ABSTRACT
Crop improvement must accelerate with increasing human population and environmental changes. Including anticipated climatic changes with information about genetic architecture in breeding programs can optimize resource use. We analyzed the genetic architecture underlying the response of Zea mays to combinations of water and nitrogen stresses. Plant growth was measured in recombinant inbreds subjected to nine combinations of five different levels of each stress. Three dimensional dose-response surfaces were fit globally and to each polymorphic allele to determine which markers were associated with different surfaces. Three quantitative trait loci that produced nonlinear response 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 flexible and extensible physiologically relevant parameters for future genetic analyses we modeled the simplest subnetwork that explains the response surfaces. The subnetwork contains two components, an elliptical paraboloid and a plane, which each combine the nitrogen and water inputs. The relative weighting of the two components and the input stresses is governed by five parameters. We identified parameter values that best fit the smoothed surfaces from the experimental lines using linear models; but these values overfit the peaks of the surfaces. Our results demonstrate that experiments using single stresses can mis-estimate the response of the plant to combinations of those same stresses and disguise loci that respond nonlinearly; and that values obtained from linear models can inadequately capture nonlinear phenomena. We encourage the application of our findings to experiments that mix crop protection measures, stresses, or both on elite and landrace germplasm.