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PLoS One. 2017; 12(12): e0189277.
Published online 2017 December 13. doi:  10.1371/journal.pone.0189277
PMCID: PMC5728570

Genetic relatedness of previously Plant-Variety-Protected commercial maize inbreds

Travis J. Beckett, Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Software, Supervision, Validation, Visualization, Writing – original draft, Writing – review & editing,1,* A. Jason Morales, Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Software, Validation, Visualization, Writing – review & editing,2 Klaus L. Koehler, Conceptualization, Data curation, Funding acquisition, Methodology, Project administration, Resources, Supervision, Writing – review & editing,2 and Torbert R. Rocheford, Funding acquisition, Supervision, Writing – review & editing1
Aimin Zhang, Editor


The emergence of high-throughput, high-density genotyping methods combined with increasingly powerful computing systems has created opportunities to further discover and exploit the genes controlling agronomic performance in elite maize breeding populations. Understanding the genetic basis of population structure in an elite set of materials is an essential step in this genetic discovery process. This paper presents a genotype-based population analysis of all maize inbreds whose Plant Variety Protection certificates had expired as of the end of 2013 (283 inbreds) as well as 66 public founder inbreds. The results provide accurate population structure information and allow for important inferences in context of the historical development of North American elite commercial maize germplasm. Genotypic data was obtained via genotyping-by-sequencing on 349 inbreds. After filtering for missing data, 77,314 high-quality markers remained. The remaining missing data (average per individual was 6.22 percent) was fully imputed at an accuracy of 83 percent. Calculation of linkage disequilibrium revealed that the average r2 of 0.20 occurs at approximately 1.1 Kb. Results of population genetics analyses agree with previously published studies that divide North American maize germplasm into three heterotic groups: Stiff Stalk, Non-Stiff Stalk, and Iodent. Principal component analysis shows that population differentiation is indeed very complex and present at many levels, yet confirms that division into three main sub-groups is optimal for population description. Clustering based on Nei’s genetic distance provides an additional empirical representation of the three main heterotic groups. Overall fixation index (FST), indicating the degree of genetic divergence between the three main heterotic groups, was 0.1361. Understanding the genetic relationships and population differentiation of elite germplasm may help breeders to maintain and potentially increase the rate of genetic gain, resulting in higher overall agronomic performance.


Maize (Zea mays subsp. mays) is one of the most important agricultural crops in the United States. Grain yields remained generally constant from 1866 to 1936, when the vast majority of maize was grown from open-pollinated seeds (see Fig 1). Foundational studies in the early 1900’s on inbreeding and heterosis introduced the idea of producing commercial maize seed on a hybrid plant resulting from a cross of two inbreds [18]. Subsequently, the replacement of open-pollinated varieties with double- and single-cross hybrids played a major role in sustained increases in grain yield since 1937 [8, 9].

Fig 1
Historical U.S. Maize Yields, 1866 to 2015.

After over three decades of widespread commercial hybrid maize production, the Plant Variety Protection Act (PVPA) was passed by the U.S. Congress in 1970 [11]. This law guaranteed intellectual property rights to developers of new plant varieties by prohibiting others from reproducing, selling, or importing any protected variety, for a period of 18 (presently 20) years [12]. New plant varieties may also be protected by U.S. patents. The legality of granting patents for plants was affirmed by rulings by the U.S. Supreme Court in Diamond v. Chakrabarty (1980) [13] and J.E.M. Ag Supply v. Pioneer (2001) [14], and by the U.S. Board of Patent Appeals and Inferences in Ex parte Hibbert (1985) [1517]. Both utility patents and PVP certificates are effective forms of germplasm protection commonly used by U.S. private-sector soybean and maize breeders [18, 19].

When a PVP certificate issued for a maize inbred expires, and there is no active patent protecting the property, the inbred then enters the public domain and is provided free of charge by the United States Department of Agriculture (USDA). Many of these now-publicly available inbred lines have made a significant contribution to current commercial germplasm. By pedigree analysis, Mikel (2011) found that the top four progenitors (by genetic contribution) of 305 maize inbreds registered by PVP and/or utility patent between the years 2004 and 2008 were 3IIH6 (12.2%), B73 (11.7%), PH207 (9.5%), and PHG29 (9.4%) [20]. Three of these inbreds, 3IIH6, PH207, and PHG29, have expired PVP certificates. All four inbreds mentioned above are included found the population used in this study. Each inbred with a newly expired PVP certificate is a readily available source of highly selected alleles and haplotype blocks that can likely improve germplasm pools in breeding programs that previously did not have access to such elite genetics [20].

Heterosis, also known as hybrid vigor, is observed when the F1 progeny of a cross between two individuals from different germplasm groups performs better than the F1 progeny of a cross between two individuals from the same germplasm group [21]. In maize, these germplasm groups are generally referred to as heterotic groups. Numerous proposals of North American maize heterotic group divisions have been made [2126]. Most are some variant of the dominant heterotic pattern of Stiff Stalk (SS) and Non-Stiff Stalk (NSS), commonly known as the female-male heterotic pattern. A representative summary of the heterotic group proposals is given in Table 1.

Table 1
Summary of proposed heterotic group divisions in maize.

Maize inbreds can be assigned to heterotic groups based on: (1) pedigree information and specific combining ability based on field trials; (2) molecular markers and genetic relatedness analysis; or (3) some combination of these two methods [27]. Many attempts to classify public maize lines into heterotic groups using molecular markers have been reported, with varying levels of success (See Table 2). Early molecular marker platforms produced small number of markers at inconsistent accuracy levels [2834]. One problem with using a small number of markers is that it can be difficult to precisely resolve the heterotic and family group membership of closely related inbred lines, as the marker set may not include all loci that are responsible for heterotic divergence. Consequently, genetic-based determination of heterotic groups and combining ability was not considered as effective as traditional field-validation at accurately identifying similar groups of germplasm out of a large group of seemingly unrelated inbred lines [29, 34]. Genotyping technology has now improved to the point where genotype-based heterotic groupings appear just as accurate as the groupings defined by pedigrees and empirical field measures of combining ability [37, 40]. Next-generation sequencing methods such as genotyping-by-sequencing (GBS) can be very helpful in determining the heterotic group position of newly released ex-PVP inbreds relative to a breeding program’s existing inbreds.

Table 2
Using molecular markers to identify heterotic groups in maize.

There are some challenges, however, presented by the GBS method. The success of GBS depends on a minimum read depth, or number of repeated sequences covering a specific locus. Read depth can vary across the genome, between separate GBS batches, and even between individuals [43]. Due to low coverage of sequencing, there may be large portions of the genome without any successful marker calls [44]. Therefore, each set of GBS data–and even each individual genotype–has a unique distribution of the number and quality of genotype calls. Fortunately, when missing data remains after filtering, it can usually be imputed at acceptable levels of accuracy–a very cost-favorable alternative to sequencing at a higher depth [43, 45, 46].

Following the development of next-generation sequencing platforms, there have been a number of studies published on genetic classification of maize inbred lines [25, 26, 3642]. Several included inbreds with expired Plant Variety Protection certificates: Nelson, et al.(2008) with 92 ex-PVP inbreds; Kahler, et al. (2010) with 33; van Heerwaarden, et al. (2012) with 137; Romay, et al. (2015), with 212; and Smith, et al. (2015) with 105. Out of these, the publication most closely aligned to the subject of this study is that authored by Romay et al. (2013) [38].

This paper presents a comprehensive genotype-based population analysis of all ex-PVP maize inbreds available as of the end of 2012. The robust array of analyses includes measures of genetic diversity, linkage disequilibrium, genotypic clustering, and heterotic groupings. Included in this study is a greater number of ex-PVP inbreds (283) and a wider range of analytical methods than found in previous publications. The results herein can help maize breeders determine how to best incorporate the ex-PVP inbreds into their existing germplasm pools.

Materials and methods

Plant material

The maize varieties used in this study include 283 ex-PVP inbreds and 66 public inbred founders. The 283 ex-PVP inbreds were those with certificates that had expired between 1994 and 2012. Distribution by proprietor of these 283 inbreds with expired Plant Variety Protection (ex-PVP) is shown in Fig 2. Pedigrees of the 283 ex-PVP lines were examined and 66 public founder inbreds were identified based on two criteria: (1) the public inbred appeared in the pedigree of at least one ex-PVP inbred; and (2) seed for that public line was available at the start of this project [47]. Seed for all 349 inbreds was requested from the USDA-ARS National Genetic Resources Program [48], and received from the USDA-ARS North-Central Regional Plant Introduction Station (NCRPIS) in Ames, Iowa. Ex-PVP inbred pedigrees were obtained from the PVP certificates, accessed at [48]. Public inbred pedigrees were obtained from the volume titled, Compilation of North American Maize Breeding Germplasm [49]. Tables with general information about both the ex-PVP and public founder inbred sets are provided in the supplementary information (see S1 and S2 Tables).

Fig 2
Plant Variety Protection certificates expired as of 2012, by proprietor.

A bar chart showing the distribution of the 283 ex-PVP inbreds used in this study, sorted by proprietor, is displayed in Fig 2. Pioneer Hi-Bred International, Inc. (Pioneer) produced the most inbreds, with nearly 40 percent of these PVP certificates. The top three proprietors, Pioneer, Holden’s Foundation Seeds, and DEKALB Plant Genetics, together held over 75 percent of PVP certificates for inbred lines used in this data set. The top seven proprietors, which also includes Novartis Seeds, Inc., United AgriSeeds, Inc., Advanta Technology Limited, and Wilson Hybrids, Inc., accounted for nearly 90 percent of PVP certificates. The remaining ex-PVP inbreds used in this study originated from twenty-one different companies, with between one and three certificates held by each company. Thus, of the North American commercial maize inbreds with PVP certificates that had expired as of the end of 2012, the vast majority (nearly 90%) came from only one-quarter of all private maize breeding programs that used PVP for their inbreds (seven out of twenty-eight companies).

Genotypic data compilation

The original genotypic data comes from two sources. The first source includes genotyping data on 224 lines whose PVP certificates had expired as of the end of 2011, as well as 67 public founder inbred lines. Partially imputed GBS data for these 291 lines was downloaded from the online GBS data repository at [50]. The build version was ZeaGBSv27, with 955,690 SNPs on AGPv2 coordinates, produced using the enzyme ApeKI and the protocol described by Elshire et al., (2011) [43, 51]. The second source consisted of GBS data on 58 additional ex-PVP inbred lines whose PVP certificates expired during the first four months of 2012. These 58 lines were grown at the Purdue Agronomy Center for Research and Education (ACRE) in West Lafayette, Indiana, in the summer of 2012. Tissue sampling and DNA extraction was performed according to the protocol of Romay et al., (2013) [38]. The DNA samples were sent to the Cornell University Institute for Genomic Diversity (Ithaca, New York), where GBS libraries were prepared and analyzed according to Elshire et al. (2011) [43], using the enzyme ApeKI for digestion and creating a library with 240,021,078 unique barcodes. The GBS pipeline for these 58 lines resulted in 546,531 unfiltered SNPs. The two genotypic data sets were aligned and merged, using TASSEL 5.0, version 20151210 [52]. A summary of the genotypic data set compilation steps is given in Table 3.

Table 3
Summary statistics of unmerged genotypic data sets, before filtering and imputing.

Data analysis

SNP characteristics

Quality control measures were employed to ensure that the genotypic data would be as accurate as possible for population structure analysis. Genotypic markers with missing data greater than ten percent and/or a minor allele frequency (MAF) less than 0.05 were removed. As the genotypic analyses assume only two alleles per locus, minor SNP statuses (i.e. tertiary and greater alleles) were changed to missing data. Additionally, any heterozygote calls were changed to missing data. Applying these filters reduced the maximum amount of missing data per inbred to no more than 30 percent for any one inbred in this data set (see Table 4). The specific level of 30 percent was chosen to balance the share of missing data between the two previously unmerged GBS sets while also minimizing the proportion of overall missing data, thus reducing overall proportion of genotypic errors caused by imputation [53]. These filter thresholds left the genotypic data set with a total of 77,314 SNPs.

Table 4
Summary statistics of merged, filtered, and imputed genotypic data sets.

The 6.22 percent of genotypic data points that remained as missing data were fully imputed using the ‘markov’ function in the package ‘NAM’ in RStudio version 0.98.1103 [5355]. This function employs a Hidden Markov Model (HMM); however, unlike other HMM-based imputation methods, the ‘markov’ function only runs in the forward direction and not the backward direction. This feature enables quicker imputation computations for very large data sets. Imputation accuracy was calculated by comparing a completed genotypic data set with a version of the same data set which included imputed values at randomly placed missing data points. Calculations to assess imputation accuracy were repeated 100 times using the same complete data set, with the average amount of randomly placed missing data across the repetitions set at 6.22 percent. The mean imputation accuracy of these repetitions was reported as the overall imputation accuracy for this data set.

Principal component analysis

Principal component analysis (PCA, or PC analysis) was performed by the ‘prcomp’ function in RStudio [55]. The optimal number of PCAs was determined by consulting both the scree plot and the PCA plots, in context of what has already been reported about the number of major maize heterotic group divisions [2126].

Linkage disequilibrium

Analysis of linkage disequilibrium (LD) was performed in RStudio [55] with the package ‘NAM’, using the function ‘ld’ [54]. Decay of LD was determined for each chromosome individually by considering all pairwise SNP marker combinations. For each SNP pair, both the distance (bp) and the coefficient of determination r2 were calculated, then plotted. A smoothing function within RStudio (’lokern’) was employed to insert a trend line for each chromosome [56]. A trend line for the mean LD over all chromosomes was also included in the plot.

Population structure

Population substructure was analyzed using RStudio [55], using various packages as described below. Nei’s distance, calculated by


was used to create the distance matrix with functions called from the package ‘NAM’ [57]. The built-in R function ‘hclust’ [55] was used to perform an hierarchical cluster analysis using Ward’s minimum-variance method [58], defined by

dijd({Xi}, {Xj}) = ||XiXj||2

A genetic clustering diagram, a dendrogram, was created and coded using the package ‘ape’ [59]. The tree was exported in Newick (also known as New Hampshire) file format, then imported into the online application Interactive Tree of Life (iTol) for color annotating [60].

Once the tree was created, the number of sub-groups was determined by a multi-step approach. First, the plots produced from principal component analysis were examined for indications of separation into clear groups. The function ‘cutree’ in RStudio [55] was then used to split the tree into sub-groups based on branch length (genetic dissimilarity), informed generally by the number of clear groups indicated by the principal component plot. Known pedigrees and results of previous studies [25, 36, 47] were then used to identify group names and confirm boundaries. Divisions of between three and eight sub-groups were examined in more detail. Maximum sub-groups were reached when further division did not appear justified based on pedigrees, results of previous studies, as well as the principal component analysis.

Genetic diversity

To assess the level of genetic variation when dividing the population into three main heterotic groups of SS, NSS, and Iodent, FST was calculated using the package ‘NAM’ [54] in RStudio [55]. This analysis produces estimates of unbiased FST statistics by a weighted analysis of variance method [61]. Overall FST was calculated as the simple average across all loci.

To reduce bias in the FST statistic, two important interrelated modifications were made [62]. Both involved filtering of the inbreds to be used in calculation of the FST statistic. First, to correct for sample size among sub-populations (or heterotic groups, in this case), a balanced number of individuals across the three heterotic groups was selected. Second, to reduce bias of allelic frequencies caused by pedigree structure, the balanced sample from each heterotic group was composed of individuals as genetically unrelated as possible. For example, within the Stiff Stalk heterotic group, the inbreds F42 and B73 are very genetically closely related. Including both of these inbreds in an allelic frequency measure would be essentially using duplicate genotypic data, and would bias the allele frequency calculated for the Stiff Stalk heterotic group. Simply excluding either one inbred, however, while retaining the other, removes the pedigree structure bias while retaining sufficient genetic diversity in the context of FST analysis.

The Iodent heterotic group contained the least number of individuals, so the filtering process was initiated within this subgroup. Filtering of the Iodent subgroup according to the two criteria described above resulted in 44 remaining inbreds. Therefore, in order to balance the data set with equal number of individuals from each heterotic group, 44 became the target number of individuals to select out of the remaining two groups. A list of the inbreds selected for FST analysis is included in the supplemental materials in S3 Table.

For the SNPs with the highest FST values, a candidate gene search was completed for a 10 kbp window on either side of the SNP. This candidate gene search was done within the B73 v2 reference genome, using the R package ‘Zbrowse’ [63].


Marker coverage and missing data

As the genotypic data set came from two different sources, it was necessary to merge the genotypic data before analysis. Consequently, out of a total of 955,690 SNP markers in the first set and 546,531 SNP markers in the second set, only 220,550 sites–or 17.2 percent–were common to both GBS sets (Table 3). Following the GBS data set merger and then filtering to remove heterozygous calls, monomorphic sites, markers with greater than 17.2 percent missing data, and SNPs with minor allele frequency (MAF) less than 0.05, the number of SNP markers remaining was 77,314 (Table 4). Missing data may not have been distributed randomly, as use of the B73 reference genome for read alignment causes inbreds closely related to B73 to have a lower proportion of missing data than inbreds more distantly related to B73 [38]. Even so, prior to population analysis, missing data was reduced to zero by imputation. Imputation accuracy was estimated to be 0.83.

Linkage disequilibrium

Fig 3 shows the decay of linkage disequilibrium (LD) across genetic distance. An average LD of r2 at 0.2 was reached at approximately 1.1 Kbp. All chromosomes followed the same general decay trend, with the exception of chromosome 7, which appeared to decay more rapidly than the rest between 100 bp and 1 Kb, reaching an average LD of 0.2 at approximately 1 Kb.

Fig 3
Decay of linkage disequilibrium with physical distance.

Population structure

The ex-PVP inbreds originated from 28 different proprietors (Fig 2 and S1 Table). The public founder inbreds originated from research programs located in 17 different states and one Canadian province (S2 Table). Population stratification was expected to follow the three principal heterotic groups of maize: Stiff Stalk, Non-Stiff Stalk, and Iodent. Two dimensional PC analysis validated this expectation (Fig 4), with three clear spatial divisions in the PCA plot corresponding with the three main population groups identified in the phylogenetic cluster analysis. A PCA plot with three principal components for each inbred line also shows a clear division into three main groups (Fig 5).

Fig 4
Principal component 1 vs. principal component 2.
Fig 5
Three-dimensional plot of principal component analysis.

Further confirmation of the generally expected population stratification is visible in the scree plot of the principal component analysis (Fig 6. The optimal number of principal components to explain genotypic variation, three, was found by visually determining the largest point of inflection, or “elbow” of the non-linear trend line [64]. To find the optimal number of principal components, more complex and empirical methods–such as the silhouette method [65] or the Gap statistic [66]–could have been employed. However, in context of prior knowledge of North American maize heterotic groups as well as phylogenetic cluster analysis based on genotypic data (see next paragraph), the “elbow” method is more than sufficient in this case. Percent variation explained by additional principal components is depicted in Fig 7.

Fig 6
Scree plot of principal component analysis.
Fig 7
Percent genetic variance explained by principal component analysis.

Phylogenetic cluster analysis produced a dendrogram that divided into three main groups, Stiff Stalk, Non-Stiff Stalk, and Iodent (Fig 8). General heterotic group assignments based on pedigree data as well as previous publications agree with the classifications assigned by the genotypic clustering method used herein [20, 25, 29, 35, 36, 47]. For a more detailed examination of heterotic group classifications, a dendrogram divided into eight principal population sub-groups was produced by the same methods of cluster analysis. This dendrogram with eight divisions is included in the supplementary materials (see S1 Fig).

Fig 8
Dendrogram of ex-PVP and public founder inbreds.

Genetic diversity

The overall genetic diversity, or mean FST, when considering divisions into SS, NSS, and Iodent heterotic groups is 0.1732. Genome-wide FST values plotted against relative marker position are presented in Fig 9. This plot reveals trends that may be worth further study, as they may be indicative of individual loci and/or genomic regions that are involved in population differentiation or possibly even heterosis.

Fig 9
Fixation index values across the genome.

Individual loci were examined for proximity to candidate genes; results are presented in Table 5. These 11 loci are representative of areas where the highest FST values for individual SNPs were found, specifically in chromosomes 2, 4, 5, 7, and 8. The four genomic regions with the highest mean FST value over a window of 70 SNPs are identified in Table 6.

Table 5
Candidate genes for SNPs with high FST values.
Table 6
Genomic regions with high FST values.


Linkage disequilibrium

The rate of LD decay reported in maize depends on the population, the genetic region(s) under study, as well as the statistical methods used to compute the values. For the population in this study, the result of LD decay (r2 at 0.2 at approximately 1.1 Kbp) appears reasonable and well within the general range reported in previous studies. As LD values reported in the literature can vary, the following summary of relevant results of LD decay provides context within which the results of this study can be evaluated.

Developments in genotyping methods led to many studies in the early 2000’s that reported on LD in maize. Tenaillon et al., (2001) [68], reported on a set of 25 maize genotypes comprised of 16 landraces and nine North American inbred lines, analyzing the LD between 21 SNP markers on chromosome 1. Their results showed that LD declines to an average r2 of 0.2 at 300 bp in the mixed set of 25 genotypes, and greater than 1 kbp in the subset that includes only the nine North American inbreds. Remington et al., (2001) [69] analyzed the LD for 102 inbred lines from a broad range of temperate and tropical origins, using over 1.5 Mb of SSR marker data centered on six candidate gene regions, and found that the decay reached an average of average r2 of 0.2 at an average of 550 bp for five of the six candidate regions. For the sixth candidate region, LD did not decay to the same level until well after 10 kbp. In another study that examined sequence variants (SNPs and indels) across 18 gene regions in 36 elite U.S. maize inbreds, Ching et al., (2002) [70] concluded that linkage disequilibrium does not significantly decay within the analyzed range of 300-500 bp. Palaisa et al., (2003) [71] found that LD surrounding two loci in a group of 82 diverse inbred lines decayed to a level of r2 at 0.2 at approximately 1,000 bp. Similarly, in a study of the adh1 locus within 32 elite North American public and proprietary inbred lines, Jung et al., (2004) [72] reported that while measurable levels of LD appeared to persist past 500 kbp, it could not be stated whether these long-range regions of sustained LD are common. (Estimates of LD at the specific level of r2 at 0.2 were not available in this study.)

More recently, Yan et al. (2009) [73] studied the extent of LD in 632 maize inbreds from temperate, tropical, and subtropical regions, using 1,229 SNP markers. They found that across all 632 inbreds, LD decayed to an average r2 of 0.2 at about 500 bp, and generally concluded that the distance of LD decay is much higher in temperate inbreds than in tropical or subtropical inbreds. Truntzler et al., (2012) [74] using a mix of inbreds from public institutions (113 inbreds) and private companies (201 inbreds) and 979 polymorphic SNP markers, reported that while there is a faster rate of LD decay for the private inbreds than the public inbreds, both sets reach r2 of 0.2 at a distance of about 1-3 kbp. Romay et al. (2013) [38], using a population that is essentially a subset of the population used in this study, found that while the LD for 212 ex-PVP inbreds declined to an average r2 of 0.2 at 10 kb, the LD decay among public inbreds was much more rapid, reaching r2 of 0.2 at 1 kb.

The calculation of decay of linkage disequilibrium is affected by many factors: composition of the germplasm set; marker characteristics such as quality and genome coverage; and the analysis method employed. While these factors may lead to variance between data sets of the physical distance observed at the standard-reported linkage equilibrium value r2 of 0.2, the general trends found in this germplasm set are consistent with the results previously reported.

Population structure

Inclusion of a scale in the dendrogram (Fig 8) allows inferences to be made about relative genetic distance between heterotic groups. A comparison between the three heterotic groups in Fig 8 reinforces the concept that commercial breeding efforts in the Plant Variety Protection era (post-1970) have continued to drive genetic divergence among Stiff Stalk, Non-Stiff Stalk, and Iodent. FST analysis confirms the divergence, with the result of 0.1732 indicating moderate levels of divergence among these three heterotic groups. A more detailed look at the FST analysis reveals several genomic regions as well as several individual SNPs with high FST values. High FST values for a particular region or SNP mean that it is more likely that the major haplotype or allele in the SS group is different than the major haplotype or allele in the NSS group. These genomic regions and individual SNPs that show high genetic diversity between heterotic groups deserve further study, as they may provide insights about the genetic basis of heterosis.

It is widely accepted among breeders and others familiar with North American maize germplasm that heterotic groups continue to diverge genetically [36, 75]. One reason for this genetic divergence of heterotic groups could be the widespread breeding practice of recycling of elite inbreds within heterotic groups to produce new inbreds, then evaluating them based on testcross performance with inbreds from other heterotic groups. The observed genetic divergence between breeding pools then may be a response to selection for heterosis in testcross hybrids. The value of a commercial inbred is not just based on its ability to efficiently produce hybrid seed, but primarily on its ability to consistently produce superior grain yield in a testcross. Therefore, as inbreds are judged by their performance in a testcross, a higher degree of genetic divergence between heterotic groups may be a result of selection over time for better hybrid performance.

Application of genetic relationships in breeding

Precise and accurate knowledge of the genetic background of a particular inbred can be very useful to a plant breeder in determining the best use of that inbred. Traditional pedigree information, supplemented by population genetics data can help a breeder decide what combination of inbreds may prove to be the best for breeding crosses and for hybrid testcrosses. Many PVP inbreds came from self-pollination of commercial hybrids. An accurate dendrogram based on genetic relationships can help breeders better understand the genetic background of PVP inbreds derived from commercial hybrids, as well as identify close genetic relatives. For one example, the P3737-derived inbreds 3IIH6, 912, 904, and 911 are located near the bottom of the tree in S9 Fig. The location of these lines within the dendrogram does not align with expectations based only on field testing and general pedigree knowledge. With robust genetic diversity analysis, however, a more clear and complete picture emerges.

The dendrogram produced in this study (Fig 8) visually identifies the heterotic group membership of each ex-PVP and pubic inbred. The divisions among Stiff Stalk, Non-Stiff Stalk, and Iodent are clear. Further sub-group divisions within the Stiff Stalk heterotic group are defined. However, the sub-group divisions within the Non-Stiff Stalk heterotic group are more difficult to resolve (see S1 Fig). Many of the ex-PVP Non-Stiff Stalk inbreds are genetically closely related, especially in the “Pioneer Mixed” and “Miscellaneous” groups. This study includes a larger number of ex-PVP inbreds and more detailed information about relationships derived directly from genotypic cluster analysis than previous studies. In general, the results presented here agree with previous classifications of maize heterotic groups [21, 25, 36, 47].

Information from this study can be useful in determining how to begin testing a newly released ex-PVP inbred line. When the PVP certificate for an inbred expires and the seed is freely available for use, the parentage of the line can be determined by consulting the pedigree on the certificate. Then the parental inbreds can be located on the dendrogram. Thus, the newly released ex-PVP inbred can be anchored to previously characterized inbreds. Such an approach can potentially save time and resources, particularly for smaller breeding programs.

Previous yield trial results of parental lines could be a logical starting point for determining the potential combining patterns and agronomic performance value of a newly released ex-PVP inbred [76]. Alternatively, if the pedigree on the certificate does not include parental inbreds that are within the current genetic cluster diagram, and if the inbred can be quickly genotyped, then the inbred can be included in a new cluster analysis where the precise genetic relationships can be determined. Even if good parental pedigree and testcross data is available for a newly expired PVP inbred, there may be merit to genotyping the inbred and determining where it falls in the cluster diagram, as this provides complementary and more precise genetic relationship information. Yield trial data coupled with this population genetic analysis may further improve a breeder’s ability to immediately identify the best material and quickly integrate it into a germplasm pool. Understanding the genetic relationships and population differentiation of elite maize germplasm is an integral part part of helping breeders to maintain and potentially increase the rate of genetic gain, resulting in higher overall agronomic performance of inbreds and hybrids.

Supporting information

S1 Table

Ex-PVP inbreds used in this study.


S2 Table

Public inbreds used in this study.


S3 Table

Subsets of inbreds used in FST calculations.


S4 Table

List of individual accession identifiers for all inbreds used in this study for genotyping-by-sequencing (GBS) data, available at [50].

In the data repository, individual accession identifiers are referred to as “Taxa”, and thus have been listed as such in this table.


S1 Fig

Dendrogram of ex-PVP and public founder inbreds, divided into eight heterotic groups.

Shown with relative scaled branch lengths, this dendrogram is based on a cluster analysis using Ward’s minimum distance variance method, and Nei’s genetic distance [57, 58]. Colors represent further divisions of heterotic groups of maize, with groups named by important founder line or by general group composition. Consultation of published pedigrees [48, 49, 67] as well as previous publications on the subject as well as previous publications on the subject [12, 20, 24] confirm the accuracy of heterotic group placement for individual inbreds.


S2 Fig

Linear dendrogram of ex-PVP and public founder inbreds, divided into eight sub-groups.

This dendrogram is based on phylogenetic cluster analysis using Ward’s minimum distance variance method, and Nei’s genetic distance [57, 58]. Tree branch lengths are scaled relatively according to the actual genetic distance matrix. Colors correlate with maize family groups as indicated in the “Heterotic Group” key. Pedigrees are included to the right of each inbred. PVP inbred pedigrees were obtained from from PVP certificates, available at [48]. Public inbred pedigrees were obtained from Gerdes et al., (1993) [49] and Cross et al., (1989) [67]. Consultation of pedigrees, as well as previous publications on the subject [12, 20, 24], confirm individual heterotic group memberships are accurate.


S3 Fig

B73 group dendrogram with inbred pedigrees.

The color surrounding the ex-PVP and public inbred names corresponds with the color assigned to each family subgroup in S1 and S2 Figs. Pedigrees are included to the right of each inbred. PVP inbred pedigrees were obtained from from PVP certificates, available at [48]. Public inbred pedigrees were obtained from Gerdes et al., (1993) [49] and Cross et al., (1989) [67]. Consultation of pedigrees, as well as previous publications on the subject [12, 20, 24], confirm individual heterotic group memberships are accurate.


S4 Fig

B14 group dendrogram with inbred pedigrees.

The color surrounding the ex-PVP and public inbred names corresponds with the color assigned to each family subgroup in S1 and S2 Figs. Pedigrees are included to the right of each inbred. PVP inbred pedigrees were obtained from from PVP certificates, available at [48]. Public inbred pedigrees were obtained from Gerdes et al., (1993) [49] and Cross et al., (1989) [67]. Consultation of pedigrees, as well as previous publications on the subject [12, 20, 24], confirm individual heterotic group memberships are accurate.


S5 Fig

B37 group dendrogram with inbred pedigrees.

The color surrounding the ex-PVP and public inbred names corresponds with the color assigned to each family subgroup in S1 and S2 Figs. Pedigrees are included to the right of each inbred. PVP inbred pedigrees were obtained from from PVP certificates, available at [48]. Public inbred pedigrees were obtained from Gerdes et al., (1993) [49] and Cross et al., (1989) [67]. Consultation of pedigrees, as well as previous publications on the subject [12, 20, 24], confirm individual heterotic group memberships are accurate.


S6 Fig

Iodent group dendrogram with inbred pedigrees.

The color surrounding the ex-PVP and public inbred names corresponds with the color assigned to each family subgroup in S1 and S2 Figs. Pedigrees are included to the right of each inbred. PVP inbred pedigrees were obtained from from PVP certificates, available at [48]. Public inbred pedigrees were obtained from Gerdes et al., (1993) [49] and Cross et al., (1989) [67]. Consultation of pedigrees, as well as previous publications on the subject [12, 20, 24], confirm individual heterotic group memberships are accurate.


S7 Fig

Lancaster group dendrogram with inbred pedigrees.

The color surrounding the ex-PVP and public inbred names corresponds with the color assigned to each family subgroup in S1 and S2 Figs. Pedigrees are included to the right of each inbred. PVP inbred pedigrees were obtained from from PVP certificates, available at [48]. Public inbred pedigrees were obtained from Gerdes et al., (1993) [49] and Cross et al., (1989) [67]. Consultation of pedigrees, as well as previous publications on the subject [12, 20, 24], confirm individual heterotic group memberships are accurate.


S8 Fig

Ohio 43 group dendrogram with inbred pedigrees.

The color surrounding the ex-PVP and public inbred names corresponds with the color assigned to each family subgroup in S1 and S2 Figs. Pedigrees are included to the right of each inbred. PVP inbred pedigrees were obtained from from PVP certificates, available at [48]. Public inbred pedigrees were obtained from Gerdes et al., (1993) [49] and Cross et al., (1989) [67]. Consultation of pedigrees, as well as previous publications on the subject [12, 20, 24], confirm individual heterotic group memberships are accurate.


S9 Fig

Pioneer Mixed group dendrogram with inbred pedigrees.

The color surrounding the ex-PVP and public inbred names corresponds with the color assigned to each family subgroup in S1 and S2 Figs. Pedigrees are included to the right of each inbred. PVP inbred pedigrees were obtained from from PVP certificates, available at [48]. Public inbred pedigrees were obtained from Gerdes et al., (1993) [49] and Cross et al., (1989) [67]. Consultation of pedigrees, as well as previous publications on the subject [12, 20, 24], confirm individual heterotic group memberships are accurate.


S10 Fig

Miscellaneous sub-group dendrogram with pedigrees.

The color surrounding the ex-PVP and public inbred names corresponds with the color assigned to each family subgroup in S1 and S2 Figs. Pedigrees are included to the right of each inbred. PVP inbred pedigrees were obtained from from PVP certificates, available at [48]. Public inbred pedigrees were obtained from Gerdes et al., (1993) [49] and Cross et al., (1989) [67]. Consultation of pedigrees, as well as previous publications on the subject [12, 20, 24], confirm individual heterotic group memberships are accurate.



The authors gratefully acknowledge the help of Alencar Xavier and William Muir, coauthors of the R software package ‘NAM’, who provided assistance in overall coding and analysis, and guidance with interpretation of FST statistics.

Funding Statement

This research was funded by a grant from Dow AgroSciences ( The funder provided additional support in the form of salaries for authors AJM and KLK, but did not have any additional role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript. The specific roles of these authors are articulated in the ‘author contributions’ section.

Data Availability

Data Availability

All genotype-by-sequencing (GBS) data are available from the database. As the samples are part of a larger data set, individual accession identifiers for all inbreds are listed S4 Table. The genotype for each individual may be obtained by pasting the "Taxa" identifier in the appropriate place on this online database webpage:


1. Shull GH. A pure-line method in corn breeding. Journal of Heredity. 1909. January 1(1):51–8. doi: 10.1093/jhered/os-5.1.51
2. Shull GH. Hybridization methods in corn breeding. Journal of Heredity. 1910. April 1;1(2):98–107. doi: 10.1093/jhered/1.2.98
3. Richey FD. The experimental basis for the present status of corn breeding. Agronomy Journal. 1922;14(1-2):1–7. doi: 10.2134/agronj1922.00021962001401-20001x
4. East EM, Hayes HK. Heterozygosis in evolution and in plant breeding. US Government Printing Office; 1912.
5. East EM. Inheritance in maize. Botanical Gazette. 1913. May 1;55(5):404–5. doi: 10.1086/331078
6. Hayes HK, East EM. Improvement in corn. Connecticut Agricultural Experiment Station; 1911.
7. Hayes HK, East EM. Further experiments on inheritance in maize. Connecticut Agricultural Experiment Station; 1915.
8. Wallace HA, Brown WL. Corn, And Its Early Fathers. Soil Science. 1957. February 1;83(2):160 doi: 10.1097/00010694-195702000-00014
9. Crabb AR. The hybrid-corn makers. Prophets of plenty. 1947.
10. USDA United States Department of Agriculture, National Agricultural Statistics Service: Quick Stats[Online Database]. National Agricultural Statistics Service, Washington D.C.; 2016.
11. USDA. United States Department of Agriculture: Plant Variety Protection Act and Regulations and Rules of Practice. Agricultural Marketing Service, Washington, DC, updated July 2013.
12. Mikel MA. Availability and analysis of proprietary dent corn inbred lines with expired US plant variety protection. Crop Science. 2006. November 1;46(6):2555–60.
13. Diamond v. Chakrabarty, 447 US 303 (1980).
14. J.E.M. AG Supply v. Pioneer Hi-Bred International, 122 US 593 (2001).
15. United States Patent and Trademark Office. Patentable Subject Matter—Living Subject Matter. Manual of Patent Examining Procedure, ch. 2100 sec. 2105. Jul 2015. URL
16. Ex parte Hibberd, 227 USPQ 433. (Bd. Pat. App. & Inter. 1985).
17. Van Brunt J. Ex parte Hibberd: Another Landmark Decision. Nature Biotechnology. 1985. December 1;3(12):1059–60. doi: 10.1038/nbt1285-1059
18. Moschini GC. Competition issues in the seed industry and the role of intellectual property. 2nd Quarter 2010;25(2). URL
19. Kurtz B, Gardner CA, Millard MJ, Nickson T, Smith JS. Global Access to Maize Germplasm Provided by the US National Plant Germplasm System and by US Plant Breeders. Crop Science. 2016;56(3):931–41. doi: 10.2135/cropsci2015.07.0439
20. Mikel MA. Genetic composition of contemporary US commercial dent corn germplasm. Crop Science. 2011. March 1;51(2):592–9. doi: 10.2135/cropsci2010.06.0332
21. Bernardo R. Essentials of plant breeding. 2014.
22. Troyer AF. Background of U.S. hybrid corn. Crop Science. 1999;39(3):601–26. doi: 10.2135/cropsci1999.0011183X003900020001x
23. Gethi JG, Labate JA, Lamkey KR, Smith ME, Kresovich S. SSR variation in important US maize inbred lines. Crop Science. 2002. May 1;42(3):951–7. doi: 10.2135/cropsci2002.0951
24. Mikel MA, Dudley JW. Evolution of North American dent corn from public to proprietary germplasm. Crop Science. 2006. May 1;46(3):1193–205. doi: 10.2135/cropsci2005.10-0371
25. Nelson PT, Coles ND, Holland JB, Bubeck DM, Smith S, Goodman MM. Molecular characterization of maize inbreds with expired US plant variety protection. Crop Science. 2008. September 1;48(5):1673–85. doi: 10.2135/cropsci2008.02.0092
26. Lu Y, Yan J, Guimaraes CT, Taba S, Hao Z, Gao S, et al. Molecular characterization of global maize breeding germplasm based on genome-wide single nucleotide polymorphisms. Theoretical and Applied Genetics. 2009. December 1;120(1):93–115. doi: 10.1007/s00122-009-1162-7 [PubMed]
27. Fan XM, Zhang YM, Yao WH, Chen HM, Tan J, Xu CX, et al. Classifying maize inbred lines into heterotic groups using a factorial mating design. Agronomy Journal. 2009. January 1;101(1):106–12. doi: 10.2134/agronj2008.0217
28. Smith OS, Smith JS, Bowen SL, Tenborg RA, Wall SJ. Similarities among a group of elite maize inbreds as measured by pedigree, F1 grain yield, grain yield, heterosis, and RFLPs. Theoretical and Applied Genetics. 1990. December 1;80(6):833–40. doi: 10.1007/BF00224201 [PubMed]
29. Dudley JW, Maroof MA, Rufener GK. Molecular markers and grouping of parents in maize breeding programs. Crop Science. 1991;31(3):718–23. doi: 10.2135/cropsci1991.0011183X003100030036x
30. Livini C, Ajmone-Marsan P, Melchinger AE, Messmer MM, Motto M. Genetic diversity of maize inbred lines within and among heterotic groups revealed by RFLPs. Theoretical and Applied Genetics. 1992. June 1;84(1-2):17–25. doi: 10.1007/BF00223976 [PubMed]
31. Melchinger AE, Messmer MM, Lee M, Woodman WL, Lamkey KR. Diversity and relationships among US maize inbreds revealed by restriction fragment length polymorphisms. Crop Science. 1991;31(3):669–78. doi: 10.2135/cropsci1991.0011183X003100030025x
32. Mumm RH, Dudley JW. A classification of 148 US maize inbreds: I. Cluster analysis based on RFLPs. Crop Science. 1994;34(4):842–51. doi: 10.2135/cropsci1994.0011183X003400040006x
33. Senior ML, Murphy JP, Goodman MM, Stuber CW. Utility of SSRs for determining genetic similarities and relationships in maize using an agarose gel system. Crop Science. 1998;38(4):1088–98. doi: 10.2135/cropsci1998.0011183X003800040034x
34. Barata C, Carena MJ. Classification of North Dakota maize inbred lines into heterotic groups based on molecular and testcross data. Euphytica. 2006. October 1;151(3):339–49. doi: 10.1007/s10681-006-9155-y
35. Kahler AL, Kahler JL, Thompson SA, Ferriss RS, Jones ES, Nelson BK, et al. North American study on essential derivation in maize: II. Selection and evaluation of a panel of simple sequence repeat loci. Crop Science. 2010. March 1;50(2):486–503. doi: 10.2135/cropsci2009.03.0121
36. van Heerwaarden J, Hufford MB, Ross-Ibarra J. Historical genomics of North American maize. Proceedings of the National Academy of Sciences. 2012. July 31;109(31):12420–5. doi: 10.1073/pnas.1209275109 [PubMed]
37. Olmos SE, Delucchi C, Ravera M, Negri ME, Mandolino C, Eyherabide GH. Genetic relatedness and population structure within the public Argentinean collection of maize inbred lines. Maydica. 2013. October 29;59(1):16–31.
38. Romay MC, Millard MJ, Glaubitz JC, Peiffer JA, Swarts KL, Casstevens TM, et al. Comprehensive genotyping of the USA national maize inbred seed bank. Genome biology. 2013. June 11;14(6):1 doi: 10.1186/gb-2013-14-6-r55 [PMC free article] [PubMed]
39. Unterseer S, Bauer E, Haberer G, Seidel M, Knaak C, Ouzunova M, et al. A powerful tool for genome analysis in maize: development and evaluation of the high density 600 k SNP genotyping array. BMC Genomics. 2014. September 29;15(1):1 doi: 10.1186/1471-2164-15-823 [PMC free article] [PubMed]
40. Smith SD, Murray SC, Heffner E. Molecular analysis of genetic diversity in a Texas maize (Zea mays L.) breeding program. Maydica. 2015. July 17;60(2015):M20.
41. Wu Y, San Vicente F, Huang K, Dhliwayo T, Costich DE, Semagn K, et al. Molecular characterization of CIMMYT maize inbred lines with genotyping-by-sequencing SNPs. Theoretical and Applied Genetics. 2016. April 1;129(4):753–65. doi: 10.1007/s00122-016-2664-8 [PMC free article] [PubMed]
42. Zhang X, Zhang H, Li L, Lan H, Ren Z, Liu D, et al. Characterizing the population structure and genetic diversity of maize breeding germplasm in Southwest China using genome-wide SNP markers. BMC genomics. 2016. August 31;17(1):697 doi: 10.1186/s12864-016-3041-3 [PMC free article] [PubMed]
43. Elshire RJ, Glaubitz JC, Sun Q, Poland JA, Kawamoto K, Buckler ES, et al. A robust, simple genotyping-by-sequencing (GBS) approach for high diversity species. PloS one. 2011. May 4;6(5):e19379 doi: 10.1371/journal.pone.0019379 [PMC free article] [PubMed]
44. Deschamps S, Llaca V, May GD. Genotyping-by-sequencing in plants. Biology. 2012. September 25;1(3):460–83. doi: 10.3390/biology1030460 [PMC free article] [PubMed]
45. Poland JA, Rife TW. Genotyping-by-sequencing for plant breeding and genetics. The Plant Genome. 2012. November 1;5(3):92–102.
46. Swarts K, Li H, Romero Navarro JA, An D, Romay MC, Hearne S, et al. Novel methods to optimize genotypic imputation for low-coverage, next-generation sequence data in crop plants. The Plant Genome. 2014. November 1;7(3). doi: 10.3835/plantgenome2014.05.0023
47. Morales AJ. Genomic approaches for improving grain yield in maize using formerly plant variety protected germplasm (Doctoral dissertation, PURDUE UNIVERSITY), 2013.
48. USDA Germplasm Resources Information Network-(GRIN)[Online Database]. USDA, ARS, National Genetic Resources Program, National Germplasm Resources Laboratory, Beltsville, Maryland, 2013.
49. Gerdes JT, Behr CF, Coors HG, Tracy WF, Avratovscukova N. Compilation of North American maize breeding germplasm. Madison: CSSA; 1993.
50. Zhao W, Canaran P, Jurkuta R, Fulton T, Glaubitz J, Buckler E, et al. Panzea: a database and resource for molecular and functional diversity in the maize genome. Nucleic Acids Research. 2006. January 1;34(suppl 1):D752–7. doi: 10.1093/nar/gkj011 [PMC free article] [PubMed]
51. Glaubitz JC, Casstevens TM, Lu F, Harriman J, Elshire RJ, Sun Q, et al. TASSEL-GBS: a high capacity genotyping by sequencing analysis pipeline. PLoS One. 2014. February 28;9(2):e90346 doi: 10.1371/journal.pone.0090346 [PMC free article] [PubMed]
52. Bradbury PJ, Zhang Z, Kroon DE, Casstevens TM, Ramdoss Y, Buckler ES. TASSEL: software for association mapping of complex traits in diverse samples. Bioinformatics. 2007. October 1;23(19):2633–5. doi: 10.1093/bioinformatics/btm308 [PubMed]
53. He S, Zhao Y, Mette MF, Bothe R, Ebmeyer E, Sharbel TF, et al. Prospects and limits of marker imputation in quantitative genetic studies in European elite wheat (Triticum aestivum L.). BMC Genomics. 2015. March 11;16(1):1 doi: 10.1186/s12864-015-1366-y [PMC free article] [PubMed]
54. Xavier A, Xu S, Muir WM, Rainey KM. NAM: association studies in multiple populations. Bioinformatics. 2015. December 1;31(23):3862–4. [PubMed]
55. Team RC. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria: 2015.
56. Herrmann E, Mächler M. lokern: Kernel Regression Smoothing with Local or Global Plug-in Bandwidth, 2013. URL R package version 2013:1-1.
57. Nei M. Genetic distance between populations. American Naturalist. 1972. May 1:283–92. doi: 10.1086/282771
58. Ward JH Jr. Hierarchical grouping to optimize an objective function. Journal of the American Statistical Association. 1963. March 1;58(301):236–44. doi: 10.1080/01621459.1963.10500845
59. Paradis E, Claude J, Strimmer K. APE: analyses of phylogenetics and evolution in R language. Bioinformatics. 2004. January 22;20(2):289–90. doi: 10.1093/bioinformatics/btg412 [PubMed]
60. Letunic I, Bork P. Interactive Tree Of Life v2: online annotation and display of phylogenetic trees made easy. Nucleic Acids Research. 2011. April 5:gkr201. doi: 10.1093/nar/gkr201 [PMC free article] [PubMed]
61. Weir BS, Cockerham CC. Estimating F-statistics for the analysis of population structure. Evolution. 1984. November 1:1358–70. doi: 10.2307/2408641 [PubMed]
62. Porto-Neto LR, Lee SH, Lee HK, Gondro C. Detection of signatures of selection using F ST. Genome-Wide Association Studies and Genomic Prediction. 2013:423–36. doi: 10.1007/978-1-62703-447-0_19
63. Ziegler GR, Hartsock RH, Baxter I. Zbrowse: an interactive GWAS results browser. PeerJ Computer Science. 2015. May 27;1:e3 doi: 10.7717/peerj-cs.3
64. Thorndike RL. Who belongs in the family? Psychometrika. 1953. December 27;18(4):267–76. doi: 10.1007/BF02289263
65. Kaufman L, Rousseeuw PJ. Finding groups in data: an introduction to cluster analysis. John Wiley & Sons; 2009. September 25.
66. Hastie T, Tibshirani R, Walther G. Estimating the number of data clusters via the Gap statistic. J Roy Stat Soc B. 2001. August;63:411–23.
67. Cross HZ. ND265: a new parental line of early corn. North Dakota Farm Research. 1989;47(3):19–21.
68. Tenaillon MI, Sawkins MC, Long AD, Gaut RL, Doebley JF, Gaut BS. Patterns of DNA sequence polymorphism along chromosome 1 of maize (Zea mays subsp. mays L.). Proceedings of the National Academy of Sciences. 2001. July 31;98(16):9161–6. doi: 10.1073/pnas.151244298 [PubMed]
69. Remington DL, Thornsberry JM, Matsuoka Y, Wilson LM, Whitt SR, Doebley J, et al. Structure of linkage disequilibrium and phenotypic associations in the maize genome. Proceedings of the National Academy of Sciences. 2001. September 25;98(20):11479–84. doi: 10.1073/pnas.201394398 [PubMed]
70. Ching AD, Caldwell KS, Jung M, Dolan M, Smith O, Tingey S, et al. SNP frequency, haplotype structure and linkage disequilibrium in elite maize inbred lines. BMC genetics. 2002. October 7;3(1):19 doi: 10.1186/1471-2156-3-19 [PMC free article] [PubMed]
71. Palaisa KA, Morgante M, Williams M, Rafalski A. Contrasting effects of selection on sequence diversity and linkage disequilibrium at two phytoene synthase loci. The Plant Cell. 2003. August 1;15(8):1795–806. doi: 10.1105/tpc.012526 [PubMed]
72. Jung M, Ching A, Bhattramakki D, Dolan M, Tingey S, Morgante M, et al. Linkage disequilibrium and sequence diversity in a 500-kbp region around the adh1 locus in elite maize germplasm. Theoretical and Applied Genetics. 2004. August 1;109(4):681–9. doi: 10.1007/s00122-004-1695-8 [PubMed]
73. Yan J, Shah T, Warburton ML, Buckler ES, McMullen MD, Crouch J. Genetic characterization and linkage disequilibrium estimation of a global maize collection using SNP markers. PloS one. 2009. December 24;4(12):e8451 doi: 10.1371/journal.pone.0008451 [PMC free article] [PubMed]
74. Truntzler M, Ranc N, Sawkins MC, Nicolas S, Manicacci D, Lespinasse D, et al. Diversity and linkage disequilibrium features in a composite public/private dent maize panel: consequences for association genetics as evaluated from a case study using flowering time. Theoretical and Applied Genetics. 2012. August 1;125(4):731–47. doi: 10.1007/s00122-012-1866-y [PubMed]
75. Lamkey CM, Lorenz AJ. Relative effect of drift and selection in diverging populations within a reciprocal recurrent selection program. Crop Science. 2014;54(2):576–85. doi: 10.2135/cropsci2013.07.0484
76. Beckett TJ. Analysis of Genetic Loci Associated with Agronomic Performance in Previously Plant-Variety-Protected Elite Commercial Maize Germplasm (Master’s thesis), PURDUE UNIVERSITY, 2016.

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