Comparing Distance-Decay Parameters: A Novel Test under Pairwise Dependence

Distance-decay models fit parametric functions to assess the relationship between similarity and spatial or environmental distance. Despite the widespread use of distance-decay models in ecology and biogeography, no method has been previously developed and validated to assess the significance of differences between the parameters (i.e. intercept and slope) of two distance-decay models. The pairwise autocorrelation of similarity and spatial distance affects the variance of parameter estimates, precluding the use of ordinary t-tests. Here, we provide a test statistic (zdep) for the equality of parameters between two distance-decay models. The test can be applied, independently, to any of the model parameters (i.e. intercept and/or slopes). The zdep statistic accounts for pairwise dependence, thus avoiding biases associated to the inflation of degrees of freedom, and it is based on the estimation of parameters' variance using site-block resampling. To validate the zdep statistic, type I and type II errors were empirically evaluated through a simulation study. We simulated six scenarios (three under the null and three under the alternative hypothesis) of distance-decay relationships using different functions: negative exponential, power-law or Gompertz function. We applied the zdep statistic and computed the proportion of rejections of the null hypothesis for alpha = 0.01, 0.05 and 0.1 in each scenario. As a case-study, we also compared distance-decay parameters across several groups of Iberian vertebrates (cyprinids, frogs, lizards and snakes, bats, rodents and carnivores). In the simulation study, the zdep statistic showed a good approximation of the nominal level (alpha, type I error) and a good statistical power (1 - type II error), the later increasing with sample size, as expected. In Iberian vertebrates, we found significant differences between ectotherms and endotherms, but not within these groups except between cyprinids and other ectotherms. The good performance of the zdep statistic makes it the best option to test for differences in parameters obtained from models fitted from data with pairwise dependence, as distance-decay models. It can also be used beyond distance-decay approaches to compare parameters of any other regression models of pairwise dependent data (as genetic distances, for example).