In most ecological and comparative studies, phenotypic integration is inferred from phenotypic correlations. Four main elements characterize phenotypic correlation: 1.strength (correlation coefficient), which is the most common measure of integration; the form of the relationship between trait pairs, including 2.the intercept and 3.the slope (scaling coefficient); and 4. the pattern of correlation across environments (plasticity integration). These elements may vary somewhat independently. For example, it is not necessary for traits to show correlated plasticity in order to remain strongly correlated in different environments. If there is correlated plasticity and two traits respond proportionally, then there will be no change in either the strength of the correlation or the form of the relationship between them. By contrast, if traits change in a coordinated fashion but disproportionately relative to one another, then the scaling relationship between them will change, reflecting a change in their functional relationship. Thus traits may show a consistent pattern of integration in various environments, while the forms of the pairwise relationships and the degree of plasticity integration varies. Although plasticity integration is not necessary to maintain phenotypic integration across environments, plasticity integration makes consistent patterns of integration more likely. Analyzing the combination of changes in correlation strength and form across environments, and the degree of plasticity integration, may provide insight into mechanisms underlying phenotypic integration and the potential for integration to constrain the evolution of adaptive plasticity in integrated traits.

Key words: constraint, correlation, functional relationship, phenotypic integration, plasticity, scaling