Multi-objective optimized genomic breeding strategies for sustainable food improvement

Abstract

The purpose of breeding programs is to obtain sustainable gains in multiple traits while controlling the loss of genetic variation. The decisions at each breeding cycle involve multiple, usually competing, objectives; these complex decisions can be supported by the insights that are gained by applying multi-objective optimization principles to breeding. The discussion in this manuscript includes the definition of several multi-objective optimized breeding approaches within the phenotypic or genomic breeding frameworks and the comparison of these approaches with the standard multi-trait breeding schemes such as tandem selection, independent culling and index selection. Proposed methods are demonstrated with two empirical data sets and simulations. In addition, we have described several graphical tools that can aid breeders in arriving at a compromise decision. The results show that the proposed methodology is a viable approach to answer several real breeding problems. In simulations, the newly proposed methods resulted in gains larger than the methods previously proposed including index selection: Compared to the best alternative breeding strategy, the gains from multi-objective optimized parental proportions approaches were about 20-30% higher at the end of long-term simulations of breeding cycles. In addition, the flexibility of the multi-objective optimized breeding strategies were displayed with methods and examples covering non-dominated selection, assignment of optimal parental proportions, using genomewide marker effects in producing optimal mating designs, and finally in selection of training populations for genomic prediction.

Fig. 1

An abstraction of methods for improving multiple traits under parental proportions and genomic mating. MOOB multi-objective optimized breeding. Assigning parental contributions involve balancing gains for k traits and inbreeding. Genomic matings seeks to balance gains, within-family variances for k traits and inbreeding

Fig. 2

These figures are obtained by plotting GEBVs from model in (eq:model) for grain yield and grain protein content in wheat (a) and barley (b) dataset. Each circle represents a genotype, and dominance ordering connects all genotypes of the same dominance with a line. The genotypes on the lower dominance ordering levels are preferable to genotypes in the higher ordering levels. Genotypes with lower dominance ordering levels should be assigned higher weights in selection. There are 18 and 31 levels of dominance for wheat and barley data sets. The axes in these figures measure the standardized GEBV values (i.e., centered by mean, scaled by standard deviation) for grain yield and grain protein content

Fig. 3

Pareto optimal solutions for parental contributions (wheat data) obtained by solving the optimization problem giving in Eq. (1) for improving grain yield (GY) and grain protein content (GPC) while controlling group coancestry, i.e, we assume we want to maximize GY, GPC, and the negative of inbreeding. The redness of the points indicates closeness to ideal solutions as calculated by the formula in Supplementary Information Equation (Eq. (2))

Fig. 4

Two ‘good’ solutions on the wheat frontier curve obtained from Fig. 3 for the wheat data. Red points indicated the individuals that have non-zero parental proportions. The size of the points are proportional to the magnitude of the parental contributions. The figures on the right side, represent the same information but on the first two principal components of the genotyping marker space. PC principal components

Fig. 5

Simulations: the results from 30 replications of 16 rounds GS and 10 rounds PS with tandem, index selection (equal weights for traits) and independent culling, and 16 rounds with three multi-trait breeding methods. Breeding population sizes 100, 200, 300, and 400. Data points (in the trend lines) represent the improvement in Trait 1 and Trait 2 in consecutive breeding cycles. The changing sizes of points represents the variability of different breeding methods at each cycle over replicated trials of the experiment (30 reps) starting from the same initial population, the larger points corresponding to larger variances (the total variance of the mean breeding values obtained by a breeding method at a certain cycle calculated over the replications)