Abstract
Crop improvement must accelerate to feed an increasing human population in the face of environmental changes. Including anticipated climatic changes with genetic architecture in breeding programs could better optimize improvement strategies. Combinations of drought and nitrogen limitation already occur world-wide. We therefore 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 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. To better understand the physiology of the response, we developed a model that reproduced the shapes of the surfaces, their most characteristic feature. The model contains two components that each combine the nitrogen and water inputs. The relative weighting of the two components and the inputs is governed by five parameters, and each QTL affects all five parameters.We estimated the model's parameter values for the experimental surfaces using a mesh of points that covered the surfaces' most distinctive regions. Surfaces computed using these values reproduced the experimental surfaces well, as judged by three different criteria at the mesh points. The modeling and shape comparison techniques used here can be extended to other complex, high-dimensional, nonlinear phenotypes. We encourage the application of our findings and methods to experiments that mix crop protection measures, stresses, or both, on elite and landrace germplasm.