Amaranths (Amaranthus sp.) belongs to the family of Amaranthaceae, which is originated in Americas and Europe. Dated backed to Mayan civilization of South and Central America, amaranth has been cultivated for more than 8,000 years. An estimated 87 accessions belonged to the genus Amaranthus, 40 of which are considered to be native America species, including cultivated grains, vegetable crops, and wild species (Chan and Sun, 1997; Mujica and Jacobsen, 2003). As a major country, the United States possessed a huge area at American continent, and had a diverse set of amaranth, as one of the places where amaranths originated (Wetzel et al., 1999). It will be of great significance to analyze the amaranths genetic group structure of this region.

Analyses of genetic diversity and population structure are important, not just for amaranths, but for many crops, and such studies have direct benefits in research on evolution and plant breeding (Chung and Park, 2010). Many molecular markers have been used to analyze diversity, such as restriction fragment length polymorphisms (RFLPs), amplified fragment length polymorphisms (AFLPs), simple sequence repeats (SSRs), and single nucleotide polymorphisms (SNPs; Bao et al., 2006; Cheng et al., 2011; Feltus et al., 2004; Jin et al., 2010; Li et al., 2012; Liang et al., 1994; Nagaraju et al., 2002; Zhao et al., 2009). Different marker systems have been used to investigate genetic diversity (Tam et al., 2005), and random amplified polymorphic DNA (RAPD) markers and SSRs have been applied to study the genetic diversity and phylogenetic relationships among Amaranthus species (Khaing et al., 2013; Lee et al., 2008; Wassom and Tranel, 2005; Xu and Sun, 2001).

Amaranths have superior nutrition, drought tolerance, disease and pest resistance, and production yield, making these native Americian crops more attractive for cultivation in developing countries and increasing their rate of consumption in recent years (Ray and Roy, 2009). Varying amounts of outcrossing and frequent interspecific and intervarietal hybridization of amaranths have resulted in a large variety of amaranth genotypes (Ray and Roy, 2009). Due to their complex genetic background, amaranths show tremendous adaptability to different ecogeographic situations (Lee et al., 2008). and have evolved many characteristics adapted to different environments, such as cold, drought, and salinity resistance.

Understanding the genetic diversity and polymorphism of Amaranthus is important. In particular, a detailed SSR analysis of the genetic diversity and population structure of U.S. amaranth accessions would make a significant contribution, as the United States has played a major role in the development of amaranths (Ray and Roy, 2009). Therefore, we used a model-based structure analysis to elucidate the genetic diversity and structure of U.S. amaranth germplasm.

Eighty two accessions belonging to 29 species were genotyped using 14 SSRs (Table 1). All plant materials including 74 accessions from the U.S. and 8 accessions from Australia were obtained from the National Genebank of the Rural Development Administration, Republic of Korea (RDA-Genebank).

Total DNA was extracted from all accessions using a DNA extraction kit (Qiagen, Seoul, Republic of Korea). Fourteen polymorphic SSR markers developed by Lee et al. (2008) were used in this study. The M13-tail polymerase chain reaction (PCR) method (Schuelke, 2000) was used to measure the size of the PCR products, as described previously(Lee et al., 2008). Using GeneScan 3.7 (Applied Biosystems, Foster City, CA, USA ), the SSR alleles were resolved on an ABI Prism 3100 DNA sequencer (Applied Biosystems) and sized precisely using GeneScan 500 ROX (6-carbon-X-rhodamine) molecular size standards (35–500 bp; Applied Biosystems).

The data were analyzed statistically using the PowerMarker V3.23 genetic analysis package (Liu and Muse, 2005) to measure the diversity at each microsatellite locus, including the total number of alleles (NA), allele frequency, major allele (allele with the highest frequency), accession-specific alleles, and polymorphism information content (PIC). Genetic distances between each pair of accessions were determined by calculating the shared allele frequencies using PowerMarker V3.23. The unweighted pair group method with arithmetic mean (UPGMA) tree and neighbor joining method (NJ) were constructed from the shared allele frequencies using MEGA 4.0 embedded in PowerMarker.

Population structure and the identification of admixed individuals were determined using the Structure modelbased software program (Pritchard et al., 2000). In this model, a number of populations (K) are assumed to be present with each population characterized by a set of allele frequencies at each locus. Individuals in the sample are then assigned to populations (clusters), or jointly to more populations if their genotypes indicate that they are admixed.

All loci are assumed to be independent, and each K population is assumed to follow Hardy–Weinberg equilibrium. The posterior probabilities were estimated using the Markov chain Monte Carlo (MCMC) method. The MCMC chains were run with a 100,000-iteration burn-in period followed by 200,000 iterations using a model allowing for admixture and correlated allele frequencies. At least three runs of Structure were performed, setting K from 1 to 10, and an average likelihood value, L(K), across all runs was calculated for each K. The model choice criterion that detected the most probable value of K was ΔK, which is an ad hoc quantity related to the second-order change of the log probability of data with respect to the number of clusters inferred by Structure (Evanno et al., 2005). An individual with more than 80% of its genome fraction value was assigned to a group.

The value of F_ST was calculated using an analysis of molecular variance (AMOVA) approach in Arlequin 3.11 (Excoffier et al., 2005; Schneider and Excoffier, 1999).

In total, 122 alleles were observed among the 82 amaranth accessions at 14 SSR loci, ranging from 4 (78N) to 14 (104H and 99N) alleles per accession, with an average of eight alleles per locus. The database of allele frequencies showed that rare alleles (frequency < 0.05) comprised 51.6% of all detected alleles, whereas intermediate (frequency 0.05–0.50) and abundant (frequency > 0.50) alleles comprised 44.3% and 4.1%, respectively (Table 2, Fig. 1). The average major allele frequency was 0.44, ranging from 0.16 in 99N to 0.93 in 78N, and the expected heterozygosity was 0.69, ranging from 0.11 in 78N to 0.90 in 99N. The average PIC was 0.65, which indicated that the 14 SSR markers exhibit good polymorphism across the accessions (Table 2).

Previously, Pritchard et al. (2000) used a model-based method to analyze the population structure and identify admixed individuals. Unfortunately, the estimated likelihood values do not indicate the exact value of K using this model (Fig. 2). Therefore, an ad hoc quantity (ΔK) was used to overcome the difficulty interpreting real K values (Evanno et al., 2005). Using this approach, an identifiable peak indicated the true value of K based on ΔK. For the 82 accessions, the highest value of ΔK was K = 3 (Fig. 2); therefore, we used K = 3 for the final analysis. When alpha is near zero, most individuals are essentially from one population. Conversely, when alpha is greater than 1, most individuals are admixed (Evanno et al., 2005; Ostrowski et al., 2006). The relatively small value of alpha (α = 0.0345) indicated that most accessions originated from one primary ancestor (Ostrowski et al., 2006).

The genetic diversity analysis of the 82 amaranth accessions indicated an average of 8.64 alleles in accessions from the United States and 2.64 for Australia, with an overall average of 5.64. The major allele in the Australian accessions was more frequent than in U.S. accessions, while the opposite was true for the PIC.

Based on the structure results, most of the 82 accessions were clearly classified into three subpopulations. Clusters 1–3 included 20, 23, and 34 accessions, respectively. Only five accessions were admixtures: three from Australia and two from the United States. Of the three subpopulations, Cluster 3 has the highest allele numbers and PIC values, while Cluster 2 had the lowest. The F_ST was 0.4221, 0.2209, and 0.4274 between Clusters 1 and 2, Clusters 1 and 3, and Clusters 2 and 3, respectively (Table 4).

A genetic distance-based analysis was performed by calculating the shared allele frequencies among the 82 accessions. An unrooted phylogram was computed using MEGA 4 (Tamura et al., 2007) embedded in the PowerMarker program (Liu and Muse, 2005). The NJ tree clustered all accessions into three main groups with a few exceptions. As shown in Fig. 4, 82 amaranth accessions were distributed among the three groups which were consistent with the results of structure. Admixtures were marked with black color. Most of the accessions from the same species were clustered into the same group.

Generally, a narrow genetic base and low genetic diversity are detrimental to a breeding program (Wolfe, 1985). Although only 74 accessions from the United States were evaluated in this study, 122 alleles were detected and the PIC was high. Therefore, we concluded that the United States, which is near the center of origin of Amaranthus, exhibits rich genetic polymorphism and this finding will be used to design effective breeding programs involving different plant characteristics aimed to meet societal demands.