Effects of heterogeneous soil-water diffusivity on vegetation pattern formation

Many mathematical models have been proposed to explain the emergence of vegetation patterns in arid and semiarid environments, but only a few of them take into account the heterogeneity in the system properties. Here we present a rigorous study of the effects of heterogeneous soil-water diffusivity on vegetation patterns, using two mathematical models. The two models differ in the pattern-forming feedback that they capture; one model captures the infiltration contrast between vegetated and bare-soil domains, whereas the other model captures the increased growth rate of denser vegetation due to an enhanced ability to extract water from the soil. In both models, the most significant effect of the heterogeneity on the soil-water diffusivity is the increased durability of patterned vegetation to a reduced precipitation rate. An additional effect is that the heterogeneity makes the desertification process, namely, the transition from a spotted vegetation pattern to a bare-soil state, more gradual than in the homogeneous system. Our findings suggest that the heterogeneity cannot be neglected in the study of critical transitions in heterogeneous ecosystems and, particularly, in the study of the desertification process due to climate changes or anthropogenic disturbances.