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 2015, Amman, Jordan) Online BioComputing Service ......... Date(D/M/Y) : 13 / 6 / 2017 Time : 14 hr 54 min Summary of the analysis of Multi-Environment Trials (MET)conducted in Randomised Complete Block Designs ........................................................................................................... This includes i. Analysis of data from individual environments ii. Tests for homogeneity of error variances, iii. Combined analysis of data for GxE interaction under homogeneous/heterogeneous errors iv. Heritability of the traits v. Tests for parallelism of regression lines vi. Common stability statistics vii. Hierarchical cluster analysis of genotypes viii. Hierarchical cluster analysis of environments REFERENCES: Kempthorne, O. (1983). The Design and Analysis of Experiments. R.E. Krieger Publishing Co., Malabar, FL. Lin, C.S., Binns, M. R. and Lefkovitch, L.P. (1986). Stability Analysis: where do we stand? Crop Science, 26:894-900. 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. Singh, M., S. Ceccarelli and J. Hamblin (1993). Estimation of heritability from varietal trials data. Theoretical and Applied Genetics 86: 437-441. Yau, S.K. and J. Hamblin (1994). Relative yield as a measure of entry performance in variable environments. Crop Science 34:813-817 ********** Notations ************************************ EnvtNum = Environments EnvtMean = Environment means CV% = Coefficient of variation (experimental errors) SEM = Standard error of predicted means of genotypes SED = Average standard error of difference between pairs of genotype effects LSDa% = Least significant difference (LSD) at a%=5%, 1% level of significance ErrMS = Error mean-square ErrDF = Degrees of freedom for Error (mean-square) P_value = Probability of greater chi-square when genotypic effects are equal (for testing statistical significance of genotypic effects) GenoNum = Genotypes GenoMean = Genotype means h2_plot = heritability in broad sense and plot basis h2_mean = heritability in broad sense and mean basis Bias_h2_plot= Bias of h2_plot in estimating heritability Se_T1 = Standard error of T1, where T1 = h2_plot, h2_mean GGx% = % Genetic gain[advance] for the x%=5%,10%,20% selection intensity and heritability= h2_mean Sig2G = Genotypic -variance component Sig2E = Error-variance component Sig2GE = Genotype x Environment variance component Se_T2 = Standard error of T2, where T2 = Sig2G, Sig2E, Sig2GE ------- Trials and parameters of the designs -------- ................................................... No. of Environments = 10 No. of replications (maximum) = 3 No. of replications (Average) = 3 No. of genotypes = 15 No. of obvervations from all the environments = 450 Variables analyzed : GYield, BYield .................................................................................... .................................................................................... Variable is GYield .................................................................................... Section 1. Analysis of data from individual environments ******* Environment is = 1 ********* Analysis of variance ==================== Variate: GYield Source of variation d.f. s.s. m.s. v.r. F pr. Rep stratum 2 27563. 13781. 0.23 Rep.Geno stratum Geno 14 666583. 47613. 0.78 0.682 Residual 28 1711141. 61112. Total 44 2405287. ******* Environment is = 2 ********* Analysis of variance ==================== Variate: GYield Source of variation d.f. s.s. m.s. v.r. F pr. Rep stratum 2 165032. 82516. 0.18 Rep.Geno stratum Geno 14 5153189. 368085. 0.79 0.672 Residual 28 13060300. 466439. Total 44 18378521. ******* Environment is = 4 ********* Analysis of variance ==================== Variate: GYield Source of variation d.f. s.s. m.s. v.r. F pr. Rep stratum 2 10000371. 5000185. 2.91 Rep.Geno stratum Geno 14 27233159. 1945226. 1.13 0.375 Residual 28 48085069. 1717324. Total 44 85318599. ******* Environment is = 5 ********* Analysis of variance ==================== Variate: GYield Source of variation d.f. s.s. m.s. v.r. F pr. Rep stratum 2 8853142. 4426571. 6.48 Rep.Geno stratum Geno 14 27816546. 1986896. 2.91 0.008 Residual 28 19133779. 683349. Total 44 55803467. ******* Environment is = 6 ********* Analysis of variance ==================== Variate: GYield Source of variation d.f. s.s. m.s. v.r. F pr. Rep stratum 2 16804. 8402. 0.02 Rep.Geno stratum Geno 14 4419494. 315678. 0.88 0.585 Residual 28 10018841. 357816. Total 44 14455139. ******* Environment is = 7 ********* Analysis of variance ==================== Variate: GYield Source of variation d.f.(m.v.) s.s. m.s. v.r. F pr. Rep stratum 2 848920. 424460. 2.90 Rep.Geno stratum Geno 14 4911812. 350844. 2.40 0.025 Residual 27(1) 3954364. 146458. Total 43(1) 9666992. ******* Environment is = 8 ********* Analysis of variance ==================== Variate: GYield Source of variation d.f. s.s. m.s. v.r. F pr. Rep stratum 2 200333. 100167. 13.87 Rep.Geno stratum Geno 14 461750. 32982. 4.57 <.001 Residual 28 202167. 7220. Total 44 864250. ******* Environment is = 10 ********* Analysis of variance ==================== Variate: GYield Source of variation d.f. s.s. m.s. v.r. F pr. Rep stratum 2 933760. 466880. 0.47 Rep.Geno stratum Geno 14 9569067. 683505. 0.69 0.769 Residual 28 27909973. 996785. Total 44 38412800. ******* Environment is = 30 ********* Analysis of variance ==================== Variate: GYield Source of variation d.f. s.s. m.s. v.r. F pr. Rep stratum 2 3598694. 1799347. 2.94 Rep.Geno stratum Geno 14 19108528. 1364895. 2.23 0.034 Residual 28 17115056. 611252. Total 44 39822278. ******* Environment is = 90 ********* Analysis of variance ==================== Variate: GYield Source of variation d.f. s.s. m.s. v.r. F pr. Rep stratum 2 1606671. 803336. 0.66 Rep.Geno stratum Geno 14 40950364. 2925026. 2.39 0.024 Residual 28 34268396. 1223871. Total 44 76825431. EnvtNum EnvtMean CV% SEM SED LSD5% LSD1% ErrMS ErrDF P_value 1 1409 17.54 142.7 201.8 413 558 61112 28.00 0.6818 2 6069 11.25 394.3 557.6 1142 1541 466439 28.00 0.6723 4 5324 24.61 756.6 1070.0 2192 2957 1717324 28.00 0.3747 5 4086 20.23 477.3 675.0 1383 1865 683349 28.00 0.0079 6 1264 47.34 345.4 488.4 1000 1350 357816 28.00 0.5846 7 2816 13.59 221.0 312.5 641 866 146458 27.00 0.0250 8 415 20.48 49.1 69.4 142 192 7220 28.00 0.0003 10 4227 23.62 576.4 815.2 1670 2253 996785 28.00 0.7688 30 5417 14.43 451.4 638.4 1308 1764 611252 28.00 0.0342 90 5872 18.84 638.7 903.3 1850 2496 1223871 28.00 0.0242 Histogram of CV% ---------------- - 16 3 *** 16 - 32 6 ****** 32 - 1 * Scale: 1 asterisk represents 1 unit. Histogram of ErrMS ------------------ - 600000 5 ***** 600000 - 1200000 3 *** 1200000 - 2 ** Scale: 1 asterisk represents 1 unit. Histogram of EnvtMean --------------------- - 2500 3 *** 2500 - 5000 3 *** 5000 - 4 **** Scale: 1 asterisk represents 1 unit. -+---------+---------+---------+---------+---------+---------+ I 6. I 45.0 I I I I I I I I I I I I 30.0 I I I I I 4. I I 10. I I 8. 5. 90. I I 1. I 15.0 I 30. I I 7. 2. I I I I I I I I I 0.0 I I -+---------+---------+---------+---------+---------+---------- 0.0 1200.0 2400.0 3600.0 4800.0 6000.0 7200.0 CV% v. EnvtMean using factor EnvtNum -+---------+---------+---------+---------+---------+---------+ I I 1800000.0 I I I 4. I I I I I I I I I 1200000.0 I 90. I I I I 10. I I I I I I 5. I 600000.0 I 30. I I 2. I I 6. I I I I I I 1. 7. I 0.0 I 8. I -+---------+---------+---------+---------+---------+---------- 0.0 1200.0 2400.0 3600.0 4800.0 6000.0 7200.0 ErrMS v. EnvtMean using factor EnvtNum .................................................................................... Section 2.0 Bartlette Test for homogeneity of error variances Pooled Error Mean-square.........................................................................= 628886 DF for Pooled Error Mean-square...............................................................= 279.0 Probability of greater chi-square (for testing homogeneity of error variances) = 0.000000 Error variances are heterogeneous at 0.05000 probability .................................................................................... Section 2.1 REML Deviance Difference Test for homogeneity of error variances Probability of greater chi-square (for testing homogeneity of error variances) = 0.000000 Error variances are heterogeneous at 0.05000 probability .................................................................................... Section 3: Combined analysis of data for GxE interaction 3.1 ANOVA under homogeneous error-variances Analysis of variance ==================== Variate: GYield Source of variation d.f.(m.v.) s.s. m.s. v.r. F pr. Envt.Rep stratum Envt 9 1.759E+09 1.955E+08 148.92 <.001 Residual 20 2.625E+07 1.313E+06 2.09 Envt.Rep.Geno stratum Geno 14 2.097E+07 1.498E+06 2.38 0.004 Envt.Geno 126 1.193E+08 9.470E+05 1.51 0.003 Residual 279(1) 1.755E+08 6.289E+05 Total 448(1) 2.101E+09 ******************************* Genotype x Environment table means ********************* Genotype 1 2 4 5 6 7 8 10 30 90 Geno.Mean 1 1167 6178 5167 4026 660 2107 441.7 4360 4000 3567 3167 3 1341 6556 5967 3423 1050 2611 316.7 4267 6100 5813 3744 4 1411 5700 6245 4314 699 2785 283.3 3680 5292 6958 3737 5 1464 5511 5617 5551 1437 2833 333.3 4013 5867 7558 4018 6 1511 5595 5489 3699 1168 3063 275.0 3133 6050 6003 3599 8 1495 5867 5445 3070 987 3181 375.0 3880 4700 6837 3584 9 1516 6389 5700 3897 1899 2596 491.7 4120 5133 5387 3713 10 1576 5611 5056 3423 1565 3061 408.3 4280 5167 6200 3635 11 1511 6189 3833 5135 1254 3048 575.0 4360 5400 5637 3694 12 1161 6455 5958 5019 1391 3501 483.3 4373 6600 6280 4122 13 1357 6389 4278 4750 1469 2845 641.7 3893 6117 6360 3810 14 1533 6456 4481 3494 1264 2816 366.7 5013 4800 5200 3542 20 1333 6044 6635 3173 1457 2308 391.7 4933 4933 6300 3751 70 1411 5933 5737 4987 1451 2740 358.3 4440 5350 5428 3784 150 1354 6167 4259 3333 1203 2817 483.3 4653 5750 4558 3458 Envt.Mean 1409 6069 5324 4086 1264 2821 415.0 4227 5417 5872 3692 3.2 Weighted ANOVA under heterogeneous error-variances Analysis of variance ==================== Variate: GEData Weight variate: AllWet Source of variation d.f. s.s. m.s. v.r. F pr. Envt1 9 9442.689 1049.188 Geno1 14 61.356 4.383 Envt1.Geno1 126 201.326 1.598 Total 149 9705.370 3.2.1 Tests of significance for Genotype and GxE interaction Genotype : DF = 14 Weighted Sum of Squares = 61.356 Prob > Chisq = 0.00000 G x E Interaction : DF = 126 Weighted Sum of Squares = 201.326 Prob > Chisq = 0.00002 .................................................................................... Section 4: Heritabilities 4.1 Environment-wise heritability estimates (h2_...) and genetic gain (GG...) EnvtNum EnvtMean h2_plot Bias_h2_plot Se_h2_plot h2_mean Se_h2_mean GG5% GG10% GG20% Sig2G Se_Sig2G Sig2E Se_Sig2E 1 1409 0.0000 0.0000 0.00000 0.0000 0.0000 0.00 0.00 0.000 0 0 54666 11655 2 6069 0.0000 0.0000 0.00000 0.0000 0.0000 0.00 0.00 0.000 0 0 417694 89053 4 5324 0.0424 0.6086 0.16029 0.1172 0.4087 3.65 3.11 2.480 75967 288909 1717324 458974 5 4086 0.3887 0.0924 0.16765 0.6561 0.1592 26.95 22.93 18.290 434516 257622 683349 182633 6 1264 0.0000 0.0000 0.00000 0.0000 0.0000 0.00 0.00 0.000 0 0 328526 70042 7 2821 0.3238 0.1101 0.17348 0.5896 0.1917 14.83 12.62 10.063 69756 46879 145689 39542 8 415 0.5432 0.0645 0.14705 0.7811 0.1013 40.71 34.63 27.625 8587 4205 7220 1930 10 4227 0.0000 0.0000 0.00000 0.0000 0.0000 0.00 0.00 0.000 0 0 873018 186128 30 5417 0.2913 0.1184 0.17307 0.5522 0.2073 14.18 12.07 9.624 251214 180377 611252 163364 90 5872 0.3252 0.1068 0.16992 0.5912 0.1871 20.50 17.45 13.914 576397 382621 1195836 308763 4.2 Correlations between mean, heritability, genetic gain, genotypic variance and error-variance EnvtMean 1.0000 h2_plot -0.1629 1.0000 h2_mean -0.0610 0.9877 1.0000 GG5% -0.2290 0.9739 0.9335 1.0000 GG10% -0.2290 0.9739 0.9335 1.0000 1.0000 GG20% -0.2290 0.9739 0.9335 1.0000 1.0000 1.0000 Sig2G 0.4837 0.4898 0.5735 0.4396 0.4396 0.4396 1.0000 Sig2E 0.7009 -0.1992 -0.1233 -0.1833 -0.1833 -0.1833 0.4167 1.0000 EnvtMean h2_plot h2_mean GG5% GG10% GG20% Sig2G Sig2E 4.3 Heritability estimate (h2_...) and genetic gain (GG...) in presence of GxE interaction Model assumed: Y= Envt eff. [Fixed terms] + Rep eff. within Envt + Geno eff. + Geno x Envt int. + error [Random terms] where Y= Response (e.g. Yield), Envt=Environment, eff.=effect, Rep=Replication, Geno=Genotype, int.=interaction h2_plot Bias_h2_plot Se_h2_plot h2_mean Se_h2_mean GG5% GG10% GG20% 0.02429 0.02664 0.02532 0.3666 0.2526 4.576 3.893 3.106 4.4 Variance components from GxE data analysis Sig2G Se_Sig2G Sig2GE Se_Sig2GE Sig2E Se_Sig2E 18302 19302 106832 43644 628318 53173 4.5 Variance components from GxE data analysis under three more models Model 1: Fixed effects=Envt + Geno + Geno.Envt & Random = Rep.Envt REML variance components analysis ================================= Response variate: GYield Fixed model: Constant + Envt + Geno + Envt.Geno Random model: Envt.Rep + Envt.Rep.Geno Number of units: 449 (1 units excluded due to zero weights or missing values) Envt.Rep.Geno used as residual term Sparse algorithm with AI optimisation Estimated variance components ----------------------------- Random term component s.e. Envt.Rep 45543. 27924. Residual variance model ----------------------- Term Model(order) Parameter Estimate s.e. Envt.Rep.Geno Identity Sigma2 628857. 53242. Deviance: -2*Log-Likelihood --------------------------- Deviance d.f. 4470.21 297 Note: deviance omits constants which depend on fixed model fitted. ******** Warning 2, code VD 39, statement 220 in for loop Command: VDisplay[Ch=ChReport; prin=model, comp, deviance, wald] Error in AI algorithm when forming denominator DF for approximate F-tests. Wald tests for fixed effects ---------------------------- Sequentially adding terms to fixed model Fixed term Wald statistic d.f. Wald/d.f. chi pr Envt 1340.73 9 148.97 <0.001 Geno 33.32 14 2.38 0.003 Envt.Geno 189.76 126 1.51 <0.001 Dropping individual terms from full fixed model Fixed term Wald statistic d.f. Wald/d.f. chi pr Envt.Geno 189.76 126 1.51 <0.001 * MESSAGE: chi-square distribution for Wald tests is an asymptotic approximation (i.e. for large samples) and underestimates the probabilities in other cases. Model 2: Fixed effects=Envt + Geno & Random = Geno.Envt + Rep.Envt REML variance components analysis ================================= Response variate: GYield Fixed model: Constant + Envt + Geno Random model: Geno.Envt + Envt.Rep + Geno.Envt.Rep Number of units: 449 (1 units excluded due to zero weights or missing values) Geno.Envt.Rep used as residual term Sparse algorithm with AI optimisation Estimated variance components ----------------------------- Random term component s.e. Geno.Envt 106802. 43641. Envt.Rep 45683. 27947. Residual variance model ----------------------- Term Model(order) Parameter Estimate s.e. Geno.Envt.Rep Identity Sigma2 628327. 53175. Deviance: -2*Log-Likelihood --------------------------- Deviance d.f. 6248.55 422 Note: deviance omits constants which depend on fixed model fitted. Tests for fixed effects ----------------------- Sequentially adding terms to fixed model Fixed term Wald statistic n.d.f. F statistic d.d.f. F pr Envt 1076.56 9 119.62 28.2 <0.001 Geno 22.08 14 1.58 126.1 0.094 Dropping individual terms from full fixed model Fixed term Wald statistic n.d.f. F statistic d.d.f. F pr Envt 1076.46 9 119.61 28.2 <0.001 Geno 22.08 14 1.58 126.1 0.094 * MESSAGE: denominator degrees of freedom for approximate F-tests are calculated using algebraic derivatives ignoring fixed/boundary/singular variance parameters. Model 3: Fixed effects=Envt & Random = Geno + Geno.Envt + Rep.Envt REML variance components analysis ================================= Response variate: GYield Fixed model: Constant + Envt Random model: Geno + Geno.Envt + Envt.Rep + Geno.Envt.Rep Number of units: 449 (1 units excluded due to zero weights or missing values) Geno.Envt.Rep used as residual term Sparse algorithm with AI optimisation Estimated variance components ----------------------------- Random term component s.e. Geno 18302. 19302. Geno.Envt 106832. 43644. Envt.Rep 45607. 27923. Residual variance model ----------------------- Term Model(order) Parameter Estimate s.e. Geno.Envt.Rep Identity Sigma2 628318. 53173. Deviance: -2*Log-Likelihood --------------------------- Deviance d.f. 6416.72 435 Note: deviance omits constants which depend on fixed model fitted. Tests for fixed effects ----------------------- Sequentially adding terms to fixed model Fixed term Wald statistic n.d.f. F statistic d.d.f. F pr Envt 1077.23 9 119.69 28.2 <0.001 Dropping individual terms from full fixed model Fixed term Wald statistic n.d.f. F statistic d.d.f. F pr Envt 1077.23 9 119.69 28.2 <0.001 * MESSAGE: denominator degrees of freedom for approximate F-tests are calculated using algebraic derivatives ignoring fixed/boundary/singular variance parameters. Model 4: Fixed effects=none & all Random = Envt+ Geno + Geno.Envt + Rep.Envt REML variance components analysis ================================= Response variate: GYield Fixed model: Constant Random model: Envt + Geno + Envt.Geno + Envt.Rep + Envt.Geno.Rep Number of units: 449 (1 units excluded due to zero weights or missing values) Envt.Geno.Rep used as residual term Sparse algorithm with AI optimisation Estimated variance components ----------------------------- Random term component s.e. Envt 4307860. 2047885. Geno 18304. 19303. Envt.Geno 106831. 43643. Envt.Rep 45611. 27924. Residual variance model ----------------------- Term Model(order) Parameter Estimate s.e. Envt.Geno.Rep Identity Sigma2 628316. 53173. Deviance: -2*Log-Likelihood --------------------------- Deviance d.f. 6565.59 443 Note: deviance omits constants which depend on fixed model fitted. * MESSAGE: No fixed model terms: Wald statistics cannot be calculated .................................................................................... Section 5: Tests for parallelism of regression lines 5.1 Partition GxE Int into heterogeneity of linear regressions under homogeneous error-variances Analysis of variance ==================== Variate: GYield Source of variation d.f.(m.v.) s.s. m.s. v.r. F pr. Envt.Rep stratum Envt 9 1.759E+09 1.955E+08 148.92 <.001 Lin 1 1.759E+09 1.759E+09 1340.28 <.001 Deviations 8 9.005E-22 1.126E-22 0.00 1.000 Residual 20 2.625E+07 1.313E+06 2.09 Envt.Rep.Geno stratum Geno 14 2.097E+07 1.498E+06 2.38 0.004 Envt.Geno 126 1.193E+08 9.470E+05 1.51 0.003 Lin.Geno 14 1.147E+07 8.192E+05 1.30 0.205 Deviations 112 1.079E+08 9.630E+05 1.53 0.003 Residual 279(1) 1.755E+08 6.289E+05 Total 448(1) 2.101E+09 Regression analysis =================== Response variate: GEData Fitted terms: Constant + AllEnvt + Geno1 + AllEnvt.Geno1 Summary of analysis ------------------- Source d.f. s.s. m.s. v.r. F pr. Regression 29 597215036. 20593622. 68.74 <.001 Residual 120 35950869. 299591. Total 149 633165905. 4249436. Percentage variance accounted for 92.9 Standard error of observations is estimated to be 547. Accumulated analysis of variance -------------------------------- Change d.f. s.s. m.s. v.r. F pr. + AllEnvt 1 586402407. 586402407. 1957.35 <.001 + Geno1 14 6989756. 499268. 1.67 0.072 + AllEnvt.Geno1 14 3822873. 273062. 0.91 0.549 Residual 120 35950869. 299591. Total 149 633165905. 4249436. 5.2 Partition GxE Int into heterogeneity of linear regressions under heterogeneous error-variances Regression analysis =================== Response variate: GEData Weight variate: AllWet Fitted terms: Constant + AllEnvt + Geno1 + AllEnvt.Geno1 Summary of analysis ------------------- Source d.f. s.s. m.s. v.r. chi pr Regression 29 9539.8 328.959 328.96 <.001 Residual 120 165.6 1.380 Total 149 9705.4 65.137 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 + AllEnvt 1 9442.689 9442.689 9442.69 <.001 + Geno1 14 61.356 4.383 4.38 <.001 + AllEnvt.Geno1 14 35.762 2.554 2.55 0.001 Residual 120 165.563 1.380 Total 149 9705.370 65.137 * MESSAGE: ratios are based on dispersion parameter with value 1. .................................................................................... Section 6: Common stability statistics 6.1 Stability indices under homogeneous error-variances GenoNum GenoMean Slope SeSlop Probb1 DeviMS ProbDev RSq% GenoCV YauH 1 3167 0.875 0.12606 0.3513 621262 0.0034 83.99 62.19 0.03663 3 3744 1.107 0.06156 0.1195 148129 0.6857 97.29 62.39 0.01585 4 3737 1.113 0.08666 0.2299 293599 0.1959 94.79 63.55 0.03950 5 4018 1.097 0.11631 0.4299 528832 0.0116 90.71 59.38 0.02798 6 3599 1.001 0.08054 0.9932 253568 0.2931 94.46 59.44 0.02250 8 3584 1.007 0.09379 0.9395 343905 0.1132 92.70 60.58 0.01921 9 3713 0.945 0.05525 0.3488 119352 0.8028 97.01 53.77 0.03144 10 3635 0.929 0.05189 0.2081 105270 0.8543 97.26 53.93 0.01285 11 3694 0.920 0.10187 0.4531 405679 0.0549 89.94 54.37 0.03123 12 4122 1.122 0.05947 0.0741 138238 0.7270 97.53 57.37 0.01526 13 3810 1.007 0.08812 0.9405 303553 0.1764 93.50 56.74 0.03940 14 3542 0.925 0.08468 0.4026 280336 0.2248 92.93 56.23 0.01360 20 3751 1.062 0.10712 0.5785 448611 0.0323 91.53 61.36 0.02380 70 3784 0.988 0.06195 0.8520 150046 0.6776 96.57 55.27 0.01113 150 3458 0.902 0.09509 0.3342 353476 0.1015 90.82 56.75 0.01741 GenoNum GenoMean Wricke Pla_Pet Plaisted Shukla 1 3167 5578639 489894 288860 690928 3 3744 1635091 255159 324973 185345 4 3737 2844787 327165 313895 340434 5 4018 4596131 431412 297857 564966 6 3599 2028564 278580 321370 235790 8 3584 2753349 321722 314733 328712 9 3713 1073016 221702 330120 113284 10 3635 1039503 219707 330427 108988 11 3694 3497666 366027 307917 424137 12 4122 1688955 258365 324480 192251 13 3810 2430222 302488 317692 287285 14 3542 2461612 304357 317404 291309 20 3751 3739272 380408 305704 455112 70 3784 1205943 229615 328903 130326 150 3458 3200992 348368 310633 386102 -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- 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 20. 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 70. 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 1. 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 GenoNum -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- 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 1. I I I I I 61.5 I I I 20. 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 70. 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 GenoCV v. GenoMean using factor GenoNum -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- I I I I I I 640000.0 I I I 1. 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 20. 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. 70. 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 GenoNum -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- I I I 1. 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 20. 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 70. 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 GenoNum -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- I I I I I I 0.040 I I I 4. 13. I I I I I I I I 1. 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 20. 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 70. 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 GenoNum Points coinciding with 9. 11. 6.2 Stability indices under heterogeneous error-variances GenoNum GenoMean SlopeW SeSlopW Probb1W DeviSSW ProbDevW RSqW% 1 3167 0.841 0.06573 0.0417 21.76 0.0054 94.76 3 3744 1.052 0.03527 0.1780 6.27 0.6175 99.00 4 3737 1.036 0.04158 0.4160 8.71 0.3677 98.57 5 4018 1.079 0.05987 0.2210 18.05 0.0208 97.30 6 3599 1.034 0.04771 0.5017 11.46 0.1768 98.11 8 3584 0.992 0.05240 0.8804 13.83 0.0863 97.54 9 3713 0.969 0.03524 0.4025 6.26 0.6187 98.82 10 3635 0.982 0.03735 0.6436 7.03 0.5338 98.71 11 3694 0.984 0.04245 0.7099 9.08 0.3359 98.35 12 4122 1.117 0.05394 0.0617 14.65 0.0663 97.94 13 3810 0.986 0.04448 0.7631 9.97 0.2674 98.20 14 3542 0.993 0.04376 0.8733 9.65 0.2908 98.28 20 3751 0.968 0.05322 0.5618 14.26 0.0751 97.34 70 3784 1.022 0.03232 0.5116 5.26 0.7294 99.11 150 3458 0.946 0.04308 0.2453 9.34 0.3141 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 70. I I I I I 1.00 I I I 14. 8. I I 11. 13. I I 10. I I I I 9. 20. 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 1. 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 GenoNum 6.3 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)% Geno1 1 3167 62.19 1571659 960359 611299 39.58 30.94 24.69 3 3744 62.39 525042 326998 198044 19.35 15.27 11.88 4 3737 63.55 418592 333227 85365 17.31 15.45 7.82 5 4018 59.38 221681 142899 78782 11.72 9.41 6.98 6 3599 59.44 639454 455599 183855 22.22 18.76 11.92 8 3584 60.58 723659 469965 253694 23.74 19.13 14.06 9 3713 53.77 607415 352996 254419 20.99 16.00 13.59 10 3635 53.93 635548 421729 213819 21.93 17.87 12.72 11 3694 54.37 717397 368855 348542 22.93 16.44 15.98 12 4122 57.37 162522 92823 69699 9.78 7.39 6.40 13 3810 56.74 490709 276205 214504 18.39 13.79 12.16 14 3542 56.23 931679 510757 420922 27.25 20.17 18.31 20 3751 61.36 601149 321736 279413 20.67 15.12 14.09 70 3784 55.27 441363 296014 145349 17.56 14.38 10.08 150 3458 56.75 1079612 599695 479917 30.05 22.39 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)% Geno1 1 3167 62.19 233392 94816 138577 15.25 9.72 11.75 3 3744 62.39 847463 512747 334716 24.59 19.12 15.45 4 3737 63.55 1069614 505012 564602 27.68 19.02 20.11 5 4018 59.38 1537671 827884 709787 30.86 22.64 20.97 6 3599 59.44 728852 375671 353181 23.72 17.03 16.51 8 3584 60.58 792313 362838 429474 24.84 16.81 18.29 9 3713 53.77 622799 481311 141488 21.26 18.69 10.13 10 3635 53.93 657936 407674 250261 22.32 17.57 13.76 11 3694 54.37 696130 463171 232959 22.59 18.42 13.07 12 4122 57.37 1369290 966745 402545 28.39 23.85 15.39 13 3810 56.74 901110 581175 319934 24.92 20.01 14.85 14 3542 56.23 467442 328590 138852 19.30 16.18 10.52 20 3751 61.36 1022350 519384 502966 26.96 19.21 18.91 70 3784 55.27 778482 553282 225200 23.32 19.66 12.54 150 3458 56.75 395894 263683 132211 18.20 14.85 10.52 6.4 Correlations between various indices GenoMean 1.0000 Slope 0.7633 1.0000 DeviMS -0.3673 -0.1752 1.0000 GenoCV -0.1419 0.5082 0.4421 1.0000 Wricke -0.3515 -0.1330 0.9875 0.4842 1.0000 Pla_Pet -0.3515 -0.1330 0.9875 0.4842 1.0000 1.0000 Plaisted 0.3515 0.1330 -0.9875 -0.4842 -1.0000 -1.0000 1.0000 Shukla -0.3515 -0.1330 0.9875 0.4842 1.0000 1.0000 -1.0000 1.0000 YauH -0.1174 0.0041 0.5005 0.2849 0.4971 0.4971 -0.4971 0.4971 1.0000 SlopeW 0.8758 0.7940 -0.4722 0.0054 -0.4434 -0.4434 0.4434 -0.4434 -0.3188 1.0000 DeviSSW -0.1513 0.0485 0.7885 0.4775 0.8104 0.8104 -0.8104 0.8104 0.3063 -0.2228 1.0000 GenoMean Slope DeviMS GenoCV Wricke Pla_Pet Plaisted Shukla YauH SlopeW DeviSSW 6.5. Correlations between genotype-ranks obtained from various indices RGenoMn 1.0000 RSlope 0.9933 1.0000 RDeviMS -0.1675 -0.1582 1.0000 RGenoCV -0.1380 -0.1118 0.6837 1.0000 RWricke -0.1670 -0.1546 0.9975 0.6858 1.0000 RPla_Pet -0.1670 -0.1546 0.9975 0.6858 1.0000 1.0000 RPlaist 0.8042 0.8089 -0.2751 -0.2233 -0.2760 -0.2760 1.0000 RShukla -0.1670 -0.1546 0.9975 0.6858 1.0000 1.0000 -0.2760 1.0000 RYauH -0.1638 -0.1266 0.2998 0.0579 0.3444 0.3444 -0.2200 0.3444 1.0000 RGenoMn RSlope RDeviMS RGenoCV RWricke RPla_Pet RPlaist RShukla RYauH .................................................................................... Section 7: Hierarchical clustering of genotypes ===================================================================================================== 7.1: 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 ---------------- 6 8 95.3 9 11 95.2 12 15 94.3 3 5 93.9 4 14 93.8 2 13 91.5 3 6 91.5 7 12 90.5 2 7 89.2 3 4 89.2 9 10 85.6 2 3 84.7 2 9 81.5 1 2 74.3 Hierarchical clusters --------------------- Level 95.0 6 8 9 11 Ungrouped 1 2 13 7 12 15 3 5 4 14 10 Level 90.0 2 13 7 12 15 3 5 6 8 4 14 9 11 Ungrouped 1 10 Level 85.0 2 13 7 12 15 3 5 6 8 4 14 9 11 10 Ungrouped 1 Level 80.0 2 13 7 12 15 3 5 6 8 4 14 9 11 10 Ungrouped 1 Level 75.0 2 13 7 12 15 3 5 6 8 4 14 9 11 10 Ungrouped 1 Level 70.0 1 2 13 7 12 15 3 5 6 8 4 14 9 11 10 Dendrogram ---------- ** Levels 100.0 90.0 80.0 70.0 1.00 1 ................. 3.00 2 ..... ) 20.00 13 .....).. ) 9.00 7 ..... ) ) 14.00 12 .....) ) ) 150.00 15 .....)..).. ) 4.00 3 ..... ) ) 6.00 5 .....) ) ) 8.00 6 .. ) ) ) 10.00 8 ..)..).. ) ) 5.00 4 ..... ) ) ) 70.00 14 .....)..)..) ) 11.00 9 .. ) ) 13.00 11 ..)..... ) ) 12.00 10 ........)..).....)........... ===================================================================================================== .................................................................................... Section 8: Hierarchical clustering of environments ===================================================================================================== 8.1: 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 9 10 97.5 1 7 97.5 4 8 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 9 10 3 4 8 Ungrouped 6 Level 90.0 1 5 7 2 9 10 3 4 8 6 Level 85.0 1 5 7 2 9 10 3 4 8 6 Level 80.0 1 5 7 2 9 10 3 4 8 6 Level 75.0 1 5 7 2 9 10 3 4 8 6 Level 70.0 1 5 7 2 9 10 3 4 8 6 Level 65.0 1 5 7 2 9 10 3 4 8 6 Level 60.0 1 5 7 2 9 10 3 4 8 6 Level 55.0 1 5 7 2 9 10 3 4 8 6 Dendrogram ---------- ** Levels 100.0 90.0 80.0 70.0 60.0 1.00 1 .. 6.00 5 ..) 8.00 7 ..)....................... 2.00 2 .. ) 30.00 9 ..) ) 90.00 10 ..) ) 4.00 3 ..)........ ) 5.00 4 .. ) ) 10.00 8 ..).. ) ) 7.00 6 .....).....)..............)........ ===================================================================================================== .................................................................................... Variable is BYield .................................................................................... Section 1. Analysis of data from individual environments ******* Environment is = 1 ********* Analysis of variance ==================== Variate: BYield Source of variation d.f. s.s. m.s. v.r. F pr. Rep stratum 2 777784. 388892. 1.26 Rep.Geno stratum Geno 14 3799242. 271374. 0.88 0.588 Residual 28 8654262. 309081. Total 44 13231288. ******* Environment is = 2 ********* Analysis of variance ==================== Variate: BYield Source of variation d.f. s.s. m.s. v.r. F pr. Rep stratum 2 4119546. 2059773. 0.48 Rep.Geno stratum Geno 14 32538208. 2324158. 0.54 0.884 Residual 28 119529884. 4268924. Total 44 156187637. ******* Environment is = 4 ********* Analysis of variance ==================== Variate: BYield Source of variation d.f. s.s. m.s. v.r. F pr. Rep stratum 2 10039205. 5019602. 0.93 Rep.Geno stratum Geno 14 106235754. 7588268. 1.41 0.215 Residual 28 151177531. 5399198. Total 44 267452490. ******* Environment is = 5 ********* Analysis of variance ==================== Variate: BYield Source of variation d.f. s.s. m.s. v.r. F pr. Rep stratum 2 19937300. 9968650. 4.04 Rep.Geno stratum Geno 14 94105088. 6721792. 2.72 0.012 Residual 28 69099005. 2467822. Total 44 183141392. ******* Environment is = 6 ********* Analysis of variance ==================== Variate: BYield Source of variation d.f. s.s. m.s. v.r. F pr. Rep stratum 2 20174. 10087. 0.01 Rep.Geno stratum Geno 14 15076102. 1076864. 1.15 0.366 Residual 28 26331985. 940428. Total 44 41428261. ******* Environment is = 7 ********* Analysis of variance ==================== Variate: BYield Source of variation d.f.(m.v.) s.s. m.s. v.r. F pr. Rep stratum 2 109633. 54816. 0.05 Rep.Geno stratum Geno 14 28918966. 2065640. 1.77 0.099 Residual 27(1) 31547231. 1168416. Total 43(1) 58081022. ******* Environment is = 8 ********* Analysis of variance ==================== Variate: BYield Source of variation d.f. s.s. m.s. v.r. F pr. Rep stratum 2 234269. 117135. 6.12 Rep.Geno stratum Geno 14 874472. 62462. 3.26 0.004 Residual 28 536105. 19147. Total 44 1644847. ******* Environment is = 10 ********* Analysis of variance ==================== Variate: BYield Source of variation d.f. s.s. m.s. v.r. F pr. Rep stratum 2 15413815. 7706907. 2.19 Rep.Geno stratum Geno 14 52986763. 3784769. 1.07 0.419 Residual 28 98731427. 3526122. Total 44 167132005. ******* Environment is = 30 ********* Analysis of variance ==================== Variate: BYield Source of variation d.f. s.s. m.s. v.r. F pr. Rep stratum 2 39499614. 19749807. 7.90 Rep.Geno stratum Geno 14 113098162. 8078440. 3.23 0.004 Residual 28 69973602. 2499057. Total 44 222571379. ******* Environment is = 90 ********* Analysis of variance ==================== Variate: BYield Source of variation d.f. s.s. m.s. v.r. F pr. Rep stratum 2 3069128. 1534564. 0.28 Rep.Geno stratum Geno 14 155000512. 11071465. 2.01 0.056 Residual 28 153925118. 5497326. Total 44 311994758. EnvtNum EnvtMean CV% SEM SED LSD5% LSD1% ErrMS ErrDF P_value 1 2142 25.95 321.0 454 930 1254 309081 28.00 0.5885 2 8990 22.98 1192.9 1687 3456 4662 4268924 28.00 0.8841 4 7399 31.40 1341.5 1897 3886 5243 5399198 28.00 0.2147 5 6239 25.18 907.0 1283 2627 3544 2467822 28.00 0.0116 6 1893 51.22 559.9 792 1622 2188 940428 28.00 0.3658 7 4183 25.84 624.1 883 1811 2445 1168416 27.00 0.0991 8 618 22.41 79.9 113 231 312 19147 28.00 0.0038 10 6433 29.19 1084.1 1533 3141 4237 3526122 28.00 0.4194 30 7918 19.97 912.7 1291 2644 3567 2499057 28.00 0.0040 90 8867 26.44 1353.7 1914 3921 5290 5497326 28.00 0.0559 Histogram of CV% ---------------- - 30 8 ******** 30 - 45 1 * 45 - 1 * Scale: 1 asterisk represents 1 unit. Histogram of ErrMS ------------------ - 2000000 4 **** 2000000 - 4000000 3 *** 4000000 - 3 *** Scale: 1 asterisk represents 1 unit. Histogram of EnvtMean --------------------- - 3000 3 *** 3000 - 6000 1 * 6000 - 6 ****** Scale: 1 asterisk represents 1 unit. -+---------+---------+---------+---------+---------+---------+ I I 60.0 I I I I I I I I I 6. I I I 45.0 I I I I I I I I I I I 4. I 30.0 I 10. I I 90. I I 1. 7. 5. I I 8. 2. I I 30. I I I 15.0 I I -+---------+---------+---------+---------+---------+---------- 0.0 1600.0 3200.0 4800.0 6400.0 8000.0 9600.0 CV% v. EnvtMean using factor EnvtNum -+---------+---------+---------+---------+---------+---------+ I I 6000000.0 I I I I I 4. 90. I I I I I I 2. I 4000000.0 I I I 10. I I I I I I I I 5. 30. I 2000000.0 I I I I I 7. I I 6. I I I I 1. I 0.0 I 8. I -+---------+---------+---------+---------+---------+---------- 0.0 1600.0 3200.0 4800.0 6400.0 8000.0 9600.0 ErrMS v. EnvtMean using factor EnvtNum .................................................................................... Section 2.0 Bartlette Test for homogeneity of error variances Pooled Error Mean-square.........................................................................= 2614717 DF for Pooled Error Mean-square...............................................................= 279.0 Probability of greater chi-square (for testing homogeneity of error variances) = 0.000000 Error variances are heterogeneous at 0.05000 probability .................................................................................... Section 2.1 REML Deviance Difference Test for homogeneity of error variances Probability of greater chi-square (for testing homogeneity of error variances) = 0.000000 Error variances are heterogeneous at 0.05000 probability .................................................................................... Section 3: Combined analysis of data for GxE interaction 3.1 ANOVA under homogeneous error-variances Analysis of variance ==================== Variate: BYield Source of variation d.f.(m.v.) s.s. m.s. v.r. F pr. Envt.Rep stratum Envt 9 3.786E+09 4.207E+08 90.26 <.001 Residual 20 9.322E+07 4.661E+06 1.78 Envt.Rep.Geno stratum Geno 14 6.118E+07 4.370E+06 1.67 0.061 Envt.Geno 126 5.415E+08 4.297E+06 1.64 <.001 Residual 279(1) 7.295E+08 2.615E+06 Total 448(1) 5.212E+09 ******************************* Genotype x Environment table means ********************* Genotype 1 2 4 5 6 7 8 10 30 90 Geno.Mean 1 1810 8587 8087 5873 928 3014 663.0 6304 4792 4898 4496 3 2341 8375 8637 5629 1544 3831 502.3 6452 10683 9410 5740 4 1929 9758 6347 6248 1061 4530 453.3 5107 7294 9948 5268 5 1971 7773 7998 9774 1778 3670 464.0 4884 7647 11692 5765 6 2608 7338 7219 6134 1571 4655 417.7 4015 10095 8423 5247 8 2163 9353 8658 4632 1370 4335 484.7 6259 8309 9998 5556 9 2219 9346 8669 5844 3014 3449 906.3 6176 6782 7475 5388 10 2669 8255 6741 4689 2780 5081 540.3 6974 7333 11385 5645 11 2349 9388 5784 7227 1771 4639 735.7 6534 10208 7546 5618 12 1515 9506 8106 7603 2029 5693 638.0 7051 8796 7806 5874 13 2323 9268 4128 7812 2710 5747 772.3 6219 9418 11373 5977 14 2141 11017 6093 5294 1998 3540 683.3 7835 6295 9828 5472 20 2122 9198 10043 4462 2018 3420 555.0 7435 7279 7492 5402 70 2102 8776 8929 7565 2157 3955 655.0 6927 6901 9044 5701 150 1874 8910 5546 4793 1675 3722 792.7 8331 6939 6694 4928 Envt.Mean 2142 8990 7399 6239 1893 4219 617.6 6433 7918 8867 5471 3.2 Weighted ANOVA under heterogeneous error-variances Analysis of variance ==================== Variate: GEData Weight variate: AllWet Source of variation d.f. s.s. m.s. v.r. F pr. Envt1 9 4228.659 469.851 Geno1 14 43.580 3.113 Envt1.Geno1 126 209.076 1.659 Total 149 4481.315 3.2.1 Tests of significance for Genotype and GxE interaction Genotype : DF = 14 Weighted Sum of Squares = 43.580 Prob > Chisq = 0.00007 G x E Interaction : DF = 126 Weighted Sum of Squares = 209.076 Prob > Chisq = 0.00000 .................................................................................... Section 4: Heritabilities 4.1 Environment-wise heritability estimates (h2_...) and genetic gain (GG...) EnvtNum EnvtMean h2_plot Bias_h2_plot Se_h2_plot h2_mean Se_h2_mean GG5% GG10% GG20% Sig2G Se_Sig2G Sig2E Se_Sig2E 1 2142 0.0000 0.0000 0.0000 0.0000 0.0000 0.00 0.00 0.00 0 0 296512 64704 2 8990 0.0000 0.0000 0.0000 0.0000 0.0000 0.00 0.00 0.00 0 0 3549719 756803 4 7399 0.1208 0.2370 0.1666 0.2918 0.3242 12.94 11.01 8.78 738127 1062032 5373887 1387532 5 6239 0.3649 0.0978 0.1695 0.6329 0.1700 31.32 26.65 21.26 1417990 874938 2467822 659553 6 1893 0.0700 0.3782 0.1618 0.1843 0.3734 12.03 10.23 8.16 66153 155314 878405 226803 7 4219 0.1886 0.1780 0.1771 0.4108 0.2801 15.91 13.53 10.80 257660 264826 1108579 292762 8 618 0.4299 0.0840 0.1636 0.6935 0.1419 33.42 28.44 22.68 14439 8052 19147 5117 10 6433 0.0239 1.0446 0.1578 0.0683 0.4313 2.46 2.09 1.67 86215 571009 3526122 942396 30 7918 0.4267 0.0846 0.1640 0.6907 0.1432 29.52 25.12 20.04 1859794 1041853 2499057 667901 90 8867 0.2711 0.1239 0.1715 0.5273 0.2164 23.57 20.05 15.99 1946108 1465786 5233141 1351191 4.2 Correlations between mean, heritability, genetic gain, genotypic variance and error-variance EnvtMean 1.0000 h2_plot -0.0156 1.0000 h2_mean 0.0069 0.9877 1.0000 GG5% -0.0610 0.9794 0.9883 1.0000 GG10% -0.0610 0.9794 0.9883 1.0000 1.0000 GG20% -0.0610 0.9794 0.9883 1.0000 1.0000 1.0000 Sig2G 0.5939 0.6222 0.6542 0.6155 0.6155 0.6155 1.0000 Sig2E 0.8744 -0.1109 -0.0505 -0.0925 -0.0925 -0.0925 0.5031 1.0000 EnvtMean h2_plot h2_mean GG5% GG10% GG20% Sig2G Sig2E 4.3 Heritability estimate (h2_...) and genetic gain (GG...) in presence of GxE interaction Model assumed: Y= Envt eff. [Fixed terms] + Rep eff. within Envt + Geno eff. + Geno x Envt int. + error [Random terms] where Y= Response (e.g. Yield), Envt=Environment, eff.=effect, Rep=Replication, Geno=Genotype, int.=interaction h2_plot Bias_h2_plot Se_h2_plot h2_mean Se_h2_mean GG5% GG10% GG20% 0.00009921 3.271 0.01801 0.002197 0.3982 0.03136 0.02668 0.02128 4.4 Variance components from GxE data analysis Sig2G Se_Sig2G Sig2GE Se_Sig2GE Sig2E Se_Sig2E 314.8 57161 557805 194881 2615189 221409 4.5 Variance components from GxE data analysis under three more models Model 1: Fixed effects=Envt + Geno + Geno.Envt & Random = Rep.Envt REML variance components analysis ================================= Response variate: BYield Fixed model: Constant + Envt + Geno + Envt.Geno Random model: Envt.Rep + Envt.Rep.Geno Number of units: 449 (1 units excluded due to zero weights or missing values) Envt.Rep.Geno used as residual term Sparse algorithm with AI optimisation Estimated variance components ----------------------------- Random term component s.e. Envt.Rep 137036. 99644. Residual variance model ----------------------- Term Model(order) Parameter Estimate s.e. Envt.Rep.Geno Identity Sigma2 2614359. 221334. Deviance: -2*Log-Likelihood --------------------------- Deviance d.f. 4893.14 297 Note: deviance omits constants which depend on fixed model fitted. ******** Warning 3, code VD 39, statement 220 in for loop Command: VDisplay[Ch=ChReport; prin=model, comp, deviance, wald] Error in AI algorithm when forming denominator DF for approximate F-tests. Wald tests for fixed effects ---------------------------- Sequentially adding terms to fixed model Fixed term Wald statistic d.f. Wald/d.f. chi pr Envt 811.46 9 90.16 <0.001 Geno 22.89 14 1.64 0.062 Envt.Geno 206.66 126 1.64 <0.001 Dropping individual terms from full fixed model Fixed term Wald statistic d.f. Wald/d.f. chi pr Envt.Geno 206.66 126 1.64 <0.001 * MESSAGE: chi-square distribution for Wald tests is an asymptotic approximation (i.e. for large samples) and underestimates the probabilities in other cases. Model 2: Fixed effects=Envt + Geno & Random = Geno.Envt + Rep.Envt REML variance components analysis ================================= Response variate: BYield Fixed model: Constant + Envt + Geno Random model: Geno.Envt + Envt.Rep + Geno.Envt.Rep Number of units: 449 (1 units excluded due to zero weights or missing values) Geno.Envt.Rep used as residual term Sparse algorithm with AI optimisation Estimated variance components ----------------------------- Random term component s.e. Geno.Envt 559701. 195043. Envt.Rep 136866. 99560. Residual variance model ----------------------- Term Model(order) Parameter Estimate s.e. Geno.Envt.Rep Identity Sigma2 2613853. 221256. Deviance: -2*Log-Likelihood --------------------------- Deviance d.f. 6861.82 422 Note: deviance omits constants which depend on fixed model fitted. Tests for fixed effects ----------------------- Sequentially adding terms to fixed model Fixed term Wald statistic n.d.f. F statistic d.d.f. F pr Envt 596.98 9 66.33 32.0 <0.001 Geno 14.03 14 1.00 126.0 0.455 Dropping individual terms from full fixed model Fixed term Wald statistic n.d.f. F statistic d.d.f. F pr Envt 596.84 9 66.32 32.0 <0.001 Geno 14.03 14 1.00 126.0 0.455 * MESSAGE: denominator degrees of freedom for approximate F-tests are calculated using algebraic derivatives ignoring fixed/boundary/singular variance parameters. Model 3: Fixed effects=Envt & Random = Geno + Geno.Envt + Rep.Envt REML variance components analysis ================================= Response variate: BYield Fixed model: Constant + Envt Random model: Geno + Geno.Envt + Envt.Rep + Geno.Envt.Rep Number of units: 449 (1 units excluded due to zero weights or missing values) Geno.Envt.Rep used as residual term Sparse algorithm with AI optimisation Estimated variance components ----------------------------- Random term component s.e. Geno 315. 57161. Geno.Envt 557805. 194881. Envt.Rep 136788. 99562. Residual variance model ----------------------- Term Model(order) Parameter Estimate s.e. Geno.Envt.Rep Identity Sigma2 2615189. 221409. Deviance: -2*Log-Likelihood --------------------------- Deviance d.f. 7044.79 435 Note: deviance omits constants which depend on fixed model fitted. Tests for fixed effects ----------------------- Sequentially adding terms to fixed model Fixed term Wald statistic n.d.f. F statistic d.d.f. F pr Envt 597.50 9 66.39 31.9 <0.001 Dropping individual terms from full fixed model Fixed term Wald statistic n.d.f. F statistic d.d.f. F pr Envt 597.50 9 66.39 31.9 <0.001 * MESSAGE: denominator degrees of freedom for approximate F-tests are calculated using algebraic derivatives ignoring fixed/boundary/singular variance parameters. Model 4: Fixed effects=none & all Random = Envt+ Geno + Geno.Envt + Rep.Envt REML variance components analysis ================================= Response variate: BYield Fixed model: Constant Random model: Envt + Geno + Envt.Geno + Envt.Rep + Envt.Geno.Rep Number of units: 449 (1 units excluded due to zero weights or missing values) Envt.Geno.Rep used as residual term Sparse algorithm with AI optimisation Estimated variance components ----------------------------- Random term component s.e. Envt 9215220. 4410703. Geno 333. 57169. Envt.Geno 557856. 194885. Envt.Rep 136790. 99562. Residual variance model ----------------------- Term Model(order) Parameter Estimate s.e. Envt.Geno.Rep Identity Sigma2 2615140. 221403. Deviance: -2*Log-Likelihood --------------------------- Deviance d.f. 7200.55 443 Note: deviance omits constants which depend on fixed model fitted. * MESSAGE: No fixed model terms: Wald statistics cannot be calculated .................................................................................... Section 5: Tests for parallelism of regression lines 5.1 Partition GxE Int into heterogeneity of linear regressions under homogeneous error-variances Analysis of variance ==================== Variate: BYield Source of variation d.f.(m.v.) s.s. m.s. v.r. F pr. Envt.Rep stratum Envt 9 3.786E+09 4.207E+08 90.26 <.001 Lin 1 3.786E+09 3.786E+09 812.34 <.001 Deviations 8 1.981E-21 2.476E-22 0.00 1.000 Residual 20 9.322E+07 4.661E+06 1.78 Envt.Rep.Geno stratum Geno 14 6.118E+07 4.370E+06 1.67 0.061 Envt.Geno 126 5.415E+08 4.297E+06 1.64 <.001 Lin.Geno 14 2.994E+07 2.139E+06 0.82 0.649 Deviations 112 5.115E+08 4.567E+06 1.75 <.001 Residual 279(1) 7.295E+08 2.615E+06 Total 448(1) 5.212E+09 Regression analysis =================== Response variate: GEData Fitted terms: Constant + AllEnvt + Geno1 + AllEnvt.Geno1 Summary of analysis ------------------- Source d.f. s.s. m.s. v.r. F pr. Regression 29 1292480446. 44568291. 31.37 <.001 Residual 120 170503850. 1420865. Total 149 1462984296. 9818687. Percentage variance accounted for 85.5 Standard error of observations is estimated to be 1192. Accumulated analysis of variance -------------------------------- Change d.f. s.s. m.s. v.r. F pr. + AllEnvt 1 1262106539. 1262106539. 888.27 <.001 + Geno1 14 20393982. 1456713. 1.03 0.433 + AllEnvt.Geno1 14 9979924. 712852. 0.50 0.928 Residual 120 170503850. 1420865. Total 149 1462984296. 9818687. 5.2 Partition GxE Int into heterogeneity of linear regressions under heterogeneous error-variances Regression analysis =================== Response variate: GEData Weight variate: AllWet Fitted terms: Constant + AllEnvt + Geno1 + AllEnvt.Geno1 Summary of analysis ------------------- Source d.f. s.s. m.s. v.r. chi pr Regression 29 4310.2 148.628 148.63 <.001 Residual 120 171.1 1.426 Total 149 4481.3 30.076 Percentage variance accounted for 95.3 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 + AllEnvt 1 4228.659 4228.659 4228.66 <.001 + Geno1 14 43.580 3.113 3.11 <.001 + AllEnvt.Geno1 14 37.959 2.711 2.71 <.001 Residual 120 171.118 1.426 Total 149 4481.315 30.076 * MESSAGE: ratios are based on dispersion parameter with value 1. .................................................................................... Section 6: Common stability statistics 6.1 Stability indices under homogeneous error-variances GenoNum GenoMean Slope SeSlop Probb1 DeviMS ProbDev RSq% GenoCV YauH 1 4496 0.813 0.1557 0.2632 2040509 0.0189 74.45 62.86 0.04840 3 5740 1.119 0.1132 0.3240 1079046 0.2767 91.48 62.00 0.02819 4 5268 1.067 0.0869 0.4622 635025 0.6662 94.34 63.56 0.03115 5 5765 1.112 0.1858 0.5627 2904907 0.0012 79.47 65.24 0.06615 6 5247 0.944 0.1408 0.7006 1667336 0.0580 83.01 59.69 0.04617 8 5556 1.112 0.0857 0.2286 618079 0.6834 94.89 62.62 0.02530 9 5388 0.892 0.0951 0.2901 760247 0.5403 90.64 52.89 0.07039 10 5645 0.964 0.1321 0.7918 1468796 0.1017 85.30 56.00 0.05131 11 5618 0.987 0.1264 0.9207 1345345 0.1420 86.94 57.13 0.02437 12 5874 1.036 0.0925 0.7084 720466 0.5797 93.25 55.61 0.03018 13 5977 1.020 0.1820 0.9163 2787555 0.0017 77.15 58.44 0.06285 14 5472 1.056 0.1360 0.6922 1555636 0.0799 86.82 62.78 0.02738 20 5402 1.001 0.1447 0.9920 1762599 0.0439 83.89 61.24 0.03442 70 5701 1.014 0.0867 0.8796 631906 0.6694 93.78 55.93 0.01282 150 4928 0.864 0.1260 0.3111 1335531 0.1457 83.64 57.98 0.04013 GenoNum GenoMean Wricke Pla_Pet Plaisted Shukla 1 4496 19279689 1863806 1366042 2361570 3 5740 9824309 1300986 1452630 1149341 4 5268 5458885 1041139 1492607 589672 5 5765 24298112 2162522 1320086 3004957 6 5247 13603640 1525946 1418021 1633871 8 5556 5995042 1073053 1487697 658410 9 5388 7057495 1136294 1477967 794622 10 5645 11859755 1422143 1433991 1410296 11 5618 10776961 1357691 1443906 1271476 12 5874 5871968 1065727 1488824 642631 13 5977 22333271 2045567 1338079 2753054 14 5472 12707198 1472586 1426230 1518943 20 5402 14100978 1555549 1413467 1697632 70 5701 5070689 1018032 1496161 539903 150 4928 12245782 1445121 1430456 1459787 -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- I I I I I I 1.12 I 3. I I 8. 5. I I I I I I I I I 1.08 I I I I I 4. I I I I 14. I I I 1.04 I I I 12. I I I I 13. I I 70. I I I 1.00 I 20. I I I I 11. I I I I I I 10. I 0.96 I I I I I 6. I I I I I I I 0.92 I I I I I I I I I 9. I I I 0.88 I I I I I 150. I I I I I I I 0.84 I I I I I I I I I 1. I I I 0.80 I I -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- 4480.0 4640.0 4800.0 4960.0 5120.0 5280.0 5440.0 5600.0 5760.0 5920.0 6080.0 Slope v. GenoMean using factor GenoNum -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- I 5. 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 1. 14. I I 8. I I I I 3. I I I 61.5 I I I 20. I I I I I I I I I 60.0 I I I 6. I I I I I I I I I 58.5 I 13. I I I I 150. I I I I I I 11. I 57.0 I I I I I I I I I 10.70. I I I 55.5 I 12. I I I I I I I I I I I 54.0 I I I I I I I I I 9. I I I 52.5 I I -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- 4480.0 4640.0 4800.0 4960.0 5120.0 5280.0 5440.0 5600.0 5760.0 5920.0 6080.0 GenoCV v. GenoMean using factor GenoNum -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- I I I I I I 3000000.0 I I I I I 5. I I I I 13. I I I 2700000.0 I I I I I I I I I I I I 2400000.0 I I I I I I I I I I I I 2100000.0 I I I 1. I I I I I I I I I 1800000.0 I I I 20. I I I I 6. I I I I 14. I 1500000.0 I I I 10. I I I I 150. 11. I I I I I 1200000.0 I I I I I 3. I I I I I I I 900000.0 I I I I I I I 9. I I 12. I I 4. 70. I 600000.0 I 8. I -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- 4480.0 4640.0 4800.0 4960.0 5120.0 5280.0 5440.0 5600.0 5760.0 5920.0 6080.0 DeviMS v. GenoMean using factor GenoNum -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- I I I I I I 25000000.0 I I I I I 5. I I I I I I I 22500000.0 I 13. I I I I I I I I I I I 20000000.0 I I I I I 1. I I I I I I I 17500000.0 I I I I I I I I I I I I 15000000.0 I I I I I 20. I I 6. I I I I I 12500000.0 I 14. I I 150. I I 10. I I I I 11. I I I 10000000.0 I 3. I I I I I I I I I I I 7500000.0 I I I 9. I I I I I I 8. 12. I I 4. I 5000000.0 I 70. I -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- 4480.0 4640.0 4800.0 4960.0 5120.0 5280.0 5440.0 5600.0 5760.0 5920.0 6080.0 Wricke v. GenoMean using factor GenoNum -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- I I I I I I 0.072 I I I 9. I I I I I I 5. I I I 0.064 I I I 13. I I I I I I I I I 0.056 I I I I I I I I I 10. I I I 0.048 I 1. I I 6. I I I I I I I I I 0.040 I 150. I I I I I I I I 20. I I I 0.032 I I I 4. 12. I I I I 14. 3. I I I I 8. I 0.024 I 11. I I I I I I I I I I I 0.016 I I I I I 70. I I I I I I I 0.008 I I -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- 4480.0 4640.0 4800.0 4960.0 5120.0 5280.0 5440.0 5600.0 5760.0 5920.0 6080.0 YauH v. GenoMean using factor GenoNum 6.2 Stability indices under heterogeneous error-variances GenoNum GenoMean SlopeW SeSlopW Probb1W DeviSSW ProbDevW RSqW% 1 4496 0.769 0.07744 0.0175 13.52 0.0951 91.56 3 5740 1.096 0.06754 0.1949 10.29 0.2455 96.68 4 5268 1.003 0.04867 0.9567 5.34 0.7205 97.92 5 5765 1.079 0.10043 0.4535 22.75 0.0037 92.71 6 5247 1.048 0.08658 0.5965 16.90 0.0311 94.17 8 5556 1.038 0.04964 0.4695 5.56 0.6968 97.98 9 5388 0.890 0.05688 0.0897 7.30 0.5051 96.44 10 5645 1.043 0.08183 0.6132 15.10 0.0572 94.72 11 5618 1.055 0.06324 0.4070 9.02 0.3407 96.86 12 5874 1.086 0.07265 0.2710 11.90 0.1555 96.11 13 5977 1.109 0.08619 0.2399 16.75 0.0328 94.82 14 5472 0.960 0.07089 0.5907 11.33 0.1836 95.30 20 5402 0.963 0.07020 0.6130 11.11 0.1954 95.41 70 5701 1.012 0.04819 0.8106 5.24 0.7320 98.00 150 4928 0.849 0.06318 0.0438 9.00 0.3421 95.23 -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- I I I I I I 1.15 I I I I I I I I I I I 13. I 1.10 I I I 3. I I 12. I I 5. I I I I 11. I 1.05 I 6. I I 8. 10. I I I I I I I I 70. I 1.00 I 4. I I I I I I I I 20. I I 14. I 0.95 I I I I I I I I I I I I 0.90 I I I 9. I I I I I I I I I 0.85 I 150. I I I I I I I I I I I 0.80 I I I I I I I I I 1. I I I 0.75 I I -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- 4480.0 4640.0 4800.0 4960.0 5120.0 5280.0 5440.0 5600.0 5760.0 5920.0 6080.0 SlopeW v. GenoMean using factor GenoNum 6.3 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)% Geno1 1 4496 62.86 6126627 4181694 1944932 55.06 45.49 31.02 3 5740 62.00 2048814 1356446 692368 24.93 20.29 14.50 4 5268 63.56 2932110 2247240 684870 32.51 28.46 15.71 5 5765 65.24 2116176 1316014 800162 25.23 19.90 15.52 6 5247 59.69 3396903 2289983 1106920 35.12 28.84 20.05 8 5556 62.62 2452937 1677048 775889 28.19 23.31 15.85 9 5388 52.89 3162669 1999238 1163430 33.01 26.24 20.02 10 5645 56.00 2908730 1518767 1389963 30.21 21.83 20.89 11 5618 57.13 2541181 1565363 975819 28.37 22.27 17.58 12 5874 55.61 1670933 1144815 526118 22.00 18.21 12.35 13 5977 58.44 2414559 995084 1419475 26.00 16.69 19.93 14 5472 62.78 3243761 1833840 1409921 32.91 24.75 21.70 20 5402 61.24 3419210 1970547 1448663 34.23 25.98 22.28 70 5701 55.93 1937794 1422061 515733 24.42 20.92 12.60 150 4928 57.98 4750131 3025601 1724531 44.23 35.30 26.65 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)% Geno1 1 4496 62.86 1230682 446418 784264 24.68 14.86 19.70 3 5740 62.00 4275294 2397539 1877755 36.02 26.97 23.87 4 5268 63.56 2470820 1473758 997062 29.84 23.05 18.96 5 5765 65.24 4990934 2452005 2538929 38.75 27.16 27.64 6 5247 59.69 2859712 1439509 1420203 32.23 22.86 22.71 8 5556 62.62 3519427 2010881 1508545 33.76 25.52 22.11 9 5388 52.89 2355377 1687713 667664 28.48 24.11 15.17 10 5645 56.00 3703198 2192418 1510780 34.09 26.23 21.78 11 5618 57.13 3071440 2137209 934231 31.19 26.02 17.20 12 5874 55.61 3627187 2699791 927396 32.42 27.97 16.39 13 5977 58.44 4727245 2943027 1784218 36.38 28.70 22.35 14 5472 62.78 3056776 1846530 1210247 31.95 24.83 20.10 20 5402 61.24 3239829 1714273 1525556 33.32 24.24 22.86 70 5701 55.93 3383102 2312110 1070992 32.26 26.67 18.15 150 4928 57.98 1618960 947973 670987 25.82 19.76 16.62 6.4 Correlations between various indices GenoMean 1.0000 Slope 0.7292 1.0000 DeviMS 0.0201 -0.0689 1.0000 GenoCV -0.2145 0.4233 0.3683 1.0000 Wricke -0.0778 -0.1269 0.9909 0.4038 1.0000 Pla_Pet -0.0778 -0.1269 0.9909 0.4038 1.0000 1.0000 Plaisted 0.0778 0.1269 -0.9909 -0.4038 -1.0000 -1.0000 1.0000 Shukla -0.0778 -0.1269 0.9909 0.4038 1.0000 1.0000 -1.0000 1.0000 YauH -0.0630 -0.3234 0.6025 -0.0872 0.6197 0.6197 -0.6197 0.6197 1.0000 SlopeW 0.8937 0.7795 0.0656 0.0082 -0.0284 -0.0284 0.0284 -0.0284 -0.1272 1.0000 DeviSSW 0.1479 0.0119 0.8667 0.2580 0.8494 0.8494 -0.8494 0.8494 0.6271 0.2549 1.0000 GenoMean Slope DeviMS GenoCV Wricke Pla_Pet Plaisted Shukla YauH SlopeW DeviSSW 6.5. Correlations between genotype-ranks obtained from various indices RGenoMn 1.0000 RSlope 0.9910 1.0000 RDeviMS -0.1530 -0.1845 1.0000 RGenoCV -0.1440 -0.0740 -0.0733 1.0000 RWricke -0.1664 -0.1638 0.3540 -0.0094 1.0000 RPla_Pet -0.1664 -0.1638 0.3540 -0.0094 1.0000 1.0000 RPlaist -0.1007 -0.0860 -0.2558 -0.2128 -0.2760 -0.2760 1.0000 RShukla -0.1664 -0.1638 0.3540 -0.0094 1.0000 1.0000 -0.2760 1.0000 RYauH -0.1652 -0.1402 0.3590 -0.0885 0.8280 0.8280 -0.2375 0.8280 1.0000 RGenoMn RSlope RDeviMS RGenoCV RWricke RPla_Pet RPlaist RShukla RYauH .................................................................................... Section 7: Hierarchical clustering of genotypes ===================================================================================================== 7.1: 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 ---------------- 2 6 96.6 13 14 94.6 2 13 93.0 12 15 92.8 9 11 92.0 2 3 90.4 7 12 88.5 9 10 87.9 2 4 87.4 2 5 86.7 1 7 85.0 2 8 83.9 2 9 82.6 1 2 77.3 Hierarchical clusters --------------------- Level 95.0 2 6 Ungrouped 1 7 12 15 13 14 3 4 5 8 9 11 10 Level 90.0 12 15 2 6 13 14 3 9 11 Ungrouped 1 7 4 5 8 10 Level 85.0 7 12 15 2 6 13 14 3 4 5 9 11 10 Ungrouped 1 8 Level 80.0 1 7 12 15 2 6 13 14 3 4 5 8 9 11 10 Level 75.0 1 7 12 15 2 6 13 14 3 4 5 8 9 11 10 Dendrogram ---------- ** Levels 100.0 90.0 80.0 1.00 1 ........ 9.00 7 ........) 14.00 12 ..... ) 150.00 15 .....)..)..... 3.00 2 .. ) 8.00 6 ..).. ) 20.00 13 .....) ) 70.00 14 .....) ) 4.00 3 .....).. ) 5.00 4 ........) ) 6.00 5 ........).. ) 10.00 8 ...........) ) 11.00 9 ..... ) ) 13.00 11 .....).. ) ) 12.00 10 ........)..)..)........ ===================================================================================================== .................................................................................... Section 8: Hierarchical clustering of environments ===================================================================================================== 8.1: 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 99.6 1 7 97.6 4 8 95.2 2 10 95.1 2 9 94.5 3 4 93.8 2 3 91.9 1 6 89.4 1 2 67.0 Hierarchical clusters --------------------- Level 95.0 1 5 7 2 10 4 8 Ungrouped 6 9 3 Level 90.0 1 5 7 2 10 9 3 4 8 Ungrouped 6 Level 85.0 1 5 7 6 2 10 9 3 4 8 Level 80.0 1 5 7 6 2 10 9 3 4 8 Level 75.0 1 5 7 6 2 10 9 3 4 8 Level 70.0 1 5 7 6 2 10 9 3 4 8 Level 65.0 1 5 7 6 2 10 9 3 4 8 Dendrogram ---------- ** Levels 100.0 90.0 80.0 70.0 1.00 1 .. 6.00 5 ..) 8.00 7 ..)..... 7.00 6 ........)........... 2.00 2 .. ) 90.00 10 ..).. ) 30.00 9 .....) ) 4.00 3 .....) ) 5.00 4 .. ) ) 10.00 8 ..)..)..............)........ ===================================================================================================== 863 864 865 STOP