Optimal Design of Low-Density SNP Arrays for Genomic Prediction: Algorithm and Applications

Low-density (LD) single nucleotide polymorphism (SNP) arrays provide a cost-effective solution for genomic prediction and selection, but algorithms and computational tools are needed for the optimal design of LD SNP chips. A multiple-objective, local optimization (MOLO) algorithm was developed for design of optimal LD SNP chips that can be imputed accurately to medium-density (MD) or high-density (HD) SNP genotypes for genomic prediction. The objective function facilitates maximization of non-gap map length and system information for the SNP chip, and the latter is computed either as locus-averaged (LASE) or haplotype-averaged Shannon entropy (HASE) and adjusted for uniformity of the SNP distribution. HASE performed better than LASE with ≤1,000 SNPs, but required considerably more computing time. Nevertheless, the differences diminished when >5,000 SNPs were selected. Optimization was accomplished conditionally on the presence of SNPs that were obligated to each chromosome. The frame location of SNPs on a chip can be either uniform (evenly spaced) or non-uniform. For the latter design, a tunable empirical Beta distribution was used to guide location distribution of frame SNPs such that both ends of each chromosome were enriched with SNPs. The SNP distribution on each chromosome was finalized through the objective function that was locally and empirically maximized. This MOLO algorithm was capable of selecting a set of approximately evenly-spaced and highly-informative SNPs, which in turn led to increased imputation accuracy compared with selection solely of evenly-spaced SNPs. Imputation accuracy increased with LD chip size, and imputation error rate was extremely low for chips with ≥3,000 SNPs. Assuming that genotyping or imputation error occurs at random, imputation error rate can be viewed as the upper limit for genomic prediction error. Our results show that about 25% of imputation error rate was propagated to genomic prediction in an Angus population. The utility of this MOLO algorithm was also demonstrated in a real application, in which a 6K SNP panel was optimized conditional on 5,260 obligatory SNP selected based on SNP-trait association in U.S. Holstein animals. With this MOLO algorithm, both imputation error rate and genomic prediction error rate were minimal.