Computer and Biometric Services Unit International Center for Agricultural Research in the Dry Areas (ICARDA) P.O. Box 5466, Aleppo, Syria (Program codes updated: 15 December 2016, Amman, Jordan) Online BioComputing Service ......... Date(D/M/Y) : 3 / 6 / 2017 Time : 12 hr 33 min Summary of the analysis of Multi-Environment Trials (MET)using data on means ........................................................................................................... This includes i. combined analysis of data for GxE interaction (heterogeneous errors assumed) ii. tests for parallelism of regression lines iii. common stability statistics iv. hierarchical cluster analysis of genotypes v. hierarchical cluster analysis of environments REFERENCES: Lin, C.S., Binns, M. R. and Lefkovitch, L.P. (1986). Stability Analysis: where do we stand? Crop Science, 26:894-900. Yau, SK and J. Hamblin (1994). Relative yield as a measure of entry performance in variable environments. Crop Science 34:813-817. Lin C.S., Binns M.R. (1988). A superiority measure of cultivar performance for cultivar x location data. Can. J. Plant Sc. 68: 193-198. ********** Notations ************************************ EnvIndex = Environmental index (as environment mean) GenoLev = Genotype levels GenoMean = Genotype means Trials and parameters of the designs ................................................... No. of Environments = 10 No. of genotypes = 15 No. of obvervations from all the environments = 150 Variables analyzed : MnGYield, MnBYield Note: We use a quadratic average of standard errors of genotypes means for all the genotypes at that location .................................................................................... Variable = MnGYield Histogram of EnvtMean --------------------- - 2500 3 *** 2500 - 5000 3 *** 5000 - 4 **** Scale: 1 asterisk represents 1 unit. Histogram of GenoMean --------------------- - 3300 1 * 3300 - 3600 4 **** 3600 - 3900 8 ******** 3900 - 2 ** Scale: 1 asterisk represents 1 unit. Histogram of PhenoCV% --------------------- - 56 4 **** 56 - 60 6 ****** 60 - 64 5 ***** 64 - 0 Scale: 1 asterisk represents 1 unit. .................................................................................... Section 1: Combined analysis of data for GxE interaction 1.1 Weighted ANOVA under heterogeneous error-variances Analysis of variance ==================== Variate: MnGYield Weight variate: Weight Source of variation d.f. s.s. m.s. v.r. F pr. Envt.Geno stratum Envt 9 9450.784 1050.087 656.96 <.001 Geno 14 61.562 4.397 2.75 0.001 Residual 126 201.399 1.598 Total 149 9713.745 1.2 Tests of significance for Genotype and GxE interaction Genotype : DF = 14 Weighted Sum of Squares = 61.562 Prob > Chisq = 0.00000 G x E Interaction : DF = 126 Weighted Sum of Squares = 201.399 Prob > Chisq = 0.00002 .................................................................................... Section 2: Tests for parallelism of regression lines 2.1 Partition GxE Int into heterogeneity of linear regressions under heterogeneous error-variances Regression analysis =================== Response variate: MnGYield Weight variate: Weight Fitted terms: Constant + EnvIndex + Geno + EnvIndex.Geno Summary of analysis ------------------- Source d.f. s.s. m.s. v.r. chi pr Regression 29 9548.1 329.246 329.25 <.001 Residual 120 165.6 1.380 Total 149 9713.7 65.193 Percentage variance accounted for 97.9 Standard error of observations is fixed at 1.00. * MESSAGE: deviance ratios are based on dispersion parameter with value 1. Accumulated analysis of variance -------------------------------- Change d.f. s.s. m.s. v.r. chi pr + EnvIndex 1 9450.784 9450.784 9450.78 <.001 + Geno 14 61.562 4.397 4.40 <.001 + EnvIndex.Geno 14 35.792 2.557 2.56 0.001 Residual 120 165.608 1.380 Total 149 9713.745 65.193 * MESSAGE: ratios are based on dispersion parameter with value 1. .................................................................................... Section 3: Common stability statistics 3.1 Stability indices under homogeneous error-variances Notes: GenoLev or Geno = Genotype levels; GenoMean= Genotype means Slope = Slope of regression line of the genotypic response on the environment mean (Finlay & wilkinson, 1963); See Lin et al. (1986) SeSlop=Standard error of the Slope; Probb1=Prob[Slope deviating from 1 under null hypothesis of unit slope; t-statistics] DeviMS = Deviation mean square (Eberhart and Russell, 1966); See Lin et al. (1986), ProbDev = Prob[Deviation from linear regression; chi-square statistic] RSq% = Percent variance accounted for by the linear regression (Finlay & Wilkinson, 1963) PhenoCV% = (phenotypic) Coefficent of variation (%)(Francis and Kannenberg, 1978; See Lin et al., 1986); YauH = Stability index of Yau and Hamblin (1994) SE(comb) = standard error of (unweighted) means of genotype means over the environments Wricke (Ecovalence), Pla_Pet (Plaisted and Peterson mean variance components from pair-wise GxE interactions), Plaisted (GxE interaction variance component after excluding the genotype), and Shukla (variance component for the genotype across environments) are GxE interaction sum of square based statistics (see, Lin et al. 1986) GenoLev GenoMean Slope SeSlop Probb1 DeviMS ProbDev RSq% PhenoCV% YauH 2 3751 1.062 0.10713 0.5791 448632 0.0284 91.53 61.36 0.02380 3 3744 1.107 0.06157 0.1196 148219 0.6838 97.28 62.39 0.01582 4 3737 1.113 0.08665 0.2297 293541 0.1887 94.79 63.55 0.03954 5 4018 1.097 0.11631 0.4297 528845 0.0095 90.71 59.39 0.02803 6 3599 1.001 0.08054 0.9934 253562 0.2863 94.46 59.44 0.02250 7 3784 0.988 0.06196 0.8520 150066 0.6759 96.57 55.28 0.01115 8 3584 1.007 0.09381 0.9394 344033 0.1062 92.70 60.58 0.01921 9 3713 0.945 0.05526 0.3488 119391 0.8024 97.00 53.77 0.03148 10 3635 0.929 0.05191 0.2083 105341 0.8542 97.26 53.93 0.01287 11 3694 0.920 0.10190 0.4534 405945 0.0495 89.94 54.37 0.03124 12 4122 1.122 0.05946 0.0740 138226 0.7261 97.53 57.37 0.01525 13 3810 1.007 0.08813 0.9410 303617 0.1689 93.50 56.73 0.03948 14 3542 0.925 0.08468 0.4026 280336 0.2174 92.93 56.23 0.01358 100 3167 0.875 0.12606 0.3512 621217 0.0025 83.99 62.18 0.03666 150 3458 0.902 0.09511 0.3346 353628 0.0947 90.82 56.76 0.01738 SE(comb) 144.6 GenoLev GenoMean Wricke Pla_Pet Plaisted Shukla 2 3751 3739027 380418 305758 455077 3 3744 1635678 255218 325020 185417 4 3737 2844712 327184 313948 340421 5 4018 4596641 431466 297905 565027 6 3599 2028516 278601 321422 235781 7 3784 1206097 229648 328954 130342 8 3584 2754377 321807 314775 328840 9 3713 1073350 221746 330169 113323 10 3635 1040079 219766 330474 109058 11 3694 3499657 366169 307950 424388 12 4122 1689044 258395 324531 192259 13 3810 2430709 302541 317739 287344 14 3542 2461645 304383 317456 291310 100 3167 5578488 489909 288913 690905 150 3458 3201792 348439 310678 386201 SE(comb) 144.6 -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- I I I 12. I I 4. I 1.11 I I I 3. I I I I 5. I I I I I 1.08 I I I I I I I I I 2. I I I 1.05 I I I I I I I I I I I I 1.02 I I I I I I I 8. 13. I I 6. I I I 0.99 I 7. I I I I I I I I I I I 0.96 I I I I I I I 9. I I I I I 0.93 I 10. I I 14. I I 11. I I I I I I I 0.90 I 150. I I I I I I I I I I 100. I 0.87 I I -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- 3000.0 3120.0 3240.0 3360.0 3480.0 3600.0 3720.0 3840.0 3960.0 4080.0 4200.0 Slope v. GenoMean using factor GenoLev -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- I I I I I I 64.5 I I I I I I I I I 4. I I I 63.0 I I I I I 3. I I 100. I I I I I 61.5 I I I 2. I I I I I I 8. I I I 60.0 I I I I I 6. 5. I I I I I I I 58.5 I I I I I I I I I I I 12. I 57.0 I I I 150. 13. I I I I 14. I I I I I 55.5 I I I 7. I I I I I I I I 11. I 54.0 I 10. I I 9. I I I I I I I I I 52.5 I I -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- 3000.0 3120.0 3240.0 3360.0 3480.0 3600.0 3720.0 3840.0 3960.0 4080.0 4200.0 PhenoCV% v. GenoMean using factor GenoLev -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- I I I I I I 640000.0 I I I 100. I I I I I I I I I 560000.0 I I I I I 5. I I I I I I I 480000.0 I I I I I 2. I I I I I I I 400000.0 I 11. I I I I I I 150. I I 8. I I I 320000.0 I I I 13. I I 4. I I 14. I I I I 6. I 240000.0 I I I I I I I I I I I I 160000.0 I I I 3. 7. I I 12. I I 9. I I 10. I I I 80000.0 I I I I I I I I I I I I 0.0 I I -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- 3000.0 3120.0 3240.0 3360.0 3480.0 3600.0 3720.0 3840.0 3960.0 4080.0 4200.0 DeviMS v. GenoMean using factor GenoLev -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- I I I 100. I I I 5400000.0 I I I I I I I I I I I I 4800000.0 I I I I I 5. I I I I I I I 4200000.0 I I I I I I I I I I I 2. I 3600000.0 I I I 11. I I I I I I 150. I I I 3000000.0 I I I I I 8. 4. I I I I I I 14. I 2400000.0 I 13. I I I I I I I I 6. I I I 1800000.0 I I I 12. I I 3. I I I I I I I 1200000.0 I 7. I I 9. I I 10. I I I I I I I 600000.0 I I -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- 3000.0 3120.0 3240.0 3360.0 3480.0 3600.0 3720.0 3840.0 3960.0 4080.0 4200.0 Wricke v. GenoMean using factor GenoLev -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- I I I I I I 0.040 I I I 4. 13. I I I I I I I I 100. I 0.036 I I I I I I I I I I I I 0.032 I I I 9. I I I I I I I I I 0.028 I 5. I I I I I I I I I I I 0.024 I 2. I I I I 6. I I I I I I I 0.020 I I I 8. I I I I I I 150. I I I 0.016 I 3. I I 12. I I I I I I 14. I I 10. I 0.012 I I I 7. I I I I I I I I I 0.008 I I -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- 3000.0 3120.0 3240.0 3360.0 3480.0 3600.0 3720.0 3840.0 3960.0 4080.0 4200.0 YauH v. GenoMean using factor GenoLev Points coinciding with 9. 11. 3.2 Stability indices under heterogeneous error-variances Notes: SlopeW, SeSlopW, Probb1W, DeviSSW, ProbDevW, RSqW%, respectively, are Slope, SeSlop, Probb1, DeviSS, ProbDev, RSq% under heterogener error variances inversely reflected as the weights GenoLev GenoMean SlopeW SeSlopW Probb1W DeviSSW ProbDevW RSqW% 2 3751 0.968 0.05320 0.5597 14.27 0.0751 97.34 3 3744 1.052 0.03528 0.1782 6.27 0.6166 99.00 4 3737 1.036 0.04156 0.4162 8.71 0.3675 98.57 5 4018 1.079 0.05987 0.2210 18.07 0.0207 97.30 6 3599 1.034 0.04770 0.5021 11.47 0.1765 98.11 7 3784 1.022 0.03232 0.5103 5.27 0.7288 99.11 8 3584 0.992 0.05239 0.8788 13.83 0.0862 97.54 9 3713 0.969 0.03525 0.4015 6.26 0.6179 98.82 10 3635 0.982 0.03737 0.6438 7.04 0.5324 98.71 11 3694 0.984 0.04245 0.7109 9.08 0.3354 98.35 12 4122 1.117 0.05385 0.0612 14.61 0.0671 97.95 13 3810 0.986 0.04445 0.7640 9.96 0.2681 98.20 14 3542 0.993 0.04374 0.8722 9.64 0.2910 98.28 100 3167 0.841 0.06572 0.0418 21.77 0.0054 94.76 150 3458 0.946 0.04307 0.2464 9.35 0.3136 98.17 -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- I I I I I I 1.16 I I I I I I I I I I I I 1.12 I 12. I I I I I I I I I I I 1.08 I 5. I I I I I I I I 3. I I I 1.04 I I I 6. 4. I I I I 7. I I I I I 1.00 I I I 14. 8. I I 11. 13. I I 10. I I I I 9. 2. I 0.96 I I I I I 150. I I I I I I I 0.92 I I I I I I I I I I I I 0.88 I I I I I I I I I I I I 0.84 I 100. I -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- 3000.0 3120.0 3240.0 3360.0 3480.0 3600.0 3720.0 3840.0 3960.0 4080.0 4200.0 SlopeW v. GenoMean using factor GenoLev 3.3 Cultivar superiority (under homogeneous error-variances) Superiority measure, P (Lin and Binns, 1988). The texts _G and _GE stand for, respectively, genetic and GxE interaction parts of the index P Standardized coefficient of cultivar superiority, SCCS where SCCS(P)%= Sqrt(P)/cultivar mean x 100. Similarly other indices have been standardized. Geno = Genotype levels; GenoMean= Genotype means PhenoCV% = (phenotypic) Coefficent of variation (%) (Francis and Kannenberg, 1978); See Lin et al. (1986) a) If the desired selection is for the higher values of the trait, e.g. grain yield, HSW, then use the following: GenoMean PhenoCV% P P_G P_GE SCCS(P)% SCCS(P_G)% SCCS(P_GE)% Geno 2 3751 61.36 601252 321843 279410 20.67 15.13 14.09 3 3744 62.39 524995 326917 198078 19.35 15.27 11.89 4 3737 63.55 418576 333254 85322 17.31 15.45 7.82 5 4018 59.39 221667 142952 78715 11.72 9.41 6.98 6 3599 59.44 639339 455535 183804 22.22 18.76 11.91 7 3784 55.28 441403 296142 145261 17.56 14.38 10.07 8 3584 60.58 723585 469868 253717 23.74 19.13 14.06 9 3713 53.77 607287 352968 254319 20.99 16.00 13.58 10 3635 53.93 635475 421729 213746 21.93 17.87 12.72 11 3694 54.37 717277 368855 348423 22.93 16.44 15.98 12 4122 57.37 162500 92880 69620 9.78 7.39 6.40 13 3810 56.73 490551 276099 214453 18.38 13.79 12.15 14 3542 56.23 931553 510757 420795 27.25 20.17 18.31 100 3167 62.18 1571183 960082 611101 39.57 30.94 24.68 150 3458 56.76 1079758 599951 479807 30.05 22.40 20.03 Else b) If the desired selection is for the lower values of the trait, e.g. days to flower/maturity, then use the following: GenoMean PhenoCV% P P_G P_GE SCCS(P)% SCCS(P_G)% SCCS(P_GE)% Geno 2 3751 61.36 1022228 519282 502946 26.96 19.21 18.91 3 3744 62.39 847567 512882 334685 24.59 19.13 15.45 4 3737 63.55 1069606 505012 564594 27.68 19.02 20.11 5 4018 59.39 1537608 827798 709810 30.86 22.64 20.97 6 3599 59.44 728806 375758 353049 23.72 17.03 16.51 7 3784 55.28 778401 553142 225259 23.32 19.66 12.54 8 3584 60.58 792407 362952 429456 24.84 16.81 18.29 9 3713 53.77 622906 481377 141529 21.26 18.69 10.13 10 3635 53.93 657979 407704 250274 22.32 17.57 13.76 11 3694 54.37 696258 463203 233055 22.59 18.42 13.07 12 4122 57.37 1369210 966606 402604 28.39 23.85 15.39 13 3810 56.73 901184 581365 319818 24.92 20.01 14.84 14 3542 56.23 467407 328617 138790 19.30 16.18 10.52 100 3167 62.18 233592 94917 138675 15.26 9.73 11.76 150 3458 56.76 395771 263538 132233 18.19 14.85 10.52 3.4 Correlations between various indices GenoMean 1.0000 Slope 0.7634 1.0000 DeviMS -0.3674 -0.1754 1.0000 PhenoCV% -0.1415 0.5084 0.4419 1.0000 Wricke -0.3516 -0.1331 0.9875 0.4841 1.0000 Pla_Pet -0.3516 -0.1331 0.9875 0.4841 1.0000 1.0000 Plaisted 0.3516 0.1331 -0.9875 -0.4841 -1.0000 -1.0000 1.0000 Shukla -0.3516 -0.1331 0.9875 0.4841 1.0000 1.0000 -1.0000 1.0000 YauH -0.1165 0.0041 0.4999 0.2838 0.4965 0.4965 -0.4965 0.4965 1.0000 SlopeW 0.8758 0.7939 -0.4723 0.0054 -0.4434 -0.4434 0.4434 -0.4434 -0.3185 1.0000 DeviSSW -0.1527 0.0474 0.7893 0.4778 0.8112 0.8112 -0.8112 0.8112 0.3064 -0.2241 1.0000 GenoMean Slope DeviMS PhenoCV% Wricke Pla_Pet Plaisted Shukla YauH SlopeW DeviSSW 3.5. Correlations between genotype-ranks obtained from various indices RGenoMn 1.0000 RSlope 0.7393 1.0000 RDeviMS -0.1893 -0.2071 1.0000 RPhenoCV% -0.0143 0.4857 0.4036 1.0000 RWricke -0.2000 -0.1357 0.9679 0.4750 1.0000 RPla_Pet -0.2000 -0.1357 0.9679 0.4750 1.0000 1.0000 RPlaist 0.2000 0.1357 -0.9679 -0.4750 -1.0000 -1.0000 1.0000 RShukla -0.2000 -0.1357 0.9679 0.4750 1.0000 1.0000 -1.0000 1.0000 RYauH 0.0179 0.0464 0.4929 0.3036 0.5071 0.5071 -0.5071 0.5071 1.0000 RGenoMn RSlope RDeviMS RPhenoCV% RWricke RPla_Pet RPlaist RShukla RYauH .................................................................................... Section 4: Hierarchical clustering of genotypes ===================================================================================================== 4.1: Hierarchical clustering of genotypes using a) Similarity/distance matrix based on: Eucledian distance b) Clustering method : Agglomerative method based on Linkage function: Averagelink (also UPGMA: unweighted pair-group method using arithmetic averages) Here, similarity between a cluster and two merged clusters is the average of the similarities of the cluster with each of the two. Average linkage cluster analysis ================================ Merging clusters ---------------- 7 9 95.3 10 12 95.2 13 15 94.3 3 5 93.9 4 6 93.8 1 2 91.5 3 7 91.5 8 13 90.5 1 8 89.2 3 4 89.2 10 11 85.6 1 3 84.7 1 10 81.6 1 14 74.3 Hierarchical clusters --------------------- Level 95.0 7 9 10 12 Ungrouped 1 2 8 13 15 3 5 4 6 11 14 Level 90.0 1 2 8 13 15 3 5 7 9 4 6 10 12 Ungrouped 11 14 Level 85.0 1 2 8 13 15 3 5 7 9 4 6 10 12 11 Ungrouped 14 Level 80.0 1 2 8 13 15 3 5 7 9 4 6 10 12 11 Ungrouped 14 Level 75.0 1 2 8 13 15 3 5 7 9 4 6 10 12 11 Ungrouped 14 Level 70.0 1 2 8 13 15 3 5 7 9 4 6 10 12 11 14 Dendrogram ---------- ** Levels 100.0 90.0 80.0 70.0 2.00 1 ..... 3.00 2 .....).. 9.00 8 ..... ) 14.00 13 .....) ) 150.00 15 .....)..).. 4.00 3 ..... ) 6.00 5 .....) ) 8.00 7 .. ) ) 10.00 9 ..)..).. ) 5.00 4 ..... ) ) 7.00 6 .....)..)..) 11.00 10 .. ) 13.00 12 ..)..... ) 12.00 11 ........)..)..... 100.00 14 .................)........... ===================================================================================================== .................................................................................... Section 5: Hierarchical clustering of environments ===================================================================================================== 5.1: Hierarchical clustering of environments using a) Similarity/distance matrix based on: Eucledian distance b) Clustering method : Agglomerative method based on Linkage function: Averagelink (also UPGMA: unweighted pair-group method using arithmetic averages) Here, similarity between a cluster and two merged clusters is the average of the similarities of the cluster with each of the two. Average linkage cluster analysis ================================ Merging clusters ---------------- 1 5 99.7 2 8 97.5 1 7 97.5 4 10 97.5 2 9 96.9 2 3 96.3 4 6 93.7 2 4 84.5 1 2 57.9 Hierarchical clusters --------------------- Level 95.0 1 5 7 2 8 9 3 4 10 Ungrouped 6 Level 90.0 1 5 7 2 8 9 3 4 10 6 Level 85.0 1 5 7 2 8 9 3 4 10 6 Level 80.0 1 5 7 2 8 9 3 4 10 6 Level 75.0 1 5 7 2 8 9 3 4 10 6 Level 70.0 1 5 7 2 8 9 3 4 10 6 Level 65.0 1 5 7 2 8 9 3 4 10 6 Level 60.0 1 5 7 2 8 9 3 4 10 6 Level 55.0 1 5 7 2 8 9 3 4 10 6 Dendrogram ---------- ** Levels 100.0 90.0 80.0 70.0 60.0 1.00 1 .. 6.00 5 ..) 8.00 7 ..)....................... 3.00 2 .. ) 9.00 8 ..) ) 20.00 9 ..) ) 4.00 3 ..)........ ) 5.00 4 .. ) ) 100.00 10 ..).. ) ) 7.00 6 .....).....)..............)........ ===================================================================================================== .................................................................................... Variable = MnBYield Histogram of EnvtMean --------------------- - 3000 3 *** 3000 - 6000 3 *** 6000 - 4 **** Scale: 1 asterisk represents 1 unit. Histogram of GenoMean --------------------- - 4400 1 * 4400 - 4800 5 ***** 4800 - 5200 7 ******* 5200 - 2 ** Scale: 1 asterisk represents 1 unit. Histogram of PhenoCV% --------------------- - 56 4 **** 56 - 60 6 ****** 60 - 64 5 ***** 64 - 0 Scale: 1 asterisk represents 1 unit. .................................................................................... Section 1: Combined analysis of data for GxE interaction 1.1 Weighted ANOVA under heterogeneous error-variances Analysis of variance ==================== Variate: MnBYield Weight variate: Weight Source of variation d.f. s.s. m.s. v.r. F pr. Envt.Geno stratum Envt 9 9432.266 1048.030 656.17 <.001 Geno 14 60.964 4.355 2.73 0.002 Residual 126 201.246 1.597 Total 149 9694.476 1.2 Tests of significance for Genotype and GxE interaction Genotype : DF = 14 Weighted Sum of Squares = 60.964 Prob > Chisq = 0.00000 G x E Interaction : DF = 126 Weighted Sum of Squares = 201.246 Prob > Chisq = 0.00002 .................................................................................... Section 2: Tests for parallelism of regression lines 2.1 Partition GxE Int into heterogeneity of linear regressions under heterogeneous error-variances Regression analysis =================== Response variate: MnBYield Weight variate: Weight Fitted terms: Constant + EnvIndex + Geno + EnvIndex.Geno Summary of analysis ------------------- Source d.f. s.s. m.s. v.r. chi pr Regression 29 9529.0 328.586 328.59 <.001 Residual 120 165.5 1.379 Total 149 9694.5 65.064 Percentage variance accounted for 97.9 Standard error of observations is fixed at 1.00. * MESSAGE: deviance ratios are based on dispersion parameter with value 1. Accumulated analysis of variance -------------------------------- Change d.f. s.s. m.s. v.r. chi pr + EnvIndex 1 9432.266 9432.266 9432.27 <.001 + Geno 14 60.964 4.355 4.35 <.001 + EnvIndex.Geno 14 35.762 2.554 2.55 0.001 Residual 120 165.484 1.379 Total 149 9694.476 65.064 * MESSAGE: ratios are based on dispersion parameter with value 1. .................................................................................... Section 3: Common stability statistics 3.1 Stability indices under homogeneous error-variances Notes: GenoLev or Geno = Genotype levels; GenoMean= Genotype means Slope = Slope of regression line of the genotypic response on the environment mean (Finlay & wilkinson, 1963); See Lin et al. (1986) SeSlop=Standard error of the Slope; Probb1=Prob[Slope deviating from 1 under null hypothesis of unit slope; t-statistics] DeviMS = Deviation mean square (Eberhart and Russell, 1966); See Lin et al. (1986), ProbDev = Prob[Deviation from linear regression; chi-square statistic] RSq% = Percent variance accounted for by the linear regression (Finlay & Wilkinson, 1963) PhenoCV% = (phenotypic) Coefficent of variation (%)(Francis and Kannenberg, 1978; See Lin et al., 1986); YauH = Stability index of Yau and Hamblin (1994) SE(comb) = standard error of (unweighted) means of genotype means over the environments Wricke (Ecovalence), Pla_Pet (Plaisted and Peterson mean variance components from pair-wise GxE interactions), Plaisted (GxE interaction variance component after excluding the genotype), and Shukla (variance component for the genotype across environments) are GxE interaction sum of square based statistics (see, Lin et al. 1986) GenoLev GenoMean Slope SeSlop Probb1 DeviMS ProbDev RSq% PhenoCV% YauH 2 4876 1.062 0.10713 0.5784 758316 0.0284 91.53 61.37 0.02382 3 4868 1.107 0.06157 0.1196 250445 0.6840 97.28 62.39 0.01583 4 4858 1.113 0.08665 0.2298 496095 0.1888 94.79 63.55 0.03952 5 5224 1.097 0.11631 0.4298 893837 0.0095 90.71 59.38 0.02802 6 4678 1.001 0.08054 0.9934 428523 0.2865 94.46 59.44 0.02244 7 4919 0.988 0.06197 0.8518 253749 0.6757 96.57 55.27 0.01113 8 4659 1.007 0.09381 0.9397 581372 0.1063 92.70 60.58 0.01920 9 4827 0.945 0.05524 0.3489 201570 0.8030 97.01 53.77 0.03141 10 4725 0.929 0.05189 0.2083 177910 0.8545 97.26 53.93 0.01284 11 4802 0.920 0.10188 0.4531 685760 0.0497 89.94 54.37 0.03129 12 5359 1.122 0.05947 0.0740 233692 0.7260 97.53 57.37 0.01527 13 4953 1.007 0.08813 0.9407 513140 0.1690 93.50 56.74 0.03935 14 4605 0.925 0.08466 0.4022 473531 0.2179 92.94 56.22 0.01359 100 4117 0.875 0.12605 0.3512 1049716 0.0025 83.99 62.19 0.03660 150 4495 0.902 0.09509 0.3344 597453 0.0949 90.82 56.75 0.01739 SE(comb) 188.0 GenoLev GenoMean Wricke Pla_Pet Plaisted Shukla 2 4876 6320856 642999 516672 769326 3 4868 2763770 431268 549247 313290 4 4858 4807305 552907 530533 575282 5 5224 7768690 729180 503414 954946 6 4678 3428215 470818 543162 398475 7 4919 2039443 388153 555880 220427 8 4659 4654520 543813 531932 555694 9 4827 1812123 374622 557961 191284 10 4725 1756631 371319 558469 184169 11 4802 5912515 618693 520412 716975 12 5359 2855636 436736 548405 325067 13 4953 4108145 511290 536935 485646 14 4605 4158812 514306 536471 492141 100 4117 9426379 827852 488234 1167470 150 4495 5409985 588781 525014 652548 SE(comb) 188.0 -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- I I I 12. I I 4. I 1.11 I I I 3. I I I I 5. I I I I I 1.08 I I I I I I I I I 2. I I I 1.05 I I I I I I I I I I I I 1.02 I I I I I I I 8. 13. I I 6. I I I 0.99 I 7. I I I I I I I I I I I 0.96 I I I I I I I 9. I I I I I 0.93 I 10. I I 14. I I 11. I I I I I I I 0.90 I 150. I I I I I I I I I I 100. I 0.87 I I -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- 4050.0 4200.0 4350.0 4500.0 4650.0 4800.0 4950.0 5100.0 5250.0 5400.0 5550.0 Slope v. GenoMean using factor GenoLev -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- I I I I I I 64.5 I I I I I I I I I 4. I I I 63.0 I I I I I 3. I I 100. I I I I I 61.5 I I I 2. I I I I I I 8. I I I 60.0 I I I I I 6. 5. I I I I I I I 58.5 I I I I I I I I I I I 12. I 57.0 I I I 150. 13. I I I I 14. I I I I I 55.5 I I I 7. I I I I I I I I 11. I 54.0 I 10. I I 9. I I I I I I I I I 52.5 I I -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- 4050.0 4200.0 4350.0 4500.0 4650.0 4800.0 4950.0 5100.0 5250.0 5400.0 5550.0 PhenoCV% v. GenoMean using factor GenoLev -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- I I I I I I 1080000.0 I I I I I 100. I I I I I I I 960000.0 I I I I I I I 5. I I I I I 840000.0 I I I I I I I I I 2. I I I 720000.0 I I I I I 11. I I I I I I I 600000.0 I 150. I I 8. I I I I I I 13. I I 4. I 480000.0 I 14. I I I I I I 6. I I I I I 360000.0 I I I I I I I I I I I 3. 7. I 240000.0 I 12. I I I I 9. I I 10. I I I I I 120000.0 I I -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- 4050.0 4200.0 4350.0 4500.0 4650.0 4800.0 4950.0 5100.0 5250.0 5400.0 5550.0 DeviMS v. GenoMean using factor GenoLev -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- I 100. I I I I I 9000000.0 I I I I I I I I I I I I 8000000.0 I I I 5. I I I I I I I I I 7000000.0 I I I I I I I I I 2. I I I 6000000.0 I I I 11. I I I I I I 150. I I I 5000000.0 I I I 4. I I 8. I I I I I I 14. 13. I 4000000.0 I I I I I I I 6. I I I I I 3000000.0 I I I 3. 12. I I I I I I I I I 2000000.0 I 7. I I 10. 9. I I I I I I I I I 1000000.0 I I -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- 4050.0 4200.0 4350.0 4500.0 4650.0 4800.0 4950.0 5100.0 5250.0 5400.0 5550.0 Wricke v. GenoMean using factor GenoLev -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- I I I I I I 0.040 I I I 4. 13. I I I I I I I I 100. I 0.036 I I I I I I I I I I I I 0.032 I I I 9. I I I I I I I I I 0.028 I 5. I I I I I I I I I I I 0.024 I 2. I I I I 6. I I I I I I I 0.020 I I I 8. I I I I I I 150. I I I 0.016 I 3. I I 12. I I I I I I 14. I I 10. I 0.012 I I I 7. I I I I I I I I I 0.008 I I -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- 4050.0 4200.0 4350.0 4500.0 4650.0 4800.0 4950.0 5100.0 5250.0 5400.0 5550.0 YauH v. GenoMean using factor GenoLev Points coinciding with 9. 11. 3.2 Stability indices under heterogeneous error-variances Notes: SlopeW, SeSlopW, Probb1W, DeviSSW, ProbDevW, RSqW%, respectively, are Slope, SeSlop, Probb1, DeviSS, ProbDev, RSq% under heterogener error variances inversely reflected as the weights GenoLev GenoMean SlopeW SeSlopW Probb1W DeviSSW ProbDevW RSqW% 2 4876 0.968 0.05328 0.5618 14.28 0.0748 97.34 3 4868 1.052 0.03531 0.1795 6.27 0.6169 99.00 4 4858 1.036 0.04159 0.4149 8.70 0.3682 98.57 5 5224 1.080 0.05992 0.2205 18.06 0.0208 97.29 6 4678 1.033 0.04769 0.5040 11.44 0.1778 98.11 7 4919 1.022 0.03236 0.5127 5.27 0.7285 99.11 8 4659 0.992 0.05245 0.8794 13.84 0.0861 97.54 9 4827 0.969 0.03525 0.4017 6.25 0.6193 98.82 10 4725 0.982 0.03735 0.6427 7.02 0.5349 98.71 11 4802 0.984 0.04248 0.7093 9.08 0.3357 98.35 12 5359 1.117 0.05390 0.0610 14.62 0.0670 97.94 13 4953 0.986 0.04445 0.7651 9.94 0.2692 98.20 14 4605 0.993 0.04376 0.8707 9.63 0.2916 98.28 100 4117 0.841 0.06574 0.0418 21.74 0.0054 94.75 150 4495 0.946 0.04310 0.2463 9.34 0.3140 98.16 -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- I I I I I I 1.16 I I I I I I I I I I I I 1.12 I 12. I I I I I I I I I I I 1.08 I 5. I I I I I I I I 3. I I I 1.04 I I I 6. 4. I I I I 7. I I I I I 1.00 I I I 14. 8. I I 11. 13. I I 10. I I I I 9. 2. I 0.96 I I I I I 150. I I I I I I I 0.92 I I I I I I I I I I I I 0.88 I I I I I I I I I I I I 0.84 I 100. I -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- 4050.0 4200.0 4350.0 4500.0 4650.0 4800.0 4950.0 5100.0 5250.0 5400.0 5550.0 SlopeW v. GenoMean using factor GenoLev 3.3 Cultivar superiority (under homogeneous error-variances) Superiority measure, P (Lin and Binns, 1988). The texts _G and _GE stand for, respectively, genetic and GxE interaction parts of the index P Standardized coefficient of cultivar superiority, SCCS where SCCS(P)%= Sqrt(P)/cultivar mean x 100. Similarly other indices have been standardized. Geno = Genotype levels; GenoMean= Genotype means PhenoCV% = (phenotypic) Coefficent of variation (%) (Francis and Kannenberg, 1978); See Lin et al. (1986) a) If the desired selection is for the higher values of the trait, e.g. grain yield, HSW, then use the following: GenoMean PhenoCV% P P_G P_GE SCCS(P)% SCCS(P_G)% SCCS(P_GE)% Geno 2 4876 61.37 1016070 543716 472354 20.67 15.12 14.09 3 4868 62.39 887318 552511 334807 19.35 15.27 11.89 4 4858 63.55 707278 563073 144205 17.31 15.45 7.82 5 5224 59.38 374602 241443 133159 11.72 9.41 6.99 6 4678 59.44 1080679 769916 310763 22.22 18.76 11.92 7 4919 55.27 745821 500100 245721 17.56 14.38 10.08 8 4659 60.58 1222822 793926 428896 23.74 19.13 14.06 9 4827 53.77 1026356 596450 429906 20.99 16.00 13.58 10 4725 53.93 1074014 712579 361435 21.93 17.87 12.72 11 4802 54.37 1212412 623174 589237 22.93 16.44 15.98 12 5359 57.37 274678 156856 117822 9.78 7.39 6.41 13 4953 56.74 829457 466771 362685 18.39 13.79 12.16 14 4605 56.22 1574323 862904 711419 27.25 20.17 18.32 100 4117 62.19 2655860 1622701 1033159 39.58 30.94 24.69 150 4495 56.75 1824551 1013318 811233 30.05 22.39 20.04 Else b) If the desired selection is for the lower values of the trait, e.g. days to flower/maturity, then use the following: GenoMean PhenoCV% P P_G P_GE SCCS(P)% SCCS(P_G)% SCCS(P_GE)% Geno 2 4876 61.37 1727811 877680 850131 26.96 19.21 18.91 3 4868 62.39 1432282 866586 565696 24.59 19.12 15.45 4 4858 63.55 1807676 853471 954205 27.68 19.02 20.11 5 5224 59.38 2598803 1399130 1199673 30.86 22.64 20.97 6 4678 59.44 1231604 634839 596765 23.72 17.03 16.51 7 4919 55.27 1315928 935165 380763 23.32 19.66 12.54 8 4659 60.58 1339141 613389 725752 24.84 16.81 18.29 9 4827 53.77 1052638 813450 239188 21.26 18.69 10.13 10 4725 53.93 1111878 689021 422858 22.32 17.57 13.76 11 4802 54.37 1176603 782876 393728 22.59 18.42 13.07 12 5359 57.37 2314141 1633709 680432 28.39 23.85 15.39 13 4953 56.74 1522776 982101 540675 24.92 20.01 14.85 14 4605 56.22 790020 555458 234562 19.30 16.18 10.52 100 4117 62.19 394588 160291 234296 15.26 9.72 11.76 150 4495 56.75 669091 445662 223429 18.20 14.85 10.52 3.4 Correlations between various indices GenoMean 1.0000 Slope 0.7633 1.0000 DeviMS -0.3671 -0.1750 1.0000 PhenoCV% -0.1416 0.5085 0.4420 1.0000 Wricke -0.3513 -0.1327 0.9875 0.4842 1.0000 Pla_Pet -0.3513 -0.1327 0.9875 0.4842 1.0000 1.0000 Plaisted 0.3513 0.1327 -0.9875 -0.4842 -1.0000 -1.0000 1.0000 Shukla -0.3513 -0.1327 0.9875 0.4842 1.0000 1.0000 -1.0000 1.0000 YauH -0.1163 0.0049 0.5013 0.2850 0.4980 0.4980 -0.4980 0.4980 1.0000 SlopeW 0.8764 0.7943 -0.4714 0.0057 -0.4425 -0.4425 0.4425 -0.4425 -0.3173 1.0000 DeviSSW -0.1515 0.0488 0.7895 0.4782 0.8114 0.8114 -0.8114 0.8114 0.3063 -0.2222 1.0000 GenoMean Slope DeviMS PhenoCV% Wricke Pla_Pet Plaisted Shukla YauH SlopeW DeviSSW 3.5. Correlations between genotype-ranks obtained from various indices RGenoMn 1.0000 RSlope 0.7393 1.0000 RDeviMS -0.1893 -0.2071 1.0000 RPhenoCV% -0.0143 0.4857 0.4036 1.0000 RWricke -0.2000 -0.1357 0.9679 0.4750 1.0000 RPla_Pet -0.2000 -0.1357 0.9679 0.4750 1.0000 1.0000 RPlaist 0.2000 0.1357 -0.9679 -0.4750 -1.0000 -1.0000 1.0000 RShukla -0.2000 -0.1357 0.9679 0.4750 1.0000 1.0000 -1.0000 1.0000 RYauH 0.0179 0.0464 0.4929 0.3036 0.5071 0.5071 -0.5071 0.5071 1.0000 RGenoMn RSlope RDeviMS RPhenoCV% RWricke RPla_Pet RPlaist RShukla RYauH .................................................................................... Section 4: Hierarchical clustering of genotypes ===================================================================================================== 4.1: Hierarchical clustering of genotypes using a) Similarity/distance matrix based on: Eucledian distance b) Clustering method : Agglomerative method based on Linkage function: Averagelink (also UPGMA: unweighted pair-group method using arithmetic averages) Here, similarity between a cluster and two merged clusters is the average of the similarities of the cluster with each of the two. Average linkage cluster analysis ================================ Merging clusters ---------------- 7 9 95.3 10 12 95.2 13 15 94.3 3 5 93.9 4 6 93.8 1 2 91.5 3 7 91.5 8 13 90.5 1 8 89.2 3 4 89.2 10 11 85.6 1 3 84.7 1 10 81.5 1 14 74.3 Hierarchical clusters --------------------- Level 95.0 7 9 10 12 Ungrouped 1 2 8 13 15 3 5 4 6 11 14 Level 90.0 1 2 8 13 15 3 5 7 9 4 6 10 12 Ungrouped 11 14 Level 85.0 1 2 8 13 15 3 5 7 9 4 6 10 12 11 Ungrouped 14 Level 80.0 1 2 8 13 15 3 5 7 9 4 6 10 12 11 Ungrouped 14 Level 75.0 1 2 8 13 15 3 5 7 9 4 6 10 12 11 Ungrouped 14 Level 70.0 1 2 8 13 15 3 5 7 9 4 6 10 12 11 14 Dendrogram ---------- ** Levels 100.0 90.0 80.0 70.0 2.00 1 ..... 3.00 2 .....).. 9.00 8 ..... ) 14.00 13 .....) ) 150.00 15 .....)..).. 4.00 3 ..... ) 6.00 5 .....) ) 8.00 7 .. ) ) 10.00 9 ..)..).. ) 5.00 4 ..... ) ) 7.00 6 .....)..)..) 11.00 10 .. ) 13.00 12 ..)..... ) 12.00 11 ........)..)..... 100.00 14 .................)........... ===================================================================================================== .................................................................................... Section 5: Hierarchical clustering of environments ===================================================================================================== 5.1: Hierarchical clustering of environments using a) Similarity/distance matrix based on: Eucledian distance b) Clustering method : Agglomerative method based on Linkage function: Averagelink (also UPGMA: unweighted pair-group method using arithmetic averages) Here, similarity between a cluster and two merged clusters is the average of the similarities of the cluster with each of the two. Average linkage cluster analysis ================================ Merging clusters ---------------- 1 5 99.7 2 8 97.5 1 7 97.5 4 10 97.5 2 9 96.9 2 3 96.3 4 6 93.7 2 4 84.5 1 2 57.9 Hierarchical clusters --------------------- Level 95.0 1 5 7 2 8 9 3 4 10 Ungrouped 6 Level 90.0 1 5 7 2 8 9 3 4 10 6 Level 85.0 1 5 7 2 8 9 3 4 10 6 Level 80.0 1 5 7 2 8 9 3 4 10 6 Level 75.0 1 5 7 2 8 9 3 4 10 6 Level 70.0 1 5 7 2 8 9 3 4 10 6 Level 65.0 1 5 7 2 8 9 3 4 10 6 Level 60.0 1 5 7 2 8 9 3 4 10 6 Level 55.0 1 5 7 2 8 9 3 4 10 6 Dendrogram ---------- ** Levels 100.0 90.0 80.0 70.0 60.0 1.00 1 .. 6.00 5 ..) 8.00 7 ..)....................... 3.00 2 .. ) 9.00 8 ..) ) 20.00 9 ..) ) 4.00 3 ..)........ ) 5.00 4 .. ) ) 100.00 10 ..).. ) ) 7.00 6 .....).....)..............)........ ===================================================================================================== .................................................................................... 570 571 572 STOP