A null model for assessing the cover-independent role of bare soil connectivity as indicator of dryland functioning and dynamics

Recent research has identified the connectivity of the bare-soil interpatch areas as a key pattern attribute that controls resource conservation and structure-function feedbacks in dryland ecosystems, and several indices have been developed for this attribute. We aimed to characterize the dependence of bare-soil connectivity on vegetation cover and provide a null model that helps differentiate the independent roles of vegetation pattern and cover in hydrological connectivity and dryland functioning. Using a simple hydrological connectivity index, Flowlength, we developed explicit theoretical expressions for its expected value and variance under a null model of random vegetation cover distribution and constant slope. We also obtained the expected value of Flowlength for a model including an aggregation parameter. We found a non-linear inverse relationship between bare-soil connectivity and vegetation cover, which accounts for sharp increases in runoff and sediment yield for low cover values. The expressions for the mean values and standard errors for the random model allow the construction of confidence intervals, and thus testing for deviations from the null random model in experimental data. We found that positive deviations of Flowlength from the expected values, either under random or aggregated-pattern null models, sharply increase before transitions to a degraded state in a spatially-explicit dryland vegetation model, suggesting that an extraordinary increase in bare-soil connectivity may lead to unavoidable degradation. Our results show that increased deviation from the expected cover-dependent bare-soil connectivity may serve as indicator of ecosystem functional status and imminent transitions.