Grid-induced biases in connectivity metric implementations that use regular grids

Graph-theoretic connectivity analyses provide opportunities to solve problems related to the management, design and maintenance of fragmented landscapes. However, several modern connectivity metrics are implemented using algorithms that are affected by a grid-induced bias. When paths through a regular grid are calculated, distance errors are introduced into the metric outputs, with patterns based on the shape and orientation of the underlying grid structure. The bias is significant in the proposed implementations of the conditional minimum transit cost method introduced by Pinto and Keitt, and the effective resistance method introduced by McRae, Dickson, Keitt and Shah. One solution for ameliorating the bias that affects regular grids is to use an irregular lattice to represent the landscape. The purpose of this paper is to serve as a timely reminder of the grid-induced bias and to provide a demonstration of the irregular grid as a simple solution to the problem.