Response Surface Methodology in Genomic Selection

One of the main objectives in plant breeding is to develop sustainable varieties with high yield and desirable characteristics to feed the World. There is an enormous amount of research dedicated to improving plant breeding by developing new methods to increase yield while minimizing cost and the negative effect on the environment. Often the new methods are evaluated using a limited amount of factor combinations (e. g. one or few environments, fixed number of individuals and markers, etc.) due to budget, time or space constraints. Yet, it is important to examine the performance of methods in all possible situations. By focusing on only one or a few factor combinations we may obtain misleading results because model performance can be highly dependent on the attributes of the experiment. Response Surface Methodology (RSM) is an optimization technique that permits estimating the combination of factor level combinations that maximize (or minimize, in some cases) the response without performing the experiment at every possible combination of the variables.
We introduce RSM as a strategy to find the combination of attribute levels that results in accurate predictions for a given GS method, and compare GS methods. We illustrate RSM with an example where we simulate backcross populations with different number of individuals, markers, QTL, and different percentage of epistasis and heritability. The response we optimize is the difference between prediction accuracy using the parametric best linear unbiased prediction method and the nonparametric support vector machine method. This response can be an important diagnostic tool to determine the underlying genetic architecture. The greatest impact on the response is due to the genetic architecture of the population and the heritability of the trait. When epistasis and heritability are highest, the advantage of using the nonparametric support vector versus the parametric best linear unbiased prediction method is greatest.