Unpacking the heritability of body mass index and other ratios

Ratios of weight to height, especially body mass index (BMI = kg/m² ), are often used in epidemiological and genetic studies of health, but the limitations of quantitative genetic analysis of ratios are not widely known. The heritability of these ratios can be closely approximated from a bivariate quantitative genetic model of weight and height which clarifies how BMI heritabilities change.

I explored this bivariate approximation and alternative measures through simulated datasets fit with linear mixed models. Simulated data were based on published heritabilities and other statistics for BMI and related anthropometric dimensions from four human samples.

Inspection of the bivariate approximation and analysis of simulated data show the heritability of weight/height crucially depends on the phenotypic (r_P ) and genetic correlations (r_A ) between weight and height. Changes in these correlations can have dramatic effects on the heritability of BMI. For example, when r_P  ≪ r_A heritability of BMI is reduced to 35-50% of its value when the correlations are equal.

Increasing adiposity likely decreases the phenotypic correlations more than the genetic correlation resulting in reduced heritability of the ratio. This contrasts with the commonly reported stability or increase of BMI heritability and implies it may result from increased genetic variance in weight in obesogenic environments. The bivariate model offers other advantages over ratios, including estimating the conditional genetic variance or heritability of weight that is unassociated with height, which may prove useful in quantitative and molecular genetic studies.