How to Investigate Four-way Nutrient Interactions in Plants: A New Look at Response Surface Methods

in Journal of the American Society for Horticultural Science
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  • 1 Department of Agronomy and Horticulture and Department of Statistics, University of Nebraska, Lincoln, NE 68583

Response surface methods refer to a set of experimental design and analysis methods to study the effect of quantitative treatments on a response of interest. In theory, these methods have a broad range of applicability. While they have gained widespread acceptance and application in manufacturing and quality improvement research, they have never caught on in the agricultural sciences. We propose that this is because there has not been specific research demonstrating their usage. In this paper, two 34 factorial experiments were performed using 100 poinsettia plants (Euphorbia pulcherrima Willd. ex Klotzsch) to measure nutrient element concentrations in leaves at three rates each of nitrogen (N), sulfur (S), iron (Fe), and manganese (Mn). Three different methods of analysis were compared—the standard analysis of variance with no regression model, the quadratic regression model commonly assumed for most standard response surface methods and the Hoerl model regression, a nonlinear alternative to quadratic response. Actual nutrient element values were compared with the values predicted by each regression model and then also evaluated to see if the visual symptomology of yellowing related to those nutrient concentrations in leaves. The Hoerl model demonstrated better ability to detect biologically relevant nonlinear two-, three-, and four-way nutrient interactions. Though there was minimal replication this model characterized the treatment effects while keeping the size of the experiment manageable both in terms of time (labor) and cost of plant analyses. Additionally, it was shown that when S, Fe, and/or Mn were deficient along with N, their visual deficiency symptoms were masked by the overall yellowing associated with N deficiency. This model is recommended as the initial experiment in a series where scientists are looking to expand information already determined for two factors. Other treatment systems that this can be used with include: levels of irrigation, pesticides, and plant growth regulators.

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