The Gaussian phenotype of biological measurements

Abstract

Biological measurements are commonly assumed to approximate Gaussian distributions, and normality is routinely assessed as a prerequisite for statistical analysis. However, whether the degree of Gaussianity itself contains biological information remains largely unexplored. Here, we quantified the Gaussianity of biological measurements using the root mean square error of normal quantile-quantile plots (QQ-RMSE). A reference distribution was constructed from 10,249 biological measurements from the National Health and Nutrition Examination Survey (NHANES) 1999-2023, enabling direct comparison of the Gaussian phenotype, defined as the degree to which a biological measurement approximates a Gaussian distribution. Biological measurements exhibited characteristic Gaussian phenotypes. Structural and capacity-related traits, including body measurements, grip strength, spirometry, and red blood cell count, consistently showed low QQ-RMSE values. Homeostatically regulated variables, such as total cholesterol, also exhibited high Gaussianity. In contrast, biomarkers associated with physiological responses or pathology, including triglycerides, C-reactive protein, liver enzymes, serum creatinine, and urinary albumin, showed progressively larger deviations from Gaussianity. Biological normalization further improved Gaussianity: the albumin-to-creatinine ratio consistently exhibited lower QQ-RMSE values than urinary albumin alone across all NHANES survey cycles. These findings indicate that Gaussianity is not merely a statistical assumption but a measurable biological property. We propose the concept of the Gaussian phenotype, in which the degree of Gaussianity reflects biological mechanisms governing variability. This study establishes the first reference atlas of Gaussianity for interpreting biological measurements.