### INTRODUCTION

^{2}above 0.3 for markers 100 to 150 apart. Uimari [22] characterized the extent of LD and estimated the LD-based actual and ancestral Ne values using 86 Finnish Landrace boars. This study reported average LD (r

^{2}) between adjacent SNP in the Illumina PorcineSNP60 BeadChip was 0.43 (57% of the adjacent SNP pairs had r

^{2}>0.2) for Finnish Landrace and Ne estimates based on the decay of r

^{2}with distance were similar to those based on the pedigree data: 80 for Finnish Landrace.

### MATERIALS AND METHODS

### Samples and genotypic data

### Characterization LD of Korean Landrace population

^{2}). The r

^{2}was equivalent to the covariance and correlation between alleles at two different loci and was computed as follows:

_{A}, P

_{a}, P

_{B}, and P

_{b}are the frequencies of alleles A, a, B, and b, respectively. P

_{AB}is the frequency of the genotype AB and D represents P

_{AB}- P

_{A}P

_{B}.

^{2}values were calculated between SNPs located on the same chromosome. Details about the physical positions of the SNPs can be found in the product literature from Illumina. To determine LD with respect to the physical distance between SNPs, we divided SNP pairs into distance bins. After establishing two classes, 0 to 0.5 Mb and 0 to 5 Mb, we subsequently classified the applicable SNPs pairs from each class into 50 distance bins with class-dependent ranges (Supplementary Table S1).

### Construction model of LD with distance

^{2}[5]:

^{2}) given by Sved in 1971 [5]. Based on this formula, a non-linear least-squares approach was used to statistically model the observed r

^{2}within R, as follows:

*y*

*is the r*

_{i}^{2}for SNP pair i at a linkage distance

*d*

*(Morgans). Parameters a and b were estimated iteratively using the least-squares method. In Figure 2, chromosome-specific megabase-to-centimorgan conversion rates were calculated from the total physical chromosome lengths stated on the UCSC Web site (genome.ucsc.edu) and from each chromosome genetic length on the porcine linkage map [26]. The study by Tortereau [26] included porcine linkage maps for four pedigrees (ILL, UIUC, USDA, ROS). Because the USDA breed of USA pedigree contained Landrace at the time of pedigree establishment, we selected USDA pedigrees for this study. We then applied this model to the data of each chromosome and estimated the described parameters. As described by Corbin [27] and Shin [28], the estimated parameters were combined by meta-analysis in R using an inverse variance method for pooling and random effects method based on the DerSimonian-Laird method (the R package “meta”) [25,27].*

_{i}### Ancestral Ne estimation

_{T}(t) is the Ne t generations ago, c is the distance between markers in Morgans, r

^{2}

_{c}is the mean value of r

^{2}for SNP pairs located c Morgans apart, and c = 1/2t when assuming linear growth [7]. To estimate N

_{T}(t), the number of previous generations was selected and the appropriate range of c was calculated. The binning process was designed to ensure sufficient SNP pairs within each bin and to obtain a representative r

^{2}mean when estimating the ancestral Ne. This process was performed for SNPs pooled across autosomes. The bin information used to estimate ancestral Ne is presented in Supplementary Table S3.

### RESULTS

### Genotype data

### LD estimation

^{2}for two loci on the same chromosome in Supplementary Figure 2. The two mean r

^{2}types for each of the distance bins were plotted against the medians of the distance bin range (Mb), as shown in Figure 2. In this study, the mean LD (r

^{2}) among the total 3.698 million SNP pairs in the Korean Landrace population was 0.135±0.204. For 36,025 SNP pairs, the distance was less than 50 kb; of these, 52.61% had an r

^{2}>0.3 and 61.87% had an r

^{2}>0.2. The average LD values for SNPs at distances of 50 kb on different autosomal chromosomes ranged from 0.379 to 0.500, and the average LD (r

^{2}) for those at distances of 5 Mb ranged from 0.099 to 0.219 (Supplementary Table S4). To identify degree of LD of each chromosomes, we observed some inter-chromosomal variations in the extent of LD. For two SNPs separated by <5 Mb, we observed the greatest and least mean LD (r

^{2}) on chromosomes 1, 13, and 14 and on chromosomes 10 and 12, respectively. These results agree with those of Uimari’s study [14], as well as results from the Korean Yorkshire population (data not shown).

^{2}decreased by approximately 40% (Figure 2a). The most rapid decrease was observed over the first 10 bins, with a decrease in the mean r

^{2}of approximately 53% (Figure 2b), either. The mean r

^{2}decreased much more slowly as the distance increased and remained constant at distances of ≥3 Mb. According to the r

^{2}calculations, 8,085 of the 3.698 million SNP pairs were in complete LD.

### Construction model of LD with distance

^{2}per SNP pair distance using our estimated parameters a and b in Equation (2), and compared the predicted r

^{2}values with those observed in other studies [24,25]. We observed that the r

^{2}values predicted using the non-linear regression equation were similar to the mean observed r

^{2}(Figure 4), suggesting that our parameters estimated using Equation (2) could explain the current situation and history of the Korean Landrace population.

### Estimation of the ancestral Ne

### DISCUSSION

^{2}) extended for long distances when the adjacent 100 SNPs of each SNP in the genome were used. Although a previous study used both mass pedigree and small genomic data [20], we used large-scale genomic data from GGP farms to characterize LD and estimate Ne with the aim of obtaining an unbiased picture of LD in the Korean Landrace population. Because domesticated pig breeds such as Landrace were strongly and artificially selected for a long period of time, the observed LD is higher at short distances and more extensive than that observed in human populations. The pattern of LD decline in the Korean Landrace population was consistent with those reported by previous studies of domesticated pig breeds [20,28] and other domesticated animals [24,25].

^{2}= 0.0, estimated Ne is infinite and if r

^{2}= 1.0, estimated Ne is zero). Uimari [22] noted this limitation of the method devised by Sved [5]. In this study, we calculated r

^{2}between one SNP with its adjacent 100 SNPs to reduce bias of r

^{2}estimation. If we used r

^{2}between one SNP with its adjacent few SNPs in this estimation, we could not take enough information about relationship between r

^{2}and distance because two SNPs interval could be short or long. So we used adjacent 100 SNPs per SNPs in r

^{2}eatimation and this was why the results could yielded accurate Ne. Another concern associated with the relationship between the estimated LD and the distance between SNPs involves the accuracy of the porcine reference genome (Build 9) used in this study. In future studies, updates to the porcine reference genome will refine the order and distances between SNPs on the commercial Illumina PorcineSNP60 version2 BeadChip. However, we considered that bias resulting from incorrect ordering of or distances between SNPs would be diluted by the large number of SNP pairs used in this study; therefore, slight overestimation and/or underestimation of LD would not be an issue. Moreover, the relationships between genetic and physical distances are known to vary across chromosomes and chromosomal regions. Therefore, we inferred the cM/Mb ratio per chromosome using position data from a physical map of the porcine reference genome and a genetic map generated using the USDA pedigree (derived from a population composed of ¼ Duroc, ¼ Large White, ¼ maternal Landrace, and ¼ high growth Landrace) in a previous study [26]. We further used genetic distances based on physical distances to estimate Ne. Accordingly, we were able to estimate Ne more reliably from these detailed estimates of genetic distances between SNPs, compared with other studies [24, 25]. Finally, another study reported that a limited sample size could bias the estimates of r

^{2}and recommended correcting these estimates for a sample size n (r

^{2}– 1/2n) before using the Sved [5] equation. However, given our large sample size, we did not need to correct the r

^{2}estimates or use corrected r

^{2}values. When estimating the Korean Landrace population Ne, we used an alternative version of the Sved [5] equation derived by Tenesa [26], which incorporated a new parameter a (equal to 2) to account for mutations. Using this formula [26], the initial value of parameter a was 2 when parameters were estimated using the non-linear regression model of R. As a result, the estimated parameter a per chromosome ranged from 2.45 to 3.35 (Figure 3), and the estimated parameter b per chromosome ranged from 39.12 to 139.77. Regarding heterogeneity in the variance of the observed r

^{2}per chromosome that declined as the distances between SNPs increased (Supplementary Figure S2), this might have affected our estimation of parameter b in Equation (2). In one study, a significant negative relationship was observed between the chromosome length and parameter b estimates from the non-linear model [24], whereas other studies of domestic livestock species reported a positive relationship [29] and still others did not investigate either type of relationship [25]. We therefore considered that the relationship between the chromosomal length and the estimated parameter b differed for each population, as did the evolution histories of each species and breed. In this study, all marker pairs were calculated only in each bin so that r

^{2}would not be affected by the chromosome length. These results were consistent with the Yorkshire LD characterization results reported by Uimari [22] and the Korean Yorkshire Ne study (in review) [14]. Furthermore, we did not observe a relationship between the chromosome length and the estimated b values.