Introduction

The earliest application of heterosis was in maize, which is widely cultivated worldwide. The grain yield of maize hybrids increased by at least 15% over that of open-pollinated varieties (Duvick 1999). There are three hypotheses regarding the genetic basis for the better-parent performance phenomenon, namely dominance (Davenport 1908; Bruce 1910), overdominance (Shull 1908; East 1908), or epistasis (Powers 1944; Williams 1959). Many studies have focused on the complex genetic mechanisms underlying the heterosis for yield-related traits in maize (Stuber et al. 1992; Cockerham and Zeng 1996; Lu et al. 2003; Frascaroli et al. 2007; Garcia et al. 2008; Tang et al. 2010; Schön et al. 2010; Larièpe et al. 2012; Guo et al. 2014; Wang et al. 2016, 2018; Li et al. 2017; Samayoa et al. 2017). These studies involved the following heterotic patterns: ‘Stiff Stalk Synthetic × Lancaster Sure Crop’ (Stuber et al. 1992; Cockerham and Zeng 1996; Lu et al. 2003; Frascaroli et al. 2007; Garcia et al. 2008; Schön et al. 2010), ‘synthetic × Flint’ (Tang et al. 2010; Guo et al. 2014), ‘Reid × Tangsipingtou’ (Wang et al. 2016, 2018; Li et al. 2017), and ‘American Dent × European Flint’ (Samayoa et al. 2017). These investigations revealed that all of the genetic effects for diverse traits varied and played a different role depending on the heterotic patterns and genetic architecture of the population. However, there has been little research on the heterosis for kernel components in the heterotic pattern ‘Reid × tem-tropic I (a synthetic population from the temperate × tropic I germplasm)’, which has been widely applied in southwestern China.

Kernel length (KL), kernel width (KW), kernel thickness (KT), and hundred-kernel weight (HKW) are important traits influencing the contribution of individual ears to maize kernel yield. There are strong relationships among kernel-related traits, including length, width, and thickness (Li et al. 2009). Previous studies examining kernel-related traits involved F2:3 families (Liu et al. 2014), recombinant inbred line (RIL) population (Yang et al. 2016; Liu et al. 2017; Zhang et al. 2017; Lan et al. 2018), immortalized F2 (IF2) population (Zhang et al. 2014, 2016), a four-way cross population (Chen et al. 2016a), and association panel (Zhang et al. 2017; Zhu et al. 2018). These studies identified many new and stable quantitative trait loci (QTLs) and single nucleotide polymorphisms (SNPs). For example, Liu et al. (2014) identified 12 stable major QTLs using F2:3 families derived from the parental lines with highly significant differences in kernel-related traits. Additionally, Zhang et al. (2014, 2016) detected 54 unconditional loci and 97 conditional QTLs at different kernel development stages in an IF2 population, which enabled the comprehensive characterization of the genetics mediating kernel development. Earlier investigations also applied the North Carolina Design III (Samayoa et al. 2017; Li et al. 2017), IF2 population (Tang et al. 2010; Guo et al. 2014), and chromosome segment substitution line test populations (Wang et al. 2016, 2018) to identify the heterotic loci and the genetic basis for the heterosis for yield-related traits. However, there remains a lack of published research describing the heterosis for kernel-related traits. Frascaroli et al. (2007) highlighted the importance of heterotic loci showing dominance and epistasis for HKW in mapping populations derived from the heterotic pattern ‘Reid × Lancaster’ with an extensive design III. Tang et al. (2010) and Guo et al. (2014) stated that the heterosis for HKW was due to cumulative genetic effects (dominance and epistasis). Wang et al. (2018) detected 63 and 57 different QTLs regarding the heterosis for four kernel-related traits in two chromosome segment substitution line test populations derived from the Reid × TSPT (Tangsipingtou) cross, thereby providing the foundation for the fine-mapping of heterotic loci for kernel size. Notably, a large ratio of incongruent heterotic loci for various heterotic patterns indicated the complexity of the genetic mechanisms for the heterosis for kernel-related traits (Li et al. 2017; Wang et al. 2018). An analysis of kernel components and the heterosis for these traits provided new insights for elucidating the genetics underlying the heterosis for maize grain yield, especially for diverse heterotic patterns.

To date, numerous genes associated with maize grain-related traits have been identified, including Opaque-2 (O2; Schmidt et al. 1987, 1992), Sugary-1 (Su1; Pan and Nelson 1984), Shrunken-2 (Sh2), and Brittle-2 (Bt2; Dickinson and Preiss 1969). Several major QTLs, such as qGW4.05 (Chen et al. 2016a, b), qKW7 (Li et al. 2016), qKL1.07 (Qin et al. 2016), and qGW1.05 (Zhou et al. 2017), and KNE4 (Zhan et al. 2018), were fine-mapped to narrow genomic regions. Notably, ZmGS3 (Li et al. 2010a) and ZmGW2-CHR4 (Li et al. 2010b), which are maize orthologs of rice genes, were identified by a homology-based cloning strategy. There are few major QTLs that have been cloned via map-based cloning, although a series of genes has been identified in the aforementioned previous studies.

In this study, we investigated the genetic basis of six kernel-related traits and the heterosis for these traits in two mapping populations. The RIL population comprised 301 lines derived from the cross between Ye478 and 08-641, whereas the IF2 population was generated from the RIL population. The parental lines Ye478 and 08-641 belong to the improved Reid (PA) and tem-tropic I group, respectively. The ‘PA × PB’ heterotic pattern is widely applied in southwestern China. The objectives of this study were to (1) identify the QTLs for kernel-related traits in the RIL and IF2 populations; (2) detect the heterotic loci for those traits; (3) identify the pleiotropic genomic regions and assess the genetic effects contributing to the heterosis in the present heterotic pattern; and (4) provide valuable information for characterizing the genetic basis of the heterosis for these traits.

Materials and methods

Plant materials and field experiments

The single-seed descent method was performed with the Ye478 × 08-641 hybrid to produce a set of 301 RILs (Liu et al. 2016). The 320 RILs before filtering the RILs with high heterozygosity were randomly divided into two groups of 160 RILs as described by Hua et al. (2002) and Tang et al. (2010). Paired crosses between the lines of both groups were performed according to the one-to-one method, thereby producing 160 F1 crosses. After repeating the procedure twice, we ultimately generated 320 crosses. We discarded the RILs with heterozygosity greater than 20% and their corresponding crosses, and an IF2 population of 298 F1 crosses was generated.

The RIL population, the parental lines, and the F1 hybrid were planted in four environments: three at the Xishuangbanna Maize Breeding Base of the Maize Research Institute of Sichuan Agricultural University, Jinghong (JH; 21°95′N, 100°76′E), in Yunnan province, China in March 2014 (JH2014), March 2015 (JH2015), and March 2016 (JH2016) as well as one at the Modern Agriculture Research and Development Center of Sichuan Agricultural University, Chongzhou (CZ; 30°33′N, 103°38′E), in Sichuan province, China on April 2016 (CZ2016). The IF2 population was evaluated under three environments (i.e., 2015JH, 2016JH, and 2016CZ). The field experiments were performed following a randomized complete block design with two repetitions. Each plot consisted of 3-m-long rows, each consisting of 14 plants, with 0.80 m separating rows. Finally, each trial was evaluated with a plant density of 57,000 plants per ha. In each environment, both mapping populations were planted adjacent and occupied a square and uniform parcel. The trials included the application of fertilizers, fungicides, and pesticides based on normal agronomic practices. Irrigation and manual weeding were applied as needed for the intensive yield of each season.

Phenotypic measurements and analysis

All plants in each plot were harvested and after measuring the total ear weight, ten well-pollinated ears in the middle of each row were randomly chosen for additional kernel evaluations. Six kernel-related traits were assessed as previously described (Liu et al. 2014). Specifically, the ear length without kernels (WKEL, cm) was calculated as the average of ten measurements of the length from the kernels at the tip of the ear to the ear tip without kernels. The HKW (in g) was calculated as the average of three replications, with the equation, HKW × (1 − moisture %)/(1 − 14%). A hundred kernels were randomly chosen from the bulked kernels and weighed with an electronic balance. The KL (in mm) was calculated as the average of three measurements of ten consecutive kernels selected from the bulked kernels from the middle of the ears. The KW (in mm) was calculated as the average of three measurements of ten consecutive kernels selected from the bulked kernels from the middle of the ears, whereas KT (in mm) was calculated as the average of three measurements of five consecutive kernels from the middle of the ears with electronic digital calipers. The volume weight (VW; in g/L) (i.e., kernel weight per unit volume) was calculated as the average of two replicated measurements of the bulked kernels with the Shanghai Qingpu LSD-G volume weight tester according to the SAC method GB1353-2009 (SAC 2009). The bulked kernels were dried under natural conditions for 15 days before the measurement (moisture content less than 14%). The average data for the phenotypic traits of the 301 RILs and the IF2 population across all environments were analyzed for the distribution of the phenotypic traits and Pearson’s correlations with PROC CORR from the statistical software package SPSS 17.0 (http://www.spss.com). Combined analyses of variance for each trait of the RIL and IF2 populations were estimated with the GLM procedure of SPSS 17.0, with genotypes as fixed effects and replications and environments as random effects. Broad-sense heritability (\(H^{2}\)) for the two mapping populations was calculated on an entry mean basis as described by Hallauer and Miranda (1988): \(h^{2} = {{\sigma_{g}^{2} } \mathord{\left/ {\vphantom {{\sigma_{g}^{2} } {\left( {\sigma_{g}^{2} + \frac{{\sigma_{ge}^{2} }}{n} + \frac{{\sigma^{2} }}{nb}} \right) \, }}} \right. \kern-0pt} {\left( {\sigma_{g}^{2} + \frac{{\sigma_{ge}^{2} }}{n} + \frac{{\sigma^{2} }}{nb}} \right) \, }}\), where \(\sigma_{g}^{2}\) denotes the genetic variance, \(\sigma_{ge}^{2}\) is the genotype × environment interaction variance, \(\sigma^{2}\) represents the residual error variance, b refers to the number of replications, and n is the number of environments. The 90% confidence interval of heritability \(\left( {h^{2} } \right)\) was estimated as described by Knapp et al. (1985). The phenotypic traits of both mapping populations were analyzed with two mixed models fitted by the restricted maximum likelihood approach:

$$Y_{mk} = \mu + G_{m} + R_{k} + \varepsilon_{mk}$$
(1)
$$Y_{mik} = \mu + G_{m} + GE_{mi} + E_{i} + R_{k} + \varepsilon_{mik}$$
(2)

where \(Y_{mk}\) denotes the phenotypic value of genotype m in replication k, \(Y_{mik}\) denotes the phenotypic value of genotype m in environment i and replication k, \(\mu\) represents the overall mean of the RIL population or the IF2 population, \(G_{m}\) is the random effect of genotype m, \(GE_{mi}\) is the random effect of the interaction between genotype m and environment i, \(E_{i}\) is the random effect of environment i, \(R_{k}\) is the random effect of replication k, and \(\varepsilon_{mk}\) and \(\varepsilon_{mik}\) represent the random experimental errors. The best linear unbiased predictions (BLUPs) for the single-environment analysis and combined analysis across all environments were performed with Eqs. (1) and (2), respectively. The adjusted means were used for the subsequent QTL mapping. The analyses were conducted with the R program for statistical computing (R Development Core 2010; lme4 package, Bates et al. 2015). The mid-parent heterosis (MPH) was calculated as follows: \(MPH_{ij} = {{F_{ij} - \left( {P_{i} + P_{j} } \right)} \mathord{\left/ {\vphantom {{F_{ij} - \left( {P_{i} + P_{j} } \right)} 2}} \right. \kern-0pt} 2}\) (Hua et al. 2003), where \(F_{ij}\) is the BLUP value of the Fij hybrid (F1 cross) from the IF2 population and \({{\left( {P_{i} + P_{j} } \right)} \mathord{\left/ {\vphantom {{\left( {P_{i} + P_{j} } \right)} 2}} \right. \kern-0pt} 2}\) is the average BLUP values for the corresponding parents (Pi and Pj from the RIL population). The genotypic dataset for the MPH depends on the dominance and epistatic effects, but epistatic effects were not included and an additive-dominance model has been assumed for the IF2 population (Tang et al. 2010; Guo et al. 2014).

Molecular linkage map construction

Genomic DNA was extracted from the juvenile leaves of 7-day-old seedlings of the RIL population and the parental inbreds (each bulk comprising ten plants per line) according to a modified CTAB method (Chen and Ronald 1999). An oligonucleotide pool assay involving 3072 SNPs was developed by the National Maize Improvement Center of China based on Illumina GoldenGate technology. The markers were used for genotyping the RIL population and the corresponding parents. After screening for heterozygous data points (< 20%), missing data points (< 20%), and segregation distortion, 683 SNPs that were distributed across all ten maize chromosomes were used to construct a linkage map, with a total length of 1786.1 cm and an average interval of 2.61 cm. The genetic map for the RIL population was generated with MapDisto 1.7.5 (http://mapdisto.free.fr/DL/) (Mathias 2012). The Kosambi mapping function was used for converting recombination frequencies to genetic distances (Kosambi 1943). Regarding the IF2 population, the genotyping data of every cross were deduced from the marker data of the corresponding RIL parents. The genetic linkage map of the RIL population was also used for the IF2 population and the MPH dataset (Hua et al. 2002; Tang et al. 2010).

QTL mapping

For the RIL population, the IF2 population, and the MPH dataset, QTLs for each trait were identified with the inclusive composite interval mapping (ICIM) (Li et al. 2007, 2008) of the QTL ICIMapping software (Meng et al. 2015). We used the ICIM-ADD method, with the p value set at 0.001 for entering variables in the stepwise regression of residual phenotypes on marker variables (PIN), whereas the p value was set at 0.002 for removing variables to detect QTLs. An empirical threshold LOD score was used for declaring significant QTLs based on a 1000-permutations test, with a type I error rate of 0.05 (Doerge and Churchill 1996) and a step size of 1 cm. Single marker analysis (SMA) to detect loci with the same empirical threshold LOD was performed for the RIL and IF2 populations. The degree of dominance was defined based on the dominance effect to additive effect ratio (|D/A|) for each QTL (Guo et al. 2014). A |D/A| > 1.26 reflected the overdominance of a locus, otherwise, the locus was considered as dominance type (Falconer and Mackay 1996). The QTLs were nominated as follows: ‘q’ + ‘the abbreviation of the trait’ + ‘chromosome’ + ‘−’ + ‘physical order or omission within the chromosome’. Overlapping or adjacent QTLs for different traits were regarded as a QTL cluster. The QTL and QTL density across all chromosomes was plotted with the R program (R Development Core 2010). In addition, the epistatic interaction (EPI) and the QTL × environment interaction (QEI) were analyzed according to the mixed-model-based composite interval mapping (MCIM) using the QTLNetwork program 2.1, (Wang et al. 1999; Yang et al. 2007, 2008). An additive by additive (AA) interaction in the RIL population was detected via combined analysis across all environments. For the IF2 population, the following four types of digenic effects were detected: AA interaction, additive by dominant (AD) interaction, dominant by additive (DA) interaction, and dominant by dominant (DD) interaction via combined analysis across all environments. We also detected these four types of EPIs in the MPH dataset based on the average data across environments. The QEI effects were analyzed in the RIL and IF2 populations via a combined analysis across all environments. The QTLs for each trait were identified along with the full QTL model containing significant additive, dominance, and epistatic effects, as well as their interactions with environments (testing window and filtration window size of 10 cm and a walking speed of 2 cm). The critical F value for selecting candidate intervals was determined by 1000-permutation tests with p < 0.05 as the experimental-wise significance level. Bonferroni correction was used to compute the comparison-wise significance threshold, assuming an experiment-wise error rate < 0.05 (Rice 1989).

Results

Phenotypic variations of kernel-related traits and the heterosis for these traits

The parental lines Ye478 and 08-641 significantly differed regarding KL, KW, and HKW (Fig. 1a). Considerable phenotypic variations for all traits were also observed in the RIL and IF2 populations (Fig. 1b). The mean KL and KW were significantly higher for the F1 hybrid than for 08-641, and the average WKEL was significantly higher for the F1 hybrid than for either parent. The average MPH for the KT, KL, KW, and HKW of the F1 hybrid were − 2.93 mm, 1.21 mm, 1.44 mm, and 1.68 g, respectively (Table S1). Similarly, the average MPH varied from − 13.5% for KT to 12.2% for KL in the IF2 population. The average WKEL for the F1 hybrid was 0.83 cm (246.2%), whereas the mean MPH of WKEL in the IF2 population was − 0.56 cm (− 23.3%). These results indicated the mean KL, KW, VW, and HKW were higher for the hybrid than for the parental lines, but the WKEL and KT exhibited the opposite trend.

Fig. 1
figure 1

Performance of six kernel-related traits for the parental lines and the hybrid F1 along with both mapping populations and the MPH dataset. a Comparison of means for six kernel-related traits among inbred Ye478, 08-641 and the F1 hybrid. The Duncan multiple range test was used for the comparison of means. Genotypes with lower-case letters were significantly different at the 0.05 probability level. Means with same letters are not significantly different. The data are shown as mean ± SD (standard deviation). b The histogram for kernel-related traits and mid-parent heterosis (MPH) for those traits in the RIL and IF2 population. WKEL ear length without kernels, KT kernel thickness, KL kernel length, KW kernel width, VW volume weight, HKW hundred-kernel weight

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Highly significant genotype, environment, genotype × environment interaction effects were detected for all traits (p < 0.01; Table 1). Similar and moderate broad-sense heritability (h2) was observed for KT, KL, KW, HKW, and VW across the RIL and IF2 populations, ranging from 60.4% for KT to 77.0% for KW in the RIL population. The heritability for WKEL was greater in the RIL population (74.5%) than in the IF2 population (64%). There were low-to-moderate significant correlations among kernel-related traits and the MPH for these traits (Table S2). Specifically, HKW was significantly positively correlated with WKEL, KT, KL, and KW across the RIL and IF2 populations. There were also weakly significant correlations between VW and KL, VW and KW, KW and KT, and KW and KL across both mapping populations. The MPH for HKW was significantly correlated with the MPH for KT, KL, and KW (p < 0.01). Additionally, the MPH for KL was significantly negatively correlated with WKEL and KT but was significantly positively correlated with KW (r = 0.54, p < 0.01). Moreover, a significantly positive correlation was detected between WKEL and KT across the mapping populations, as well as between the MPH for WKEL and KT (p < 0.01). These results revealed the strong correlations among yield components.

Table 1 Mean squares from the combined analyses of variance and heritabilities on a family mean for kernel-related traits in the RILs and IF2 population under three environments
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Identification of QTLs for kernel-related traits and the heterosis for these traits

The main features of 100 putative QTLs for the six traits investigated in this study are summarized in Table S3. More than half of the QTLs were simultaneously identified via single environment analysis and combined analysis across all environments (Table S4). Each QTL accounted for 0.40–25.89% of the phenotypic variation, with the contribution of more than half of these QTLs less than 5% (Fig. 2). The number of QTLs varied from two for KT and VW in the RIL population to 11 for KW in the IF2 population. Additionally, two QTLs were simultaneously detected across the RIL and IF2 populations, and two QTLs in the RIL population also influenced the MPH. Only two heterotic loci were co-mapped in the IF2 population. Moreover, 16, 34, and 44 QTLs were specific for the RIL population, IF2 population, and the MPH dataset, respectively.

Fig. 2
figure 2

Frequency distribution of QTL with PVE (phenotypic variance explained by each QTL) for six kernel-related traits and the mid-parent heterosis (MPH) level in the RILs and IF2 population. The vertical and dashed lines indicate the median values

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We identified 18 QTLs for WKEL, five QTLs in the RIL population, four QTLs in the IF2 population, and ten QTLs for MPH (Table S3; Fig. 3). These QTLs were distributed across all chromosomes, except for chromosomes 4 and 5. The total contribution of all QTLs was similar in both mapping populations and the MPH dataset, and individual QTLs explained between 1.48% (for MPH) and 16.37% (for the IF2 population) of the phenotypic variation [i.e., phenotypic variation explained (PVE)]. The environmentally stable QTL qWKEL3-1, which was specific for the RIL population, had a high PVE of 9.99% and an additive effect of − 0.24 cm. At the qWKEL2-2 locus, which was present across the RIL and IF2 populations, the Ye478 allele decreased the WKEL. In addition, most of the heterotic loci with minor effects had negative dominance effects.

Fig. 3
figure 3

QTL distribution for six kernel-related traits and heterosis for those traits in the RIL and IF2 populations. The red rectangles indicate QTLs with negative additive effects (or dominant effects for mid-parent heterosis (MPH)), while the blue rectangles represent positive additive effects (or dominant effects for MPH). The width of the rectangle indicates the confidence interval of QTL. The heatmap of QTL density across ten chromosomes was indicated at the bottom of the figure and below the X-axis. WKEL ear length without kernels, KT kernel thickness, KL kernel length, KW kernel width, VW volume weight, HKW hundred-kernel weight

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For KT, two QTL in the RIL population, three QTL in the IF2 population, and eight heterotic loci were identified across all chromosomes, except for chromosomes 9 and 10. Each QTL explained a range of 2.4–10.3%. The total PVE was considerably higher for MPH than for either mapping populations. At bin 8.06, the IF2-specific qKT8-1 and the heterotic locus qKT8-1 were detected under two single environments. The qKT8-1 locus for MPH (bin 2.08) had the highest PVE (10.3%). No QTLs were identified in both populations as well as in the MPH dataset.

For KL, we identified 16 QTLs across all chromosomes, except for chromosome 7, as well as four QTLs in the RIL population, six QTLs in the IF2 population, and eight QTLs for MPH. Of these QTLs, nine had a PVE of less than 2%. The IF2-specific qKL9 harboring the favorable allele from 08-641, had the highest PVE (25.86%). The QTL qKL2-2 for MPH was also co-located in the RIL population, but not in the IF2 population. Another locus in the IF2 population, qKL4, which exhibited an overdominance effect, had a similar dominance effect on MPH, and the favorable allele was contributed by 08-641.

For KW, we detected four QTLs in the RIL population, 11 QTLs in the IF2 population, and five heterotic loci across all chromosomes. The total PVE in the IF2 population was much higher than in the RIL population or the MPH dataset. Individual QTLs had a PVE between 0.59 and 16.35% for MPH. The environmentally stable QTL qKW3 had an additive effect of 0.13 mm and a PVE of 7.52% in the IF2 population. Notably, qKW9-3 exhibited an overdominance effect in the IF2 population, and also affected the MPH for KW.

Sixteen QTLs were identified for VW, with two QTLs in the RIL population, nine QTLs in the IF2 population, and seven QTLs for MPH. The total contribution of all QTLs for VW was similar to that for KW in both populations and the MPH dataset. The QTL qVW5 in the IF2 population, which was detected in two single-environment analyses, had the highest PVE (9.32%) and harbored the favorable allele from Ye478. The QTL qVW3-1 at bin 3.04 was simultaneously detected in the RIL and IF2 populations, and the favorable allele was contributed by 08-641. The heterotic locus qVW3-4 exhibited a high dominance effect and was also identified in the RIL population.

Eighteen QTLs were detected for HKW, with three QTLs in the RIL population, five QTLs in the IF2 population, and ten QTLs for MPH. These QTLs were distributed across all chromosomes, except for chromosome 10. Individual QTLs had a PVE of 0.40–23.24% for MPH. Five of the alleles derived from Ye478 in both populations were associated with increases in HKW. Most of these heterotic loci explained less than 1% of the phenotypic variation. There was no QTL congruency among both populations and the MPH dataset.

Analysis of the degree of dominance on heterosis

The |D/A| ratio for each locus (Falconer and Mackay 1996; Guo et al. 2014) calculated based on SMA and ICIM (Fig. 4) was used to assess the relative importance of the degree of dominance on the heterosis for kernel-related traits. In the IF2 population, more than 70% of the genomic markers for KW exhibited dominance (|D/A| < 1.26), as did over 60% of the genomic markers for VW and over 55% of the genomic markers for WKEL, KT, KL, and HKW. Regarding the degree of dominance estimated for the RIL and IF2 populations, more than 60% of the genomic markers for WKEL and HKW, more than 50% of the genomic markers for KW, and more than 39% of the genomic markers for KT, KL, and VW exhibited dominance. The SMA results indicated that more than 90% of the significant markers for all traits exhibited dominance in the IF2 population. Nearly 50% of the QTLs for KL exhibited dominance, as did 66.7% of the QTLs for KT, 75% of the QTLs for WKEL, over 80% of the QTLs for KW and VW, and 100% of the QTLs for HKW. These findings suggested that the loci exhibiting dominance contributed to the heterosis for kernel-related traits, especially for WKEL, HKW, and KW. Additionally, a weakly significant correlation was detected between total heterozygosity and VW variations. Furthermore, total heterozygosity was weakly significantly correlated with the MPH for KT, KL, and VW (Table S5).

Fig. 4
figure 4

Distribution of markers in the whole genome and significant loci for all six kernel-related traits exhibiting dominance and over-dominance effect. The degree of dominance was defined as a ratio of the dominance effect to additive effect (D/A) for each marker and QTL (Guo et al. 2014). For the IF2 population, the ratio D/A was calculated by a ratio of dominance effects to additive effects for genomic markers and QTL. The ratio D/A of genomic markers (MPH/RIL) was estimated by the ratio of additive effects from the RIL population to dominance effects from the MPH dataset. SMA single-marker analysis, ICIM inclusive composite interval mapping, PO positive overdominance, PD positive dominance, ND negative dominance, NO negative overdominance, WKEL ear length without kernels, KT kernel thickness, KL kernel length, KW kernel width, VW volume weight, HKW hundred-kernel weight

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Analysis of the epistatic interaction and the QTL × environment interaction

In the present study, we analyzed digenic interactions in both populations and the MPH dataset (Table S6). Six pairs of loci with low heritability (h2 < 2%) were associated with EPIs, with three pairs for HKW in the RIL population and the remaining pairs for WKEL, KT, and KW in the IF2 population. Notably, epistasis was not detected for MPH. We also analyzed the QEIs (Table S7). Only five loci with low contributions interacted with environments, with two loci in the RIL population and three loci in the IF2 population. Many of these loci exhibiting EPIs and QEIs were co-located with QTLs for the trait means. For example, the major QTL for WKEL, qWKEL2-4, interacted with the locus on chromosome 7 exhibiting AA and DD interactions, and also interacted with the 2016JH environment.

QTL pleiotropy

This study included an investigation of QTL pleiotropy. A total of 20 QTL clusters comprising 46 QTLs were detected across all chromosomes (Table 2). Some of these QTLs were localized to the genomic regions related to various kernel-related traits and the heterosis for these traits, suggesting that these loci affected the phenotypic variation and MPH of various traits. Pleiotropic effects were detected for half of these clusters. For example, QC1-2 influenced both KL and the MPH for KW, whereas QC6-3 affected KW and the MPH for HKW. We also detected five clusters that affected various trait means, but not the MPH; three of these clusters were specific for the IF2 population and two were identified in both mapping populations. The QC5-1 cluster at bin 5.00–5.03 had a pleiotropic effect on KW, HKW, and VW in the IF2 population. Additionally, five clusters contained overlapping QTLs specific for the MPH for various traits. The QC1-1 cluster, which was in a 7 cm region at bin 1.02, affected the MPH for KL and KW. Moreover, QC10 at bin 10.07 contained three QTLs for the MPH for WKEL and KL, which were mapped to the same position.

Table 2 QTL clusters for kernel-related traits and mid-parent heterosis detected in the RILs and IF2 population
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Discussion

QTL congruency for kernel-related traits

Maize kernel yield is influenced by a long development period involving many complex factors. Kernel size and weight are secondary traits but are very important for the final kernel yield (Li et al. 2009; Liu et al. 2014). Considering kernel size as a whole, there are also strong relationships among the kernel components investigated in our study (Liu et al. 2014, 2017; Lan et al. 2018). Compared with the corresponding mid-parent values, the KT was lower, whereas KL, KW, and HKW were higher in the hybrids. Although we observed moderate-to-high heritability for the kernel-related traits, many of the detected QTLs were still specific for the populations and environments. Recent studies identified numerous QTLs or SNPs for kernel-related traits in diverse genetic populations (Liu et al. 2014, 2017; Zhang et al. 2014, 2016, 2017; Chen et al. 2016a, b, 2017; Yang et al. 2016; Lan et al. 2018; Zhu et al. 2018). Some QTLs identified in the current study were also detected in the reported studies. Nine QTLs (qKT8-1, qKT5-3, qKL1-5, qKL3, qKW2-1, qKW2-3, qKW3, qKW9-1, qKW9-2, qKW10-2, and qVW3-2) overlapped with the meta-QTLs affecting kernel-related traits summarized by Chen et al. (2017). Of these QTLs, Zhang et al. (2016) revealed that qKT5-3 for KT overlapped with conqKV5 for kernel volume between 190 and 191 Mbp on chromosome 5 in an analysis during developmental stage DAP43|DAP36 (i.e., when kernel volume at 43 days after pollination was conditioned on kernel volume at 36 days after pollination). Three clusters (QC2-2, QC5-1, and QC9-2) were co-localized with the meta-QTLs for grain yield, ear-related traits, and kernel-related traits identified by Chen et al. (2017). The QTLs qVW7 (for VW) and qKV7 (for kernel volume), which overlapped between 103 and 109 Mbp on chromosome 7 at 50 days after pollination, were also detected in an IF2 population by Zhang et al. (2016). In addition, qKT3 and qHKW3-3 at bin 3.08 were mapped in the same interval and contained the significant SNP chr3.S_212832592 associated with KT and HKW in 10 RIL populations reported by Liu et al. (2017). Interestingly, qKL2-1 for KL reportedly contains an important linkage disequilibrium block affecting kernel shape in previously analyzed RILs and in an association panel (Zhang et al. 2017). Additionally, qVW3-4, which influences the VW mean and the MPH for VW, is located close to the Shrunken-2 gene (sh2; Dickinson and Preiss 1969) at position 216.4 Mb on chromosome 3; this gene helps control starch levels in the maize endosperm. Three QTLs, qKT1, qKW4, and qKW5-2, included or were close to three maize orthologs of cloned rice genes, ZmGS3 (Li et al. 2010a), ZmGW2-CHR4, and ZmGW2-CHR5 (Li et al. 2010b), respectively. Notably, qKW5-2 for KW and qKL5-2 for the MPH for KL were mapped in the same position. These findings suggested that the underlying loci for the final kernel yield may affect kernel development after pollination. Moreover, there may be a common genetic mechanism of kernel-related traits or such causal relationships across different backgrounds. Furthermore, interval co-mapping with known genes may be useful for clarifying the specific phenotypes associated with these genes. Future studies will need to verify these potential relationships.

Dominance effects account for the MPH for kernel-related traits

Dominance (Davenport 1908; Bruce 1910), overdominance (Shull 1908; East 1908), or epistasis (Powers 1944; Williams 1959) are genetic effects that have been used to explain the genetic mechanism underlying heterosis. In the current study, dominance was exhibited by over half of the QTLs for kernel-related traits. The total PVE of the heterotic loci for KT, KL, and HKW was more than 39%, and higher than that in the RIL and IF2 populations. However, the total PVE of the QTLs for KW and VW in the IF2 population was more than 43%, and much higher than that in the RIL population and that for the MPH for KW and VW. These results suggested that the low degree of dominance contributed to the heterosis for kernel-related traits, and are consistent with the phenotypic differences between the F1 and parental lines. However, no EPIs were detected for MPH. Thus, the genetic basis for kernel-related traits and the heterosis for these traits with low heritability (data not shown) may be mainly explained by single-locus QTLs. However, statistical and experimental errors may have substantially influenced our ability to detect EPIs for the heterosis for kernel-related traits. Compared with the results of our study, an investigation by Frascaroli et al. (2007) revealed a lower total PVE for the heterotic loci and EPIs for HKW following the Reid × Lancaster hybridization. Tang et al. (2010) proposed that the dominance effects of heterotic loci at the single-locus level as well as the AA interactions are important genetic factors related to the heterosis for HKW. Additionally, Guo et al. (2014) concluded that the cumulative dominance effects, including dominance, overdominance, and epistasis, were responsible for most of the heterosis for HKW. Therefore, the heterotic loci for kernel-related traits at the single-locus level appear to be important for the final kernel yield. These findings may also be relevant for future attempts at fine-mapping the heterotic loci for kernel-related traits. Moreover, the weakly significant correlations between total heterozygosity and the MPH for KT, KL, and VW suggest that the overall heterozygosity minimally affects kernel-related traits and heterosis (Hua et al. 2003), which is inconsistent with the results of studies by Frascaroli et al. (2007) and Larièpe et al. (2012). Other earlier investigations confirmed that the detection of QTLs is biased by dominance, epistasis, and the linkage disequilibrium between QTLs (Melchinger et al. 2007; Schön et al. 2010; Tang et al. 2010; Guo et al. 2014). In the current study, only six QTLs were identified in the RIL and IF2 populations as well as in the MPH dataset. Additionally, 94% of the QTLs were specific for the MPH or the populations, implying heterosis and performance per se are controlled by different genetic mechanisms (Tang et al. 2010; Wei et al. 2016; Wang et al. 2018). A more thorough examination of the type of gene action revealed a low degree of dominance for most of QTLs in the IF2 population. For example, qKL4 and qKW9-3 in the IF2 population, with |D/A| > 3, were also identified in the MPH dataset, but not in the RIL population, indicating that loci with large dominance effects result in the biased detection of additive effects. The QTL qWKEL2-4, which exhibited an EPI and QEI, was only identified in the IF2 population, suggesting that EPIs and QEIs may influence the detection of QTLs. Inconsistencies in the QTLs may be partly due to the types of gene action, and there may be identical genetic models of action for the MPH and hybrid performance per se (Guo et al. 2014).

Cumulative influence of kernel-related traits on the heterosis for yield

Similar to a previous study (Wang et al. 2018), we revealed low-to-moderate significant correlations among the MPH for kernel-related traits, including r(KL, KT), r(KL, KW), r(HKW, KL), and r(HKW, KW). As expected, ten QTL clusters were associated with the overlapping relationships among the heterosis for diverse traits. However, few consistent QTLs were observed to simultaneously affect the trait means and the MPH. On the basis of significant correlations and pleiotropic regions, the heterosis for kernel-related traits is not completely trait-specific (Flint-Garcia et al. 2009). We also noticed that the current F1 hybrid between Ye478 and 08-641 exhibited high heterosis for kernel yield, with a considerably higher kernel weight per ear and kernel number per row when compared with the parental lines (data not shown). Nevertheless, there were no significant differences in the KT, KL, KW, VW, and HKW between the F1 hybrid and the inbred parent Ye478. It seems that the high heterosis for yield may be due to the cumulative influence of the heterosis for kernel size (Flint-Garcia et al. 2009), which may help to explain why the ratio of the loci exhibiting overdominance for ear weight per ear, kernel weight per ear, and kernel number per row was greater than that for the kernel-related traits.

QTL pleiotropy influenced the kernel-related traits and heterosis

Many studies have addressed the QTL pleiotropy for yield-related traits and for the MPH for these traits (Frascaroli et al. 2007; Chen et al. 2017; Li et al. 2017; Zhang et al. 2017; Wang et al. 2018). In this study, we detected 20 QTL clusters, some of which were mapped to the same positions of clusters derived from other heterotic patterns (Wang et al. 2018). However, few investigations have focused on the heterosis for kernel-related traits. The QC2-1 region affected the MPH for WKEL and HKW and overlapped with the pleiotropic region for the MPH for KT, KL, KW, and HKW between 18 and 24 Mbp on chromosome 2 in the progeny of the crosses from Reid × TSPT (Wang et al. 2018). The QC6-1 region for KL and the MPH for WKEL and KW overlapped with MQTL-42, which controls ear-related traits and kernel-related traits (Chen et al. 2017), and is co-localized with hKL6a for the heterosis for KL (Wang et al. 2018). At bin 9.01-9.02, QC9-1 was observed to affect the VW and MPH for HKW, and overlapped with the heterotic loci for KT and HKW between 13 and 16 Mbp on chromosome 9 (Wang et al. 2018). These findings are indicative of a likely common genetic basis for the heterosis for kernel-related traits between PA × PB and PA × TSPT, and may be useful for future maize breeding based on marker-assisted selection. Additionally, overlapping regions were detected for the trait means and the MPH in different studies. The heterotic clusters QC2-4 and QC2-5 were co-localized with the meta-QTLs for kernel-related traits reported by Chen et al. (2017). Moreover, QC2-5 for the MPH for KT and VW overlapped with qKD2b for kernel density between 209 and 215 Mbp on chromosome 2 at 29 days after pollination (Zhang et al. 2016). Furthermore, the QC8 region for the MPH for KT, HKW, and WKEL overlapped with qKD8a for kernel density near position 164 Mbp on chromosome 8 at 50 days after pollination (Zhang et al. 2016). This region also includes the meta-QTLs for grain yield, ear-related traits, and kernel-related traits described by Chen et al. (2017). Similarly, the QC10 region, which is associated with the MPH for KL and WKEL, was previously identified as a region influencing grain yield, ear-related traits, and kernel-related traits (Chen et al. 2017) and was mapped to an overlapping and pleiotropic region affecting kernel weight and kernel density at three kernel-development stages (Zhang et al. 2016). These findings imply there may be some overlap in the genetic mechanisms underlying kernel-related traits and the heterosis for these traits. Furthermore, the heterotic loci for final kernel size may be associated with the loci responsible for kernel development.

In summary, heterotic loci at the single-locus level with a low degree of dominance are considerably important for the heterosis for kernel-related traits in the IF2 population analyzed in this study. We also determined that the genetic mechanisms influencing kernel-related traits and the MPH for these traits are likely not completely independent. Additionally, pleiotropic and heterotic regions (bins 2.03, 6.04–6.05, and 9.01–9.02) were repeatedly observed across the heterotic patterns ‘Reid × PB’ and ‘Reid × TSPT’ in an earlier study. These findings may provide important insights into the genetic basis for the MPH for kernel-related traits. These results related to the heterosis for kernel size may help to characterize the heterosis for total grain yield and contribute to the genetic dissection of heterosis in future studies.