Variation in plasticity of personality traits implies that the ranking of personality measures changes between environmental contexts: calculating the cross-environmental correlation

Studies increasingly explore whether there is variation between individuals in how they adjust their behavior to different environmental contexts using random regression analysis (RR). RR estimates the between-individual variance in elevation (expected behavior in the mean environment) and variance in plasticity (individual-specific adjustment of behavior to the environment) and the covariance between these properties. These (co)variances allow deriving both environment-specific repeatability estimates and the individual-level correlation in behavior between environmental conditions, both of which are of key interest for understanding consistency in behavior over space and time, a core issue in animal personality research. However, very few studies use the RR estimates to produce this information. In this paper, I outline how to extract this information (including example code in R) and apply the approach to 16 estimates based on nine published RR studies. Despite the fact that the behaviors have a decent repeatability under different environmental conditions, I find that in half the cases, the cross-environmental correlation is low (< 0.4). This implies that individuals differ in their behavioral trait values but that the ranking of these individual values tends to change between environmental conditions. This level of inconsistency in animal personality traits appears not to have been fully appreciated, and future studies on plasticity using RR should explicitly include it.