The distinction between repeatability and correlation in studies of animal behaviour

We review the concepts of correlation and repeatability, as they are key components to studies of consistent individual differences in behaviour, commonly termed personality. These two concepts are widely used in an interchangeable way, which is sensible when studying consistency of behaviour within a single context. However, their quantitative values and qualitative meaning can diverge greatly when they are applied to understanding consistency of behaviour across contexts. Some scenarios exist where one is defined, and the other is not. Importantly, in scenarios where they are both defined, they need not be of the same sign. We provide an explicit mathematical analysis of the two concepts to disambiguate their meanings. Finally, we use an explicit, but simple, mathematical analysis to address the meaning of negative correlations across contexts, an issue that has been widely and conspicuously avoided to date in discussions of behavioural correlations. We hope that our mathematical investigation of the different aspects of consistent individual differences in behaviour encapsulated by correlations and repeatabilities can facilitate the application of these quantities in empirical studies of animal personality.