Genetic Structure and Diversity Among Maize Inbred Lines as Inferred From DNA Microsatellites

Corresponding author: John Doebley, University of Wisconsin, 445 Henry Mall, Madison, WI 53705., jdoebley{at}wisc.edu (E-mail)

Communicating editor: J. A. BIRCHLER

	ABSTRACT

TOP ABSTRACT MATERIALS AND METHODS RESULTS DISCUSSION LITERATURE CITED

Two hundred and sixty maize inbred lines, representative of the genetic diversity among essentially all public lines of importance to temperate breeding and many important tropical and subtropical lines, were assayed for polymorphism at 94 microsatellite loci. The 2039 alleles identified served as raw data for estimating genetic structure and diversity. A model-based clustering analysis placed the inbred lines in five clusters that correspond to major breeding groups plus a set of lines showing evidence of mixed origins. A "phylogenetic" tree was constructed to further assess the genetic structure of maize inbreds, showing good agreement with the pedigree information and the cluster analysis. Tropical and subtropical inbreds possess a greater number of alleles and greater gene diversity than their temperate counterparts. The temperate Stiff Stalk lines are on average the most divergent from all other inbred groups. Comparison of diversity in equivalent samples of inbreds and open-pollinated landraces revealed that maize inbreds capture <80% of the alleles in the landraces, suggesting that landraces can provide additional genetic diversity for maize breeding. The contributions of four different segments of the landrace gene pool to each inbred group's gene pool were estimated using a novel likelihood-based model. The estimates are largely consistent with known histories of the inbreds and indicate that tropical highland germplasm is poorly represented in maize inbreds. Core sets of inbreds that capture maximal allelic richness were defined. These or similar core sets can be used for a variety of genetic applications in maize.

MAIZE (Zea mays L. ssp. mays) inbred lines represent a fundamental resource for studies in genetics and breeding. While maize inbreds are used extensively in hybrid corn production (ANDERSON and BROWN 1952 ; TROYER 2001 ), they have also been critical for diverse genetic studies including the development of linkage maps (BURR et al. 1988 ), quantitative trait locus mapping (EDWARDS et al. 1987 ; AUSTIN et al. 2001 ), molecular evolution (HENRY and DAMERVAL 1997 ; CHING et al. 2002 ), developmental genetics (POETHIG 1988 ; FOWLER and FREELING 1996 ), and physiological genetics (CROSBIE et al. 1978 ). Most recently, a set of diverse maize inbreds has been employed to perform the first phenotype-genotype association analyses in a plant species (THORNSBERRY et al. 2001 ) and to estimate linkage disequilibrium in maize (REMINGTON et al. 2001 ; TENAILLON et al. 2001 ).

The intelligent exploitation of maize inbreds for genetic analyses requires a detailed knowledge of genetic and historical relationships among these lines and an understanding of the partitioning of genetic diversity among them. For example, developmental mutants of maize can exhibit strikingly different phenotypes when assayed in the genetic backgrounds of different maize inbred lines (POETHIG 1988 ). Knowledge of the relationships among lines would help identify a set of inbreds that have maximal diversity for the analysis of the effects of genetic background. Single-nucleotide polymorphism discovery in maize can be optimized by selecting a set of lines that capture the maximum number of alleles or haplotypes. Use of maize inbreds in association analyses requires that population structure among lines be factored into the analysis (THORNSBERRY et al. 2001 ).

In this article, we analyze the genetic structure and diversity among maize inbred lines using DNA microsatellites or simple sequence repeats (SSRs) and a comprehensive set of 260 inbreds that represent well the diversity available among currently and historically used lines. We show that these lines can be partitioned into five groups, that diversity is greatest among tropical inbreds, that maize inbreds capture 80% of the allelic diversity in open-pollinated accessions, and that one level of population structure cannot fully explain linkage disequilibrium among inbreds. We also define core sets of inbreds that capture maximal allelic diversity for given sample sizes, investigate the relationship between pedigree and genetic distance, and identify the portions of the broader maize germplasm pool from which maize inbreds were derived.

	MATERIALS AND METHODS

TOP ABSTRACT MATERIALS AND METHODS RESULTS DISCUSSION LITERATURE CITED

Plant materials:
A set of 260 inbred lines representing a sample of the most important public lines from the United States, Europe, Canada, South Africa, and Thailand, along with lines from the International Center for the Improvement of Maize and Wheat (CIMMYT) and the International Institute of Tropical Agriculture (IITA), was chosen to represent the diversity available among current and historic lines used in breeding. These include essentially all public lines of importance to temperate breeding and many important tropical and subtropical lines. The 260 lines and their pedigrees are listed in supplemental Table S1 at http://www.genetics.org/supplemental/. Seed of most lines are still available from their original sources (see http://www.panzea.org/), but we have also provided seed samples to both the North Central Regional Plant Introduction Station (NCRPIS, Ames, IA) and the National Seed Storage Laboratory (Fort Collins, CO). Most, if not all, lines should be available from the NCRPIS in 2004.

SSR genotyping:
The lines were genotyped at Celera AgGen (Davis, CA). The details of the genotyping have been published elsewhere (ROMERO-SEVERSON et al. 2001 ). Briefly, DNA was extracted from individual plants by the cTAB method, and the microsatellite regions were amplified by PCR with fluorescent-labeled primers. PCR products were size separated on Applied Biosystems (Foster City, CA) fragment analyzers equipped with GeneScan software, and the PCR products were classified to specific alleles (bins) by GeneScan and Genotyper software programs (ROMERO-SEVERSON et al. 2001 ). We used 100 SSR loci that are evenly distributed throughout the genome. A list of the SSR loci with their chromosomal locations has been deposited as supplemental Table S2 at http://www.genetics.org/supplemental/. Primer sequences are available at the MaizeGDB (http://www.maizegdb.org).

Preanalysis:
We began with 264 lines, some of which were assayed two to four times for the 100 SSR loci, giving a total of 339 assays. Of the 33,900 SSR genotypes, 4.3% amplified more than one band per inbred line, perhaps because of residual heterozygosity, contamination, or the amplification of similar sequences in two separate genomic regions. To minimize the effect of contamination, we dropped 7 assays with heterozygosity >0.20, an unexpectedly high value for a maize inbred. Further, 4 other assays, which represented the sole assays for 4 lines, were excluded from the study because their position in a preliminary cluster analysis was strongly discordant with their known pedigrees, suggesting a seed or sample mix-up. We also dropped 4 loci with mean within-line heterozygosity >0.10, suggesting that these loci did not faithfully amplify a single locus or that allele calling was problematic. We dropped 2 loci with availability (defined as 1 - proportion of missing or null data) <0.80, suggesting that the locus could not be amplified in the PCR reaction for many lines. The final data set consists of 260 lines and 94 loci.

We performed multiple SSR assays for some lines. So that each inbred is represented only by a single entry in our data set for statistical analyses, we built consensus genotypes for inbreds that were assayed more than once. The main criterion for constructing the consensus genotype was that any allele with frequency >25% is counted, but if three or more alleles have frequency >25%, then we regard the genotype as missing. The second criterion is that if one assay gave a null phenotype but another gave a visible allele, then the inbred was considered homozygous for the visible allele. Since there was a high degree of concordance among replicate assays, inferred consensus genotypes based on these criteria represent only 1.9% of the final data set.

Summary statistics and tests:
We used PowerMarker (LIU 2002 ) to calculate observed heterozygosity, gene diversity (or expected heterozygosity), number of private alleles, number of group-specific alleles, pairwise F-statistics, and stepwise mutation model index. Gene diversity was calculated at each locus as

where p_u is the frequency of the uth allele, n is the sample size, and is the inbreeding coefficient estimated from genotype frequencies (WEIR 1996 ). Stepwise mutation model index was defined as the maximal proportion of alleles that follow a stepwise mutation pattern (MATSUOKA et al. 2002A ). AMOVA was performed (EXCOFFIER et al. 1992 ).

To evaluate the probability that each of the 260 inbreds would have a unique genotype (fingerprint) for a given number of SSRs, 10,000 random samples of 260 lines were drawn from the empirical distribution of allele frequencies on the basis of the observed data for our 260 inbreds. For these random samples, the probability that all 260 simulated lines had a unique genotype was directly estimated for different numbers of loci. To compare the relationship of pedigree distance and genetic distance, we used a Mantel test (MANTEL 1967 ) by setting the permutation number to 100,000. Pedigree distances were calculated as 1 - Malécot coefficient of coancestry (MALECOT 1948 ), using pedigree information from a variety of sources (see supplemental Table S1 at http://www.genetics.org/supplemental/).

Analysis of genetic structure:
Lines were subdivided into genetic clusters using a model-based approach with the software package STRUCTURE (PRITCHARD et al. 2000 ). Given a value for the number of subpopulations (clusters), this method assigns lines from the entire sample to clusters in a way that Hardy-Weinberg disequilibrium and linkage disequilibrium (LD) were maximally explained. We excluded seven popcorn lines and five sweet corn lines in this analysis (see RESULTS). At least six runs of STRUCTURE were done by setting the number of populations (K) from 1 to 10. For each run, burn-in time and replication number were both set to 500,000. The run with the maximum likelihood was used to assign lines to clusters. Lines with membership probabilities 0.80 were assigned to clusters; lines with membership probabilities <0.80 for all groups were assigned to a "mixed" group. The three largest clusters were then further subdivided by the same method.

To construct a phylogenetic tree, we used the log-transformed proportion-of-shared-alleles distance that is free of the stepwise assumption, enjoys low variance, and is widely used with multilocus SSR data (MATSUOKA et al. 2002B ). We used the Fitch-Margoliash least-squares algorithm implemented in the computer program Phylip to construct phylogenetic trees (FELSENSTEIN 1993 ). The tree was rooted using five samples of the maize wild relative, teosinte (Z. mays ssp. parviglumis) as the outgroup (MATSUOKA et al. 2002B ).

Analysis of allelic richness:
We wanted to compare the allelic richness in maize inbreds to that in open-pollinated landrace accessions to estimate the extent to which our set of 260 inbreds captures the diversity present in maize overall. For comparison, we used a previously published data set for 193 maize landrace samples that represent the entire maize germplasm pool (MATSUOKA et al. 2002B ). To compare the allelic richness of inbreds to landraces, we need to adjust for the inbreeding coefficient since inbreds are mostly homozygous while landraces have a high degree of heterozygosity. We also need to adjust for sample size since our sample has 260 inbreds but only 193 landraces. We used two approaches. First, we compared sets of randomly chosen lines from the inbred and landrace data sets with the same sample sizes. The inbred and landrace genotypes were first broken into alleles to simulate the selfing process. Then, the allele number was counted for randomly drawn samples of size 3–193 in steps of five. Second, we used a parametric simulation to simulate the creation of 260 inbreds from the landraces. The inbreeding coefficient () for inbreds was estimated to be 0.965. For each locus, we sampled two alleles with replacement to generate a diploid genotype. If the two alleles are the same, then the simulated inbred is made homozygous. If the two alleles are different, then the simulated inbred is made heterozygous with probability 1 - and made a/a with probability /2 and b/b with probability /2. This procedure was repeated to create 10,000 independent samples of 260 inbreds from which the mean number of alleles and other summary statistics were calculated. The summary statistics for these simulated data were compared with the actual inbred data.

Estimating the historical sources for inbreds:
To estimate the historical sources for each inbred group, we used SSR data for 104 representative accessions from four likely historical germplasm pools: Southern Dent, Northern Flint, Tropical Highland maize, and Tropical Lowland maize (supplemental Table S3 at http://www.genetics.org/supplemental/; MATSUOKA et al. 2002B ). We calculated the likelihood of the allelic constitution of an inbred group [e.g., non-Stiff Stalk (NSS)] or specific inbred line, given different proportions of ancestry from the four historical germplasm pools. Assuming that the loci are independent, the likelihood is

where P is a vector of the proportions of ancestry from the four historical germplasm pools, a_l is number of alleles at the lth locus, f_klj is the frequency of the jth allele at the lth locus in the kth population as estimated from the 104 representative landrace lines, n_lj is the count of the jth allele at the lth locus for the inbreds group (or line), and p_k is the probability that the allele originated from the kth population. This function was maximized by sequential quadratic programming. Several starting points were chosen to check the global convergence. Standard deviation and confidence interval were inferred from the likelihood surface using established methods (EDWARDS 1972 ).

Defining core sets of inbreds:
We developed a new algorithm for building core sets of germplasm by maximizing allelic richness using simulated annealing (KIRKPATRICK et al. 1983 ). Given the complete set of lines (L), the algorithm works by first randomly selecting a subset of lines (l). Each line has a weight (w) based on the number of private alleles in that line. Next, between 1 and the minimum (l, L - l), additional lines are chosen from the remainder of the complete set (unselected lines) on the basis of their weights and swapped with the same number of the initially selected l lines also chosen on the basis of their weights. The number of alleles (n) is then evaluated and the swap is accepted if it increases n but accepted only with some probability (P) if n is the same or less. The probability of acceptance is dependent on the level of decrease in allelic richness and on the iteration number such that P is larger in earlier iterations. Swapping is continued for a predefined number of iterations. Since P gradually decreases with iterations (time), the method simulates an annealing process. Under this approach, lines with more private alleles have a larger probability to be included in the core set. Our algorithm can also incorporate a weight for the agronomic quality of the inbred and can allow some inbreds to be designated as "conserved" such that they are automatically included in the core set. The details of the algorithm will be given in a separate article (K. LIU and S. MUSE, unpublished results).

Linkage disequillibria:
The matrix of P values for the pairwise estimates of LD among all 94 SSR loci was evaluated in PowerMarker by the permutation version of Fisher's exact test (LIU 2002 ). The numbers of locus pairs with LD P values less than threshold values of 0.05, 0.01, 0.001 were counted for the observed data. This analysis was performed on each of the clusters of inbreds defined by the program STRUCTURE as well as the entire set of inbreds. Because the P value of the exact test is affected by sample size and the clusters varied widely in size, we evaluated the effect of sample size on the proportion of significant LD P values by drawing random samples from the entire set of 260 lines of a size equal to the actual number of lines in the cluster. These random samples were drawn without replacement, the exact test was performed on each, and the mean proportion of significant LD P values for 100 replicates was used to compare with the actual results for each cluster.

	RESULTS

TOP ABSTRACT MATERIALS AND METHODS RESULTS DISCUSSION LITERATURE CITED

SSR diversity:
We surveyed 260 diverse maize inbred lines using 94 SSRs. The inbreds can be roughly grouped as including 82 tropical lines, 35 temperate Stiff Stalk lines, 131 temperate non-Stiff Stalk lines, seven popcorn lines, and five sweet corn lines. The pedigrees for each line are available online (supplemental Table S1 at http://www.genetics.org/supplemental/). Among the lines, we detected a total of 2039 alleles or an average of 21.7 alleles per locus (Table 1). A large number of private alleles (556 or 27%) are found in only 1 of the 260 inbred lines. Most alleles are at low frequency (Fig 1).

View larger version (23K): [in this window] [in a new window] [Download PPT slide]   Figure 1. Histogram of allele frequencies for the 2039 total alleles.

The number of alleles is not equivalent among loci. Loci with dinucleotide repeat motifs have considerably more alleles (average = 23.9) than loci with repeat motifs of three nucleotides or larger (average = 9.9; Table 1). This difference is also seen for gene diversity, with dinucleotide SSRs (average = 0.839) having a higher gene diversity than longer-repeat SSRs (average = 0.707). The mean gene diversity of all SSRs is 0.818.

SSRs are often presumed to follow a stepwise mutation process due to changes in the number of repeats. However, because size differences among alleles are estimated on the basis of the combined molecular weights of the SSR plus its flanking sequences, indels in the flanking sequences can contribute to allelic variation as well (MATSUOKA et al. 2002A ). These indels can cause a violation of the expectation that allele sizes differ strictly by multiples of the repeat motif. We calculated a stepwise mutation index, or the maximal proportion of alleles at a locus that are simple multiples of the repeat motif length. For all 94 loci, the average stepwise mutation model index was 0.832 with dinucleotide SSRs (0.853) showing a higher index than other repeat loci (0.720).

The large number of alleles per locus and the common occurrence of private alleles suggest that a relatively small number of SSRs would be sufficient to uniquely fingerprint maize inbreds. For the 260 inbred lines that we sampled, the following six loci form a unique profile: bnlg244, bnlg2238, bnlg619, bnlg1191, bnlg1046, and dupssr28. Assuming the allele distribution of our inbred data is representative of all maize inbreds, the probability of sampling 260 independent lines without generating the same genotype for any two lines will be >0.99 by randomly selecting 10 loci. This number is 9 if one uses only dinucleotide SSRs and 12 if one uses longer-repeat SSRs. Thus, very few SSRs are necessary if one wishes to uniquely fingerprint maize inbreds.

Genetic structure of inbred lines:
We wished to assess the degree of relatedness among lines and to identify clusters of genetically similar lines. To do this, we used a model-based approach with the program STRUCTURE to subdivide the lines into clusters (PRITCHARD et al. 2000 ). Five sweet corn lines and seven popcorn lines were assigned to two predefined groups (sweet and popcorn) and were excluded in the STRUCTURE analysis. This was done because a pilot analysis showed that incorporating these 12 lines in the analysis interfered with the ability of STRUCTURE to converge on a robust solution. K (number of populations) = 3 was found to converge well and showed comparable or higher likelihoods than K = 4–10 among runs of the program. We used the run with highest log-likelihood at K = 3 for the observed data to define the model-based groups (Table 2).

The model-based groups are largely consistent with known pedigrees of the lines (M. M. GOODMAN and J. S. SMITH, personal observation). The largest group has 94 lines, most of which are regarded by breeders as temperate NSS lines. The next group has 58 lines, most of which are either tropical or semitropical (TS) lines. The smallest group has 33 lines, all of which are temperate Stiff Stalk (SS) lines. The remaining 63 lines have <80% membership in any one group and were assigned to a mixed group. Supplemental Table S4 at http://www.genetics.org/supplemental/ shows the proportional membership for these mixed lines in the three groups. Most mixed lines are either NSS-TS or NSS-SS mixtures. Only four lines (Tzi16, Tzi25, Hi27, and CML92) present high membership of TS and SS.

STRUCTURE analysis was repeated to break the three main clusters into subclusters (Table 2). The SS group split into four subgroups, the TS group into five, and the NSS group into seven. Supplemental Table S5 at http://www.genetics.org/supplemental/ shows the proportional membership of the lines in the subgroups for the group to which they belong.

A Fitch-Margoliash "phylogenetic" tree was constructed to further assess the genetic structure of maize inbreds (Fig 2). The tree shows good agreement with the pedigree information and STRUCTURE analysis (see DISCUSSION). A version of the tree with the names of the inbreds is available online (supplemental Figure S1 at http://www.genetics.org/supplemental/).

View larger version (55K): [in this window] [in a new window] [Download PPT slide]   Figure 2. Fitch-Margoliash tree for the 260 inbred lines using the log-transformed proportion of shared alleles distance. The tree was rooted using five teosinte (Z. mays ssp. parviglumis) samples as outgroups. A version of this tree with the names of the individual inbred lines can be found as supplemental Figure S1 at http://www.genetics.org/supplemental/.

Genetic diversity within inbred groups:
Gene diversity and mean numbers of alleles for the 94 SSRs were calculated for each group of inbreds (Table 1). The TS group is the most diverse with 13.49 alleles per locus and gene diversity of 0.81. NSS has less diversity than TS does, as revealed by the decreased allele number (12.84) and gene diversity (0.78). SS was found to be less diverse than NSS and TS. Our samples of sweet and popcorn include only a few lines, and thus the small numbers of alleles in these groups were expected. In all groups, dinucleotide loci have a much larger allele number than longer-repeat loci. Gene diversity shows a similar trend.

Maize inbreds show a high number of line-specific (556 or 27%) or group-specific (765 or 38%) alleles (Table 1). Far more line- and group-specific alleles are found in the TS group (204 and 305) than in the NSS group (121 and 173) despite a much smaller sample size for TS, indicating far greater diversity in tropical than in temperate inbreds.

An AMOVA revealed that most (90.16%) of the genetic variation resides within groups and only a small percentage resides between groups (8.32%) or within lines (1.51%). Overall F_st among groups is 0.086 (95% confidence interval 0.080–0.092) with F_st for each locus ranging from 0.02 to 0.17. Pairwise comparisons show a low level of differentiation between TS and NSS (F_st = 0.06), but more substantial differentiation between SS and the other groups (Table 3). Popcorn is also highly differentiated from all the other groups. A similar pattern of differentiation among groups is seen using Nei's minimum distance.

Allelic richness of maize inbreds:
Comparison of diversity in inbreds to that in open-pollinated landraces shows that the latter possess much greater diversity. For the landraces, the number of alleles (2697 or 28.7 alleles/locus) and overall gene diversity (0.84) are higher than that for the inbreds (2039 or 21.7; 0.82). To compare allelic richness in inbreds vs. landraces for equal sample sizes, we randomly selected equal numbers of samples from both germplasm pools (see MATERIALS AND METHODS). This analysis revealed the greater allelic richness in landraces when the samples are equivalent (Fig 3). When the sample size is small (<20), the inbreds capture 88% as many alleles as the landraces. When the sample size is large (>100), inbreds capture 78% as many alleles as the landraces.

View larger version (29K): [in this window] [in a new window] [Download PPT slide]   Figure 3. Plots of the expected number of alleles in samples of different sizes. For a given sample size, 1000 replicates were sampled from the inbred or landrace data set without replacement and the genotypes were randomly broken into alleles. Then the mean number was calculated to give the plot from sample size 3 to 193.

We also compared allelic richness in inbreds vs. landraces, using a parametric simulation. Simulated samples of 260 inbred lines drawn from the landrace gene pool had an average gene diversity of 0.837 (standard error = 0.0015), which is very close to the value for the landrace sample (0.840). The minimal value of gene diversity in the simulations is 0.832, which is still higher than that of our actual inbred sample (0.820). The mean number of alleles obtained by the simulations is 2292 and the standard error is 15. The total number for the inbred sample (2039) is not in the 99% confidence interval [2239, 2334], indicating that if one randomly created a set of 260 inbreds from the landrace gene pool, it would contain substantially more allelic diversity than our actual set of 260 inbreds.

Relationship of inbreds to landraces:
To understand the relationship between the inbreds and landraces, we estimated the proportion of each inbred group's gene pool that was derived from four different segments of the landrace gene pool (Northern Flint, Southern Dent, Tropical Lowland, and Tropical Highland). TS has its origin mostly from Tropical Lowland (66%) and Tropical Highland (18%; Table 4). NSS and SS show very similar origins, each being composed of roughly equal proportions of Northern Flint, Southern Dent, and Tropical Lowland. Popcorn has a high proportion of Northern Flint germplasm (40%) with most of the rest of its genome coming from Tropical Lowland (26%) and Southern Dent (23%). Sweet corn has the largest contribution from Northern Flint germplasm (72%). Overall, Tropical Highland maize has made a more modest contribution to our set of inbreds than have the other three historical sources. Variances for these estimates are usually small (SD < 1%). Estimates of historical sources for individual inbreds are included in supplemental Table S4 at http://www.genetics.org/supplemental/.

Comparison of SSR and pedigree relationships:
A Mantel test shows a highly significant (P < 10^-6) correlation between pedigree and SSR distance, although the correlation coefficient is relatively small (r = 0.57). A plot of pedigree by SSR distances shows a generally strong relationship but with many outliers (Fig 4).

View larger version (24K): [in this window] [in a new window] [Download PPT slide]   Figure 4. Plot of the SSR proportion of shared allele distance by the pedigree-based (1 - Malécot's coefficient of coancestry) distance for maize inbreds.

Core sets of inbreds:
We defined core sets of inbreds that capture the maximum number of alleles for a given sample size (Table 5). In selecting these sets, we constrained the selection to include 6 lines (A632, B37, B73, C103, Mo17, and Oh43) of high agronomic importance. We also eliminated 8 lines (A654, B2, CM37, CMV3, CO109, I205, Q6199, and R109B) because of poor agronomic quality under our field conditions. Additional core sets of different sizes can be found in supplemental Tables S6 and S7 at http://www.genetics.org/supplemental/. Our study shows that 10 lines capture 28% of the 2039 SSR alleles in the 260 lines, 20 lines capture 46% of the alleles, 30 lines capture 58%, and 50 lines capture 73%. To recover all 2039 alleles, 193 lines were needed. The core sets generally include a large proportion of TS lines as expected since these lines have the greatest allelic richness.

Linkage disequilibria:
We assessed extent of LD among SSRs for our sample of inbreds. LD was significant at a 0.01 level between 66% of the SSR marker pairs when all lines were included in the analysis (Table 6). The proportion of significant pairwise LD tests was less within each model-based group. Reduced power to detect LD with fewer lines could contribute to a part of this reduction. However, when we evaluated the percentage of significant pairwise tests in sets of randomly chosen inbreds of the same size as a given group, we observed that sample size alone fails to explain all the reductions (Table 6). This suggests that either linkage or population structure within the NSS, TS, and SS groups contributes to LD. In particular, SS shows a much larger observed LD value, which may be a consequence of the fact that the SS group actually consists of four well-defined subgroups.

	DISCUSSION

TOP ABSTRACT MATERIALS AND METHODS RESULTS DISCUSSION LITERATURE CITED

SSR diversity:
Previous studies have shown that maize contains abundant SSRs (SENIOR and HEUN 1993 ; SENIOR et al. 1996 , SENIOR et al. 1998 ) and that these SSRs are highly polymorphic even among small samples of maize inbreds (CHIN et al. 1996 ; TARAMINO and TINGEY 1996 ). These pioneering studies were conducted using relatively small numbers of inbreds (9–94) and loci (6–70). We have extended these earlier analyses by using both a large number of SSRs (94) and a much larger number of inbreds (260) that encompass a much greater portion of the maize gene pool. Our analyses uncovered abundant allelic variation with an average of 21.7 alleles per locus over 94 loci. This value greatly exceeds the previously reported values of 5.21 (SENIOR et al. 1998 ), 6.6 (TARAMINO and TINGEY 1996 ), 4.9 (LU and BERNARDO 2001 ), and 6.9 (MATSUOKA et al. 2002A ) alleles per locus. The larger number of alleles observed in the present study can be attributed to the larger number of inbreds surveyed, the more diverse selection of inbreds (tropical, subtropical, and temperate), and the inclusion of more dinucleotide repeat SSRs, which tend to be more polymorphic than SSRs with longer-repeat motifs (VIGOUROUX et al. 2002 ).

We have also observed higher values of gene diversity than those seen in previous analyses of SSR variation in maize inbreds. Gene diversity for our sample of SSRs and inbreds was 0.82 as compared to values of 0.59 (SENIOR et al. 1998 ), 0.76 (TARAMINO and TINGEY 1996 ), 0.59 (SMITH et al. 1997 ), and 0.62 (MATSUOKA et al. 2002A ). Since estimates of gene diversity are not affected by differences in sample size, the higher value that we observed is likely a function of our use of a greater portion of dinucleotide repeat SSRs and of our more diverse set of inbreds. If one considers only SSRs with trinucleotide or longer-repeat motifs, then gene diversity in our sample (0.71) falls nearer to these previous reports.

We also showed that most maize SSR alleles fit a stepwise mutation model with 83% of the alleles fitting multiples of the length of the repeat motif of their respective loci. The 17% of alleles that deviate from the stepwise pattern likely represent cases where there have been indels in the regions flanking microsatellite repeats (MATSUOKA et al. 2002A ). The failure of these SSRs to fit a stepwise model exactly cautions against the use of models that assume a stepwise mutation process. In particular, estimates of genetic distance such as (µ)² (GOLDSTEIN et al. 1995 ) or measures of population subdivision based on the stepwise mutation model (SLATKIN 1995 ) would be inappropriate with our data.

Genetic structure:
Maize inbreds have a complex history, having been derived from multiple open-pollinated varieties and crosses among the inbreds themselves (GERDES et al. 1993 ). This history makes it difficult to place maize inbreds into realistic groups that reflect their degree of genetic similarity. Pedigree information provides a useful guide; however, selection and genetic drift during inbreeding can cause considerable discrepancies between pedigree and genetic constitution. Moreover, pedigree information for some inbreds is incomplete, inaccurate, or conflicting.

We used the model-based approach of PRITCHARD et al. 2000 to define natural groups of maize inbreds. In performing this analysis, we discovered that the inclusion of small numbers of sweet (five) and popcorn (seven) lines in the analysis prevented the convergence to a robust solution. Apparently, these two groups are represented by too few lines to form distinct clusters, while at the same time they are too divergent from the other lines to fit into the clusters for those lines. Only when the sweet and popcorn lines were excluded did STRUCTURE converge on a robust solution with three clusters representing the temperate SSs, other temperate lines (NSSs), and TS lines. Thus, along with the predefined sweet and popcorn lines, we classify maize inbreds into five groups. Sixty-three lines did not fit into one of these five groups since they consist of a mixture of two or more of the primary groups. A comparison of genetic distances among the five groups indicates that SS are the most divergent (Table 4), a result consistent with the observation that the SS lines typically provide a strong heterotic response in crosses with other maize inbreds (HALLAUER et al. 1988 ).

Inbreds in each of the three model-based groups were analyzed again using STRUCTURE to identify subclusters of related lines (Table 2). The SS group split into four tight subgroups of lines derived from B14, B73, B37, and N28 (see ANONYMOUS 1999 ). The TS group split into five distinct subgroups with a clear relationship to the origin of these lines. For example, lines in the TZI subgroup are fully tropical and many are from the IITA's streak-breeding-resistance program. The Suwan subgroup consisted mainly of tropical lines that were derived from the Suwan-1 composite population, principally of Caribbean origin (SRIWATANAPONGSE et al. 1993 ), plus B96 from Maíz Amargo of Argentina. The CML-late subgroup is composed of tropical lines tracing back to CIMMYT's late-maturing Tuxpeño composite populations. The CML-early subgroup contained lines derived from CIMMYT's early-maturing (in the tropics) Tuxpeño-related materials and other intermediate-maturity sources. The NC subgroup consists of lines derived from Latin American tropical hybrids. Lines in the subgroup CML-P were largely derived from the La Posta Population 43 (CIMMYT 1987 ).

The NSS group is organized into seven subgroups that reflect known heterotic groups (ANONYMOUS 1999 ). The lines in subgroup Hy:T8:Wf9 all trace to these three lines that were important in the era of double-cross hybrids. Lines in subgroup M14:Oh43 all trace to M14, which was an important inbred in the 1940s and 1950s, and Oh43, which is still among our most important breeding sources. Several lines (A556, MS1334, ND246, and W401) with no known relationship to one another were grouped loosely within the CO109:Mo17 subgroup. Mo17 and CO109 represent important, but independent, breeding sources. Subgroup C103 consists mostly of Lancaster germplasm (HALLAUER et al. 1988 ) with an additional contribution from B57. Lines within subgroup Ga:SC (Georgia and South Carolina) are mostly southern U.S. germplasm with the notable exception of line 4226. Subgroup NSS-X is a heterogeneous mixture of mostly older lines. The K64W subgroup contains a set of related white lines.

A Fitch-Margoliash tree based on the SSR data shows generally good agreement with the pedigree information and STRUCTURE analysis (Fig 2, supplemental Figure S1 at http://www.genetics.org/supplemental/). There is a general separation of the TS, NSS, and SS lines. Mixed lines are usually located between clusters of TS/NSS/SS lines. Within the SS lines, the four subgroups defined by the STRUCTURE analysis are perfectly matched with four clades. For the TS group, the tree has three clades that correspond to subgroups NC, Suwan, and CML-late. For the NSS lines, the tree has three clades that largely correspond to subgroups Hy:T8:Wf9, M14:Oh43, and K64W. All of the sweet corns fall in the same clade, as did all of the popcorns. The European (F2, F7, and EP1) lines and one Canadian (CO255) line are closely grouped together, and this clade is neighbor to the sweet corn clade as expected since all these lines were derived from the Northern Flint landrace of the northern United States and adjacent Canada (GALINAT 1971 ; DOEBLEY et al. 1986 ). NSS-X is also contained within a single large clade, despite the fact that these lines have heterogeneous pedigrees.

Genetic diversity among inbred groups:
The amount of genetic diversity within each of the model-based groups is not equivalent. Rather, gene diversity is highest in tropical inbreds (TS), followed by NSS, sweet corn, SS, and popcorn in that order. The greater diversity of the TS lines is again shown by the fact that TS lines contain more alleles than NSS (1268 vs. 1207) despite the fact that the sample size for TS was much smaller (58 vs. 94). TS lines also possess by far the greatest number of group-specific alleles (305). These data argue strongly that TS inbreds represent an important source of diversity for broadening the genetic base for maize breeding (GOODMAN 1985 ; GOODMAN and CARSON 2000 ).

Of the 2039 alleles, 556 (27%) occur in only one inbred, and 765 alleles (38%) are restricted to a single model-based group of inbreds. These large proportions of private alleles are probably a function of the high mutation rate for maize SSRs (VIGOUROUX et al. 2002 ), allowing much new allelic variation to arise within lines after their initial development. This feature of maize SSRs contributes to their considerable discriminatory power, enabling one to fingerprint uniquely our entire set of 260 lines with as few as 10 SSRs. This discriminatory power makes SSRs ideal markers for use in varietal identification (SMITH et al. 1997 ) and for monitoring gene flow between lines (DALE et al. 2002 ). SSRs can also be used to determine pedigrees in maize inbreds and hybrids but more (e.g., 60 or more SSR loci) are required to trace pedigrees than to provide for unique line identification especially when closely related inbreds are considered (BERRY et al. 2002 ).

We also compared diversity in maize inbreds relative to the open-pollinated landraces from which the inbreds were ultimately derived. For this purpose, we used a sample of 193 landrace accessions that represent the entire maize germplasm pool. In particular, we examined the number of alleles captured in our set of 260 inbreds as compared to the number of alleles expected to be captured if these 260 lines represented a random sample of the maize gene pool. The results, whether obtained by a random sampling approach or parametric simulation, revealed a deficit of alleles within the 260 inbreds relative to expectations. For example, a set of 260 inbreds selected at random from the maize gene pool would be expected to capture 2292 alleles on the basis of the parametric simulations while the actual set of 260 lines captures only 2039. This result argues that plant breeders could capture additional diversity by working with landrace accessions (GOODMAN 1985 ). It is likely that the landraces contain numerous agronomically useful alleles not represented in the inbreds and advanced populations with which breeders presently work.

Historical sources of maize inbreds:
To better understand the relationship between our set of 260 inbreds and the broader maize germplasm pool from which they were derived, we made maximum-likelihood estimates of the portions of four segments of the landrace gene pool (Northern Flint, Southern Dent, Tropical Lowland, and Tropical Highland) represented in the five inbred groups. The results are consistent with historical records, pedigree information, and geography. The temperate NSS and SS are composed of a near-equal mix of Tropical Lowland, Southern Dent, and Northern Flint, although the Northern Flint portion is a bit smaller. Since Southern Dents themselves are thought to have been recently derived from Tropical Lowland germplasm (GALINAT 1985 ; DOEBLEY et al. 1988 ), the high portion of Tropical Lowland germplasm in NSS and SS lines likely represents a tropical contribution that came via the Southern Dents. The observation that NSS and SS are composed of only 25% Northern Flint is consistent with prior observations (DOEBLEY et al. 1988 ).

The sweet corn lines possess the highest portion of Northern Flint, which is consistent with their origin from the flints of the eastern United States (GALINAT 1971 ). The TS lines are composed largely of Tropical Lowland germplasm with a much smaller contribution from Tropical Highland germplasm. Overall, Tropical Highland germplasm is the least well represented among our 260 maize inbreds, although it is probably the most diverse segment of the maize gene pool (MATSUOKA et al. 2002B ; J. DOEBLEY, unpublished data). This result suggests that maize breeders should consider maize of the Tropical Highlands as a source of new allelic diversity. However, Highland Tropical germplasm has consistently proven difficult to integrate into temperate breeding programs because of its susceptibility to heat stress and fungal pathogens when grown at lower elevations (GOODMAN 1999 ).

In addition to our estimates of historical contributions to the inbred groups, we have estimated the historical sources for each of our individual 260 inbreds (supplemental Table S4 at http://www.genetics.org/supplemental/). The only inbred in our sample with a high proportion of Tropical Highland germplasm (72%) is CML349, which is a Tropical Highland inbred line. This again points to the possibility of using Tropical Highland germplasm to increase diversity within maize inbreds. The top four lines in terms of Northern Flint contribution (IA2132, IL14H, IL101t, and P39) are all sweet corn. Some European lines (F2, F7) and one Canadian line (CO255) also have >50% Northern Flint origin. Va35, a southern U.S. line, was found to have the largest Southern Dent proportion (63%).

Pedigree vs. genetic distance:
Previous studies using molecular markers have generally shown a strong correlation between molecular marker and pedigree-based distance measures (SMITH and SMITH 1992 ; BERNARDO et al. 1997 ; SMITH et al. 1997 ; BERNARDO et al. 2000 ; BERNARDO and KAHLER 2001 ). Nonetheless, estimates of relatedness based on pedigree data can differ from those based on molecular marker data (BERNARDO and KAHLER 2001 ). Calculations of relatedness based upon pedigree data are dependent upon the assumptions that both parents contribute an equal number of alleles (i.e., no selection, mutation, or genetic drift) and that the pedigree data are accurate. Another assumption is that founder genotypes (genotypes for which no further pedigree information on ancestors is available) are unrelated by pedigree. All of these assumptions can be violated.

We observed a highly significant correlation between pedigree- and SSR-based distances, although a much weaker correlation (0.57) than that seen in some previous studies. For example, SMITH et al. 1997 reported a correlation of 0.81 between SSR and pedigree distances for maize inbreds. Since their sample of inbreds included many commercial lines with detailed pedigrees, it is not surprising that they observed a stronger correlation than we did with our more diverse set of lines. Similarly, BERNARDO et al. 2000 observed a correlation of 0.92 between SSR and pedigree distances using a small set of public inbreds with well-documented pedigrees. Our study also differs from these two prior studies in using a higher proportion of dinucleotide SSRs, which with their higher mutation rate could weaken the correlation between SSR and pedigree distance.

Linkage disequilibrium:
Overall, 66% of SSR pairs exhibited significant LD. Smaller percentages of SSR pairs showed significant LD within the model-based groups, due in part to reduced statistical power with the smaller sample sizes. Sets of inbreds chosen at random from the full set of 260, but of the same size as one of the model-based groups, showed less LD than the actual model-based groups themselves (Table 6). This result suggests that the observed LD is largely due to population structure (or linkage) within groups as opposed to higher-level population structure among the entire set of lines. In particular, we observe a large excess of SSR pairs in LD within SS (29%) as compared to the expected number (4%), suggesting either considerable population structure or linkage effects among SS lines. This result is in apparent disagreement with those of REMINGTON et al. 2001 who found that higher-level structure makes an important contribution to LD and who observed the least evidence for LD within SS lines. This disagreement is likely a result of different sampling. REMINGTON et al. 2001 had fewer inbreds that were chosen in a manner to avoid closely related lines, while our larger set included many closely related lines, especially closely related SS lines.

Perspective:
There is a heightened awareness of the necessity for maintaining genetic diversity for the study of natural variation and for crop improvement. However, when stocks are placed in germplasm banks without an adequate understanding of the amount and distribution of genetic variation within those stocks, potential users of these resources are confronted with the difficulty of choosing a diverse and representative selection from long lists of essentially anonymous accessions. In this article, we have shown that maize inbreds possess a great depth of allelic diversity. This diversity is not distributed randomly among the lines, but rather diversity is structured into five groups along breeding group (SS vs. NSS) and ecological (temperate vs. tropical) axes. Similarly, the amount of diversity is not equivalent among groups, but rather tropical-subtropical inbreds possess greater diversity than their temperate counterparts. It is also clear that allelic diversity in some portions of the broader maize gene pool is not well represented in available inbreds. In particular, we found that the diversity in Tropical Highland maize is poorly represented among available inbreds, suggesting that Tropical Highland germplasm could be tapped to identify new alleles of agronomic importance. Finally, to aid researchers working with maize, we have defined both core sets of maize inbreds and a method for choosing core sets to best represent diversity among a set of inbreds. These results should help maize researchers to make more informed choices of inbreds for research and breeding.

	ACKNOWLEDGMENTS

We thank Bruce Weir for comments on the manuscript. This work was supported by the U.S. National Science Foundation grant DBI-0096033.

Manuscript received June 10, 2003; Accepted for publication August 20, 2003.

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