Background

Elephant grass [Pennisetum purpureum Schumach. syn. Cenchrus purpureus (Schumach.) Morrone] is a perennial tropical grass with high photosynthetic efficiency (C4 photosynthetic pathway) that is naturally found in several African countries [1]. It has a range of adaptation to different levels of altitude, precipitation, and soils, and has important agronomic traits [2], particularly its high biomass production. Depending on the environment and cultivar characteristics, green biomass can reach 300 Mg ha− 1 year− 1 [3]; consequently, elephant grass is used for multiple purposes, including the production of bio-based compounds [4] and molecules with pharmaceutical and industrial applications [5,6,7]. It has been targeted by bioenergy programs, because its annual dry matter production is greater than that of sugarcane or eucalyptus, which are the most-used biomass energy sources in Brazil [2, 8]. However, the most common use for elephant grass in Brazil is in animal feed, particularly for dairy cattle.

Elephant grass is a tetraploid species (2n = 4x = 28) with two genomes (A′A′BB) [9]. Its genome is homologous to that of pearl millet [Pennisetum glaucum (L.) R. Br. syn. Cenchrus americanus (L.) Morrone], and cytogenetic studies have been conducted on these species in order to identify hybrids [9, 10]. Elephant grass has not been significantly studied, so its genomic information is little-known compared to that of more economically important crops. An RNAseq study [11], two studies on genome sequencing [12, 13], and one transcriptomic and metabolomic study [7] have been published for elephant grass. However, much is still needed to be elucidated for the next-generation breeding of elephant grass [14]. For example, few trait-marker association studies have been conducted because of the low availability of molecular markers, but simple sequence repeat (SSR) markers have been transferred from pearl millet to elephant grass [15] and used in genetic diversity studies to increase gene bank diversity [16]. Although SSR markers appear in the genome at a lower frequency than single nucleotide polymorphisms (SNPs), they can be used in genomic association studies. For example, SSR markers have been used to identify loci associated with yield components and fiber quality in cotton [17], resistance to Sclerotinia sclerotiorum in Brassica napus [18], and quantitative traits contributing to yield in sugarcane [19]. In general, many SSR markers are used in trait-marker association studies, but few may provide satisfactory results in species with limited sequence information, such as creeping bentgrass (Agrostis stolonifera L.) [20].

Genomic association studies identify candidate genes and markers linked to important traits. When considering multipurpose traits (i.e., traits with different purposes, such as animal feeding and bioenergy), the development of selection procedures based on molecular markers can radically streamline and accelerate elephant grass improvement [21]. Appropriate targets for breeding elephantgrass for forage and bioenergy use are agronomic traits (height, green biomass, and dry biomass) and quality traits (acid and neutral detergent fiber, lignin content, biomass digestibility, and dry matter concentration). Because elephant grass is vegetatively propagated and crosses are not widely used, the use of germplasm collections for association mapping is based on historical and naturally occurring recombination events.

In this context, the goals of this study were to (i) investigate changes in predictive accuracy using genomic relationship information in statistical models, (ii) investigate significant associations between SSR markers and eight traits, evaluated in different cuttings, in a germplasm collection of elephant grass genotypes, and (iii) identify candidate genes linked to these traits with their respective gene annotations. By achieving these goals, we aimed to increase the speed and accuracy of breeding elephant grass for different purposes.

Results

Genetic variation, genotype by cutting interaction, and predictive accuracy using a single-step, genome-based best linear unbiased prediction (ssGBLUP) model

Initially, a ssGBLUP model was used to fit the full dataset in order to investigate genetic variability and the genotype by cutting interaction and residual genetic variability and the genotype by cutting interaction. Genetic variability (p < 0.05) was detected for seven traits (height, green biomass, dry biomass, dry matter concentration, acid detergent fiber, neutral detergent fiber, and lignin content) but not biomass digestibility (Fig. 1). Regarding the genotype by cutting interaction, a significant effect (p < 0.05) for all traits was observed (Fig. 1). It is noteworthy that, in the individual analysis of each cutting, significant genetic variability was detected for all traits.

Fig. 1
figure 1

Likelihood ratio tests for genetic effects (Genetic), genotype by cutting effects (G × C), residual genetic effects (Res G), residual genotype by cutting interaction effects (Res G × C), block effects (Block) and permanent environment effects (PE) considering ssGBLUP model. All bars above the dashed red line are significant by chi-square test at 5% probability \( \left({X}_{5\%}^2=3.84\right) \)

Full size image

Log-likelihood ratio tests revealed that residual genetic effects were significant (p < 0.05) for height, green biomass, and dry biomass but not for biomass quality traits (i.e., dry matter concentration, acid detergent fiber, neutral detergent fiber, biomass digestibility, and lignin content) (p > 0.05) (Fig. 1). There was a significant residual genotype by cutting interaction (p < 0.05) for green biomass, dry biomass, dry matter concentration, and lignin (Fig. 1).

The predictive accuracy of the ssGBLUP model (considering the H− 1 matrix) ranged from 0.58 (biomass digestibility) to 0.84 (acid detergent fiber, dry matter concentration, and lignin). When the model did not include the relationship between the genotypes (simple repeatability plus the genotype by cutting interaction model), the accuracy ranged from 0.59 (biomass digestibility) to 0.89 (dry biomass). Inclusion of the relationship matrix in the ssGBLUP model increased the accuracy of the biomass quality traits (Fig. 2), except for biomass digestibility.

Fig. 2
figure 2

Accuracy of breeding value for the simple repeatability plus genotype by cutting interaction model and ssGBLUP model

Full size image

Overall means and accuracies for each cutting

Because a significant effect of the genotype by cutting interaction was observed for all traits (ssGBLUP model, Fig. 1), trait-marker associations were investigated for each cutting. The overall means and accuracies of each cutting are presented in Fig. 3. The accuracy values ranged from 0.47 (acid detergent fiber and biomass digestibility for the fifth cutting and biomass digestibility for the first cutting) to 0.88 (dry matter concentration for the second cutting). In general, the overall means for all traits varied widely among the cuttings, corroborating the significant genotype by cutting interaction. For example, the second cutting had the highest values for height, green biomass, dry biomass, acid detergent fiber, neutral detergent fiber, and lignin, but had the lowest values for biomass digestibility.

Fig. 3
figure 3

Overall means (bars plot) with the standard errors and accuracy of breeding values (radar plot) for five cuttings recorded in 90 genotypes of elephant grass

Full size image

Genome association study

We analyzed 90 elephant grass genotypes that had phenotypic data and SSR alleles available, and identified one allele of the M28 marker (M28_161) that was significantly associated with biomass digestibility. This association was detected only for the first cutting. A Manhattan plot (Fig. 4, right) shows the − log(P − value) for all SSRs that affected biomass digestibility, while the quantile-quantile (QQ) plot (Fig. 4, left) displays significant deviations of the observed − log(P − value) from those expected.

Fig. 4
figure 4

QQ-plot (on the left) and Manhattan plot (on the right) for genome association of biomass digestibility phenotype with SSR markers on the first cut of elephant grass. Dashed red lines on Manhattan plot (false discovery rate) indicate the minimum threshold to select significant markers. The arrow highlights a major trait-marker association

Full size image

To identify the linkage of all markers, we performed linkage disequilibrium analysis (Fig. 5). In this analysis, we were interested in identifying markers that may have been linked to M28_161, which was significantly linked to high values of biomass digestibility. One allele of the SSR marker M35 (M35_202) showed moderate linkage disequilibrium (r2 = 0.20) to M28_161, and, in general, its presence was detected in elephant grass genotypes with low values of biomass digestibility. All other r2-values were lower than 0.11, and varied from 0.00 to 0.11.

Fig. 5
figure 5

Linkage disequilibrium (r2-values) between all markers used in this study with the marker M28_161, which was found as significantly associated with biomass digestibility in elephant grass

Full size image

Annotation of M28_161 and M35_202 markers, in silico pathway analysis, and allelic contribution

A BLAST search revealed that the two SSR markers (M28_161 and M35_202) are close to candidate genes that have annotated functions in other grasses (Table 1). In some cases (i.e., Setaria viridis chromosome 3 and Panicum halli chromosomes 5 and 7), M28_161 is close to candidate genes linked to pathways influenced by plant hormones (salicylic acid or abscisic acid). However, in most cases, M28_161 and M35_202 are associated with candidate genes involved in the synthesis of cell wall components. In P. halli, M28_161 is close to candidate genes involved in lignin biosynthetic processes and cell wall organization (chromosome 7), and in Panicum virgatum, it is close to a candidate gene involved in lignin catabolic processes and oxidation-reduction processes (located on chromosome 8). In S. viridis, both M28_161 and M35_202 were found to have orthologous regions. M28_161 is close to a candidate gene on chromosome 3 that plays a role in xyloglucan biosynthesis, while M35_202 is close to a candidate gene on chromosome 7 that functions in lignin biosynthesis. For Setaria italica, a successful BLAST search was conducted for the M28_161 sequence, but no candidate genes related to digestibility were found. However, for C. americanus, no BLAST results were obtained when using the M28 and M35 sequences.

Table 1 Candidate genes, in the genome of other C4 species, that are near to homologous sequences to the SSR markers M28_161 and M35_202
Full size table

Discussion

Genetic variation and genotype by cutting interaction

We observed a significant effect of the genotype by cutting interaction for all eight traits analyzed, so the genomic association study was conducted by considering a single cutting at a time. The lack of genetic variability (i.e., for biomass digestibility) revealed by the ssGBLUP analysis does not mean that there was no genetic variability, because the interaction effect may have reduced it. Residual terms were added to the ssGBLUP model to capture nonadditive effects. For crops that exhibit clonal propagation and are not lines (such as elephant grass), nonadditive effects represent epistatic and dominance effects [22], and additive effects were not explained by the genomic relationship matrix, so these effects would not have inflated the residual estimates or overlaid the other effects. The nonsignificant residual genetic effect for the biomass quality traits indicates that part of the additive fraction that plays a role in the genetic architecture of these traits could be explained by only a few markers (87 alleles). For the morpho-agronomic traits the residual genetic effect was significant, so the genomic relationship matrix constructed from 87 markers did not explain the additive genetic fraction for height, green biomass, and dry biomass.

Predictive accuracy

Cell component fractions that could affect forage digestibility include cellulose, lignin, hemicellulose, and cell wall proteins [23]. Therefore, biomass digestibility is dependent upon several components which makes it a complex trait that may be explained by the fact of the accuracy has been moderate magnitude considering the genomic information. Recent transcriptomic and genomic studies [7, 11,12,13] and the development of SNPs for elephant grass [12] have increased accuracy, and studies using molecular markers have been important for the development of SNP markers. New genotyping, sequencing, and bioinformatics tools have increased accuracy and decreased the price per sequenced base or molecular genotype [14], and selection time [24].

Trait-marker association analysis

None of the agronomic traits (height, green biomass, and dry biomass) and four of the quality traits (acid and neutral detergent fiber, dry matter concentration, and lignin content) were associated with SSR markers. This was probably related to the low number of SSR markers used (18 SSR markers that originated in 87 alleles) when compared to the genome size of elephant grass, which has recently been estimated as 2.1 Gb [13]. However, one quality trait (biomass digestibility) was associated with the SSR marker M28_161 when the dataset from the first cutting was analyzed. This marker was in linkage disequilibrium with M35_202, so is associated with biomass digestibility. However, these markers are linked to different values of biomass digestibility, because M28_161 was significantly associated with high values of biomass digestibility while M35_202 was more frequently detected in genotypes with low values of biomass digestibility. This is an interesting result considering that digestibility is an important trait for many plant species, and understanding its impact on plant quality and the genomic regions associated with it has been the focus of many research groups [25,26,27].

The SSR markers used here were previously developed for pearl millet [28, 29], and were identified by our group to cross-amplify the elephant grass genome [15]. It is unknown to what extent these markers are distributed in the elephant grass genome, but our analysis shows that some markers have moderate linkage disequilibrium. The average similarity coefficient among 107 accessions of the Active Elephant Grass Germplasm Bank maintained by Embrapa Gado de Leite (where the genotypes were obtained) was 0.651, which indicates genetic variability [15]. In addition, Azevedo et al. [15] detected only one group of similarity for the genotypes used in the present study. In this context, neither the small number of markers used here nor the absence of population structure correction were obstacles to detect marker M28_161 as being significantly associated with biomass digestibility. Although trait-marker association analysis can be performed using non-specific markers (such as diversity arrays technology) or by SNP genotyping, SSR markers are important when genome sequencing and bioinformatics are not trivial tasks.

Marker annotation and in silico pathway

We ran BLAST searches using sequences of the markers M28_161 and M35_202, and the genome of the related C4 grasses S. italica, S. viridis, P. virgatum, P. halli, and C. americanus. These species are closely related to elephant grass [30, 31]. No results were found for the C. americanus genome sequence, which was unexpected because the SSR markers used here were developed from pearl millet [15] and the A′A′ genome of elephant grass is homologous to the A genome of pearl millet [9, 10]. For the other species, six candidate genes that are associated with the biosynthesis of cell wall molecules were identified.

One candidate gene annotated on chromosome 3 of S. viridis (Sevir. 3G340800) is orthologous to locus AT2G20370 of Arabidopsis thaliana, and codes for a xyloglucan galactosyltransferase responsible for different functions, including the synthesis of cell wall materials. Xyloglucan, which is a component of the plant cell wall, is a type of hemicellulose that has the ability to bind to cellulose to form a cellulose-xyloglucan network linked through hydrogen bonds (see review by Pauly and Keegstra [23]). It is unclear whether xyloglucan decreases biomass digestibility, but it is associated with lignin, which is a cell wall component that commonly negatively affects digestibility. Xyloglucan binds to cellulose to form an aggregate that, in some types of cell, can be embedded in a matrix that contains lignin [23]. However, it is important to note that although xyloglucan is the most abundant hemicellulose in the primary cell walls of dicotyledons, in grasses such as elephant grass, its abundance is lower [23]. The effects of xyloglucan galactosyltransferase on biomass digestibility in elephant grass should be carefully evaluated.

No markers were associated with lignin content. Lignin is the second-most abundant biopolymer on Earth [32], and is a highly condensed phenylpropanoid matrix that is relatively difficult to digest by ruminal microorganisms and intestinal enzymes [33]. In many plant species, there is a negative correlation between lignin content and digestibility [34, 35] that can affect animal performance, because a small increase in dry matter digestibility (1%) can increase beef cattle daily weight gains by 3.2% [36]. In general, the quality of forage grasses decreases as they mature as a consequence of secondary cell wall deposition and the lignification of sclerenchyma cells. This does not mean that decreasing the lignin content is the only way to improve plant digestibility, but it is commonly accepted that lignin is a potential target for that purpose. In this context, the candidate genes Pahal. G00901, Pavir. 8KG357500, and Sevir. 7G164200, annotated in the P. halli, P. virgatum, and S. viridis genomes, respectively, are useful assets. These candidate genes are orthologous to the loci AT5G48930, AT3G09220, and AT5G48930 in Arabidopsis. AT5G48930 is a hydroxycinnamoyl-Coenzyme A shikimate/quinate hydroxycinnamoyltransferase that is involved in the phenylpropanoid pathway, and plays a role in the production of hydroxycinnamyl alcohols (or monolignols) that serve as the building blocks of lignin [37]. The lignin content can also affect bioenergy production [38], and can be decreased or increased depending on how the biomass is treated for energy generation. For example, for the conversion of lignocellulosic biomass to ethanol, polysaccharides from the cell wall need to be hydrolyzed to simple sugars and then fermented to ethanol [39]. In this case, reducing the lignin content can increase ethanol production through conventional biomass fermentation [38]. However, when considering biomass combustion, more lignin is needed for high energy conversion [40]. The molecular basis of lignin content in elephant grass is unknown, but the candidate genes identified here can be used as targets for gene manipulation. Either by transgenesis or gene editing, the manipulation of genes associated with lignin production can result in germplasm that is ideal for animal feeding or bioenergy [35, 38, 41, 42].

Some candidate genes are associated with plant hormones (salicylic acid or abscisic acid), the cross-talk of which plays an important role in the molecular responses of plants to stress [43], and two of them are involved in responses to biotic and abiotic stressors. The candidate gene Pahal. G00889 (annotated on chromosome 7 of P. halli) is orthologous to locus AT5G05190 in Arabidopsis, in which a hypothetical protein is involved in different functions, including responses to fungi [44]. The candidate gene Pahal. E03247 (also from P. halli) has an orthologous locus in Arabidopsis (AT3G05880) that codes for a small and highly hydrophobic protein that is involved in the hyperosmotic salinity response and response to cold. Validating these candidate genes in elephant grass would increase our knowledge of how this species responds to stressors such as spittlebug (Cercopidae) attack and drought or flooding, which are important factors for breeding programs in Brazil [14].

Conclusions

This study showed that, even by using a few SSR markers, it is possible to identify candidate genes associated with biomass digestibility. It also showed that it was possible to increase predictive accuracy in elephant grass by incorporating genomic relationship information. Because there is little genomic information for elephant grass available, our findings may improve elephant grass breeding. For example, marker-assisted selection can be applied, and markers associated with biomass digestibility have the potential to drive elephant grass selection for different uses (e.g., bioenergy production and animal feed). Further validation of the candidate genes revealed here may lead to a better understanding of biomass digestibility variation and its genomic basis.

Methods

Plant materials and experimental information

One hundred elephant grass genotypes (Additional file 1: Table S1) from the Active Elephant Grass Germplasm Bank (Embrapa Gado de Leite, Brazil) were planted in 0.20-m-deep furrows with 80 kg ha− 1 P2O5 fertilizer applied at planting on December 23rd, 2011. The red-yellow latosol soil at the Embrapa Gado de Leite experimental station in Coronel Pacheco, MG, Brazil (latitude 21°33′18′′ S, longitude 43°15′51′′ W, 417 m.a.s.l.) had the following chemical properties: pH (5.4), H + Al (2.31 cmolc dm− 3), P (1.1 cmolc dm− 3), K (23 mg dm− 3), and exchangeable cations Al3+ (0.2 cmolc dm− 3), Ca2+ (1.4 cmolc dm− 3), and Mg2+ (0.7 cmolc dm− 3). The plots consisted of 4-m rows that were planted side by side, 1.5 m apart. Plots were allocated in a 10 × 10 simple lattice design, with two replications. At 30 days after planting, the plots were cut to 0.30-m stubble height (uniformly cut). The number of days to reach each of the six growing seasons (cuttings) started at this time. Maintenance fertilization was made with 300 kg ha− 1 of a N-P2O5-K2O formulation (20:05:20 blended granular fertilizer) after all cuttings. Fertilization was conducted according to the results of a soil analysis.

Six cuttings were conducted: the first cutting (September 28th, 2012) was performed at 250 regrowth days, the second (June 5th, 2013) at 250 regrowth days, the third (April 16th, 2014) at 315 regrowth days, the fourth (January 16th, 2015) at 275 regrowth days, the fifth (November 27th, 2015) at 315 regrowth days, and the sixth (June 24th, 2016) at 210 regrowth days. The fourth cutting collected propagation material, i.e., no phenotypic data were obtained at this cutting. We declare that all plant materials in this study represent voucher specimens that have been deposited in a publicly available herbarium (Active Elephant Grass Germplasm Bank) and that comply with institutional, national, and international guidelines for the collection and cultivation of any plant materials.

Phenotypic traits

The plants were phenotyped at first, second, third, fifth, and sixth cuttings for each of the following traits: (i) height (m) was obtained from the arithmetic mean of the height of three randomly selected plants in each plot, measured from ground level to the curve of the last completely expanded leaf; (ii) green biomass (Mg ha− 1) was obtained from a cutting taken at 7.5 cm stubble height in a 3-m section in the middle of the rows using a gasoline-powered strimmer and that was collected by hand. The 3-m section was immediately weighed in the field to provide estimates of green biomass; (iii) dry biomass (Mg ha− 1) was quantified by multiplying the green biomass by the dry matter concentration (%); (iv) acid detergent fiber (g Kg− 1), (v) neutral detergent fiber (g Kg− 1), and (vi) lignin content (g Kg− 1) were determined following the methodology proposed by Goering [45]; (vii) biomass digestibility (g Kg− 1) was determined by the method described by Tilley and Terry [46]; and (viii) dry matter concentration (%) was obtained by sampling three complete plants from each plot, which were dried in a kiln after weighing (fresh weight) until weight stabilization. The samples were weighed (dry weight) again, and the dry matter concentration was determined by the ratio between dry weight and fresh weight. This trait was used as a common denominator for the estimation of biomass digestibility. For acid detergent fiber, neutral detergent fiber, lignin content, and biomass digestibility, random samples of three complete plants from each plot were collected before cutting the experimental plots. These samples were dried in a forced-air circulation oven at 56 °C for 72 h. After drying, the samples were ground to small particles (1 mm) in a Wiley type grinder and analyzed as described above. For the third, fifth, and sixth cuttings, acid and neutral detergent fiber, lignin content, biomass digestibility, and dry matter concentration were measured using near-infrared spectroscopy (NIRS). Data generated from the first and second cuttings, and from other experiments (i.e., by traditional methodologies of biomass quality analysis), were used for NIRS calibration. The phenotypic data are shown in Additional file 2: Table S2.

Genotyping, quality control, and imputation

Eighteen SSR markers were used for genotyping, as described by Azevedo et al. [15]. The alleles for each marker are shown in Additional file 3: Table S3. Due to the multiallelic nature of SSR markers associated with the polyploidy of elephant grass, each allele was considered a marker (totaling 111 markers). For each marker, individuals were coded as 0 (absence of allele) or 1 (presence of allele) according to Viana et al. [47]. SSRs with more than 15% missing values (i.e., a call rate of at least 85%) and/or a frequency of minor alleles of above 1% were removed. The following imputation algorithm was used for the missing value data point in a marker matrix (Mi): \( {M}_i=\left\{\begin{array}{c} if:{p}_i\le 0.5\to {M}_i=0\ \\ {} if:0.5<{p}_i\le 1\to {M}_i=1\end{array}\right. \), where pi is the allele frequency associated with the presence of a marker at locus i. The algorithm was directly implemented as an R function. After quality control, 87 markers were used. According to previous studies [28, 29, 48, 49], the SSR markers used here are on chromosomes 1, 3, 4, 5, 6, and 7 of pearl millet.

ssGBLUP

A mixed model methodology was adopted for statistical analyses using ssGBLUP [50, 51]. The statistical model was denoted by the following expression: y = Xm + Za + Zg + Wb + Ti + Tr + Qp + ε, where y is the vector of responses across the five cuttings (only using phenotypic data); m is the vector of the effects of the measurement-replication combination (assumed as fixed) added to the overall mean; a is the vector of genetic effects (assumed as random); g is the vector of residual genetic effects (assumed as random); b is the vector of block effects (assumed as random); i is the vector of the genotype by cutting interaction; r is the vector of the residual genotype by cutting interaction; p is the vector of permanent environment effects (random); ε is the vector of residues (random); and X, Z, W, T, and Q represent the incidence matrices for these effects.

The following distributions of random effects were considered: \( a\sim N\left(G\bigotimes {\sigma}_a^2\right) \); \( g\sim N\left(I\bigotimes {\sigma}_{rg}^2\right) \); \( b\sim N\left(I\bigotimes {\sigma}_b^2\right) \); \( i\sim N\left({G}_i\bigotimes {\sigma}_i^2\right) \); \( r\sim N\left(I\bigotimes {\sigma}_{ri}^2\right) \); \( p\sim N\left(I\bigotimes {\sigma}_p^2\right) \); and \( \varepsilon \sim N\left(I\bigotimes {\sigma}_e^2\right) \), where G is a matrix of genomic additive relationships, I is an identity matrix of appropriate dimensions, Gi is a matrix of genomic interactions (genotype by cutting interaction), \( {\sigma}_a^2 \), \( {\sigma}_{rg}^2 \), \( {\sigma}_b^2 \), \( {\sigma}_i^2 \), \( {\sigma}_{ri}^2 \), \( {\sigma}_p^2, \) and \( {\sigma}_e^2 \) are the additive, residual genetic, block, genotype by cutting interaction, residual genotype by cutting interaction, permanent environment, and residual variance components, respectively. The model above includes residual genetic effects and residual genotype by cutting interactions, according to Oakey et al. [22].

An additive relationship matrix structure (G) was used according to Resende et al. [24], and is denoted by the expression \( G=\frac{Z^{\ast }{Z}^{\ast \prime }}{\sum_i^n{p}_i\left(1-{p}_i\right)} \), where Z∗ = Z − P, in which Z is a matrix containing marker genotypes and P is a matrix with pi elements in column i.

Due to the presence of 10 genotypes that were not genotyped, the inverse of the genomic relationship matrix (H−1) was adopted, according to Legarra et al. [50]. The expression states that \( {H}^{-1}={A}^{-1}+\left[\begin{array}{cc}0& 0\\ {}0& {G}^{\ast -1}-{A}_{22}^{-1}\end{array}\right] \), where A−1 is the inverse of the pedigree relationship for all elephant grass genotypes and \( {A}_{22}^{-1} \) is the inverse of the pedigree relationship for only genotyped elephant grass genotypes. A and A22 was an identity matrix for this study because there was no information about the pedigree. To compute the exact inverse of G to compose the H−1 matrix, we used the algorithm G∗ = 0.95G + 0.05A22 [52].

From the matrix H−1, the ssGBLUP procedure was run according to the specified model. For the random effects of the model, significance of the likelihood ratio test was evaluated using a chi-square test with one degree of freedom. ssGBLUP was performed using ASReml 4.1 software [53].

The accuracy (\( {r}_{\hat{a}a} \)) of the additive effect considering the ssGLUP model was estimated as \( {r}_{\hat{a}a}=\sqrt{1-\frac{PEV_a}{{\hat{\sigma}}_a^2}} \), where PEVa is the predictive error variance that is obtained by diagonal elements inverse of the left-hand side of the mixed model equation for the additive effect.

Simple repeatability plus genotype by cutting (G × C) interaction model

The model was run without considering the relationship (simple repeatability plus G x C interaction model) between the genotypes, as follows: y = Xm + Zg + Wb + Ti + Qp + ε, where y is the vector of response across the five cuttings (using only phenotypic data); m is the vector of the effects of the measurement-replication combination (assumed as fixed) added to the overall mean; g is the vector of genetic effects (assumed as random); b is the vector of block effects (assumed as random); i is the vector of the genotype by cutting interaction; p is the vector of the permanent environment effects (random); ε is the vector of residues (random); and X, Z, W, T, and Q represent the incidence matrices for these effects.

The following distributions of random effects were considered: \( g\sim N\left(I\bigotimes {\sigma}_g^2\right) \); \( b\sim N\left(I\bigotimes {\sigma}_b^2\right) \); \( i\sim N\left({G}_i\bigotimes {\sigma}_i^2\right) \); \( p\sim N\left(I\bigotimes {\sigma}_p^2\right) \); and \( \varepsilon \sim N\left(I\bigotimes {\sigma}_e^2\right), \) where I is an identity matrix of appropriate dimensions and \( {\sigma}_g^2 \), \( {\sigma}_b^2 \), \( {\sigma}_i^2 \), \( {\sigma}_p^2, \) and \( {\sigma}_e^2 \) are the genetic, block, genotype by cutting interaction, permanent environment, and residual variance components, respectively. The simple repeatability plus G × C interaction model was performed in ASReml 4.1 [53].

The accuracy (\( {r}_{\hat{g}g} \)) of the genotype effect (genetic effects) considering the simple repeatability plus G x C interaction model was estimated as \( {r}_{\hat{g}g}=\sqrt{1-\frac{PEV_g}{{\hat{\sigma}}_g^2}} \), where PEVg is the predictive error variance that was obtained by the diagonal elements inverse of the left-hand side of the mixed model equation for the genetic effect.

Genome association study

The 90 elephant grass genotypes that had been genotyped and phenotyped were used in the genome association study. The R package “sommer” (GWAS2 function [54]) revealed a significant association between the markers and the phenotypic traits. The genotype by cutting interaction was included in the association study for each cutting using the model y = Xm + Mu + Za + Zg + Wb + ε, where y is the vector of response for each cutting; m is the vector of the effects of the replication (assumed as fixed) added to the overall mean; u is the vector of markers (assumed as fixed); a is the vector of genetic effects (assumed as random); g is the vector of residual genetic effects (assumed as random); b is the vector of block effects (assumed as random); ε is the vector of residue (random); and X, M, Z, and W represent the incidence matrices for these effects.

The following distributions of random effects were considered: \( a\sim N\left(G\bigotimes {\sigma}_a^2\right) \), \( g\sim N\left(I\bigotimes {\sigma}_{rg}^2\right) \), \( b\sim N\left(I\bigotimes {\sigma}_b^2\right), \) and \( \varepsilon \sim N\left(I\bigotimes {\sigma}_e^2\right) \). In these expressions, G is a matrix of genomic additive relationships, I is an identity matrix of appropriate dimensions, and \( {\sigma}_a^2 \), \( {\sigma}_{rg}^2 \), \( {\sigma}_{b,}^2 \) and \( {\sigma}_{\varepsilon}^2 \) are the additive, residual genetic, block, and residual variances, respectively.

Markers with − log(P − value) up to the false discovery rate (FDR) threshold were considered candidate markers. To compute the FDR, a 0.02 threshold level and p < 0.05 were set.

We used the LD.Measures function in the R package LDcorSV to compute linkage disequilibrium (r2), as described by Hill and Robertson [55]: \( {r}^2=\frac{{\left[p(AB)-p(A)p(B)\right]}^2}{p(A)p(B)\left[1-p(A)\right]\left[1-p(B)\right]} \), where p(AB) is the frequency of the haplotype AB and p(A) and p(B) are the frequencies of alleles A and B, respectively. Therefore, r2 ranged from 0 (when the two markers were in perfect equilibrium) to 1 (when the two markers provided identical information). Manhattan plots and QQ plots were obtained using the “sommer” package [54] in R [56].

Alignment, candidate genes, and gene annotation

A list of candidate genes was assembled by BLAST, with default parameters set, using the plant comparative genomics portal Phytozome [57] based on related species (reference genomes; e.g., S. italica, S. viridis, P. virgatum, and P. halli). A BLAST search of the C. americanus genome was performed on the US National Center for Biotechnology Information website (https://blast.ncbi.nlm.nih.gov/Blast.cgi). For these searches, sequences of the primers M28R (CGAATACGTATGGAGAACTGCGCATC) and M35R (ATCCACCCGACGAAGGAAACGA) were used. For gene annotation, ortholog genes in A. thaliana were searched using the Arabidopsis Information Resource database [58].