Genomic Prediction Within and Across Biparental Families: Means and Variances of Prediction Accuracy and Usefulness of Deterministic Equations

Abstract

A major application of genomic prediction (GP) in plant breeding is the identification of superior inbred lines within families derived from biparental crosses. When models for various traits were trained within related or unrelated biparental families (BPFs), experimental studies found substantial variation in prediction accuracy (PA), but little is known about the underlying factors. We used SNP marker genotypes of inbred lines from either elite germplasm or landraces of maize (Zea mays L.) as parents to generate in silico 300 BPFs of doubled-haploid lines. We analyzed PA within each BPF for 50 simulated polygenic traits, using genomic best linear unbiased prediction (GBLUP) models trained with individuals from either full-sib (FSF), half-sib (HSF), or unrelated families (URF) for various sizes (Ntrain) of the training set and different heritabilities (h2). In addition, we modified two deterministic equations for forecasting PA to account for inbreeding and genetic variance unexplained by the training set. Averaged across traits, PA was high within FSF (0.41–0.97) with large variation only for Ntrain<50 and h2 <0.6. For HSF and URF, PA was on average ∼40–60% lower and varied substantially among different combinations of BPFs used for model training and prediction as well as different traits. As exemplified by HSF results, PA of across-family GP can be very low if causal variants not segregating in the training set account for a sizeable proportion of the genetic variance among predicted individuals. Deterministic equations accurately forecast the PA expected over many traits, yet cannot capture trait-specific deviations. We conclude that model training within BPFs generally yields stable PA, whereas a high level of uncertainty is encountered in across-family GP. Our study shows the extent of variation in PA that must be at least reckoned with in practice and offers a starting point for the design of training sets composed of multiple BPFs.

Genomic Prediction Within and Among Doubled-Haploid Libraries from Maize Landraces

“…Averaged across the four DHL, there was considerable variation in r among traits (Table 2). Such variation was also observed among segregating biparental populations in experiments with maize (Lehermeier et al 2014;Lian et al 2014) and in simulations (Schopp et al 2017b). A possible explanation is that each trait has a different genetic architecture, so that covariances among individuals estimated by genomewide markers may not equally well reflect the conditions at the underlying QTL.…”

“…However, no pattern could be recognized between the LPS of pairwise combinations of DHL and the observed r because means of r were quite low, and there was a large variation of r for different combinations of TS/PS and traits (Table 3). In predictions across unrelated biparental families (Schopp et al 2017b), the LPS was only loosely correlated with the prediction accuracy, whereas the parameter u ii * , referring to the proportion of polymorphic markers between two DHL, was much more important. However, in our study, we observed no association between u ii * ( Figure S4) and r.…”

“…A possible explanation for the low r values in scenario LwL is that many QTL, which segregate in the PS, do not segregate in the DHL serving as the TS. Thus, the effects of those genomic regions of the PS cannot be properly predicted from the TS, which gives poor r, as demonstrated for biparental families by Schopp et al (2017b). A further reason is the difference in allele substitution effects of markers between two DHL (Lehermeier et al 2015;Han et al 2018).…”

“…The prediction accuracies for the scenarios sL and LwL were forecasted with deterministic equations originally devised by Table 2 Prediction accuracy (r 6 SE) of seven agronomic traits from GP for scenario sL, obtained with GBLUP by LOOCV using N i = 50 sampled from the EF lines or DH lines from the landraces GB, SF, SM, and WA, as well as the means of the forecasted prediction accuracies r D and r W across traits Daetwyler et al (2008Daetwyler et al ( , 2010, denoted as r D , and Wientjes et al (2013Wientjes et al ( , 2015, denoted as r W . However, we used a modified version of these equations proposed by Schopp et al (2017b) accounting for (i) inbreeding of the genotypes, because all our genotypes were pure-breeding lines, and (ii) the different proportion of polymorphic markers in the TS and PS. A further modification (multiplication by r 2 MM=2 ) proposed by Lian et al (2014) was implemented, which accounts for incomplete linkage between quantitative trait loci (QTL) and markers by assuming that the QTL position is located close to the midpoint between markers.…”

“…Assumption (ii) would not hold true if detrimental alleles have negative epistatic effects in the DHL, as discussed above. Further, if allele frequencies of SNPs and QTL are different, this can lead to a substantial bias in r D and r W (Schopp et al 2017b). The latter problem most likely applies to our study, because we used a SNP array optimized for temperate and tropical dent germplasm (Ganal et al 2011) that is prone to ascertainment bias in flint materials (Frascaroli et al 2013).…”