Inherent conflicts between reaction norm slope and plasticity indices when comparing plasticity: a conceptual framework and empirical test.

Phenotypic plasticity index (PI), the slope of reaction norm (K) and relative distances plasticity index (RDPI), the most commonly used estimators, have occasionally been found to generate different plasticity rankings between groups (species, populations, cultivars or genotypes). However, no effort has been made to determine how frequent this incongruence is, and the factors that influence the occurrence of the incongruence. To address these problems, we first proposed a conceptual framework and then tested the framework (its predictions) by reanalyzing 1248 sets of published data. Our framework reveals inherent conflicts between K and PI or RDPI when comparing plasticity between two groups, and the frequency of these conflicts increases with increasing inter-group initial trait difference and/or K values of the groups compared. More importantly, the estimators also affect the magnitude of the inter-group plasticity differences even when they do not change groups' plasticity rankings. The above-mentioned effects of plasticity estimators were confirmed by our empirical test using data from the literature, and the conflicts occur in 203 (16%) of the 1248 comparisons between K and indices, indicating that a considerable proportion of the comparative conclusions on plasticity in literature are estimator-dependent. The frequency of the conflicts is influenced by phylogenetic relatedness of the groups compared, being lower when comparing within relative to between species, but not by specific types of environments, traits and species. Our study indicates that care is needed to select estimator when comparing groups' plasticity, and that the conclusions in relevant literature should be treated with great caution.