A linear profit function for economic weights of linear phenotypic selection indices in plant breeding

The profit function (net returns minus costs) allows breeders to derive trait economic weights to predict the net genetic merit (H) using the linear phenotypic selection index (LPSI). Economic weight is the increase in profit achieved by improving a particular trait by one unit and should reflect the market situation and not only preferences or arbitrary values. In maize (Zea mays L.) and wheat (Triticum aestivum) breeding programs, only grain yield has a specific market price, which makes application of a profit function difficult. Assuming the traits' phenotypic values have multivariate normal distribution, we used the market price of grain yield and its conditional expectation given all the traits of interest to construct a profit function and derive trait economic weights in maize and wheat breeding. Using simulated and real maize and wheat datasets, we validated the profit function by comparing its results with the results obtained from a set of economic weights from the literature. The criteria to validate the function were the estimated values of the LPSI selection response and the correlation between LPSI and H. For our approach, the maize and wheat selection responses were 1,567.13 and 1,291.5, whereas the correlations were .87 and .85, respectively. For the other economic weights, the selection responses were 0.79 and 2.67, whereas the correlations were .58 and .82, respectively. The simulated dataset results were similar. Thus, the profit function is a good option to assign economic weights in plant breeding.