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The influence of soil nutrients on woody plants is poorly understood. Are trees - fire and other disturbance factors being equal - generally promoted by nutrient-rich or by nutrient-poor soils? To determine the edaphic parameters controlling woody cover, we sampled soils and summed the extent of the crowns of trees and tall shrubs on 364 plots at 20 sites in Namibia and adjacent South Africa, ranging from desert lichen-fields to caesalpiniaceous woodland with associated mean annual rainfall of 11 mm to 535 mm. Our analysis included the macro-nutrients N, P, Mg, K and Ca and the trace elements Mn, Fe, Cu and Zn. A boundary line analysis showed that woody cover was densest, with the greatest large-scale heterogeneity, at intermediate nutrient contents, but consistently constrained at extreme nutrient richness as well as poverty. If aridity exerted the ultimate constraint at extreme nutrient richness, no such correlation with climate apparently applies at extreme nutrient poverty, where our graphs show an ’oligotrophic decline’. Notwithstanding the importance of water, we suggest that extreme nutrient richness and poverty both favour grasses over tree seedlings. This is because catabolic dystrophy - a regime in which the supply of catabolic nutrients shortfalls their demand - is unlikely in environments where nutrient richness allows catabolic rates to match anabolic rates or where nutrient poverty constrains anabolic rates. We also reason that surpluses of photosynthate resulting from dystrophy can be allocated to lignin and that the potential for woody growth thus corresponds to soils of intermediate nutrient content. This explains why woody cover is consistently but not homogeneously densest in nutritionally intermediate plots in our dataset. Hence, the abundance of woody plants in various biomes may be determined partly by soil nutrient content, particularly of Cu, Zn, and other elements indispensible for catabolism.