Soybean (Glycine max (L.) Merr.), grown worldwide as the major crop, enrich seed protein and oil. Nowadays, obtaining high and steady yield is the main goal to soybean researchers. Molecular markers have provided a powerful new tool for breeders to search for new sources of variation and to investigate genetic factors controlling quantitatively inherited traits. Plant height is an important factor of yield, Wilcox et al (1981) found plant height have greater effect on yield. Luo (2001) confirmed the lower plants were stronger resistance to lodging and high-yielding in the research of soybean density cultivation. Wang et al (2004) detected 5 soybean height QTLs from a BC₂F₄ lines derived from the cross of IA2008×PI468916, 4 height QTLs of position matched to yield, further verified that plant height related to yield. Currently, mapping QTLs tend to use the data of field trials with multiple years and sites, but the stability and validity of the QTL mapping still stay in the traditional quantitative genetics research stage. Therefore, research based on stability analysis of traits and quantitative genetics is necessary (Wang et al., 2007).

With the development of molecular genetics and molecular marker technology, some high-density integrated genetic maps, such as the map by Gong (2006), have been constructed, especially soymap2 with high density (Song et al., 2004), lay the foundation for soybean height QTL from fine-mapping to gene mapping. The information of 78 soybean plant height QTLs by using CIM and MIM methods were listed in the public database Soybase (http://soybase.org/) and published in recent published papers. Sun (2006) investigated the developmental behavior of plant height QTL by unconditional and conditional QTL mapping methods (Zhu, 1995). But the reports on matured soybean plant height QTL under different environment were rare.

Mining the major QTL has become a hot spot recently years. Psychologist Glass (1976) firstly widely used Meta-analysis in physic, sociology, and behavioral science, integrated and obtained the better result conveniently. Goffinet and Gerber (2000) used meta-analysis to increase their precision and validity by mathematical model to refine integrated QTLs. In soybean, Guo (2006) integrated 62 QTL associations for resistance to soybean cyst nematode in soybean and obtained 10 consensus QTLs and the corresponding markers. Qi (2009) integrated and analyzed 65 QTLs for soybean 100-SW, and 12 consensus QTLs and the corresponding markers have been obtained. These results laid the foundation for marker-assisted selection (MAS) and gene cloning in soybean.

In the present study, we aimed to detect real QTLs under different environments. Using genetic statistics software Windows QTL Cartographer Ver. 2.5 (Wang et al., 2007), we constructed a set of soybean height from the RILs in 2006~2008, which was used to study the consistency of QTLs across places and years as well as to detect real QTLs. We collected the information of mapping QTLs from the present study from many different populations and environments. Finally, we integrated these data to the reference map, 12 consensus QTLs of soybean height were obtained, which could be used for MAS of soybean height.

1 Results and Analysis
1.1 The phenotypic information in RIL
The phenotypic results of RIL population between 2006 and 2008 were shown in table 1. The difference of maternal parent in height was significant. All plant height data displayed a typical quantitative genetic model-approximate normal distribution, and it was suitable for QTL mapping (Figure 1).

Table 1 The height of the parents of RIL population between 2006 and 2008

Figure 1 The frequency distribution of soybean height of RIL population in three years

1.2 QTL mapping of height in RILs
Based on the mixed linear model approach, we analyzed the data of soybean height in 2006~2008, including CIM (Composite Interval Mapping) and MIM (Multiple Interval Mapping) methods. In this population, 4 QTLs were detected by CIM, and another 11 QTLs were detected by MIM (Table2, Table 3). Compared with different mapping methods, CIM and MIM detected twice or more times QTLs on LG B1, LG D1a, LG G, the CI deviation was small, so the real QTLs could exist on these LGs. The explained variation of all QTLs ranged from 4.00% to 59.70% with a LOD-value between 3.04 and 10.1. On LG B1, QphB1-1 was mapped between Satt509 and Satt229, its CI was 192.9~254.8 cM, explaining about 39.00% of the variation with an additive effect of 9.69; QphB1-2 and QphB1-3 were mapped between Satt251 and Satt229, CIs of them were 192.6~261.5 cM and 261.5~329 cM, explaining about 59.70% of the variation with an additive effect of 12.20; QphB1-4, QphB1-5, and QphB1-6 were mapped between Satt509 and Satt197, Satt197 and Satt251, Sat_099 and Sat_113, CIs of them were 83~121.6 cM, 135~185.9 cM, and 356.5~422.2 cM, with the same additive effect of 12.20. On LG D1a, QphD1a-1 was mapped between Sat_062 and Sat_106, CI was 198.9~206.3 cM, explaining about 10.0% of the variation with an additive effect of -10.53; QphD1a-2 was mapped between Sat_062 and Sat_106, its CI was 198.4~207.7 cM, explaining about 9.10% of the variation with an additive effect of -13.18; QphD1a-3 was mapped between Satt220 and Sat_062, its CI was 140.9~170.0 cM, explaining about 4.00% of the variation with an additive effect of -4.53, three QTLs were detected overlap of the confidence interval and QTL of soybean height maybe exist on LG D1a. On LG G, QphG-1 was mapped between Satt199 and Sat_094, its CI was 0.4~6.6 cM, explaining about 11.00% of the variation with an additive effect of -7.57; QphG-2 was mapped between Satt505 and Satt288, its CI was 0.2~17.8 cM, explaining about 13.00% of the variation with an additive effect of -4.98; QphG-3 was mapped between Satt199 and Sat_094, its CI was 0~15.7 cM, explaining about 13.80% of the variation with an additive effect of -7.16. The major QTLs of height maybe exist on LG G, the additive effect was between -4.98 and 7.57, explaining from 11.0% to 13.80% of the variation.

Table 2 The results of plant height QTL by CIM

Table 3 The results of plant height QTL by MIM

Table 4 Information of soybean height QTLs

With the method of meta-analysis, 12 consensus QTLs of soybean height were obtained and located on LG B1, LG C2, LG D1a, LG F, LG G, LG K, and LG M (Table 5). As Figure 2 showed, QTLs were integrated on LG B1, three consensus QTLs were analyzed from three, two, three original QTLs, respectively, the minimum CI could reach 0.24 cM.

Table 5 Meta-analysis of soybean height QTLs

Figure 2 Meta-analysis of height QTLs on LG B1

2 Discussion
In recent years, many studies on QTL mapping of soybean height used one-year phenotypic data, but little based on the multiple years and sites with different methods. From a statistical point of view, the accuracy of QTL position and affect could be detected if the database were analyzed in different locations and years (Jansen et al., 1995). In this research, the phenotype of Charleston has a distant genetic relationship and obvious differences result from different environment and the selected randomness of phenotype measuring. The phenotypic data of parents didn’t change the result of QTL mapping, which based on the linkage map drawn by Zhang (2004) and phenotypic data were measured from 149 individuals. It is better to try and replenish different mapping method, different environments of the same material QTL mapping, QTL×Environment (Q×E) interaction, to obtain the real QTL with genetic stability and explaining high phenotypic variation, to improve the traits and accelerate the development of breeding (Guo et al., 2003). Epistatic effects of QTLs and QE interaction effects were considered on protein and oil content in soybean by mixed linear approach (Shan et al., 2008; 2009). Based on different model, CIM and MIM were different mapping methods (Zeng, 1994; Kao, 1999). In the present study, 15 QTLs of soybean height were detected by CIM and MIM in different environments. The objective of planting under different environments is to minimize the error, QTLs were detected twice or more times would be the major QTL.

Wang and Paigen (2002) found that 18 of the 22 human HDL-C QTLs were within the murine HDL-C QTL for guiding future research on the genetic regulation of HDL concentrations and for finding gene targets for up regulating HDL levels in mice and humans. 127 plant height QTLs of maize were refined by means of "overview" analysis. At last, 40 "real" QTLs were identified (Wang et al., 2006). CI of QTLs was greatly narrowed down by the method of Meta-analysis. The “real” QTLs with precise locations were then compared with genes affecting plant height in maize and rice, and a number of candidate genes for plant height QTG were found. Based on data of soybean height from different populations and mapping methods, the method of meta-analysis was used to integrate and obtain the major QTL, shrink the confidence interval, and improve the accuracy and validity of QTL position. In present study, 78 QTLs of height that have been reported were collected, and 56 QTLs were integrated. In the end, 12 consensus QTLs and their corresponding markers were obtained respectively. 3 QTLs were detected twice or more times by CIM and MIM on LG B1, LG D1a and LG G and furthermore used in Meta-analysis. The minimum CI was shrunk to 0.24 cM and false positive decreased greatly. According to this result, it is better to select markers covering the target segment for fine-mapping and gene mining, the real QTL is important for researching on improving soybean yield.

3 Materials and Methods
3.1 Materials and methods for QTL mapping
3.1.1 Plant materials and experimental design
A total of 149 F_2:14-F_2:16 population derived recombinant inbred lines (RILs) were advanced by single-seed-descent from crosses between ‘Charleston’ (provided by Dr. Lijuan Qiu, Chinese Agricultural Academy of Science, Beijing, China) and ‘Dongnong594’ (developed by Northeast Agricultural University, Harbin, Heilongjiang, China). RILs were planted in experimental land of the Crop Research and Breeding Center of Land-Reclamation in Harbin between 2006 and 2008. The plants were cultured in a randomized experimental single-row plot (1 m in length and 0.5 m in width) for two or three repeats. The timing and frequency of cultural management procedures for the trials were consistent with soybean production practices under their respective environments. In our study, the RIL population was performed in duplicate in 2006 and 2007, whereas it was performed in triplicate during 2008.

3.1.2 Measurement of soybean height
Five plants of each line were randomly harvested and used for the phonotype values calculation. According to the "Bean Germplasm Description Specifications and Data Standards", measurement of plant height was performed by distance from cotyledon section to the top of the main stem each plant in soybean maturity, and an average of five replications was used.

3.1.3 Statistical analysis
The linkage map of RIL population was constructed by Zhang (2004). QTLs under different environments were separately mapped by software Windows QTL Cartographer Ver. 2.5. QTL position was determined with P<0.005 and LOD>3.0 as the threshold.

3.2 Materials and methods of Meta-analysis
Mapping information of soybean height QTLs, including names, traits, chromosomes, markers LGs, marker and population was collected from the public database Soybase (www.soybase.org) and recent reports. QTLs of one population for a given trait under a given environment were integrated as one experiment, and QTLs analyzed by the mean of several locations, were also integrated as one experiment. Two important parameters of QTL were the map position (most likely position and CI) and explained proportion of phenotypic variance, respectively. When the CI for QTL position was not available in literature, the formula proposed by Darvasi (1993; 1997) was used to calculate 95% CI.

Although the QTLs from different populations had different backgrounds and obtained by different methods, all QTLs were projected from original maps to the reference map, soymap2 (Song et al., 2004), by most likely position and CI with homothetic function. Calculations referred to reference (Chardon, 2004). Most projected QTLs were in a cluster in the integrated map. Based on the analysis principle of the software BioMercator 2.1, the QTL cluster was that the CI of original QTL covered half with each other, or the CI of original QTL covered another, reference to Qi (2009).

Meta-analysis was used to estimate the existence of the real QTL and CI. The basic process of meta-analysis was as follows. QTLs from many independent experiments associated on the same LG at neighboring interval were used to calculate a real QTL. This QTL could give five models, and the minimum Akaike Information Criteria (AIC) value was used to choose the best model QTL, called real QTL. The formula was estimated and described by Goffinet and Gerber (2000).

The height QTL was analyzed by software BioMercator ver. 2.1-tools-Meta analysis. The consensus QTLs were determined by the smallest AIC value.

Authors' contributions
Ya'nan Sun is first writer who perform this experiment, data analysis and write manuscript; Huaihai Luan and Chunyan Liu participated the experiment design and conducted this experiment; Zhaoming Qi and Dapeng Shan participated the field experiment; Guohua Hu and Qingshan Chen are the persons who take charge of this project, including experiment design, data analysis, writing and modifying of the manuscript, and corresponding authors of this manuscript. All authors have read and approved the final manuscript.

Acknowledgments
This study was partially supported by the ‘Transgenic Specific Technology’ program (2009ZX08009-013B), the Chinese ‘Introducing International Super Agricultural Science and Technology’ program (2006-G1(A)) and the ‘Public Agricultural research special funds projects’ (200903003).

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