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The number of SNPs required for QTL discovery is justified by the distance at which linkage disequilibrium has decayed. Simulations and real potato SNP data showed how to estimate and interpret LD decay. The magnitude of linkage disequilibrium (LD) and its decay with genetic distance determine the resolution of association mapping, and are useful for assessing the desired numbers of SNPs on arrays. To study LD and LD decay in tetraploid potato, we simulated autotetraploid genotypes and used it to explore the dependence on: (1) the number of haplotypes in the population (the amount of genetic variation) and (2) the percentage of haplotype specific SNPs (hs-SNPs). Several estimators for short-range LD were explored, such as the average r 2 , median r 2 , and other percentiles of r 2 (80, 90, and 95 %). For LD decay, we looked at LD ½,90 , the distance at which the short-range LD is halved when using the 90 % percentile of r 2 at short range, as estimator for LD. Simulations showed that the performance of various estimators for LD decay strongly depended on the number of haplotypes, although the real value of LD decay was not influenced very much by this number. The estimator LD ½,90 was chosen to evaluate LD decay in 537 tetraploid varieties. LD ½,90 values were 1.5 Mb for varieties released before 1945 and 0.6 Mb in varieties released after 2005. LD ½,90 values within three different subpopulations ranged from 0.7 to 0.9 Mb. LD ½,90 was 2.5 Mb for introgressed regions, indicating large haplotype blocks. In pericentromeric heterochromatin, LD decay was negligible. This study demonstrates that several related factors influencing LD decay could be disentangled, that no universal approach can be suggested, and that the estimation of LD decay has to be performed with great care and knowledge of the sampled material.

Evaluation of LD decay and various LD-decay estimators in simulated and SNP-array data of tetraploid potato