Characterization of a global germplasm collection and its potential utilization for analysis of complex quantitative traits in maize
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- Yang, X., Gao, S., Xu, S. et al. Mol Breeding (2011) 28: 511. doi:10.1007/s11032-010-9500-7
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Association mapping is a powerful approach for exploring the molecular basis of phenotypic variations in plants. A maize (Zea mays L.) association mapping panel including 527 inbred lines with tropical, subtropical and temperate backgrounds, representing the global maize diversity, was genotyped using 1,536 single nucleotide polymorphisms (SNPs). In total, 926 SNPs with minor allele frequencies of ≥0.1 were used to estimate the pattern of genetic diversity and relatedness among individuals. The analysis revealed broad phenotypic diversity and complex genetic relatedness in the maize panel. Two different Bayesian approaches identified three specific subpopulations, which were then reconfirmed by principal component analysis (PCA) and tree-based analyses. Marker–trait associations were performed to assess the suitability of different models for false-positive correction by population structure (Q matrix/PCA) and familial kinship (K matrix) alone or in combination in this panel. The K, Q + K and PCA + K models could reduce the false positives, and the Q + K model performed slightly better for flowering time, ear height and ear diameter. Our findings suggest that this maize panel is suitable for association mapping in order to understand the relationship between genotypic and phenotypic variations for agriculturally complex quantitative traits using optimal statistical methods.
KeywordsMaizeGenetic diversityGenetic relatednessAssociation mappingPhenotypic variation
Maize (Zea mays L.) is one of the most important crops in the world, serving as a source of food, feed and fuel. To address global demands due mainly to continuing population growth and energy insufficiencies, improvement of maize productivity and quality through breeding is vital (Tester and Langridge 2010). The availability of the maize genome sequence (Schnable et al. 2009; Vielle-Calzada et al. 2009) and advanced high-throughput genotyping techniques (Gupta et al. 2008; Varshney et al. 2009) will provide new insights into complex quantitative traits for maize improvement. Linkage mapping is a powerful and popular approach for identifying the genes or loci which affect the natural phenotypic variations. Generally, the resolution provided by linkage mapping is low (10–30 cM) unless huge mapping populations are used (Salvi et al. 2007; Ducrocq et al. 2009), whereas association mapping provides a complementary approach with higher resolution due to advances in rapid and cost-effective genotyping technologies and the development of statistical methods (Yu and Buckler 2006; Zhu et al. 2008; Myles et al. 2009). Since first successfully applied in maize (Thornsberry et al. 2001), a series of association mapping studies has been performed to investigate the causal variants associated with flowering time (Camus-Kulandaivelu et al. 2006; Salvi et al. 2007; Ducrocq et al. 2009; Pressoir et al. 2009), kernel starch related traits (Wilson et al. 2004), maysin synthesis (Szalma et al. 2005), forage quality related traits (Andersen et al. 2007), carotenoid content (Harjes et al. 2008; Yan et al. 2010a), kernel oil related traits (Belo et al. 2008) and kernel size (Li et al. 2010a, b), and the details have been summarized in a recent review (Yan et al. 2010b). Maize is an ideal crop for association mapping due to its great genetic diversity and rapid linkage disequilibrium (LD) decay (Yan et al. 2010b).
Successful association mapping of a species requires firstly the creation of a desirable germplasm collection that reflects genetic diversity, extent of LD decay and genetic relatedness in a population, which determine the mapping resolution and power (Zhu et al. 2008). Generally, germplasm collections need to encompass adequate genetic diversity to cover most variations for the traits of interest. Maize exhibits extensive genetic variation, so much so that the average diversity at the nucleotide level between any two maize lines is higher than that between humans and chimps (Buckler and Stevens 2005). Furthermore, the LD decays rapidly in diverse maize genotypes, to the extent of 2–5 kb in the elite inbred lines (Yan et al. 2009). These observations imply that the association mapping panel involving advanced breeding lines could provide adequate diversity and resolution for quantitative trait loci (QTL) analysis in maize. In choosing lines to construct an association mapping panel, one should consider the balance between genetic diversity and germplasm adaptation. Since maize originated from the tropical center of Mexico and then dispersed to other temperate regions worldwide, adaptation should be an important factor that must be considered for precise phenotyping in a given environment. Thus, developing an association mapping panel from elite lines chosen from breeding programs will have two obvious advantages: (1) partial avoidance of the adaptation issue with good field performance; (2) the ability to conveniently introgress the identified genes or QTL into elite genotypes used in breeding programs. Recent studies demonstrated that complex quantitative traits in maize, such as flowering time (Buckler et al. 2009) and oil content (Laurie et al. 2004), are controlled by a large number of genes/QTL with minor effects. For statistical significance, a reasonable sample size may be required to obtain enough power to identify such genes/QTL with subtle effects. However, in the reported analyses of maize association, 100–300 genotypes were usually used, which might only be adequate to identify genes with strong effects (Thornsberry et al. 2001; Wilson et al. 2004; Szalma et al. 2005; Harjes et al. 2008; Pressoir et al. 2009; Yan et al. 2010a; Li et al. 2010a, b).
Due to domestication and selection by breeders, complex patterns of genetic relatedness are common in maize association panels, generating numerous spurious associations (Yu and Buckler 2006; Zhu et al. 2008; Myles et al. 2009), which makes correcting spurious associations a major challenge for association mapping. Random molecular markers throughout the genome are generally used to estimate the genetic relatedness among individuals. Genome control (GC) (Devlin and Roeder 1999; Zheng et al. 2005) and the structured association (SA) (Pritchard et al. 2000b) are two major methods first used to control false-positive associations. The SA method, often used by the program STRUCTURE to estimate population structure (Q matrix) (Pritchard et al. 2000a; Falush et al. 2003), was further refined by incorporating the relative kinship into the mixed-liner model (MLM), thereby efficiently reducing spurious associations when genetic relatedness among individuals is complex (Yu et al. 2006; Kang et al. 2008; Stich et al. 2008; Zhu and Yu 2009). Recently, it was suggested that principal component analysis (PCA) is a fast and effective way to infer population structure (Patterson et al. 2006; Price et al. 2006), and it showed some promise in replacing the Q matrix in the mixed model (Zhao et al. 2007; Zhu and Yu 2009). The development of statistical methods makes association mapping appealing for exploring the genetic architecture of quantitative traits, but additional research is required to improve the statistical methods for association mapping, especially for genome-wide association studies (GWAS).
We have assembled a global germplasm collection with more than 1,000 maize elite inbreds representing the major temperate and tropical/subtropical breeding programs of China, CIMMYT and Germplasm Enhancement of Maize (GEM). Some of the lines in the collection have been described in previous studies (Yang et al. 2010). All the lines were genotyped using the 1,536-SNP GoldenGate assay and phenotyped in Beijing and Sanya, China from 2005 to 2008 (Yang et al. 2010), and Ya’an, China in 2009. Finally, based on the genetic diversity information provided by single nucleotide polymorphism (SNP) markers and adaptation data obtained from the field experiments, 527 lines were chosen for the present study. Our objectives were: (1) to estimate the phenotypic and genetic diversity of the elite maize inbred collection; (2) to examine the population structure and familial relatedness of the elite maize inbreds collection; and (3) to evaluate the power and the appropriate statistical models of this panel for association analysis.
Materials and methods
Plant germplasm, phenotyping and genotyping
A set of 527 global diverse lines, representative of tropical, subtropical and temperate germplasm, was collected to construct a large association panel in maize. This collection included 54 lines from the GEM project, 235 lines from the CIMMYT maize breeding programs and 238 lines from China. The latter contained a small association panel of 143 elite lines of the parents of commercial hybrids widely used in China, lines derived from Chinese landraces, high-oil lines and high provitamin A lines (Yang et al. 2010). Pedigree details are summarized in Electronic Supplementary Material Table S1.
All 527 lines (excepted the 54 GEM lines) were divided into two groups (temperate and tropical/subtropical) based on pedigree information and planted in one-row plots in an incompletely randomized block design within the group with two replicates at the agronomy farm of Sichuan Agricultural University, Ya’an, Sichuan in the summer of 2009. Five plants and five self-pollinated mature ears per line were used to score plant and ear traits, respectively. The measured traits included the following: days to pollen shedding, days to silk, plant height, ear height, leaf width, leaf length, tassel length, number of tassel branches, ear length, ear diameter, cob diameter and number of kernel rows.
Leaf tissue samples for the whole association panel were obtained from the bulk of at least six individuals for each line. DNA was extracted by a modified CTAB procedure according to Murray and Thompson (1980). All 527 lines were genotyped using GoldenGate assays (Illumina, San Diego, CA, USA) containing 1,536 SNPs (Yan et al. 2010c). The SNP genotyping was performed on an Illumina BeadStation 500G at Cornell University Life Sciences Core Laboratories Center using the protocol supported by Illumina Company (Fan et al. 2006). The details of the SNP genotyping procedure and allele scoring have been described in previous studies (Yan et al. 2010c). Of the 1,536 SNPs genotyped, 1,067 SNPs having missing data less than 20% and of good quality were used for subsequent analysis, among which 926 SNPs with minor allelic frequencies (MAFs) ≥0.1 were used for genotypic data analyses.
Genotypic data analyses
The number of alleles, MAFs, gene diversity, observed heterozygosity and polymorphic information content (PIC) were calculated using Powermarker version 3.25 (Liu and Muse 2005). The statistical significance of differences in all estimators, except the number of alleles, was assessed across loci using the Wilcoxon paired test.
Two Bayesian Markov chain Monte Carlo programs, STRUCTURE (Pritchard et al. 2000a; Falush et al. 2003) and INSTRUCT (Gao et al. 2007), were used to infer population structure and to assign genotypes to subpopulations. In both analyses, three independent simulations having 150,000 MCMC (Markov chain Monte Carlo) replications and 100,000 burn-ins were performed with the number of subpopulations (k) ranging from 1 to 15. For STRUCTURE, the ancestry model allowed for population mixture and correlated allele frequencies; the k value was determined by the log likelihood of the data (LnP(D)) in the STRUCTURE output and an ad hoc statistic ∆k based on the second-order rate of change in LnP(D) between successive k (Evanno et al. 2005). INSTRUCT runs allowed inference of population structure and selfing rates at individual levels. Optimal k was inferred using the log likelihood of the data and deviance information criterion (DIC). Results of replicate simulations from both programs were integrated by using the CLUMPP software (Jakobsson and Rosenberg 2007). The correlation coefficients of membership probabilities estimated from STRUCTURE and INSTRUCT were calculated for each k using PROC CORR in SAS 8.02 (SAS Institute 1999). To compare the results from STRUCTURE/INSTRUCT with the pedigree knowledge, lines with membership probabilities ≥0.60 were assigned to corresponding clusters; lines with membership probabilities <0.60 were assigned to a mixed group. Structure results of individual assignments to corresponding groups were graphically displayed using the DISTRUCT software (Rosenberg 2004).
An analysis of molecular variance (AMOVA) (Excoffier et al. 1992) and F-statistics (Fst) across all subpopulations and between pairwise subpopulations were performed using Arlequin V3.11 (Excoffier et al. 2005) to investigate population differentiations among the subpopulations clustered by STRUCTURE. Additionally, Nei’s genetic distances (Nei 1972) among these given subpopulations and individuals were calculated using Powermarker version 3.25 (Liu and Muse 2005). The Nei’s genetic distance (Nei 1972) among individuals was then used to construct a neighbor-joining (NJ) phylogenetic tree with 1000 runs of bootstrapping using Powermarker version 3.25 (Liu and Muse 2005). Furthermore, the Nei’s genetic matrices created were double-centered, and used to obtain eigenvectors by the modules DCENTER and EIGEN implemented in NTSYSpc 2.1 (Rohlf 2000). Finally, the relative kinship coefficients were calculated using the SPAGeDi software package (Hardy and Vekemans 2002). All negative values between individuals were set to 0 (Yu et al. 2006).
Phenotypic data analyses
Descriptive statistical analyses were carried out using SAS 8.02 (SAS Institute 1999). The trait means of all lines were used in subsequent analyses. The Shannon–Weaver indices (Poole 1974), measuring genetic diversity in categorical data, were calculated to investigate the phenotypic diversity in this maize panel. The details have been described in a previous study (Yang et al. 2010). Briefly, the phenotypic values were subdivided into ten classes with an interval of 0.5 SD using the means and SD of each trait in the maize panel; the number and frequency of phenotypic classes were used to calculate the Shannon–Weaver indices as defined by Poole (1974). The effects of population structure on all traits were tested using PROC GLM in SAS 8.02 (SAS Institute 1999). When the population structure was estimated by STRUCTURE, the model statement included two of the three components of the k = 3 Q matrix from the STRUCTURE analysis, while the top 10 axes of variations from NTSYSpc analysis were included for PCA. The principal components with the top axis numbers ranging from 1 to 9 were additionally used to evaluate the effects of population structure on flowering time (represented by days to pollen shedding), ear height and ear diameter.
Evaluation of the maize association panel
The statistical power of this maize panel for identifying genetic factors associated with quantitative traits was evaluated using various population size and genetic effects without considering population structure and relative kinship. We assumed that the population size was 100, 200, 300, 400, 500, 600, 700, 800, 900 and 1,000, and that the genetic effect (the ratio of explained total phenotypic variance) was 0.01, 0.02, 0.03, 0.04 and 0.05. All evaluations were performed using the Genetic Power Calculator (GPC, Purcell et al. 2003). The LD coefficient, r2, was assumed to be 0.8 as GWAS for numerous small genetic effects required high LD in maize (r2 > 0.8) (Gore et al. 2009). The power of detecting the causal genetic factors was given at a type I error rate of 0.05.
To assess the effect of genetic relatedness on association mapping on various quantitative traits and to identify the perfect model to correct for genetic relatedness in this maize panel, data for three traits, including flowering time (represented by days to pollen shedding), ear height and ear diameter, were collected to conduct marker–trait associations using 1067 SNPs. These SNPs were not expected to have significant effects on related traits as they were randomly selected and had low marker coverage across the whole genome. Six models were used to evaluate the effects of population structure (Q, PC) and relative kinship (K) on three traits for marker–trait associations: (1) the GLM model, without controlling for population structure and relative kinship; (2) the Q model, controlling for Q; (3) the PCA model, controlling for PC; (4) the K model, controlling for K; (5) the Q + K model, controlling for both Q and K; and (6) the PCA + K model, controlling for both PC and K. The GLM, Q and PCA models were performed using a general linear model (GLM) in TASSEL V2.1; the K, Q + K and PCA + K models were performed using mixed linear model (MLM) in TASSEL V2.1 (Yu et al. 2006; Zhang et al. 2009). The quantile–quantile plots of estimated –log10(p) were displayed using the observed P values from marker–trait associations, and deviations from the expectation demonstrated that the statistical analysis may cause spurious associations. Before carrying out model comparisons, we first determined the optimal dimension for PCA and PCA + K models by testing the PCA models with various numbers of dimensions using these three traits and the 1067 SNPs measured above. The top 10 axes of variations from the NTSYSpc analysis were used.
Phenotypic variations of measured quantitative traits
Phenotypic variations for 12 traits and the effects of population structure on each trait in this maize panel
Min ± SD
Max ± SD
Mean ± SD
Days to pollen (days)
60.5 ± 0.7
97.5 ± 3.5
79.6 ± 6.1
Days to silk (days)
60.5 ± 0.7
102.0 ± 1.4
82.3 ± 6.6
Plant height (cm)
105.2 ± 0.9
235.2 ± 17.3
172.6 ± 25.9
Ear height (cm)
14.9 ± 4.4
125.4 ± 1.4
65.8 ± 19.0
Leaf width (cm)
5.5 ± 0.7
12.4 ± 0.0
9.0 ± 1.2
Leaf length (cm)
49.7 ± 0.7
109.4 ± 0.3
76.0 ± 10.1
Tassel length (cm)
16.1 ± 2.2
50.3 ± 6.2
29.4 ± 4.7
Number of tassel branches
1.7 ± 0.4
27.7 ± 5.0
10.8 ± 4.8
Ear length (cm)
5.0 ± 0.0
18.2 ± 0.0
11.0 ± 2.1
Ear diameter (cm)
1.9 ± 0.6
4.8 ± 0.0
3.3 ± 0.5
Cob diameter (cm)
1.0 ± 0.0
3.1 ± 0.1
2.1 ± 0.3
Number of kernel rows
8.0 ± 0.0
19.7 ± 0.5
12.7 ± 1.8
Summary of SNPs
Population structure and genetic clustering
Similarly, PCA based on Nei’s genetic distances presented a picture with all lines separating into SS, NSS and TST subpopulations, with the mixed subpopulation being in the middle of these three defined subpopulations (Fig. 3b). The top two principal components clearly separated these subpopulations. The first principal component (PC1) accounted for 18.2% of the genetic variation in this maize panel and reflected the differentiation between SS and NSS or TST, whereas the second (PC2) accounted for 6.9% of the genetic variation and reflected the differentiation between NSS and TST. It appeared that SS was relatively distant from NSS and TST, while NSS and TST were close to each other in this collection.
Population divergence and genetic diversity
The results for detecting the three subpopulations by using different statistical methods such as STRUCTURE/INSTRUCT, NJ tree-based, and PCA were quite consistent. Fst values across the three subpopulations averaged 0.11 (P < 0.001), which was confirmed by AMOVA analysis, and we found that only 10.7% (P < 0.001) of the total genetic variation was partitioned among subpopulations and 89.3% (P < 0.001) within subpopulations. The pairwise Fst between the three subpopulations was 0.25 (P < 0.001) for SS versus NSS, 0.31 (P < 0.001) for SS versus TST and 0.09 (P < 0.001) for NSS versus TST. This result demonstrates that there was much higher differentiation between SS and NSS or TST, while it was significantly lower between NSS and TST. A similar pattern of differentiation among subpopulations was supported by Nei’s minimum genetic distance (Table S3).
MAF, heterozygosity, gene diversity and PIC for 926 SNPs were also estimated within inferred subpopulations and compared (Fig. 1). Compared to the entire panel, all three subpopulations including SS, NSS and TST had significantly lower MAFs (z = −15.2 to −4.2, all P < 0.01) (Fig. 1a). Among subpopulations, MAFs within SS (0.27) and TST (0.26) were similar but lower than within NSS (0.29). A similar picture was also obtained for genetic diversity within subpopulations estimated by gene diversity and PIC (Fig. 1c, d). For heterozygosity of SNPs, SS had the highest level of heterozygosity among all subpopulations, followed by TST and NSS in that order (Fig. 1b).
The distribution of kinship coefficients between 0 and 0.50 (Fig. S2) represents 99.7% of the data. A total of 56.1% of kinship coefficients were 0, suggesting that there was no relatedness between these pairs of lines. A significant fraction (38.0%) indicated weak similarity, with kinship coefficients varying from 0 (excluding 0) to 0.10. Only 5.6% showed various degrees of relatedness, with kinship coefficients ranging from 0.10 (excluding 0.10) to 0.50. For the remaining 0.3% of the data, the kinship coefficients varied from 0.50 to 1.26 with an average of 0.68. This pattern of genetic relatedness demonstrated that few lines showed strong similarities, and most lines were weakly or modestly related in this complex maize panel.
Effects of sample size on association power
The statistical power for detecting the significant variants in an association panel was assessed with various sample sizes and effect sizes (Fig. S3). When the sample size of an association panel was less than 100, less than 33% of the significant variants were captured even when they had moderate effects (effect = 0.05). As expected, a significant increase of power was observed when the sample size or genetic effects increased. When the sample size reached 500, the association panel was large enough to capture most of the significant variants (>78%) accounting for over 3% of the phenotypic variation. For this panel with 527 individuals, over 81% of the significant variants explaining ≥3% of phenotypic variations were captured, 62% for 2%, and 35% for 1%.
Correction of spurious associations
Various levels were observed for effects of population structure on phenotype in this maize panel (Table 1). For all measured traits, the percentage of phenotypic variations explained by the Q matrix from STRUCTURE analysis (RQ2) averaged 12.1%, with a range from 0.6 (leaf width) to 37.3% (days to pollen shedding). Half of the traits were influenced weakly by population structure as the RQ2 values were lower than 10%. The phenotypic variations explained by the top 10 axes of variations from PCA analysis (RPCA2) showed similar difference levels among various traits for effects of population structure. However, the RPCA2 values were higher than the RQ2 values, especially for plant height with the values increasing from 7.9% for RQ2 to 22.6% for RPCA2. Subsequently, three traits, representing three levels of the effects of population structure on phenotype, were used to determine the optimal dimension of PCA for associations, and to evaluate the performance of various statistical models in controlling spurious associations. Population structure, estimated by STRUCTURE and PCA, accounted for 37.3% (40.0%) of phenotypic variations for flowering time (represented by days to pollen shedding), 15.9% (24.1%) for ear height, and 6.9% (16.1%) for ear diameter in this maize panel.
Genetic diversity and population structure
SNPs are biallelic and less informative compared to multiallelic simple sequence repeats (SSRs). Nevertheless, the high-throughput and cost-effective SNP genotyping system can achieve a large number of markers (i.e. thousands to millions) that may overcome the disadvantages of the SNPs. The utility of SSRs and SNPs in assessment of population structure was compared using 89 SSRs and 847 SNPs, showing that SSRs performed better at clustering individuals into populations than SNPs, but that the population structure assessed by both marker systems was consistent (Hamblin et al. 2007). More recently, SNP markers have been used successfully for maize genetic diversity and population structure analysis with fairly consistent results (Lu et al. 2009; Yan et al. 2009; Inghelandt et al. 2010; Yang et al. 2010). Inghelandt et al. (2010) and Yu et al. (2009) further pointed out that between 7 and 11 times more SNPs than SSRs should be used for analyzing population structure and genetic diversity, while 10 times more should be used for estimating relative kinship. Therefore, the genetic diversity and relatedness presented here should be similar to those assessed by about 100 SSRs with 10 SSRs per chromosome on average.
The 527 maize lines had a higher gene diversity value (0.39) when compared to the gene diversity of around 0.32 across three sets of maize inbred lines: a set of 259 lines from the USA representative of global diversity (Hamblin et al. 2007), a set of 770 global maize lines from six countries (Lu et al. 2009) and a set of 1537 elite lines representing European and North-American diversity (Inghelandt et al. 2010). The comparably abundant genetic diversity in this panel was primarily due to the broad range of the germplasm, as all maize collections were estimated using similar numbers of SNP markers (except the European and North-American collection which were estimated using many more markers than the others).
Our study identified three separate subpopulations within the global maize germplasm. This result was confirmed by STRUCTURE, INSTRUCT, PCA and phylogenetic tree-based analyses. Despite the wide application of the STRUCTURE program for identifying population structure, spurious inference of population structure often occurred for partially selfed populations because of the algorithm assumptions (Falush et al. 2003). The panel of inbred maize lines did not conform to the assumption of Hardy–Weinberg equilibrium, and low genetic divergence occurred among some individuals because of similar pedigree. Based on STRUCTURE, Gao et al. (2007) developed another approach, INSTRUCT, to assign individuals within partially selfing populations into more appropriate subpopulations without the assumption of Hardy–Weinberg equilibrium. However, the inferred population structure was consistent for both methods, although individual assignments tended to show low correlation when k was set above 7 (data not shown). Although consistent subpopulations were inferred by STRUCTURE, INSTRUCT, PCA and tree-based analyses, the assessment of individual relationships was different: membership probabilities or values are given by STRUCTURE/INSTRUCT or PCA, whereas tree-based analysis only classifies individuals to a fixed position on a tree. This demonstrates that a phylogenetic tree does not represent well the relationships among individuals with complex genetic relatedness, although it may generate similar results. This phenomenon also explained why individuals within mixed subpopulations inferred by STRUCTURE/INSTRUCT clustered into one of the three clades.
Historically, two maize groups, temperate and tropical/subtropical, were formed during the distribution of maize from the tropical center of origin in Mexico to northern climates. The population subdivision in this panel, like that by Liu et al. (2003) and Flint-Garcia et al. (2005), supported maize adaptation and separated temperate and tropical/subtropical lines into independent subpopulations, SS + NSS and TST, as described by Yan et al. (2009). However, investigations by Vigouroux et al. (2008) and Camus-Kulandaivelu et al. (2006) suggested that the Northern Flint subpopulation played a unique role in the adaptation of maize to temperate climates and was the first to split from the maize population. The difference is probably caused by few Northern Flint lines in this association panel. Further, the temperate population in this panel was divided into two subpopulations, SS and NSS. The pairwise Fst of 0.25 (P < 0.001) also indicated the existence of significant population differentiation between the SS and NSS subpopulations. Additionally, a few small subpopulations separated from NSS with the increase of k presumed in STRUCTURE analysis, consistent with previous studies in which three to seven subpopulations still existed apart from the SS subpopulation, namely the Reid subpopulation in the studies of Wang et al. (2008) and Yang et al. (2010) and the BSSS subpopulation in Xie et al. (2008) and Lu et al. (2009). Contrary to NSS, SS and TST did not show any separation except for a few lines clustering with the mixed subpopulation. This may be due to the limited lines used for SS and the CIMMYT maize breeding history for TST, as discussed previously (Dhliwayo et al. 2009).
The fact that maize originated from tropical environments suggests that there should be much more diversity in the tropical lines, which is well supported by previous estimation using molecular markers (Liu et al. 2003; Yan et al. 2009). Although most of the lines were of the tropical/subtropical group in this study, the genetic diversity of this group was not the richest. A similar finding was also reported in a previous study using the same set of SNP markers in 770 maize inbred lines representing tropical, subtropical and temperate maize germplasm (Lu et al. 2009). This may be partially due to the fact that the SNPs used in this study were originally developed from 27 founder lines between a common temperate line B73 and 26 other diverse (temperate and tropical) lines (McMullen et al. 2009), potentially causing bias estimation of the diversity, especially within the tropical and subtropical germplasm (Hamblin et al. 2007; Lu et al. 2009; Yan et al. 2010c). However, Lu et al. (2009) also demonstrated that these types of markers had no or very few effects on the inferences of population structure. With the development of next-generation sequencing techniques, the inexpensive cost of sequencing a genome (Varshney et al. 2009) may allow further detailed studies to achieve the final solution to this problem.
Power and statistical models
When using an association panel to uncover a variant for quantitative traits of interest, a primary consideration should be the power of this panel, namely the probability of detecting the causal variant. Studies of power evaluations have suggested that population size is one of the most fundamental decisions when identifying associations (Long and Langley 1999; Spencer et al. 2009). It is reasonable that as the population size increases, the probability of identifying presumed causal alleles present in a panel will consequently increase. Long and Langley (1999) found that a panel with 500 individuals was sufficient to detect the presence of causal variants even with small effects, consistent with our results. Our panel with 527 individuals achieved over 81% of the variants explaining ≥3% of phenotypic variations based on the assumption of an LD coefficient of 0.8. This indicated that the population size of our panel is suitable for most quantitative traits with modest effects.
Marker density is another determinant for increasing the power of association analysis (Mackay et al. 2009), especially for GWAS. It is often related to the LD pattern of a maize association panel at the genome-wide level. The number of SNPs genotyped in this panel is too small to precisely estimate LD between linked SNPs. Nevertheless, the LD pattern in a maize panel of 632 diverse breeding lines was roughly estimated within 2–5 kb at the genome-wide level when the LD coefficient was set to 0.1 (r2 = 0.1) using 1536 SNPs from 582 genes (Yan et al. 2009). We supposed that a similar LD pattern occurred in our association panel based on a similar genetic diversity. Therefore, 240,000–480,000 markers will be required to perform GWAS when the LD coefficient is set to 0.1. The cutoff of r2 = 0.1 may be too low to achieve enough power, and we would need to add more markers to increase the LD level to r2 = 0.8. However, r2 did not increase significantly when the LD distance decreased tenfold to between 0.2 and 0.5 kb in the study by Yan et al. (2009). This result implied that the power may not be increased significantly even if the number of markers is increased tenfold to between 2.4 and 4.8 million. Myles et al. (2009) roughly estimated that more than 10 million markers may ideally be needed to perform GWAS in maize, and this would be a significant challenge. Since less than 10% of the maize genome encodes over 32,000 genes (Schnable et al. 2009), an alternative should be to develop markers only from gene-rich regions using the exome resequencing strategy (Ng et al. 2009) similar to that developed and applied in human studies with the rapid development of next-generation sequencing technology. This approach may allow us to use the most informative markers for GWAS in maize to achieve the highest power (Yan et al. 2010b).
An ideal association panel is a population with uniform genetic background, which will not significantly influence the expression of traits. Most cultivated plants, such as maize, which have experienced domestication and breeding, show complex patterns of genetic relatedness among individuals. In such a situation, association analysis often generates a large number of false-positive associations, especially for the traits associated with adaptation (Yu and Buckler 2006; Zhu et al. 2008; Myles et al. 2009). As expected, the integration of genetic relatedness into statistical methods greatly reduced spurious associations in our study, as well as in others (Yu et al. 2006; Zhu and Yu 2009; Stich et al. 2008; Yang et al. 2010). The Q model performed well for correcting false-positive associations, although it did not completely control the population structure. This is because the STRUCTURE program divides the maize panel into a few discrete populations, and the Q matrix only gives a rough dissection of population differentiation. Consequently, it was suggested that the PCA model dissects the phenotypic variation from population structure along continuous axes (Patterson et al. 2006; Price et al. 2006). Indeed, the PCA model performed better compared to the Q model; however, a few residual false-positive associations still existed.
It was reported that association analysis using the PCA model was not sensitive to the dimension numbers of principal components (Patterson et al. 2006; Price et al. 2006). In the present study, we found that the type I error control was sensitive to the number of PCs when the axes ranged from 1 to 4, but the results were consistent when they were ≥4. The dimension numbers of principal components for type I error control were also trait-dependent (Fig. 4; Table S4). This is not surprising, as the effects of population structure vary among complex quantitative traits in maize (Flint-Garcia et al. 2005; Yang et al. 2010). The PCA models with the first top component reduced nearly half of the false-positive associations for all traits. All these results suggest that it is appropriate to evaluate the correlation between PCA models and the dimension number of principal components for various traits in a given newly constructed association panel.
The K model and two mixed models (Q + K and PCA + K) performed well for all traits in this maize model. It seems that a K matrix incorporated into the K model was sufficient to minimize false-positive associations, consistent with other model simulations and comparisons (Yu et al. 2006; Zhu and Yu 2009; Stich et al. 2008; Yang et al. 2010). However, both the Q + K and PCA + K models performed slightly better than the K model for all three traits. As the estimation of the Q matrix is computationally intense, the PCA + K model may be an ideal choice for association analysis, especially for most large, genome-wide data sets.
Potential utilization of this maize panel and further perspectives
An adequate understanding of genetic variation, pattern of complex genetic relatedness and the performance of statistical methods in the maize panel allowed us to uncover the actual variants affecting quantitative traits. A subset of this panel with 155 lines has been successfully applied using a candidate-gene association approach in the validation of several genes controlling relatively simple traits, such as crtRB1 (Yan et al. 2010a), ZmGW2 (Li et al. 2010a), and ZmGS3 (Li et al. 2010b). The detected variants can be converted into functional markers (Andersen and Lübberstedt 2003) and then used for maize improvement by marker-assisted selection. For example, the action of two genes, lcyE and crtRB1, encoding the key enzyme of the carotenoid pathway, was confirmed using association analysis and the functional sequence polymorphisms were used to develop functional markers related to β-carotenoid content (Harjes et al. 2008; Yan et al. 2010a). Using these functional markers, the favorable alleles from these two genes were jointly introgressed through marker-assisted selection into adapted elite tropical breeding lines (provitamin A ranging 8–10 μg g−1) in HarvestPlus/CIMMYT breeding programs which target developing countries (Yan et al. 2010a). All the high provitamin A lines selected via marker-assisted selection in these programs are lines from, or derived from, one of the association mapping panels used to identify the favorable alleles. Thus, the natural variation of quantitative traits hidden in the maize panel will greatly assist targeted efforts to improve traits of interest.
Although an association mapping panel with about 500 genotypes can help to capture most of the variations that are ≥3%, it may still not be large enough to obtain sufficient power for some important complex quantitative traits in maize controlled by a great number of genes with small effects. For example, only a few QTL with effects greater than 3% in the approximately 50 QTL identified affected flowering time in the Nested Association Mapping (NAM) population (Buckler et al. 2009). Therefore, sample size should be one of the most important factors to be carefully considered in future maize GWAS, especially for the complex traits. In GWAS for human diseases, genes or SNPs with effects <0.5% were also identified when combining large numbers of individuals from different groups. For example, more than 50 variants (each of which can only explain 0.3–0.5% of variation) affecting human height were identified when about 63,000 individuals were combined (Visscher 2008). It would be very difficult for any single researcher or institution to handle such a large phenotyping maize trial. However, many maize association mapping panels with different sizes and genetic backgrounds have already been developed and phenotyped for the same or similar traits (Flint-Garcia et al. 2005; Yang et al. 2010) and could be genotyped using common and high-density markers (i.e. a commercial maize 50 K array) by different maize researchers worldwide. It will be extremely useful to exploit the genetic architecture of complex traits by combining the information from all the possible panels and traits using appropriate statistical methods in the future.
We thank Drs. Pixley Kevin, Palacios Natalia and Taba Suketoshi from CIMMYT for providing partial materials used in this study. We gratefully acknowledge the editor Dr. Roberto Tuberosa and two anonymous reviewers for their valuable suggestions. This research was supported by the National Hi-Tech Research and Development Program of China (2006AA100103, 2006AA10Z183, 2006AA10A107), the NSFC-CIMMYT Project (30821140352), and the Genetically Modified Varieties Breeding Science and Technology Projects of China.