Large effects and the infinitesimal model.

Area of Science:

• Quantitative genetics
• Population genetics
• Statistical genetics

Background:

• The infinitesimal model assumes many loci with similar effect sizes for quantitative traits.
• This model relies on the Central Limit Theorem, predicting Normal distributions for trait variations.

Purpose of the Study:

• Investigate the impact of non-similar genetic effect sizes on quantitative genetics models.
• Explore alternative statistical distributions when effect sizes vary.

Main Methods:

• Analyzed tail exponents of effect size distributions from genome-wide association studies (GWAS).
• Applied a different Central Limit Theorem for non-Gaussian distributions.
• Investigated implications for trait evolution models.

Main Results:

• Empirical tail exponents for human disease traits fall between 1 and 2.
• This suggests stable distributions, where large effects remain significant.
• Independence of offspring trait deviations implies Gaussianity only under specific conditions.

Conclusions:

• The assumption of similar effect sizes is critical for the Gaussian nature of the infinitesimal model.
• Non-Gaussian models are necessary when genetic effect sizes have heavy tails.
• Tracking large-effect loci is crucial for understanding trait evolution with non-Gaussian genetics.