As population structure can result in spurious associations, it has constrained the use of association studies in human and plant genetics. Association mapping, however, holds great promise if true signals of functional association can be separated from the vast number of false signals generated by population structure. We have developed a unified mixed-model approach to account for multiple levels of relatedness simultaneously as detected by random genetic markers. We applied this new approach to two samples: a family-based sample of 14 human families, for quantitative gene expression dissection, and a sample of 277 diverse maize inbred lines with complex familial relationships and population structure, for quantitative trait dissection. Our method demonstrates improved control of both type I and type II error rates over other methods. As this new method crosses the boundary between family-based and structured association samples, it provides a powerful complement to currently available methods for association mapping.

Sorghum, an African grass related to sugar cane and maize, is grown for food, feed, fibre and fuel. We present an initial analysis of the approximately 730-megabase Sorghum bicolor (L.) Moench genome, placing approximately 98% of genes in their chromosomal context using whole-genome shotgun sequence validated by genetic, physical and syntenic information. Genetic recombination is largely confined to about one-third of the sorghum genome with gene order and density similar to those of rice. Retrotransposon accumulation in recombinationally recalcitrant heterochromatin explains the approximately 75% larger genome size of sorghum compared with rice. Although gene and repetitive DNA distributions have been preserved since palaeopolyploidization approximately 70 million years ago, most duplicated gene sets lost one member before the sorghum-rice divergence. Concerted evolution makes one duplicated chromosomal segment appear to be only a few million years old. About 24% of genes are grass-specific and 7% are sorghum-specific. Recent gene and microRNA duplications may contribute to sorghum's drought tolerance.

Flowering time is a complex trait that controls adaptation of plants to their local environment in the outcrossing species Zea mays (maize). We dissected variation for flowering time with a set of 5000 recombinant inbred lines (maize Nested Association Mapping population, NAM). Nearly a million plants were assayed in eight environments but showed no evidence for any single large-effect quantitative trait loci (QTLs). Instead, we identified evidence for numerous small-effect QTLs shared among families; however, allelic effects differ across founder lines. We identified no individual QTLs at which allelic effects are determined by geographic origin or large effects for epistasis or environmental interactions. Thus, a simple additive model accurately predicts flowering time for maize, in contrast to the genetic architecture observed in the selfing plant species rice and Arabidopsis.

Maize genetic diversity has been used to understand the molecular basis of phenotypic variation and to improve agricultural efficiency and sustainability. We crossed 25 diverse inbred maize lines to the B73 reference line, capturing a total of 136,000 recombination events. Variation for recombination frequencies was observed among families, influenced by local (cis) genetic variation. We identified evidence for numerous minor single-locus effects but little two-locus linkage disequilibrium or segregation distortion, which indicated a limited role for genes with large effects and epistatic interactions on fitness. We observed excess residual heterozygosity in pericentromeric regions, which suggested that selection in inbred lines has been less efficient in these regions because of reduced recombination frequency. This implies that pericentromeric regions may contribute disproportionally to heterosis.

Association studies based on linkage disequilibrium (LD) can provide high resolution for identifying genes that may contribute to phenotypic variation. We report patterns of local and genomewide LD in 102 maize inbred lines representing much of the worldwide genetic diversity used in maize breeding, and address its implications for association studies in maize. In a survey of six genes, we found that intragenic LD generally declined rapidly with distance (r 2 < 0.1 within 1500 bp), but rates of decline were highly variable among genes. This rapid decline probably reflects large effective population sizes in maize during its evolution and high levels of recombination within genes. A set of 47 simple sequence repeat (SSR) loci showed stronger evidence of genome-wide LD than did single-nucleotide polymorphisms (SNPs) in candidate genes. LD was greatly reduced but not eliminated by grouping lines into three empirically determined subpopulations. SSR data also supplied evidence that divergent artificial selection on flowering time may have played a role in generating population structure. Provided the effects of population structure are effectively controlled, this research suggests that association studies show great promise for identifying the genetic basis of important traits in maize with very high resolution. In plant genetic studies, recombinant inbred lines have been very successful for mapping quantitative trait loci (QTLs) to 10-30 cM regions (1, 2), but association studies based on linkage disequilibrium (LD) may allow identification of the actual genes represented by QTLs. Only polymorphisms with extremely tight linkage to a locus with phenotypic effects are likely to be significantly associated with the trait in a randomly mating population, providing much finer resolution than genetic mapping. Association methods have been especially important for studying the genetic basis of human diseases, for which controlled genetic experiments are not feasible. However, these methods also have great potential for resolving individual genes responsible for QTLs (3-5).The resolution of association studies in a test sample depends on the structure of LD across the genome. LD, or the correlation between alleles at different sites, is generally dependent on the history of recombination between polymorphisms. However, factors such as genetic drift, selection within populations, and population admixture can also cause LD between markers and traits. [Following common practice (6, 7), we refer to gametic phase disequilibrium as LD whether or not it is caused by linkage.] Because many factors affect LD, its genomic structure in particular crop plants must be empirically determined before association studies can be applied. In maize, for example, divergent selection for adaptive traits such as time of maturation in different regions may have created LD among chromosomal regions containing major genes for these traits.Our goal in this study was to evaluate patterns of LD among 102 maize inbred lines representing the diversity ...

Accelerating crop improvement in sorghum, a staple food for people in semiarid regions across the developing world, is key to ensuring global food security in the context of climate change. To facilitate gene discovery and molecular breeding in sorghum, we have characterized ∼265,000 single nucleotide polymorphisms (SNPs) in 971 worldwide accessions that have adapted to diverse agroclimatic conditions. Using this genome-wide SNP map, we have characterized population structure with respect to geographic origin and morphological type and identified patterns of ancient crop diffusion to diverse agroclimatic regions across Africa and Asia. To better understand the genomic patterns of diversification in sorghum, we quantified variation in nucleotide diversity, linkage disequilibrium, and recombination rates across the genome. Analyzing nucleotide diversity in landraces, we find evidence of selective sweeps around starch metabolism genes, whereas in landrace-derived introgression lines, we find introgressions around known height and maturity loci. To identify additional loci underlying variation in major agroclimatic traits, we performed genome-wide association studies (GWAS) on plant height components and inflorescence architecture. GWAS maps several classical loci for plant height, candidate genes for inflorescence architecture. Finally, we trace the independent spread of multiple haplotypes carrying alleles for short stature or long inflorescence branches. This genome-wide map of SNP variation in sorghum provides a basis for crop improvement through marker-assisted breeding and genomic selection.Sorghum bicolor | quantitative trait locus | adaptation

SummaryCrop improvement and the dissection of complex genetic traits require germplasm diversity. Although this necessary phenotypic variability exists in diverse maize, most research is conducted using a small subset of inbred lines. An association population of 302 lines is now available -a valuable research tool that captures a large proportion of the alleles in cultivated maize. Provided that appropriate statistical models correcting for population structure are included, this tool can be used in association analyses to provide high-resolution evaluation of multiple alleles. This study describes the population structure of the 302 lines, and investigates the relationship between population structure and various measures of phenotypic and breeding value. On average, our estimates of population structure account for 9.3% of phenotypic variation, roughly equivalent to a major quantitative trait locus (QTL), with a high of 35%. Inclusion of population structure in association models is critical to meaningful analyses. This new association population has the potential to identify QTL with small effects, which will aid in dissecting complex traits and in planning future projects to exploit the rich diversity present in maize.

Historically, association tests have been used extensively in medical genetics, but have had virtually no application in plant genetics. One obstacle to their application is the structured populations often found in crop plants, which may lead to nonfunctional, spurious associations. In this study, statistical methods to account for population structure were extended for use with quantitative variation and applied to our evaluation of maize flowering time. Mutagenesis and quantitative trait locus (QTL) studies suggested that the maize gene Dwarf8 might affect the quantitative variation of maize flowering time and plant height. The wheat orthologs of this gene contributed to the increased yields seen in the 'Green Revolution' varieties. We used association approaches to evaluate Dwarf8 sequence polymorphisms from 92 maize inbred lines. Population structure was estimated using a Bayesian analysis of 141 simple sequence repeat (SSR) loci. Our results indicate that a suite of polymorphisms associate with differences in flowering time, which include a deletion that may alter a key domain in the coding region. The distribution of nonsynonymous polymorphisms suggests that Dwarf8 has been a target of selection.