On testing biological data for the presence of a boundary

Under the boundary line model for a biological data set, where one variable is a biological response (e.g. crop yield) to an independent variable (e.g. available water content of the soil), we interpret the upper (or lower) boundary on a plot of the dependent variable (ordinate) against the independent variable (abscissa) as representing the maximum (or minimum) possible response for a given value of the independent variable. This concept has been widely used in soil science, agronomy and plant physiology; but it has been subject to criticism. In particular, no methods that are used to analyse the boundary line quantify the evidence that the envelope of the plot represents a boundary (in the sense of some limiting response to the independent variable) rather than simply being a fringe of extreme values of no intrinsic biological interest. In this article, we present a novel procedure that tests a data set for evidence of a boundary by considering its statistical properties in the region of the proposed boundary. The method is demonstrated using both simulated and real data sets.