de Villemereuil P, Morrissey M B, Nakagawa S, Schielzeth H
School of Biological Sciences, University of Auckland, Auckland, New Zealand.
School of Evolutionary Biology, University of St Andrews, St Andrews, UK.
J Evol Biol. 2018 Apr;31(4):621-632. doi: 10.1111/jeb.13232. Epub 2018 Feb 15.
Linear mixed-effects models are frequently used for estimating quantitative genetic parameters, including the heritability, as well as the repeatability, of traits. Heritability acts as a filter that determines how efficiently phenotypic selection translates into evolutionary change, whereas repeatability informs us about the individual consistency of phenotypic traits. As quantities of biological interest, it is important that the denominator, the phenotypic variance in both cases, reflects the amount of phenotypic variance in the relevant ecological setting. The current practice of quantifying heritabilities and repeatabilities from mixed-effects models frequently deprives their denominator of variance explained by fixed effects (often leading to upward bias of heritabilities and repeatabilities), and it has been suggested to omit fixed effects when estimating heritabilities in particular. We advocate an alternative option of fitting models incorporating all relevant effects, while including the variance explained by fixed effects into the estimation of the phenotypic variance. The approach is easily implemented and allows optimizing the estimation of phenotypic variance, for example by the exclusion of variance arising from experimental design effects while still including all biologically relevant sources of variation. We address the estimation and interpretation of heritabilities in situations in which potential covariates are themselves heritable traits of the organism. Furthermore, we discuss complications that arise in generalized and nonlinear mixed models with fixed effects. In these cases, the variance parameters on the data scale 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.
线性混合效应模型常用于估计数量遗传参数，包括性状的遗传力以及重复性。遗传力起着一种筛选作用，它决定了表型选择转化为进化变化的效率，而重复性则让我们了解表型性状的个体一致性。作为生物学上感兴趣的量，重要的是，分母（在这两种情况下都是表型方差）要反映相关生态环境中的表型方差量。目前从混合效应模型中量化遗传力和重复性的做法常常使其分母中由固定效应解释的方差缺失（这通常会导致遗传力和重复性的向上偏差），并且有人建议在估计遗传力时尤其要忽略固定效应。我们提倡一种替代方案，即拟合包含所有相关效应的模型，同时将由固定效应解释的方差纳入表型方差的估计中。该方法易于实施，并且能够优化表型方差的估计，例如通过排除由实验设计效应产生的方差，同时仍包含所有生物学上相关的变异来源。我们探讨了在潜在协变量本身就是生物体可遗传性状的情况下遗传力的估计和解释。此外，我们还讨论了具有固定效应的广义和非线性混合模型中出现的复杂情况。在这些情况下，数据尺度上的方差参数取决于截距的位置，因此取决于固定效应的尺度。在固定效应的生物学相关范围内进行积分在这些情况下提供了一个更好的解决方案。
