The role of landscape heterogeneity in regulating plant functional diversity under different precipitation and grazing regimes in semi-arid savannas

•Savanna landscapes show a high spatial heterogeneity in soil conditions.•We simulated landscape heterogeneity in terms of soil textures and depths using an ecohydrological model.•Soil heterogeneity in the landscape drives plant functional diversity and ecosystem functioning.•Precipitation and livestock grazing modulate the impact of landscape soil heterogeneity on savanna vegetation.