Summary 1.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. 2. 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. 3. 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. 4. 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. 5. 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.

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.

Individual animals frequently exhibit repeatable differences from other members of their population, differences now commonly referred to as 'animal personality'. Personality differences can arise, for example, from differences in permanent environmental effects-including parental and epigenetic contributors-and the effect of additive genetic variation. Although several studies have evaluated the heritability of behaviour, less is known about general patterns of heritability and additive genetic variation in animal personality. As overall variation in behaviour includes both the among-individual differences that reflect different personalities and temporary environmental effects, it is possible for personality to be largely genetically influenced even when heritability of behaviour per se is quite low. The relative contribution of additive genetic variation to personality variation can be estimated whenever both repeatability and heritability are estimated for the same data. Using published estimates to address this issue, we found that approximately 52% of animal personality variation was attributable to additive genetic variation. Thus, while the heritability of behaviour is often moderate or low, the heritability of personality is much higher. Our results therefore (i) demonstrate that genetic differences are likely to be a major contributor to variation in animal personality and (ii) support the phenotypic gambit: that evolutionary inferences drawn from repeatability estimates may often be justified.

The pace-of-life syndrome hypothesis predicts that individual differences in behaviour should integrate with morphological, physiological, and life-history traits along a slow to fast pace-of-life continuum. For example, individuals with a "slow" pace-of-life are expected to exhibit a slower growth rate, delayed reproduction, longer lifespans, have stronger immune responses, and are expected to avoid risky situations relative to "fast" individuals.If supported this hypothesis would help resolve ecological and evolutionary questions regarding the origin and maintenance of phenotypic variation. Support for the pace-of-life syndrome hypothesis has, however, been mixed. Here we conducted a meta-analysis of 42 articles and 179 estimates testing the pace-of-life syndrome hypothesis as it applies to the integration of behaviours with physiological or life-history traits. We found little overall support for the pace-of-life syndrome hypothesis with the mean support estimated as r = 0.06. Support for the pace-of-life syndrome hypothesis was significantly higher in invertebrates (r = 0.23) than vertebrates (r = 0.02) and significantly higher when based onThe lack of overall support found in our analyses suggests that general assertions 24 regarding phenotypic integration due to "pace-of-life" and should be re-evaluated. 25 4 Significance StatementThe pace-of-life syndrome hypothesis has been proposed as an overall organizational framework for the integration of behavioural, life-history, and physiological traits. This hypothesis provides potentially profound insights into how and why phenotypic traits might covary and why phenotypic variation may be maintained within populations. Over the last seven years this organizational framework has been intensively investigated as it pertains to relationships between behaviour and other traits. Here we conducted an overall analysis of whether the hypothesis was supported. Despite considerable research investment across behavioural ecology, we did not find that available data supported the pace-of-life syndrome hypothesis. This suggests that either the hypothesis has been inappropriately tested or is not generally applicable.

No abstract