Root proliferation and marginal patch value

We describe and test a simple model of optimal root proliferation in a soil consisting of patches of various quality, with quality defined as the rate of supply of limiting soil resource. Assuming that roots deplete resources in the patch, the model predicts that root biomass will be allocated such that the marginal gains from each patch are equilibrated. With the further assumption that marginal returns are correlated with patch quality, the generally assumed positive relation between patch quality and root proliferation is predicted. This secondary prediction is tested with the grass Sorghum vulgare grown in containers consisting of four patches of variable limiting N-supply. Mean fine root biomass showed a strong positive relation between patch quality and biomass consistent with the foraging hypothesis, especially when expressed on a per primary root basis. However, the high within-individual variation and the insensitivity of primary roots imply that much of the root behavior remains unexplained by the model.