Extent of third-order linkage disequilibrium in a composite line of Iberian pigs

Abstract

Background: Previous studies on linkage disequilibrium have investigated second order linkage disequilibrium in animal and plant populations. The objective of this paper was to investigate the genome-wide levels of third order linkage disequilibrium in a composite line founded by admixture of four Iberian pig strains. A model for the generation of third order linkage disequilibrium by population admixture is proposed. A computer Expectation-Maximization algorithm is developed and applied to the estimation of third order linkage disequilibrium at inter- and intra-chromosomal level using 26,347 SNPs typed in 306 sows. The relationship of third order linkage disequilibrium with physical distance was investigated over 35 million triplets in SSC12. Basic and normalized estimates of inter and intra-chromosomal third order linkage disequilibrium are reported.

Results: Genome-wide analyses revealed that third order linkage disequilibrium is rather common among linked loci in this Iberian pig line. It is shown that population admixture of multiple populations may explain the observed levels of third order linkage disequilibrium although it could be generated by genetic drift. Third order linkage disequilibrium decreases rapidly up to 4 Mb and then declines slowly. The short distances between consecutive markers explain the maintenance of the observed third order linkage disequilibria levels when using a model incorporating the break-up of disequilibrium by recombination. Genome-wide testing also revealed that only 3.6% of the normalized estimates were different from 1, - 1, 0, or from a not well-defined situation in which there is only one possible value for the third order linkage disequilibrium parameter, given allele frequencies and pairwise linkage disequilibria parameters.

Conclusions: Third order linkage disequilibrium is common among linked markers in the analyzed pig line and may have been generated by population admixture of multiple populations or by genetic drift. As with second order linkage disequilibrium, the absolute value of the third order linkage disequilibrium decreases with physical distance. Normalization of third order linkage disequilibrium should be avoided for closely linked bi-allelic loci.

Keywords: High order linkage disequilibrium; Iberian pigs; Linkage disequilibrium; Third order linkage disequilibrium.

Fig. 1

Configurations of all possible haplotypes for a three-locus system. Each arrow represents a one-time mutation in one of the SNPs (T/t, M/m, and K/k). Complementary haplotypes share the same color and superscript

Fig. 2

Break-up of third order linkage disequilibrium over time due to recombination. The same recombination fraction between each pair of consecutive SNPs, c, in a triplet is assumed

Fig. 3

Third order linkage disequilibrium parameter estimates for the 18 autosomes of a closed line of Iberian pigs

Fig. 4

Three dimension plot of two of the estimates of the second order linkage disequilibrium parameter (δ_TM, and δ_TK) versus estimates of the third order linkage disequilibrium parameter (δ_TMK) for all consecutive SNP triplets (Inter-chromosomal) and random SNPs from three different chromosomes (Inter-chromosomal)

Fig. 5

Plot of the third order linkage disequilibrium parameter (δ_TMK) versus one of the allele frequencies in consecutives (intra-chromosomal) and random triplets (inter-chromosomal)

Fig. 6

Histogram of frequencies of the observed distribution of the number of haplotypes in intra-chromosomal (blue) and inter-chromosomal (red)

Fig. 7

Plot of the third order linkage disequilibrium versus physical distance in over 35 millions triplets of SSC12. Red, blue and green lines represent the 25, 50 and 75% percentiles of the distribution. There are four intervals of one percentile each between each of the two: 25, 50 and 75% percentiles

Fig. 8

Hexbin histogram of the distribution of the number of haplotypes in a triplet with the proportion of third order linkage disequilibrium versus all disequilibria (β_TMK) distance in over 35 millions triplets of SSC12. The plot was carried out with hexbin package of R, which is a set of functions for creating, manipulating and plotting hexagon bins. The colors on the right hand side of the figure illustrate the amount of counts (associate to each color) that are represented for each hexagon in the figure

Fig. 9

Fictive metabolic pathway illustrating how third order linkage disequilibrium could lead to epistasis