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.

1. Evolutionary ecologists increasingly study reaction norms that are expressed repeatedly within the same individual's lifetime. For example, foragers continuously alter anti-predator vigilance in response to momentto-moment changes in predation risk. Variation in this form of plasticity occurs both among and within individuals. Among-individual variation in plasticity (individual by environment interaction or I 9 E) is commonly studied; by contrast, despite increasing interest in its evolution and ecology, within-individual variation in phenotypic plasticity is not. 2. We outline a study design based on repeated measures and a multilevel extension of random regression models that enables quantification of variation in reaction norms at different hierarchical levels (such as among and within individuals). The approach enables the calculation of repeatability of reaction norm intercepts (average phenotype) and slopes (level of phenotypic plasticity); these indices are not specific to measurement or scaling and are readily comparable across data sets. 3. The proposed study design also enables calculation of repeatability at different temporal scales (such as shortand long-term repeatability), thereby answering calls for the development of approaches enabling scale-dependent repeatability calculations. 4. We introduce a simulation package in the R statistical language to assess power, imprecision and bias for multilevel random regression that may be utilised for realistic data sets (unequal sample sizes across individuals, missing data, etc). 5. We apply the idea to a worked example to illustrate its utility. We conclude that consideration of multilevel variation in reaction norms deepens our understanding of the hierarchical structuring of labile characters and helps reveal the biology in heterogeneous patterns of within-individual variance that would otherwise remain 'unexplained' residual variance.

We present a novel perspective on life-history evolution that combines recent theoretical advances in fluctuating density-dependent selection with the notion of pace-of-life syndromes (POLSs) in behavioural ecology. These ideas posit phenotypic co-variation in life-history, physiological, morphological and behavioural traits as a continuum from the highly fecund, short-lived, bold, aggressive and highly dispersive 'fast' types at one end of the POLS to the less fecund, long-lived, cautious, shy, plastic and socially responsive 'slow' types at the other. We propose that such variation in life histories and the associated individual differences in behaviour can be explained through their eco-evolutionary dynamics with population density - a single and ubiquitous selective factor that is present in all biological systems. Contrasting regimes of environmental stochasticity are expected to affect population density in time and space and create differing patterns of fluctuating density-dependent selection, which generates variation in fast versus slow life histories within and among populations. We therefore predict that a major axis of phenotypic co-variation in life-history, physiological, morphological and behavioural traits (i.e. the POLS) should align with these stochastic fluctuations in the multivariate fitness landscape created by variation in density-dependent selection. Phenotypic plasticity and/or genetic (co-)variation oriented along this major POLS axis are thus expected to facilitate rapid and adaptively integrated changes in various aspects of life histories within and among populations and/or species. The fluctuating density-dependent selection POLS framework presented here therefore provides a series of clear testable predictions, the investigation of which should further our fundamental understanding of life-history evolution and thus our ability to predict natural population dynamics.

Repeatable behavioural traits (‘personality’) have been shown to covary with fitness, but it remains poorly understood how such behaviour–fitness relationships come about. We applied a multivariate approach to reveal the mechanistic pathways by which variation in exploratory and aggressive behaviour is translated into variation in reproductive success in a natural population of blue tits, Cyanistes caeruleus. Using path analysis, we demonstrate a key role for provisioning behaviour in mediating the link between personality and reproductive success (number of fledged offspring). Aggressive males fed their nestlings at lower rates than less aggressive individuals. At the same time, their low parental investment was associated with increased female effort, thereby positively affecting fledgling production. Whereas male exploratory behaviour was unrelated to provisioning behaviour and reproductive success, fast-exploring females fed their offspring at higher rates and initiated breeding earlier, thus increasing reproductive success. Our findings provide strong support for specific mechanistic pathways linking components of behavioural syndromes to reproductive success. Importantly, relationships between behavioural phenotypes and reproductive success were obscured when considering simple bivariate relationships, underlining the importance of adopting multivariate views and statistical tools as path analysis to the study of behavioural evolution.

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Biologists often study phenotypic evolution assuming that phenotypes consist of a set of quasi-independent units that have been shaped by selection to accomplish a particular function. In the evolutionary literature, such quasiindependent functional units are called 'evolutionary characters', and a framework based on evolutionary principles has been developed to characterize them. This framework mainly focuses on 'fixed' characters, i.e. those that vary exclusively between individuals. In this paper, we introduce multilevel variation and thereby expand the framework to labile characters, focusing on behaviour as a worked example. We first propose a concept of 'behavioural characters' based on the original evolutionary character concept. We then detail how integration of variation between individuals (cf. 'personality') and within individuals (cf. 'individual plasticity') into the framework gives rise to a whole suite of novel testable predictions about the evolutionary character concept. We further propose a corresponding statistical methodology to test whether observed behaviours should be considered expressions of a hypothesized evolutionary character. We illustrate the application of our framework by characterizing the behavioural character 'aggressiveness' in wild great tits, Parus major.

Labile characters allow individuals to flexibly adjust their phenotype to changes in environmental conditions. There is growing evidence that individuals can differ both in average expression and level of plasticity in this type of character. Both of these aspects are studied in conjunction within a reaction norm framework. Theoreticians have investigated the factors promoting variation in reaction norm intercepts (average phenotype) and slopes (level of plasticity) of a key labile character: behaviour. A general prediction from their work is that selection will favour the evolution of repeatable individual variation in level of plasticity only under certain ecological conditions. While factors promoting individual repeatability of plasticity have thus been identified, empirical estimates of this phenomenon are largely lacking for wild populations. We assayed aggressiveness of individual male great tits (Parus major) twice during their egg-laying stage and twice during their egg-incubation stage to quantify each male's level of seasonal plasticity. This procedure was applied during six consecutive years; all males breeding in our plots during those years were assayed, resulting in repeated measures of individual reaction norms for any individual breeding in multiple years. We quantified among- and within-individual variation in reaction norm components, allowing us to estimate repeatability of seasonal plasticity. Using social pedigree information, we further partitioned reaction norm components into their additive genetic and permanent environmental counterparts. Cross-year individual repeatability for the intercepts (average aggressiveness) and slopes (level of seasonal plasticity) of the aggressiveness reaction norms were 0·574 and 0·516 respectively. The mean of the posterior distributions suggested modest heritabilities (h = 0·260 for intercepts; h = 0·266 for slopes), but these estimates were relatively uncertain. Males behaved more aggressively in areas with higher breeding densities, and became less aggressive and less plastic with increasing age; plasticity thus varied within individuals and was multidimensional in nature. This empirical study quantified cross-year individual repeatability, heritability and age-related reversible plasticity in behaviour. Acknowledging such patterns of multi-level variation is important not only for testing behavioural ecology theory concerning the evolution of repeatable differences in behavioural plasticity but also for predicting how reversible plasticity may evolve in natural populations.

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