Here, we report the results from a GWAS of intelligence in middle to older adulthood. Despite the fact that no specific genetic variants have been robustly associated with human intelligence, apart perhaps for APOE at older ages,34, 35 our results show for the first time that a substantial proportion (∼40–50%) of variation in human intelligence is associated with common SNPs (minor allele frequency >0.01) that are in LD with causal variants. These results are consistent with a highly polygenic model because we detect variation across the entire genome. If the narrow-sense heritability for intelligence is ∼0.6 in the age groups studied in the CAGES samples,3, 36 then not all additive variation is accounted for by our analyses. One reason for this difference could be that causal variants for intelligence have, on average, a lower minor allele frequency than the SNPs on the chip used. Such a frequency difference causes imperfect LD between the genotyped SNPs and unobserved causal variants. Traditional pedigree analysis is not affected by such imperfect LD because it is based on the correct expected identity-by-descent coefficients at loci (including loci with causal variants) of relatives. It is also possible that causal variants are present in regions of the genome not well covered by the commercial SNP arrays. Nevertheless, our results suggest that common SNPs that are in LD with unknown causal variants account for more than half of all additive genetic variation for human intelligence. The method we have used here does not attempt to test the effects of single SNPs; rather, it tests their accumulated effects. It estimates the joint effect of genotyped SNPs and that effect reflects their LD with unknown causal variants. These variants are not necessarily common SNPs or, indeed, even SNPs; however, causal variants are in sufficient LD with the genotyped SNPs to be captured.29

One genome-wide significant association, FNBP1L, was reported with fluid intelligence from a gene-based test for association.27 FNBP1L (previously known as Toca-1) binds to both CDC42 and WASL, promoting CDC42-induced actin polymerization by activating the N-WASP–WIP complex,37 and is thus implicated in a pathway that links cell surface signals to the actin cytoskeleton, a system that allows the movement of cells and cellular processes. FNBP1L is strongly expressed in neurons, including hippocampal neurons, in developing brains and regulates neuronal morphology. The genome-wide significance threshold for the gene-based test is different to that for the SNP-based test because fewer hypotheses were tested (∼17 800). This result did not replicate in the NCNG sample; however, the sample size of the validation cohort was much smaller than the discovery set and it will be necessary to attempt replication of this finding in larger samples before pursuing it further.

Only 1% (approximately) of the variance was explained in the prediction analysis due to the individual SNP effects being very small and therefore estimated with much error, which detracts to a great extent from the accuracy (8–11%) of the prediction equation.29 Our finding that 40–50% of phenotypic variation is explained by all SNPs is fully consistent with the low precision of a predictor based upon a discovery sample of ∼3500 individuals; estimation of the SNPs’ effects is different from prediction accuracy.29, 38 The difference lies in the precision with which individual SNP effects are estimated. Although we can obtain an unbiased estimate of a SNP effect (using, for example, a least squares estimator), a prediction of a phenotype using the estimated SNP effect suffers from the sampling variance with which the effect is estimated. In the case of intelligence, the individual effect sizes are very small so that they are estimated with much error. One explanation of this apparent paradox is to consider the extreme case of a single variant when it is known that this variant is associated with the trait but the effect size is not known and needs to be estimated. Estimating its effect size will be unbiased across repeated samples from the same population and the standard error of estimation informs about the precision (standard error) of the estimate of effect size. This is the scenario analogous to our estimate of the variance explained by all SNPs. Now consider that, for each (unbiased) estimate of effect size, we make a prediction of phenotypes in an independent sample based upon the estimated effect size of the variant in the discovery sample. The correlation between predicted value and actual phenotype will depend on how well the variant has been estimated—the worse the estimate of the effect size of the variant in the discovery sample, the worse will be the variance explained by the predictor in the validation sample. This is the scenario analogous to our prediction analysis.

There are other possible reasons for being unable to predict phenotypes with greater precision. First, different cognitive phenotypes were used in each cohort. However, this should not be over-emphasized as it has been shown clearly that the general factors derived from different mental test batteries tend to rank people almost identically.2 In the case of crystallized intelligence—where single tests were used—different vocabulary tests are very highly correlated. Second, there may be genetic differences between the UK and Norwegian populations, which could result in dissimilar patterns of LD39 (Supplementary Figure 1). However, this is unlikely to be important because LD is very similar across European populations.39

The reason why this and other GWAS analyses of complex diseases and traits are unable to detect strong individual signals—and why there has been much concern about the ‘missing heritability’40—is probably because the individual effects of common SNPs are too small to pass the stringent genome-wide significance level. This suggests that human intelligence and perhaps other complex traits are highly polygenic, and that very large sample sizes are required to detect such small individual effects, if the same experimental design is used, which relies on LD between common SNPs and causal variants. These findings are consistent with the recently reported results for other complex traits, including schizophrenia33 and human height.28 If genetic variation that is not captured through LD with common SNPs is due to rare variants with large effect sizes, then other experimental designs such as those employing exome or whole genome resequencing may facilitate the identification of genes and/or gene variants that are associated with human intelligence.

Can the results reported here be explained by population stratification or a correlation between environmental and genetic similarity? A number of reasons suggest strongly that these explanations are unlikely. The results were consistent when we estimated genetic variance within sub-populations and when we adjusted for up to 20 principal components (Supplementary Table 2). The observation that individual cohorts do not show an inflation of the test statistic, but the combined sample does, would require undetected spurious phenotype–genotype associations due to stratification in all cohorts to be in the same direction, which seems very unlikely. We recently showed that when investigating a trait under polygenic inheritance, increasing the sample size would indeed be expected to increase the inflation factor.41 A correlation between environmental and genetic similarity might occur if similarity due to environmental factors between relatives segregates with the degree of separation. For example, cousins five times removed might be more similar than cousins six times removed because they have a more similar environment. This argument applies to single SNP associations with any complex trait, and there is no evidence that the robustly associated variants from GWAS are spurious in this respect. Moreover, we estimated the actual amount of genome sharing between very distant relatives, which is different from the expected amount of sharing if we knew the entire pedigree of all individuals. In fact, the more distantly related a pair of individuals is from the pedigree, the larger the amount of variation in actual genome-wide sharing around this expectation (see Supplementary Information for further detail).28, 42 Finally, we partitioned genetic variation to individual chromosomes by fitting the relationship matrices from all autosomes simultaneously in the model. For very distant relatives, as we have in our study, this method is robust to stratification.29

What do our results imply about the heritability of intelligence? If our estimated relationships had been based on all causal variants instead of being derived from SNPs that may be in LD with such variants, then we would have had an unbiased estimate of the full narrow-sense heritability. Therefore, our estimates provide a lower bound for the narrow-sense heritability, due to imperfect LD between the genotyped SNPs and unknown causal variants. Our estimates are based upon realized relationships between very distant relatives and not on pedigree relationships between close relatives. This breaks up a possible correlation (confounding) between genetic and environmental factors, since the variation in realized relationships given pedigree relations is large for distant relatives. Our estimates of the phenotypic variance explained by all SNPs are ∼0.4–0.5, and we therefore conclude that the narrow-sense heritability for human intelligence is large and consistent with the inference from twin and family studies.

The estimates of the total proportion of variance explained for g f and g c are not significantly different from each other. Nor are the prediction accuracies for g f and g c in the Norwegian replication sample. However, a larger sample size is required to differentiate between any genetic architecture of these two traits.

In summary, we report the first study to show that a large proportion of the heritability estimate of intelligence in middle to older adulthood can be traced to biological variation using SNP data. It is the first to show biologically and unequivocally that human intelligence is highly polygenic and that purely genetic (SNP) information can be used to predict intelligence. Our findings imply that very large sample sizes will be needed to detect individual loci with genome-wide significance and that the majority of additive genetic variation for human intelligence is not explained by rare variants that are not in LD with common SNPs.