Broad sense repeatability, which refers to the extent to which individual differences in trait scores are maintained over time, is of increasing interest to researchers studying behavioural or physiological traits. Broad sense repeatability is most often inferred from the statistic R (the intraclass correlation, or narrow sense repeatability). However, R ignores change over time, despite the inherent longitudinal nature of the data (repeated measures over time). Here, we begin by showing that most studies ignore time-related change when estimating broad sense repeatability, and estimate R with low statistical power. Given this problem, we (1) outline how and why ignoring time-related change in scores (that occurs for whatever reason) can seriously affect estimates of the broad sense repeatability of behavioural or physiological traits, (2) discuss conditions in which various indices of R can or cannot provide reliable estimates of broad sense repeatability, and (3) provide suggestions for experimental designs for future studies. Finally, given that we already have abundant evidence that many labile traits are 'repeatable' in that broad sense (i.e. R>. 0), we suggest a shift in focus towards obtaining robust estimates of the repeatability of behavioural and physiological traits. Given how labile these traits are, this will require greater experimental (and/or statistical) control and larger sample sizes in order to detect and quantify change over time (if present).

Over the years, theoreticians and empiricists working in a wide range of disciplines, including physiology, ethology, psychology, and behavioral ecology, have suggested a variety of reasons why individual differences in behavior might change over time, such that different individuals become more similar (convergence) or less similar (divergence) to one another. Virtually none of these investigators have suggested that convergence or divergence will continue forever, instead proposing that these patterns will be restricted to particular periods over the course of a longer study. However, to date, few empiricists have documented time-specific convergence or divergence, in part because the experimental designs and statistical methods suitable for describing these patterns are not widely known. Here, we begin by reviewing an array of influential hypotheses that predict convergence or divergence in individual differences over timescales ranging from minutes to years, and that suggest how and why such patterns are likely to change over time (e.g., divergence followed by maintenance). Then, we describe experimental designs and statistical methods that can be used to determine if (and when) individual differences converged, diverged, or were maintained at the same level at specific periods during a longitudinal study. Finally, we describe why the concepts described herein help explain the discrepancy between what theoreticians and empiricists mean when they describe the emergence of individual differences or personality, how they might be used to study situations in which convergence and divergence patterns alternate over time, and how they might be used to study time-specific changes in other attributes of behavior, including individual differences in intraindividual variability (predictability), or genotypic differences in behavior.