Fixed-effect variance and the estimation of repeatabilities and heritabilities: issues and solutions.

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.

Common garden experiments in the genomic era: new perspectives and opportunities.

The study of local adaptation is rendered difficult by many evolutionary confounding phenomena (for example, genetic drift and demographic history). When complex traits are involved in local adaptation, phenomena such as phenotypic plasticity further hamper evolutionary biologists to study the complex relationships between phenotype, genotype and environment. In this perspective paper, we suggest that the common garden experiment, specifically designed to deal with phenotypic plasticity, has a clear role to play in the study of local adaptation, even (if not specifically) in the genomic era. After a quick review of some high-throughput genotyping protocols relevant in the context of a common garden, we explore how to improve common garden analyses with dense marker panel data and recent statistical methods. We then show how combining approaches from population genomics and genome-wide association studies with the settings of a common garden can yield to a very efficient, thorough and integrative study of local adaptation. Especially, evidence from genomic (for example, genome scan) and phenotypic origins constitute independent insights into the possibility of local adaptation scenarios, and genome-wide association studies in the context of a common garden experiment allow to decipher the genetic bases of adaptive traits.

Detecting adaptive evolution based on association with ecological gradients: orientation matters!

Population genetic signatures of local adaptation are frequently investigated by identifying loci with allele frequencies that exhibit high correlation with ecological variables. One difficulty with this approach is that ecological associations might be confounded by geographic variation at selectively neutral loci. Here, we consider populations that underwent spatial expansion from their original range, and for which geographical variation of adaptive allele frequency coincides with habitat gradients. Using range expansion simulations, we asked whether our ability to detect genomic regions involved in adaptation could be impacted by the orientation of the ecological gradients. For three ecological association methods tested, we found, counter-intuitively, fewer false-positive associations when ecological gradients aligned along the main axis of expansion than when they aligned along any other direction. This result has important consequences for the analysis of genomic data under non-equilibrium population genetic models. Alignment of gradients with expansion axes is likely to be common in scenarios in which expanding species track their ecological niche during climate change while adapting to changing environments at their rear edge.