Dose-response surface fits to drought and nitrogen limitation applied together allow mapping of loci that exhibit nonlinear responses

Crop improvement must accelerate to feed an increasing human population in the face of environmental changes. Breeding programs can include anticipated climatic changes and genetic architecture to optimize improvement strategies. We analyzed the genetic architecture underlying the response of Zea mays to combinations of water and nitrogen stresses. Recombinant inbreds were subjected to nine combinations of the two stresses using an optimized response surface design, and their growth was measured. Three-dimensional dose response surfaces were fit globally and to each polymorphic allele to determine which genetic markers were associated with different response surfaces. Three quantitative trait loci that produced nonlinear surfaces were mapped. Alleles that performed better in combinations of mid-range stresses were typically not the alleles that performed best under combinations of extreme stresses. To develop physiologically relevant models for future genetic analyses, we modeled the network that explains the response surfaces. The network contains two components, an elliptical paraboloid and a plane, that each combine the nitrogen and water inputs. The relative weighting of the two components and the inputs is governed by five parameters. We estimated parameter values for the smoothed surfaces from the experimental lines using a set of points that covered the most distinctive regions of the three-dimensional surfaces. Surfaces computed using these values reproduced the smoothed experimental surfaces well, especially in the neighborhood of the peaks, as judged by three different criteria. The parameters exaggerated the amplitudes of the simulated surfaces. Experiments using single stresses could misestimate responses to their combinations and disguise loci that respond nonlinearly. The three-dimensional shape evaluation strategy used here more thoroughly compares nonlinear, nonplanar responses. We encourage the application of our findings and methods to experiments that mix crop protection measures, stresses, or both, on elite and landrace germplasm.