Genotype -by- environment interaction

Genotype-by-Environment Interaction (GEI) is a prevalent issue among crop farmers, plant breeders, geneticists, and production agronomists. This book brings together contributions from expert plant breeders and quantitative geneticists to better understand the relationship between crop performance and environment. This information can reduce the cost of extensive genotype evaluation by eliminating unnecessary testing sites and by fine-tuning breeding programs. Molecular aspects of GEI are discussed for the first time and key bibliographical references on GEI are included in an appendix. Genotype -by- Environment Interaction......Page 1 Table of Contents......Page 6 Preface......Page 3 The Editors......Page 5 I. Introduction......Page 8 Table of Contents......Page 0 II. Relative Importance of Error Rates......Page 9 A. Error Rates For Yield Comparisons......Page 10 B. Error Rates for Stability Variance......Page 11 III. Stability for Unbalanced Data......Page 12 IV. Simultaneous Selection for Yield and Stability......Page 14 V. Contribution of Environmental Variables to Genotype-by-Environment Interaction......Page 18 References......Page 19 I. Introduction......Page 22 B. Additional Information......Page 23 C. Description of the Models......Page 25 D. Example Data Set......Page 26 A. The Additive Model as Base Line......Page 27 B. Including One Quantitative Environmental Covariate......Page 29 C. Including One Quantitative Genotypic Covariate......Page 31 D. Including Several Quantitative Environmental Covariates......Page 32 E. Including One Qualitative Genotypic Covariate......Page 33 1. Quantitative-quantitative......Page 35 3. Qualitative-qualitative......Page 37 A. One-way Reduced Rank Regression with One Term......Page 40 B. One-way Reduced Rank Regression with Several Terms......Page 43 D. Reduced Rank Regression Independent of Covariates......Page 44 A. Genotypes Fixed and Environments Random......Page 45 C. Genotypes Fixed, Environments Random, and Random Interaction Depending on Genotype......Page 47 D. Software......Page 48 C. Fixed or Random......Page 49 A. Decomposing Main Effects......Page 50 F. Generalized Linear and Bilinear Models......Page 51 References......Page 52 I. Introduction......Page 57 II. Framework for Analysis of Genotypic Variation......Page 58 A. Analysis of Variance......Page 63 B. Direct and Indirect Selection......Page 64 C. Pattern Analysis......Page 65 III. Partition of the Genotype by Environment Interaction......Page 66 A. Theoretical Development......Page 67 1. Partitioning GxE interaction by heterogeneity of variances......Page 68 2. Partitioning of the GxE interaction by reranking......Page 70 1. Numerical example of Muir et al. (1992)......Page 74 2. Wheat example......Page 76 IV. Discussion......Page 84 References......Page 88 I. Introduction......Page 91 II. The AMMI Model......Page 92 III. Research Challenges: Interaction and Noise......Page 93 IV. Understanding Genotypes and Environments......Page 94 A. General Perspective......Page 95 B. Environmental Interpretation......Page 98 C. Plant Morphology and Physiology......Page 101 D. Breeding, Selection, and Hemtability......Page 102 V. Evidence of Accuracy Gain......Page 104 A. Validation Evidence......Page 105 B. Additional Evidence......Page 107 C. Practical Implications......Page 110 VI. Experimental Design......Page 113 A. Algorithm Variations and Refinement......Page 115 B. Degrees of Freedom......Page 116 C. Confidence Intervals......Page 117 E. Related Analyses......Page 118 G. Selection Triathlon and Experimental Design......Page 120 VIII. Conclusions......Page 121 References......Page 122 I. Introduction......Page 129 A. QTL Analyses......Page 132 B. QxE Analyses......Page 136 A. Background......Page 139 B. Characterization of Lines and Environments......Page 140 1. Comparison of results from IM and MT analyses.......Page 144 2. Identified QTL and QxE.......Page 145 A. Evidence for QxE ?......Page 149 B. Suggestion......Page 151 References......Page 152 I. Introduction......Page 156 II. Model and Stability Statistics......Page 157 III. Ranking Ability - Simulations......Page 161 1. Parametric global tests......Page 163 2. Global tests based on ranks......Page 165 3. Robust global tests......Page 167 1. Parametric tests for pairwise comparisons......Page 169 2. Rank tests/robust tests for pairwise comparisons......Page 171 V. Estimating the Stability Variance When Some G x E Combinations are Missing......Page 172 VI. Unequal Number of Replications Per Environment and Heterogeneous Error Variances......Page 173 VII. Partitioning Different Sources of G x E Interaction......Page 175 VIII. A Concluding Remark......Page 176 References......Page 177 I. Introduction......Page 180 II. SHMM and Its Relationship to COI......Page 181 A. SHMM Clustering Method for Grouping Sites or Genotypes......Page 182 B. Lack of Fit of SHMM......Page 183 B. Constrained Non-COI SHMM Solutions......Page 184 2. Constrained SVD Non-COI Solution for Two Sites......Page 185 5. When Attempted Non-COI Solution Still Shows COI......Page 188 6. Algorithm for Constrained LS Non-COI Solutions......Page 189 7. Which Constrained Solution to Use......Page 190 A. Results......Page 191 VI. Other SHMM-based Methods......Page 200 VIII. Acknowledgment......Page 202 References......Page 203 I. Introduction......Page 204 II. Least Squares Estimates......Page 206 III. Testing Significance of the Multiplicative Terms......Page 207 A. Gollob's F-Test......Page 208 1. F2-Type Approximations......Page 209 2. F1-Type Approximations......Page 212 3. The FR Test......Page 213 IV. Hypothesis Testing Example......Page 214 V. Using "Shrinkage" to Obtain Better Estimates......Page 216 A. Shrinkage Estimators Analogous to Blups......Page 217 B. Computation of Shrinkage Estimates......Page 218 C. Shrinkage Estimation of SHMM......Page 219 D. Comparisons of Shrinkage Estimators, Truncated Models, and Blups......Page 220 E. The Question of Optimality......Page 222 VI. Shrinkage Estimation Example......Page 224 A. Interpretation as a Stability Analysis......Page 226 VII. Choosing a Model Form......Page 228 B. Mandel's Tests for Concurrent and Nonconcurrent Regression......Page 229 A. Test Procedures......Page 231 C. Shrinkage Estimates in Unreplicated Rials......Page 233 IX. Software......Page 235 References......Page 236 Appendix......Page 238 B. FORSHMM......Page 239 I.Introduction......Page 240 A. Introductory Comments......Page 243 C. Bredenkamo-Approach......Page 245 F. Rank-Interaction by Van Der Laan and De Kroon......Page 246 G. Application of Spearman's Rank-Correlation and Kendall's Coefficient of Concordance to Quantify Genotype-Environment Relationships and to Group Environments or Genotypes......Page 249 H. Genotype-Specific Measures for a Quantitative Estimation of Phenotypic Stability......Page 257 I. Numerical Example......Page 264 III. Conclusions and Recommendation......Page 272 References......Page 273 I. Introduction......Page 277 2. Binomial Approach.......Page 279 3. Nonparametric Approach Based On Residuals.......Page 280 B. Probability of Several Traits Outperforming a Check......Page 281 5. Application.......Page 283 C. Relationship Between Reliability and Other Stability Measures......Page 286 D. Comparing the Repeatability of Reliabilities with Other Measures......Page 291 E. Evaluating Across Environment Variability Using Reliability Functions......Page 292 2. Location, Slope And Shape Of Reliability Functions.......Page 293 3. Application.......Page 294 III. Discussion......Page 296 A. Testing Equality of Reliabilities for k Test Entries Based on Normally Distributed Differences and the Wald Test......Page 298 B. Computing Univariates and Multivariate Reliabilities Using Residuals From a Linear Model......Page 300 C. Relationship Between Stability Parameters and Variance of the Test-Check Differences......Page 303 1. Program 1......Page 304 2. Program 2......Page 306 3. Program 3......Page 309 References......Page 310 I. Introduction......Page 312 II. Characterizing Target Environments......Page 313 III. Selecting Optimal Testing Sites......Page 315 IV. Developing Optimal Population Types......Page 316 A. Impact on Mean Performance......Page 318 B. Impact on Environmental Sensitivity......Page 324 A. Selection Indices......Page 327 B. Stability......Page 330 C. Mean Performance and Stability......Page 332 D. Alternative Traits......Page 334 References......Page 338 1. The Model......Page 343 B. Method of Generating Populations......Page 344 D. Method of Generating GEI......Page 345 F. Summary of Results......Page 346 A. The VAPGeP Model......Page 347 2. Method of Computing Genie Proportion......Page 348 B. Procedure of Selecting Positive or Super Positive Parental Lines......Page 349 1). Analysis of Variance Method.......Page 350 2). Yield Prediction Method.......Page 351 D. Implications of the VAPGeP Model......Page 352 References......Page 353 I. Introduction......Page 354 A. Variance of Genotypes......Page 355 B. Ecovalence......Page 356 C. Regression Coefficients......Page 357 D. Grouping by Clusters......Page 358 1. Relation Between Different Stability Parameters and the Mean......Page 359 2. Repeatability......Page 360 III. Prediction For a Set of Environments......Page 362 A. Principal Components......Page 363 B. Cluster Analysis......Page 364 A. Main Effects Only......Page 365 C. Principal Components......Page 366 E. Experimental Results......Page 367 V. Conclusions......Page 368 References......Page 370 I. Introduction......Page 373 A.The Rationale of the Application of Spatial Analysis to Plant Nutrition Experiments......Page 375 2. Tea (Camellia sinensis) nutritional experiment, 1992/1993, Tzaneen, North Eastern Transvaal......Page 377 1. Diagnosing the presence of fertility gradients......Page 379 2. Data-analytic procedures......Page 380 A. Diagnostics......Page 386 C. Evidence That The AMMI1 Predicted Residuals Capture a Spatial Pattern Which is Caused by Soil and/or Plant Variables: Fertilizer Experiment With Tea (Camellia sinensis).......Page 387 IV. Discussion......Page 398 References......Page 403 II. Basic Printed Bibliography......Page 405 References......Page 406 New developments in selecting for phenotypic stability in crop breeding; Incorporating additional information on genotypes and environments in models for two-way genotype by environment tables; Relationships among analytica methods used to study genotype-by-environment interactions and evaluation of their impact on response to selection; AMMI analysis of yield trials; Identification of quantitative trait loci that are affected by environment; Analysis of genotype-by-environment interaction and phenotypic; Using the shifted multiplicative model cluster methods for crossover genotype-by environment interaction; Statistical tests and estimators of multiplicative models for genotype-by-environment interaction; Nonparametric analysis of genotype x environment interactions by ranks; Analysis of multiple environment trials using the probability of outperforming a check; Breeding for reliability of performance across unpredictable environments; Characterization and predicting genotype by environment interaction: variable active genic vx. parental genic proportions model; Selection of genotypes and prediction of performance by analysing genotype-by-environment interaction; Spatial analysis of field experiments: fertilizer experiments with wheat (Triticum aestivum) and tea (Camellia sinensis); Bibliography on genotype-by-environment interaction This volume aims at providing an up-to-date compendium of techniques for analyzing Genotype-by-Environment Interaction (GEI). It brings together contributions from knowledgeable plant breeders and quantitative geneticists to understand the relationship between crop performance and environment.