Reference Consortium. For neuroticism, G plus K estimates were ~30%, even slightly exceeding the narrow-sense heritability estimates meta-analytically derived from family and adoption studies with heterogeneous measurements of personality [33]. However, the K component was dropped for extraversion in our model selection procedure. We believe that is due to the stringent statistical test, as described by Xia et al. if a component only explains ~5% of the phenotypic variance in GS:SFHS, it might escape from model selection procedure (and K is 5% for extraversion). Furthermore, results were less consistent between GREML-KIN and GREML-MS for personality traits. These convergences and divergences between our two methods, and published results, are potentially diagnostic for the genetic architecture of the traits under study.

The GREML-SC method of estimating heritability from unrelated individuals using common genome-wide SNPs, often produces lower heritability estimates than those derived using family-based studies because it relies on LD between genotyped SNPs and causal variants at the population level. Should LD between genotyped SNPs and causal variants be low, then the genetic similarity between a pair of individuals at the causal variant will be different to the genetic similarity at genotyped SNPs, resulting in an underestimation of heritability. In within-family and twin studies, relatedness is based on identity by decent (IBD), where segments of DNA have been inherited from a recent common ancestor. Should a region be IBD between a pair of individuals, then all variants within that segment, except de novo mutations, are shared. Population-based SNP methods are sensitive to allele frequency, whereas IBD methods are blind to such effects. Therefore, the discrepancy between heritability estimates is consistent with the idea that causal variants in low LD with genotyped SNPs account for difference between IBD methods and population-based estimates derived using molecular genetic data.

In the current study, we investigate if variants in poor LD with genotyped SNPs account for additional heritability by using DNA from close family members. Higher genetic relatedness within families leads to an increase in the LD between genotyped SNPs and potentially causal variants, resulting in heritability estimates in our study that are comparable to pedigree-based methods. This provides evidence that for intelligence the gap between the heritability estimates derived using IBD methods and those derived using SNP-based population methods is most likely due to causal variants in low LD with genotyped SNPs. In addition, we were able to model this missing variance and separate it from the additive common genetic effects that are estimated in a GREML-SC analysis based on unrelated individuals. The additional source of additive genetic variance from closely related family members, captured here in our kinship matrix (GRM kin ), would be unmeasured in a GWAS on unrelated individuals using genotyped data.

The use of related individuals can result in the confounding of pedigree genetic effects with shared family environmental effects. We were able to adjust for phenotype similarity driven by couple similarity, family similarity and sibling similarity, but some residual, uncorrected confounding might remain. Potential sources include geographical confounding, e.g., cousins attending the same school, and other environmental similarities that we could not adjust for. Such confounding was not modelled by Xia et al. and if present may represent a source of environmental variance still present in the genetic estimates of GREML-KIN. However, previous work by Conley et al. [68] has shown that although environmental similarity can be correlated with relatedness, the effect this has on heritability is minor.

The three similarity matrices, SRM Sib , SRM Family and SRM Couple captured phenotypic similarity shared between siblings, nuclear family members and couples, respectively. The similarity shared between siblings is a product of additive genetic effects, dominance genetic effects, in addition to any environmental influences. However, by including the GRM g and the GRM kin , what variance remained in SRM Sib is mainly due to environmental influences and some of the total dominance genetic effect as the additive genetic effects are captured by GRM g and GRM kin . Similarly, SRM Family models similarity between nuclear family members, which is composed of additive genetic effects and environmental factors. In the presence of GRM g and GRM kin , what remained in SRM Family will be variance attributable to environmental factors. The SRM Couple represents the similarity between couples, which is mainly due to environmental influences, as well as the effects of assortative mating. However, the effect of couple environment and assortative mating are not confounded with the other matrices SRM’s nor with either of the GRM’s, because of this both the effects of assortative mating and the effects of any shared environmental influences acting to increase couple similarity will remain in the SRM couple .

It should be noted that, the average age of participants in GS:SFHS is 47.4-years-old, which means that the people still cohabiting together are most likely couples whereas parents-offspring and siblings no longer live in the same household. Additionally, dominance has been shown to have little impact on complex traits [69]. Therefore, in our selected model, the variance explained by SRM Sib , SRM Family and SRM Couple will represent past environment shared by siblings and little dominance (SRM Sib ), past environment shared by nuclear family members (SRM Family ) and assortative mating, in addition to potential current environmental factors shared by couples (SRM Couple ).

However, the replication of the GREML-KIN findings with GREML-MS in the subsample of unrelated individuals provides further evidence that the heritability estimates are not majorly affected by residual confounding. Indeed, for intelligence and education both of these methods provide highly similar estimates differing by <4 and 7 percentage points, respectively, well within one standard error of GREML-MS. These estimates in turn are highly similar to the estimate found using traditional pedigree-based analyses [63], indicating that the total narrow-sense heritability of intelligence can be captured using GREML-KIN. When using genotyped or imputed data, GREML-MS has been shown to underestimate the contribution made by rare variants to a polygenic traits by as much as 20% [64]. This is most likely due to the low imputation quality of rare SNPs, which can be ameliorated by using whole-genome sequencing data (WGS) to derive a heritability estimate. However, for traits where very rare variants have an effect (minor allele count > 5), a downward bias is still apparent with WGS [64]. GREML-KIN can also capture non-SNP-associated variants like CNVs, which will also be missed by GREML-MS. This indicates that the accuracy of the heritability estimate provided by GREML-MS is dependent on the frequency of the causal variants that make up trait architecture, albeit much less so than using GREML-SC on genotyped data alone. Using GREML-KIN only a minor underestimation of heritability is seen in Evans et al. [64]. Supplementary Figs. 15 and 16 where regardless of MAF, heritability estimates are as accurate for genotyped data as they are for WGS. This suggests that, in the absence of environmental confounding, GREML-KIN approximates the true heritability better than GREML-MS. However, it should be noted that family-based analysis would be unsuitable for some phenotypes, such as those based on area or household measurements, as is the case with socioeconomic status or household income [70]. Converging estimates from the different methods increase our confidence in their interpretation as genetic effects, whereas the divergences between methods can help diagnose potential unmeasured sources contributing to broad-sense heritability or confounding.

The patterns found in our GREML-MS analyses were consistent with the findings of Evans et al. [64] for neuroticism and fluid intelligence. However, both GREML-KIN and GREML-MS estimates for neuroticism and extraversion fell short of estimates of broad-sense heritability in twin studies (47% [33]; 45% [71]). As previous research has suggested [33, 72], this is consistent with epistasis playing a major role in personality genetics, as a non-additive genetic component is not captured well outside of twin studies. Previous research [72] did not discuss gene-environment correlation and interaction as a plausible cause for heritability estimates being higher in twin than in adoption and family studies, presumably because the shared environment contribution to personality variation was usually estimated not to be different from zero. Still, the difference between twin estimates of heritability and those presented here may also be explained to some extent by gene-by-environment interactions and gene-environment correlations [32].

Another noteworthy divergence occurred between GREML-KIN and GREML-MS results for the personality traits. For extraversion, SNPs with a MAF of 0.001–0.01 explained 17.0% (SE = 9.2) while the K component explained only 4.9% (SE = 5.1) and was dropped from the final selected model. However, the G plus K estimate for extraversion is 16.2%, which is not significantly different from the total heritability estimate provided by GREML-MS (20.9%). This is consistent with the interpretation that there is an effect of the K component for extraversion, which is too small to attain statistical significance in this sample. The results of neuroticism also do not match between GREML-KIN and GREML-MS. The total heritability estimate for GREML-MS was 11.4%, similar to the G estimate, but in GREML-KIN the K explained a further 19% (SE = 2.5), while almost no effect was found for SNPs with a MAF of 0.001–0.01 using GREML-MS. As the GREML-KIN estimate is closer to twin and family study estimates of the narrow-sense heritability for neuroticism, this discrepancy might mean that the causal variants involved in neuroticism are even rarer, or perhaps due to non-SNP-associated genetic variants captured by GREML-KIN, but missed in GREML-MS. Potentially, the slightly lower measurement reliabilities for our personality measures may explain why results are less consistent than for intelligence.

The pattern we found using GREML-KIN is consistent with rare variants explaining much of the gap between heritability estimates from pedigree and GREML-SC analyses, although CNVs, and structural variation could also play a part, because they are poorly tagged by genotyped SNPs as well. This can be seen in Evans et al. [64], who used two genomic matrices, corresponding to the GRM g and the GRM kin in the current study (for continuity, we will use our terms to describe their matrices). By varying the frequency of the causal variants in a simulated data set, Evans et al. showed that even when using only array markers, the total variance captured by these two matrices was equal to the true heritability in the data set, irrespective of the frequency of the causal variants. Consistent with the notion that the pedigree genetic effects captured by the GRM kin are due to the effect of rare variants, GRM kin captured an increasingly greater proportion of variance as the causal variant frequency fell. The reverse was true for the GRM g , which captured less variance as causal variant frequency fell.

We found further, more direct support for an important role of rare variants using GREML-MS, which showed that for each of the cognitive variables examined here, a large contribution to phenotypic variance was made by SNPs with a MAF between 0.001 and 0.01. For extraversion, almost all of the heritability was tagged by low-MAF SNPs. Altogether this indicates that the genetic signal to be found in imputed GWAS is much larger than GREML-SC estimates based on genotyped unrelated individuals would suggest.

In our GREML-MS results for general intelligence and extraversion the relationship between MAF and cumulative genetic variance explained was not proportionately linear, with increasing contributions being made to the genetic variance explained as MAF fell. This pattern contradicts the neutral evolutionary model [65] and suggests that rarer variants have a larger effect on intelligence and extraversion. This is consistent with previous findings that genetic variance in regions of the genome that have undergone purifying selection also make the greatest contributions to intelligence differences [24].

The GREML-KIN results favour the inclusion of a large K component for all traits except extraversion. This is consistent with a major contribution by rare and other poorly tagged variants. Previous work has already suggested a role for mutation-selection balance acting on harm avoidance and novelty seeking [73], traits that are related to neuroticism and extraversion, respectively [74].

A limitation of this the GREML-KIN approach is that X-specific variance will go unnoticed. This is due to males being haploid and females being diploid at these regions and so the expected relationship on X chromosome is different between pairs of individual of the same sex and pairs of individuals of different sexes, even though they share the same degree of relationship, e.g., ~0.5 for mothers-and-daughters but 0 for fathers-and-sons. As all unmodelled variance remains in the residuals, the majority of the variance due to the X chromosome will, therefore, remain in the residuals.

Another limitation is that the variance analyses are blind to the direction of effects and the number of variants involved in each genetic component. If, as we would predict, future work finds that variants with the lowest minor allele frequencies tend to have larger negative effects on intelligence, it would imply a coupling between the selection coefficient of alleles and their effect on intelligence, as selective pressure would act to minimise the frequency of highly deleterious variants. If this coupling were strong [75], future work might infer that selection on intelligence was important in the past, even though current selective pressure appears to go in the opposite direction [76]. If the impact of intelligence on fitness were limited to instances of pleiotropy with, for example, health, as some initial research suggests [20, 21], the coupling between the selection coefficients of alleles and their effect sizes would be expected to be weaker. Selective pressure would act on the health-linked variants, whereas intelligence-linked variants would only be selected to the extent of their pleiotropic effects on health. This would de-couple the selection coefficient of an allele and its effect on intelligence. Therefore, such analyses could disentangle how much directly or indirectly intelligence has been under selection. Future work can use the SNPs known to affect intelligence and personality [17, 18] to empirically quantify the coupling between allele frequency (indicating selection strength) and effect size in order to test this explanation directly, as has been demonstrated for height and BMI [62]. Targeted re-sequencing of enriched genetic regions [24, 77, 78] might be necessary to find very rare genetic variants associated with intelligence and personality, as has proven fruitful for example in prostate cancer research [79].

The sibling similarity component, which was retained in all models of intelligence, tracks the meta-analytic estimate of shared environmental variance (11%) from twin studies almost exactly. However, in our study the sibling component might also include the quarter of the dominance variation that siblings share, because siblings are the only relationship in this study where dominance plays a significant role [44]. In the classical twin design, dominance variation (making dizygotic twins more dissimilar than half the similarity of monozygotic twins) can be obscured by shared environment effects (making dizygotic twins more similar). There is some evidence from other approaches that dominance only plays a minor role in intelligence differences [80,81,82,83].

The family similarity component was only retained in the model for extraversion, although the point estimate was non-zero in the full neuroticism model as well. This is consistent with meta-analytic estimates of shared environment for adults [71]. However, it may also be due to some level of confounding between K and F, where the association between extraversion and the F is due to contributions of the genetic factors accounted for by the K.

The couple similarity component is somewhat complex to interpret. For intelligence and education, there is evidence of assortative mating [84], which will increase both the genetic and environmental similarity between couples. The couple similarity component may mostly reflect this spousal similarity, and possibly also the effects of more recent environmental influences. Beyond that, intelligence is not perfectly stable across the life course and studies of twins in earlier childhood frequently find a sizeable shared environment component. The importance of shared environment is usually said to decline from childhood to adulthood [85], as individuals pick their environmental individual niches (i.e., active gene-environment correlation), but this is based only on environment shared with siblings. However, it may also be that the current environment remains important and that the spouse is a better aggregated indicator of the current environment than the sibling with whom one usually no longer shares a home in adulthood. We find no couple similarity component for personality, which is consistent with much weaker assortative mating on personality, especially neuroticism and extraversion [86,87,88].

In the current study, we were able to exploit the high LD found between members of the same family to estimate the contribution of genetic effects that are normally missed in GREML-SC analyses of GWAS data. Using GREML-KIN, we simultaneously modelled the effect of the family, sibling and couple similarity to avoid potential environmental confounds inflating our estimates of the genetic effects. For intelligence and education, we find that genetic variants poorly tagged on current genotyping platforms explained a substantial proportion of the phenotypic variance, raising our heritability estimates to match those derived using pedigree-based quantitative methods. Such variants can include CNVs, structural variants, and rare variants. We find similar effects for neuroticism. For extraversion, pedigree-associated variants appear to play a smaller role in phenotypic variation. GREML-MS analyses, used with data imputed to the HRC reference panel, allowed us to examine lower frequency variants in a sample of unrelated individuals and provides strong convergent evidence, especially for intelligence and educational attainment. These results indicate that future GWAS using HRC imputation will be successful in finding the large majority of variants associated with intelligence. However for neuroticism whole-genome sequencing is likely to be more successful as our results from GREML-KIN suggest a large contribution from non-SNP/very rare/poorly tagged genetic variants. Finally, our results suggest mutation-selection balance has maintained heritable variation in intelligence, and potentially to some degree also in neuroticism and extraversion, explaining why differences in these traits persist to this day despite selection. Future work should directly measure rare variants, as well as CNVs and structural variants, and test the direction of their effects.