Constraint lines are a relatively novel tool for the analysis of fundamental processes in multivariate systems. Several authors have proposed that fundamental physiological and ecological processes are likely to appear as constraints (or limits) on observed patterns of statistical variation. Such constraints often appear as lines delimiting a scattered field of data points, and some authors have therefore called the observed phenomenon "threshold effects" or "edge effects" which are defined by "boundary conditions". Constraint lines (another descriptor that is sometimes used is "performance envelopes") are used to quantitatively define such limits.
Constraint lines are most useful under conditions where other variables that could account for some of the variation contributing to an observed effect, have not been measured. In this instance, linear or curvilinear regressions fitted to the entire data set will often yield highly significant relationships, even though they may only account for a very small portion of the overall observed variation. In addition, such procedures violate parametric assumptions about the homogeneity of variance.
In the complete original data set, univariate statistics are not satisfactory: no single hypothesis or variable will account for a large portion of the variation, and multiple hypotheses are rarely mutually exclusive. Under the assumption that the phenomena underlying threshold effects account for a larger portion of the variation near the extremes of distribution, the use of standard statistical procedures to isolate data points near the extremes will subsequently permit the application of conventional parametric regressions to perform fits on points at or near the extremes. Such a procedure will deliver a constraint line that quantifies the extremes of variation.
We are working on novel applications of constraint lines to the analysis of telemetered dive behavior data from pinnipeds to characterize animal performance.
Take a look at this interesting publication on constraint lines:
Guo Q, Brown JH, Enquist BJ (1998) Using constraint lines to characterize plant performance. OIKOS 83: 237-245.
