Fixed effect variance and the estimation of the heritability: Issues and solutions

Abstract

Linear mixed effects models are frequently used for estimating quantitative genetic parameters, including the heritability, of traits of interest. Heritability is an important metric, because it acts as a filter that determines how efficiently phenotypic selection translates into evolutionary change. As a quantity of biological interest, it is important that the denominator, the phenotypic variance, actually reflects the amount of phenotypic variance in the relevant ecological stetting. The current practice of quantifying heritability from mixed effects models frequently deprives the heritability of variance explained by fixed effects (often leading to upward-bias) and it has been suggested to omit fixed effects when estimating heritabilities. We advocate an alternative option of fitting complex models incorporating all relevant effects, while including the variance explained by fixed effects into the estimation of heritabilities. The approach is easily implemented (an example is provided) and allows corrections for the estimation of heritability, such as the exclusion of variance arising from experimental design effects while still including all biologically relevant sources of variation. We explore the complications arising depending on the nature of the covariates included as fixed effects (e.g. biological or experimental origin, characteristics of biological covariates). Furthermore, we discuss fixed effects in non-linear and generalized linear models when fixed effects. In these cases, the variance parameters depend on the location of the intercept and hence on the scaling of the fixed effects. Integration over the biologically relevant range of fixed effects offers a preferred solution in those situations.