Yield improvement in corn can be attributed to genetic improvement, changes in cultural management, climate change, and the interactions among these factors. Estimates of the contribution of genetic improvement to the overall grain yield improvement in corn range from 40 to 100%. Genetic gains in grain yield of corn are principally due to the improvement in the genotype by management interaction associated with increased stress tolerance. A prolonged anthesis-silking interval (ASI), and reductions in both ears per plant (barrenness) and kernel set per plant have been identified as the traits most likely to be evident when hybrids of different eras are compared under stressful field conditions. QTL experiments aimed at mapping the specific QTL associated with stress tolerance include pre-defined treatments (e.g. water stress vs. no stress, nitrogen fertilization vs. no fertilizer) to detect markers and/or linkage blocks associated with the treatment responses. Accurate QTL mapping of the genetic factors underlying these responses to stress requires the estimation and testing of QTL by stress level interactions rather than simply mapping QTL for each stress condition separately, and then inferring the effect of a QTL on stress response by overlapping results across conditions. We will present our experiences with a Linear Mixed Model approach to estimate and interpret the responses to inter-plant competition of 8 corn substitution lines following measurements of grain yield and 2 vegetative, 1 developmental, and 2 stress-related traits.