Combination of twelve alleles at six quantitative trait loci determines grain weight in rice

Grain weight, which is controlled by quantitative trait loci (QTLs), is one of the most important determinants of rice yield. Although many QTLs for grain weight have been identified, little is known about how different alleles in different QTLs coordinate to determine grain weight. In the present study, six grain-weight-QTLs were detected in seven mapping populations (two F2, one F3, and four recombinant inbred lines) developed by crossing ‘Lemont’, a United States japonica variety, with ‘Yangdao 4’, a Chinese indica variety. In each of the six loci, one allele from one parent increased grain weight and one allele from another parent decreased it. Thus, the 12 alleles at the six QTLs were subjected to regression analysis to examine whether they acted additively across loci leading to a linear relationship between the predicted breeding value of QTL and phenotype. Results suggested that a combination of the 12 alleles determined grain weight. In addition, plants carrying more grain-weight-increasing alleles had heavier grains than those carrying more grain-weight-decreasing alleles. This trend was consistent in the seven mapping populations. Thus, these six QTLs might be used in marker-assisted selection of grain weight, by stacking different grain-weight-increasing or -decreasing alleles.

Occasionally, an allele at a specific QTL has a positive effect on grain shape while another has a negative effect. Theoretically, grain shape or weight can be manipulated by pyramiding different alleles with positive or negative effects on these traits. In rice breeding, many alleles have been mapped at different QTLs; however, which and how many alleles should be used in the marker-assisted selection of a desired phenotype are still important issues.
In a previous study, we developed two F 2 and one F 3 mapping populations by crossing 'Lemont', a United States sheath blight-susceptible japonica variety, with 'Yangdao 4', a Chinese sheath blight-resistant indica variety. The F 2 and F 3 mapping populations were initially used to identify the sheath blight-resistant QTL [42], not for mapping grain-weight-related QTLs. Six grain-weight-related QTLs were detected while analyzing the F 2 and F 3 populations, and we found that 12 alleles within these six grain-weight-QTLs acted cumulatively to control grain weight. In the present study, we used data from seven mapping populations, including the two F 2 and the F 3 populations developed in a previous study [42], and four recombinant inbred lines populations developed using the same parents, to elucidate how the 12 alleles in the six QTLs regulated grain weight and to test if these 12 alleles act additively across loci, leading to a linear relationship between the predictive breeding value of QTL and phenotype, or epistatically, leading to a nonlinear relationship between QTL values and phenotype.

Mapping populations
'Lemont', a sheath blight-susceptible United States cultivar, was crossed with 'Yangdao 4', a relatively sheath blight-resistant Chinese cultivar, producing two F 2 , one F 3 , and four recombinant inbred line (RIL) populations (F 7 to F 10 ), which were used in the present study.
Detailed information on the two F 2 , the F 3 , and two of the RIL (F 7 and F 8 ) mapping populations is given in Zeng et al. [43]. Briefly, the first F 2 mapping population (n = 190 individuals) was planted in May 2011 and the second F 2 mapping population (n = 182 individuals) was sown in May 2012, both in Hangzhou, China; the F 3 mapping population (n = 160 lines, each including 18 individuals that were arranged in three rows with six plants each), deriving from the former F 2 populations, was planted in November 2012 in Hainan, China. The F 7 and F 8 RIL populations (n = 220 lines) were sown in May 2014 in Hangzhou and in November 2014 in Hainan, respectively.
The F 9 RIL population (n = 220 lines) was planted in May 2015 at China National Rice Research Institute (CNRRI) farm in Hangzhou (119˚95 0 E, 30˚07 0 N) and the F 10 RIL population (n = 220 lines) was sown in November 2015 at CNRRI trial station in Hainan (110˚02 0 E, 18˚48 0 N). Eighteen plants were grown from each of the F 7 , F 8 , F 9 and F 10 lines, arranged in three rows of six plants each, with 17 cm between plants and 20 cm between rows. Field management followed the common agronomic practices in Hangzhou or Hainan.

Grain weight determination
Rice grains were sun-dried after harvest and stored at room temperature for at least one month before determining grain weight. One-hundred fully filled grains were randomly selected from the upper half of the panicles of each individual plant in the F 2 populations and weighed using an electronic balance. As some indica/japonica hybrids were sterile, some of the individuals in the mapping populations did not have 100 fully filled grains; in this case, all available grains were used. In the F 3 , F 7 , and F 8 populations, 50 fully filled grains were selected from 10 plants within each line (five grains per individual plant) and weighed. More than 100 fully filled grains from each line were measured in F 9 and more than 80 fully filled grains from each line were measured in F 10 . The 50-to 100-grain weight data were converted to 1000-grain weight and used in the analysis.

Marker assays and QTL analysis
The strategy for identifying grain-weight-related QTLs followed the method described in Zeng et al. [43]. Briefly, we first detected the QTLs responsible for grain weight using the three primary mapping populations (F 2 and F 3 populations), and then confirmed mapping results using four permanent mapping populations (F 7 to F 10 ).
One hundred and seventy nine polymorphic co-dominant markers covering 12 rice chromosomes were used to identify the QTLs responsible for grain weight in the F 2 population planted in 2011 in Hangzhou and in the F 3 population planted in 2012 in Hainan. Detailed information on these 179 markers is given in Wen et al. [42]. The six grain-weight-related QTLs detected in these two populations (see Results section) were further examined in the F 2 populations planted in 2012 in Hangzhou, using 44 markers that covered the regions of these six QTLs, as described in Zeng et al. [43].
The six grain-weight-related QTLs yielded by the three primary mapping populations were further confirmed using the four RIL populations (F 7 to F 10 ) and 33 polymorphic markers (S1 Fig) that covered the regions of the six QTLs.

Statistical analyses
Shapiro-Wilk tests, two-way ANOVA, and linear regression analysis were performed in SAS 8.01 (SAS Institute, Cary, NC, USA).

Grain-weight-QTLs confirmation using RIL populations
The six grain-weight-QTLs detected in the three primary mapping populations were further confirmed in the four RIL populations (n = 220 lines) using 33 polymorphic markers that covered the regions of the six QTLs. These 33 markers represented 274.8 cM, with an average of 10.2 cM between adjacent markers (S1 Fig). All the six grain-weight-QTLs identified in the three primary mapping populations were detected in the four RIL populations (

QTLs-by-environment and QTLs-by-population interactions
Using a two-way ANOVA, we examined if the six grain-weight-QTLs significantly interacted with environments or mapping populations. The closest markers to the six QTLs in each mapping population were used to represent the QTL genotypes. Only three significant QTLs were detected in the F 3 population planted in 2012 in Hainan and in the F 2 population planted in 2012 in Hangzhou (Table 1). We used multiple interval mapping to identify the closest markers to the other three putative grain-weight-QTLs in these two populations, and the heterozygotes of F 2 populations were omitted from the following two-way ANOVA.
No significant interactions were detected between each of the six grain-weight-QTLs and environment ( Table 2), suggesting that the effects of these QTLs were stable across the different mapping environments. In addition, no significant interactions were detected between grain-weight-QTLs and populations, except for qGW-7 (Table 3). This is in agreement with Table 2. Quantitative trait loci (QTLs)-by-environment interactions examined using two-way analysis of variance. As seven mapping environments were considered (three primary and four recombinant inbred line mapping populations), there were six degrees of freedom. Because there were two genotypes at each QTL (heterozygotes were omitted and not used in the analysis), the degree of freedom for QTL was 1. the fact that qGW-7 was not detected in two populations: it was present in five populations (Table 1).

Digenic epistasis in the seven mapping populations
Digenic epistatic loci were detected using inclusive composite interval mapping (ICIM) and the QTL IciMapping software, and their significance was further confirmed by two-way ANOVA. No significant digenic epistatic QTLs were detected in the F 2 population planted in 2011 in Hangzhou, using the 179 markers that covered the 12 rice chromosomes. Ten pairs of digenic epistatic loci were found in the F 3 population that derived from this F 2 population ( Table 4) and seven of them were significant, according to the two-way ANOVA performed using one of the flanking markers to represent the loci (S1 Table). One pair of digenic epistatic loci was detected in the F 2 population grown in 2012 in Hangzhou (Table 5) using 44 markers, and this was confirmed significant by the two-way ANOVA (S2 Table). No significant digenic epistatic loci were detected in the RIL populations, probably because only 33 markers were used to genotype these populations. These results suggested that epistasis is involved in the regulation of grain weight (Tables 4 and 5), although no significant interactions were detected among the six grain-weight-related QTLs (qGW-1, qGW-3-1, qGW-3-2, qGW-4, qGW-7, and qGW-10).

Regulation of grain weight by 12 alleles in six QTLs
Based on the QTLs-by-environment interaction analysis, the effects of the six grain-weight-QTLs were stable across the different environments. These six QTLs did not significantly Table 3. Quantitative trait loci (QTLs)-by-population interactions examined using two-way analysis of variance. As there were three types of mapping populations (F 2 , F 3 , and recombinant inbred line populations), there were two degrees of freedom. There were two genotypes at each QTL (heterozygotes were omitted and not used in analysis) and the degree of freedom for QTL was 1. interact, according to ICIM results. We further analyzed the coordination between the different alleles from these six QTLs regulating grain weight.
A linear regression analysis was performed to examine if the 12 alleles in the six QTLs acted additively across loci leading to a linear relationship between the predicted breeding values of QTLs and the phenotype. Such a linear relationship implies that plants carrying more grainweight-increasing alleles have heavier grains than those carrying more grain-weight-decreasing alleles. We first calculated the genotypic value of each individual plant (or line) in the seven mapping populations, which was used as the predictive breeding value of each individual plant or line. The genotypic value of an individual plant or line was calculated by adding the estimated additive effects of each of the six QTLs in the RIL populations. A positive additive effect was used if a locus carried a grain-weight-increasing allele, and a negative additive effect was used if a locus carried a grain-weight-decreasing allele. For the F 2 mapping populations, the genotypic value of an individual plant was calculated by adding the estimated additive effects and dominance effects of each of the six QTLs. The dominance effects of heterozygotes were summed to the additive effects of the homozygotes across the six loci in the F 2 populations. The additive or dominance effects of the six QTLs are listed in Table 1. Because only three significant QTLs were detected in the F 3 population planted in 2012 in Hainan and in the F 2 population planted in 2012 in Hangzhou, the additive or dominance effects of the other three putative QTLs were resolved by the MIM method using Windows QTL Cartographer 2.5. Linear regression analysis between the genotypic value and grain weight of all individual plants or lines in the seven mapping populations (Fig 2) revealed significant relationships (F 2 grown in 2011, F = 96.95, P < 0.0001; F 2 grown in 2012, F = 41.36, P < 0.0001; F 3 , F = 65.42, P < 0.0001; F 7 , F = 120.14, P < 0.0001; F 8 , F = 92.02, P < 0.0001; F 9 , F = 79.39, P < 0.0001, and F 10 , F = 103.74, P < 0.0001). The coefficient of determination (R 2 ) was used as an estimate of the cumulative heritability of the six QTLs, revealing it was 41%, 18%, 32%, 39%, 33%, 30%, and 36% for the F 2 grown in 2011, F 2 grown in 2012, F 3 , F 7 , F 8 , F 9 , and F 10 , respectively. These results demonstrated that the 12 alleles in the six QTLs acted additively in grain weight regulation. Thus, plants carrying more grain-weight-increasing alleles had heavier grains than those carrying more grain-weight-decreasing alleles.

Discussion
Seven mapping populations (two F 2 , one F 3 , and four RIL) and three genetic linkage maps were used in the present study to identify the QTLs responsible for rice grain weight. A common linkage map generated with 179 markers, which covered the 12 rice chromosomes, was used to detect QTLs in the F 2 population planted in 2011 in Hangzhou and in its descendant F 3 population planted in 2012 in Hainan. This yielded six grain-weight-QTLs, which were further examined in a second F 2 population planted in 2012 in Hangzhou. To save time and labor, we did not analyze this population with the 179 markers covering the 12 chromosomes. Instead, we constructed a linkage map with 44 markers covering the regions of the grainweight-QTLs detected in the F 2 and F 3 populations.
The six QTLs detected in the three primary mapping populations were further confirmed using four RIL populations, using a common linkage map constructed with 33 markers that covered the locations of these QTLs. This method saved time and labor but some of the grainweight-QTLs with minor effect might have been neglected, as only two of the seven mapping populations were analyzed with markers covering all 12 chromosomes. Still, this strategy was successfully used for identifying the QTLs responsible for grain length in a previous study [43] and, because we could confirm the QTLs detected in the present study, we believe this is a reliable method for studying relevant traits concerning rice grain shape or weight.
To compare the positions of the QTLs found in the present and in previous studies, we first determined the largest marker-flanking intervals of the six grain-weight-QTLs according to the mapping results in the four RIL populations (Table 1), as we believed that the results were more accurate in RIL than in F 2 or F 3 . The largest marker intervals for qGW-1, qGW-3-1, qGW-3-2, qGW-4, qGW-7, and qGW-10 were D134B-D144A, D309-D315, D335C-D336B, D456-D457B, D746-RM234, and D1042-RM496, respectively. The genes/QTLs responsible for grain shape or grain weight that were cloned or fine mapped on chromosomes 1, 3, 4, and 7 in previous studies were illustrated and compared with the QTLs detected in the present study Regulation of rice grain weight by twelve alleles (Fig 3). Chromosome 10 was not illustrated because no grain-shape-QTLs or grain-weight-QTLs were cloned or fine mapped on this chromosome. There were no QTLs co-localized with qGW-4 or qGW-10 but qGW-1 was co-localized with qGRL1.1, a QTL identified by Singh et al. [24]. However, it is not clear whether the two QTLs are in the same gene. The QTL qGW-3-1 was adjacent to qGL-3-1, a grain-length-QTL that we previously identified using the same 'Lemont' × 'Yangdao 4' mapping populations [43]. It is possible that qGW-3-1 and qGL-3-1 are in the same gene, but further studies are needed to confirm this. The qGW-3-2 was co-localized with qTGW3.2 [32] and qGL-3-2 [43], the latter being a grain-length-related QTL identified by us in a previous study using the same mapping populations. Thus, qGW-3-2 and qGL-3-2 might be in the same gene. The qGW-7 was co-localized with SRS1 [16], GL7/GW7 [17,18], GS7 [37], qSS7 [38], and qGL-7 [43]. Although SRS1 [16] and GL7/GW7 [17,18] were cloned, it is not clear if qGW-7 is allelic to either or both of them, based on the available information.
Grain weight is one of the most important determinants of rice yield. Because it directly influences grain yield, it has attracted great attention within the rice genetic research community. A large number of QTLs responsible for grain weight have been reported in previous studies, but it is still not clear how the different alleles in the several grain-weight-QTLs coordinated to determine grain weight. In the present study, we found an allele increasing and another decreasing grain weight within each of the six grain-weight-QTLs identified. We also found that plants carrying more grain-weight-increasing alleles had heavier grains than those carrying more grain-weigh-decreasing alleles. Regression analysis indicated that the 12 alleles in the six QTLs acted additively across loci, leading to a linear relationship between genotypic values and phenotype. Given that these six QTLs did not interact with each other, they might be involved in six independent pathways. Although the six QTLs detected in this study were mapped in relatively rough marker intervals, the closest markers to these QTLs can be used in marker-assisted breeding to pyramid the number of alleles needed to form a desired phenotype. However, caution must be taken because it is not known if the effect of the 12 alleles from the six QTLs is maintained when genes are introduced into different genetic backgrounds.