Mixed linear model (MLM) methods have proven useful in controlling for population structure and relatedness within genome-wide association studies. However, MLM-based methods can be computationally challenging for large datasets. We report a compression approach, called 'compressed MLM', that decreases the effective sample size of such datasets by clustering individuals into groups. We also present a complementary approach, 'population parameters previously determined' (P3D), that eliminates the need to re-compute variance components. We applied these two methods both independently and combined in selected genetic association datasets from human, dog and maize. The joint implementation of these two methods markedly reduced computing time and either maintained or improved statistical power. We used simulations to demonstrate the usefulness in controlling for substructure in genetic association datasets for a range

Supplementary data are available at Bioinformatics online.

There is tremendous interest in using association mapping to identify genes responsible for quantitative variation of complex traits with agricultural and evolutionary importance. Recent advances in genomic technology, impetus to exploit natural diversity, and development of robust statistical analysis methods make association mapping appealing and affordable to plant research programs. Association mapping identifi es quantitative trait loci (QTLs) by examining the marker-trait associations that can be attributed to the strength of linkage disequilibrium between markers and functional polymorphisms across a set of diverse germplasm. General understanding of association mapping has increased signifi cantly since its debut in plants. We have seen a more concerted effort in assembling various association-mapping populations and initiating experiments through either candidategene or genome-wide approaches in different plant species. In this review, we describe the current status of association mapping in plants and outline opportunities and challenges in complex trait dissection and genomics-assisted crop improvement.

Whereas breeders have exploited diversity in maize for yield improvements, there has been limited progress in using beneficial alleles in undomesticated varieties. Characterizing standing variation in this complex genome has been challenging, with only a small fraction of it described to date. Using a population genetics scoring model, we identified 55 million SNPs in 103 lines across pre-domestication and domesticated Zea mays varieties, including a representative from the sister genus Tripsacum. We find that structural variations are pervasive in the Z. mays genome and are enriched at loci associated with important traits. By investigating the drivers of genome size variation, we find that the larger Tripsacum genome can be explained by transposable element abundance rather than an allopolyploid origin. In contrast, intraspecies genome size variation seems to be controlled by chromosomal knob content. There is tremendous overlap in key gene content in maize and Tripsacum, suggesting that adaptations from Tripsacum (for example, perennialism and frost and drought tolerance) can likely be integrated into maize.

A-Maize-ing Maize is one of our oldest and most important crops, having been domesticated approximately 9000 years ago in central Mexico. Schnable et al. (p. 1112 ; see the cover) present the results of sequencing the B73 inbred maize line. The findings elucidate how maize became diploid after an ancestral doubling of its chromosomes and reveals transposable element movement and activity and recombination. Vielle-Calzada et al. (p. 1078 ) have sequenced the Palomero Toluqueño ( Palomero ) landrace, a highland popcorn from Mexico, which, when compared to the B73 line, reveals multiple loci impacted by domestication. Swanson-Wagner et al. (p. 1118 ) exploit possession of the genome to analyze expression differences occurring between lines. The identification of single nucleotide polymorphisms and copy number variations among lines was used by Gore et al. (p. 1115 ) to generate a Haplotype map of maize. While chromosomal diversity in maize is high, it is likely that recombination is the major force affecting the levels of heterozygosity in maize. The availability of the maize genome will help to guide future agricultural and biofuel applications (see the Perspective by Feuillet and Eversole ).

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Height is one of the most heritable and easily measured traits in maize (Zea mays L.). Given a pedigree or estimates of the genomic identity-by-state among related plants, height is also accurately predictable. But, mapping alleles explaining natural variation in maize height remains a formidable challenge. To address this challenge, we measured the plant height, ear height, flowering time, and node counts of plants grown in >64,500 plots across 13 environments. These plots contained >7300 inbreds representing most publically available maize inbreds in the United States and families of the maize Nested Association Mapping (NAM) panel. Joint-linkage mapping of quantitative trait loci (QTL), fine mapping in near isogenic lines (NILs), genome-wide association studies (GWAS), and genomic best linear unbiased prediction (GBLUP) were performed. The heritability of maize height was estimated to be >90%. Mapping NAM family-nested QTL revealed the largest explained 2.1 ± 0.9% of height variation. The effects of two tropical alleles at this QTL were independently validated by fine mapping in NIL families. Several significant associations found by GWAS colocalized with established height loci, including brassinosteroid-deficient dwarf1, dwarf plant1, and semi-dwarf2. GBLUP explained >80% of height variation in the panels and outperformed bootstrap aggregation of family-nested QTL models in evaluations of prediction accuracy. These results revealed maize height was under strong genetic control and had a highly polygenic genetic architecture. They also showed that multiple models of genetic architecture differing in polygenicity and effect sizes can plausibly explain a population’s variation in maize height, but they may vary in predictive efficacy.

Tocopherols, tocotrienols, and plastochromanols (collectively termed tocochromanols) are lipid-soluble antioxidants synthesized by all plants. Their dietary intake, primarily from seed oils, provides vitamin E and other health benefits. Tocochromanol biosynthesis has been dissected in the dicot Arabidopsis thaliana, which has green, photosynthetic seeds, but our understanding of tocochromanol accumulation in major crops, whose seeds are nonphotosynthetic, remains limited. To understand the genetic control of tocochromanols in grain, we conducted a joint linkage and genome-wide association study in the 5000-line U.S. maize (Zea mays) nested association mapping panel. Fifty-two quantitative trait loci for individual and total tocochromanols were identified, and of the 14 resolved to individual genes, six encode novel activities affecting tocochromanols in plants. These include two chlorophyll biosynthetic enzymes that explain the majority of tocopherol variation, which was not predicted given that, like most major cereal crops, maize grain is nonphotosynthetic. This comprehensive assessment of natural variation in vitamin E levels in maize establishes the foundation for improving tocochromanol and vitamin E content in seeds of maize and other major cereal crops.