Volume 3  Issue 1  Pages 0110
Article ID: 2017aaps0001
Improving Soybean Variety Trial Analysis with Augmented Models
Adams Kusi Appiah ^{1}, Rebecca Helget ^{2}, and Jixiang Wu ^{2*}
^{1} Department of Mathematics and Statistics, South Dakota State University, Brookings, SD 57007 USA.
^{2} Department of Agronomy, Horticulture and Plant Science, South Dakota State University, Brookings, SD 57007 USA.
^{ }
Abstract:
Plant breeders intend to evaluate a large number of new varieties in order to select genotypes with great yield potential through various variety trials. Thus, a large experimental field may be needed. A prerequisite in most experimental designs is homogeneity among experimental plots within each block. However, it is sometimes difficult to ensure that experimental plots are uniform within each field block regarding soil fertility and soil conditions that may significantly impact yield and other important traits. In this study, a classical randomized complete block (RCB) with three field replications (rowblocking) was “augmented” based on the field plot layout in a oneyear soybean variety trial. Data for yield and yield components of 12 soybean varieties were collected and analyzed with several augmented models. Results showed that variety had highly significant impacts on grain yield, 100pod weight, and seed 100pod weight. Soil heterogeneity existed in the row direction for yield. Further analyses showed that, soil conditions contributed to the significance impact of cultivar on grain yield but number of seeds, 100pod weight, or 100pod seed weight was not significantly affected.
Keywords: Augmented experimental design; blocking design; linear mixed model approach and soybean
Cite this article as: Appiah, A.K., Helget, R., Wu, J., 2017. Improving Soybean Variety Trial Analysis with Augmented Models. Advances in Agronomy and Plant Science 03(01), 0110.
Introduction
Soybean (Glycine max (L.) Merrill), as one of the most widely grown leguminous crops and one of the most economically important crops in the world (Guo et al., 2011), is a versatile and fascinating crop with innumerable possibilities of not only improving agriculture but also supporting industries. This crop has been seen an increase in world production through a combination of increased production area and greater yield to meet the rising demand. Increasing soybean yield has been attributed to improve agronomic practice as well as enhancement of selecting genetic potentials for higher yield of new soybeans varieties (De Bruin and Pedersen, 2008; Rowntree et al., 2013; Specht and Williams, 1984). In USA, substantial increase in yield of soybeans due to successive release of new genotypes of soybeans was reported (Boerma, 1979; Rowntree et al., 2013; Specht and Williams, 1984).
Over 2,700 of different crops including soybeans with improved agronomic traits have been developed and officially released to the farmers for general cultivation all over the world (Maluszynski, 2001; Shu, 2009). It is a common practice that new lines are evaluated before their official release to the farmers. Earlystage evaluation in soybean breeding programs is commonly practiced on a large number of new varieties. Thus, at the prescreening stage, a large experimental field may be needed for evaluation and subsequently for selection of varieties with great yield potentials. A prerequisite in most experimental designs is homogenous experimental plots within each block. However, it is sometimes difficult to ensure that experimental plots are uniform within each field block with respect to soil fertility and soil conditions that may significantly impact yield and yield components. Therefore, field observations may not be highly consistent with genetically highyielding due to nonuniform soil condition (Keuls and Sieben, 1955).
One effective approach to overcoming soil heterogeneity problems is to augment standard experimental designs which were introduced and later extended (Federer, 1956; Federer, 1961; Federer, 2002; Federer and Raghavarao, 1975; Federer et al., 2001). An augmented design sometimes occurs in plant breeding programs, which could be viewed as rectangular rowcolumn design, equivalent to a twodimensional control (Bondalapati et al., 2014a; Harshbarger and Davis, 1952; Lin and Poushinsky, 1985). In a similar manner, a classical randomized complete block (RCB) design, a conventional oneway blocking design, could be augmented by including column and/or row effects based on a field plot layout or field management to improve statistical analyses. This “augmented RCB design” with appropriate statistical methods could help control field variation and select more promising varieties for further investigation. However, appropriate analysis for these different augmented designs is highly desired (Federer and Wolfinger, 1998). Linear mixed model approaches appear to be effective for several augmented experimental designs (Bondalapati et al., 2014b; Wu et al., 2013).
In this study, we considered augmenting a classical RCB design to detect the direction of soil variation (row, column, or two directions) based on the field plot layouts in a oneyear soybean variety trial with 12 soybean cultivars. A linear mixed model approach was applied to analyze several augmented RCB designs. The major purpose of this study was to improve crop trial data analysis via augmenting a classical oneway blocking design.
Materials and Methods
Materials and field experiments
Twelve soybean cultivars including Wensman W 3178R2, Asgrow AG1733, Dairyland DSR1808/R27, Wensman W, Prairie BR. PB1843R2 3160NR2, Prairie BR. PB1722R2, Pioneer P16T04R, Rea 78G12, Stine 16RD66, Mustang 16624, Latham L1783R2, Channel 1805R2 were grown in 2013. The experiment was conducted at the South Dakota State University Volga Research Farm (N 44°17.915’ W 096°55.393’). A randomized complete block design with three replications following the row direction was employed. The previous crop was spring wheat. Each fourrow plot was 5ft wide and 30ft long. Soil type was Brandt silty clay loam, 02% slope, and nonirrigated. Conventional tillage was employed. Row spacing was 30 inches with seeding rate of approximate 165,000 per ac. Weeds were controlled using dual IIPre, GlyphosatePost. Planting was done on June 3^{rd} and harvested. Prior to planting, each plot was sampled by extracting from 015cm. The soil test included phosphorus (P, ppm), organic matter (OM, %), potassium (K, ppm), pH, Zinc (Zn, ppm), Iron (Fe, ppm), Manganese (Mn, ppm), Copper (Cu, ppm), Calcium (Ca, ppm), Magnesium (Mg, ppm), Sodium (Na, ppm), and Cation Exchange Capacity (CEC, meq/100g). The South Dakota State University Soil Testing Lab used the Olsen (sodium bicarbonate) test procedure for routine P tests, weight loss (lost on ignition) procedure for OM, Ammonium Acetate procedure for routine K, Ca, and Mg tests, water procedure for pH, and Na tests, and DTPA solution method for Zn, Fe, Mn, and Cu. Soil testing was performed to determine physical conditions, fertility (nutrient) status, and chemical properties that may affect soybean crop production.
Data collection
Prior to field harvest, we measured height of 10 normally developed plants (PH, inches) for each plot. In addition, we cut all plants within 1m area in the middle of second or fifth row of 6row plot and saved these plants in one paper bag. In addition to 1m population size, we measured the following traits: number of plants (NP/m), whole bag weight (WBW, g), and whole pod weight (WPW, g). Number of seed (NS/100pod), 100pod weight (HPW, g), and seed weight of 100pod (SWHP, g) were determined by based on randomly selected 100 pods from the 1m sample for each plot. Ohaus scout pro portable balance, 6000g, 115 Vac was used to measure weight. Grain yield (GY) were harvested from the third and forth rows on October 1^{st} (group 0s and 1s) and October 9^{th} (group 2s) and then converted to bu/ac.
Statistical models and statistical methods
Three different linear models were chosen for our data analysis. These models were used to predict cultivar effects, row and column blocking effects (rowcolumn). The response model of row, column, and row and column were used to describe the soil conditions variation in the experiment. Model one (M1) is a conventional RCB design model. Model two (M2) only includes column blocking based on the field plot layout. Model three (M3) is augmented RCB with twoway blocking effects.
Soil heterogeneity was investigated by examination of the significance of blocking or column effects with all the three models. If row and/or column effects are not significant, the soil variation can be considered homogeneous.
Where represents the yield or yield component; is the overall mean for the whole experiment, is a genotypic effect,); is the block effect, is the random column effect, and represents the random error.
For the purpose of estimating the variance components, genotype and block effects were treated as random variables. All statistical analyses were processed using R (R Core Team, 2014). An R package “minque” (Wu, 2014) incorporated with a groupbased jackknife resampling approach with 10 randomly divided groups was used to estimate the variance components through the minimum norm quadratic unbiased estimation (MINQUE) method (Rao, 1971). Separate analyses were performed for each measured component trait. To assess the impact of soil conditions on yield and yield components, a stepwise regression was performed to select the best soil condition variables using the R package “leaps” (Lumley and Miller, 2004). The residuals with removal of effects from soil components were used for additional analysis. Means of cultivar yield were compared using LSD of 0.05 if a Ftest was significant.
Results and Discussion
Mean performances of soybean cultivar grain yield and yield traits
Means for 12 soybean genotypes grain yield and yield traits in 2013 and presented in (Table 2). Mean grain yield ranged from 29.00 (Pioneer P16T04R) to 35.95 bu/ac (Wensman W 3160NR2). Plant height varied from 34.98 (Prairie BR. PB1843R2) to 40.47 inches (Pioneer P16T04R). Pioneer P16T04R had the lowest yield but with the tallest plants, indicating possible negative correlation between yield and vegetative growth under this condition. Variation in plant height among varieties might have occurred due to their differences in genetic background.
The minimum number of seed was produced by Stine 16RD66 (211.67) while the maximum was Channel 1805R2 (261.67). The average number of plants varied from 23.33 m^{1} (Rea 78G12) to 28.33 m^{1} (Dairyland DSR1808/R27). The highest average whole bag weight was obtained for Channel 1805R2 (619.97 g) and the lowest was Mustang 16624 (534.23g). The mean values of whole pod weight ranged from 300.7 (Pioneer P16T04R) to 363g (Channel 1805R2). The mean values for 100pod weight varied from 40.07 (Mustang 16624) to 55.9g (Pioneer P16T04R). The highest seed weight of 100pod was obtained with Pioneer P16T04R (41.03g) and the lowest was Rea 78G12 (29.07g).
Table 1. Variety with corresponding replication and plot number in 2013
Variety name  Trt.No  Rep. and Plot No.  
Wensman W 3178R2  1  101  209  302 
Asgrow AG1733  2  102  207  312 
Dairyland DSR1808/R27  3  103  202  310 
Wensman W 3160NR2  4  104  210  311 
Prairie BR. PB1843R2  5  105  201  306 
Prairie BR. PB1722R2  6  106  212  305 
Pioneer P16T04R  7  107  204  304 
Rea 78G12  8  108  203  307 
Stine 16RD66  9  109  205  308 
Mustang 16624  10  110  211  301 
Latham L1783R2  11  111  206  303 
Channel 1805R2  12  112  208  309 
Trt. No=Treatment number, Rep. =Replication
Table 2. Mean grain yield and yield component traits of 12 soybean cultivars tested at Volga in 2013
Variety Name  Yield and components traits  
GY
(kg/ha) 
PH
(cm) 
NS  NP  WBW
(g) 
WPW
(g) 
HPW
(g) 
SHPW
(g) 

Asgrow AG1733  34.94  35.12  234.67  25.33  572.37  347.2  49.27  36.1 
Channel 1805R2  32.71  38.23  261.67  23.67  619.97  363  55.67  39.63 
Dairyland DSR1808/R27  34.32  35.45  240.67  28.33  574.2  338.6  46.57  33.77 
Latham L1783R2  34.62  35.83  231.33  25.33  572.07  319.7  43.3  31.17 
Mustang 16624  30.87  36.15  240  24.67  534.23  306.8  40.07  27.87 
Pioneer P16T04R  29.56  40.47  253  26.33  556.23  300.7  55.9  41.03 
Prairie BR. PB1722R2  35.69  36.12  236.33  27.33  560.53  330.2  47.53  35.1 
Prairie BR. PB1843R2  35.68  34.98  239.67  24.67  557.83  356.8  47.47  34.67 
Rea 78G12  29.97  35.67  244.33  23.33  547.87  303.6  41.27  29.07 
Stine 16RD66  33.3  36.32  211.67  24.67  568.87  322.2  41.17  29.6 
Wensman W 3160NR2  35.97  36.15  253.33  28.33  612  362.6  53.93  39.03 
Wensman W 3178R2  35.65  35.45  247.67  23.67  590.43  347.9  55.43  40.5 
Table 2. Mean grain yield and yield component traits of 12 soybean cultivars tested at Volga in 2013
GY=grain yield, PH=plant height, NP=number of plants, WBW= whole bag weight, WPW=whole pod weight, NS=number of seed per pod, HPW=100pod weight, SWHP=seed weight of 100pod
Analysis of variance for yield and yield components traits based on the three models
Analyses of variance (ANOVA) were obtained for each of the three models for the 12 soybean cultivars yield and yield component traits and presented in (Table 3). The purposes of the ANOVA of individual yield and yield traits using three different models were to determine whether there is soil heterogeneity and to characterize its property, i.e., soil trends in the row or column direction. The adjustment by including column effects in this RCB design could be the most extended when soil variation occurred in one or two direction. This helps detect if soil fertility impacted yield and yield components. Significant effect of row blocking did not give undue advantage to some cultivar.
For model 1 (M1), grain yield, number of seed, 100pod weight, and seed weight of 100pod were highly influenced by cultivars. Cultivar effects on plant height were significant at the probability level of 0.01. Significant rowblock effect on grain yield was detected. There was no evidence of significant rowblocking effect on other yield traits at the probability level of 0.05. Thus, based on M1, soil heterogeneity existed for yield in row direction while homogenous for most of the traits considered in this study.
For model 2 (M2), there was evidence showing that cultivar had highly significant impacts on plant height, number of seed, 100pod weight, and seed of 100pod weight. No significant column effects on yield and yield component traits were detected at the probability level of 0.05.
For model 3 (M3), there was evidence showing that cultivars had highly significant impacts on grain yield, plant height, number of seed, 100pod weight, and seed of 100pod weight. There was no evidence showing that rowblocking had significant impacts on yield component traits except grain yield. There was no significant columnblocking for all these traits.
The results based on the three models showed that soil heterogeneity existed in row direction for soybean grain yield. Some important soil condition variables were selected by stepwise regression approach to have had some contributions to yield and yield component traits. Soil variables (OM, pH, Zn, Fe, Mn, Mg, and Na) simultaneously contributed about 41% to the total variation of soybean grain yield (Table 4). Similarly, 11% of the total variation in plant height was attributed to P and K soil contents, 10% in number of plants to OM, P, K, Fe, Mn, Cu, and CEC, 23% of the variation in whole pod weight to OM, K, Zn and Fe, 13% of total variation in 100pod weight to P, pH, Mn, Na, and 15% in seed weight of 100pod to OM, P, Mg soil nutrients. The contributions of these soil variables were removed and ANOVA were performed for the residuals of each trait to reveal the genetic impact on yield traits without the effects of soil conditions. From the results in Table 5, based on all the three models, same conclusions could be drawn. Number of seed, plant height, 100pod weight, and seed of 100pod weight were highly influenced by cultivar. Blockings especially, rowblocking which was having effect on grain yield now had no impact on yield traits. With no blocking effects the experimental plot is considered to be homogenous; an ideal field plot for prescreening soybean cultivars. With the soil conditions effect removed, cultivar effect on grain yield is now insignificant. Thus, the genetic performance of these cultivars was similar and their grain yield performance on a homogenous experimental plot did not see any significant difference. Selecting genotypes based on higher yield performance may be misleading. Yield traits such as plant height, number of seed, 100pod weight and seed weight of 100pod were consistently influenced by cultivar with and without the effects of soil conditions. Number of seed, and 100seed weight are primary determinant of soybean production (Liu et al., 2005; Orf et al., 1999; Specht et al., 1999) and cultivars with superior performances for these traits should be included in the selection process. These traits were not significantly influenced by soil conditions in this study.
Table 3. Analysis of variance for twelve soybean cultivars by model 1 (M1), model 2 (M2) and model 3 (M3) of yield traits for Volga in 2013
SoV  DF  Mean Square Error  
GY
(kg/ha) 
PH
(cm) 
WBW
(g) 
NP  WPW
(g) 
NS  HPW
(g) 
SWHP
(g) 

M1  
Trt  11  16.27***  7.19**  1866.60  9.18  1551  490.1***  107.09 ***  64.55***  
Blk  2  51.76***  0.60  285.10  1.03  1886  28.50  11.88  12.33+  
Err  22  2.58  0.82  2170.50  7.73  1026  84.50  7.52  4.80  
M2  
Trt  11  16.27+  7.19***  1866.60  9.179  1550.9  490.10***  107.09***  64.55***  
Col  2  0.58  2.06+  766.40  0.486  2237.9  66.60  3.03  1.83  
Err  22  7.24  0.69  2126.70  7.774  994.4  81.10  8.33  5.75  
M3  
Trt  11  16.27***  7.19***  1866.60  9.18  1550.9  490.10***  107.09***  64.55***  
Blk  2  51.76***  0.60  285.10  1.03  2237.9  28.50  11.88  12.33  
Col  2  0.58  2.06+  766.40  0.49  1885.5  66.6 0  3.03  1.83  
Err  20  2.78  0.70  2310.9  8.45  905.2  86.30  7.97  5.10  
SoV= source of variation, DF= degree of freedom, Trt= treatment (variety), Blk=Block blocking, Col = Column blocking, Err=error, GY=grain yield, PH=plant height, NP=number of plants, WBW= whole bag weight, WPW=whole pod weight, NS=number of seed per pod, HPW=100pod weight, SWHP=seed weight of 100pod.
‘*’, ‘**’, ‘***’,’+’ are significant at probability levels of 0.05, 0.01, 0.00 and 0.1 respectively
Table 4. Stepwise regression of soil condition variables
GY
(kg/ha) 
PH
(cm) 
NP  NS  WBW
(g) 
WPW
(g) 
HPW
(g) 
SHPW
(g) 

4.21OM+  0.17P+  6.86OM*  1.04 P  72.39OM+  55.99Zn*  0.55P+  5.74OM+  
13.75pH  0.04K*  0.47P*  1.06K+  0.16Ca*  21.28pH  0.41P+  
5.56Zn*  0.15K**  53.31Zn  4.10Na+  0.52Mn  0.05Mg  
0.25Fe  0.39Fe+  3.87Fe  0.61Na  
0.40Mn  0.43Mn  
0.05Mg  0.57Cu+  
0.25Na  0.78CEC  
0.41  0.10  0.11  0.04  0.08  0.23  0.13  0.15 
GY=grain yield, PH=plant height, NP=number of plants, WBW= whole bag weight, WPW=whole pod weight, NS=number of seed per pod, HPW=100pod weight, SWHP=seed weight of 100pod.
*, **, + , are significant at probability levels of 0.05, 0.01, and 0.1 respectively
Table 5. Analysis of variance for the residuals of yield traits by model 1 (M1), model 2 (M2) and model 3 (M3) for Volga in 2013
SoV  DF  Mean Square Error  
GY
(kg/ha) 
PH
(cm) 
NS  WBW
(g) 
NP  WPW
(g) 
HPW
(g) 
SWHP
(g) 

M1  
Trt  11  5.88  5.90***  442.6***  1707  7.08  791.30  69.00***  46.92*** 
Row  2  3.13  0.25  108.9  1102  0.36  1127.20  8.15  9.79 
Err  22  4.03  0.82  78.1  1586  5.24  886.50  12.75  5.47 
M2  
Trt  11  5.89  5.90***  442.60***  1707.2  7.08  791.3  69.00***  46.92*** 
Col  2  0.71  1.08  27.2  582.2  6.18  1000.5  3.78  1.48 
Err  22  4.28  0.75  85.5  1633.7  4.77  898.0  13.15  6.23 
M3  
Trt  11  5.88  5.90***  442.6***  1707.2  7.08  791.30  69.00***  46.92*** 
Row  2  3.13  0.25  108.9  1101.9  0.36  1127.20  8.15  9.79 
Col  2  0.36  1.08  27.2  582.2  6.18  1000.50  3.78  1.48 
Err  20  4.39  0.80  83.1  1686.8  5.15  875.10  13.65  5.87 
SoV= source of variation, DF= degree of freedom, Trt= treatment (variety), Row=Row blocking, Col = Column blocking, Err=error, GY=grain yield, PH=plant height, NP=number of plants, WBW= whole bag weight, WPW=whole pod weight, NS=number of seed per pod, HPW=100pod weight, SWHP=seed weight of 100pod.
‘***’ is significant at probability level of 0.00
Multiple comparisons among 12 soybean cultivars
The primary objective of a field test in early stage of genotype selection is to compare the phenotypic expression of genotypes and select the ones with desirable qualities. Least significant difference (LSD) has been commonly used to compare the significance difference between means of two varieties. The LSD values were calculated based on model 1 and the results are presented in (Table 6). The means of cultivar Wensman W 3160NR2 and Prairie BR. PB1722R2 are not significantly different from each other. Thus, the variety (Wensman W 3160NR2) with the highest yield was statistically comparable to Prairie BR PB1722R2, Prairie BR PB1843R2, Wensman W 3178R2, Asgrow AG1733, Latham L1783R2, Dairyland DSR1808/R27, and Stine 16RD66. Similarly, variety with the lowest yield (Pioneer P16T04R) was same as Rea 78G12, and Mustang 16624. On the other hand, means of cultivar Wensman W 3160NR2 and Pioneer P16T04R were statistically different.
Variance components for yield and yield component traits
Since the inclusion of column effects based on the field plot design resulted in an unbalanced data, a linear mixed model approach was also used to analyze the data due to the ability to handle unbalanced date sets (Bondalapati et al., 2014a; Wu, 2014; Wu et al., 2013). Assuming random effects of variety and blocks made it possible to estimate various variance components. The variance components and the proportional were estimated to assess the amount of variation and significant contributions to variable (yield or a yield components trait) due to cultivar, blocks and random error based on the models considered in this study.
Table 6. Least significant difference (LSD) comparisons of twelve soybean varieties in 2013 at Volga
Variety  Means  
1  Wensman W 3160NR2  35.97a 
2  Prairie BR. PB1722R2  35.69a 
3  Prairie BR. PB1843R2  35.68a 
4  Wensman W 3178R2  35.65a 
5  Asgrow AG1733  34.94ab 
6  Latham L1783R2  34.62ab 
7  Dairyland DSR1808/R27  34.32ab 
8  Stine 16RD66  33.30abc 
9  Channel 1805R2  32.71bc 
10  Mustang 16624  30.87cd 
11  Rea 78G12  29.97d 
12  Pioneer P16T04R  29.56d 
LSD ( ), = 2.72 (2013)
Table 7. Estimated variance components of yield trait for Volga in 2013
GY  PH  WBW  NP  WPW  NS  HPW  SWHP  
V  M1  
V_{T}  4.55***  2.09***  77.91  0.61  168.32  134.26***  33.17***  20.09*** 
V_{R}  4.12*  0.02  0.00  0.00  70.67  0.00  0.42  0.62 
V_{e}  2.59  0.83  2160.29  7.69  1033.53  86.16  7.60  4.71 
M2  
V_{T}  2.83*  2.29***  92.39  0.46  199.94  138.40**  32.69***  19.51*** 
V_{C}  0.01  0.06  44.65  0.00  109.02  1.13  0.00  0.00 
V_{e}  7.26  0.70  2115.95  7.80  975.24  80.69  8.43  5.82 
M3  
V_{T}  4.48***  2.28***  105.43  0.37  204.97  133.98***  32.74***  19.72*** 
V_{R}  4.10*  0.01  0.00  0.00  75.71  0.00  0.46  0.66 
V_{C}  0.02  0.06  11.53  0.00  100.32  0.06  0.09  0.03 
V_{e}  2.73  0.71  2326.83  8.49  920.27  87.32  7.94  5.10 
V= variance component, V_{T} = Treatment (variety) variance, V_{R} =Row blocking variance, V_{C }= Column blocking variance, V_{e}=error variance, GY=grain yield, PH=plant height, NP=number of plants, WBW= whole bag weight, WPW=whole pod weight, NS=number of seed per pod, HPW=100pod weight, SWHP=seed weight of 100pod.
‘*’, ‘**’, ‘***’, are significant at probability levels of 0.05, 0.01, and 0.00 respectively
Table 7 lists the estimates of cultivar, blocks and random error variance components for soybean yield and yield component traits based on the three models. Cultivar had highly significant effects on grain yield, plant height, number of seed, 100pod weight, and seed weight of 100pod from all the three models. Row effects had significant impact on grain yield from M1 and M3. Column effects did not have significant impact on yield and yield traits from M2 and M3. Including column effects in the model did not improve the results for all traits. Proportionately, cultivar contribution to total variation in soybean grain yield were 40%, 28%, and 40% based on M1, M2, and M3, respectively (Table 8). Similar, cultivar contributed (M1=71%, M2=75%, and M3=74%), (M1=61%, M2=63%, and M3=60%), (M1=80%, M2=79%, and M3=79%), and (M1=78%, M2=77%, and M3=77%) to the total variation in plant height, number of seed, 100pod weight and seed weight of 100pod respectively. These traits were mainly affected by cultivar effects. The other traits such as number of plants, whole bag weight and whole pod weight were more influenced by unknown mechanisms thus random error proportional component larger than cultivar components these traits.
Table 8. Estimated proportional variance components of yield traits for Volga in 2013
V  GY  PH  WBW  NP  WPW  NS  HPW  SWHP 
M1  
V_{T}  0.40  0.71  0.04  0.06  0.13  0.61  0.80  0.78 
V_{R}  0.36  0.01  0.00  0.00  0.05  0.00  0.01  0.02 
V_{e}  0.23  0.28  0.96  0.94  0.81  0.39  0.19  0.19 
M2  
V_{T}  0.28  0.75  0.05  0.06  0.16  0.63  0.79  0.77 
V_{C}  0.00  0.02  0.02  0.00  0.08  0.00  0.00  0.00 
V_{e}  0.72  0.23  0.93  0.94  0.76  0.37  0.21  0.23 
M3  
V_{T}  0.40  0.74  0.05  0.04  0.16  0.60  0.79  0.77 
V_{R}  0.36  0.00  0.00  0.00  0.06  0.00  0.01  0.03 
V_{C}  0.00  0.02  0.01  0.00  0.08  0.00  0.00  0.00 
V_{e}  0.24  0.24  0.94  0.96  0.69  0.40  0.19  0.20 
V= variance component, V_{T} = Treatment (variety) variance, V_{R} =Row blocking variance, V_{C }= Column blocking variance, V_{e}=error variance, GY=grain yield, PH=plant height, NP=number of plants, WBW= whole bag weight, WPW=whole pod weight, NS=number of seed per pod, HPW=100pod weight, SWHP=seed weight of 100pod.
Table 9. Estimated variance components for the soil properties in 2013 at Volga
V  GY  OM  P  K  pH  Zn  Fe  Cu  Mn  Ca  Mg  Na  CEC 
V_{R}  3.74  0.08*  3.35*  112.84*  0.01*  0.02*  46.74*  0.002^  6.18*  86.78*  611.10*  1.50+  1.83* 
V_{C}  0.02  0.00  0.61  52.29+  0.00  0.00  0.30  0.001  0.21  0.00  4.95  0.00  0.01 
V_{e}  7.37  0.04  10.72  131.853  0.01  0.04  18.57  0.005  7.33  4772.45  240.80  4.99  1.04 
V= variance component, V_{R} =Row blocking variance, V_{C }= Column blocking variance, V_{e}=error variance, GY=grain yield
*, ^, +, are Significant at 0.00, 0.05, 0.1
Soil uniformity analysis
It is often of interest to plants breeders, the trend of soil variations to aid blocking to ensure homogeneous experimental block. Uniformity tests on soil conditions variables and soybean grain yield were performed. The estimated variance component for row and column effects are presented in Table 9. Soil variations existed in the row direction except Na at probability level of 0.05. At 0.1 alpha level of significance, rowcolumns direction existed for soil K nutrient. Potassium is a macronutrient needed by plants for better growth and development. Potassium, from a stepwise regression analysis, showed significant effect on plant height, number of plants, and whole bag weight. Thus, with respect to soil K nutrient, homogenous block assumption required by most standard design is violated. The results suggested that the blocking following the row direction was more appropriate than the column direction. The results were also consistent with those from our augmented experimental design analyses.
Summary
In many breeding programs augmenting the experimental design based on the field layout can be a valuable aid to improve selection precision. Yield and yield component data from a oneyear soybean variety trial were analyzed by augmenting a classical RCB design for further understanding of soil variability that impacted yield and yield component traits. In order to check for the existence of soil heterogeneity, the data was analyzed based on three models. This study demonstrated that augmented models could detect heterogeneity existed in multiple directions for K soil nutrient and row direction for the soil properties considered in this study.
References
Boerma, H.R., 1979: Comparison of past and recently developed soybean cultivars in maturity groups VI, VII, and VIII. Crop Science 19, 611613.
Bondalapati, K.D., J. Wu, and K.D. Glover, 2014a: An augmented additivedominance (AD) model for analysis of multiparental spring wheat F2 hybrids. Austalian Journal of Crop Science 8, 14411447.
Bondalapati, K.D., J. Wu, and K.D. Glover, 2014b: An augmented additivedominance (AD) model for analysis of multiparental spring wheat F2 hybrids. Australian Journal of Crop Science 8, 14411447.
De Bruin, J.L., and P. Pedersen, 2008: Yield Improvement and Stability for Soybean Cultivars with Resistance to Ichinohe. Agronomy journal 100, 13541359.
Federer, W.T., 1956: Augmented (or hoonuiaku) designs. Hawaii Plant, Rec. 2:191–208.
Federer, W.T., 1961: Augmented designs with oneway elimination of heterogeneity. Biometrics 17, 447473.
Federer, W.T., 2002: Construction and analysis of an augmented lattice square design. Biometrical journal 44, 251257.
Federer, W.T., and D. Raghavarao, 1975: On augmented designs. Biometrics, 2935.
Federer, W.T., and R.D. Wolfinger, 1998: SAS code for recovering intereffect information in experiments with incomplete block and lattice rectangle designs. Agronomy Journal 90, 545551.
Federer, W.T., M. Reynolds, and J. Crossa, 2001: Combining results from augmented designs over sites. Agronomy Journal 93, 389395.
Guo, W., X. Yan, H. Liao, L. Qin, J. Zhao, and X. Li, 2011: A soybean Îøexpansin gene GmEXPB2 intrinsically involved in root system architecture responses to abiotic stresses [electronic resource]. Plant journal 66, 541552.
Harshbarger, B., and L.L. Davis, 1952: Latinized rectangular lattices. Biometrics 8, 7384.
Keuls, M., and J.W. Sieben, 1955: Two statistical problems in plant selection. Euphytica 4, 3444.
Lin, C.S., and G. Poushinsky, 1985: A modified augmented design (Type 2) for rectangular plots. Canadian Journal of Plant Science 65, 743749.
Liu, X., J. Jin, S. Herbert, Q. Zhang, and G. Wang, 2005: Yield components, dry matter, LAI and LAD of soybeans in Northeast China. Field Crops Research 93, 8593.
Lumley, T., and A. Miller, 2004: Leaps: regression subset selection. R package version 2.
Maluszynski, M., 2001: Officially released mutant varieties–the FAO/IAEA Database. Plant Cell, Tissue and Organ Culture 65, 175177.
Orf, J., K. Chase, T. Jarvik, L. Mansur, P. Cregan, F. Adler, and K. Lark, 1999: Genetics of soybean agronomic traits: I. Comparison of three related recombinant inbred populations. Crop Science 39, 16421651.
R Core Team, 2014: R: A Language and Environment for Statistical Computing, R version 3.1.1 (20140710) ed. R Foundation for Statistical Computing.
Rao, C.R., 1971: Estimation of variance and covariance components—MINQUE theory. Journal of multivariate analysis 1, 257275.
Rowntree, S.C., J.J. Suhre, N.H. Weidenbenner, E.W. Wilson, V.M. Davis, S.L. Naeve, S.N. Casteel, B.W. Diers, P.D. Esker, and J.E. Specht, 2013: Genetic gain× management interactions in soybean: I. Planting date. Crop Science 53, 11281138.
Shu, Q.Y., 2009: A summary of the international symposium on induced mutations in plants Induced plant mutations in the genomics era.
Specht, J.E., and J.H. Williams, 1984: Contribution of genetic technology to soybean productivity—Retrospect and prospect. Genetic contributions to yield gains of five major crop plants, 4974.
Specht, J.E., D.J. Hume, and S.V. Kumudini, 1999: Soybean yield potential—a genetic and physiological perspective. Crop Science 39, 15601570.
Wu, J., 2014: minque: An R Package for Linear Mixed Model Analyses Package ‘minque’.
Wu, J.X., K. Bondalapati, K. Glover, W. Berzonsky, J.N. Jenkins, and J.C. McCarty, 2013: Genetic analysis without replications: model evaluation and application in spring wheat. Euphytica 190, 447458.