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 (Zeamays 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 ([Formula: see text]) of the training set and different heritabilities ([Formula: see text] 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 [Formula: see text] and [Formula: see text] [Formula: see text] 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.

Keywords: GBLUP; GenPred; Genomic Selection; Shared Data Resources; biparental families; deterministic accuracy; genomic prediction; linkage disequilibrium; plant breeding.

Figure 1

(A) Boxplots of empirical prediction accuracies ${\rho }_{ABT}$ in BPFs of DH lines, and (B) variance components of different factors influencing the variation of ${\rho }_{ABRT}.$ Parents of BPFs were sampled from ancestral population Elite, and SNP markers were used to calculate the genomic relationship matrix $\mathit{G}\text{.}$ Results are shown for different pedigree relationships (FSF, HSF, and URF) between the predicted family (BPF_pred) $A$ and training family (BPF_train) $B,$ as well as for different sample sizes $N_{train}$and heritabilities $h^2.$

Figure 2

(A) Boxplots of empirical prediction accuracies ${\rho }_{ABT}$ in BPFs of DH lines and (B) variance components of different factors influencing the variation of ${\rho }_{ABRT}.$ Parents of BPFs were sampled from ancestral population Elite (left) or Landrace (right), and either genotypes at SNP markers or at QTL were used to calculate the genomic relationship matrix $\mathit{G}\text{.}$ Results are shown for different pedigree relationships (FSF, HSF, and URF) between the predicted family (BPF_pred) $A$ and training family (BPF_train) $B$ and refer to $N_{train}=100$ and $h^2=\mathrm{0.6.}$

Figure 3

Empirical prediction accuracy $\rho$ in BPFs of DH lines plotted against deterministic prediction accuracies ${\rho }^W$ and ${\rho }^D.$ The top two graphs refer to observations for single traits (${\rho }_{AT}$ for FSF and ${\rho }_{ABT}$ otherwise), and the bottom row to means over traits ($\overline{{\rho }_A}$ for FSF and $\overline{{\rho }_{AB}}$ otherwise). Parents of BPFs were sampled from ancestral population Elite and genotypes at SNP markers were used to calculate the genomic relationship matrix $\mathit{G}\text{.}$ Results are shown for a random sample of 10,000 data points, $N_{train}=100$ and $h^2=\mathrm{0.6.}$

Figure 4

(A) Chromosome segment substitution effects (CSSE_A,_W in red and CSSE_B,_W in blue) and correlation between local TBVs and local GEBVs in the predicted family $A$ (green) averaged in sliding windows $W$ (see Materials and Methods for definition). GEBVs were calculated from QTL effects estimated by RR-BLUP in training set (HSF) $B.$ Results are shown for $N_{train}=250$ and two traits T1 and T2 with $h^2=1$ and large differences in prediction accuracy $\rho .$ Both traits were generated from the same set of 1000 QTL with ${\theta }_{AB}\approx 0.40,$ but different QTL effects. (B) Correlation between local TBVs and local GEBVs (green lines) shown together with true QTL effects (diamonds) and estimated QTL effects (circles) for T1 and T2 in $B$ on chromosome 5. Colors indicate QTL segregating in both $A$ and $B$ (orange) or only in $A$ (purple); grey bars in the background reflect the windows $W.$