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

Linear mixed e‚ects 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 €lter that determines how eciently phenotypic selection translates into evolutionary change. As a quantity of biological interest, it is important that the denominator, the phenotypic variance, actually reƒects the amount of phenotypic variance in the relevant ecological steŠing. Œe current practice of quantifying heritability from mixed e‚ects models frequently deprives the heritability of variance explained by €xed e‚ects (o‰en leading to upward-bias) and it has been suggested to omit €xed e‚ects when estimating heritabilities. We advocate an alternative option of €Šing complex models incorporating all relevant e‚ects, while including the variance explained by €xed e‚ects into the estimation of heritabilities. Œe 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 e‚ects while still including all biologically relevant sources of variation. We explore the complications arising depending on the nature of the covariates included as €xed e‚ects (e.g. biological or experimental origin, characteristics of biological covariates). Furthermore, we discuss €xed e‚ects in non-linear and generalized linear models when €xed e‚ects. In these cases, the variance parameters depend on the location of the intercept and hence on the scaling of the €xed e‚ects. Integration over the biologically relevant range of €xed e‚ects o‚ers a preferred solution in those situations.