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Journal ArticleDOI

Quantifying individual variation in behaviour: mixed-effect modelling approaches

TL;DR: 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 is provided.
Abstract: 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.
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Journal Article
TL;DR: For the next few weeks the course is going to be exploring a field that’s actually older than classical population genetics, although the approach it’ll be taking to it involves the use of population genetic machinery.
Abstract: So far in this course we have dealt entirely with the evolution of characters that are controlled by simple Mendelian inheritance at a single locus. There are notes on the course website about gametic disequilibrium and how allele frequencies change at two loci simultaneously, but we didn’t discuss them. In every example we’ve considered we’ve imagined that we could understand something about evolution by examining the evolution of a single gene. That’s the domain of classical population genetics. For the next few weeks we’re going to be exploring a field that’s actually older than classical population genetics, although the approach we’ll be taking to it involves the use of population genetic machinery. If you know a little about the history of evolutionary biology, you may know that after the rediscovery of Mendel’s work in 1900 there was a heated debate between the “biometricians” (e.g., Galton and Pearson) and the “Mendelians” (e.g., de Vries, Correns, Bateson, and Morgan). Biometricians asserted that the really important variation in evolution didn’t follow Mendelian rules. Height, weight, skin color, and similar traits seemed to

9,847 citations

Journal ArticleDOI
TL;DR: The role of feedbacks in recent models of adaptive personalities, and guidelines for empirical testing of model assumptions and predictions are provided, to provide a roadmap for including state-behaviour Feedbacks in behavioural ecology research.
Abstract: An exciting area in behavioural ecology focuses on understanding why animals exhibit consistent among-individual differences in behaviour (animal personalities). Animal personality has been proposed to emerge as an adaptation to individual differences in state variables, leading to the question of why individuals differ consistently in state. Recent theory emphasizes the role that positive feedbacks between state and behaviour can play in producing consistent among-individual covariance between state and behaviour, hence state-dependent personality. We review the role of feedbacks in recent models of adaptive personalities, and provide guidelines for empirical testing of model assumptions and predictions. We discuss the importance of the mediating effects of ecology on these feedbacks, and provide a roadmap for including state–behaviour feedbacks in behavioural ecology research.

463 citations

Journal ArticleDOI
TL;DR: How between-individual differences in behavioural plasticity can result from additive and interactive effects of genetic make-up and past environmental conditions, and under which conditions natural selection might favour this form of between- individual variation is discussed.

331 citations

Journal ArticleDOI
TL;DR: It is demonstrated that genetic differences are likely to be a major contributor to variation in animal personality and support the phenotypic gambit: that evolutionary inferences drawn from repeatability estimates may often be justified.
Abstract: Individual animals frequently exhibit repeatable differences from other members of their population, differences now commonly referred to as ‘animal personality’. Personality differences can arise,...

303 citations

References
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Book
01 Jan 1981
TL;DR: The genetic constitution of a population: Hardy-Weinberg equilibrium and changes in gene frequency: migration mutation, changes of variance, and heritability are studied.
Abstract: Part 1 Genetic constitution of a population: Hardy-Weinberg equilibrium. Part 2 Changes in gene frequency: migration mutation. Part 3 Small populations - changes in gene frequency under simplified conditions. Part 4 Small populations - less simplified conditions. Part 5 Small populations - pedigreed populations and close inbreeding. Part 6 Continuous variation. Part 7 Values and means. Part 8 Variance. Part 9 Resemblance between relatives. Part 10 Heritability. Part 11 Selection - the response and its prediction. Part 12 Selection - the results of experiments. Part 13 Selection - information from relatives. Part 14 Inbreeding and crossbreeding - changes of mean value. Part 15 Inbreeding and crossbreeding - changes of variance. Part 16 Inbreeding and crossbreeding - applications. Part 17 Scale. Part 18 Threshold characters. Part 19 Correlated characters. Part 20 Metric characters under natural selection.

20,288 citations

Book
29 Mar 2013
TL;DR: Linear Mixed-Effects and Nonlinear Mixed-effects (NLME) models have been studied in the literature as mentioned in this paper, where the structure of grouped data has been used for fitting LME models.
Abstract: Linear Mixed-Effects * Theory and Computational Methods for LME Models * Structure of Grouped Data * Fitting LME Models * Extending the Basic LME Model * Nonlinear Mixed-Effects * Theory and Computational Methods for NLME Models * Fitting NLME Models

10,715 citations

Journal Article
TL;DR: For the next few weeks the course is going to be exploring a field that’s actually older than classical population genetics, although the approach it’ll be taking to it involves the use of population genetic machinery.
Abstract: So far in this course we have dealt entirely with the evolution of characters that are controlled by simple Mendelian inheritance at a single locus. There are notes on the course website about gametic disequilibrium and how allele frequencies change at two loci simultaneously, but we didn’t discuss them. In every example we’ve considered we’ve imagined that we could understand something about evolution by examining the evolution of a single gene. That’s the domain of classical population genetics. For the next few weeks we’re going to be exploring a field that’s actually older than classical population genetics, although the approach we’ll be taking to it involves the use of population genetic machinery. If you know a little about the history of evolutionary biology, you may know that after the rediscovery of Mendel’s work in 1900 there was a heated debate between the “biometricians” (e.g., Galton and Pearson) and the “Mendelians” (e.g., de Vries, Correns, Bateson, and Morgan). Biometricians asserted that the really important variation in evolution didn’t follow Mendelian rules. Height, weight, skin color, and similar traits seemed to

9,847 citations

Book
01 Jan 1999
TL;DR: In this paper, the authors proposed a multilevel regression model to estimate within-and between-group correlations using a combination of within-group correlation and cross-group evidence.
Abstract: Preface second edition Preface to first edition Introduction Multilevel analysis Probability models This book Prerequisites Notation Multilevel Theories, Multi-Stage Sampling and Multilevel Models Dependence as a nuisance Dependence as an interesting phenomenon Macro-level, micro-level, and cross-level relations Glommary Statistical Treatment of Clustered Data Aggregation Disaggregation The intraclass correlation Within-group and between group variance Testing for group differences Design effects in two-stage samples Reliability of aggregated variables Within-and between group relations Regressions Correlations Estimation of within-and between-group correlations Combination of within-group evidence Glommary The Random Intercept Model Terminology and notation A regression model: fixed effects only Variable intercepts: fixed or random parameters? When to use random coefficient models Definition of the random intercept model More explanatory variables Within-and between-group regressions Parameter estimation 'Estimating' random group effects: posterior means Posterior confidence intervals Three-level random intercept models Glommary The Hierarchical Linear Model Random slopes Heteroscedasticity Do not force ?01 to be 0! Interpretation of random slope variances Explanation of random intercepts and slopes Cross-level interaction effects A general formulation of fixed and random parts Specification of random slope models Centering variables with random slopes? Estimation Three or more levels Glommary Testing and Model Specification Tests for fixed parameters Multiparameter tests for fixed effects Deviance tests More powerful tests for variance parameters Other tests for parameters in the random part Confidence intervals for parameters in the random part Model specification Working upward from level one Joint consideration of level-one and level-two variables Concluding remarks on model specification Glommary How Much Does the Model Explain? Explained variance Negative values of R2? Definition of the proportion of explained variance in two-level models Explained variance in three-level models Explained variance in models with random slopes Components of variance Random intercept models Random slope models Glommary Heteroscedasticity Heteroscedasticity at level one Linear variance functions Quadratic variance functions Heteroscedasticity at level two Glommary Missing Data General issues for missing data Implications for design Missing values of the dependent variable Full maximum likelihood Imputation The imputation method Putting together the multiple results Multiple imputations by chained equations Choice of the imputation model Glommary Assumptions of the Hierarchical Linear Model Assumptions of the hierarchical linear model Following the logic of the hierarchical linear model Include contextual effects Check whether variables have random effects Explained variance Specification of the fixed part Specification of the random part Testing for heteroscedasticity What to do in case of heteroscedasticity Inspection of level-one residuals Residuals at level two Influence of level-two units More general distributional assumptions Glommary Designing Multilevel Studies Some introductory notes on power Estimating a population mean Measurement of subjects Estimating association between variables Cross-level interaction effects Allocating treatment to groups or individuals Exploring the variance structure The intraclass correlation Variance parameters Glommary Other Methods and Models Bayesian inference Sandwich estimators for standard errors Latent class models Glommary Imperfect Hierarchies A two-level model with a crossed random factor Crossed random effects in three-level models Multiple membership models Multiple membership multiple classification models Glommary Survey Weights Model-based and design-based inference Descriptive and analytic use of surveys Two kinds of weights Choosing between model-based and design-based analysis Inclusion probabilities and two-level weights Exploring the informativeness of the sampling design Example: Metacognitive strategies as measured in the PISA study Sampling design Model-based analysis of data divided into parts Inclusion of weights in the model How to assign weights in multilevel models Appendix. Matrix expressions for the single-level estimators Glommary Longitudinal Data Fixed occasions The compound symmetry models Random slopes The fully multivariate model Multivariate regression analysis Explained variance Variable occasion designs Populations of curves Random functions Explaining the functions 27415.2.4 Changing covariates Autocorrelated residuals Glommary Multivariate Multilevel Models Why analyze multiple dependent variables simultaneously? The multivariate random intercept model Multivariate random slope models Glommary Discrete Dependent Variables Hierarchical generalized linear models Introduction to multilevel logistic regression Heterogeneous proportions The logit function: Log-odds The empty model The random intercept model Estimation Aggregation Further topics on multilevel logistic regression Random slope model Representation as a threshold model Residual intraclass correlation coefficient Explained variance Consequences of adding effects to the model Ordered categorical variables Multilevel event history analysis Multilevel Poisson regression Glommary Software Special software for multilevel modeling HLM MLwiN The MIXOR suite and SuperMix Modules in general-purpose software packages SAS procedures VARCOMP, MIXED, GLIMMIX, and NLMIXED R Stata SPSS, commands VARCOMP and MIXED Other multilevel software PinT Optimal Design MLPowSim Mplus Latent Gold REALCOM WinBUGS References Index

9,578 citations

Journal ArticleDOI
TL;DR: The use (and misuse) of GLMMs in ecology and evolution are reviewed, estimation and inference are discussed, and 'best-practice' data analysis procedures for scientists facing this challenge are summarized.
Abstract: How should ecologists and evolutionary biologists analyze nonnormal data that involve random effects? Nonnormal data such as counts or proportions often defy classical statistical procedures. Generalized linear mixed models (GLMMs) provide a more flexible approach for analyzing nonnormal data when random effects are present. The explosion of research on GLMMs in the last decade has generated considerable uncertainty for practitioners in ecology and evolution. Despite the availability of accurate techniques for estimating GLMM parameters in simple cases, complex GLMMs are challenging to fit and statistical inference such as hypothesis testing remains difficult. We review the use (and misuse) of GLMMs in ecology and evolution, discuss estimation and inference and summarize 'best-practice' data analysis procedures for scientists facing this challenge.

7,207 citations


"Quantifying individual variation in..." refers background or methods in this paper

  • ...Mixed-effect models incorporate two types of parameters: fixed and random ones, and hence consist of two key parts (Eisenhart 1947; Bennington & Thayne 1994; Pinheiro & Bates 2000; Bolker et al. 2009): 1 The effects that predictor variables – which can be continuous (covariates) or categorical (factors) – have on the mean of response variables....

    [...]

  • ...We also strongly recommend that readers properly familiarize themselves with basic model assumptions prior to applying these tools themselves (cf. Pinheiro & Bates 2000; Bolker et al. 2009; Zuur et al. 2009)....

    [...]

  • ...…Bayesian methods), how inferences are drawn (e.g. P-values vs. information criterion), or specifics of dealing with non-normal error distributions (Bolker et al. 2009; Zuur et al. 2009; Nakagawa & Schielzeth 2010; see also Text S1, Supporting information); those issues have been extensively…...

    [...]

  • ...…two types of parameters: fixed and random ones, and hence consist of two key parts (Eisenhart 1947; Bennington & Thayne 1994; Pinheiro & Bates 2000; Bolker et al. 2009): 1 The effects that predictor variables – which can be continuous (covariates) or categorical (factors) – have on the mean of…...

    [...]

  • ...Despite major advantages, MMs are complex tools and therefore easily misspecified or interpreted inappropriately (Bennington & Thayne 1994; Bolker et al. 2009; van de Pol & Wright 2009; Schielzeth & Forstmeier 2009; Zuur et al. 2009; Hadfield et al. 2010)....

    [...]

Trending Questions (1)
How does the non-random distribution of behavioural phenotypes affect ecological and evolutionary processes?

The provided paper does not directly address the non-random distribution of behavioural phenotypes and its effects on ecological and evolutionary processes.