Domesticated apple (Malus x domestica Borkh.) is a major global crop and the genetic diversity held within the pool of cultivated varieties is important for the development of future cultivars. The aim of this study was to investigate the diversity held within the domesticated form, through the analysis of a major international germplasm collection of cultivated varieties, the UK National Fruit Collection, consisting of over 2,000 selections of named cultivars and seedling varieties. We utilised Diversity Array Technology (DArT) markers to assess the genetic diversity within the collection. Clustering attempts, using the software STRUCTURE revealed that the accessions formed a complex and historically admixed group for which clear clustering was challenging. Comparison of accessions using the Jaccard similarity coefficient allowed us to identify clonal and duplicate material as well as revealing pairs and groups that appeared more closely related than a standard parent-offspring or full-sibling relations. From further investigation, we were able to propose a number of new pedigrees, which revealed that some historically important cultivars were more closely related than previously documented and that some of them were partially inbred. We were also able to elucidate a number of parent-offspring relationships that had resulted in a number of important polyploid cultivars. This included reuniting polyploid cultivars that in some cases dated as far back as the 18th century, with diploid parents that potentially date back as far as the 13th century.
This paper illustrates novel use of nonparametric regression in the challenging problem of reliably identifying true association patterns in high dimensional data without the cost, inherent in existing methods, of increasing the false positives. The proposed nonparametric association test (NPAT) treats p-values from multiple hypothesis tests as summaries of association that preserves the correlation in the data and capitalises on this correlation to increase power while minimising false discoveries, relative to existing methods. Distributional results are used to support estimation of the tuning parameter and significance thresholds for NPAT. The method is applied to the WTCCC study of Crohn's disease and results compared with a sequence kernel association test (SKAT) that conversely uses nonparametric regression techniques to group sets of explanatory variables, prior to association testing. Results show that NPAT is efficient, computationally tractable and produces findings comparable with Bonferroni correction while SKAT misses a strong association signal in the data.
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