Linear mixed‐effects models are powerful tools for analysing complex datasets with repeated or clustered observations, a common data structure in ecology and evolution. Mixed‐effects models involve complex fitting procedures and make several assumptions, in particular about the distribution of residual and random effects. Violations of these assumptions are common in real datasets, yet it is not always clear how much these violations matter to accurate and unbiased estimation. Here we address the consequences of violations in distributional assumptions and the impact of missing random effect components on model estimates. In particular, we evaluate the effects of skewed, bimodal and heteroscedastic random effect and residual variances, of missing random effect terms and of correlated fixed effect predictors. We focus on bias and prediction error on estimates of fixed and random effects. Model estimates were usually robust to violations of assumptions, with the exception of slight upward biases in estimates of random effect variance if the generating distribution was bimodal but was modelled by Gaussian error distributions. Further, estimates for (random effect) components that violated distributional assumptions became less precise but remained unbiased. However, this particular problem did not affect other parameters of the model. The same pattern was found for strongly correlated fixed effects, which led to imprecise, but unbiased estimates, with uncertainty estimates reflecting imprecision. Unmodelled sources of random effect variance had predictable effects on variance component estimates. The pattern is best viewed as a cascade of hierarchical grouping factors. Variances trickle down the hierarchy such that missing higher‐level random effect variances pool at lower levels and missing lower‐level and crossed random effect variances manifest as residual variance. Overall, our results show remarkable robustness of mixed‐effects models that should allow researchers to use mixed‐effects models even if the distributional assumptions are objectively violated. However, this does not free researchers from careful evaluation of the model. Estimates that are based on data that show clear violations of key assumptions should be treated with caution because individual datasets might give highly imprecise estimates, even if they will be unbiased on average across datasets.

Summary: Growing interest in proximate and ultimate causes and consequences of between‐ and within‐individual variation in labile components of the phenotype – such as behaviour or physiology – characterizes current research in evolutionary ecology. The study of individual variation requires tools for quantification and decomposition of phenotypic variation into between‐ and within‐individual components. This is essential as variance components differ in their ecological and evolutionary implications. We provide an overview of how mixed‐effect models can be used to partition variation in, and correlations among, phenotypic attributes into between‐ and within‐individual variance components. Optimal sampling schemes to accurately estimate (with sufficient power) a wide range of repeatabilities and key (co)variance components, such as between‐ and within‐individual correlations, are detailed. Mixed‐effect models enable the usage of unambiguous terminology for patterns of biological variation that currently lack a formal statistical definition (e.g. ‘animal personality’ or ‘behavioural syndromes’), and facilitate cross‐fertilisation between disciplines such as behavioural ecology, ecological physiology and quantitative genetics.

Individual animals differ in the way they cope with challenges in their environment, comparable with variation in human personalities. The proximate basis of variation in personality traits has received considerable attention, and one general finding is that personality traits have a substantial genetic basis. This poses the question of how variation in personality is maintained in natural populations. We show that selection on a personality trait with high heritability fluctuates across years within a natural bird population. Annual adult survival was related to this personality trait (behaviour in novel environments) but the effects were always opposite for males and females, and reversed between years. The number of offspring surviving to breeding was also related to their parents' personalities, and again selection changed between years. The observed annual changes in selection pressures coincided with changes in environmental conditions (masting of beeches) that affect the competitive regimes of the birds. We expect that the observed fluctuations in environmental factors lead to fluctuations in competition for space and food, and these, in association with variations in population density, lead to a variation in selection pressure, which maintains genetic variation in personalities.

"Natural selection and animal personality" published on 01 Jan 2005 by Brill.