Impact of epistasis and QTL×environment interaction on the accumulation of seed mass of soybean (Glycine max L. Merr.)

Summary

The accumulation of seed mass in soybean is affected by both genotype and environment. The aim of the present study was to measure additive, epistatic and quantitative trait locus (QTL)×environment (QE) interaction effects of QTLs on the development of 100-seed weight in a population of 143 F₅ derived recombinant inbred lines (RILs) developed from the cross between the soybean cultivars ‘Charleston’ and ‘Dong Nong 594’. Broad-sense heritability of 100-seed weight from 30 days (30D) to 80D stages was 0·58, 0·52, 0·62, 0·60, 0·66 and 0·57, respectively. A total of 17 QTLs with conditional additive (a) effect and/or conditional additive×environment interaction (ae) effect at specific stages were identified in ten linkage groups by conditional mapping. Of them, only 4 QTLs had significant a effect or ae effect at different stages of seed development. Among QTLs with significant a effect, five acted positively and six acted negatively on seed development. A total of 35 epistatic pairwise QTLs of 100-seed weight were identified by conditional mapping at different developmental stages. Five pairs of QTL showed the additive×additive epistatic (aa) effect and 16 QTLs showed the aa×environment interaction (aae) effect at the different developmental stages. QTLs with aa effect as well with their environmental interaction effect appeared to vary at different developmental stages. Overall, the results indicated that 100-seed weight in soybean is under developmental, genetic and environmental control.

1. Introduction

Seed weight, measured as mass per 100 seeds, is an important yield component of soybean and is normally positively correlated with seed yield (Burris et al., 1973; Smith & Camper, 1975; Burton et al., 1987). Seed weight is polygenically controlled and can range from 6 to 55 g per 100 seeds (Maughan et al., 1996). It has been critical for the production of many oriental specialty food items, including tofu, natto, sprout and miso (Mian et al., 1996). For example, soybean seed used for sprouts should possess small seed weight, whereas soybean seed used for tofu should have large seed weight. The demand for these products in the international market was steadily increasing at a rate of 3–5% every year (Griffis & Wiedermann, 1990). Thus, the seed weight of soybean was increasingly emphasized by breeders.

A variety of quantitative trait loci (QTLs) associated with soybean seed weight were identified in the past decade (Mansur et al., 1996; Mian et al., 1996; Hoeck et al., 2003; Zhang et al., 2004a; Panthee et al., 2005), and soybean breeders have made progress in breeding programmes based on these QTLs. However, the genetic basis that underlies seed formation and development remains unclear, since the trait is controlled by multiple genes at different growth stages. Zhu (1995) proposed a conditional statistical method for calculating the dynamics of the causal genetic effects and variance components in developmental quantitative traits. Using this method, Atchley & Zhu (1997) analysed conditional epigenetic variability in mice, and Yan et al. (1998) detected QTLs with the developmental behaviour of plant height in rice. More recently, the association of developmental behaviour of quantitative traits, including morphological and seed quality traits, with molecular markers in soybean was reported (Sun et al., 2006; Li et al., 2007).

Soybean seed weight is a complex trait that is influenced by sets of genes during plant development. The genetic architecture of the complex trait consists of not only the actions of genes in a single locus, but also the inter-locus interactions. More and more evidence indicated that the complexity of the genetic architecture could be largely attributed to epistasis effect, which plays a significant role in heterosis, inbreeding depression, adaptation, reproductive isolation and speciation (Yang & Zhu, 2005). Evolution studies have elucidated that assembly and maintenance of favourable epistatic combinations adapted to a specific environment are a major mechanism of adaptation in various plant species (Allard, 1996). As was taken as an obvious example, the reproductive isolation between species arises through the accumulation of complementary genes that have no effect within a taxon, but which have a deleterious phenotypic effect when combined with genes from other taxa (Lynch, 1991; Orr, 1995; Hutter, 1997). Li et al. (1997) analysed inter-gene pool populations derived from crosses between indica and japonica cultivars of rice (Oryza sativa L.) using markers throughout the genome; the results showed that the performance of grain yield components is conditioned by high levels of digenic epistatic interactions in addition to the main effects of individual loci. Kulwal et al. (2005) analysed the grain protein content in hexaploid wheat using two different populations, and the results showed that a sizable proportion of the genetic variation was respectively due to interaction effects (28·59 and 54·03%) and QTL main effects (7·24 and 7·22%). William & Paul (2002) analysed the control of seed yield and other agronomic traits in the common bean using recombinant inbred lines (RILs) and revealed that both the main effect and epistatic QTL effect affected these traits. These results (Li et al., 1997; William & Paul, 2002; Kulwal et al., 2005) suggested that genetic variation is controlled by genes (QTLs) interactions to a certain extent.

QTL×environment (QE) interaction is another important component affecting quantitative traits. QE interaction reduces the association between phenotypic and genotypic values, and leads to variable levels of the significance of QTL effects across environments (Hayes et al., 1993; Romagosa et al., 1996). Paterson et al. (1991) analysed three traits in F₂ population of a tomato cross and found that only 4 of 29 QTLs were detected in all three environments. Lu et al. (1996) analysed six important agronomic traits in rice using a set of double haploid (DH) lines and reported that only 7 of 22 QTLs were significant in all three environments. Zhuang et al. (1997) analysed yield components and plant height in rice using F₂ lines and found that only 17 of the total 44 QTLs were detected in more than one environment. Yan et al. (1998) and Cao et al. (2001) reported that obviously QE interaction influences the development of plant height in rice. In soybean, QTLs for plant height and lodging were less consistent across environments, but were more consistent for maturity, indicating that QE interaction is trait-dependent (Lee et al., 1996). These studies suggested that individual QTLs are sensitive to changes of the environment and that QE interaction plays an important role in affecting quantitative traits.

The impact of epistatic effect and QE interaction effect on plant height development of rice has been analysed by Cao et al. (2001). However, little information was available on soybean developmental behaviour. Sets of genes are expressed selectively at different growth stages of seed development and are influenced by both genotype and environment; hence, we found it necessary to investigate the epistatic effects as well the QE interaction effect during seed development of soybean by combining the statistical procedures for analysing conditional genetic effects (Zhu, 1995) and the QTL mapping method based on mixed model approaches (Wang et al., 1999; Zhu, 1999). The temporal gene expressions including additive (a) effect, additive×additive epistatic (aa) effect and their QE interaction effect on seed weight are also discussed in the present study.

2. Materials and methods

(i) Plant materials and field trials

The mapping population, consisting of 143 F₅ derived RILs, was advanced by single-seed descent from crosses between ‘Charleston’ (provided by Dr R. L. Nelson, NSRL, University of Illinois, Champaign, Urbana, IL, USA) and ‘Dong Nong 594’ (developed by Northeast Agriculture University, Harbin, China). The RILs were extracted at F₅ generation, advanced without selection for seed size and maturity, and used for this study at F_5:9, F_5:10 and F_5:11.

The RILs and their parents were grown in a randomized complete block design with three replications at Harbin, China (45°N, fine-mesic chernozen soil) in 2004, 2005 and 2006. Rows were 3 m long with a space of 6 cm between two plants, and two-row plots were used. The field location was different each year, soil types differed slightly, planting dates differed by 2 days, the herbicides acetochlor and chlorimuron-ethyl were applied in different years, and soybean was rotated with corn. Furthermore, mean temperature and rainfall varied each year (23·1°C, 477·6 mm in 2004; 24·9°C, 569·1 mm in 2005; and 27·4°C, 544·8 mm in 2005). Therefore, the environments in the 3 years were quite diverse.

Each plot for a single genotype provided 20 plants as seed donors per time point and there were three replications of the two row plots. Pods were picked from five to seven nodes of the main stem every 10 days from 30 days after flowering until maturity. The 30 day (30D) sample represented the R2 stage and the 80D sample represented the R8 stage of growth with intervening stages with about 10D intervals. Seeds were dried for 30 min in an oven at 105°C and continuously dried at 50–70°C until the seed weight was stable.

(ii) Construction of the genetic linkage map

In a previous study (data not shown), one genetic linkage map including 164 SSR markers and 35 RAPD markers was constructed using 143 F₅ derived RILs from the cross between ‘Charleston’ and ‘Dong Nong 594’. The order of most markers is consistent with Cregan's map (Cregan et al., 1999). This genetic linkage map covered 3067·28 cM and the average distance between markers was 15·65 cM with the longest distance being 48·8 cM and the shortest distance being 0·5 cM. The average number of markers on each linkage group was 9·7 with an average length of 153·36 cM.

(iii) Statistical analysis

Wang et al. (1999) developed a program (QTLMapper version 1.0) to analyse QTLs with a and aa effects, as well as their environmental interaction effects on the RIL population at the harvesting stage. The phenotypic value of the kth RIL line in environment h can be partitioned by the following mixed linear model (Zhu, 1999):

(1)

The meaning of each parameter is as described in Wang et al. (1999) and Luo et al. (2001) : y _hk is the phenotypic value of a quantitative trait measured on the kth RIL in environment h; μ is the population mean; a _i and a _j are a effects (fixed effects) of the two putative QTLs Q _i and Q _j, respectively; aa _ij is the aa effect (fixed effect) between Q _i and Q _j; , and are coefficients of QTL effect derived according to the observed genotypes of the markers M _i−, M _i+ and M _j−, M _j+ flanking the QTLs; is the random effect of environment h with the coefficient ; and are the random ae effects with coefficients and for Q _i and Q _j, respectively; is the random aa×environment interaction (aae) effect with the coefficient ; is the effect of marker f nested within the hth environment with coefficient ; is the effect of marker×marker interaction nested within the hth environment with coefficient ; and ε_hk is the residual effect. The marker factors and in the model are used to absorb a and aa effects of background QTLs (additional segregating QTLs other than the loci examined).

Conditional QTL analysis was conducted with the phenotypic value at time t, given the phenotypic behaviour at time (t−1), using QTLMapper version 1.0 (Wang et al., 1999). Like that in eqn (1), the conditional value y _{hk(t/(t−1))} can be partitioned as

(2)

with all the parameters defined as conditional effects. The QTLs detected by conditional mapping will reflect the net expression of genes during the time period from time (t−1) to time t, independent of the genetic effects before time (t−1).

The conditional phenotypic value y _{hk(t/(t−1))} of 100-seed weight behaviour was obtained by the mixed model approaches for the conditional genetics of developmental quantitative traits (Zhu, 1995). The environment effect or replication effect is assumed to be random. However, the three environments/replications are not a random sample, due to year, field, population and other conditions. So the likelihood-ratio threshold was chosen as α=0·01 for claiming putative QTLs, the genetic effects of which were further tested by a t-test with the jack-knifing re-sampling procedure. QTL was presented when genetic main effects (a and aa effects) or QE interaction effects (ae and aae effects) were significantly different from zero (P⩽0·01).

Broad-sense heritability of 100-seed weight was computed as h ²=h _g² /((h _g²+h _e²)/n), where h _g² and h _e² are the estimates of genetic and residual variance, respectively, derived from the expected mean squares of the variance and n is the number of replications (Blum et al., 2001).

3. Results

(i) Phenotypic variation

Phenotypic values of 100-seed weight at different developmental periods across diverse environments were evaluated at Harbin, China, for 2004, 2005 and 2006 (Table 1). The differences between the two parents were significant at all stages measured across environments. The trait values for ‘Dong Nong 594’ were higher than those of ‘Charleston’ across environments. In contrast, 100-seed weight variation for 143 RILs across diverse environments was not significant. Both skew and kurtosis values of 100-seed weight were less than 1·0 at all growth stages measured in diverse environments, suggesting that the segregation of this trait fits a normal distribution model. Broad-sense heritability of 100-seed weight for 30D to 80D stages was 0·58, 0·52, 0·62, 0·60, 0·66 and 0·57, respectively.

Table 1. Statistical analysis of mean 100-seed weights (grams) at different days after pollination (D) for the parental cultivars and the F₅ derived RIL population. The means represent pods gathered from 5–7 nodes of each of 12 plants per genotype and from two plots per year. The experiment was conducted over 3 years, all in different fields at Harbin, China

CV, coefficient of variation.

(ii) Analysis of QTL epistasis effects during seed development

Both aa and aae effects were analysed using QTLMapper version 1.0 along with a and ae effects. A total of 35 epistatic pairwise QTLs were identified by conditional mapping in different developmental stages (Table 2). Of them, epistatic effects of three pairs of QTLs (swC2_1-swD1b_2 at 40D, 60D and 70D; swC2_1-swL_1 at 50D, 60D and 80D; and swC2_3-swD1b_1 at 30D, 40D and 60D) were detected at three stages. Epistatic effects of seven pairs of QTLs (swA1_1-swC2_3 at 40D and 70D; swC2_1-swC2_3 at 30D and 40D; swC2_1-swD1b_1 at 30D and 40D; swC2_1-swD1b_3 at 30D and 80D; swC2_3-swD1b_3 at 30D and 80D; swC2_3-swE_2 at 40D and 70D; and swD1b_1-swE_2 at 60D and 70D) were identified at two stages. Others could be identified at only one stage. This might indicate that aa effect existed mostly for a short time period, so that they would hardly be observed during different developmental stages. This was implied by the fact that aa effects were contributed by transient gene expression, but a effects were contributed by continuous gene expression.

Table 2. Estimated epistatic (aa) and epistasis×environment interaction (aae) effects of seed weight QTL at six different stages for 2004, 2005 and 2006 at Harbin, China

* P<0·01.

** P<0·005.

aae was an important component of the total QE interaction effects. A total of 35 pairs of QTLs were detected with conditional epistatic effects, 16 pairs having only aae effect, and five pairs having only aa effect. Other pairs had both aa and aae effects (Table 2). These results indicated that environment could greatly affect the gene expression with epistatic effects during quantitative trait development.

(iii) Analysis of QE interaction during seed development

A total of 17 QTLs with conditional a and/or ae effects at some specific stages were identified in ten linkage groups by conditional mapping (Table 3). Of them, 13 QTLs had significant a effect at the 0·01 or 0·005 level. Five QTLs (swA1_2 at 50D and 80D stages; swC2_2 from 30D to 80D stages; swC2_3 at 30D, 40D, 60D and 70D stages; swD1b_2 at 40D stage; swL_1 at 60D stage; and swM_1 at 40D stage) had positive effects on seed development and six QTLs (swA1_1 at 70D and 80D stages; swA2_1 at 40D, 50D and 70D stages; swE_1 at 50D and 80D stages; swE_2 at 40D and 60D stages; swF_2 at 60D stage; and swG_1 at 50D and 70D stages) had negative effects on seed development, whereas others inconsistently had positive or negative effects at different stages. Four QTLs (swA1_2 at 50D and 80D stages; swE_1 at 50D and 80D stages; swG_1 at 50D and 70D stages; and swM_1 at 40D stage) had significant a effect, but no significant ae effect, and only QTL swC2_2 (from 30D to 80D stages) had significant a effect, which affected seed development during all development stages. The higher seed weight parent, ‘Dong Nong 594’, contributed alleles (QTL swC2_2, QTL swC2_3 and QTL swM_1) for increasing seed weight at different stages, but QTL swA1_1 and QTL swA2_1 decreased seed weight at different stages. QTL swC2_1 increased seed weight at 30D and 70D stages, but decreased seed weight at 40D and 50D stages, suggesting that the impact of some QTLs was different at the different development stages.

Table 3. Estimated additive (a) and additive×environment interaction (ae) effects of seed weight QTL at six different stages for 2004, 2005 and 2006 at Harbin, China

* P<0·01.

** P<0·005.

^a S.E.M.: mean±S.D./, where N is the number of each allele.

A total of 13 QTLs possessed significant ae effect at the different developmental stages (Table 3). Of them, eight QTLs (swA2_1 at 40D stage; swC1_1 at 50D stage; swC2_1 at 50D stage; swC2_2 at 30D, 40D, 60D and 70D stages; swD1b_1 at 30D stage; swD1b_2 at 60D stage; swD1b_3 at 30D stage; and swF_1 at 50D stage) had significant ae effect at different stages in all three environments, 12 QTLs (swA1_1 at 40D and 70D stages; swA2_1 at 50D stage; swC1_1 at 60D stage; swC2_1 at 30D, 70D and 80D stages; swC2_2 at 50D stage; swC2_3 at 40D stage; swD1b_1 at 40D, 60D and 70D stages; swD1b_2 at 70D stage; swD1b_3 at 80D stage; swE_2 at 40D and 60D stages; swF_2 at 60D stage; and swL_1 at 60D and 80D stages) had significant ae effect in two environments, and nine QTLs (swA1_1 at 80D stage; swA2_1 at 70D stage; swC2_1 at 40D, 60D and 80D stages; swC2_2 at 80D stage; swC2_3 at 30D, 60D and 70D stages; swD1b_2 at 40D stage; swE_2 at 70D stage; swF_1 at 80D stage; and swL_1 at 50D stage) had ae effect only in one environment. Four QTLs (swC1_1 at 50D, 60D and 80D stages; swD1b_1 at 30D, 40D, 60D and 70D stages; swD1b_3 at 30D and 80D stages; and swF_1 at 50D and 80D stages) had significant ae effect but no significant a effect. Five QTLs (swA1_1 at 40D, 70D and 80D stages; swA2_1 at 40D and 50D stages; swD1b_1 at 30D, 60D and 70D stages; swE_2 at 40D, 60D and 70D stages; and swL_1 at 50D, 60D and 80D stages) contributed a positive ae effect in seed weight increment at different developmental stages. One QTL (swC1_1 at 50D and 80D stages) showed a negative ae effect and other QTLs showed positive or negative ae effect on seed development in 2004. Three QTLs (swC2_2 from 30D to 80D stages; swD1b_2 at 40D, 60D and 70D stages; and swF_1 at 50D and 80D stages) showed increased ae effect, four QTLs (swD1b_1 at 30D and 40D stages; swD1b_3 at 30D and 80D stages; swF_2 at 60D stage; and swL_1 at 60D stage) showed decreased ae effect and other QTLs showed increased or decreased ae effect in 2005. Two QTLs (swE_2 at 40D and 60D stages; and swL_1 at 80D stage) showed increased ae effect, four QTLs (swA1_1 at 70D stage; swC2_1 at 50D and 80D stages; swF_1 at 50D stage; and swF_2 at 60D stage) showed decreased ae effect and other QTLs showed increased or decreased ae effect in 2006. Only one QTL (swE_2 at 40D and 60D stages) showed increased ae effect at different developmental stages in 2 years (2004 and 2006).

A total of nine QTLs (swA1_2 at 70D and 80D stages; swA2_1 at 40D and 50D stages; swC2_1 at 30D, 40D, 50D and 70D stages; swC2_2 from 30D to 80D stages; swC2_3 from 30D to 70D stages; swD1b_2 at 40D stage; swE_2 at 40D and 60D stages; swF_2 at 60D stage; and swL_1 at 60D stage) were detected with both a and ae effects at different developmental stages (Table 3).

4. Discussion

The conventional statistics revealed that the development of some quantitative traits like morphological traits was controlled by the interactions of many genes that might behave differentially during different growth periods, and that gene expression was modified by interactions with other genes and by environment (Atchley & Zhu, 1997; Vodkin et al., 2004). Previous works on QTL analysis of seed quantitative traits of soybean have concentrated on QTLs and QE interaction measured at the harvesting stage (Mansur et al., 1996; Mian et al., 1996). But no information has been available so far on the impact of epistasis and QE epistasis on seed weight at different developmental stages of soybean. In the present study, QTLs with a and aa effects as well as with their environmental interaction effects, were shown to vary at different stages of seed development of soybean.

QE interaction was an important component affecting quantitative traits. Understanding QE interaction is of importance to the breeding programme and to marker-assisted selection and to map-based gene cloning. Usually, QE interaction effect is treated as random effect, especially in different years. This implies that QTLs would be affected by different environments. QE interaction has been reported by comparing QTLs detected in specific environments (Paterson et al., 1991; Stuber et al., 1992; Lu et al., 1997). However, QTLs detected separately in each environment was not the real QE interaction (Jansen et al., 1995). The mixed model approaches for QTL mapping can provide unbiased prediction on QE interaction when the experiment was conducted under multiple environments (Zhu, 1999). Regarding 100-seed weight during seed development, four QTLs (swA1_2, swE_1, swG_1 and swM_1) had only a effect in different developmental stages, and four QTLs (swC1_1, swD1b_1, swD1b_3 and swF_1) had only significant ae effect. Other QTLs had both a and ae effects at different developmental stages. QTLs with only QE effects were mainly determined by environments; therefore marker-assisted selection (MAS) using this type of QTL was ineffective. This suggested that QTLs with a effect should be applied in MAS rather than QTLs with QE effects.

A total of six QTLs with significant a effect (swA1_2, swC2_2, swC2_3, swD1b_2, swL_1 and swM_1) were positive with seed sizing up, and six QTLs (swA1_1, swA2_1, swE_1, swE_2, swF_2 and swG_1) were negative with seed development at different stages. The a effect of other QTLs varied with seed development. For example, QTL swC2_1 was served to increase seed weight at 30D and 70D stages, but to decrease seed weight at 40D and 50D stages. The finding that QTL with significant a effect was positive/negative to the development of seed weight seemed to meet different breeding goals in MAS than other types of QTLs. The parent (Dong Nong 594, with bigger seed) contributed alleles for increasing seed weight at QTLs swC2_2, swC2_3 and swM_1 at different developmental stages, but for decreasing seed weight at QTLs swA1_1 and swA2_1 at different developmental stages. If all of QTLs affecting the development of seed weight is in the same direction, it will greatly promote selection accuracy in seed weight by the accumulation of gene effects.

Epistasis among different loci played an important role in plant evolution (Lynch, 1991; Orr, 1995; Hutter, 1997). Recently, QTL mapping suggested that epistasis was the main genetic basis of complex traits (Li et al., 1997; William & Paul, 2002; Hyten et al., 2004; Kulwal et al., 2005). In the present study, 35 pairs of QTLs with epistasis effect were detected; five pairs of them (swD1b_2-swM_1, swD1b_2-swF_2, swD1b_2-swL_1, swD1b_2-swG_1 and swE_2-swG_1) showed only aa effect and 16 pairs of them showed only aae effect at different developmental stages (Table 3). This result further indicated that epistasis on seed weight of soybean was ubiquitous. In the present study, most of the QTLs shared epistasis effect with other QTLs. However, swC2_2 with both a and ae effects was not associated with other QTLs and independently affected the development of seed weight.

In the past, the phenotypic values of 100-seed weight were only measured at the final stage for QTL analysis in soybean (Mansur et al., 1996; Mian et al., 1996; Hoeck et al., 2003; Hyten et al., 2004; Zhang et al., 2004a; Panthee et al., 2005). Hoeck et al. (2003) used three populations to identify seed weight QTL and found that Satt322 in MLG C2 was associated with seed weight. The QTL swC2_3 in the present study was located at chromosomal locations similar to those identified by Hoeck et al. (2003). Watanabe et al. (2004) identified QTLs associated with seed weight near Satt157 in MLG D1b+W, which was similar to swD1b_1 in the present study.

For marker-assisted selection, the simultaneous application of many markers, taking into account epistasis, will lead to a highly effective selection of phenotype (Watanabe et al., 2004). The epistasis impact on some traits of soybean has been reported earlier (Tukamuhabwa et al., 2002; Watanabe et al., 2004; Primomo et al., 2005). Tukamuhabwa et al. (2002) studied pod shattering using diallel cross of ten pure breeding lines; the results showed that epistatic effect remarkably influenced pod shatter in soybean. Primomo et al. (2005) analysed isoflavone content in soybean seed through 207 RILs from the cross between ‘AC756’ and ‘RCAT Angora’ using SSR markers; the results suggested that 23 pairs of epistatic QTLs remarkably affected isoflavone content. Watanabe et al. (2004) studied reproductive development and seed quality trait through F₈ derived RILs from the cross between ‘Misuzudaizu’ and ‘Moshidou gong 503’ using SSR markers; the results indicated that somes pair of epistatic QTLs influenced flower time, maturity and reproductive period, especially two pairs of epistatic QTLs impacting seed weight.

When a population of small size becomes separated from a larger parental population, the founding event will be effective to produce a new genetic environment that leads the separated population to better adapt to the population bottleneck (Templeton, 1979, 1980; Gavrilets & Hastings, 1996). This phenomenon in which, physiologically, interaction genes re-adapt to one another in new genetic alignments is called the genetic ‘revolution’ by Mayr (1954). Once genotypic frequencies in the populations are disturbed by selection, or population bottleneck, such a cryptic molecular variation can act as a potential source of strong phenotypic effects via epistasis (Carson & Templeton, 1984; Goodnight, 1987, 1988, 1995; Tachida & Cockerham, 1989; Whitlock et al., 1995). Most of the QTLs identified in different developmental stages have epistatic effect with other QTLs in the same or different linkage map in the present study (Tables 2 and 3). Although epistatic effect impacting seed development of a population was not accurately estimated, the results of the present study demonstrated that epistatic effect impacted seed development, not only at the harvest period but also at different development periods.

The simulations of 95% confidence interval associated with the estimation of QTL position for F2, DH and RIL populations fell below 30 cM and ranged from 4 to 55 cM (Bandaranayake et al., 2004). For example, the QTLs in an RIL population of Arabidopsis thaliana having a narrow confidence interval (4·6 cM for plant height, and 6·3 cM for days to flowering) controlled a large proportion of the variability for a given trait (73% variability of plant height at 47 days and 75% variability at days to flowering). However, other QTLs having a large confidence interval (23 cM) only explain a small amount of the variation (16%) for a given trait. In the present study, average distance between markers was 15·65 cM with the longest distance being 48·8 cM and the shortest distance being 0·5 cM and mostly fell below the range of 95% confidence interval for RIL population, which made the results of the present study reliable, although the position and variability of some QTLs, located in large confidence interval, may imprecisely be estimated.

In general, QTL mapping based on data collected from a relatively small population is likely to detect the loci with large effects and to miss the loci with small effects (Edwards et al., 1992; Tanksley, 1993), which may lead to type I error to a certain extent. Therefore, the number of the putative QTLs identified in the present study should be considered the minimum of all those segregating in the population. Moreover, the non-normal distribution of trait can lead to a type I error (Allison et al., 1999). In general, both skew and kurtosis values of 100-seed weight were less than 1·0 at all growth stages measured in diverse environments in the present study, suggesting that the segregation of this trait fits a normal distribution model (Table 1). However, the segregation of 100-seed weight did not absolutely fit a normal distribution model (in a few cases, both skew and kurtosis values were 1·0), which may lead to type I error to a certain extent. Furthermore, erroneously assuming a normal distribution can lead to a biased estimate of the major gene (QTL) effect (Shete et al., 2004). Densely spaced markers (close markers) were required for detecting accurate QTLs. A relatively sparse marker was used to detect QTL, especially to small effect QTL, which also could lead to type I error (Zhang et al., 2004b).