a, Relationships between phosphatase activities and total phosphorus concentrations in soils from 83 sites under lowland tropical forest in Panama. The figure shows phosphomonoesterase activity (blue circles, left) and phosphodiesterase activity (red circles, right). The hydrolysis product is methylumbelliferone and the model fits are negative exponential functions determined by nonlinear regression. The activity of both phosphatases decreases markedly at total phosphorus concentrations >400 mg P kg−1. b, The proportion of species at a site that has a negative association with soil phosphorus (low-phosphorus affinity, blue circles and blue line) or positive association with soil phosphorus (high-phosphorus affinity, red circles and red line) against total soil phosphorus for 72 lowland tropical forests in Panama. The models are sigmoidal fits and phosphorus associations are defined as effect sizes >0.8 (positive affinity) or <−0.8 (negative affinity). The point at which the proportion of low-affinity species exceeds the proportion of high-affinity species corresponds to a total phosphorus concentration of 435 mg P kg−1.