Fig 1.
(A) We use Fisher’s concept of a multi-dimensional trait space. Under stabilizing selection, an individual’s fitness declines with distance from the optimal phenotype [40]. (B) The selection coefficient experienced by a variant is proportional to the sum of squared effects on all traits. (C) We compute the distribution of derived allele frequencies (q) conditional on s and demography. (D) The distribution of effect sizes for trait 1 (b1) is normally distributed given s. (E) The generative model for q, β, and the observed Z-score at any given site. In C and D, the curves for effectively neutral, moderate and strong selection correspond to and 10−2 respectively.
Fig 2.
Inference of model parameters.
(A)–(C) The joint distributions of minor allele frequencies (MAFs), z-scores, and numbers of hits per trait depend on model parameters as illustrated here. Each graph shows simulated distributions of genome-wide significant hits, with the graphs in each row differing in one of the main axes of our model. (D)–(F) True values of the distributions of f(s) as well as h2/L and L are indicated by the dashed lines; inferences are indicated by solid lines or by point estimates with sleeves and bars indicating 90% bootstrap CIs. The inferred parameters differing between the pair of traits in each row are highlighted in gray. See Sect 9 in S1 Note for parameter values used. Figure data available at: https://doi.org/10.5281/zenodo.17041176.
Fig 3.
Parameter estimates for example traits.
(A) CDF of the distributions of selection coefficients for newly-arising mutations, f(s), estimated for each trait separately, using trait-specific distributions, with 90% confidence envelopes. (B) CDF of the single shared distribution (SSD) of selection coefficients for newly-arising mutations, estimated using all 95 traits together. (C) Properties of example traits. h2 and L are estimated using f(s) from the SSD. Figure data available at: https://doi.org/10.5281/zenodo.17041176.
Fig 4.
(A) QQ-plot of residual p-values for height (each data point is a SNP) under three models: the SSD model provides a good fit to the distribution of z-scores, while two other models fit poorly. (B) For BMI, the SSD model fits most of the z-score distribution, but a few hits are more significant than expected, notably at FTO. (C) QQ-plots for model fits (by trait) for TSD, SSD, and α-models. Figure data available at: https://doi.org/10.5281/zenodo.17041176.
Fig 5.
The distribution allele ages of GWAS hits for all 95 traits (solid blue), estimated using Relate, compared to the distribution of allele ages predicted by our model (dashed blue). Also shown, the distribution of allele ages for neutral frequency-matched SNPs (solid red) and the distribution predicted by a neutral model (dashed red). Allele ages were converted to years by assuming 28 years per generation [54]. Figure data available at: https://doi.org/10.5281/zenodo.17041176.
Fig 6.
Shared genetic architecture under the SSD model.
(A) Distribution of allele frequencies for all causal variants (black), and for genome-wide significant hits (light/dark blue), for our inferred f(s) given British population history. (B) Distributions of selection coefficients at causal variants with different minor allele frequencies. (C) Distributions of squared effect sizes , shown here for three example minor allele frequencies; note that effect sizes are scaled by the natural units of h2/L. For traits with high h2/L, variants within both the light and dark blue regions are genome-wide significant (GWS); for traits with low h2/L, only the dark blue regions are significant. See Sect 9 in S1 Note for parameter values used. Figure data available at: https://doi.org/10.5281/zenodo.17041176.
Fig 7.
Heritability and target size underlie differences between trait architectures:
examples for three traits. (A) Height (blue) and platelet crit (red) have the same heritability per site h2/L, but height has a much higher mutational target size L. This results in many more hits for height (1533) than for platelet crit (648) (2 left panels). However, the marginal distributions of effect sizes, MAFs, and z-scores of hits are nearly identical for the two traits (3 right panels). (B) Height (blue) and FEV1 (gold) differ in h2/L, but have similar L. Consequently, the joint distribution of z-scores and MAFs of their hits are markedly different (2 left panels), as are the marginal distributions of hit effect sizes, MAFs and z-scores (right). (C) After scaling by their respective , and imposing the more stringent scaled significance threshold (corresponding to FEV1) for both traits, the joint distribution of z-scores and MAFs of their hits (2 left panels) and the corresponding marginal distributions (3 right panels) are highly similar. Figure data available at: https://doi.org/10.5281/zenodo.17041176.