Linear Phenotypic Selection Index Research Articles

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

AbstractThe 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.

Identification of Disease Resistance Parents and Genome-Wide Association Mapping of Resistance in Spring Wheat.

The likelihood of success in developing modern cultivars depend on multiple factors, including the identification of suitable parents to initiate new crosses, and characterizations of genomic regions associated with target traits. The objectives of the present study were to (a) determine the best economic weights of four major wheat diseases (leaf spot, common bunt, leaf rust, and stripe rust) and grain yield for multi-trait restrictive linear phenotypic selection index (RLPSI), (b) select the top 10% cultivars and lines (hereafter referred as genotypes) with better resistance to combinations of the four diseases and acceptable grain yield as potential parents, and (c) map genomic regions associated with resistance to each disease using genome-wide association study (GWAS). A diversity panel of 196 spring wheat genotypes was evaluated for their reaction to stripe rust at eight environments, leaf rust at four environments, leaf spot at three environments, common bunt at two environments, and grain yield at five environments. The panel was genotyped with the Wheat 90K SNP array and a few KASP SNPs of which we used 23,342 markers for statistical analyses. The RLPSI analysis performed by restricting the expected genetic gain for yield displayed significant (p < 0.05) differences among the 3125 economic weights. Using the best four economic weights, a subset of 22 of the 196 genotypes were selected as potential parents with resistance to the four diseases and acceptable grain yield. GWAS identified 37 genomic regions, which included 12 for common bunt, 13 for leaf rust, 5 for stripe rust, and 7 for leaf spot. Each genomic region explained from 6.6 to 16.9% and together accounted for 39.4% of the stripe rust, 49.1% of the leaf spot, 94.0% of the leaf rust, and 97.9% of the common bunt phenotypic variance combined across all environments. Results from this study provide valuable information for wheat breeders selecting parental combinations for new crosses to develop improved germplasm with enhanced resistance to the four diseases as well as the physical positions of genomic regions that confer resistance, which facilitates direct comparisons for independent mapping studies in the future.

Identification of Spring Wheat with Superior Agronomic Performance under Contrasting Nitrogen Managements Using Linear Phenotypic Selection Indices.

Both the Linear Phenotypic Selection Index (LPSI) and the Restrictive Linear Phenotypic Selection Index (RLPSI) have been widely used to select parents and progenies, but the effect of economic weights on the selection parameters (the expected genetic gain, response to selection, and the correlation between the indices and genetic merits) have not been investigated in detail. Here, we (i) assessed combinations of 2304 economic weights using four traits (maturity, plant height, grain yield and grain protein content) recorded under four organically (low nitrogen) and five conventionally (high nitrogen) managed environments, (ii) compared single-trait and multi-trait selection indices (LPSI vs. RLPSI by imposing restrictions to the expected genetic gain of either yield or grain protein content), and (iii) selected a subset of about 10% spring wheat cultivars that performed very well under organic and/or conventional management systems. The multi-trait selection indices, with and without imposing restrictions, were superior to single trait selection. However, the selection parameters differed quite a lot depending on the economic weights, which suggests the need for optimizing the weights. Twenty-two of the 196 cultivars that showed superior performance under organic and/or conventional management systems were consistently selected using all five of the selected economic weights, and at least two of the selection scenarios. The selected cultivars belonged to the Canada Western Red Spring (16 cultivars), the Canada Northern Hard Red (3), and the Canada Prairie Spring Red (3), and required 83–93 days to maturity, were 72–100 cm tall, and produced from 4.0 to 6.2 t ha−1 grain yield with 14.6–17.7% GPC. The selected cultivars would be highly useful, not only as potential trait donors for breeding under an organic management system, but also for other studies, including nitrogen use efficiency.

Efficiency of a Constrained Linear Genomic Selection Index To Predict the Net Genetic Merit in Plants.

The constrained linear genomic selection index (CLGSI) is a linear combination of genomic estimated breeding values useful for predicting the net genetic merit, which in turn is a linear combination of true unobservable breeding values of the traits weighted by their respective economic values. The CLGSI is the most general genomic index and allows imposing constraints on the expected genetic gain per trait to make some traits change their mean values based on a predetermined level, while the rest of them remain without restrictions. In addition, it includes the unconstrained linear genomic index as a particular case. Using two real datasets and simulated data for seven selection cycles, we compared the theoretical results of the CLGSI with the theoretical results of the constrained linear phenotypic selection index (CLPSI). The criteria used to compare CLGSI vs. CLPSI efficiency were the estimated expected genetic gain per trait values, the selection response, and the interval between selection cycles. The results indicated that because the interval between selection cycles is shorter for the CLGSI than for the CLPSI, CLGSI is more efficient than CLPSI per unit of time, but its efficiency could be lower per selection cycle. Thus, CLGSI is a good option for performing genomic selection when there are genotyped candidates for selection.

Optimum and Decorrelated Constrained Multistage Linear Phenotypic Selection Indices Theory.

Some authors have evaluated the unconstrained optimum and decorrelated multistage linear phenotypic selection indices (OMLPSI and DMLPSI, respectively) theory. We extended this index theory to the constrained multistage linear phenotypic selection index context, where we denoted OMLPSI and DMLPSI as OCMLPSI and DCMLPSI, respectively. The OCMLPSI (DCMLPSI) is the most general multistage index and includes the OMLPSI (DMLPSI) as a particular case. The OCMLPSI (DCMLPSI) predicts the individual net genetic merit at different individual ages and allows imposing constraints on the genetic gains to make some traits change their mean values based on a predetermined level, while the rest of them remain without restrictions. The OCMLPSI takes into consideration the index correlation values among stages, whereas the DCMLPSI imposes the restriction that the index correlation values among stages be null. The criteria to evaluate OCMLPSI efficiency vs. DCMLPSI efficiency were that the total response of each index must be lower than or equal to the single-stage constrained linear phenotypic selection index response and that the expected genetic gain per trait values should be similar to the constraints imposed by the breeder. We used one real and one simulated dataset to validate the efficiency of the indices. The results indicated that OCMLPSI accuracy when predicting the selection response and expected genetic gain per trait was higher than DCMLPSI accuracy when predicting them. Thus, breeders should use the OCMLPSI when making a phenotypic selection.

The Relative Efficiency of Two Multistage Linear Phenotypic Selection Indices to Predict the Net Genetic Merit

Multistage linear phenotypic selection indices predict the individual net genetic merit at different individual ages or stages and are cost‐saving strategies for improving several traits. In a two‐stage context, we compared the relative efficiency of the optimum multistage linear phenotypic selection index (OMLPSI) and the decorrelated multistage linear phenotypic selection index (DMLPSI) theory to predict the individual net genetic merit and selection response using a real and a simulated dataset. In addition, we described a method for obtaining the OMLPSI selection intensity in a two‐stage context. The criteria used to compare the relative efficiency of both indices were that the total selection response of each index must be lower than or equal to the single‐stage linear phenotypic selection index (LPSI) selection response, similar to the accuracy of each index to predict the net genetic merit. Using four different total proportions (p = 0.05, 0.10, 0.20, and 0.30) for the real dataset, the total DMLPSI selection response was 22.80% higher than the estimated single‐stage LPSI selection response, whereas the total OMLPSI selection response was only 2.21% higher than the estimated single‐stage LPSI selection response. In addition, at Stage 2, OMLPSI accuracy was 62.24% higher than the DMLPSI accuracy for predicting the net genetic merit. We found similar results for the simulated data. Thus, we recommend using OMLPSI when performing the multistage phenotypic selection.

A Predetermined Proportional Gains Eigen Selection Index Method

The most general linear phenotypic selection index (PSI) is the predetermined proportional gains phenotypic selection index (PPG‐PSI) that allows imposing restrictions on the trait expected genetic gain values to make some traits change their mean values based on a predetermined level, while the rest of the traits remain without restrictions. However, due to the increasing number of restricted traits: (i) PPG‐PSI accuracy decreases; (ii) the proportional constant associated with this index can be negative, in which case, its results have no meaning in practice; and (iii) the PPG‐PSI can shift the population means in the opposite direction to the predetermined desired direction. Based on the eigen selection index method (ESIM), we propose a PPG‐ESIM that does not require a proportional constant, and due to the properties associated with eigen analysis, it is possible to use the theory of similar matrices to change the direction of the eigenvector values without affecting PPG‐ESIM accuracy, which helps to eliminate the problem indicated in the third point above, associated with the standard PPG‐PSI. The PPG‐ESIM uses the first eigenvector as its vector of coefficients, and the first eigenvalue in the selection response. Two simulated and one real data set, each with four traits, were used to validate PPG‐ESIM efficiency vs. PPG‐PSI efficiency; the simulated and real results indicated that PPG‐ESIM efficiency was higher than PPG‐PSI efficiency. We concluded that PPG‐ESIM is an efficient selection index that can be used in any selection program as a good alternative to PPG‐PSI.