Failing the four-gamete test enables exact phasing: the Corners' Algorithm.

Background: Failing the four-gamete test for two polymorphic DNA markers is an indication that two or three rather than four haplotypes segregate in the population. The objective of this paper is to show that when just three haplotypes are segregating, all three haplotypes can be fully and unambiguously phase-resolved.

Theory And Methods: The Corners' Algorithm tests the four corners in a 3 × 3 table of two-locus genotypes. If one of the four corners is filled with zeroes, then the missing haplotype is identified and the phases of all three haplotypes can be unambiguously resolved for all individuals. Three applications of this method are proposed when the four-gamete test fails: (1) direct estimation of linkage disequilibrium (LD), (2) haplotype-based genome-wide association studies (GWAS) of three haplotypes (single-marker GWAS tests for two out of three haplotypes only), and (3) haplotyping of chromosomal regions that are comprised of pairs of single nucleotide polymorphisms (SNPs) that consist of just three haplotypes. An example based on 435 sows with performance records for total number of piglets born is used to illustrate the methods.

Results: Of 20,339 SNPs, approximately 50% of the pairs of flanking SNPs failed the four-gamete test. For those, the expectation maximization (EM) algorithm gave the same results. The average of the absolute value of the difference in r between flanking SNPs across the genome between the two methods was 0.00082. Single-marker GWAS (using two of three haplotypes) detected significant associations for total number of piglets born on chromosomes 1, 2, 6, 9, 10, 12, 13, 14, 15, and 18. Haplotype-based GWAS using the third haplotype resolved with the Corners' Algorithm detected additional significant associations for total number of piglets born on chromosomes 2, 5, 10, 13, 14, 15, and 18. Estimated substitution effects ranged from 0.40 to 1.35 piglets. Haplotyping of chromosomal regions that failed the four-gamete test for any pair of SNPs covered 961 Mb out of the 2249 Mb by the SNP array.

Conclusions: The Corner's Algorithm allows to fully phase haplotypes when the four-gamete test fails. Longer haplotypes in chromosomal regions in which the four-gamete test fails for any pair of SNPs can be used as a multi-allelic marker with increased polymorphism information content.