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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. Electronic supplementary material The online version of this article (10.1186/s12863-018-0661-4) contains supplementary material, which is available to authorized users.

Background The aim of this work was to study the effects on litter size of variants of the porcine genes RBP4, ESR1 and IGF2, currently used in genetic tests for different purposes. Moreover, we investigated a possible effect of the interaction between RBP4-MspI and ESR1-PvuII polymorphisms. The IGF2-intron3-G3072A polymorphism is actually used to select lean growth, but other possible effects of this polymorphism on reproductive traits need to be evaluated. Methods Detection of polymorphisms in the genomic and cDNA sequences of RBP4 gene was carried out. RBP4-MspI and IGF2-intron3-G3072A were genotyped in a hyperprolific Chinese-European line (Tai-Zumu) and three new RBP4 polymorphisms were genotyped in different pig breeds. A bivariate animal model was implemented in association analyses considering the number of piglets born alive at early (NBA12) and later parities (NBA3+ ) as different traits. A joint analysis of RBP4-MspI and ESR1-PvuII was performed to test their possible interaction. In the IGF2 analysis, paternal or maternal imprinting effects were also considered. Results Four different RBP4 haplotypes were detected (TGAC, GGAG, GAAG and GATG) in different pig breeds and wild boars. A significant interaction effect between RBP4-MspI and ESR1-PvuII polymorphisms of 0.61 ± 0.29 piglets was detected on NBA3+. The IGF2 analysis revealed a significant increase on NBA3+ of 0.74 ± 0.37 piglets for the paternally inherited allele A. Conclusions All the analyzed pig and wild boar populations shared one of the four detected RBP4 haplotypes. This suggests an ancestral origin of the quoted haplotype. The joint use of RBP4-MspI and ESR1-PvuII polymorphisms could be implemented to select for higher prolificacy in the Tai-Zumu line. In this population, the paternal allele IGF2-intron3-3072A increased litter size from the third parity. The non-additive effects on litter size reported here should be tested before implementation in other pig breeding schemes.