Mol Genet Genomics (2010) 284:263–271 DOI 10.1007/s00438-010-0566-z
ORIGINAL PAPER
Functional mapping of quantitative trait loci associated with rice tillering G. F. Liu • M. Li • J. Wen • Y. Du Y.-M. Zhang
•
Received: 9 March 2010 / Accepted: 22 July 2010 / Published online: 6 August 2010 Springer-Verlag 2010
Abstract Several biologically significant parameters that are related to rice tillering are closely associated with rice grain yield. Although identification of the genes that control rice tillering and therefore influence crop yield would be valuable for rice production management and genetic improvement, these genes remain largely unidentified. In this study, we carried out functional mapping of quantitative trait loci (QTLs) for rice tillering in 129 doubled haploid lines, which were derived from a cross between IR64 and Azucena. We measured the average number of tillers in each plot at seven developmental stages and fit the growth trajectory of rice tillering with the Wang–Lan–Ding mathematical model. Four biologically meaningful parameters in this model––the potential maximum for tiller number (K), the optimum tiller time (t0), and the increased rate (r), or the reduced rate (c) at the time of deviation from t0––were our defined variables for multi-marker joint analysis under the framework of penalized maximum likelihood, as well as composite interval mapping. We detected a total of 27 QTLs that accounted for 2.49–8.54% of the total phenotypic
Communicated by S. Omholt. G. F. Liu and M. Li contributed equally to this work. G. F. Liu Guangdong Key Lab of Plant Molecular Breeding, South China Agricultural University, Guangzhou 510642, People’s Republic of China e-mail:
[email protected] M. Li J. Wen Y. Du Y.-M. Zhang (&) Section on Statistical Genomics, State Key Laboratory of Crop Genetics and Germplasm Enhancement, Nanjing Agricultural University, Nanjing 210095, China e-mail:
[email protected]
variance. Nine common QTLs across multi-marker joint analysis and composite interval mapping showed high stability, while one QTL was environment-specific and three were epistatic. We also identified several genomic segments that are associated with multiple traits. Our results describe the genetic basis of rice tiller development, enable further marker-assisted selection in rice cultivar development, and provide useful information for rice production management. Keywords Functional mapping Nonlinear regression model Penalized maximum likelihood Quantitative trait locus Rice tillering
Introduction Rice tillering is an important agronomic trait, as the tiller number per plant determines the panicle number, which is a key component of rice grain yield (Yan et al. 1998). High tiller numbers are often the goal for genetic improvement and breeding in rice, which seek to maximize the crop yield. Tillering of rice is a variable trait that changes over time. During changes in tillering, several characteristic biological features play important roles, and these characteristics could be optimized to manage rice production and improve its genetic foundation. For example, parameters such as the optimum tillering time provide useful information about rice production management. However, to optimize these traits the associated genes must be identified, and little is currently known about the genes that influence these parameters. To address this gap in knowledge, we used functional mapping (Ma et al. 2002) to identify quantitative trait loci (QTLs) that influence rice tillering. Over the past several decades, several studies have attempted to identify the genetic mechanism(s) of rice
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264
tillering. Early studies that used classic quantitative genetics analyses showed that the rice tiller number is controlled by different genetic mechanisms, such as equally dominant genes (Li 1977), additive genes (Murai and Kinoshita 1986; Ahmad et al. 1986), additive-dominant-epistatic genes (Perera et al. 1986), and polygenes (Xiong 1992; Xu and Shen 1991). The introduction of molecular markers has facilitated mapping of QTL in numerous species (Tanksley 1993). With this technology several QTLs or genes associated with rice tillering have been detected (Xiao et al. 1995a, b; Iwata et al. 1995; Lin et al. 1996; Wu et al. 1996; Li et al. 2003; Jiang et al. 2004; Liu et al. 2006): 17 of these loci were recently identified (http://www.gramene.org/db/mutant/search.core). Cloning of these genes and characterization of their encoded products will provide information about the genetics of tiller development. Identification of genes that influence tiller growth may ultimately help geneticists improve rice yield (Li et al. 2003; Zou et al. 2006). However, in most of these previous genetic analyses the phenotypic parameters were measured at a specific developmental stage, most often the final stage. These genetic studies only looked at one stage of rice tiller growth, as opposed to the entire developmental process, which could be influenced by numerous genes. To more thoroughly understand rice tiller development, we should investigate the dynamic expression of QTLs throughout the whole development period (Bradshaw and Settler 1995; Plomion et al. 1996; Price and Tomos 1997; Yan et al. 1998; Wu et al. 1999; Dong et al. 2004). Functional mapping is an appropriate method because it integrates a mathematical equation that describes a biological developmental process with the genetic mapping framework (Ma et al. 2002; Wu and Lin 2006). This approach can be used to elucidate the genetic mechanism(s) of rice tiller development, which occurs during two different developmental stages: the first stage is the increase in rice tiller number with time (exponential growth), and the second stage is the decrease in rice tiller number with time (development resistance). Cui et al. (2006, 2008) derived a parametric approach to model the exponential growth, as well as a nonparametric approach based on the Legendre function to model the development resistance. However, with this method, the whole development curve cannot be described by one mathematical model. Wang et al. (1982) developed a second-order ordinary differential equation model of insect developmental rate with respect to temperature, named the Wang–Lan–Ding (WLD) model. There are two important assumptions in this model: the first is that the effect of temperature on insect development obeys the logistic law in the optimum temperature range, and the second is that insect development is
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Mol Genet Genomics (2010) 284:263–271
resistant to temperature deviations from the optimum value. Thus, the biological significances of some parameters in the WLD model are similar to those in logistic model, and the parameter c in the WLD model is related to the reduced rate of insect development. These results have been verified in the applied study of Zhang and Tian (1995). More important, the curve of the WLD model accurately describes the entire developmental process of rice tillering. Therefore, the WLD model can be applied to fit the curve of rice tillering, and the estimates of parameters in the model can be used to carry out functional mapping of QTLs for rice tillering. In this study, a doubled haploid (DH) population was chosen, and the tiller number was measured at seven different stages of development. The WLD model was used to fit a curve for the rice tiller number for each plot. Four biologically significant parameters––the maximum tiller number (K), the optimum tiller time (t0) and the increase and decrease in the rates (r and c)––were used to perform functional mapping of QTLs for rice tillering under the framework of a full genetic model, which included main and environmental effects as well as environmental and epistatic interactions.
Materials and methods Mapping population The International Rice Research Institute in the Philippines kindly provided 135 DH lines that were derived from a cross between the indica cultivar IR64 and the upland aromatic japonica cultivar Azucena (Huang et al. 1994; Li et al. 1997). Because of insufficient seed for some of the DH lines, only 129 lines were used in this study. The field experiment was conducted at an experimental farm at the South China Agricultural University (23080 N, 113170 E), Guangzhou, China. The whole linkage map consists of 175 markers, which cover the 12 chromosomes in rice. The entire length of the linkage map is 2,031.6 cM, and the average distance between two markers is 12.5 cM. Phenotypic evaluation The seeds of the DH lines were soaked on 18 July 2006, and the germinated seeds were sown in a seedling bed on 22 July 2006. The seedlings were transplanted to a paddy field on 11 August 2006, planted two plants per hill, and spaced 16.7 cm 9 20.0 cm apart. Each plot consisted of 13 rows of 6.2 m with 32 plants each, and all of the plots were arranged in a completely randomized block with two replicates. The field was maintained according to local standard practices.
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After transplantation, the number of tillers was counted on August 27, September 6, September 14, September 23, October 1, October 7 and October 14, when all of the lines had headed. The plants counted were the same 20 randomly selected plants from the middle of each row. The average number of tillers in each plot for the seven stages was used for the analyses. The Wang–Lan–Ding mathematical model for rice tiller The phenotypic performance (y) of each plot during the seven measurement times (t) can be described by the equation: h t t i K min y¼ 1 exp 1 þh exp½rðt t Þ c t 0 ti max 1 exp ð1Þ c (Wang et al. 1982). In the above model, the first term is a logistic model. In the logistic model, the parameter K is the upper limit of the rice tillering number (y), and K is therefore the potential maximum of rice tillering; t0 is the inflexion point of the logistic curve, or the optimum time; and r is the increased rate. If t is close to the maximum time tmax, model K 1 exp tmaxct . This (1) becomes y ¼ 1þexp½rðtt 0 Þ means that c is related to the decrease in y at the time deviation from t0. Thus, c is the decreased rate. The DUD (do not use derivatives) method was used to estimate all of the model (1) parameters of the (t1, y1), … (t7, y7) curve for each plot with SAS software v9.13. Some outliers for the estimates of all model parameters were deleted in the detection of QTL, according to the two times standard deviation rule. We used the values 10r and 10c, not r and c, because the r and c parameters estimated were too small. QTL mapping for rice tillering Two methods were employed to conduct QTL analysis: multi-marker joint analysis and composite interval mapping (CIM) of Windows QTL Cartographer v2.5 (Wang et al. 2007). For multi-marker joint analysis, estimation of the model parameter of interest for the ith DH line at the jth replication, zij, can be described by the following model: zij ¼ l þ
R1 X
xij ej þ
j¼1
þ
m X
Phenotypic variation in the functional parameters of the tiller number
xiðR1þkÞ ak
xiðR1þkÞ xiðR1þlÞ ðaaÞkl
k¼1 l¼kþ1
þ
j¼1 k¼1
Results
k¼1
m1 X m X R1 X m X
where l is the total average; ej is the replicate effect (j = 1); R is the number of replicates; m is the number of markers; a is the additive effect; aa is the additive-byadditive interaction effects; ae is the additive-by-replicate interaction effect; x is a variable for various effects; and ei is a residual error with an assumed Nð0; r2 Þ distribution. When marker information was incomplete, that is, for dominant and missing markers, conditional probabilities of QTL genotypes were used to impute 30 completeinformation marker data sets, although 10–20 imputed data sets may suffice (Sen and Churchill 2001; Xu and Jia 2007). Each data set was analyzed under the framework of model (2) with the penalized maximum likelihood method (Zhang and Xu 2005). Samples that had an LOD statistic of greater than two were counted. A QTL that had greater than 10% of the number of samples with an LOD [2 compared to the total number of imputed samples (30) was considered real. The QTL position is an average that was weighted by the total genetic variance of the detected QTL (Dou et al. 2010). For the CIM, we adopted the standard model (Model 6) that combines stepwise forward regression with backward elimination at a walk speed of 1 cM to search for QTLs and identify co-factors. The window size was set to 10 cM, and the maximum five background markers with the highest P value were used as co-factors to control the genetic background for each trait. The critical threshold value for the LOD score obtained from 1,000 imputation experiments was used to declare the presence of a putative QTL in a given genomic region. The QTL confidence intervals (90–95%) were defined as a map interval that corresponds to one LOD decline on either side of the peak. The additive and dominant effects of each QTL for all of the traits were calculated as well. QTL nomenclature was used according to the method of McCouch et al. (1997), starting with ‘q’, followed by an abbreviation of the trait name (for example K), the name of the chromosome (number), and the number of QTLs that affect the trait on the chromosome. The detected QTLs were visually represented with MapChart 2.2 software (Voorrips 2002).
xij xiðR1þkÞ ðaeÞjk þ ei
ð2Þ
We measured the rice tiller number at seven different stages for each DH line. The data sets were used to estimate the parameters in model (1). Specifically, four parameters (K, 10r, t0 and 10c) that have biological meanings were identified, and the mean value, standard deviation,
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Mol Genet Genomics (2010) 284:263–271
Table 1 A statistical summary of the four functional parameters (10c, K, 10r, and t0) of the Wang–Lan–Ding model for the rice tiller number
Parameter
Sample size
10c
253
K
254
10r
250
t0
252
Mean
Standard deviation
Coefficient of variation (%)
Skewness
Kurtosis
2.22
1.01
45.50
0.27
1.29
10.23
3.22
31.46
1.20
2.85
1.78
0.62
35.09
0.86
1.28
5.59
3.74
67.01
1.02
1.11
Table 2 Simple and partial correlation coefficients of the functional parameters for the rice tiller number 10c 10c K 10r t0
K
10r
t0
0.0502
-0.0844
-0.0062
0.1083
-0.0883
-0.1352*
0.3462**
0.1173
0.6443**
0.5834** -0.5455**
-0.6162**
*, ** P values \ 0.05 and \ 0.01, respectively. The simple and partial correlation coefficients are listed in the top right and bottom left corners, respectively
coefficient of variation, skewness, and kurtosis for these parameters are listed in Table 1. All four parameters exhibited continuous distribution, and the skewness and kurtosis deviated from normal distribution. According to the quantitative genetics theory (Gai et al. 2003), major genes or gene interactions are responsible for these traits. Correlation analysis of the functional parameters of tiller number The simple and partial correlation coefficients for the functional parameters for the rice tiller number are listed in the top right and lower left corners of Table 2, respectively. For simple correlation analysis, only two simple correlation coefficients were significant at the 0.01 level (two-tailed): the correlation between t0 and K, which was positive, and the correlation between t0 and r, which was negative. However, for partial correlation analysis, four partial correlation coefficients were significant, including one correlation between c and r (P \ 0.05) and one correlation between K and r (P \ 0.01) besides the two previously mentioned correlations in the simple correlation analysis. Mapping QTLs that are associated with functional parameters of tiller number A total of 27 QTLs that represents 2.49–8.54% of the total phenotypic variance was detected with multi-marker joint analysis. The locations and confidence intervals of these QTLs are shown in Fig. 1. A summary of all of the QTLs that were detected with multi-marker joint analysis is listed in Table 3 (for main-effect QTLs) and Table 4 (for
123
epistatic QTLs and environment-by-QTL interaction). Table 3 also contains a summary of QTLs that was detected in both the CIM and single-marker ANOVA analysis. For the potential maximum of tiller number (K), a total of 12 significant QTLs and 1 epistatic QTL was detected with multi-marker joint analysis. Of these QTLs, five (qk-1-1, qk-4-2, qk-6-1, qk-9 and qk-12-2) are also detected in the CIM of two replications with the same approximate region and direction (Table 3). The low probabilities (2.13 9 10-8–4.77 9 10-2) obtained from the single- and two-marker ANOVA analyses validate these results (Tables 3, 4; Fig. 2). For the optimum time of tiller number (t0), a total of seven significant QTLs and one epistatic QTL was detected with multi-marker joint analysis. Of these QTLs, two (qt01-2 and qt0-1-3) are identified as well in the CIM of two replications and all QTLs had low probabilities (2.65 9 10-7–2.15 9 10-2) from the single- and twomarker ANOVA analyses (Tables 3, 4; Fig. 2). It is interesting that four QTLs (qt0-1-2, qt0-1-3, qt0-4 and qt0-6) related to t0 are very close to the four QTLs (qk-1-1, qk-1-2, qk-4-2 and qk-6-1) that are related to K. This may explain the high simple and partial correlations between K and t0. For the parameter r, a total of four significant QTLs and one epistatic QTL was detected with multi-marker joint analysis. Of these QTLs, two (qr-1-2 and qr-8) are common QTLs in the CIM of two replications, and all of the QTLs had low probabilities (2.73 9 10-6–3.82 9 10-3) with the single- and two-marker ANOVA analyses (Tables 3, 4; Fig. 2). There were some common QTLs among r, K and t0; for example, qr-1-2 was linked to qt0-13 or qk-1-2, and qr-1-1 was associated with one locus of the epistatic QTL for t0. This may explain why there is a significant correlation between r and t0, as well as r and K. For the parameter c, one significant QTL-by-environment was detected with multi-marker joint analysis, and this QTL was also identified by two-factor ANOVA analysis (P = 9.66 9 10-3) (Table 4). Although qc-4 was detected in the CIM of the second replication (Table 3), this QTL was not identified with multi-marker joint analysis. As is shown in Fig. 1, there are no common QTLs between c and the other parameters. This result implies that
Mol Genet Genomics (2010) 284:263–271 ch1
ch2
ch3
RZ67 RZ70
156.3
RZ225
72.7 82.9 94.1
pRD10B RG648 RG424
125.1 129.3 141.2 161.0 171.9 176.3 184.9
RG162 RG172 CDO544 RG653 Amy2A RG433 Cat-1
qt0-6
ch10
RG341 AF6 RG457 Sdh-1 RG463 RG901 CDO344 RG958 RG181
qk-12-2
RG1109 RZ536 Npb186
40.3 44.8 54.1 67.4 84.3 86.4 87.5 103.6 113.6
RG574 RZ816
qk-12-2
RG103
123.7 139.6 144.2
0.0 9.3
qk-12-2
qk-9
107.2
ch12
qk-12-1
CDO127 RZ638 RZ400 RG118 Adh1 RG1094 RG167 Npb44 RG247
qto-11i2
RG241 RZ625CDO93 CDO98 G2155 RG134 RZ500 RZ638
0.0 6.0 19.1 32.5 35.8 46.3 58.2 62.4 63.2
qc-11e
34.0 41.5 44.6 61.4 71.7 75.6
G1084 RG257
ch11 qt0-10
0.0 6.6
qk-9
RG757 CDO590 C711 G103 RZ206 RZ422 Amy3ABC RZ228 RZ12 RG667 RG451 RZ792 RZ404
123.8 136.6
RZ398 RG213 Amp-3 Est-2 RZ144 RZ667 Pgi-2
qk-6-2
Pgi-1 CDO87 RG910 RG418A
RG313 RZ556 RG403 RG229 RG13 CDO105 RZ649
qr-5i2
280.6 287.7 297.2 315.9
qt0-4
RZ448 RZ519
qk-4-2
232.8 248.1
qk-4-2
CDO337 RZ337A
138.8 141.5 153.7 159.6
qk-4-2
208.2 210.1
RG163 RZ590 RG214 RG143 RG620
36.0 42.6 62.2 71.0 88.4 92.7 102.3
0.0 20.8 30.9 33.6 35.4 41.1
qk-3
RZ284 RZ394 pRD10A RZ403 RG179
110.2
RG556 RZ390
qr-8
CDO59 RG711 Est-9 RZ337B CDO497 CDO418 RZ978 CDO38 RG351
33.1 38.7 49.2 62.2 69.1 74.4 77.2 80.7 96.5 107.8 133.1 145.1 156.2 162.7 178.5
RZ143 RG20 A5J560 A3E396 A18A1120 TGMS1.2 A10K250 AG8_Aro RZ617 RG978 RG1 Amy3DE RZ66 AC5 RG418B Amp-2 CDO99
0.0 2.5 3.3 16.7 24.0 60.3 71.6 81.1 86.0 93.4 112.0 120.2 121.1
qr-8
103.1 105.0 119.2 122.4 135.4 150.7 162.3 168.1 177.6
qk-7
RG769 RZ488 RG511 RG477 PGMS0.7
qk-7i2
25.8 42.3 44.0 62.6 71.7
137.1 153.0 171.7 174.2 179.2
qk-3i1
0.0 6.0
RZ574
ch9
ch8 RG773
99.8
qr-3
RZ58 CDO686 Amy1AC RG95 RG654 RG256 RZ213 RZ123 RG520
104.2 114.4 123.4 136.2 144.7 149.8 159.9 165.2 178.4
0.0 0.9
qk-6-1
RZ318 PalI
ch6
ch5 RG218 RZ262 RG190 RG908 RG91 RG449 RG788 RZ565 RZ675
qk-6-1
68.4 74.7
0.0 8.1 16.7 29.5 43.4 46.6 62.9 71.3 88.4
qk-5
RG157
RG104 RG348 RZ329 RZ892 RG100 RG191 RZ678
qc-4
40.6
ch4
0.0 7.8 21.0 27.9 37.7 40.5 58.1
qk-4-1
0.0 13.0 18.3
RG437 RG544 RG171
qt0-2
qr-1-2
qk-1-2
ch7
qt0-1-3
qt0-1-2
qt0-1-2
qk-1-1
RZ801 RG810 RG331
qr-1-1
214.2 216.7 225.9
qt0-1-3
RZ19 RG690 RZ730 qr-1-2
159.0 167.3 180.6
qk-1-1
RG345 RG381
qt0-1-1
132.7 135.2
qt0-1i1
RG472 RG246 K5 U10 RG532 W1 RG173 Amy1B RZ276 RG146
qr-1i1
0.0 19.2 35.5 40.3 45.1 60.5 76.1 91.1 95.0 98.2
0.0
267
Fig. 1 The locations of the QTLs that were identified with multimarker joint analysis and composite interval mapping. The identified QTLs are associated with the functional parameters of rice tillering in
the double haploid population that was derived from a cross between the IR64 and Azucena strains
there is no significant correlation between c and the rest of our defined parameters.
(K), the tillering rate (r or c) and the suitable tillering time (t0), although rice tillering is a single trait. These parameters are useful for both rice breeding and production management. Finally, the joint multi-QTL analysis under the framework of penalized maximum likelihood was used to detect QTLs for rice tillering, because this method has a higher power of QTL detection compared to the CIM (Table 3). As a result, a total of 27 QTLs, accounting for 2.49–8.54% of the total phenotypic variance, was detected. Nine common QTLs across multi-marker joint analysis and CIM showed high stability, while one QTL was environment-specific and three were epistatic. We also identified several genomic segments that affect multiple phenotypic traits. Our results expand the current knowledge of rice tiller genetics and enable further marker-assisted selection in rice cultivar development. However, further fine mapping and cloning of the QTLs associated with rice tillering are needed in the near future. The final productive tiller number affects the rice grain yield. It is important to obtain the potential maximum number of tillers in rice breeding because it helps us
Discussion Compared to previous studies in the detection of QTLs for rice tillering, we employed several new techniques to more thoroughly study the genetics of rice tillering. First, we utilized the WLD mathematical model to describe the whole biological development process of rice tillering, and the assumptions of the WLD model accurately reflect the growth trajectory of a rice tiller. If we had used a logistic model, which does not consider the development resistance, to fit the growth curve of a rice tiller, there would have been relatively large error, which would have resulted in decreased power of QTL detection. Although the whole biological development process has been described by Cui et al. (2006), the exponential growth and the development resistance are described separately. Then, rice tillering can be partitioned into several features: the tillering potential
123
123
6
6
7
9
qk-6-1
qk-6-2
qk-7
qk-9
a
t0
3 8
qr-3 qr-8
1
1
2
4
6
10
qt0-1-2
qt0-1-3
qt0-2
qt0-4
qt0-6
qt0-10
1
1
qr-1-2
qt0-1-1
1
qr-1-1
r
-0.56 (0.07) 2.77 (0.60) 2.73
0.69 (0.12) 4.16 (1.34) 4.04
-0.68 (0.10) 3.99 (1.16) 4.03
-1.00 (0.15) 8.66 (2.71) 8.54
-0.56 (0.05) 2.62 (0.42) 2.66
1,356.57
-0.54 (0.07) 2.91 (0.71) 2.54
1,165.47–1,177.40 -0.58 (0.09) 3.16 (0.99) 2.90
1,036.19
968.28
LOD
-0.80 (0.15) 5.37 (1.80) 5.46 -0.61 (0.09) 3.43 (1.00) 3.17
Effect
RG257
RZ398
RZ590
RZ58
RZ801
RG690
RG345
RZ574 Amp-2, CDO99
RZ801, RG810, RG331
W1
-0.55 (0.04) 2.72 (0.28) 2.56
0.13 (0.02) 2.82 (0.74) 3.93
0.14 (0.02) 2.63 (0.95) 4.37
1,036.19
859.13
330.09
214.16
167.28
132.69
0.82 (0.09) 3.25 (0.76) 4.04
-0.78 (0.07) 3.04 (0.58) 3.72
0.67 (0.02) 2.14 (0.11) 2.68
-0.99 (0.14) 4.71 (1.35) 5.97
-0.84 (0.06) 3.02 (0.44) 4.28
-0.78 (0.04) 2.79 (0.30) 3.66
504.19 0.13 (0.01) 2.56 (0.48) 3.79 1,564.39–1,577.22 -0.16 (0.02) 3.72 (0.84) 5.86
214.16–225.94
60.53
2,021.68–2,031.63 -0.74 (0.09) 5.00 (1.28) 4.69
2,002.34
RZ228, RZ12, RG667, RG451 1,658.35–1,689.24 -0.62 (0.07) 3.58 (0.80) 3.32
CDO497
RG172, CDO544
RZ398
RG13
859.13
728.36
720.29
159.02–167.28 214.16
Position (cM)
2
1,704.95 -0.72 (0.05) 2.62 (0.29) 3.15 Pk The probability is derived from the Chi-square statistic i¼1 2 ln Pi v22k
10r
5
qk-5
RZ590
RG958, RG181
4
qk-4-2
RZ262
RG418A
qk-12-2 12
4
qk-4-1
RG463
3
qk-3
RZ19, RG690 RZ801
qk-12-1 12
1 1
4
qc-4
qk-1-1 qk-1-2
10c
Marker linked to QTL
Chr Multi-marker joint analysis
K
Trait QTL
2.2E-2
4.1E-3
1.5E-3
1.4E-2
2.7E-7
5.5E-4
4.6E-3
1.0E-3 1.2E-5
2.7E-6a
3.3E-3
5.0E-8a
1.1E-3
2.1E-8
1.2E-2
2.5E-2a
1.1E-3
4.8E-2
3.4E-7
2.5E-2
2.0E-2
7.4E-6a 4.3E-5
RZ801
RG690
Amp-2
RZ801
RG958
RG667
RZ398
RZ590
RZ19
RG908
214.17 4.99
173.29 3.98
1,564.40 3.91
214.17 4.01
2.98
2.79
2.79
2.79
2.93 2.88
3.92
2.93 2,021.69 3.53
1,678.64 2.95
2.93
2.88
850.52 7.05 1,036.20 3.25
2.93
2.88
859.14 4.87
163.03 5.50
2.92
r2
Replication
9.43 2
8.43 1
8.67 1
7.92 1
-1.33 13.23 1
-1.48 13.82 2
-0.23 10.80 1
0.21 10.95 1
-1.13
-0.81
-0.82
0.80
-1.74 22.41 2
-0.96 12.04 1
-1.48 15.30 2
-0.47 11.97 2
LOD Critical Effect value
748.99 3.63
Nearest Position marker (cM)
P value Composite interval mapping
Table 3 Main-effect QTLs that are associated with the functional parameters of rice tillering that were identified with multi-marker joint analysis from 30 imputed data sets; single-marker analysis with the associated P values and composite interval mapping
268 Mol Genet Genomics (2010) 284:263–271
Mol Genet Genomics (2010) 284:263–271
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Table 4 QTL-by-replication and epistatic QTLs that are associated with the functional parameters of rice tiller that were identified with multimarker joint analysis of 30 imputed data sets, as well as the two-factor ANOVA with the associated P values QTL2 (or replicate)
Trait QTL1 Chromosome Marker linked Position to QTL (cM) 10c
Effect
Chromosome Marker linked Position to QTL (cM)
LOD
P value r2 (%)
11
RZ400
1,779.92
K
3
RZ284
541.50
7
Est-9
1,340.29
0.54 (0.06) 2.79 (0.63) 2.49 9.0E-3
10r
1
RG246
19.24
5
RZ67
1,003.71
-0.12 (0.01) 2.38 (0.33) 3.31 4.9E-3
t0
1
K5, U10
35.48–40.34 11
RZ638, RZ400
1,779.92–1,792.96
a
-0.20 (0.00) 2.19 (0.14) 3.80 9.7E-3
The probability is derived from the Chi-square statistic
Pk
i¼1
0.82 (0.08) 3.28 (0.65) 4.10 7.0E-4a
2 ln Pi v22k
Fig. 2 A graphical representation of the phenotypic effects of the identified epistatic QTLs that are associated with the three biologically meaningful parameters of the rice tiller number. a The potential maximum of rice tiller (K); b the increased rate of rice tiller (10r); and c the optimum time of rice tiller (t0)
understand the potential for rice tillering and because the final productive tiller number, 9.4 ± 2.9, is significantly related to the potential maximum tiller number, 10.2 ± 3.2 (r = 0.9785, n = 254, P \ 0.01). In addition, the optimum tiller time and the tiller rate may also provide useful information for rice production management. Therefore, the results presented here will help us understand the genetics of rice tillering and manage rice production. Genetic crosses between the IR64 and Azucena strains have been widely used to detect QTLs that are associated with rice tillering (Yan et al. 1998; Hittalmani et al. 2003). However, the methodologies used in these previous studies differ greatly from that used in this study. For example, Hittalmani et al. (2003) used the AMMI analyses of Gauch (1992) to estimate genotype-by-environment interactions
for 11 growth- and grain yield-related traits in nine locations. Yan et al. (1998) used the conditional QTL mapping method proposed by Zhu (1995) to dynamically dissect the developmental behavior of tiller number. Among 11 common QTLs identified by both conditional and unconditional methods, nine were further detected in this study. The QTL located between markers RZ730 and RZ801 may be a cluster of three QTLs that individually influence the K, r and t0 parameters. This could explain why a strong QTL at this position, derived from the pleiotropic effect of the semi-dwarfism allele sd1 on tillering (Zou et al. 2006), has never been detected. Our results also agree with the previously published results of Liu et al. (2009). All of the tiller number loci that were detected by Liu et al. (2009) on chromosomes 1, 2, 3, 6 and 8 may be associated with
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related loci on the same chromosome that influence K, r and t0. More important, of the three major QTLs that were previously identified by Cui et al. (2006), the two QTLs on chromosome 1 were also detected by the approach described here, and the third QTL on chromosome 9 is proximal to an additional QTL that was found in this study. The multi-marker joint analysis approach differs in several ways from classic methods, such as CIM (Jansen 1993; Zeng 1993) and multiple interval mapping (Kao et al. 1999). First, the joint analysis approach can jointly analyze the data sets with multiple environments or replications. This increases the sample size and allows for the detection of more QTLs compared to CIM (Table 3). Second, the main and environmental effects, as well as environmental and epistatic interactions, can be simultaneously considered in one genetic model with the joint analysis approach. A singleQTL model with the appropriate markers included as cofactors is tested once in the CIM, while in multiple interval mapping, a multi-QTL and their interaction genetic model is studied. No interaction was included in the genetic model of the CIM, and two kinds of interactions––QTL-by-environment and interaction between the loci without main effects––were not discussed in the multiple interval mapping. Although only one environment was studied, the joint analysis for multiple replications seems to be the most powerful method for QTL detection. Therefore, we recommend the joint analysis approach for future similar studies. Acknowledgments We are grateful to the Chief Editor, Dr. Stefan Hohmann; the Communicating Editor, Dr. Stig W. Omholt; the two anonymous reviewers; and Dr. Sara J. Miller of Cornell University for their constructive comments and suggestions, which significantly improved this manuscript. This work was supported by the National Basic Research Program of China (2006CB101708), the National Natural Science Foundation of China (30971848), the Jiangsu Natural Science Foundation (BK2008335), the 111 Project (B08025) and the State Key Laboratory of Crop Genetics and Germplasm Enhancement (ZW2007001). Conflict of interest The authors declare that they have no conflicts of interest.
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