2.5. Linkage Disequilibrium (LD) and Effective Population Size

The LD analysis and Ne estimation were performed based on the data of 100,000 SNPs randomly selected across scaffolds >10 Mb. The r² statistic was computed to measure the LD level between all possible pairs of SNPs located on the same scaffold using SNP1101 software. Equation (2) was used to estimate the r² values [51]:

where: D = P_AB−P_AP_B and P_A, P_a, P_B, and P_b are the frequencies of alleles A, a, B, and b, respectively; and P_AB presents the frequency of haplotype AB. Since haplotypes were not reconstructed, an unbiased estimator of D was computed using Equation (3) [52]:

where: N is the total number of samples and N_AABB, N_AABb, N_AaBB, and N_AaBb are the number of genotypes AABB, AABb, AaBb and AaBb, respectively. In addition, sample size correction for unphased data was made to all computed r² using Equation (4) as [53,54]:

where n is the number of sampled haplotypes. The LD decay was assessed in three distance sets of ≤100 kb, ≤1000 kb, and ≤10 Mb, and SNP pairs were binned in each distance set using bin sizes of 10 kb, 100 kb, and 1000 kb, respectively. The average r² of each bin was plotted against the median size of the bin to depict the LD decay across the genome distances.

In addition, Equation (5) was used to estimate the effective population size based on the expectations for r² over different genomic intervals [55]:

where: c shows the median of the recombination distance between SNPs in Morgans. The age of Ne at a given distance was estimated by 1/(2c) as suggested by Hayes et al. [56]. The recombination rate was assumed to be 1 centiMorgan per million base pairs. The Ne was assessed at 200, 150, 100, 50, 10, and 5 generations ago to monitor the changes in population size.