Nonlocal interactions between vegetation induce spatial patterning

Vegetation pattern provides useful signals for vegetation protection and can be identified as an early warning of desertification. In some arid or semi-arid regions, vegetation absorbs water through nonlocal interaction of roots. In this study, we present a vegetation model with nonlocal interaction which is characterized by an integral term with a kernel function. Mathematical analysis provides the conditions for the generation of stationary pattern. Numerical simulations exhibit different spatial distributions of vegetation. Densities of vegetation and water show an inverse relationship at same spatial locations due to water transport mechanism. The results reveal that the interaction intensity and the shape of the kernel function can cause the transition of vegetation pattern. Specifically, the vegetation biomass increases as the interaction intensity decreases or as the nonlocal interaction distance increases. We demonstrate that the nonlocal interactions between roots of vegetation is a key mechanism for the formation of vegetation pattern, which provides a theoretical basis for the preservation and restoration of vegetation.