InDelGT: An integrated pipeline for extracting indel genotypes for genetic mapping in a hybrid population using next-generation sequencing data.

Premise: Although several software packages are available for genotyping insertion/deletion (indel) polymorphisms in genomes using next-generation sequencing data, simultaneously calling indel genotypes across many individuals for use in genetic mapping remains challenging. Methods and Results: We present an integrated pipeline, InDelGT, for the extraction of indel genotypes from a segregating population such as backcross or F2 lines, or from an F1 cross between outbred species. The InDelGT algorithm is implemented in three steps: generating an indel catalog, calling indel genotypes, and analyzing indel segregation. We demonstrated the use of the pipeline with an example data set from an F1 hybrid population of Populus and successfully constructed the two parental genetic linkage maps. Conclusions: InDelGT is a practical tool that can quickly genotype a large number of indel markers within a population following Mendelian segregation. The InDelGT pipeline is freely available on GitHub (https://github.com/tongchf/InDelGT).

A Novel Strategy for Constructing an Integrated Linkage Map in an F1 Hybrid Population of Populus deltoides and Populus simonii.

The genetic linkage maps of the traditional F2 population in inbred lines were estimated from the frequency of recombination events in both parents, providing full genetic information for genetic and genomic studies. However, in outbred forest trees, it is almost impossible to generate the F2 population because of their high heterozygosity and long generation times. We proposed a novel strategy to construct an integrated genetic linkage map that contained both parental recombination information, with restriction-site-associated DNA sequencing (RADSeq) data in an F1 hybrid population of Populus deltoides and Populus simonii. We selected a large number of specific RAD tags to construct the linkage map, each of which contained two SNPs, one heterozygous only in the female parent and the other heterozygous only in the male. Consequently, the integrated map contained a total of 1154 RAD tags and 19 linkage groups, with a total length of 5255.49 cM and an average genetic distance of 4.63 cM. Meanwhile, the two parent-specific linkage maps were also constructed with SNPs that were heterozygous in one parent and homozygous in the other. We found that the integrated linkage map was more consensus with the genomic sequences of P. simonii and P. deltoides. Additionally, the likelihood of the marker order in each linkage group of the integrated map was greater than that in both parental maps. The integrated linkage map was more accurate than the parent-specific linkage maps constructed in the same F1 hybrid population, providing a powerful genetic resource for identifying the quantitative trait loci (QTLs) with dominant effects, assembling genomic sequences, and performing comparative genomics in related Populus species. More importantly, this novel strategy can be used in other outbred species to build an integrated linkage map.

A Novel Strategy to Reveal the Landscape of Crossovers in an F1 Hybrid Population of Populus deltoides and Populus simonii.

Although the crossover (CO) patterns of different species have been extensively investigated, little is known about the landscape of CO patterns in Populus because of its high heterozygosity and long-time generation. A novel strategy was proposed to reveal the difference of CO rate and interference between Populus deltoides and Populus simonii using their F1 hybrid population. We chose restriction site-associated DNA (RAD) tags that contained two SNPs, one only receiving the CO information from the female P. deltoides and the other from the male P. simonii. These RAD tags allowed us to investigate the CO patterns between the two outbred species, instead of using the traditional backcross populations in inbred lines. We found that the CO rate in P. deltoides was generally greater than that in P. simonii, and that the CO interference was a common phenomenon across the two genomes. The COs landscape of the different Populus species facilitates not only to understand the evolutionary mechanism for adaptability but also to rebuild the statistical model for precisely constructing genetic linkage maps that are critical in genome assembly in Populus. Additionally, the novel strategy could be applied in other outbred species for investigating the CO patterns.

Multivariate genome-wide association study of leaf shape in a Populus deltoides and P. simonii F1 pedigree.

Leaf morphology exhibits tremendous diversity between and within species, and is likely related to adaptation to environmental factors. Most poplar species are of great economic and ecological values and their leaf morphology can be a good predictor for wood productivity and environment adaptation. It is important to understand the genetic mechanism behind variation in leaf shape. Although some initial efforts have been made to identify quantitative trait loci (QTLs) for poplar leaf traits, more effort needs to be expended to unravel the polygenic architecture of the complex traits of leaf shape. Here, we performed a genome-wide association analysis (GWAS) of poplar leaf shape traits in a randomized complete block design with clones from F1 hybrids of Populus deltoides and Populus simonii. A total of 35 SNPs were identified as significantly associated with the multiple traits of a moderate number of regular polar radii between the leaf centroid and its edge points, which could represent the leaf shape, based on a multivariate linear mixed model. In contrast, the univariate linear mixed model was applied as single leaf traits for GWAS, leading to genomic inflation; thus, no significant SNPs were detected for leaf length, measures of leaf width, leaf area, or the ratio of leaf length to leaf width under genomic control. Investigation of the candidate genes showed that most flanking regions of the significant leaf shape-associated SNPs harbored genes that were related to leaf growth and development and to the regulation of leaf morphology. The combined use of the traditional experimental design and the multivariate linear mixed model could greatly improve the power in GWAS because the multiple trait data from a large number of individuals with replicates of clones were incorporated into the statistical model. The results of this study will enhance the understanding of the genetic mechanism of leaf shape variation in Populus. In addition, a moderate number of regular leaf polar radii can largely represent the leaf shape and can be used for GWAS of such a complicated trait in Populus, instead of the higher-dimensional regular radius data that were previously considered to well represent leaf shape.

Genome Assembly of Salicaceae Populus deltoides (Eastern Cottonwood) I-69 Based on Nanopore Sequencing and Hi-C Technologies.

Populus deltoides has important ecological and economic values, widely used in poplar breeding programs due to its superior characteristics such as rapid growth and resistance to disease. Although the genome sequence of P. deltoides WV94 is available, the assembly is fragmented. Here, we reported an improved chromosome-level assembly of the P. deltoides cultivar I-69 by combining Nanopore sequencing and chromosome conformation capture (Hi-C) technologies. The assembly was 429.3 Mb in size and contained 657 contigs with a contig N50 length of 2.62 Mb. Hi-C scaffolding of the contigs generated 19 chromosome-level sequences, which covered 97.4% (418 Mb) of the total assembly size. Moreover, repetitive sequences annotation showed that 39.28% of the P. deltoides genome was composed of interspersed elements, including retroelements (23.66%), DNA transposons (6.83%), and unclassified elements (8.79%). We also identified a total of 44 362 protein-coding genes in the current P. deltoides assembly. Compared with the previous genome assembly of P. deltoides WV94, the current assembly had some significantly improved qualities: the contig N50 increased 3.5-fold and the proportion of gaps decreased from 3.2% to 0.08%. This high-quality, well-annotated genome assembly provides a reliable genomic resource for identifying genome variants among individuals, mining candidate genes that control growth and wood quality traits, and facilitating further application of genomics-assisted breeding in populations related to P. deltoides.

Multivariate linear mixed model enhanced the power of identifying genome-wide association to poplar tree heights in a randomized complete block design.

With the advances in high-throughput sequencing technologies, it is not difficult to extract tens of thousands of single-nucleotide polymorphisms (SNPs) across many individuals in a fast and cheap way, making it possible to perform genome-wide association studies (GWAS) of quantitative traits in outbred forest trees. It is very valuable to apply traditional breeding experiments in GWAS for identifying genome variants associated with ecologically and economically important traits in Populus. Here, we reported a GWAS of tree height measured at multiple time points from a randomized complete block design (RCBD), which was established with clones from an F1 hybrid population of Populus deltoides and Populus simonii. A total of 22,670 SNPs across 172 clones in the RCBD were obtained with restriction site-associated DNA sequencing (RADseq) technology. The multivariate mixed linear model was applied by incorporating the pedigree relationship matrix of individuals to test the association of each SNP to the tree heights over 8 time points. Consequently, 41 SNPs were identified significantly associated with the tree height under the P-value threshold determined by Bonferroni correction at the significant level of 0.01. These SNPs were distributed on all but two chromosomes (Chr02 and Chr18) and explained the phenotypic variance ranged from 0.26% to 2.64%, amounting to 63.68% in total. Comparison with previous mapping studies for poplar height as well as the candidate genes of these detected SNPs were also investigated. We therefore showed that the application of multivariate linear mixed model to the longitudinal phenotypic data from the traditional breeding experimental design facilitated to identify far more genome-wide variants for tree height in poplar. The significant SNPs identified in this study would enhance understanding of molecular mechanism for growth traits and would accelerate marker-assisted breeding programs in Populus.

High-Quality SNP Linkage Maps Improved QTL Mapping and Genome Assembly in Populus.

With the advances in high-throughput sequencing technologies and the development of new software for extracting single nucleotide polymorphisms (SNPs) across a mapping population, it is possible to construct high-quality genetic maps with thousands of SNPs in outbred forest trees. Two parent-specific linkage maps were constructed with restriction site-associated DNA sequencing data from an F1 hybrid population derived from Populus deltoides and Populus simonii, and applied in QTL mapping and genome assembly. The female P. deltoides map contained 4018 SNPs, which were divided into 19 linkage groups under a wide range of LOD thresholds from 7 to 55. The male P. simonii map showed similar characteristics, consisting of 2097 SNPs, which also belonged to 19 linkage groups under LOD thresholds of 7 to 29. The SNP order of each linkage group was optimal among different ordering results from several available software. Moreover, the linkage maps allowed the detection of 39 QTLs underlying tree height and 47 for diameter at breast height. In addition, the linkage maps improved the anchoring of 689 contigs of P. simonii to chromosomes. The 2 parental genetic maps of Populus are of high quality, especially in terms of SNP data quality, the SNP order within linkage groups, and the perfect match between the number of linkage groups and the karyotype of Populus, as well as the excellent performances in QTL mapping and genome assembly. Both approaches for extracting and ordering SNPs could be applied to other species for constructing high-quality genetic maps.

gmRAD: an integrated SNP calling pipeline for genetic mapping with RADseq across a hybrid population.

Restriction site-associated DNA sequencing (RADseq) is a powerful technology that has been extensively applied in population genetics, phylogenetics and genetic mapping. Although many software packages are available for ecological and evolutionary studies, a few effective tools are available for extracting genotype data with RADseq for genetic mapping, a prerequisite for quantitative trait locus mapping, comparative genomics and genome scaffold assembly. Here, we present an integrated pipeline called gmRAD for generating single nucleotide polymorphism (SNP) genotypes from RADseq data, de novo, across a genetic mapping population derived by crossing two parents. As an analytical strategy, the software takes five steps to implement the whole algorithms, including clustering the first (forward) reads of each parent, building two parental references, generating parental SNP catalogs, calling SNP genotypes across all individuals and filtering the genotype data for genetic linkage mapping. All the steps can be completed with a simple command line, but they can be also performed optionally if prerequisite files are available. To validate its application, we also performed a real data analysis with RADseq data from an F1 hybrid population derived by crossing Populus deltoides and Populus simonii. The software gmRAD is freely available at https://github.com/tongchf/gmRAD.

De Novo Genome Assembly of Populus simonii Further Supports That Populus simonii and Populus trichocarpa Belong to Different Sections.

Populus simonii is an important tree in the genus Populus, widely distributed in the Northern Hemisphere and having a long cultivation history. Although this species has ecologically and economically important values, its genome sequence is currently not available, hindering the development of new varieties with wider adaptive and commercial traits. Here, we report a chromosome-level genome assembly of P. simonii using PacBio long-read sequencing data aided by Illumina paired-end reads and related genetic linkage maps. The assembly is 441.38 Mb in length and contain 686 contigs with a contig N50 of 1.94 Mb. With the linkage maps, 336 contigs were successfully anchored into 19 pseudochromosomes, accounting for 90.2% of the assembled genome size. Genomic integrity assessment showed that 1,347 (97.9%) of the 1,375 genes conserved among all embryophytes can be found in the P. simonii assembly. Genomic repeat analysis revealed that 41.47% of the P. simonii genome is composed of repetitive elements, of which 40.17% contained interspersed repeats. A total of 45,459 genes were predicted from the P. simonii genome sequence and 39,833 (87.6%) of the genes were annotated with one or more related functions. Phylogenetic analysis indicated that P. simonii and Populus trichocarpa should be placed in different sections, contrary to the previous classification according to morphology. The genome assembly not only provides an important genetic resource for the comparative and functional genomics of different Populus species, but also furnishes one of the closest reference sequences for identifying genomic variants in an F1 hybrid population derived by crossing P. simonii with other Populus species.

Identification of recombination events in outbred species with next-generation sequencing data.

BACKGROUND: Meiotic recombination events include crossovers and non-crossovers or gene conversions. Although the rate of crossovers is often used for genetic mapping, the gene conversion events are not well studied especially in outbred species, which could produce distorted markers and thus affect the precision of genetic maps. RESULTS: We proposed a strategy for identifying gene conversion events in Populus with the next-generation sequencing (NGS) data from the two parents and their progeny in an F1 hybrid population. The strategy first involved phasing the heterozygous SNPs of the parents to obtain the parental haplotype blocks by NGS analytical tools, permitting to identify the parental gene conversion events with progeny genotypes. By incorporating available genetic linkage maps, longer haplotype blocks each corresponding to a chromosome can be created, not only allowing to detect crossover events but also possibly to locate a crossover in a small region. Our analysis revealed that gene conversions are more abundant than crossovers in Populus, with a higher probability to generate distorted markers in the regions involved than in the other regions on genome. The analytical procedures were implemented with Perl scripts as a freely available package, findGCO at https://github.com/tongchf/findGCO . CONCLUSIONS: The novel strategy and the new developed Perl package permit to identify gene conversion events with the next-generation sequencing technology in a hybrid population of outbred species. The new method revealed that in a genetic mapping population some distorted genetic markers are possibly due to the gene conversion events.

MVQTLCIM: composite interval mapping of multivariate traits in a hybrid F1 population of outbred species.

BACKGROUND: With the plummeting cost of the next-generation sequencing technologies, high-density genetic linkage maps could be constructed in a forest hybrid F1 population. However, based on such genetic maps, quantitative trait loci (QTL) mapping cannot be directly conducted with traditional statistical methods or tools because the linkage phase and segregation pattern of molecular markers are not always fixed as in inbred lines. RESULTS: We implemented the traditional composite interval mapping (CIM) method to multivariate trait data in forest trees and developed the corresponding software, mvqtlcim. Our method not only incorporated the various segregations and linkage phases of molecular markers, but also applied Takeuchi's information criterion (TIC) to discriminate the QTL segregation type among several possible alternatives. QTL mapping was performed in a hybrid F1 population of Populus deltoides and P. simonii, and 12 QTLs were detected for tree height over 6 time points. The software package allowed many options for parameters as well as parallel computing for permutation tests. The features of the software were demonstrated with the real data analysis and a large number of Monte Carlo simulations. CONCLUSIONS: We provided a powerful tool for QTL mapping of multiple or longitudinal traits in an outbred F1 population, in which the traditional software for QTL mapping cannot be used. This tool will facilitate studying of QTL mapping and thus will accelerate molecular breeding programs especially in forest trees. The tool package is freely available from https://github.com/tongchf /mvqtlcim.

De novo SNP discovery and genetic linkage mapping in poplar using restriction site associated DNA and whole-genome sequencing technologies.

BACKGROUND: Restriction site associated DNA sequencing (RAD-seq), a next-generation sequencing technology, has greatly facilitated genetic linkage mapping studies in outbred species. RAD-seq is capable of discovering thousands of genetic markers for linkage mapping across many individuals, and can be applied in species with or without a reference genome. Although several analytical tools are available for RAD-seq data, alternative strategies are necessary for improving the marker quality and hence the genetic mapping accuracy. RESULTS: We demonstrate a strategy for constructing dense genetic linkage maps in hybrid forest trees by combining RAD-seq and whole-genome sequencing technologies. We performed RAD-seq of 150 progeny and whole-genome sequencing of the two parents in an F1 hybrid population of Populus deltoides × P. simonii. Two rough references were assembled from the whole-genome sequencing reads of the two parents separately. Based on the parental reference sequences, 3442 high-quality single nucleotide polymorphisms (SNPs) were identified that segregate in the ratio of 1:1. The maternal linkage map of P. deltoides was constructed with 2012 SNPs, containing 19 linkage groups and spanning 4067.16 cM of the genome with an average distance of 2.04 cM between adjacent markers, while the male map of P. simonii consisted of 1430 SNPs and the same number of linkage groups with a total length of 4356.04 cM and an average interval distance of 3.09 cM. Collinearity between the parental linkage maps and the reference genome of P. trichocarpa was also investigated. Compared with the result on the basis of the existing reference genome, our strategy identified more high-quality SNPs and generated parental linkage groups that nicely match the karyotype of Populus. CONCLUSIONS: The strategy of simultaneously using RAD and whole-genome sequencing technologies can be applied to constructing high-density genetic maps in forest trees regardless of whether a reference genome exists. The two parental linkage maps constructed here provide more accurate genetic resources for unraveling quantitative trait loci and accelerating molecular breeding programs, as well as for comparative genomics in Populus.

Construction of High-Density Linkage Maps of Populus deltoides × P. simonii Using Restriction-Site Associated DNA Sequencing.

Although numerous linkage maps have been constructed in the genus Populus, they are typically sparse and thus have limited applications due to low throughput of traditional molecular markers. Restriction-site associated DNA sequencing (RADSeq) technology allows us to identify a large number of single nucleotide polymorphisms (SNP) across genomes of many individuals in a fast and cost-effective way, and makes it possible to construct high-density genetic linkage maps. We performed RADSeq for 299 progeny and their two parents in an F1 hybrid population generated by crossing the female Populus deltoides 'I-69' and male Populus simonii 'L3'. A total of 2,545 high quality SNP markers were obtained and two parent-specific linkage maps were constructed. The female genetic map contained 1601 SNPs and 20 linkage groups, spanning 4,249.12 cM of the genome with an average distance of 2.69 cM between adjacent markers, while the male map consisted of 940 SNPs and also 20 linkage groups with a total length of 3,816.24 cM and an average marker interval distance of 4.15 cM. Finally, our analysis revealed that synteny and collinearity are highly conserved between the parental linkage maps and the reference genome of P. trichocarpa. We demonstrated that RAD sequencing is a powerful technique capable of rapidly generating a large number of SNPs for constructing genetic maps in outbred forest trees. The high-quality linkage maps constructed here provided reliable genetic resources to facilitate locating quantitative trait loci (QTLs) that control growth and wood quality traits in the hybrid population.

Allotetraploid and autotetraploid models of linkage analysis.

As a group of important plant species in agriculture and biology, polyploids have been increasingly studied in terms of their genome structure and organization. There are two types of polyploids, allopolyploids and autopolyploids, each resulting from a different genetic origin, which undergo meiotic divisions of a distinct complexity. A set of statistical models has been developed for linkage analysis, respectively for each type, by taking into account their unique meiotic behavior, i.e. preferential pairing for allopolyploids and double reduction for autopolyploids. We synthesized these models and modified them to accommodate the linkage analysis of less informative dominant markers. By reanalysing a published data set of varying ploidy in Arabidopsis, we corrected the estimates of the meiotic recombination frequency aimed to study the significance of polyploidization.

An allometric model for mapping seed development in plants.

Despite a tremendous effort to map quantitative trait loci (QTLs) responsible for agriculturally and biologically important traits in plants, our understanding of how a QTL governs the developmental process of plant seeds remains elusive. In this article, we address this issue by describing a model for functional mapping of seed development through the incorporation of the relationship between vegetative and reproductive growth. The time difference of reproductive from vegetative growth is described by Reeve and Huxley's allometric equation. Thus, the implementation of this equation into the framework of functional mapping allows dynamic QTLs for seed development to be identified more precisely. By estimating and testing mathematical parameters that define Reeve and Huxley's allometric equations of seed growth, the dynamic pattern of the genetic effects of the QTLs identified can be analyzed. We used the model to analyze a soybean data, leading to the detection of QTLs that control the growth of seed dry weight. Three dynamic QTLs, located in two different linkage groups, were detected to affect growth curves of seed dry weight. The QTLs detected may be used to improve seed yield with marker-assisted selection by altering the pattern of seed development in a hope to achieve a maximum size of seeds at a harvest time.

Structural mapping: how to study the genetic architecture of a phenotypic trait through its formation mechanism.

Traditional approaches for genetic mapping are to simply associate the genotypes of a quantitative trait locus (QTL) with the phenotypic variation of a complex trait. A more mechanistic strategy has emerged to dissect the trait phenotype into its structural components and map specific QTLs that control the mechanistic and structural formation of a complex trait. We describe and assess such a strategy, called structural mapping, by integrating the internal structural basis of trait formation into a QTL mapping framework. Electrical impedance spectroscopy (EIS) has been instrumental for describing the structural components of a phenotypic trait and their interactions. By building robust mathematical models on circuit EIS data and embedding these models within a mixture model-based likelihood for QTL mapping, structural mapping implements the EM algorithm to obtain maximum likelihood estimates of QTL genotype-specific EIS parameters. The uniqueness of structural mapping is to make it possible to test a number of hypotheses about the pattern of the genetic control of structural components. We validated structural mapping by analyzing an EIS data collected for QTL mapping of frost hardiness in a controlled cross of jujube trees. The statistical properties of parameter estimates were examined by simulation studies. Structural mapping can be a powerful alternative for genetic mapping of complex traits by taking account into the biological and physical mechanisms underlying their formation.

A statistical model for QTL mapping in polysomic autotetraploids underlying double reduction.

As a group of economically important species, linkage mapping of polysomic autotetraploids, including potato, sugarcane and rose, is difficult to conduct due to their unique meiotic property of double reduction that allows sister chromatids to enter into the same gamete. We describe and assess a statistical model for mapping quantitative trait loci (QTLs) in polysomic autotetraploids. The model incorporates double reduction, built in the mixture model-based framework and implemented with the expectation-maximization algorithm. It allows the simultaneous estimation of QTL positions, QTL effects and the degree of double reduction as well as the assessment of the estimation precision of these parameters. We performed computer simulation to examine the statistical properties of the method and validate its use through analyzing real data in tetraploid switchgrass.

Analysis of synonymous codon usage patterns in seven different citrus species.

We used large samples of expressed sequence tags to characterize the patterns of codon usage bias (CUB) in seven different Citrus species and to analyze their evolutionary effect on selection and base composition. We found that A- and T-ending codons are predominant in Citrus species. Next, we identified 21 codons for 18 different amino acids that were considered preferred codons in all seven species. We then performed correspondence analysis and constructed plots for the effective number of codons (ENCs) to analyze synonymous codon usage. Multiple regression analysis showed that gene expression in each species had a constant influence on the frequency of optional codons (FOP). Base composition differences between the proportions were large. Finally, positive selection was detected during the evolutionary process of the different Citrus species. Overall, our results suggest that codon usages were the result of positive selection. Codon usage variation among Citrus genes is influenced by translational selection, mutational bias, and gene length. CUB is strongly affected by selection pressure at the translational level, and gene length plays only a minor role. One possible explanation for this is that the selection-mediated codon bias is consistently strong in Citrus, which is one of the most widely cultivated fruit trees.

A unifying framework for bivalent multilocus linkage analysis of allotetraploids.

An allotetraploid has four paired sets of chromosomes derived from different diploid species, whose meiotic behavior is qualitatively different from the underlying diploids. According to a traditional view, meiotic pairing occurs only between homologous chromosomes, but new evidence indicates that homoeologous chromosomes may also pair to a lesser extent compared with homolog pairing. Here, we describe and assess a unifying analytical framework that incorporates differential chromosomal pairing into a multilocus linkage model. The preferential pairing factor is used to quantify the probability difference of pairing occurring between homologous chromosomes and homoeologous chromosomes. The unifying framework allows simultaneous estimation of the linkage, genetic interference and preferential pairing factor using commonly existing multiplex markers. We compared the unifying approach and traditional approaches assuming random chromosomal pairing by analyzing marker data collected in a full-sib family of tetraploid switchgrass, a bioenergy species whose diploid origins are undefined, but with subgenomes that are genetically well differentiated. The unifying framework provides a better tool for estimating the meiotic linkage and constructing a genetic map for allotetraploids.

A multivalent three-point linkage analysis model of autotetraploids.

Because of its widespread occurrence and role in shaping evolutionary processes in the biological kingdom, especially in plants, polyploidy has been increasingly studied from cytological to molecular levels. By inferring gene order, gene distances and gene homology, linkage mapping with molecular markers has proven powerful for investigating genome structure and organization. Here we review and assess a general statistical model for three-point linkage analysis in autotetraploids by integrating double reduction, a phenomenon that commonly occurs in autopolyploids whose chromosomes are derived from a single ancestral species. This model does not require any assumption on the distribution of the occurrence of double reduction and can handle the complexity of multilocus linkage in terms of crossover interference. Implemented with the expectation-maximization (EM) algorithms, the model can estimate and test the recombination fractions between less informative dominant markers, thus facilitating its practical implications for any autopolyploids in most of which inexpensive dominant markers are still used for their genetic and evolutionary studies. The model was applied to reanalyze a published data in tetraploid switchgrass, validating its practical usefulness and utilization.