Exploration of data for analysis using boundary line methodology

The boundary line model has been proposed for interpretation of the plot of a biological response (such as crop yield) against a potentially-limiting variable from observations in a large set of scenarios across which other factors show uncontrolled variation. Under this model the upper bound of the distribution of data represents the limiting effect of the potential factor on the response. Methods have been proposed to fit this model, but we propose that an initial exploratory data analysis step is needed to evaluate evidence that (i) the model is plausible and (ii) that any limiting upper bound is exhibited by the data set (which could, in principle, not include any cases where the factor is limiting). We propose a statistic based on the density of observations in upper sections of early convex hull peels of the data plot. We evaluate this approach using various data sets, some of which have been used for boundary line analysis in previous studies.