Permutation Tests to Identify Significant Constraint or Promotion Within Biological Scatterplots

Scatterplots of biological datasets often have no-data zones, which suggest constraint or promotion of dependent variables. Although methods exist to estimate boundary lines—that is, to fit lines to the edges of scatters of data points—there are, to our knowledge, none available to assess the significance of the areal extents of no-data zones. Accordingly, we propose a flexible boundary line definition paired with a permutation test of the magnitude of no-data zones—rather than testing the shape or slope of the line as current methods do. Our proposed permutation test can be used with any method of defining a boundary line. We demonstrate our approach with empirical datasets, find no-data zones that methods such as quantile regressions fail to detect, and discuss how our approach can quantify constraint and promotion relationships that are not always apparent with other statistics.