a, Modelled responses of common species to resin phosphate as adult trees and saplings. Trees were defined as being 100 mm dbh and saplings were defined as being 10 mm dbh. The responses of trees and saplings are unrelated by simple linear regression (R2 = 0.006; P = 0.74). As trees 90% of species have a positive response to increasing resin phosphate concentrations (points above the horizontal dotted line), and as saplings 84% of species have a positive response to increasing resin phosphate concentrations (points to the right of the vertical dotted line). Only three common species responded negatively as both small and large trees. b, Piecewise linear regression model using common widespread species, showing the relationship fitted to the response of growth (log-transformed) to resin phosphate concentration for trees >100 mm dbh (top) and saplings <100 mm dbh (bottom). The black line is the community-wide mean, or fixed response. Each grey line is the fit for one species and blue dots are the growth rates of individual trees. For trees, the break point between large and small responses to phosphorus is at 1.6 mg P kg−1 resin phosphate (red dashed vertical line; 95% credible interval 1.3–2.0). To the left of this break, s1 = 0.16 (95% credible interval 0.06–0.28) and to the right, s2 = 0.01 (−0.01–0.03). For saplings, s2 was significantly positive. However, the two slopes had widely overlapping credible intervals, forcing us to accept the null hypothesis of no change in slope. c, Specific phosphatase activity and resin phosphate for 83 sites under lowland tropical forest in Panama, showing phosphomonoesterase activity and phosphodiesterase activity expressed on the basis of the soil microbial biomass carbon (left) and total soil organic carbon (right). For both transformations, the relationships are almost identical to those for non-standardized activities, but the models explain a slightly smaller proportion of the variance. The hydrolysis product is methylumbelliferone and model fits are exponential functions determined by nonlinear regression. d, The proportion of the widespread species at a site that have negative or positive associations with soil phosphorus, against the resin phosphate concentration for 72 lowland tropical forests in Panama. Species with negative associations with soil phosphorus (low-phosphorus affinity), open blue circles and blue line; species with positive associations with soil phosphorus (high-phosphorus affinity), red circles and red line. The point at which the proportion of low-affinity species equals the proportion of high-affinity species corresponds to a resin phosphate concentration of 2.18 mg P kg−1.