Quantifying the predictability of behaviour: statistical approaches for the study of between-individual variation in the within-individual variance

1. Many aspects of animal behaviour differ consistently between individuals, giving rise to the growing field of animal personality research. While between-individual variation has long been of interest to biologists, the role of within-individual variation has received less attention. Indeed, many models assume that the extent of within-individual variation is the same across individuals despite the fact that individuals may often differ in their variability. Recently, the importance of within-individual variability or predictability has been recognized within the field of animal behaviour. However, there is a lack of a consensus on how best to quantify it. This situation, in turn, has led to the development of a variety of different methods aimed at assessing how variable or predictable different individuals are. Here, we review the indices that have been proposed as proxies of individual predictability. We then introduce existing techniques called hierarchical generalized linear models (HGLMs) and double-hierarchical generalized linear models (DHGLMs) as general tools for quantifying predictability. HGLMs and DHGLMs are extensions of random intercept mixed models that exploit the fact that variation in variances as well as variation in means can be modelled within a single overarching framework. Explicit modelling of the within-individual residual variation by (D)HGLMs makes more efficient use of the data, performs better on unbalanced data sets and captures more of the uncertainty involved in modelling within-individual variation than other proposed indices. In addition, (D)HGLMs yield an estimator of population-wide variation in predictability, which can serve as a standardized effect size for comparisons across traits and studies. We call this estimator CVP, the coefficient of variation in predictability. The different methods described here and the standardized effect size CVP should open new avenues for studying individuality in animal behaviour. Since sound understanding of individual variation is central to many studies in ecology and evolution, these methods have wide application both in the field of animal personality research and beyond.