The results from our data show that about 23% of variants associated with 41 diseases and other human traits are pleiotropic, and that variants with higher degree of pleiotropy are more common and have average larger effect sizes than less pleiotropic or non-pleiotropic variants (Fig. 1). The proportion of pleiotropic loci found is lower than that reported by Chesmore et al. (2018) (44%) and by Shikov et al. (2020) (49%), and much smaller than that reported by Watanabe et al. (2019) (60%). These differences, however, can be ascribed to a much lower number of traits considered in our study (41) with respect to those considered by Chesmore et al. (2018) (1094 traits), Watanabe et al. (2019) (558 traits) and by Shikov et al. (2020) (543 traits). In addition, as suggested by Shikov et al. (2020), the large proportion of pleiotropic variants detected by Watanabe et al. (2019) could be explained by the use by these authors of sparsely defined trait domains.
In agreement with the results of Chesmore et al. (2018), we found a tendency for the average mean effect size of pleiotropic loci to increase with the degree of pleiotropy (Fig. 1a), which is also in agreement with other observations (Wagner and Zhang 2011). However, Chesmore et al. (2018) reported a decrease in the variance of effect sizes with the degree of pleiotropy whereas we observed an increase in the standard deviation (Fig. 1b). The discrepancy is due to a different way of calculation. Chesmore et al. (2018) calculated the variance of the average values of the multiple effects ascribed to a pleiotropic locus. As they discussed, because the larger the degree of pleiotropy the larger the number of effect sizes averaged, the variance of the mean is decreased with the degree of pleiotropy because of the law of large numbers. In fact, doing the calculation of the variance in that way, we also obtained a decline in the standard deviation of effects within the degree of pleiotropy (Supplemental Fig. S5). In contrast, in our Fig. 1b, we obtained the standard deviation of effect sizes within pleiotropic loci, and then averaged those standard deviations over loci with the same pleiotropic class, observing an increase in the standard deviation with the degree of pleiotropy. Therefore, more pleiotropic loci have a higher disparity of effects on the multiple traits they affect than less pleiotropic loci.
Another difference between our results and those of Chesmore et al. (2018) refers to the levels of pleiotropy found. Whereas we found loci with a maximum of 12 (dichotomous and quantitative traits) associated traits, Chesmore et al. (2018) investigated only dichotomous traits and found loci with a degree of pleiotropy up to 53. This difference can be again ascribed to the much larger number of traits considered by Chesmore et al. (2018) (more than 1000 versus 41). To have the highest possible robustness in the data, we grouped traits with similar genetic architecture, and we analyzed a very restricted set of traits, in particular, only traits for which at least three studies had been reported in the Catalog and for which at least 30 loci had been detected.
We found an increase in minor allele frequency with the degree of pleiotropy (Fig. 1c), in accordance with the observation of Shikov et al. (2020) that rare variants tend to be less pleiotropic than common ones. In agreement with this increase in frequency and effect sizes, the proportional contribution to heritability for each of the traits from more pleiotropic loci was found to be higher than that of less pleiotropic or non-pleiotropic ones (Fig. 1d). Thus, it appears that highly pleiotropic loci may contribute substantially to heritability. This observation is concordant with the idea of the ‘omnigenic’ model suggested by Boyle et al. (2017), for which most loci of the genome might contribute in one way or another to heritability, with genes of high effect size (possibly the most pleiotropic ones) at the center of the genomic network. To explain the larger frequency for more pleiotropic variants, Shikov et al. (2020) provided three possible explanations. First, that a lack of rare pleiotropic variants may be a consequence of a lack of statistical power for their detection. Second, that common variants may have spurious pleiotropy resulting from linkage disequilibrium with different causal variants. In fact, inferring pleiotropy from molecular markers is difficult if the linkage disequilibrium relationships between markers and causal variants are not known with precision (Gianola et al. 2015). And third, that natural purifying selection against highly pleiotropic deleterious variants of large effect size would result in segregating pleiotropic variants with lower effect sizes and higher frequencies. As stated by Shikov et al. (2020), the fact that natural selection against deleterious mutations has been shown to operate on complex trait variation (Gazal et al. 2018; Zeng et al. 2018), would support the third explanation. However, the other two explanations may also play a role.
We analyzed the relationship between the degree of pleiotropy of variants and the strength of background selection attached to their positions. We found that, for the analysis with fewer traits (Pickrell et al. 2016, and our own study) with about 40 traits each, there was a non-significant relationship between B and the degree of pleiotropy (Fig. 3a, b). Nevertheless, some of the most pleiotropic loci found in our study (Table S2) were associated with low values of B, particularly gene GCKR (B = 0.099), which was also found as highly pleiotropic by Chesmore et al. (2018), thus denoting a high impact of background selection. For the larger datasets (Watanabe et al. 2019; Shikov et al. 2020) with many more traits (more than 500) and pleiotropic SNPs (about one hundred and fifty thousand), there was a consistent significant and negative relationship between B and the degree of pleiotropy (Fig. 3c, d). The discrepancy between the non-significant relationships found for the two first datasets and these ones can be that the latter are more comprehensive studies, but there may be other explanations. The results in Fig. 3 refer to different sources of data, considering the average B value of genes in the case of our own data, and that of genomic regions in the case of the other studies. However, for Watanabe et al. (2019) data, the trends were repeated when the average B was obtained from genes (Fig. S3c, d) as well as for individual SNPs (Fig. S3e, f). Moreover, for Shikov et al. (2020) results, the trends were also similar if individual SNPs were considered (Fig. S4c, d). These general tendencies are also shown in Supplemental Material Fig. S6, which shows the mean value of B for a range of pleiotropic degree classes for the main datasets available. Note that the data from Pickrell et al. (2016) and Shikov et al. (2020) do not have results for the non-pleiotropic class, which could contribute to the non-significant relationship found in the former. Therefore, the negative relationship found between B and the degree of pleiotropy is very robust. An additional source of difference between the datasets is that our results arise from the GWAS Catalog whereas those from Watanabe et al. (2019) and Shikov et al. (2020) were obtained from the UK Biobank, and there could be differences between both sources of data, which remain to be disclosed.
Since the relationship between the rate of recombination and the degree of pleiotropy was nearly invariable (Fig. 2), the negative relationship between B and the degree of pleiotropy indicates that the reduction of B with the degree of pleiotropy is not explained by a reduced recombination rate for highly pleiotropic regions. In any case, we obtained the partial regression of B on the degree of pleiotropy, which accounts for the effect of recombination rate. Thus, it can be concluded that more pleiotropic variants are associated with stronger purifying selection. Therefore, even though highly pleiotropic loci detected by GWAS seem to have larger effect sizes (Chesmore et al. 2018 and our Fig. 1a) and frequencies (Fig. 1c), they seem to be subjected to stronger selection than less pleiotropic ones. Variants with a large effect size and a common frequency are easier to detect by GWAS (see Supplementary Material Table S3 for an illustration of this), so this may explain the observations. In fact, the magnitude of pleiotropy is inevitably underestimated because of sampling error and lack of power (Hill and Zhang 2012). In addition, the effect sizes refer to a quantitative trait that may be related with fitness to a higher or lower degree (Keightley and Hill 1990). It has been shown theoretically that variants with a large effect on a quantitative trait but a low correlated effect on fitness can be those more easily detected by GWAS and also those contributing more to the heritability of the trait (Caballero et al. 2015). Finally, in regions of low recombination, a reduction of the effective population size is expected (Hudson and Kaplan 1995; Nordborg et al. 1996; Santiago and Caballero 1998, 2016; Nicolaisen and Desai 2013; Caballero 2020, p. 106). This would imply a larger impact of genetic drift, and therefore, the possibility that deleterious alleles can reach higher frequencies than expected, as has been already shown for schizophrenia variants (Pardiñas et al. 2018). In summary, our results show that highly pleiotropic variants are associated with intense background selection, but those found by GWAS tend to have a larger effect and frequency than less pleiotropic variants. Thus, it may be hypothesized that an unknown number of highly pleiotropic variants of low effect/frequency may pass undetected by GWAS, explaining these results.
The study by Shikov et al. (2020) disclosed that protein-level pleiotropy due to ubiquitously expressed genes is the most prevalent form of pleiotropy. This is coherent with the recognized implication of the general metabolic pathways in pleiotropic effects (Kacser and Burns 1981). It is then consistent with the view that ubiquitous and general function proteins must be constrained by purifying selection. Note, however, that the B statistic can also be affected by other selection effects such as hitchhiking of favorable alleles and biased gene conversion (McVicker et al. 2009), so that its value does not only describe negative selection. In addition, many pleiotropic effects are expected to act in the same direction of reducing fitness, but some can operate as antagonistic pleiotropy (Rodríguez et al. 2017), as found for psychiatric disorders (Muntané et al. 2021). Thus, it is necessary to further disentangle the selection forces involved in highly pleiotropic loci.