PLANT BREEDING TOOLS- SOFTWARE FOR PLANT BREEDERS.pdf

12th National Convention on Statistics (NCS) EDSA Shangri-La Hotel, Mandaluyong City

October 1-2, 2013

PLANT BREEDING TOOLS: SOFTWARE FOR PLANT BREEDERS by

Nellwyn Sales, Violeta Bartolome, Alexander Caeda, Alaine Gulles, Rose Imee Zhella Morantte, Leilani Nora,

Angel Manica Raquel, Christoffer Edd Relente, Darwin Talay and Guoyou Ye

For additional information, please contact: Authors name: Nellwyn Sales Designation: Specialist Affiliation: International Rice Research Institute Address: College, Los Baos, Laguna Tel. no.: 5362701 loc 2238 E-mail: [email protected]

Co-authors name Violeta Bartolome, Alexander Caeda, Alaine Gulles, Rose Imee

Zhella Morantte, Leilani Nora, Angel Manica Raquel, Christoffer Edd Relente, Darwin Talay and Guoyou

Designation: Senior Associate Scientist - Biometrics, Senior Specialist - Software Engineering, Assistant Scientist, Specialist, Assistant Scientist, Programmer, Programmer, Programmer and Senior Scientist - Breeding Informatics Specialist

Affiliation: International Rice Research Institute Address: College, Los Baos, Laguna Tel. no.: 5362701 loc 2238 E-mail: [email protected], [email protected], [email protected],

[email protected], [email protected], [email protected], [email protected], [email protected] and [email protected]

PBTools: Software for Plant Breeders

Nellwyn Sales, Violeta Bartolome, Alexander Caeda, Darwin Talay, Alaine Gulles, Rose Imee Zhella Morantte, Leilani Nora, Angel Manica Raquel,

Christoffer Edd Relente and Guoyou Ye

Abstract

Data from plant breeding trials need to be analyzed properly, with greater speed to support selection decision making. Genetic information should also be derived from breeding trials to determine more efficient breeding strategies. Although general statistical software can be used to analyze breeding trials, many practical breeders are seeking easy-to-use analytical tools.

PBTools is a free statistical application developed primarily for plant breeders. It was created using the Eclipse Rich Client Platform (RCP) and R language. It has a user-friendly graphical user interface (GUI). Its current version provides modules for the following: data management in spreadsheet view, randomization for commonly used experimental designs, single- and multiple-environment analysis, QTL analysis, selection index, commonly used mating designs, and generation mean analysis, some of which are presented in the paper. Keywords: statistical software, plant breeding Introduction

Plant breeding research generally involves use of statistical techniques to determine valid conclusions which aid in selection decision making. Users depend on statistical software to generate reliable results quickly. However, most software are developed for general statistical analysis only and are costly. Some are freeware but have limited functionality or are difficult to use.

R is a language and an environment for statistical computing and graphics. Many classical and modern statistical methods have been well implemented in R, mainly through hundreds of add-on packages contributed by leading statisticians. New add-on packages can be rapidly developed by exploring the functions of existing packages. R has become increasingly popular. However, some users find its command line interface challenging. Software with a GUI involving menus, dialog boxes, and spreadsheets is generally more preferred.

Plant Breeding Tools (PBTools) is a free statistical application created using the Eclipse Rich Client Platform (RCP), a platform for building and deploying rich client applications, and R language. It has been developed to assist plant breeders in the design and analysis of data. It has an easy to navigate GUI that does not require users to have programming skills to perform data manipulation and analysis.

Its current version provides modules for data management in spreadsheet view, randomization for commonly used experimental designs, single- and multiple-environment analysis, QTL analysis, selection index, commonly used mating designs, and generation mean analysis.

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An introduction of the features of PBTools is provided in this paper. PBTools Environment Main Window

The PBTools main window (Figure 1) has a menu bar which houses five items: Project, Data, Analysis, Randomization, and Help. The Project menu contains functions for creating and managing projects. The Data menu contains functions for reading, managing and manipulating datasets. The Analysis Menu contains functions to perform statistical analysis. The Randomization Menu contains functions for generating random assignment of factor levels for commonly used experimental designs in plant breeding. Finally, the Help Menu is used to access PBTools users manual and some information about the software.

Figure 1. PBTools Main Window.

Figure 2 presents the submenu items under the Data, Analysis, and Randomization menus.

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Figure 2. Submenu items for the Data, Analysis, and Randomization menus.

The PBTools main window is divided into two panels: the Project Explorer panel and the Editor panel. The Project Explorer panel functions as a file manager of the active project, where names of data files and analysis results files are displayed in tree form, while the Editor panel serves as viewer for selected data (by means of the Data Viewer tab) and/or results of analysis (via the Results Viewer tab).

When the name of a data file is selected by double-clicking in the Project

Explorer tree, the file is displayed in a Data Viewer tab in spreadsheet form in the Editor panel (Figure 3). Data values can be edited in the Data Viewer. Data manipulation can also be performed here using options available in a toolbar or the submenu items under the Data menu.

Figure 3. Data Viewer Tab in the Editor Panel of PBTools. When an analysis is performed or the filename of an output file is selected under

the Output folder in the Project Explorer tree, the results are displayed in a Results Viewer tab (Figure 4). Depending on the contents of the results folder, the Results Viewer may have an Output page and/or Graph page.

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Figure 4. Results Viewer (Output and Graph Tabs) in the Editor Panel of PBTools. Handling Data

PBTools uses comma-separated values (csv) format for data files. Data files are created outside of PBTools and imported into the Data folder of the active project. Data files (.rda or .txt) may also be imported into PBTools but they will be automatically converted into .csv format. To represent missing observations, the user can use NA, period, blank or space.

A selected file is displayed in a Data Viewer tab in the Editor panel. Several Data

Viewers can be seen simultaneously inside the Editor Panel.

Data values can be edited in the Data Viewer. Data manipulation can also be performed using options available in a toolbar in the Data Viewer (Figure 5) or the submenu items under the Data menu. These options are: inserting row(s)/column(s) from the data, deleting row(s)/column(s) from the data, creating a new variable, editing variable information, sorting, aggregating, reshaping, merging, and appending data sets and creating data subset.

Figure 5. Toolbar for Data Manipulation in the Data Viewer Tab.

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Randomization for Some Experimental Designs

The Randomization menu allows users to generate randomization of treatments for single- and multi-factor designs. Randomization in PBTools is currently available for the following designs: randomized complete block (RCB), lattice, alpha-lattice, augmented Latin square, and augmented RCB design. Depending on the design, the user needs to provide information on a dialog box (Figure 6).

Figure 6. Sample Dialog Box for Generating Randomization and Layout.

A field book in csv format is created (Figure 7) and the layout (saved in a text file) is displayed in the Data Viewer (Figure 8).

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Figure 7. Sample Field Book after the Randomization.

Figure 8. Sample Layout after the Randomization.

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Analysis Prior to doing analysis in PBTools, a data set must first be selected and opened in the Data Viewer. When the needed data set is active, the desired submenu option can be selected from the Analysis menu. Single-environment analysis Analyses using mixed models for the following designs are available in PBTools: Randomized Complete Block (RCB), Augmented RCB, Augmented Latin Square, Alpha-Lattice and Row-Column. The user should specify in the dialog box some required information and preferred output or graphs to be generated. If the Environment field is specified, the analysis will be done per environment level. Otherwise, the data will be treated as if it came from one environment. The user also has the option to regard genotype as fixed or random factor while the remaining terms in the model are regarded as random. As illustration, Figures 9 to 11 show the filled-up tabs for a sample analysis in RCB.

Figure 9. Model Specifications Tab of Single-Environment

Analysis Dialog Box.

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Figure 10. Options Tab of Single-Environment Analysis Dialog Box.

Figure 11. Graph Tab of Single-Environment Analysis Dialog Box.

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After providing necessary information and desired options in the dialog box, the text and graph outputs will be displayed separately in tabs in the Editor panel. Additional csv files containing the computed residuals and summary statistics (if genotype is fixed) or predicted means (if genotype is random) are saved inside the results folder. These generated files can be accessed through the Project Explorer.

Figure 12 shows the sample partial text output of the single-environment

analysis. If genotype is regarded as fixed, the output of the analysis includes the following: some descriptive statistics of the response variable per environment level; data summary; estimates of the variance components of the model; test for the significance of genotypic effect wherein the denominator degrees of freedom in F test is computed according to a general Satterthwaite approximation; least-square means of the genotypes; summary statistics of the standard errors of the difference; and, pairwise mean comparison using Dunnett's procedure if comparing treatments with a control and HSD if performing all pairwise mean comparisons. If genotype is regarded as random, the output of the analysis includes the following: some descriptive statistics of the response variable per environment level; data summary; estimates of the variance components of the model; test for the significance of genotypic effect using -2 loglikelihood ratio test; test for the significance of the check/control effect, predicted genotype means derived using the Best Linear Unbiased Prediction (BLUP); least-square means of the checks (if checks/controls are specified); and, estimate of heritability. Genotypic and phenotypic correlation can be performed if two or more response variables are specified.

DATA FILE: E:/NSALES/pbtools workspace/testing/Data/2013DS_IRvarieties.csv

SINGLE-ENVIRONMENT ANALYSIS

DESIGN: Randomized Complete Block (RCB)

==============================

GENOTYPE AS: Fixed

==============================

------------------------------

RESPONSE VARIABLE: YIELD

------------------------------

DESCRIPTIVE STATISTICS:

Variable ENV N_NonMissObs Mean StdDev

1 YIELD 1 100 4349.44 781.2752

2 YIELD 2 100 4338.00 791.9981

------------------------------

ANALYSIS FOR: ENV = 1

------------------------------

DATA SUMMARY:

Number of observations read: 100

Number of observations used: 100

Factors Number of Levels Levels

ENTRY 50 IR36 IR64 IR72 ... IRRI168

REP 2 1 2

10

VARIANCE COMPONENTS TABLE:

Groups Variance Std.Dev.

1 REP 3029.013 55.03647

2 Residual 239417.453 489.30303

TESTING FOR THE SIGNIFICANCE OF GENOTYPIC EFFECT:

Analysis of Variance Table with Satterthwaite Denominator Df

Df Sum Sq Mean Sq F value Denom Pr(>F)

ENTRY 49 48306379 985844.5 4.1177 49 0.0000

GENOTYPE LSMEANS AND STANDARD ERRORS:

ENTRY LSMean StdErrMean

1 IR36 3247.5 348.1689

2 IR64 4461.0 348.1689

3 IR72 3603.5 348.1689

4 IRRI102 4109.5 348.1689

5 IRRI103 3826.5 348.1689

6 IRRI104 4336.5 348.1689

7 IRRI105 4193.0 348.1689

8 IRRI106 4091.5 348.1689

9 IRRI108 4470.5 348.1689

10 IRRI109 4697.5 348.1689

11 IRRI112 4443.0 348.1689

12 IRRI113 4807.5 348.1689

13 IRRI115 4262.5 348.1689

14 IRRI116 5218.0 348.1689

15 IRRI117 4571.5 348.1689

16 IRRI118 5056.5 348.1689

17 IRRI119 5530.5 348.1689

18 IRRI120 5016.5 348.1689

19 IRRI122 4779.5 348.1689

20 IRRI123 5193.5 348.1689

21 IRRI124 3657.0 348.1689

22 IRRI125 3229.0 348.1689

23 IRRI127 3313.0 348.1689

24 IRRI128 2962.5 348.1689

25 IRRI133 3386.5 348.1689

26 IRRI134 3765.5 348.1689

27 IRRI135 4742.0 348.1689

28 IRRI136 4650.5 348.1689

29 IRRI139 3468.0 348.1689

30 IRRI140 4172.5 348.1689

31 IRRI141 5002.0 348.1689

32 IRRI143 4403.0 348.1689

33 IRRI145 3907.0 348.1689

34 IRRI146 5871.5 348.1689

35 IRRI147 4368.5 348.1689

36 IRRI148 4315.0 348.1689

37 IRRI149 4400.0 348.1689

38 IRRI150 5076.5 348.1689

39 IRRI151 4041.0 348.1689

40 IRRI152 3323.0 348.1689

41 IRRI154 5120.0 348.1689

42 IRRI155 3490.0 348.1689

43 IRRI156 5182.0 348.1689

44 IRRI157 3134.0 348.1689

11

45 IRRI161 4840.0 348.1689

46 IRRI162 4863.5 348.1689

47 IRRI163 4328.5 348.1689

48 IRRI164 4943.0 348.1689

49 IRRI165 4058.5 348.1689

50 IRRI168 5542.5 348.1689

STANDARD ERROR OF THE DIFFERENCE (SED):

Estimate

Minimum 489.3030

Average 489.3030

Maximum 489.3030

SIGNIFICANT PAIRWISE COMPARISONS (IF ANY):

Compared with control(s)

Trmt[i] Trmt[j] Difference Lower Upper

1 IRRI113 IR36 1560.0 29.371879 3090.628

2 IRRI116 IR36 1970.5 439.871879 3501.128

3 IRRI118 IR36 1809.0 278.371879 3339.628

4 IRRI119 IR36 2283.0 752.371879 3813.628

5 IRRI120 IR36 1769.0 238.371879 3299.628

6 IRRI122 IR36 1532.0 1.371879 3062.628

7 IRRI123 IR36 1946.0 415.371879 3476.628

8 IRRI141 IR36 1754.5 223.871879 3285.128

9 IRRI146 IR36 2624.0 1093.371879 4154.628

10 IRRI150 IR36 1829.0 298.371879 3359.628

11 IRRI154 IR36 1872.5 341.871879 3403.128

12 IRRI156 IR36 1934.5 403.871879 3465.128

13 IRRI161 IR36 1592.5 61.871879 3123.128

14 IRRI162 IR36 1616.0 85.371879 3146.628

15 IRRI164 IR36 1695.5 164.871879 3226.128

16 IRRI168 IR36 2295.0 764.371879 3825.628

17 IRRI116 IR72 1614.5 82.445583 3146.554

18 IRRI119 IR72 1927.0 394.945583 3459.054

19 IRRI123 IR72 1590.0 57.945583 3122.054

20 IRRI146 IR72 2268.0 735.945583 3800.054

21 IRRI156 IR72 1578.5 46.445583 3110.554

22 IRRI168 IR72 1939.0 406.945583 3471.054

==============================

GENOTYPE AS: Random

==============================

------------------------------

RESPONSE VARIABLE: YIELD

------------------------------



1 YIELD 1 100 4349.44 781.2752

2 YIELD 2 100 4338.00 791.9981

------------------------------


------------------------------

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DATA SUMMARY:




ENTRY 50 IR36 IR64 IR72 ... IRRI168

REP 2 1 2



1 Test:Check 365200.468 604.31818

2 REP 3029.351 55.03954

3 Residual 239417.912 489.30350

TESTING FOR THE SIGNIFICANCE OF GENOTYPIC EFFECT USING -2 LOGLIKELIHOOD RATIO

TEST:

Formula for Model1: YIELD ~ 1 + Check + (1|REP) + (1|Test:Check)

Formula for Model2: YIELD ~ 1 + Check + (1|REP)

AIC BIC logLik Chisq Df Pr(>Chisq)

Model2 1566.855 1582.486 -777.4273

Model1 1546.951 1565.187 -766.4756 21.9034 1 0.0000

TESTING FOR THE SIGNIFICANCE OF CHECK EFFECT:



Check 3 912075.5 304025.2 1.2699 45.9965 0.2958

PREDICTED MEANS:

ENTRY Means

1 IRRI102 4177.854

2 IRRI103 3964.718

3 IRRI104 4348.815

4 IRRI105 4240.740

5 IRRI106 4164.297

6 IRRI108 4449.734

7 IRRI109 4620.695

8 IRRI112 4429.023

9 IRRI113 4703.539

10 IRRI115 4293.083

11 IRRI116 5012.700

12 IRRI117 4525.800

13 IRRI118 4891.069

14 IRRI119 5248.053

15 IRRI120 4860.944

16 IRRI122 4682.452

17 IRRI123 4994.248

18 IRRI124 3837.062

19 IRRI125 3514.722

20 IRRI127 3577.985

21 IRRI128 3314.012

22 IRRI133 3633.340

23 IRRI134 3918.777

24 IRRI135 4654.209

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25 IRRI136 4585.298

26 IRRI139 3694.720

27 IRRI140 4225.301

28 IRRI141 4850.023

29 IRRI143 4398.898

30 IRRI145 4025.345

31 IRRI146 5504.871

32 IRRI147 4372.915

33 IRRI148 4332.622

34 IRRI149 4396.638

35 IRRI150 4906.132

36 IRRI151 4126.264

37 IRRI152 3585.516

38 IRRI154 4938.893

39 IRRI155 3711.289

40 IRRI156 4985.587

41 IRRI157 3443.174

42 IRRI161 4728.016

43 IRRI162 4745.715

44 IRRI163 4342.789

45 IRRI164 4805.589

46 IRRI165 4139.444

47 IRRI168 5257.091

CHECK/CONTROL LSMEANS:

ENTRY LSMean StdErrMean

1 IR36 3247.5 697.4388

2 IR64 4461.0 697.4388

3 IR72 3603.5 697.4388

HERITABILITY:

0.75

==============================

GENOTYPIC CORRELATIONS:

Site: 1

YIELD PLTHGT

YIELD 0.4687

PLTHGT 0.4687

PHENOTYPIC CORRELATIONS:

Site: 1

YIELD PLTHGT

YIELD 0.4342

PLTHGT 0.4342

==============================

Figure 12. Sample Partial Text Output of the Single-environment Analysis.

Generated graphs can be viewed by clicking the Graph Tab of the displayed results folder. Sample generated graphs are shown in Figure 13. The distribution of the

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values of the response variable can be assessed by looking at the boxplot and histogram while for the distribution of the residuals, diagnostic plots and heatmap are available.

Figure 13. Sample graph outputs for Single-Environment Analysis.

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Multi-environment analysis For experiments done in multiple environments, analysis can be done across environments. Two options are available for multi-environment analysis: one-stage and two-stage. One-stage analysis requires raw data while two-stage analysis requires summary data generated from single environment analysis as input. In this paper, only one-stage analysis is presented. One-stage analysis is available for RCB, Alpha-Lattice and Row-Column designs. Sample filled-up tabs for RCB are shown in Figures 14 to 16.

Figure 14. Model Specifications Tab of Multi-Environment Analysis

(One-Stage) Dialog Box.

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Figure 15. Options Tab of Multi-Environment Analysis (One-Stage)

Dialog Box.

Figure 16. Graph Tab of Multi-Environment Analysis (One-Stage) Dialog Box.

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After processing the analysis, a text output is displayed in the Editor panel. Figure 17 shows the sample partial result of the analysis. If genotype is regarded as fixed, the output of the analysis includes the following: data summary; some descriptive statistics of the response variable; estimates of the variance components of the model; test for the significance of genotypic effect wherein the denominator degrees of freedom in F test is computed according to a general Satterthwaite approximation; test for the significance of environment and genotypic environment effects using -2 loglikelihood ratio test; genotypic environment means; least-square means of the genotypes; summary statistics of the standard errors of the difference; pairwise mean comparison using Dunnett's procedure if comparing treatments with a control and HSD if performing all pairwise mean comparisons; stability analysis using Finlay-Wilkinson model and Shuklas model; and, additive main effects and multiplicative interaction (AMMI) analysis. If genotype is regarded as random, the output of the analysis includes the following: data summary; some descriptive statistics of the response variable; estimates of the variance components of the model; test for the significance of genotypic, environment and genotypic environment effects using -2 loglikelihood ratio test; genotypic environment means; predicted genotype means derived using the Best Linear Unbiased Prediction (BLUP); and, estimate of heritability.

DATA FILE: E:/NSALES/pbtools workspace/testing/Data/RCB_ME.csv

MULTI-ENVIRONMENT ANALYSIS (ONE-STAGE)


==============================

GENOTYPE AS: Fixed

==============================

------------------------------

RESPONSE VARIABLE: Yield

------------------------------

DATA SUMMARY:




Env 11 E1 E10 E11 ... E9

Genotype 15 GEN1 GEN10 GEN11 ... GEN9

Block 3 1 2 3


Variable N_NonMissObs Mean StdDev

1 Yield 495 1718.596 1117.791



1 Genotype:Env 664747.696 815.32061

2 Block:Env 6497.161 80.60497

3 Env 530979.863 728.68365

4 Residual 94709.288 307.74874

18




Genotype 14 1386210 99015 1.0455 139.9947 0.4127

TESTING FOR THE SIGNIFICANCE OF ENVIRONMENT EFFECT USING -2 LOGLIKELIHOOD RATIO

TEST:

Formula for Model1: Yield ~ 1 + Genotype + (1|Env) + (1|Block:Env) + (1|Genotype:Env)

Formula for Model2: Yield ~ 1 + Genotype + (1|Block:Env) + (1|Genotype:Env)


Model2 7513.743 7589.425 -3738.871

Model1 7457.593 7537.480 -3709.797 58.1496 1 0.0000

TESTING FOR THE SIGNIFICANCE OF GENOTYPE X ENVIRONMENT EFFECT USING -2

LOGLIKELIHOOD RATIO TEST:

Formula for Model1: Yield ~ 1 + Genotype + (1|Env) + (1|Block:Env) + (1|Genotype:Env)

Formula for Model2: Yield ~ 1 + Genotype + (1|Env) + (1|Block:Env)


Model2 7942.529 8018.211 -3953.264

Model1 7457.593 7537.480 -3709.797 486.9356 1 0.0000

GENOTYPE X ENVIRONMENT MEANS: (some rows are deleted)

Genotype Env Yield_means

1 GEN1 E1 2958.1639

2 GEN1 E5 352.6978

3 GEN1 E4 1294.7984

4 GEN1 E11 2072.8784

5 GEN1 E7 514.8013

6 GEN1 E3 1373.9847

7 GEN1 E6 1800.7020

8 GEN1 E10 1026.3886

9 GEN1 E2 782.0394

10 GEN1 E9 4034.1663

.

.

.

165 GEN9 E9 1517.3235

GENOTYPE LSMEANS AND STANDARD ERRORS:

Genotype LSMean StdErrMean

1 GEN1 1500.965 334.2864

2 GEN10 1804.918 334.2864

3 GEN11 1902.555 334.2864

4 GEN12 2023.497 334.2864

5 GEN13 1953.552 334.2864

6 GEN14 2163.924 334.2864

7 GEN15 1829.575 334.2864

8 GEN2 1826.130 334.2864

9 GEN3 1615.296 334.2864

10 GEN4 1557.518 334.2864

19

11 GEN5 1246.419 334.2864

12 GEN6 1606.112 334.2864

13 GEN7 1523.806 334.2864

14 GEN8 1871.903 334.2864

15 GEN9 1352.776 334.2864


Estimate

Minimum 355.8134

Average 355.8134

Maximum 355.8134

SIGNIFICANT PAIRWISE COMPARISONS (IF ANY):

Compared with control(s)

(No significant pairwise comparisons.)

STABILITY ANALYSIS USING FINLAY-WILKINSON MODEL:

Slope SE t.value Prob MSReg MSDev

GEN1 1.2781068 0.2844126 4.493847 1.502182e-03 9332417.6 462123.09

GEN10 0.6527849 0.2813760 2.319973 4.548779e-02 2434445.5 452307.80

GEN11 1.6932433 0.2287290 7.402837 4.091093e-05 16379423.5 298883.70

GEN12 1.6800025 0.2291829 7.330400 4.418676e-05 16124257.8 300071.21

GEN13 1.0057795 0.3020917 3.329384 8.807711e-03 5779170.2 521359.88

GEN14 1.5848878 0.5707898 2.776658 2.151802e-02 14350165.8 1861282.35

GEN15 1.0948669 0.3462029 3.162501 1.150386e-02 6848296.6 684733.14

GEN2 1.1363548 0.2719630 4.178344 2.381936e-03 7377136.1 422551.36

GEN3 0.8969413 0.4169984 2.150947 5.994425e-02 4596083.4 993410.28

GEN4 0.3024868 0.2899820 1.043123 3.240997e-01 522724.4 480398.97

GEN5 0.7151867 0.1240071 5.767305 2.703442e-04 2922125.1 87852.27

GEN6 0.6888218 0.2543126 2.708563 2.405402e-02 2710651.2 369484.01

GEN7 0.6136909 0.2464923 2.489696 3.443918e-02 2151588.5 347109.54

GEN8 0.9025519 0.3482402 2.591751 2.912969e-02 4653763.4 692815.70

GEN9 0.7542942 0.2547682 2.960708 1.594118e-02 3250434.9 370809.14

STABILITY ANALYSIS USING SHUKLA'S MODEL:

lower est. upper

GEN1 264.805740 703.6167 1869.584

GEN10 16.424694 738.2801 33185.250

GEN11 151.126221 937.3589 5813.959

GEN12 135.445669 943.9686 6578.851

GEN13 177.323849 786.7224 3490.405

GEN14 182.708778 1427.7333 11156.674

GEN15 211.352595 953.4036 4300.767

GEN2 163.700619 778.2112 3699.514

GEN3 125.120648 944.0875 7123.534

GEN4 5.338358 687.2203 88467.608

GEN5 3.165181 218.8051 15125.728

GEN6 46.682322 511.4079 5602.508

GEN7 28.716855 497.1291 8606.003

GEN8 160.228588 787.3109 3868.589

GEN9 124.674720 621.5542 3098.701

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AMMI ANALYSIS:

Percentage of Total Variation Accounted for by the Principal Components:

percent acum Df Sum.Sq Mean.Sq F.value Pr.F

PC1 38.2 38.2 23 101890340.4 4430014.80 46.77 0.0000

PC2 23.9 62.1 21 63620736.9 3029558.90 31.99 0.0000

PC3 19.2 81.3 19 51267271.5 2698277.45 28.49 0.0000

PC4 8.7 90.0 17 23217503.0 1365735.47 14.42 0.0000

PC5 5.4 95.4 15 14268487.9 951232.52 10.04 0.0000

PC6 2.4 97.8 13 6282476.7 483267.44 5.10 0.0000

PC7 1.2 99.0 11 3123773.8 283979.43 3.00 0.0008

PC8 0.6 99.6 9 1635022.9 181669.21 1.92 0.0487

PC9 0.4 100.0 7 1129431.9 161347.42 1.70 0.1084

PC10 0.0 100.0 5 100764.4 20152.87 0.21 0.9582

PC11 0.0 100.0 3 0.0 0.00 0.00 1.0000

==============================

GENOTYPE AS: Random

==============================

------------------------------

RESPONSE VARIABLE: Yield

------------------------------

DATA SUMMARY:




Env 11 E1 E10 E11 ... E9

Genotype 15 GEN1 GEN10 GEN11 ... GEN9

Block 3 1 2 3


Variable N_NonMissObs Mean StdDev

1 Yield 495 1718.596 1117.791



1 Genotype:Env 664747.522 815.32050

2 Block:Env 6497.219 80.60533

3 Genotype 2876.978 53.63747

4 Env 530984.967 728.68715

5 Residual 94709.311 307.74878

TESTING FOR THE SIGNIFICANCE OF GENOTYPIC EFFECT USING -2 LOGLIKELIHOOD RATIO

TEST:

Formula for Model1: Yield ~ 1 + (1|Genotype) + (1|Env) + (1|Block:Env) + (1|Genotype:Env)

Formula for Model2: Yield ~ 1 + (1|Env) + (1|Block:Env) + (1|Genotype:Env)


Model2 7627.446 7648.469 -3808.723

Model1 7629.433 7654.661 -3808.717 0.0127 1 0.9102

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TESTING FOR THE SIGNIFICANCE OF ENVIRONMENT EFFECT USING -2 LOGLIKELIHOOD RATIO

TEST:


Formula for Model2: Yield ~ 1 + (1|Genotype) + (1|Block:Env) + (1|Genotype:Env)


Model2 7686.930 7707.953 -3838.465

Model1 7629.433 7654.661 -3808.717 59.4969 1 0.0000

TESTING FOR THE SIGNIFICANCE OF GENOTYPE X ENVIRONMENT EFFECT USING -2

LOGLIKELIHOOD RATIO TEST:


Formula for Model2: Yield ~ 1 + (1|Genotype) + (1|Env) + (1|Block:Env)


Model2 8114.369 8135.392 -4052.184

Model1 7629.433 7654.661 -3808.717 486.9356 1 0.0000

GENOTYPE X ENVIRONMENT MEANS: (some rows are deleted)

Genotype Env Yield_means

1 GEN1 E1 2967.6279

2 GEN1 E5 362.1033

3 GEN1 E4 1304.2393

4 GEN1 E11 2082.3420

5 GEN1 E7 524.2095

6 GEN1 E3 1383.4127

7 GEN1 E6 1810.1753

.

.

.

165 GEN9 E9 1533.2220

PREDICTED GENOTYPE MEANS:

Genotype Mean

1 GEN1 1709.135

2 GEN10 1722.349

3 GEN11 1726.594

4 GEN12 1731.851

5 GEN13 1728.811

6 GEN14 1737.956

7 GEN15 1723.421

8 GEN2 1723.271

9 GEN3 1714.106

10 GEN4 1711.594

11 GEN5 1698.069

12 GEN6 1713.706

13 GEN7 1710.128

14 GEN8 1725.261

15 GEN9 1702.693

HERITABILITY:

0.05

Figure 17. Sample Partial Text Output of Multi-environment (One-stage) Analysis.

22

Sample generated graphs are shown in Figure 18. Boxplot and histogram are available for the evaluation of the distribution of the values of the response variable while diagnostic plots for the distribution of the residuals. If AMMI analysis is requested, biplots are generated to aid in the assessment of the interaction between genotype and environment.

Figure 18. Sample graph outputs of Multi-environment (One-stage) Analysis.

23

Quantitative Trait Locus (QTL) Analysis

To link certain complex traits to specific regions of the chromosomes, quantitative trait locus (QTL) analysis can be used. In the current version of PBTools, QTL analysis is done per environment level only. The following files are needed as input: a csv file containing phenotypic data which can be either the predicted means or raw data, a tab-delimited txt file containing genotypic data and a tab-delimited txt file containing the genetic map. Both the genotypic data and genetic map files should be in the Flapjack format. The dialog box for QTL analysis with raw data as input are shown in Figures 19 to 21.

Figure 19. Data Input Tab of QTL Analysis Dialog Box.

Figure 20. Model Specifications Tab of QTL Analysis Dialog Box.

24

Figure 21. Options Tab of QTL Analysis Dialog Box.

A text file is generated after the analysis. Figure 22 shows the sample partial text output which contains the following: results of the single-environment analysis; LOD scores of all the markers; and statistics on the selected/significant markers.

DATA FILE: E:/NSALES/pbtools workspace/SampleProject/Data/QTL_pheno.csv

SINGLE-ENVIRONMENT ANALYSIS


------------------------------

RESPONSE VARIABLE: HEIGHT

------------------------------



1 HEIGHT 1 606 88.69455 31.62887

2 HEIGHT 2 606 86.69455 31.62887

------------------------------


------------------------------

DATA SUMMARY:




GENOTYPE 202 G_001 G_002 G_003 ... P2

REP 3 1 2 3

25



1 REP 611.3356 24.72520

2 Residual 302.7346 17.39927




GENOTYPE 201 235948.7 1173.874 3.8776 401.9975 0.0000

GENOTYPE LSMEANS AND STANDARD ERRORS: (some rows are deleted)

GENOTYPE LSMean StdErrMean

1 G_001 106.09469 17.45067

2 G_002 69.11523 17.45067

3 G_003 131.68455 17.45067

4 G_004 116.59435 17.45067

5 G_005 110.58281 17.45067

6 G_006 65.38761 17.45067

7 G_007 77.01282 17.45067

8 G_008 99.30493 17.45067

9 G_009 90.64883 17.45067

10 G_010 61.68259 17.45067

.

.

.

202 P2 77.78512 17.45067


Estimate

Minimum 14.2064

Average 14.2064

Maximum 14.2064

==============================

QTL ANALYSIS

METHOD: CIM

------------------------------

RESPONSE VARIABLE: HEIGHT

------------------------------

------------------------------


------------------------------

QTL RESULT (ALL): (some rows are deleted)

marker Chr Pos LOD

1 M_0001 1 0 0.998238082

2 M_0002 1 1 1.029862513

3 M_0006 1 5 1.097213383

4 1_loc10 1 10 0.683066798

5 M_0018 1 17 0.127036203

6 1_loc20 1 20 0.107014795

7 M_0022 1 21 0.098035804

26

8 1_loc30 1 30 0.126238502

9 M_0032 1 31 0.124952527

10 1_loc40 1 40 0.675666296

11 M_0042 1 41 7.910819471

12 1_loc50 1 50 9.507940316

13 M_0053 1 52 8.808176807

14 M_0056 1 55 7.075115150

15 M_0058 1 57 6.531686512

16 1_loc60 1 60 0.023835142

17 M_0062 1 61 0.010078575

18 M_0063 1 62 0.497989434

19 M_0066 1 65 0.511330577

20 M_0069 1 68 1.022791170

21 1_loc70 1 70 0.849382305

22 M_0076 1 75 0.286639058

23 M_0081 1 80 0.157442187

24 M_0083 1 82 1.915089343

25 M_0085 1 84 2.384399583

.

.

.

284 M_1087 7 150 0.154691409

QTL RESULT (SELECTED):

marker Chr Pos LOD m.eff Rsq

1 1_loc50 1 50 9.507940 8.388484 0.03366559

2 2_loc10 2 10 7.066201 -6.655585 0.05975959

3 M_0340 3 42 6.479474 -4.977133 0.07389893

4 M_0543 4 74 3.921155 4.776014 0.09046470

5 6_loc120 6 120 3.699853 3.778455 0.14220448

6 M_0989 7 52 10.649286 7.272148 0.17627526

Figure 22. Sample Partial Text Output of QTL Analysis

Sample generated graphs are shown in Figure 23. These include heatmap of LOD scores and recombination fractions, plot of pairwise genotypic differences, marker map, visualization of genotypes, plot of missing genotypes and QTL maps.

28

Figure 23. Sample graph outputs of QTL analysis. Selection Index Analysis To be able to select favorable genotypes based on several traits, a linear function of these traits referred to as selection index can be used. Four phenotypic selection indices and two molecular selection indices are available in PBTools. If any of the phenotypic selection indices is selected, a csv file containing the weights is needed while for the molecular selection indices, weights, marker and QTL files should be specified. The dialog box for selection index analysis appears in Figure 24.

Figure 24. Dialog box for Selection Index Analysis.

29

Figure 25 shows the sample output of the analysis. The output includes genetic

and phenotypic correlation matrices, molecular covariance matrix, statistics on the values of the selection index and breeding values, characteristics of the selected individuals, and values of the selection index for all individuals.

DATA FILE: E:/Program Files/PBTools/Projects/SampleProject/Data/SI_ traits.csv

Lande and Thompson Selection Index

DESIGN: Lattice

Genetic and Phenotypic Correlation Matrices

GENETIC CORRELATION MATRIX

MFL1 FFL1 EHT1 PHT1 GY1 MFL.2 FFL2 EHT2 PHT2 GY2

MFL1 1.00 0.88 0.19 -0.33 -0.62 0.96 0.88 0.23 -0.25 -0.36

FFL1 0.88 1.00 0.18 -0.20 -0.77 0.83 0.68 0.15 -0.28 -0.41

EHT1 0.19 0.18 1.00 0.75 -0.03 0.18 0.04 1.09 0.96 0.13

PHT1 -0.33 -0.20 0.75 1.00 0.32 -0.23 -0.28 0.75 1.09 0.28

GY1 -0.62 -0.77 -0.03 0.32 1.00 -0.59 -0.70 0.09 0.40 0.98

MFL.2 0.96 0.83 0.18 -0.23 -0.59 1.00 0.91 0.31 -0.23 -0.52

FFL2 0.88 0.68 0.04 -0.28 -0.70 0.91 1.00 0.27 -0.23 -0.61

EHT2 0.23 0.15 1.09 0.75 0.09 0.31 0.27 1.00 0.77 -0.08

PHT2 -0.25 -0.28 0.96 1.09 0.40 -0.23 -0.23 0.77 1.00 0.20

GY2 -0.36 -0.41 0.13 0.28 0.98 -0.52 -0.61 -0.08 0.20 1.00

PHENOTYPIC CORRELATION MATRIX


MFL1 1.00 0.71 0.01 -0.37 -0.47 0.63 0.56 0.10 -0.17 -0.29

FFL1 0.71 1.00 0.04 -0.26 -0.48 0.54 0.51 0.03 -0.20 -0.31

EHT1 0.01 0.04 1.00 0.80 0.07 0.13 0.06 0.71 0.51 0.06

PHT1 -0.37 -0.26 0.80 1.00 0.32 -0.14 -0.15 0.49 0.53 0.17

GY1 -0.47 -0.48 0.07 0.32 1.00 -0.35 -0.39 0.04 0.15 0.44

MFL.2 0.63 0.54 0.13 -0.14 -0.35 1.00 0.72 0.05 -0.31 -0.40

FFL2 0.56 0.51 0.06 -0.15 -0.39 0.72 1.00 0.05 -0.21 -0.45

EHT2 0.10 0.03 0.71 0.49 0.04 0.05 0.05 1.00 0.81 0.15

PHT2 -0.17 -0.20 0.51 0.53 0.15 -0.31 -0.21 0.81 1.00 0.34

GY2 -0.29 -0.31 0.06 0.17 0.44 -0.40 -0.45 0.15 0.34 1.00

MOLECULAR COVARIANCE MATRIX


MFL1 1.00 0.33 0.69 0.63 0.11 0.43 -0.23 0.48 0.79 0.37

FFL1 0.33 1.00 0.46 0.37 0.02 0.24 0.22 0.16 0.23 -0.12

EHT1 0.69 0.46 1.00 0.48 0.23 0.51 -0.41 0.58 0.41 0.13

PHT1 0.63 0.37 0.48 1.00 -0.21 0.47 0.25 0.48 0.50 -0.10

GY1 0.11 0.02 0.23 -0.21 1.00 -0.04 -0.34 -0.01 0.27 -0.18

MFL.2 0.43 0.24 0.51 0.47 -0.04 1.00 0.15 0.73 0.31 0.04

FFL2 -0.23 0.22 -0.41 0.25 -0.34 0.15 1.00 -0.14 -0.04 -0.16

EHT2 0.48 0.16 0.58 0.48 -0.01 0.73 -0.14 1.00 0.32 0.01

PHT2 0.79 0.23 0.41 0.50 0.27 0.31 -0.04 0.32 1.00 -0.02

GY2 0.37 -0.12 0.13 -0.10 -0.18 0.04 -0.16 0.01 -0.02 1.00

30

COVARIANCE BETWEEN SELECTION INDEX AND BREEDING VALUE: 3.205508

VARIANCE OF THE SELECTION INDEX: 1.50582

VARIANCE OF THE BREEDING VALUE: 6.145354

CORRELATION BETWEEN SELECTION INDEX AND BREEDING VALUE: 0.9999

VALUES OF THE TRAITS, SELECTION INDEX, MEANS, GAINS FOR THE 5% SELECTED

INDIVIDUALS

MFL1 FFL1 EHT1 PHT1 GY1 MFL.2 FFL2

Entry 240 102.01 102.12 80.53 140.12 0.00 100.70 100.74

Entry 2 104.88 104.42 100.22 148.82 28.72 99.60 100.36

Entry 21 101.23 100.75 93.45 163.42 34.45 100.23 98.34

Entry 132 104.69 104.71 75.75 126.00 44.00 97.88 100.35

Entry 167 106.75 105.49 81.67 132.64 0.83 106.21 108.25

Entry 179 104.39 101.50 76.00 126.03 23.78 100.74 99.34

Entry 220 105.34 104.37 78.75 137.92 97.16 99.84 98.31

Entry 174 103.13 102.54 96.84 146.33 47.44 96.59 99.25

Entry 165 104.61 103.66 90.75 150.25 79.00 99.32 103.80

Entry 161 103.12 99.05 85.75 148.50 82.50 101.46 103.00

Entry 87 101.53 100.88 103.66 156.84 68.33 102.34 99.20

Mean of

Selected Individuals 103.79 102.68 87.58 143.35 46.02 100.44 100.99

Mean of

all Individuals 102.01 102.12 80.53 140.12 75.99 100.70 100.74

Selection Differential 1.78 0.56 7.04 3.23 -29.97 -0.26 0.26

Expected Genetic Gain

for 5% 1.57 1.64 1.52 1.19 -1.13 1.95 1.37

EHT2 PHT2 GY2 LT index

Entry 240 78.47 133.44 0.00 2.88

Entry 2 106.75 161.75 140.00 2.59

Entry 21 89.69 156.81 1.50 2.34

Entry 132 76.09 127.28 33.39 2.24

Entry 167 75.00 113.64 0.00 2.14

Entry 179 74.31 124.14 9.24 2.14

Entry 220 87.00 143.50 129.50 1.94

Entry 174 94.93 149.59 18.61 1.83

Entry 165 96.25 160.25 41.00 1.80

Entry 161 76.50 125.69 12.75 1.74

Entry 87 91.95 140.56 35.00 1.70

Mean of Selected Individuals 86.08 139.69 38.27 NA

Mean of all Individuals 78.47 133.44 51.70 NA

Selection Differential 7.61 6.26 -13.43 NA

Expected Genetic Gain for 5% 1.73 1.08 -1.02 NA

31

VALUES OF THE TRAITS AND THE SELECTION INDEX FOR ALL INDIVIDUALS


Entry 1 102.21 100.25 71.45 123.75 42.45 99.29 98.95 68.51 117.47 16.87

Entry 2 104.88 104.42 100.22 148.82 28.72 99.60 100.36 106.75 161.75 140.00

Entry 3 98.97 100.44 80.17 154.36 77.78 97.93 96.82 66.75 133.75 116.00

.

.

.

(some rows are deleted)

Figure 25. Sample Partial Text Output of Selection Index Analysis. Mating Designs

Several mating designs were developed to estimate genetic variance components. Experiments which used the following mating designs can be analyzed in PBTools: North Carolina I to III, Triple Test Cross and Diallel I to IV. For each mating design, the experiment can be laid out in any of these four experimental designs: Completely Randomized, RCB, Alpha-Lattice, and Row-Column design. In this paper, only analyses for North Carolina II and Diallel II are presented.

For North Carolina II, analysis can be done per environment level or across

environments. To illustrate analysis per environment level, a sample completed dialog box is shown in Figure 26.

Figure 26. Dialog Box for North Carolina Experiment II.

32

The results of the analysis as shown in Figure 27 includes data summary, ANOVA table (assuming fixed model), estimates of the variance components and estimates of the genetic variance components.

DATA FILE: E:/NSALES/pbtools workspace/SampleProject/Data/NCII_ME.csv

DESIGN: NORTH CAROLINA EXPERIMENT II IN RCB (INBRED)

-----------------------------

RESPONSE VARIABLE: Y

-----------------------------

-----------------------------

ANALYSIS FOR: Env = A

-----------------------------

DATA SUMMARY:

Factors No of Levels Levels

Env 1 A

Female 8 1 2 3 ... 8

Male 8 10 11 12 ... 9

Block 3 1 2 3



ANOVA TABLE FOR THE EXPERIMENT:

Df Sum Sq Mean Sq F value Pr(>F)

Block 2 22.3531 11.1766 1.14 0.3220

Male 7 1112.6490 158.9498 16.26 0.0000

Female 7 735.2669 105.0381 10.75 0.0000

Male:Female 49 823.1469 16.7989 1.72 0.0086

Residuals 126 1231.4730 9.7736

-------

REMARK: Raw dataset is balanced.

LINEAR MIXED MODEL FIT BY RESTRICTED MAXIMUM LIKELIHOOD:

Formula: Y ~ 1 + (1|Block) + (1|Male) + (1|Female) + (1|Male:Female)

AIC BIC logLik deviance REMLdev

1057.665 1077.21 -522.8323 1047.758 1045.665

Fixed Effects:

Estimate Std. Error t value

(Intercept) 55.6076 1.1379 48.8702

Random Effects:

Groups Variance Std. Deviation

Male:Female 2.3418 1.5303

Female 3.6767 1.9175

Male 5.9229 2.4337

Block 0.0219 0.1481

Residual 9.7736 3.1263

33

ESTIMATES OF GENETIC VARIANCE COMPONENTS:

Estimate

VA 9.599670

VD 2.341800

Narrow sense heritability(plot-mean based) 0.442075

Broad sense heritability(plot-mean based) 0.549917

Dominance Ratio 0.698492

Figure 27. Sample Text Output of North Carolina II Per Environment Analysis

For multiple-environment analysis, the sample output as shown in Figure 28 includes data summary, ANOVA table (assuming fixed model), estimates of the variance components and estimates of the genetic variance components.

DATA FILE: E:/NSALES/pbtools workspace/SampleProject/Data/NCII_ME.csv

MULTIPLE ENVIRONMENT ANALYSIS

DESIGN: NORTH CAROLINA EXPERIMENT II IN RCB (INBRED)

-----------------------------

RESPONSE VARIABLE: Y

-----------------------------

DATA SUMMARY:


Env 2 A B

Female 8 1 2 3 ... 8

Male 8 10 11 12 ... 9

Block 3 1 2 3



ANOVA TABLE:


Env 1 8.7665 8.7665 0.38 0.5724

Env:Block 4 93.0194 23.2549 2.21 0.0682

Male 7 840.6569 120.0938 11.43 0.0000

Female 7 821.7501 117.3929 11.17 0.0000

Male:Female 49 1233.6320 25.1762 2.40 0.0000

Env:Male 7 493.0000 70.4286 6.70 0.0000

Env:Female 7 215.9051 30.8436 2.93 0.0057

Env:Male:Female 49 974.2153 19.8819 1.89 0.0009

Residuals 252 2648.7840 10.5110

-------


34

LINEAR MIXED MODEL FIT BY RESTRICTED MAXIMUM LIKELIHOOD:

Formula: Y ~ 1 + (1|Env) + (1|Env:Block) + (1|Male) + (1|Female) +

(1|Male:Female) + (1|Env:Male) + (1|Env:Female) + (1|Env:Male:Female)

AIC BIC logLik deviance REMLdev

2147.079 2186.586 -1063.54 2128.376 2127.079

Fixed Effects:

Estimate Std. Error t value

(Intercept) 55.7587 0.7634 73.042

Random Effects:

Groups Variance Std. Deviation

Env:Male:Female 3.1506 1.7750

Male:Female 0.8681 0.9317

Env:Female 0.3985 0.6313

Env:Male 1.8441 1.3580

Female 1.7219 1.3122

Male 1.0554 1.0273

Env:Block 0.1792 0.4233

Env 0.0000 0.0000

Residual 10.5157 3.2428


Estimate

VA 2.777330

VAxE 2.242660

VD 0.868100

VDxE 3.150620

h2-narrow sense 0.142031

H2-broad sense 0.186425


Figure 28. Sample Text Output of North Carolina II Mulit-environment Analysis

In cases where information on effects due to reciprocal, maternal, general

combining ability (GCA) and the specific combining ability (SCA) of parents in crosses are of interest, diallel design can be used. In analyzing such designs, PBTools makes use of the Griffing Method. The sample dialog box for Diallel II analysis is shown in Figure 29.

35

Figure 29. Dialog Box for Diallel Analysis (Griffing Method 2).

Partial results are shown in Figure 30. This consists of data summary, test for the significance of the crosses, test for the significance of GCA and SCA effects, GCA, SCA and residual variance estimates, estimates of genetic variance components and estimates of the GCA and SCA effects.

36

DATA FILE: E:/NSALES/pbtools workspace/SampleProject/Data/Diallel_M2.csv

DIALLEL ANALYSIS: GRIFFING METHOD II IN RCB (CROSS)

-----------------------------

RESPONSE VARIABLE: Plant_height

-----------------------------

-----------------------------

ANALYSIS FOR: Env = Normal

-----------------------------

DATA SUMMARY:


P1 7 1 2 3 4 5 6 7

P2 7 1 2 3 4 5 6 7

Block 3 1 2 3

Env 1 Normal



TESTING FOR THE SIGNIFICANCE OF CROSS EFFECT: (Crosses = P1:P2)

Formula for Model 1: Plant_height ~ Crosses + (1|Block)

Formula for Model 2: Plant_height ~ (1|Block)


Model2 758.9207 766.2131 -376.4603

Model1 466.3195 539.2440 -203.1597 346.6012 1 0.0000

MATRIX OF MEANS:

1 2 3 4 5 6 7

1 142.9000 148.3333 163.9000 152.9000 142.3667 160.6667 191.3333

2 129.6667 142.9000 143.9000 131.5667 143.5333 186.6667

3 131.5667 163.5667 136.9000 166.4333 189.7667

4 159.3333 149.8000 164.8000 200.2333

5 122.4333 138.9000 175.7667

6 146.1333 195.5667

7 157.5333

ANALYSIS OF VARIANCE:

SV Df Sum Sq Mean Sq F value Pr(>F)

GCA 6 7784.37 1297.39 6.05 0.0008

SCA 21 4500.58 214.31 14.56 0.0000

Error 54 794.66 14.72

ESTIMATES OF VARIANCE COMPONENTS:

Estimate Std. Error

GCA 120.3424 217.0737

SCA 199.5973 66.1426

Error 14.7160 2.8321

37


Estimate

VA 481.369471

VD 798.389175




GENERAL COMBINING ABILITY EFFECTS (diagonal), SPECIFIC COMBINING

ABILITY EFFECTS (above diagonal):

1 2 3 4 5 6 7

1 -0.6608 3.1454 10.8935 -7.5806 1.1861 3.7083 13.0157

2 -10.5571 -0.2102 -6.6843 0.2824 -3.5287 18.2454

3 -2.7386 5.1639 -2.2028 11.5528 13.5269

4 4.7354 3.2231 2.4454 16.5194

5 -14.5646 -4.1546 11.3528

6 1.2132 15.3750

7 22.5725

TABLE OF STANDARD ERRORS AND LSDs:

Std. Error LSD

Gi 1.1839

Sii 2.9299

Sij 3.4430

Gi-Gj 1.8084 3.6256

Sii-Sjj 4.0437 8.1070

Sij-Sik 5.1149 10.2547

Sij-Skl 4.7845 9.5924

Figure 30. Sample Text Output of Diallel II Per Environment Analysis.

For multiple-environment analysis, the sample output as shown in Figure 31 includes data summary, test for the significance of the crosses environment effect, test for the significance of GCA and SCA effects, estimates of the GCA and SCA effects, GCA, SCA and residual variance estimates and estimates of genetic variance components.

38

DATA FILE: E:/NSALES/pbtools workspace/SampleProject/Data/Diallel_M2.csv

MULTIPLE ENVIRONMENT ANALYSIS

DIALLEL ANALYSIS: GRIFFING METHOD II IN RCB (CROSS)

-----------------------------

RESPONSE VARIABLE: Plant_height

-----------------------------

DATA SUMMARY:


P1 7 1 2 3 4 5 6 7

P2 7 1 2 3 4 5 6 7

Env 2 Normal Saline

Block 3 1 2 3


Number of missing observations: 0

ANOVA TABLE:


Env 1 17111.43 17111.43 28.18 0.0061

Block(Env) 4 2429.29 607.32 14.44 0.0000

Crosses 27 80041.58 2964.50 31.42 0.0000

Crosses x Env 27 2547.46 94.35 2.24 0.0019

Error 108 4543.85 42.07

-------


ANOVA TABLE:


GCA 6 54367.67 9061.28 51.14 0.0001

SCA 21 25673.91 1222.57 17.30 0.0000

GCAxE 6 1063.14 177.19 4.21 0.0008

SCAxE 21 1484.32 70.68 1.68 0.0450

Error 108 4543.85 42.07

-------


MATRIX OF MEANS:

1 2 3 4 5 6 7

1 131.0000 133.8333 153.5500 140.7333 128.9000 154.4333 182.2833

2 116.8333 130.5500 133.8500 122.7167 129.0500 175.9000

3 122.0000 154.5000 131.2167 153.2167 177.7833

4 137.3333 138.5667 155.7833 195.2333

5 111.8833 132.5667 166.3333

6 143.0167 188.6167

7 155.1000

-------


39

GENERAL COMBINING ABILITY EFFECTS, SPECIFIC COMBINING ABILITY EFFECTS (above

diagonal)

1 2 3 4 5 6 7

1 1.4884 11.7329 -6.4745 -1.7227 6.5181 12.5181

2 -0.5819 -2.6727 2.7792 -8.1801 16.8199

3 8.5051 1.8069 6.5144 9.2310

4 3.7662 3.6903 21.2903

5 -2.9412 8.9755

6 13.9662

7

GCA -1.6418 -12.3270 -2.8548 2.5360 -14.0492 3.2434 25.0934

TABLE OF STANDARD ERRORS AND LSDs:

Std. Error LSD

Gi 0.8172

Sii 2.3767

Sij 2.0225

Gi-Gj 1.2483 2.4743

Sii-Sjj 2.7913 5.5328

Sij-Sik 3.5307 6.9985

Sij-Skl 3.3027 6.5465

ESTIMATES OF VARIANCE COMPONENTS:

Estimate

GCA 143.1889

SCA 191.9809

GCAxE 3.9448

SCAxE 9.5364

Error 42.0727


Estimate

VA 572.755727

VAxE 15.779056

VD 767.923608

VDxE 38.145415




Figure 31. Sample Text Output of Diallel II Multi-environment Analysis.

Future Direction

In succeeding versions, analysis for other experimental designs will be made available for single-environment analysis. Also, other input data options will be introduced. This includes allowing subsampling data for mating designs and accepting input files of different formats for QTL analysis. Finally, a module for multi-environment QTL analysis will also be added.

Documents

PLANT BREEDING TOOLS- SOFTWARE FOR PLANT BREEDERS.pdf