The codispersion map: a graphical tool to visualize the association between two spatial variables

Abstract

The codispersion coefficient quantifies the association between two spatial processes for a particular direction (spatial lag) on a two‐dimensional space. When this coefficient is computed for many directions, it is useful to display those values on a single graph. In this article, we suggest a graphical tool called a codispersion map to visualize the spatial correlation between two sequences on a plane. We describe how to construct a codispersion map for regular and non‐regular lattices, providing algorithms in both cases. Three numerical examples are given to illustrate how useful this map can be to detect those directions for which the codispersion coefficient attains its maximum and minimum values. We also provide the R code to construct the codispersion map in practice.

Sensitivity of Codispersion to Noise and Error in Ecological and Environmental Data

“…We used codispersion maps (Buckley et al, 2016a;Vallejos et al, 2015) to explore the possible patterns and features caused by the introduction of noise and to evaluate the performance of the codispersion coefficient when the process was contaminated with one of the distortions described above. Recall that the generation of the noise is through statistical models that do not necessarily include a particular direction in space.…”

“…Recall that the generation of the noise is through statistical models that do not necessarily include a particular direction in space. The effects of specific directional contamination on codispersion was investigated by Vallejos et al (2015). The only effect observed when the forest image was contaminated with salt-and-pepper noise (Figure 1) was a trend of decreasing codispersion between the original and contaminated images with an increase in the percentage of contamination (Figure 8).…”

“…Preliminary experiments were introduced by Vallejos et al (2015) but here we present a more extensive study. The contamination scheme was generated by using Monte Carlo simulations according to (1).…”

“…Although accounting for spatial covariation has become routine in ecological data analysis (Fortin & Dale, 2005), ecologists and environmental scientists have been slower to appreciate and account for anisotropic patterns and processes (but see, e.g., Ellison et al, 2014). Codispersion (Vallejos et al, 2015) measures lag-dependent spatial covariation in two or more spatial processes, which may be anisotropic. Codispersion recently has been used to analyze ecological data and provide new insights into potential ecological processes that underlie observed patterns in co-occurrence between pairs of species (Buckley et al, 2016a) and in relationships between attributes of individual species and the underlying environment (Buckley et al, 2016b).…”

Foundation Species Across a Latitudinal Gradient in China

“…The codispersion coefficient ranges from − 1 to 1, with positive values indicating a positive spatial association and negative values indicating a negative spatial association for a given spatial lag and direction. These values can be visualized with a codisperison graph (Vallejos et al, 2015). Buckley et al (2016 a ) introduced codispersion analysis to ecologists through an exploration of spatial patterns of species co-occurrence.…”