Permutation Tests to Identify Significant Constraint or Promotion Within Biological Scatterplots

Abstract

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.