Within-individual Correlations Research Articles

Within-individual versus between-individual predictors of antisocial behaviour: A longitudinal study of young people in Victoria, Australia.

In an influential 2002 paper, Farrington and colleagues argued that to understand 'causes' of delinquency, within-individual analyses of longitudinal data are required (compared to the vast majority of analyses that have focused on between-individual differences). The current paper aimed to complete similar analyses to those conducted by Farrington and colleagues by focusing on the developmental correlates and risk factors for antisocial behaviour and by comparing within-individual and between-individual predictors of antisocial behaviour using data from the youngest Victorian cohort of the International Youth Development Study, a state-wide representative sample of 927 students from Victoria, Australia. Data analysed in the current paper are from participants in Year 6 (age 11-12 years) in 2003 to Year 11 (age 16-17 years) in 2008 (N = 791; 85% retention) with data collected almost annually. Participants completed a self-report survey of risk and protective factors and antisocial behaviour. Complete data were available for 563 participants. The results of this study showed all but one of the forward- (family conflict) and backward-lagged (low attachment to parents) correlations were statistically significant for the within-individual analyses compared with all analyses being statistically significant for the between-individual analyses. In general, between-individual correlations were greater in magnitude than within-individual correlations. Given that forward-lagged within-individual correlations provide more salient measures of causes of delinquency, it is important that longitudinal studies with multi-wave data analyse and report their data using both between-individual and within-individual correlations to inform current prevention and early intervention programs seeking to reduce rates of antisocial behaviour.

Sources of intraspecific variation in sleep behaviour of wild great tits

Ecologists have recently begun to recognize sleep as a behaviour that is important in animal ecology. The first steps have been taken to characterize sleep in free-living birds, but it is unclear to what extent these results can be generalized between species. To describe sleep behaviour in the wild, we videorecorded great tits, Parus major, in their roosting boxes during two consecutive winters and individuals in captivity for comparison. Here, we examined endogenous and exogenous correlates of sleep behaviour in free-living great tits and addressed the potential confounding issues of studying avian sleep in captivity. Like that in blue tits, Cyanistes caeruleus, sleep behaviour in great tits was strongly related to season, and was affected by sex, age and the environment. Although literature suggests relationships between sleep and risk-taking behaviours, possibly arising from stable differences in physiological state, sleep behaviour appeared to be plastic in great tits, and was not predicted by between-individual variation in exploratory tendencies. Captive tits initiated sleep later than wild individuals, even under natural photoperiodic conditions, suggesting that captivity alters timing and duration of sleep in great tits. Long-term repeatability in sleep behaviour was low for all variables, except morning latency (high repeatability) and evening box entry time, evening latency and frequency of awakenings (no detectable repeatability). Variation in sleep behaviour may largely represent within-individual differences in daily sleep requirements. Our study describes how different observable components of sleep are intercorrelated by providing evidence for significant within-individual correlations between sleep behaviours, which represent the integration of plasticity between traits. Consistent with low repeatability, low between-individual correlations suggest substantial behavioural plasticity in sleep, rather than a correlational structure leading to clear sleep ‘syndromes’. Our study provides quantitative evidence for the factors producing phenotypic plasticity in behavioural sleep in an ecological context.

Regeneration rate after fission in the fissiparous sea star Allostichaster capensis (Asteroidea)

Many studies have focused on the regeneration rate of arms in Asteroidea but no studies have focused on the regeneration rate after fission. Allostichaster capensis is a fissiparous sea star with a wide range of distribution. In Golfo Nuevo (42°46’49’’ S - 64°59’ 26’’ W) sea stars undergo fission every spring and summer and regenerate the rest of the year. To analyze the regeneration rate, we conducted an experiment with sea stars collected just before fission. After sea stars underwent fission, the length of the three non-regenerating and the three regenerating arms were measured weekly. The arm length (regenerating and non-regenerating) was used in non-Linear Mixed Effect models in order to account for within-individual correlation in different models. The regenerating arms regenerate according to a Quadratic model, while the non-regenerating arms regenerate according to a linear model. In the regenerating arms, the regeneration rate was estimated to be 0.1 mm.week-1 and in the non-regenerating arms, the growth rate was 0.004 mm.week -1. Sea stars regenerate ca. 20 % of the arm in one month, and it takes about 5 months to be completely regenerated. At the beginning, the regeneration rate is fast generating the growth of the arms, once the pyloric caeca and gonads are present inside the arms the regeneration rate slows down probably due to allocation to gametes and pyloric caeca and arms. The factors that regulate the regeneration rate are unknown. However, food availability and energy storage seem to play an important role.

Metabolic decoupling in daily life in patients with panic disorder and agoraphobia

Various studies have assessed autonomic and respiratory underpinnings of panic attacks, yet the psychophysiological functioning of panic disorder (PD) patients has rarely been examined under naturalistic conditions at times when acute attacks were not reported. We hypothesized that emotional activation in daily life causes physiologically demonstrable deviations from efficient metabolic regulation in PD patients. Metabolic coupling was estimated as within-individual correlations between heart rate (HR) and indices of metabolic activity, i.e., physical activity (measured by 3-axial accelerometry, Acc), and minute ventilation (Vm, measured by calibrated inductive plethysmography, as proxy for oxygen consumption). A total of 565 daytime hours were recorded in 19 PD patients and 20 healthy controls (HC). Pairwise cross-correlations of minute-by-minute averages of these metabolic indices were calculated for each participant and then correlated with several indices of self-reported anxiety. Ambulatory HR was elevated in PD (p = .05, d = 0.67). Patients showed reduced HR-Acc (p < .006, d = 0.97) and HR-Vm coupling (p < .009, d = 0.91). Combining Vm and Acc to predict HR showed the strongest group separation (p < .002, d = 1.07). Discriminant analyses, based on the combination of Vm and Acc to predict HR, classified 77% of all participants correctly. In PD, HR-Acc coupling was inversely related to trait anxiety sensitivity, as well as tonic and phasic daytime anxiety. The novel method that was used demonstrates that anxiety in PD may reduce efficient long-term metabolic coupling. Metabolic decoupling may serve as physiological characteristic of PD and might aid diagnostics for PD and other anxiety disorders. This measure deserves further study in research on health consequences of anxiety and psychosocial stress.

Legitimization and Delegitimization of Social Hierarchy

Although status and wealth are related facets of social stratification, their association is only moderate. In this article, we demonstrate that justification of wealth versus status can be independent processes. To this end, we introduce a novel, nondeclarative measure of system justification. The measure is based on within-individual correlations between the judgments of how a group “is doing” and how it “should be doing.” Two studies demonstrated that the between-group differentiation in terms of material wealth was delegitimized—the more a group was perceived as wealthy, the less it was desired to be wealthy. However, the between-group differentiation in terms of status was generally legitimized—the more a group was perceived as influential, the more it was desired to be influential. We conclude by discussing the role of sociopolitical context in active legitimization and delegitimization of different aspects of the system.

Familial aggregation of candidate phenotypes for borderline personality disorder.

Borderline personality disorder (BPD) and its core Diagnostic and Statistical Manual of Mental Disorders (DSM) factor-analytically derived phenotypes aggregate in families. To potentially inform future conceptualizations of BPD, this study examined the familial aggregation and co-aggregation with BPD of 3 additional candidate phenotypes for BPD psychopathology: anxiousness, aggressiveness, and cognitive dysregulation. Participants included 347 probands (126 with BPD, 128 without BPD, and 93 with major depressive disorder) and 814 parents and siblings of probands. All participants completed diagnostic assessments and scales assessing the candidate phenotypes. The familial aggregation of phenotypes (correlation of level of phenotype between family members), the familial co-aggregation of phenotypes with BPD (correlation of phenotype with BPD between family members), and the within-individual correlation of phenotypes with BPD were assessed. All 3 candidate phenotypes showed high levels of familial aggregation (rs = .14 - .53, ps < .001), the magnitudes of which were comparable with DSM-based core sectors of psychopathology. Anxiousness and cognitive dysregulation showed strong within-individual associations with BPD (rs = .55 and .46, respectively; ps < .001) and substantial familial co-aggregation with BPD (rs = .12 and .13, respectively; ps ≤ .002). In contrast, aggressiveness showed a weak within-individual association with BPD (r = .11, p = .12) and little familial co-aggregation with BPD (r = .05, p = .21). These findings suggest that anxiousness and cognitive dysregulation are promising phenotypes for BPD psychopathology that move beyond factor-analytically based conceptualizations. In contrast, aggressiveness was only weakly related to BPD, suggesting that this phenotype may not represent an essential feature of this disorder.

Within-individual correlations reveal link between a behavioral syndrome, condition and cortisol in free-ranging Belding's ground squirrels.

Animals often exhibit consistent individual differences in behavior (i.e. animal personality) and correlations between behaviors (i.e. behavioral syndromes), yet the causes of those patterns of behavioral variation remain insufficiently understood. Many authors hypothesize that state-dependent behavior produces animal personality and behavioral syndromes. However, empirical studies assessing patterns of covariation among behavioral traits and state variables have produced mixed results. New statistical methods that partition correlations into between-individual and residual within-individual correlations offer an opportunity to more sufficiently quantify relationships among behaviors and state variables to assess hypotheses of animal personality and behavioral syndromes. In a population of wild Belding's ground squirrels (Urocitellus beldingi) we repeatedly measured activity, exploration, and response to restraint behaviors alongside glucocorticoids and nutritional condition. We used multivariate mixed models to determine whether between-individual or within-individual correlations drive phenotypic relationships among traits. Squirrels had consistent individual differences for all five traits. At the between-individual level, activity and exploration were positively correlated whereas both traits negatively correlated with response to restraint, demonstrating a behavioral syndrome. At the within-individual level, condition negatively correlated with cortisol, activity and exploration. Importantly, this indicates that although behavior is state-dependent, which may play a role in animal personality and behavioral syndromes, feedback mechanisms between condition and behavior appear not to produce consistent individual differences in behavior and correlations between them.

Baseline and stress-induced glucocorticoid concentrations are not repeatable but covary within individual great tits (Parus major)

In evolutionary endocrinology, there is a growing interest in the extent and basis of individual variation in endocrine traits, especially circulating concentrations of hormones. This is important because if targeted by selection, such individual differences present the opportunity for an evolutionary response to selection. It is therefore necessary to examine whether hormone traits are repeatable in natural populations. However, research in this area is complicated by the fact that different hormone traits can be correlated. The nature of these trait correlations (i.e., phenotypic, within-, or among-individual) is critically relevant in terms of the evolutionary implications, and these in turn, depend on the repeatability of each hormone trait. By decomposing phenotypic correlations between hormone traits into their within- and among-individual components it is possible to describe the multivariate nature of endocrine traits and generate inferences about their evolution. In the present study, we repeatedly captured individual great tits (Parus major) from a wild population and measured plasma concentrations of corticosterone. Using a mixed-modeling approach, we estimated repeatabilities in both initial (cf. baseline; CORT0) and stress-induced concentrations (CORT30) and the correlations between those traits among- and within-individuals. We found a lack of repeatability in both CORT0 and CORT30. Moreover, we found a strong phenotypic correlation between CORT0 and CORT30, and due to the lack of repeatability for both traits, there was no among-individual correlation between these two traits—i.e., an individual’s average concentration of CORT0 was not correlated with its average concentration of CORT30. Instead, the phenotypic correlation was the result of a strong within-individual correlation, which implies that an underlying environmental factor co-modulates changes in initial and stress-induced concentrations within the same individual over time. These results demonstrate that (i) a phenotypic correlation between two hormone traits does not imply that the traits are correlated among individuals; (ii) the importance of repeated sampling to partition within- and among-individual variances and correlations among labile physiological traits; and (iii) that environmental factors explain a considerable fraction of the variation and co-variation in hormone concentrations.

The importance of individual developmental variation in stage-structured population models.

Population stage structure is fundamental to ecology, and models of this structure have proven useful in many different systems. Many ecological variables other than stage, such as habitat type, site occupancy and metapopulation status are also modelled using transitions among discrete states. Transitions among life stages can be characterised by the distribution of time spent in each stage, including the mean and variance of each stage duration and within-individual correlations among multiple stage durations. Three modelling traditions represent stage durations differently. Matrix models can be derived as a long-run approximation from any distribution of stage durations, but they are often interpreted directly as a Markov model for stage transitions. Statistical stage-duration distribution models accommodate the variation typical of cohort development data, but such realism has rarely been incorporated in population theory or statistical population models. Delay-differential equation models include lags but no variation, except in limited cases. We synthesise these models in one framework and illustrate how individual variation and correlations in development can impact population growth. Furthermore, different development models can yield the same long-term matrix transition rates but different sensitivities and elasticities. Finally, we discuss future directions for estimating realistic stage duration models from data.

The evolution of signal–reward correlations in bee- and hummingbird-pollinated species ofSalvia

Within-individual variation in floral advertising and reward traits is a feature experienced by pollinators that visit different flowers of the same plant. Pollinators can use advertising traits to gather information about the quality and amount of rewards, leading to the evolution of signal-reward correlations. As long as plants differ in the reliability of their signals and pollinators base their foraging decisions on this information, natural selection should act on within-individual correlations between signals and rewards. Because birds and bees differ in their cognitive capabilities, and use different floral traits as signals, we tested the occurrence of adaptive divergence of the within-individual signal-reward correlations among Salvia species that are pollinated either by bees or by hummingbirds. They are expected to use different floral advertising traits: frontal traits in the case of bees and side traits in the case of hummingbirds. We confirmed this expectation as bee- and hummingbird-pollinated species differed in which specific traits are predominantly associated with nectar reward at the within-individual level. Our findings highlight the adaptive value of within-individual variation and covariation patterns, commonly disregarded as 'environmental noise', and are consistent with the hypothesis that pollinator-mediated selection affects the correlation pattern among floral traits.

Methods for Quantifying Training in Sprint Kayak

The aims of this study were to determine the validity of the session rating of perceived exertion (session-RPE) method by comparing 3 different scales of perceived exertion with common measures of training load (TL). A secondary aim was to verify the relationship between TLs, fitness, and performance in Sprint Kayak athletes. After laboratory assessment of maximal oxygen uptake (V[Combining Dot Above]O2peak) and lactate threshold, the athletes performed on water time trials over 200 and 1,000 m. Training load was quantified for external (distance and speed) and internal (session-RPE: 6-20, category ratio [CR]-10 and CR-100 scales, training impulse [TRIMP], and individual TRIMP). Ten (6 male, 4 female) well-trained junior Sprint Kayak athletes (age 17.1 ± 1.2 years; V[Combining Dot Above]O2peak 4.2 ± 0.7 L·min) were monitored over a 7-week period. There were large-to-very large within-individual correlations between the session distance and the various heart rate (HR) and RPE-based methods for quantifying TL (0.58-0.91). Correlations between the mean session speed and various HR- and RPE-based methods for quantifying TL were small to large (0.12-0.50). The within-individual relationships between the various objective and subjective methods of internal TL were large to very large (0.62-0.94). Moderate-to-large inverse relationships were found between mean session-RPE TL and various aerobic fitness variables (-0.58 to -0.37). Large-to-very large relationships were found between mean session-RPE TL and on water performance (0.57-0.75). In conclusion, session-RPE is a valid method for monitoring TL for junior Sprint Kayak athletes, regardless of the RPE scale used. The session-RPE TL relates to fitness and performance, supporting the use of session-RPE in Sprint Kayak training.

Among- and within-individual correlations between basal and maximal metabolic rates in birds.

The aerobic capacity model proposes that endothermy is a by-product of selection favouring high maximal metabolic rates (MMR) and its mechanistic coupling with basal metabolic rate (BMR). Attempts to validate this model in birds are equivocal and restricted to phenotypic correlations (rP), thus failing to distinguish among- and within-individual correlations (rind and re). We examined 300 paired measurements of BMR and MMR from 60 house sparrows before and after two levels of experimental manipulation - testosterone implants and immune challenge. Overall, repeatability was significant in both BMR (R=0.25±0.06) and MMR (R=0.52±0.06). Only the testosterone treatment altered the rP between BMR and MMR, which resulted from contrasting effects on rind and re. While rind was high and significant (0.62±0.22) in sham-implanted birds, re was negative and marginally non-significant (-0.15±0.09) in testosterone-treated birds. Thus, the expected mechanistic link between BMR and MMR was apparent, but only in birds with low testosterone levels.

Validating the Remarriage Belief Inventory as a Dyadic Measure for Stepcouples

Stepcouples remain a comparatively understudied group and few established measures specific to these couples exist. The Remarriage Belief Inventory assesses beliefs and attitudes relevant to couple dynamics in stepfamilies and has been validated using samples of individuals. An important next step in instrument development is the examination of the factorial structure for use with husband–wife dyads. Results from a dyadic confirmatory factor analysis using a sample of 631 stepcouples confirmed the structure of a final 21-item measure with seven subscales, with all but one subscale having adequate individual reliability. Within-couple correlations showed a strong relationship among many remarriage beliefs, yet they suggest that husbands and wives may be differentially influenced by partners’ beliefs. Within-individual correlations among subscales provide support for basic criterion validity. Implications and the future utility of this measure to examine dyadic processes in stepfamilies are discussed.

Multivariate zero-inflated modeling with latent predictors: Modeling feedback behavior

In educational studies, the use of computer-based assessments leads to the collection of multiple outcomes to assess student performance. The student-specific outcomes are correlated and often measured in different scales, such as continuous and count outcomes. A multivariate zero-inflated model with random effects is proposed and adapted for the challenging situation where the multiple outcomes are zero-inflated and possibly right truncated. The joint model consists of a Bernoulli component to deal with the problem of extra zeros, and a multivariate truncated component to model correlated mixed response outcomes from the same subject. In a Bayesian modeling approach, MCMC methods are used for parameter estimation. Using a simulation study, it is shown that the within-individual correlation between counts can be accurately estimated together with the other model parameters. The multivariate zero-inflated model is applied to a computer-based feedback study about computer literacy, where first-year bachelor students were given the opportunity to receive additional feedback. The total number of feedback pages visited and the total feedback processing time are modeled using a Poisson and a Gamma distribution, respectively. The joint modeling framework is extended to incorporate explanatory latent variables (student performance and speed of working), to explore individual heterogeneity in feedback behavior in a computer-based assessment.

Genome-wide Association Analysis for Multiple Continuous Secondary Phenotypes

There is increasing interest in the joint analysis of multiple phenotypes in genome-wide association studies (GWASs), especially for the analysis of multiple secondary phenotypes in case-control studies and in detecting pleiotropic effects. Multiple phenotypes often measure the same underlying trait. By taking advantage of similarity across phenotypes, one could potentially gain statistical power in association analysis. Because continuous phenotypes are likely to be measured on different scales, we propose a scaled marginal model for testing and estimating the common effect of single-nucleotide polymorphism (SNP) on multiple secondary phenotypes in case-control studies. This approach improves power in comparison to individual phenotype analysis and traditional multivariate analysis when phenotypes are positively correlated and measure an underlying trait in the same direction (after transformation) by borrowing strength across outcomes with a one degree of freedom (1-DF) test and jointly estimating outcome-specific scales along with the SNP and covariate effects. To account for case-control ascertainment bias for the analysis of multiple secondary phenotypes, we propose weighted estimating equations for fitting scaled marginal models. This weighted estimating equation approach is robust to departures from normality of continuous multiple phenotypes and the misspecification of within-individual correlation among multiple phenotypes. Statistical power improves when the within-individual correlation is correctly specified. We perform simulation studies to show the proposed 1-DF common effect test outperforms several alternative methods. We apply the proposed method to investigate SNP associations with smoking behavior measured with multiple secondary smoking phenotypes in a lung cancer case-control GWAS and identify several SNPs of biological interest.

Testing for the presence of coping styles in a wild mammal

Coping styles represent alternative response patterns in reaction to a stressor. The coping style model provides a set of predictions about correlations between behavioural and neurophysiological reactions to a stressful situation. According to this model, high levels of activity should be correlated with high levels of aggressiveness at the behavioural level, and to high sympathetic reactivity, low parasympathetic reactivity (higher heart rate levels) and low hypothalamus–pituitary–adrenocortical (HPA) axis reactivity (low production of glucocorticoids in response to a stressor). More recent versions of the model, however, are challenging this view and consider the possibility of independent axes of coping style and stress reactivity. The coping style model has mainly been tested on artificially selected or inbred lines in laboratory settings. Such a situation restricts its generalization to a larger number of species and there is a need for studies testing it in the wild under more natural situations. Here, we test the predictions of the coping style model in a wild alpine marmot, Marmota marmota, population. We show that several behavioural (i.e. exploration in an open field, impulsivity and docility) and neurophysiological traits (i.e. heart rate, breathing rate and cortisol production) assumed to represent individual differences in coping style were significantly repeatable over 2–3 years. Not all the correlations between traits predicted by the coping style model were found in marmots, which supports the more recent two-axes model. Furthermore, most correlations were observed at the between-individual level, and the within-individual correlations (i.e. phenotypic plasticity) were weaker. Overall, our results support the prediction of the coping style model, but highlight the fact that the association between traits found in artificial conditions may be weaker in a more natural setting.

Methodological queries about point‐of‐care haemoglobin data

I read with interest the article by Skelton et al. 1, and wish to express some concerns about the statistical analyses in this paper. I note in Table 1 that the authors observed mean (SD) pre-operative haemoglobin concentration (Hb) values from the co-oximeter (SpHb), HemoCueHb and laboratory Hb of 12.5 (1.5) g.dl−1, 12.1 (1.4) g.dl−1 and 11.9 (1.5) g.dl−1, respectively. The postoperative values were 12.1 (1.5) g.dl−1, 10.4 (1.2) g.dl−1 and 10.5 (1.2) g.dl−1, respectively. I assume that the bias in this study was calculated for each datapoint, as SpHb/lab Hb and HemoCueHb/lab Hb. Based on these data, one would presume that the mean values for bias for the co-oximeter and HemoCue would be approximately +0.6 g.dl−1 and +0.2 g.dl−1 in the pre-operative period and +1.6 g.dl−1 and −0.1 g.dl−1 in the postoperative period, that is that the co-oximeter has positive bias at the pre- and postoperative time points. However, the authors report that the direction of change for each bias value (within the text and in Figs. 2 and 3) is opposite to what one would expect from reviewing the mean values in Table 1. If mean SpHb is higher than lab Hb, then shouldn't the bias values be positive as opposed to negative? As a result, there is uncertainty about whether the Bland-Altman analysis was performed correctly. I wonder whether the difference (bias) was calculated for lab Hb/SpHb and lab Hb/HemocueHb for the Bland-Altman analyses, which would explain the error in the direction of change for the bias values. I also note that the captions for the graphs in Figs. 2 and 3 refer to the wrong device (HemoCue vs co-oximeter) in each case, adding to the confusion regarding the data presentation. In our study 2, we observed a positive bias for SpHb compared with lab Hb values in the pre-operative and postoperative periods (1.22 g.dl−1 pre-operatively, 0.14 g.dl−1 immediately postoperatively and 1.36 g.dl−1 24 h postoperatively). Not surprisingly, I was somewhat surprised to see a marked difference in the direction of change for the bias values for the SpHb/lab Hb values described by the authors. Lastly, I would be interested to know why the authors did not use appropriate modelling for the Bland-Altman analyses in order to account for within-individual correlations 3.

Factors Affecting Perception of Effort (Session Rating of Perceived Exertion) During Rugby League Training

The purpose of this study was to examine the validity of session rating of perceived exertion (sRPE) for monitoring training intensity in rugby league. Thirty-two professional rugby league players participated in this study. Training-load (TL) data were collected during an entire season and assessed via microtechnology (heart-rate [HR] monitors, global positioning systems [GPS], and accelerometers) and sRPE. Within-individual correlation analysis was used to determine relationships between sRPE and various other measures of training intensity and load. Stepwise multiple regressions were used to determine a predictive equation to estimate sRPE during rugby league training. There were significant within-individual correlations between sRPE and various other internal and external measures of intensity and load. The stepwise multiple-regression analysis also revealed that 62.4% of the adjusted variance in sRPE-TL could be explained by TL measures of distance, impacts, body load, and training impulse (y = 37.21 + 0.93 distance - 0.39 impacts + 0.18 body load + 0.03 training impulse). Furthermore, 35.2% of the adjusted variance in sRPE could be explained by exercise-intensity measures of percentage of peak HR (%HRpeak), impacts/min, m/min, and body load/min (y = -0.01 + 0.37%HRpeak + 0.10 impacts/min + 0.17 m/min + 0.09 body load/min). A combination of internal and external TL factors predicts sRPE in rugby league training better than any individual measures alone. These findings provide new evidence to support the use of sRPE as a global measure of exercise intensity in rugby league training.

Penalized regression, mixed effects models and appropriate modelling

Linear mixed effects methods for the analysis of longitudinal data provide a convenient framework for modelling within-individual correlation across time. Using spline functions allows for flexible modelling of the response as a smooth function of time. A computational connection between linear mixed effects modelling and spline smoothing has resulted in a cross-fertilization of these two fields. The connection has popularized the use of spline functions in longitudinal data analysis and the use of mixed effects software in smoothing analyses. However, care must be taken in exploiting this connection, as resulting estimates of the underlying population mean might not track the data well and associated standard errors might not reflect the true variability in the data. We discuss these shortcomings and suggest some easy-to-compute methods to eliminate them.

Quantifying individual variation in behaviour: mixed‐effect modelling approaches

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.