Example data and analysis for Landscape Ecology Perspective article (2021)

Abstract

Perspective

A simplified perspective on the index of spatial autocorrelation

Thomas J. DeWitt Department of Ecology & Conservation Biology, Texas A&M University, College Station TX 77843-2258

Abstract This Perspective highlights a method reported in a recent issue of Landscape Ecology that trues Moran’s I to its conceptual ideals and existing intuition regarding correlations. The method creates a null distribution of I (or a simplified value) using random data permutations. The position of observed I, or a simpler analog, in its null distribution is projected to equivalent position in the theoretical distribution for regular correlations. Projection is accomplished by converting the cumulative proportion of data at I to r using the inverse t-distribution and the t/r equivalence. The original metric, rectified as an r statistic, is deemed Ir and is interpreted as one would a regular correlation. Ir normalized in this manner allows meaningful comparison within and among studies, provides for synthetic work such as meta-analysis, and can be used with other spatial pattern statistics to partition clumping and gradient effects. Ir preserves the conceptual ideals of the traditional metric yet also aligns with intuition and perceptions already established for r. Rectifying I in this manner therefore may foster expanded and sustained use in the fields of landscape ecology and geography.