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) : 22 / 6 / 2017 Time : 10 hr 14 min Summary of the analysis of Multi-Environment Trials (MET)conducted in Incomplete 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: Cullis, B.R., Smith, A., Coombes, N.(2006). On the design of early generation variety trials with correlated data. Journal of Agricultural, Biological and Environmental Statistics, 11: 381-393. 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. Piepho, H.-P. and J. Möhring (2007).Computing heritability and selection response from unbalanced plant breeding trials. Genetics 177: 1881-1888. Singh, M. and Ceccarelli, S. (1995). Estimation of heritability using variety trials data in incomplete blocks. Theoretical and Applied Genetics, 90:142-145. Yau, SK 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) Eff% = % Efficiency of the incomplete block design over the complete block design SEM = Standard error of predicted means of genotypes SED = Average standard error of difference between pairs of genotype effects LSDa% = Average least significant difference (LSD) at a%=5%, 1% level of significance RCBSEM = Standard error of predicted means of genotypes when incomplete blocks are ignored 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 h2C = heritability from Cullis et al. (2006); mean basis and broad sense h2_Ad_hoc = heritability from Piepho & Möhring (2007); mean basis and broad sense 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 ........................................................................................................... NOTE: To compare results under complete block design, request for the analysis from the MET CB module. ........................................................................................................... ....................................................................................................... Trials and parameters of the designs No. of Environments = 10 No. of replications (maximum) = 3 No. of replications (average) = 3 No. of incomplete blocks/replication (maximum) = 8 No. of genotypes = 64 No. of obvervations from all the environments = 1920 Variables analyzed : GYield, BYield ......................................................................................... .................................................................................... Variable is GYield .................................................................................... Section 1. Analysis of data from individual environments EnvtNum EnvtMean CV% Eff% SEM SED LSD5% LSD1% RCBSEM ErrMS ErrDF P_value 1 355 22.85 102.1 51.0 68.1 134.9 178.3 51.5 6573 124.0 0.0000000 3 2000 12.12 100.0 150.3 198.0 391.9 517.9 150.3 58801 125.0 0.0000000 4 1044 12.07 111.0 80.3 107.6 212.9 281.4 84.1 15880 125.0 0.0000000 5 3361 12.95 109.6 295.8 371.1 734.5 970.8 306.7 189582 125.0 0.0058774 6 4230 10.19 120.2 290.6 371.1 734.5 970.8 313.3 185913 125.0 0.0000000 7 1189 13.98 127.3 105.2 143.6 284.2 375.6 117.6 27625 125.0 0.0000000 8 4856 7.42 158.7 232.2 313.9 621.2 821.0 284.4 129928 125.0 0.0002433 9 1681 21.15 127.6 370.0 307.3 608.2 803.8 386.9 126462 125.0 0.0013182 20 706 15.63 105.5 66.5 93.3 184.7 244.1 68.1 12189 125.0 0.0000000 100 1969 14.33 192.4 185.6 246.5 487.9 644.9 241.8 79635 125.0 0.0000000 Histogram of CV% ---------------- - 12 2 ** 12 - 18 6 ****** 18 - 2 ** Scale: 1 asterisk represents 1 unit. Histogram of Eff% ----------------- - 120 5 ***** 120 - 160 4 **** 160 - 1 * Scale: 1 asterisk represents 1 unit. Histogram of ErrMS ------------------ - 80000 6 ****** 80000 - 160000 2 ** 160000 - 2 ** Scale: 1 asterisk represents 1 unit. Histogram of EnvtMean --------------------- - 2000 6 ****** 2000 - 4000 2 ** 4000 - 2 ** Scale: 1 asterisk represents 1 unit. -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- I 1. I I I I I 22.0 I I I I I I I 9. I I I I I 20.0 I I I I I I I I I I I I 18.0 I I I I I I I I I I I I 16.0 I I I 20. I I I I I I I I 100. I 14.0 I 7. I I I I I I 5. I I I I I 12.0 I 4. 3. I I I I I I I I I I 6. I 10.0 I I I I I I I I I I I I 8.0 I I I I I 8. I I I I I I I 6.0 I I -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- 0.0 500.0 1000.0 1500.0 2000.0 2500.0 3000.0 3500.0 4000.0 4500.0 5000.0 CV% v. EnvtMean using factor EnvtNum -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- I I I I I I 192.0 I 100. I I I I I I I I I I I 180.0 I I I I I I I I I I I I 168.0 I I I I I I I I I I I 8. I 156.0 I I I I I I I I I I I I 144.0 I I I I I I I I I I I I 132.0 I I I I I 7. 9. I I I I I I I 120.0 I 6. I I I I I I I I I I 4. 5. I 108.0 I I I 20. I I I I 1. I I 3. I I I 96.0 I I -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0 22.0 24.0 Eff% v. CV% using factor EnvtNum -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- I I I I I I 200000.0 I I I I I I I 5. 6. I I I I I 175000.0 I I I I I I I I I I I I 150000.0 I I I I I I I I I I I 8. I 125000.0 I 9. I I I I I I I I I I I 100000.0 I I I I I I I I I I I 100. I 75000.0 I I I I I I I I I 3. I I I 50000.0 I I I I I I I I I I I 7. I 25000.0 I I I I I 4. I I 20. I I 1. I I I 0.0 I I -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- 0.0 500.0 1000.0 1500.0 2000.0 2500.0 3000.0 3500.0 4000.0 4500.0 5000.0 ErrMS v. EnvtMean using factor EnvtNum ................................................................................... Section 2.0 Bartlette Test for homogeneity of error variances Pooled Error Mean-square.........................................................................= 83320 DF for Pooled Error Mean-square...............................................................= 1249 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 REML analysis- Wald tests under homogeneous error-variances For significance of genotype and G x E interaction, see the results corresponding to the rows of Geno and Envt.Geno respectively. ******** Warning 2, code VD 39, statement 103 in for loop Command: VDisp[Prin=Wald; Ch=ChReport; PTerms=Geno+Geno.Envt] 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 1521.10 9 169.01 <0.001 Geno 515.81 63 8.19 <0.001 Envt.Geno 1312.81 567 2.32 <0.001 Dropping individual terms from full fixed model Fixed term Wald statistic d.f. Wald/d.f. chi pr Envt.Geno 1312.81 567 2.32 <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. ******************************* Genotype x Environment table means ********************* Genotype 1 3 4 5 6 7 8 9 20 100 Geno.Mean 1 416.4 1892 1175 3335 4406 1080 4926 1571 820.3 1601 2122 4 358.4 1976 1005 3824 4950 1246 4894 2192 757.7 1976 2318 5 350.2 2292 1219 2721 3175 1302 5063 1295 810.5 2048 2028 6 204.4 1614 624 3018 3872 939 4889 1873 660.9 1878 1957 7 336.8 2145 1082 2939 3934 973 4850 1420 627.2 1661 1997 8 431.5 2584 1288 3546 4226 1133 4944 1235 740.3 2175 2230 9 573.4 2548 1477 3252 4408 1137 4952 1344 792.8 1601 2209 10 333.8 1894 1243 2755 3625 931 4505 1361 627.2 2048 1932 11 420.2 2400 756 2597 3964 1047 4678 1700 857.8 2486 2091 12 469.1 2465 1584 3893 4173 1183 4968 1611 919.9 1857 2312 13 419.2 1287 724 4033 4850 1151 4848 2172 935.7 2167 2259 14 424.9 2467 1157 3422 4308 1168 5370 1630 842.4 2081 2287 15 523.5 1528 727 2996 4209 1592 4847 1537 936.3 2153 2105 16 432.4 1416 563 3608 3765 1595 4569 1650 831.3 2308 2074 17 475.7 1573 539 3308 3536 1564 4412 1379 850.4 2037 1967 18 472.8 1887 689 3200 3968 1694 4690 1628 900.7 1979 2111 19 564.4 1902 809 3031 4055 1451 4428 1874 866.0 2272 2125 20 530.6 1472 665 3486 4042 1317 5013 1799 940.1 2175 2144 21 415.6 2116 850 3495 3818 1656 4694 1420 603.4 1963 2103 22 510.7 1702 647 3010 4027 1576 4617 1840 752.8 2400 2108 23 31.0 991 641 3314 3851 643 4244 1382 49.5 1523 1667 24 118.6 1656 934 3286 3589 1059 4879 1779 366.7 1538 1921 25 113.6 1158 462 2937 3582 1078 4399 1909 273.7 2008 1792 26 309.3 1718 809 3069 3651 877 4952 1718 690.8 2010 1980 27 389.6 2031 1262 3350 4257 897 4955 1632 748.5 2193 2171 28 152.3 1331 850 3486 3985 711 4166 1367 271.7 1006 1732 29 419.3 2057 1341 3202 3597 1006 4813 1305 718.9 1759 2022 30 74.7 1053 805 3069 4317 1007 4873 1834 530.2 1884 1945 31 188.7 1808 933 2982 4478 1181 4907 1532 631.5 1930 2057 32 418.2 2302 1176 3499 4662 1079 5043 1877 852.4 2368 2328 33 38.6 1499 603 2999 4327 1009 4741 1896 212.3 1990 1931 34 339.3 2254 1134 3574 4626 1501 4895 1625 767.4 2202 2292 35 156.6 1661 1032 3598 3440 777 4326 1485 534.5 1601 1861 36 407.9 2079 1129 3006 4444 1320 4828 1716 750.3 2001 2168 37 279.6 2351 934 3082 3595 881 4461 1572 769.4 1548 1947 38 267.4 2120 1392 3723 4872 1231 5363 1555 860.6 1370 2275 39 329.9 2412 1367 3538 4358 1158 4843 1426 710.6 2311 2245 40 398.4 2401 1100 3042 4738 1467 5196 1633 1026.2 2297 2330 41 339.2 2360 1459 3496 4099 1198 4967 1629 796.9 2071 2241 42 215.6 1604 1342 2995 4720 952 5336 2426 588.3 1754 2193 43 338.7 2018 1401 3302 4108 1198 4463 1342 664.3 1708 2054 44 313.6 2231 874 3678 4108 1335 4743 1527 753.6 2140 2170 45 445.0 1764 1166 3505 5102 1042 4733 2059 566.7 1685 2207 46 278.4 2261 1100 3535 4029 1081 5197 1323 689.2 2026 2152 47 347.6 1987 844 3495 4199 1466 5186 1673 555.0 1860 2161 48 317.6 2261 1207 3534 4667 1307 5070 1508 725.8 2251 2285 49 276.1 2193 1223 3821 4817 1181 4810 2045 670.8 2285 2332 50 322.5 1585 914 3470 4333 1173 5045 1953 696.0 2103 2159 51 323.6 2147 766 3274 4606 1253 5205 2316 687.1 2288 2287 52 272.6 1951 1058 3580 4510 1535 5423 2121 687.4 1868 2301 53 311.4 2032 910 4142 4447 1283 4944 2090 707.6 1774 2264 54 77.6 1229 810 3317 4192 999 4216 1589 505.5 1621 1856 55 471.4 2424 1351 3275 4762 1194 4786 1532 771.2 1806 2237 56 640.1 2616 1429 3761 4594 1173 4938 1662 855.1 1352 2302 57 361.4 2419 1643 3498 4772 1234 5229 1655 642.8 1925 2338 58 490.1 2003 880 3476 4414 1235 4738 2175 781.5 2246 2244 59 363.8 2237 1332 3517 4849 1122 4783 2287 624.8 1874 2299 60 417.3 2508 1563 3669 4648 1227 4825 1574 459.0 1740 2263 61 433.4 2308 1236 3350 4158 1324 5104 1703 803.7 2424 2284 62 537.2 2401 1098 3081 3642 826 5378 1436 982.7 2198 2158 63 401.6 2344 1205 3205 4185 1264 5031 1410 822.0 2036 2190 64 469.4 2255 783 3798 4220 1305 4439 1599 890.0 2122 2188 200 350.1 2475 1384 3723 4774 1143 5033 1485 719.2 2280 2337 300 387.7 2374 1090 3384 4098 1422 5154 1711 719.7 2163 2250 Envt.Mean 353.1 2000 1044 3361 4230 1189 4856 1681 706.3 1969 Grand Mean 2140 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 45803.310 5089.257 Geno1 63 1224.915 19.443 Envt1.Geno1 567 1793.969 3.164 Total 639 48822.194 3.2.1 Tests of significance for Genotype and GxE interaction Genotype : DF = 63 Weighted Sum of Squares = 1224.915 Prob > Chisq = 0.00000 G x E Interaction : DF = 567 Weighted Sum of Squares = 1793.969 Prob > Chisq = 0.00000 ................................................................................... Section 4: Heritabilities 4.1 Environment-wise heritability estimates (h2_...), biases, genetic gains (GG...) and variance components EnvtNum EnvtMean h2_plot Bias_h2_plot Se_h2_plot h2C h2_Ad_hoc h2_mean Se_h2_mean GG5% GG10% GG20% Sig2G Se_Sig2G Sig2E Se_Sig2E 1 353 0.6766 0.01042 0.05842 0.8607 0.8631 0.8626 0.03165 65.64 55.85 44.55 14642 3065 6997 986 3 2000 0.7185 0.00868 0.04989 0.8845 0.8845 0.8845 0.02520 37.57 31.97 25.50 150118 30340 58801 7408 4 1044 0.8301 0.00540 0.03423 0.9309 0.9312 0.9361 0.01451 53.54 45.55 36.33 78396 15038 16046 2219 5 3361 0.1452 0.05126 0.08499 0.3228 0.3240 0.3376 0.15310 6.48 5.51 4.40 33012 20233 194290 26457 6 4230 0.3870 0.02258 0.08341 0.6308 0.6259 0.6545 0.07951 13.39 11.39 9.09 115226 33633 182491 24785 7 1189 0.6044 0.01307 0.06666 0.8040 0.8025 0.8209 0.04099 32.18 27.38 21.84 41907 9402 27433 3756 8 4856 0.2101 0.04078 0.08947 0.4163 0.4144 0.4439 0.13306 5.28 4.50 3.59 34859 16339 131024 17975 9 1681 0.1851 0.04450 0.08820 0.3802 0.3736 0.4052 0.14095 13.11 11.15 8.89 28160 14537 123995 16792 20 706 0.7088 0.00922 0.05305 0.8723 0.8723 0.8796 0.02723 47.24 40.19 32.06 29745 6103 12217 1677 100 1969 0.3942 0.02346 0.08579 0.6334 0.6360 0.6613 0.08047 19.63 16.70 13.32 53105 15636 81615 11329 4.2 Correlations between mean, heritability, genotypic variance and error-variance EnvtMean 1.0000 h2_plot -0.6943 1.0000 h2C -0.6725 0.9895 1.0000 h2_Ad_hoc -0.6737 0.9896 0.9999 1.0000 h2_mean -0.6663 0.9859 0.9994 0.9993 1.0000 GG5% -0.8241 0.9019 0.8815 0.8831 0.8723 1.0000 GG10% -0.8241 0.9019 0.8815 0.8831 0.8723 1.0000 1.0000 GG20% -0.8241 0.9019 0.8815 0.8831 0.8723 1.0000 1.0000 1.0000 Sig2G 0.2319 0.3086 0.3308 0.3273 0.3312 -0.0152 -0.0152 -0.0152 1.0000 Sig2E 0.8472 -0.8616 -0.8510 -0.8523 -0.8504 -0.8865 -0.8865 -0.8865 0.1141 1.0000 EnvtMean h2_plot h2C h2_Ad_hoc 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 + [incomplete]Block eff. within Rep 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% 0.1290 0.007039 0.02864 0.7294 0.05169 11.16 9.497 7.575 4.4 Variance components from GxE data analysis Sig2G Se_Sig2G Sig2GE Se_Sig2GE Sig2E Se_Sig2E 18386 4573 40238 4436 83895 3636 4.5 Variance components from GxE data analysis under three more models Model 1: Fixed effects=Envt + Geno + Geno.Envt & Random = Rep.Envt/Blk REML variance components analysis ================================= Response variate: GYield Fixed model: Constant + Envt + Geno + Envt.Geno Random model: Envt.Rep + Envt.Rep.Blk Number of units: 1919 (1 units excluded due to zero weights or missing values) Residual term has been added to model Sparse algorithm with AI optimisation Estimated variance components ----------------------------- Random term component s.e. Envt.Rep 34618. 13020. Envt.Rep.Blk 41531. 5624. Residual variance model ----------------------- Term Model(order) Parameter Estimate s.e. Residual Identity Sigma2 83530. 3647. Deviance: -2*Log-Likelihood --------------------------- Deviance d.f. 16817.41 1276 Note: deviance omits constants which depend on fixed model fitted. ******** Warning 3, code VD 39, statement 239 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 1521.10 9 169.01 <0.001 Geno 515.81 63 8.19 <0.001 Envt.Geno 1312.81 567 2.32 <0.001 Dropping individual terms from full fixed model Fixed term Wald statistic d.f. Wald/d.f. chi pr Envt.Geno 1312.81 567 2.32 <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/Blk REML variance components analysis ================================= Response variate: GYield Fixed model: Constant + Envt + Geno Random model: Geno.Envt + Envt.Rep + Envt.Rep.Blk Number of units: 1919 (1 units excluded due to zero weights or missing values) Residual term has been added to model Sparse algorithm with AI optimisation Estimated variance components ----------------------------- Random term component s.e. Geno.Envt 40258. 4438. Envt.Rep 34691. 13019. Envt.Rep.Blk 40900. 5310. Residual variance model ----------------------- Term Model(order) Parameter Estimate s.e. Residual Identity Sigma2 83911. 3638. Deviance: -2*Log-Likelihood --------------------------- Deviance d.f. 23907.08 1842 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 1454.55 9 161.62 21.9 <0.001 Geno 224.35 63 3.56 561.7 <0.001 Dropping individual terms from full fixed model Fixed term Wald statistic n.d.f. F statistic d.d.f. F pr Envt 1454.87 9 161.65 21.9 <0.001 Geno 224.35 63 3.56 561.7 <0.001 * 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/Blk REML variance components analysis ================================= Response variate: GYield Fixed model: Constant + Envt Random model: Geno + Geno.Envt + Envt.Rep + Envt.Rep.Blk Number of units: 1919 (1 units excluded due to zero weights or missing values) Residual term has been added to model Sparse algorithm with AI optimisation Estimated variance components ----------------------------- Random term component s.e. Geno 18386. 4573. Geno.Envt 40238. 4436. Envt.Rep 34670. 13018. Envt.Rep.Blk 41060. 5319. Residual variance model ----------------------- Term Model(order) Parameter Estimate s.e. Residual Identity Sigma2 83895. 3636. Deviance: -2*Log-Likelihood --------------------------- Deviance d.f. 24613.70 1904 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 1454.84 9 161.65 21.9 <0.001 Dropping individual terms from full fixed model Fixed term Wald statistic n.d.f. F statistic d.d.f. F pr Envt 1454.84 9 161.65 21.9 <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/Blk REML variance components analysis ================================= Response variate: GYield Fixed model: Constant Random model: Envt + Geno + Envt.Geno + Envt.Rep + Envt.Rep.Blk Number of units: 1919 (1 units excluded due to zero weights or missing values) Residual term has been added to model Sparse algorithm with AI optimisation Estimated variance components ----------------------------- Random term component s.e. Envt 2302699. 1092268. Geno 18386. 4573. Envt.Geno 40238. 4436. Envt.Rep 34670. 13018. Envt.Rep.Blk 41060. 5319. Residual variance model ----------------------- Term Model(order) Parameter Estimate s.e. Residual Identity Sigma2 83895. 3636. Deviance: -2*Log-Likelihood --------------------------- Deviance d.f. 24756.91 1912 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 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 127 1356315406. 10679649. 157.51 <.001 Residual 512 34714388. 67802. Total 639 1391029793. 2176885. Percentage variance accounted for 96.9 Standard error of observations is estimated to be 260. Accumulated analysis of variance -------------------------------- Change d.f. s.s. m.s. v.r. F pr. + AllEnvt 1 1334586522. 1334586522. 19683.72 <.001 + Geno1 63 16197998. 257111. 3.79 <.001 + AllEnvt.Geno1 63 5530886. 87792. 1.29 0.072 Residual 512 34714388. 67802. Total 639 1391029793. 2176885. 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 127 47244. 372.001 372.00 <.001 Residual 512 1578. 3.082 Total 639 48822. 76.404 Percentage variance accounted for 96.0 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 45803.310 45803.310 45803.31 <.001 + Geno1 63 1224.915 19.443 19.44 <.001 + AllEnvt.Geno1 63 215.864 3.426 3.43 <.001 Residual 512 1578.105 3.082 Total 639 48822.194 76.404 * 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 2122 1.016 0.03743 0.6768 29213 0.3948 98.79 73.28 0.01391 4 2318 1.088 0.05579 0.1515 64910 0.0171 97.68 72.23 0.01102 5 2028 0.868 0.09077 0.1847 171818 0.0000 90.95 67.97 0.02611 6 1957 0.997 0.04730 0.9440 46655 0.0988 98.01 78.19 0.02896 7 1997 0.967 0.04088 0.4395 34855 0.2634 98.41 74.22 0.00763 8 2230 1.007 0.06052 0.9142 76386 0.0052 96.84 69.70 0.02613 9 2209 0.985 0.06902 0.8385 99347 0.0004 95.75 69.24 0.06942 10 1932 0.873 0.04436 0.0214 41026 0.1608 97.73 69.51 0.01501 11 2091 0.903 0.07844 0.2530 128310 0.0000 93.60 67.73 0.03732 12 2312 0.987 0.05892 0.8269 72391 0.0079 96.88 65.87 0.03813 13 2259 1.090 0.09399 0.3667 184202 0.0000 93.68 75.60 0.05430 14 2287 1.055 0.03963 0.2035 32745 0.3082 98.74 70.61 0.00911 15 2105 0.948 0.06424 0.4405 86064 0.0018 96.01 69.79 0.06721 16 2074 0.923 0.08010 0.3675 133796 0.0000 93.61 69.80 0.06071 17 1967 0.867 0.06619 0.0797 91355 0.0010 94.99 68.64 0.06713 18 2111 0.916 0.05004 0.1335 52219 0.0594 97.38 66.87 0.05288 19 2125 0.873 0.04346 0.0189 39389 0.1841 97.81 63.11 0.05565 20 2144 0.991 0.06266 0.8871 81880 0.0029 96.51 71.47 0.06320 21 2103 0.941 0.05366 0.3036 60047 0.0279 97.15 68.99 0.03120 22 2108 0.909 0.06364 0.1921 84465 0.0022 95.76 66.93 0.05900 23 1667 1.015 0.05952 0.8063 73886 0.0067 96.99 93.96 0.10606 24 1921 0.993 0.05203 0.8959 56447 0.0397 97.58 79.56 0.05036 25 1792 0.937 0.07262 0.4082 109973 0.0001 94.84 81.45 0.08146 26 1980 0.969 0.04876 0.5479 49580 0.0759 97.77 75.26 0.01060 27 2171 1.010 0.03355 0.7786 23475 0.5628 99.02 71.09 0.01407 28 1732 0.991 0.07216 0.9036 108597 0.0001 95.42 88.90 0.04909 29 2022 0.917 0.05269 0.1550 57898 0.0345 97.11 69.96 0.02490 30 1945 1.054 0.06841 0.4511 97582 0.0005 96.33 83.89 0.07085 31 2057 1.039 0.03579 0.3031 26717 0.4643 98.94 77.28 0.02065 32 2328 1.049 0.03276 0.1763 22380 0.5975 99.13 68.84 0.00848 33 1931 1.064 0.05500 0.2779 63082 0.0206 97.65 84.75 0.11188 34 2292 1.033 0.03275 0.3452 22362 0.5981 99.10 68.88 0.00775 35 1861 0.923 0.05965 0.2337 74194 0.0065 96.36 76.76 0.03041 36 2168 0.977 0.03384 0.5193 23873 0.5503 98.93 68.93 0.00497 37 1947 0.894 0.05261 0.0780 57726 0.0351 96.96 70.82 0.01830 38 2275 1.135 0.06824 0.0833 97113 0.0005 96.84 77.02 0.03905 39 2245 1.008 0.04847 0.8796 48981 0.0801 97.96 68.94 0.01914 40 2330 1.031 0.05725 0.6068 68338 0.0121 97.29 68.16 0.02296 41 2241 0.980 0.03928 0.6213 32169 0.3213 98.57 66.97 0.01806 42 2193 1.093 0.08927 0.3267 166174 0.0000 94.30 77.87 0.06422 43 2054 0.928 0.04275 0.1284 38114 0.2042 98.12 69.30 0.02049 44 2170 0.994 0.04077 0.8942 34658 0.2673 98.51 70.21 0.01082 45 2207 1.077 0.07623 0.3398 121178 0.0000 95.67 75.79 0.02892 46 2152 1.050 0.04609 0.3137 44307 0.1216 98.29 74.81 0.01370 47 2161 1.058 0.03505 0.1389 25619 0.4967 99.02 74.82 0.01600 48 2285 1.069 0.03226 0.0642 21702 0.6192 99.19 71.49 0.00869 49 2332 1.068 0.04882 0.2017 49710 0.0750 98.15 70.28 0.01766 50 2159 1.048 0.04161 0.2831 36107 0.2392 98.60 74.33 0.01100 51 2287 1.076 0.05692 0.2182 67560 0.0131 97.54 72.43 0.02791 52 2301 1.098 0.04373 0.0555 39873 0.1770 98.59 73.10 0.02314 53 2264 1.077 0.06088 0.2389 77295 0.0047 97.20 73.36 0.01713 54 1856 0.978 0.05647 0.7129 66505 0.0146 97.08 81.33 0.05257 55 2237 1.010 0.05674 0.8653 67138 0.0136 97.23 69.58 0.02343 56 2302 1.018 0.07893 0.8299 129915 0.0000 94.83 68.88 0.08946 57 2338 1.079 0.05295 0.1735 58456 0.0326 97.87 70.93 0.03507 58 2244 0.986 0.04384 0.7605 40081 0.1740 98.25 67.43 0.02471 59 2299 1.040 0.06243 0.5394 81269 0.0031 96.85 69.85 0.02320 60 2263 1.039 0.06672 0.5737 92833 0.0009 96.41 71.04 0.05182 61 2284 0.988 0.03679 0.7573 28226 0.4215 98.77 66.21 0.00874 62 2158 0.972 0.08462 0.7515 149319 0.0000 93.57 70.63 0.06471 63 2190 0.988 0.04034 0.7774 33928 0.2824 98.52 69.13 0.01161 64 2188 0.955 0.05598 0.4432 65349 0.0164 96.99 67.34 0.02850 200 2337 1.081 0.04956 0.1409 51228 0.0651 98.14 71.01 0.01787 300 2250 1.005 0.03619 0.8897 27305 0.4473 98.85 68.34 0.00572 GenoNum GenoMean Wricke Pla_Pet Plaisted Shukla 1 2122 239166 48988 71689 26286 4 2318 682485 74007 70882 77133 5 2028 1736565 133497 68963 198031 6 1957 373488 56568 71444 41693 7 1997 301898 52528 71575 33481 8 2230 612035 70031 71010 69053 9 2209 799179 80593 70669 90517 10 1932 662218 72864 70919 74809 11 2091 1221139 104408 69901 138914 12 2312 582826 68383 71063 65703 13 2259 1642251 128174 69134 187214 14 2287 324737 53817 71533 36101 15 2105 745217 77548 70767 84328 16 2074 1192410 102786 69953 135619 17 1967 1098530 97488 70124 124851 18 2111 563313 67282 71099 63465 19 2125 653806 72389 70934 73844 20 2144 656797 72558 70928 74187 21 2103 552941 66696 71117 62275 22 2108 847113 83299 70582 96015 23 1667 595835 69117 71039 67195 24 1921 452610 61034 71300 50767 25 1792 963551 89870 70370 109370 26 1980 416154 58976 71367 46586 27 2171 189785 46201 71779 20623 28 1732 870471 84617 70539 98694 29 2022 605918 69686 71021 68351 30 1945 841890 83004 70591 95416 31 2057 246098 49379 71676 27081 32 2328 228267 48372 71709 25036 33 1931 590159 68797 71050 66544 34 2292 201392 46856 71758 21954 35 1861 716643 75935 70819 81051 36 2168 201823 46880 71757 22003 37 1947 697385 74848 70855 78842 38 2275 1156953 100785 70018 131552 39 2245 393049 57672 71409 43936 40 2330 566305 67450 71093 63808 41 2241 265847 50493 71640 29347 42 2193 1510783 120754 69374 172135 43 2054 414498 58883 71370 46396 44 2170 277916 51174 71618 30731 45 2207 1094299 97249 70132 124366 46 2152 405660 58384 71386 45383 47 2161 274149 50962 71625 30299 48 2285 273558 50929 71626 30231 49 2332 493835 63360 71225 55496 50 2159 336666 54490 71511 37469 51 2287 661141 72803 70920 74685 52 2301 518875 64774 71180 58368 53 2264 743532 77453 70771 84135 54 1856 541711 66062 71138 60987 55 2237 539166 65919 71143 60695 56 2302 1045722 94507 70220 118795 57 2338 598152 69248 71035 67460 58 2244 324637 53811 71533 36089 59 2299 683550 74067 70880 77255 60 2263 774606 79206 70714 87699 61 2284 228697 48397 71708 25086 62 2158 1210601 103813 69920 137706 63 2190 274324 50972 71625 30319 64 2188 565319 67395 71095 63695 200 2337 546626 66340 71129 61551 300 2250 218998 47849 71725 23973 -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- I I I I I I 1.16 I I I I I I I I I 38. I I I 1.12 I I I I I I I 52. I I 42. I I 13. 4. I 1.08 I 45. 53. 57. I I 51. I I 33. 48. 49. I I 47. I I 30. 14. I I 46. 32. I 1.04 I 31. 60. 59. I I 34. 40. I I I I 56. I I 23. 1. I I 27. 8.39. I 1.00 I I I 28. 24. 6. 20.44. I I 9. 58. 61.12. I I 54. 36. 41. I I 62. I I 7. I 0.96 I I I 64. I I 15. I I 21. I I 25. I I 16. I 0.92 I 35. 29. I I 18. I I 11.22. I I I I 37. I I I 0.88 I I I 10. 19. I I 17. 5. I I I I I I I 0.84 I I -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- 1600.0 1680.0 1760.0 1840.0 1920.0 2000.0 2080.0 2160.0 2240.0 2320.0 2400.0 Slope v. GenoMean using factor GenoNum Points coinciding with 7. 26. Points coinciding with 16 43. Points coinciding with 6. 50. Points coinciding with .39 55. Points coinciding with 9. 63. Points coinciding with 57. 200. Points coinciding with 39. 300. -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- I 23. I I I I I 92.0 I I I I I I I I I I I 28. I 88.0 I I I I I I I I I I I 33. I 84.0 I 30. I I I I I I I I 25. 54. I I I 80.0 I I I 24. I I I I 6. 42. I I 31. 38. I I 35. I 76.0 I 45. I I 26. 13. I I 46. I I 7. 50. I I 1. 53. 52. I I 51. I 72.0 I 4. I I 20.27. 60.48. 200. I I 37. 62. 14. 57. I I 29. 16. 15. 44. 8. 59. 49. I I 10. 43. 9. 55. I I 17. 21. 36. 39. 3456.32. I 68.0 I 5. 11. 40. I I 64. 58. I I 18. 41. I I 61.12. I I I I I 64.0 I I I 19. I I I I I I I I I 60.0 I I -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- 1600.0 1680.0 1760.0 1840.0 1920.0 2000.0 2080.0 2160.0 2240.0 2320.0 2400.0 GenoCV v. GenoMean using factor GenoNum Points coinciding with 18. 22. Points coinciding with 6. 47. Points coinciding with 9. 63. Points coinciding with 39. 300. -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- I I I I I 13. I 180000.0 I I I I I 5. I I I I 42. I I I 160000.0 I I I I I I I 62. I I I I I 140000.0 I I I I I 16. I I 56. I I 11. I I I 120000.0 I 45. I I I I I I 28. 25. I I I I I 100000.0 I 9. I I 30. 38. I I 60. I I 17. I I 15. I I 22. 20. I 80000.0 I 59. I I 8. 53. I I 23. 35. 12. I I 40. I I 54. 64. 55. 51. I I 33. 4. I 60000.0 I 21. 57. I I 24.37. 29. I I 18. I I 26. 39. 49. I I 6. I I 46. I 40000.0 I 10. 19. 58. 52. I I 43. 50. I I 7. 44.63. 41. 14. I I 1. I I 31. 47. 300. 61. I I 27. 34. 32. I 20000.0 I I -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- 1600.0 1680.0 1760.0 1840.0 1920.0 2000.0 2080.0 2160.0 2240.0 2320.0 2400.0 DeviMS v. GenoMean using factor GenoNum Points coinciding with 27. 36. Points coinciding with 34. 48. Points coinciding with 49. 200. -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- I I I I I I 2000000.0 I I I I I I I I I I I I 1750000.0 I 5. I I I I I I 13. I I I I I 1500000.0 I 42. I I I I I I I I I I I 1250000.0 I I I 11. 62. I I 38. I I I I 17. 45. I I 56. I 1000000.0 I I I 25. I I I I 28. I I 30. 22. I I 9. 60. I 750000.0 I 15. 53. I I 35. 37. I I 10. 1920. 51. 4. I I 29. 8. I I 23. 33. 18. 64. 1240. I I 54. 21. 55. 200. I 500000.0 I 52. 49. I I 24. I I 26. 43. 46. I I 6. 39. I I 50. 58. 14. I I 7. 44.63. 48. I 250000.0 I 31. 1. 41. I I 27. 300. 34. 32. I I I I I I I I I 0.0 I I -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- 1600.0 1680.0 1760.0 1840.0 1920.0 2000.0 2080.0 2160.0 2240.0 2320.0 2400.0 Wricke v. GenoMean using factor GenoNum Points coinciding with 11 16. Points coinciding with 27. 36. Points coinciding with 44. 47. Points coinciding with 0. 57. Points coinciding with 1. 59. Points coinciding with 34. 61. -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- I I I I I I 0.120 I I I I I I I 33. I I I I I 0.105 I 23. I I I I I I I I I I I 0.090 I 56. I I I I I I 25. I I I I I 0.075 I I I I I 30. 9. I I 17. 15. I I 62. 42. I I 20. I 0.060 I 16. 22. I I I I 19. 13. I I 54. 18. 60. I I 28. 24. I I I 0.045 I I I I I 38. I I 11. 12. I I 57. I I I 0.030 I 35. 6. 21. 45. I I 64. 51. I I 5. 858. I I 55. 52.40. I I 31. 39. I I 37. 41.53. 49. I 0.015 I 10. 1. 27. I I 46. 63. I I 26. 44. 14. 4. I I 7. 34. 32. I I 36. 300. I I I 0.000 I I -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- 1600.0 1680.0 1760.0 1840.0 1920.0 2000.0 2080.0 2160.0 2240.0 2320.0 2400.0 YauH v. GenoMean using factor GenoNum Points coinciding with 5. 29. Points coinciding with 31. 43. Points coinciding with 27. 47. Points coinciding with 34. 48. 61. Points coinciding with 44. 50. Points coinciding with 52. 59. Points coinciding with 49. 200. 6.2 Stability indices under heterogeneous error-variances GenoNum GenoMean SlopeW SeSlopW Probb1W DeviSSW ProbDevW RSqW% 1 2122 0.965 0.04189 0.4252 10.05 0.2617 98.33 4 2318 1.060 0.03783 0.1535 8.19 0.4149 98.86 5 2028 0.961 0.06960 0.5861 27.73 0.0005 95.47 6 1957 0.971 0.05581 0.6188 17.83 0.0225 97.10 7 1997 0.965 0.04117 0.4248 9.70 0.2864 98.39 8 2230 1.038 0.05700 0.5185 18.60 0.0171 97.35 9 2209 0.970 0.07763 0.7111 34.51 0.0000 94.52 10 1932 0.909 0.05627 0.1445 18.13 0.0203 96.65 11 2091 0.943 0.08542 0.5240 41.77 0.0000 93.07 12 2312 1.019 0.07580 0.8094 32.90 0.0001 95.23 13 2259 0.978 0.10581 0.8434 64.10 0.0000 90.37 14 2287 1.066 0.03752 0.1182 8.06 0.4278 98.90 15 2105 0.896 0.09452 0.3053 51.15 0.0000 90.81 16 2074 0.898 0.11254 0.3926 72.51 0.0000 87.45 17 1967 0.839 0.10438 0.1610 62.38 0.0000 87.60 18 2111 0.913 0.09229 0.3722 48.77 0.0000 91.49 19 2125 0.869 0.06507 0.0790 24.24 0.0021 95.17 20 2144 0.909 0.09656 0.3744 53.38 0.0000 90.69 21 2103 0.970 0.07533 0.7016 32.49 0.0001 94.82 22 2108 0.902 0.09565 0.3346 52.38 0.0000 90.71 23 1667 0.940 0.07310 0.4362 30.59 0.0002 94.81 24 1921 1.011 0.04533 0.8136 11.77 0.1619 98.22 25 1792 0.932 0.07853 0.4109 35.31 0.0000 93.95 26 1980 0.948 0.04901 0.3155 13.75 0.0884 97.64 27 2171 1.004 0.05291 0.9383 16.03 0.0420 97.56 28 1732 0.902 0.07063 0.2046 28.56 0.0004 94.75 29 2022 0.927 0.05971 0.2582 20.41 0.0089 96.39 30 1945 1.014 0.06995 0.8483 28.01 0.0005 95.87 31 2057 1.040 0.02791 0.1874 4.46 0.8133 99.36 32 2328 1.057 0.03888 0.1830 8.66 0.3721 98.79 33 1931 1.060 0.05480 0.3036 17.19 0.0281 97.65 34 2292 1.073 0.03754 0.0868 8.07 0.4268 98.91 35 1861 0.929 0.05319 0.2214 16.20 0.0396 97.13 36 2168 0.989 0.02278 0.6375 2.97 0.9362 99.52 37 1947 0.924 0.06307 0.2599 22.77 0.0037 95.95 38 2275 1.109 0.07965 0.2094 36.32 0.0000 95.54 39 2245 1.067 0.05970 0.2954 20.40 0.0089 97.25 40 2330 1.066 0.05766 0.2888 19.04 0.0147 97.42 41 2241 1.047 0.06392 0.4867 23.39 0.0029 96.74 42 2193 1.082 0.08512 0.3660 41.49 0.0000 94.69 43 2054 0.955 0.06510 0.5132 24.26 0.0021 95.97 44 2170 1.025 0.04571 0.6024 11.96 0.1529 98.24 45 2207 0.996 0.06904 0.9509 27.29 0.0006 95.83 46 2152 1.069 0.03507 0.0835 7.04 0.5323 99.04 47 2161 1.048 0.05564 0.4179 17.72 0.0234 97.52 48 2285 1.098 0.02898 0.0095 4.81 0.7778 99.38 49 2332 1.105 0.04435 0.0458 11.26 0.1872 98.57 50 2159 1.015 0.04314 0.7324 10.66 0.2219 98.40 51 2287 1.086 0.05572 0.1607 17.77 0.0230 97.68 52 2301 1.115 0.04765 0.0417 13.00 0.1119 98.38 53 2264 1.060 0.04464 0.2128 11.41 0.1796 98.43 54 1856 0.949 0.05169 0.3523 15.30 0.0536 97.39 55 2237 1.007 0.05497 0.9076 17.30 0.0271 97.38 56 2302 0.971 0.08370 0.7345 40.11 0.0000 93.68 57 2338 1.118 0.09038 0.2279 46.77 0.0000 94.41 58 2244 0.969 0.04776 0.5292 13.06 0.1098 97.85 59 2299 1.057 0.06048 0.3775 20.94 0.0073 97.13 60 2263 1.067 0.10616 0.5443 64.52 0.0000 91.75 61 2284 1.039 0.03292 0.2655 6.21 0.6243 99.10 62 2158 0.959 0.08667 0.6474 43.00 0.0000 93.10 63 2190 1.017 0.03304 0.6189 6.25 0.6193 99.06 64 2188 0.946 0.06827 0.4498 26.68 0.0008 95.50 200 2337 1.113 0.05753 0.0856 18.95 0.0151 97.64 300 2250 1.055 0.03629 0.1675 7.54 0.4797 98.95 -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- I I I I I I 1.12 I 57. I I 52. 200. I I 38. 49. I I 48. I I I I 51. I 1.08 I 42. I I 34. I I 46. 3960.14. 40. I I 33. 53. 432. I I 300. 59. I I 47. 41. I 1.04 I 31. 8. 61. I I I I 44. I I 63. 12. I I 24.30. 50. I I 27. 55. I 1.00 I I I 45. I I 36. I I 13. I I 6. 21. 9. 56. I I 7. 1. 58. I 0.96 I 5. 62. I I 43. I I 54. 26. 64. I I 23. 11. I I 25. I I 35. 37. 29. I 0.92 I I I 18. I I 10. 20. I I 28. 16. 22. I I 15. I I I 0.88 I I I I I 19. I I I I I I I 0.84 I 17. I I I I I I I I I I I 0.80 I I -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- 1600.0 1680.0 1760.0 1840.0 1920.0 2000.0 2080.0 2160.0 2240.0 2320.0 2400.0 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 2122 73.28 205526 178568 26959 21.36 19.91 7.736 4 2318 72.23 94458 80846 13612 13.26 12.27 5.034 5 2028 67.97 395156 239618 155538 31.00 24.14 19.450 6 1957 78.19 333596 290755 42841 29.51 27.55 10.574 7 1997 74.22 307012 261389 45623 27.75 25.60 10.696 8 2230 69.70 171862 119920 51942 18.59 15.53 10.219 9 2209 69.24 192572 130760 61812 19.87 16.37 11.257 10 1932 69.51 389627 310213 79414 32.30 28.82 14.584 11 2091 67.73 304717 198009 106707 26.40 21.28 15.625 12 2312 65.87 126071 83113 42958 15.36 12.47 8.964 13 2259 75.60 176764 106354 70409 18.61 14.44 11.748 14 2287 70.61 128370 93742 34628 15.67 13.39 8.137 15 2105 69.79 270091 189163 80929 24.69 20.66 13.515 16 2074 69.80 306791 208828 97963 26.71 22.04 15.093 17 1967 68.64 392636 283148 109488 31.85 27.05 16.818 18 2111 66.87 254692 185581 69111 23.91 20.41 12.455 19 2125 63.11 248377 176790 71588 23.45 19.78 12.589 20 2144 71.47 232084 165940 66144 22.47 19.00 11.996 21 2103 68.99 249765 190255 59511 23.76 20.74 11.599 22 2108 66.93 268626 187075 81551 24.58 20.52 13.545 23 1667 93.96 586792 554444 32348 45.95 44.67 10.790 24 1921 79.56 358521 319485 39036 31.18 29.43 10.287 25 1792 81.45 502615 430489 72126 39.56 36.61 14.986 26 1980 75.26 330094 273523 56571 29.01 26.41 12.010 27 2171 71.09 177054 150413 26642 19.38 17.86 7.517 28 1732 88.90 531521 487602 43920 42.08 40.31 12.097 29 2022 69.96 316403 243675 72728 27.82 24.42 13.338 30 1945 83.89 348348 300493 47855 30.35 28.19 11.249 31 2057 77.28 244653 219759 24893 24.05 22.79 7.670 32 2328 68.84 92073 76915 15158 13.04 11.91 5.289 33 1931 84.75 336188 310844 25344 30.02 28.87 8.242 34 2292 68.88 106815 91666 15149 14.26 13.21 5.371 35 1861 76.76 426733 368833 57899 35.10 32.63 12.929 36 2168 68.93 182000 152218 29782 19.68 17.99 7.959 37 1947 70.82 368043 298500 69543 31.15 28.06 13.542 38 2275 77.02 146366 98807 47559 16.81 13.81 9.584 39 2245 68.94 144439 112654 31785 16.93 14.95 7.940 40 2330 68.16 125592 76118 49474 15.21 11.84 9.547 41 2241 66.97 146481 114516 31965 17.08 15.10 7.977 42 2193 77.87 202174 138650 63524 20.50 16.98 11.491 43 2054 69.30 263984 221467 42517 25.01 22.91 10.037 44 2170 70.21 182181 151050 31131 19.67 17.91 8.130 45 2207 75.79 164361 131660 32701 18.37 16.44 8.194 46 2152 74.81 202113 161310 40803 20.89 18.66 9.387 47 2161 74.82 182291 156145 26146 19.76 18.28 7.482 48 2285 71.49 112113 94632 17481 14.65 13.46 5.786 49 2332 70.28 81169 75169 6000 12.22 11.76 3.321 50 2159 74.33 181636 157052 24584 19.74 18.35 7.261 51 2287 72.43 124892 93897 30994 15.46 13.40 7.699 52 2301 73.10 110091 87900 22191 14.42 12.89 6.475 53 2264 73.36 126870 103917 22953 15.73 14.24 6.692 54 1856 81.33 405252 373568 31684 34.31 32.94 9.593 55 2237 69.58 150106 116516 33590 17.32 15.26 8.192 56 2302 68.88 142745 87291 55454 16.41 12.83 10.229 57 2338 70.93 97288 72948 24340 13.34 11.55 6.673 58 2244 67.43 137940 113341 24599 16.55 15.00 6.990 59 2299 69.85 103278 88655 14624 13.98 12.95 5.260 60 2263 71.04 133975 104421 29555 16.17 14.28 7.597 61 2284 66.21 131900 94859 37041 15.90 13.48 8.425 62 2158 70.63 271719 157971 113748 24.16 18.42 15.630 63 2190 69.13 182928 140231 42697 19.53 17.10 9.434 64 2188 67.34 187622 141513 46109 19.80 17.19 9.814 200 2337 71.01 96628 73434 23194 13.30 11.60 6.517 300 2250 68.34 143396 110242 33155 16.83 14.75 8.091 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 2122 73.28 268095 235949 32147 24.40 22.89 8.45 4 2318 72.23 464080 389357 74723 29.39 26.92 11.79 5 2028 67.97 264703 175402 89302 25.37 20.65 14.74 6 1957 78.19 163121 136235 26886 20.63 18.86 8.38 7 1997 74.22 193989 157654 36336 22.06 19.88 9.55 8 2230 69.70 403912 315871 88041 28.50 25.20 13.30 9 2209 69.24 374059 298892 75166 27.69 24.75 12.41 10 1932 69.51 168968 123447 45521 21.27 18.18 11.04 11 2091 67.73 316782 214680 102102 26.92 22.16 15.28 12 2312 65.87 442966 384431 58534 28.78 26.81 10.46 13 2259 75.60 445623 338955 106668 29.55 25.78 14.46 14 2287 70.61 422439 362579 59860 28.42 26.33 10.70 15 2105 69.79 269451 224098 45353 24.66 22.49 10.12 16 2074 69.80 263492 203709 59784 24.75 21.77 11.79 17 1967 68.64 190723 141528 49195 22.20 19.12 11.27 18 2111 66.87 262359 228032 34327 24.27 22.62 8.78 19 2125 63.11 280027 238002 42026 24.90 22.95 9.65 20 2144 71.47 285690 250962 34729 24.93 23.37 8.69 21 2103 68.99 267371 222913 44458 24.59 22.45 10.03 22 2108 66.93 277343 226382 50962 24.98 22.57 10.71 23 1667 93.96 64944 26800 38144 15.29 9.82 11.72 24 1921 79.56 134090 117710 16381 19.07 17.86 6.66 25 1792 81.45 103487 63606 39881 17.95 14.07 11.14 26 1980 75.26 175135 148474 26660 21.13 19.46 8.25 27 2171 71.09 316630 270907 45723 25.91 23.97 9.85 28 1732 88.90 89931 44114 45817 17.31 12.12 12.36 29 2022 69.96 208846 171962 36883 22.60 20.51 9.50 30 1945 83.89 182249 129705 52544 21.95 18.52 11.79 31 2057 77.28 243985 193189 50796 24.01 21.37 10.96 32 2328 68.84 463960 398138 65822 29.26 27.11 11.02 33 1931 84.75 183227 123050 60178 22.16 18.16 12.70 34 2292 68.88 428494 366696 61798 28.56 26.42 10.85 35 1861 76.76 127910 90602 37308 19.22 16.17 10.38 36 2168 68.93 308040 268497 39543 25.60 23.90 9.17 37 1947 70.82 180810 131020 49790 21.84 18.59 11.46 38 2275 77.02 450857 352814 98043 29.51 26.10 13.76 39 2245 68.94 405776 327960 77816 28.37 25.51 12.42 40 2330 68.16 484577 399958 84619 29.88 27.15 12.49 41 2241 66.97 371189 324805 46384 27.18 25.43 9.61 42 2193 77.87 373334 287254 86080 27.86 24.44 13.38 43 2054 69.30 234051 191595 42457 23.55 21.31 10.03 44 2170 70.21 325330 270053 55277 26.28 23.94 10.83 45 2207 75.79 384703 297535 87168 28.11 24.72 13.38 46 2152 74.81 320236 256729 63507 26.30 23.55 11.71 47 2161 74.82 299395 263339 36056 25.32 23.75 8.79 48 2285 71.49 434900 360835 74065 28.86 26.29 11.91 49 2332 70.28 483237 402145 81093 29.81 27.19 12.21 50 2159 74.33 296981 262165 34816 25.24 23.71 8.64 51 2287 72.43 434734 362273 72460 28.84 26.32 11.77 52 2301 73.10 419927 374347 45580 28.17 26.59 9.28 53 2264 73.36 406947 343345 63602 28.18 25.88 11.14 54 1856 81.33 128736 88278 40458 19.34 16.01 10.84 55 2237 69.58 397701 321459 76242 28.19 25.34 12.34 56 2302 68.88 457335 375606 81729 29.38 26.62 12.42 57 2338 70.93 488048 407338 80710 29.88 27.30 12.15 58 2244 67.43 367733 326791 40942 27.03 25.48 9.02 59 2299 69.85 443597 372795 70802 28.97 26.56 11.57 60 2263 71.04 428983 342431 86552 28.94 25.86 13.00 61 2284 66.21 408679 360392 48288 27.98 26.28 9.62 62 2158 70.63 346788 260981 85807 27.29 23.67 13.57 63 2190 69.13 336757 284989 51768 26.49 24.37 10.39 64 2188 67.34 351308 283169 68139 27.09 24.32 11.93 200 2337 71.01 506019 406190 99829 30.44 27.27 13.52 300 2250 68.34 375374 332112 43262 27.23 25.61 9.24 6.4 Correlations between various indices GenoMean 1.0000 Slope 0.5087 1.0000 DeviMS -0.1335 -0.0592 1.0000 GenoCV -0.6458 0.3193 0.1801 1.0000 Wricke -0.1367 -0.1201 0.9629 0.1174 1.0000 Pla_Pet -0.1367 -0.1201 0.9629 0.1174 1.0000 1.0000 Plaisted 0.1367 0.1201 -0.9629 -0.1174 -1.0000 -1.0000 1.0000 Shukla -0.1367 -0.1201 0.9629 0.1174 1.0000 1.0000 -1.0000 1.0000 YauH -0.4325 -0.1213 0.5828 0.4343 0.5357 0.5357 -0.5357 0.5357 1.0000 SlopeW 0.6461 0.8308 -0.2561 0.0077 -0.2763 -0.2763 0.2763 -0.2763 -0.3826 1.0000 DeviSSW -0.0939 -0.2457 0.6948 -0.0504 0.6928 0.6928 -0.6928 0.6928 0.6438 -0.4253 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 0.1498 1.0000 RDeviMS -0.1568 -0.1578 1.0000 RGenoCV -0.2065 0.2038 0.0367 1.0000 RWricke -0.1106 -0.1481 0.4929 0.0016 1.0000 RPla_Pet -0.1106 -0.1481 0.4929 0.0016 1.0000 1.0000 RPlaist 0.0635 0.3919 -0.3794 -0.0051 -0.4143 -0.4143 1.0000 RShukla -0.1106 -0.1481 0.4929 0.0016 1.0000 1.0000 -0.4143 1.0000 RYauH -0.1738 -0.0756 0.2999 0.0205 0.2801 0.2801 -0.2716 0.2801 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 ---------------- 32 46 99.3 59 64 99.3 37 63 99.1 17 20 99.0 4 24 99.0 6 37 98.7 13 16 98.6 39 61 98.6 12 59 98.6 7 53 98.6 2 47 98.5 5 27 98.5 42 62 98.4 14 15 98.3 12 39 98.3 55 58 98.1 25 30 98.1 2 57 98.0 1 34 97.9 12 32 97.8 13 17 97.8 6 12 97.7 5 8 97.7 28 31 97.7 6 44 97.4 48 56 97.4 2 43 97.3 45 50 97.2 10 54 97.2 5 41 97.1 1 29 97.1 48 49 97.1 19 42 97.1 7 10 96.9 21 26 96.9 6 25 96.7 13 14 96.7 4 22 96.6 7 55 96.4 33 52 96.3 13 18 96.3 23 28 96.1 45 51 96.1 5 35 96.1 1 6 95.7 45 48 95.5 21 33 95.2 4 23 94.9 7 36 94.8 2 45 94.8 1 38 94.8 13 19 94.7 3 60 94.5 2 11 93.5 3 9 93.0 1 7 92.8 3 5 92.1 4 21 91.8 2 13 90.4 1 2 89.3 1 3 88.1 1 40 84.3 1 4 83.2 Hierarchical clusters --------------------- Level 95.0 1 34 29 6 37 63 12 59 64 39 61 32 46 44 25 30 7 53 10 54 55 58 2 47 57 43 45 50 51 48 56 49 13 16 17 20 14 15 18 19 42 62 5 27 8 41 35 4 24 22 23 28 31 21 26 33 52 Ungrouped 38 36 11 3 60 9 40 Level 90.0 1 34 29 6 37 63 12 59 64 39 61 32 46 44 25 30 38 7 53 10 54 55 58 36 2 47 57 43 45 50 51 48 56 49 11 13 16 17 20 14 15 18 19 42 62 3 60 9 5 27 8 41 35 4 24 22 23 28 31 21 26 33 52 Ungrouped 40 Level 85.0 1 34 29 6 37 63 12 59 64 39 61 32 46 44 25 30 38 7 53 10 54 55 58 36 2 47 57 43 45 50 51 48 56 49 11 13 16 17 20 14 15 18 19 42 62 3 60 9 5 27 8 41 35 4 24 22 23 28 31 21 26 33 52 Ungrouped 40 Level 80.0 1 34 29 6 37 63 12 59 64 39 61 32 46 44 25 30 38 7 53 10 54 55 58 36 2 47 57 43 45 50 51 48 56 49 11 13 16 17 20 14 15 18 19 42 62 3 60 9 5 27 8 41 35 40 4 24 22 23 28 31 21 26 33 52 Dendrogram ---------- ** Levels 100.0 90.0 80.0 1.00 1 .. 36.00 34 ..) 31.00 29 ..) 8.00 6 ..) 39.00 37 ..) 200.00 63 ..) 14.00 12 ..) 61.00 59 ..) 300.00 64 ..) 41.00 39 ..) 63.00 61 ..) 34.00 32 ..) 48.00 46 ..) 46.00 44 ..) 27.00 25 ..) 32.00 30 ..).. 40.00 38 .....) 9.00 7 .. ) 55.00 53 ..) ) 12.00 10 ..) ) 56.00 54 ..) ) 57.00 55 ..) ) 60.00 58 ..)..) 38.00 36 .....).. 4.00 2 .. ) 49.00 47 ..) ) 59.00 57 ..) ) 45.00 43 ..).. ) 47.00 45 .. ) ) 52.00 50 ..) ) ) 53.00 51 ..) ) ) 50.00 48 ..) ) ) 58.00 56 ..) ) ) 51.00 49 ..)..) ) 13.00 11 .....) ) 15.00 13 .. ) ) 18.00 16 ..) ) ) 19.00 17 ..) ) ) 22.00 20 ..) ) ) 16.00 14 ..) ) ) 17.00 15 ..) ) ) 20.00 18 ..)..) ) 21.00 19 .. ) ) 44.00 42 ..) ) ) 64.00 62 ..)..)..) 5.00 3 ..... ) 62.00 60 .....) ) 11.00 9 .....) ) 7.00 5 .. ) ) 29.00 27 ..) ) ) 10.00 8 ..) ) ) 43.00 41 ..) ) ) 37.00 35 ..)..)..).. 42.00 40 ...........) 6.00 4 .. ) 26.00 24 ..) ) 24.00 22 ..).. ) 25.00 23 .. ) ) 30.00 28 ..) ) ) 33.00 31 ..)..) ) 23.00 21 .. ) ) 28.00 26 ..) ) ) 35.00 33 ..) ) ) 54.00 52 ..)..).....)........... ===================================================================================================== ................................................................................... 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 9 99.3 3 6 99.1 2 10 99.0 2 8 98.5 1 3 97.8 5 7 97.3 1 2 93.7 4 5 92.1 1 4 61.8 Hierarchical clusters --------------------- Level 95.0 1 9 3 6 2 10 8 5 7 Ungrouped 4 Level 90.0 1 9 3 6 2 10 8 4 5 7 Level 85.0 1 9 3 6 2 10 8 4 5 7 Level 80.0 1 9 3 6 2 10 8 4 5 7 Level 75.0 1 9 3 6 2 10 8 4 5 7 Level 70.0 1 9 3 6 2 10 8 4 5 7 Level 65.0 1 9 3 6 2 10 8 4 5 7 Level 60.0 1 9 3 6 2 10 8 4 5 7 Dendrogram ---------- ** Levels 100.0 90.0 80.0 70.0 60.0 1.00 1 .. 20.00 9 ..) 4.00 3 ..) 7.00 6 ..).. 3.00 2 .. ) 100.00 10 ..) ) 9.00 8 ..)..)................. 5.00 4 ..... ) 6.00 5 .. ) ) 8.00 7 ..)..).................)........... ===================================================================================================== .................................................................................... Variable is BYield .................................................................................... Section 1. Analysis of data from individual environments EnvtNum EnvtMean CV% Eff% SEM SED LSD5% LSD1% RCBSEM ErrMS ErrDF P_value 1 532 31.78 100.1 102.0 139.5 276 365 102.1 28579 124.0 0.0000 3 2946 25.58 100.0 457.7 615.4 1218 1610 457.7 568150 125.0 0.0000 4 1595 22.81 103.8 221.8 306.5 607 802 225.7 132378 125.0 0.0000 5 4994 26.17 100.0 776.6 1067.3 2112 2792 776.6 1708845 125.0 0.8411 6 6359 21.86 102.9 851.0 1167.4 2310 3054 862.5 1931850 125.0 0.0116 7 1799 25.50 108.4 281.0 390.2 772 1021 292.0 210314 125.0 0.0000 8 7233 21.95 100.3 931.0 1308.9 2590 3424 932.2 2520116 125.0 0.6613 9 2454 33.91 107.3 652.2 706.6 1398 1848 665.8 692227 125.0 0.0143 20 1089 25.12 100.9 161.7 227.2 450 594 162.4 74843 125.0 0.0000 100 2944 26.03 116.9 471.7 656.8 1300 1718 502.1 587300 125.0 0.4761 Histogram of CV% ---------------- - 25 3 *** 25 - 30 5 ***** 30 - 2 ** Scale: 1 asterisk represents 1 unit. Histogram of Eff% ----------------- - 104 7 ******* 104 - 112 2 ** 112 - 1 * Scale: 1 asterisk represents 1 unit. Histogram of ErrMS ------------------ - 1000000 7 ******* 1000000 - 2000000 2 ** 2000000 - 1 * Scale: 1 asterisk represents 1 unit. Histogram of EnvtMean --------------------- - 2500 5 ***** 2500 - 5000 3 *** 5000 - 2 ** Scale: 1 asterisk represents 1 unit. -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- I I I I I 9. I 33.6 I I I I I I I I I I I I 32.0 I I I 1. I I I I I I I I I 30.4 I I I I I I I I I I I I 28.8 I I I I I I I I I I I I 27.2 I I I I I I I I I 100. 5. I I I 25.6 I 7. 3. I I I I 20. I I I I I I I 24.0 I I I I I I I I I 4. I I I 22.4 I I I I I 6. 8. I I I I I I I 20.8 I I -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- 0.0 800.0 1600.0 2400.0 3200.0 4000.0 4800.0 5600.0 6400.0 7200.0 8000.0 CV% v. EnvtMean using factor EnvtNum -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- I I I I I I 117.5 I I I 100. I I I I I I I I I 115.0 I I I I I I I I I I I I 112.5 I I I I I I I I I I I I 110.0 I I I I I I I I I 7. I I I 107.5 I 9. I I I I I I I I I I I 105.0 I I I I I I I 4. I I I I 6. I 102.5 I I I I I I I I I 20. I I 8. I 100.0 I 3. 5. 1. I I I I I I I I I I I 97.5 I I -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- 21.0 22.5 24.0 25.5 27.0 28.5 30.0 31.5 33.0 34.5 36.0 Eff% v. CV% using factor EnvtNum -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- I I I 8. I I I 2400000.0 I I I I I I I I I I I I 2100000.0 I I I I I I I 6. I I I I I 1800000.0 I I I I I 5. I I I I I I I 1500000.0 I I I I I I I I I I I I 1200000.0 I I I I I I I I I I I I 900000.0 I I I I I I I I I 9. I I I 600000.0 I 100. I I 3. I I I I I I I I I 300000.0 I I I I I 7. I I 4. I I I I 1. 20. I 0.0 I I -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- 0.0 800.0 1600.0 2400.0 3200.0 4000.0 4800.0 5600.0 6400.0 7200.0 8000.0 ErrMS v. EnvtMean using factor EnvtNum ................................................................................... Section 2.0 Bartlette Test for homogeneity of error variances Pooled Error Mean-square.........................................................................= 846114 DF for Pooled Error Mean-square...............................................................= 1249 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 REML analysis- Wald tests under homogeneous error-variances For significance of genotype and G x E interaction, see the results corresponding to the rows of Geno and Envt.Geno respectively. ******** Warning 4, code VD 39, statement 103 in for loop Command: VDisp[Prin=Wald; Ch=ChReport; PTerms=Geno+Geno.Envt] 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 1382.10 9 153.57 <0.001 Geno 142.94 63 2.27 <0.001 Envt.Geno 668.11 567 1.18 0.002 Dropping individual terms from full fixed model Fixed term Wald statistic d.f. Wald/d.f. chi pr Envt.Geno 668.11 567 1.18 0.002 * MESSAGE: chi-square distribution for Wald tests is an asymptotic approximation (i.e. for large samples) and underestimates the probabilities in other cases. ******************************* Genotype x Environment table means ********************* Genotype 1 3 4 5 6 7 8 9 20 100 Geno.Mean 1 585.7 3050 1537 5112 6383 1307 8393 2601 1267 2168 3240 4 539.8 2997 1446 5904 5052 1838 7463 2593 1119 3507 3246 5 490.2 2958 1866 3573 4773 1680 7927 1623 1317 2695 2890 6 333.9 2339 935 5080 5505 1738 7470 2713 1215 2731 3006 7 575.7 3385 1769 4139 5560 1477 7028 2215 1075 2757 2998 8 609.4 3348 2167 4851 7219 1834 6163 1354 1148 2959 3165 9 1058.4 3927 2716 3572 6226 1569 7413 1879 1076 2090 3153 10 434.5 2683 1994 3991 5832 1423 7007 1968 980 2838 2915 11 530.4 4173 997 3549 5066 1494 5808 2351 1320 4017 2931 12 756.2 3328 2336 6130 6487 1686 7492 2262 1479 2606 3456 13 625.8 1893 1191 6039 7719 1733 8090 2902 1331 3490 3501 14 659.0 3197 1905 4873 6986 1768 6203 2471 1141 3036 3224 15 624.9 2337 1165 4944 6328 2338 7881 2418 1114 3528 3268 16 579.7 2111 835 4893 7370 2171 8665 2204 1178 3402 3341 17 668.3 2069 992 5480 5215 2646 7415 1963 1363 3406 3122 18 802.7 2138 1139 5074 5616 2939 8145 2313 1297 3435 3290 19 786.4 2890 1232 4252 6653 2476 5939 3091 1200 3402 3192 20 804.9 2196 762 6123 6346 2256 6703 2557 1437 2940 3212 21 740.4 3075 1274 4986 4807 2480 6980 1524 852 2632 2935 22 685.6 2572 1138 4609 7493 2268 7788 3425 1010 4102 3509 23 73.2 1681 809 5245 5405 977 6108 1515 70 2708 2459 24 177.5 2938 1740 4878 5017 1494 6982 2610 655 2509 2900 25 173.4 1659 792 5026 4931 1698 6650 2357 435 3114 2684 26 445.9 2878 1152 3753 5494 1545 8492 2498 1052 3136 3045 27 673.6 2404 1862 5147 6424 1302 7112 2553 1249 3071 3180 28 245.6 2273 1587 5453 5761 1367 7219 2308 468 1866 2855 29 494.9 3173 2336 5435 5541 1589 6601 1788 1234 2283 3047 30 116.5 1187 1515 4511 5767 1377 8355 2883 835 3006 2955 31 238.0 2555 1280 3705 6431 1865 6334 2012 1116 2808 2834 32 566.4 2562 1887 4818 6143 2072 6961 3368 1538 3317 3323 33 70.6 2071 984 5309 6987 1775 7645 3199 303 3013 3136 34 517.3 3533 1618 5230 8755 2460 6944 2438 1223 3161 3588 35 246.5 2297 1373 5880 6125 1141 5720 1336 951 2618 2769 36 632.4 3495 1741 4951 7268 1617 7208 3327 1122 3517 3488 37 406.9 3645 1359 4668 5432 1335 6607 2559 1143 2478 2963 38 428.6 3614 2278 4907 6520 1988 7834 2016 1281 2013 3288 39 379.0 3726 1830 5538 6879 1575 8194 2155 941 3089 3431 40 606.3 3568 1913 5703 6636 2082 7997 2019 1164 2985 3467 41 449.8 3356 2140 4806 4508 2126 6592 3023 1302 3239 3154 42 316.9 2414 2048 4462 6595 1580 6445 3660 1035 3500 3206 43 525.5 2460 2163 5286 6912 1830 7176 1647 1054 2145 3120 44 409.3 3010 1294 5555 7030 1998 6640 1795 1009 2768 3151 45 691.6 2322 1508 5843 7703 1327 6921 3618 818 2924 3368 46 497.2 3678 1633 4516 6274 1436 8014 1636 1272 2682 3164 47 622.2 3078 1533 4784 7889 2431 6855 2508 921 2869 3349 48 488.7 3682 2362 4473 6398 1744 7865 2092 1079 3226 3341 49 385.7 3067 1672 6700 6815 1342 6750 3141 1245 3131 3425 50 584.9 2345 1399 4525 5643 1852 7995 3181 894 3117 3154 51 561.0 3020 1118 5219 7550 1892 7038 3229 1027 3148 3380 52 483.6 3336 1588 4971 6388 2589 7753 3701 1021 2874 3470 53 509.8 2794 1338 5239 6406 2043 4924 2951 1240 2670 3011 54 97.1 1973 1286 4694 5543 1177 4351 2198 851 2257 2443 55 666.3 4627 1861 5375 7842 1700 7632 2352 1301 2848 3620 56 938.6 3659 2537 5727 7647 1748 7042 2760 1168 1947 3517 57 489.6 2800 2309 5551 6378 1884 7379 2411 973 3074 3325 58 597.4 2420 1331 4584 4881 1850 7692 3785 1325 3473 3194 59 535.0 3564 2019 5780 8242 1598 7847 3092 1142 3237 3706 60 561.0 4037 1642 4943 6880 1480 7657 1745 764 2487 3220 61 762.5 3840 1620 4361 6961 2256 8992 2241 1283 3241 3556 62 892.6 3796 1340 3757 5155 1573 9050 2016 1478 2688 3175 63 638.0 3038 1797 4666 7103 1704 7081 2157 1198 3389 3277 64 808.6 3260 1287 4944 5884 2354 6690 1680 1479 2947 3133 200 364.8 3734 2301 5804 8664 1259 7525 2478 1026 3169 3633 300 625.7 3319 1484 5734 5562 1968 8064 2577 1108 2946 3339 Envt.Mean 529.5 2946 1595 4994 6359 1799 7233 2454 1089 2944 Grand Mean 3196 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 11834.912 1314.990 Geno1 63 447.398 7.102 Envt1.Geno1 567 861.731 1.520 Total 639 13144.041 3.2.1 Tests of significance for Genotype and GxE interaction Genotype : DF = 63 Weighted Sum of Squares = 447.398 Prob > Chisq = 0.00000 G x E Interaction : DF = 567 Weighted Sum of Squares = 861.731 Prob > Chisq = 0.00000 ................................................................................... Section 4: Heritabilities 4.1 Environment-wise heritability estimates (h2_...), biases, genetic gains (GG...) and variance components EnvtNum EnvtMean h2_plot Bias_h2_plot Se_h2_plot h2C h2_Ad_hoc h2_mean Se_h2_mean GG5% GG10% GG20% Sig2G Se_Sig2G Sig2E Se_Sig2E 1 529 0.5300 0.015 0.07089 0.7706 0.7711 0.7718 0.05011 61.97 52.73 42.06 32787 7703 29076 3682 3 2946 0.3391 0.023 0.08068 0.6062 0.6062 0.6062 0.08594 29.43 25.04 19.97 291484 88939 568150 71580 4 1595 0.5598 0.014 0.07044 0.7830 0.7835 0.7923 0.04704 47.47 40.39 32.22 170014 39200 133699 18306 5 4994 0.0000 0.000 0.00000 0.0000 0.0000 0.0000 0.00000 0.00 0.00 0.00 0 0 1607984 165412 6 6359 0.1245 0.056 0.08237 0.2918 0.2939 0.2990 0.15841 9.44 8.04 6.41 283563 194362 1994337 268710 7 1799 0.2972 0.029 0.08615 0.5404 0.5405 0.5592 0.10167 25.66 21.83 17.41 89536 31233 211738 28788 8 7233 0.0000 0.000 0.00000 0.0000 0.0000 0.0000 0.00000 0.00 0.00 0.00 1 0 2433316 265497 9 2454 0.1220 0.062 0.08586 0.2791 0.2793 0.2943 0.16643 14.19 12.07 9.63 96768 70678 696185 93865 20 1089 0.3861 0.021 0.08098 0.6503 0.6515 0.6536 0.07736 33.64 28.62 22.83 48272 13641 76757 10430 100 2944 0.0004 14.185 0.07917 0.0012 0.0012 0.0013 0.23708 0.04 0.03 0.03 259 46459 586588 79049 4.2 Correlations between mean, heritability, genotypic variance and error-variance EnvtMean 1.0000 h2_plot -0.7517 1.0000 h2C -0.7478 0.9825 1.0000 h2_Ad_hoc -0.7472 0.9824 1.0000 1.0000 h2_mean -0.7495 0.9806 0.9998 0.9998 1.0000 GG5% -0.7687 0.9752 0.9487 0.9486 0.9459 1.0000 GG10% -0.7687 0.9752 0.9487 0.9486 0.9459 1.0000 1.0000 GG20% -0.7687 0.9752 0.9487 0.9486 0.9459 1.0000 1.0000 1.0000 Sig2G 0.0734 0.2981 0.3973 0.3980 0.3992 0.1945 0.1945 0.1945 1.0000 Sig2E 0.9889 -0.7466 -0.7479 -0.7473 -0.7497 -0.7396 -0.7396 -0.7396 0.0007 1.0000 EnvtMean h2_plot h2C h2_Ad_hoc 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 + [incomplete]Block eff. within Rep 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% 0.03429 0.004759 0.01267 0.4880 0.09802 8.100 6.891 5.497 4.4 Variance components from GxE data analysis Sig2G Se_Sig2G Sig2GE Se_Sig2GE Sig2E Se_Sig2E 32271 12172 53352 23869 855519 36106 4.5 Variance components from GxE data analysis under three more models Model 1: Fixed effects=Envt + Geno + Geno.Envt & Random = Rep.Envt/Blk REML variance components analysis ================================= Response variate: BYield Fixed model: Constant + Envt + Geno + Envt.Geno Random model: Envt.Rep + Envt.Rep.Blk Number of units: 1919 (1 units excluded due to zero weights or missing values) Residual term has been added to model Sparse algorithm with AI optimisation Estimated variance components ----------------------------- Random term component s.e. Envt.Rep 80225. 31866. Envt.Rep.Blk 54803. 22112. Residual variance model ----------------------- Term Model(order) Parameter Estimate s.e. Residual Identity Sigma2 853836. 37280. Deviance: -2*Log-Likelihood --------------------------- Deviance d.f. 19551.78 1276 Note: deviance omits constants which depend on fixed model fitted. ******** Warning 5, code VD 39, statement 239 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 1382.10 9 153.57 <0.001 Geno 142.94 63 2.27 <0.001 Envt.Geno 668.11 567 1.18 0.002 Dropping individual terms from full fixed model Fixed term Wald statistic d.f. Wald/d.f. chi pr Envt.Geno 668.11 567 1.18 0.002 * 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/Blk REML variance components analysis ================================= Response variate: BYield Fixed model: Constant + Envt + Geno Random model: Geno.Envt + Envt.Rep + Envt.Rep.Blk Number of units: 1919 (1 units excluded due to zero weights or missing values) Residual term has been added to model Sparse algorithm with AI optimisation Estimated variance components ----------------------------- Random term component s.e. Geno.Envt 53361. 23874. Envt.Rep 80716. 31821. Envt.Rep.Blk 50597. 16788. Residual variance model ----------------------- Term Model(order) Parameter Estimate s.e. Residual Identity Sigma2 855863. 36168. Deviance: -2*Log-Likelihood --------------------------- Deviance d.f. 27538.00 1842 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 1348.58 9 149.84 21.0 <0.001 Geno 121.21 63 1.92 566.3 <0.001 Dropping individual terms from full fixed model Fixed term Wald statistic n.d.f. F statistic d.d.f. F pr Envt 1349.10 9 149.90 21.0 <0.001 Geno 121.21 63 1.92 566.3 <0.001 * 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/Blk REML variance components analysis ================================= Response variate: BYield Fixed model: Constant + Envt Random model: Geno + Geno.Envt + Envt.Rep + Envt.Rep.Blk Number of units: 1919 (1 units excluded due to zero weights or missing values) Residual term has been added to model Sparse algorithm with AI optimisation Estimated variance components ----------------------------- Random term component s.e. Geno 32271. 12172. Geno.Envt 53352. 23869. Envt.Rep 80635. 31820. Envt.Rep.Blk 51289. 16663. Residual variance model ----------------------- Term Model(order) Parameter Estimate s.e. Residual Identity Sigma2 855519. 36106. Deviance: -2*Log-Likelihood --------------------------- Deviance d.f. 28305.64 1904 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 1348.83 9 149.87 21.0 <0.001 Dropping individual terms from full fixed model Fixed term Wald statistic n.d.f. F statistic d.d.f. F pr Envt 1348.83 9 149.87 21.0 <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/Blk REML variance components analysis ================================= Response variate: BYield Fixed model: Constant Random model: Envt + Geno + Envt.Geno + Envt.Rep + Envt.Rep.Blk Number of units: 1919 (1 units excluded due to zero weights or missing values) Residual term has been added to model Sparse algorithm with AI optimisation Estimated variance components ----------------------------- Random term component s.e. Envt 5107546. 2423916. Geno 32269. 12172. Envt.Geno 53353. 23870. Envt.Rep 80635. 31820. Envt.Rep.Blk 51289. 16663. Residual variance model ----------------------- Term Model(order) Parameter Estimate s.e. Residual Identity Sigma2 855519. 36106. Deviance: -2*Log-Likelihood --------------------------- Deviance d.f. 28456.02 1912 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 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 127 3039591879. 23933794. 75.59 <.001 Residual 512 162106655. 316615. Total 639 3201698534. 5010483. Percentage variance accounted for 93.7 Standard error of observations is estimated to be 563. Accumulated analysis of variance -------------------------------- Change d.f. s.s. m.s. v.r. F pr. + AllEnvt 1 2961903510. 2961903510. 9354.92 <.001 + Geno1 63 43310296. 687465. 2.17 <.001 + AllEnvt.Geno1 63 34378073. 545684. 1.72 <.001 Residual 512 162106655. 316615. Total 639 3201698534. 5010483. 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 127 12369.7 97.399 97.40 <.001 Residual 512 774.3 1.512 Total 639 13144.0 20.570 Percentage variance accounted for 92.6 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 11834.912 11834.912 11834.91 <.001 + Geno1 63 447.398 7.102 7.10 <.001 + AllEnvt.Geno1 63 87.425 1.388 1.39 0.023 Residual 512 774.306 1.512 Total 639 13144.041 20.570 * 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 3240 1.114 0.06679 0.1256 206436 0.6634 96.86 79.09 0.02386 4 3246 0.962 0.08792 0.6810 357759 0.2559 92.96 69.45 0.01341 5 2890 0.898 0.11025 0.3799 562510 0.0439 87.88 74.55 0.03537 6 3006 0.996 0.06178 0.9505 176616 0.7563 96.64 76.29 0.03429 7 2998 0.898 0.05120 0.0823 121308 0.9035 97.15 68.82 0.01360 8 3165 0.947 0.09691 0.6000 434595 0.1385 91.31 70.63 0.04554 9 3153 0.898 0.11838 0.4146 648580 0.0190 86.27 68.94 0.19131 10 2915 0.923 0.04981 0.1602 114836 0.9169 97.44 72.63 0.01871 11 2931 0.740 0.11768 0.0578 640885 0.0206 81.05 62.76 0.07532 12 3456 1.025 0.06818 0.7188 215105 0.6359 96.16 68.46 0.04695 13 3501 1.203 0.08480 0.0433 332768 0.3076 95.70 79.47 0.04473 14 3224 0.926 0.06145 0.2657 174775 0.7619 96.17 66.30 0.01239 15 3268 1.045 0.06309 0.4950 184192 0.7331 96.81 73.57 0.03086 16 3341 1.204 0.08433 0.0417 329131 0.3158 95.75 83.33 0.05171 17 3122 0.941 0.10085 0.5773 470714 0.1015 90.54 71.46 0.07641 18 3290 0.992 0.10179 0.9393 479505 0.0940 91.26 71.20 0.09317 19 3192 0.838 0.08029 0.0787 298320 0.3905 92.31 61.69 0.05725 20 3212 0.982 0.09312 0.8555 401269 0.1822 92.46 71.80 0.08964 21 2935 0.877 0.08604 0.1892 342618 0.2864 91.95 70.28 0.06600 22 3509 1.087 0.09411 0.3802 409921 0.1699 93.64 72.35 0.05623 23 2459 0.994 0.07185 0.9352 238923 0.5611 95.49 93.55 0.10440 24 2900 0.926 0.06147 0.2625 174845 0.7617 96.17 73.66 0.05398 25 2684 0.941 0.08246 0.4960 314687 0.3495 93.49 81.94 0.07468 26 3045 1.030 0.10292 0.7747 490193 0.0855 91.69 79.76 0.02011 27 3180 0.991 0.04410 0.8365 89989 0.9591 98.24 71.20 0.02590 28 2855 1.045 0.06594 0.5109 201237 0.6798 96.53 84.35 0.05262 29 3047 0.895 0.07509 0.1998 260954 0.4944 94.00 68.45 0.04580 30 2955 1.092 0.11130 0.4339 573267 0.0397 91.36 87.18 0.09440 31 2834 0.911 0.06076 0.1797 170847 0.7737 96.13 74.14 0.03084 32 3323 0.899 0.05196 0.0882 124959 0.8954 97.07 62.17 0.03226 33 3136 1.167 0.07085 0.0457 232295 0.5817 96.78 85.66 0.14617 34 3588 1.118 0.11065 0.3188 566662 0.0423 91.82 73.36 0.02372 35 2769 0.960 0.09862 0.6924 450111 0.1214 91.23 81.84 0.04345 36 3488 1.031 0.06103 0.6221 172359 0.7691 96.93 67.98 0.01776 37 2963 0.893 0.05929 0.1091 162667 0.7977 96.17 69.54 0.02247 38 3288 1.036 0.07884 0.6579 287681 0.4187 95.02 73.11 0.04905 39 3431 1.154 0.04339 0.0074 87116 0.9629 98.74 76.74 0.02876 40 3467 1.089 0.04705 0.0946 102430 0.9399 98.35 71.76 0.01300 41 3154 0.763 0.07886 0.0171 287786 0.4184 91.15 57.18 0.03881 42 3206 0.913 0.08934 0.3580 369356 0.2343 91.99 67.01 0.06596 43 3120 1.045 0.07522 0.5643 261861 0.4917 95.52 77.53 0.03774 44 3151 1.042 0.06645 0.5439 204323 0.6701 96.46 76.21 0.02013 45 3368 1.103 0.10276 0.3469 488741 0.0866 92.69 76.79 0.06240 46 3164 1.058 0.07576 0.4696 265632 0.4807 95.56 77.34 0.02987 47 3349 1.048 0.08459 0.5883 331139 0.3113 94.42 72.76 0.02425 48 3341 1.016 0.06956 0.8260 223935 0.6080 95.93 70.22 0.03554 49 3425 1.055 0.09668 0.5853 432590 0.1408 92.92 72.16 0.03951 50 3154 1.001 0.07883 0.9927 287567 0.4190 94.68 73.73 0.02481 51 3380 1.074 0.06964 0.3191 224430 0.6064 96.34 73.25 0.02536 52 3470 1.007 0.07067 0.9245 231162 0.5853 95.73 67.08 0.04343 53 3011 0.801 0.10034 0.0831 465904 0.1059 87.46 64.02 0.02444 54 2443 0.759 0.08911 0.0269 367474 0.2377 88.83 74.26 0.04716 55 3620 1.120 0.09010 0.2181 375659 0.2232 94.47 71.97 0.03599 56 3517 1.038 0.10102 0.7138 472324 0.1001 92.08 69.43 0.09939 57 3325 1.017 0.04412 0.7150 90093 0.9589 98.33 69.86 0.02438 58 3194 0.895 0.11039 0.3675 563923 0.0434 87.78 67.27 0.05442 59 3706 1.186 0.06179 0.0166 176692 0.7561 97.61 73.39 0.01695 60 3220 1.099 0.07531 0.2230 262494 0.4898 95.93 78.88 0.04101 61 3556 1.130 0.09002 0.1862 375061 0.2242 94.57 73.88 0.03149 62 3175 1.009 0.14380 0.9522 956960 0.0007 84.27 77.70 0.09850 63 3277 1.011 0.05138 0.8306 122175 0.9016 97.72 70.70 0.01173 64 3133 0.889 0.05801 0.0918 155714 0.8174 96.29 65.42 0.06896 200 3633 1.213 0.09758 0.0606 440695 0.1315 94.46 77.66 0.06389 300 3339 1.035 0.06997 0.6291 226575 0.5997 96.03 71.58 0.00970 GenoNum GenoMean Wricke Pla_Pet Plaisted Shukla 1 3240 2255296 300550 348017 253083 4 3246 2927164 338468 346794 330143 5 2890 4985854 454656 343046 566265 6 3006 1413654 253050 349550 156550 7 2998 1448840 255036 349485 160586 8 3165 3606282 376796 345558 408034 9 3153 5668853 493202 341803 644602 10 2915 1193822 240643 349950 131337 11 2931 8265156 639731 337076 942386 12 3456 1750785 272077 348936 195218 13 3501 4576371 431545 343792 519299 14 3224 1648439 266301 349122 183479 15 3268 1567674 261742 349269 174216 16 3341 4564324 430865 343814 517917 17 3122 3924592 394761 344978 444543 18 3290 3839004 389930 345134 434727 19 3192 3597635 376308 345573 407043 20 3212 3224345 355241 346253 364228 21 2935 3446365 367771 345849 389693 22 3509 3632953 378301 345509 411094 23 2459 1913068 281236 348640 213831 24 2900 1652762 266545 349114 183975 25 2684 2677576 324382 347248 301516 26 3045 3964510 397014 344906 449122 27 3180 724002 214128 350805 77450 28 2855 1705153 269501 349019 189984 29 3047 2597388 319857 347394 292319 30 2955 4975227 454056 343065 565046 31 2834 1736119 271249 348962 193536 32 3323 1470406 256253 349446 163059 33 3136 3156054 351386 346377 356395 34 3588 5173641 465254 342704 587803 35 2769 3676628 380766 345430 416103 36 3488 1424145 253642 349530 157754 37 2963 1829939 276544 348792 204296 38 3288 2362251 306586 347823 265350 39 3431 1800933 274907 348844 200969 40 3467 1187611 240293 349961 130624 41 3154 4892232 449372 343217 555527 42 3206 3306165 359858 346104 373613 43 3120 2189586 296841 348137 245546 44 3151 1716653 270150 348998 191303 45 3368 4398077 421483 344116 498850 46 3164 2278107 301837 347976 255699 47 3349 2754410 328719 347109 310329 48 3341 1803033 275025 348841 201210 49 3425 3600509 376470 345568 407372 50 3154 2300564 303105 347935 258275 51 3380 2048695 288890 348393 229387 52 3470 1851511 277761 348752 206770 53 3011 5553171 486673 342013 631334 54 2443 5625221 490740 341882 639597 55 3620 3676309 380748 345430 416066 56 3517 3846802 390370 345120 435621 57 3325 733641 214672 350788 78556 58 3194 5025750 456907 342973 570841 59 3706 3022649 343857 346620 341095 60 3220 2558077 317638 347466 287810 61 3556 3784556 386857 345233 428482 62 3175 7659344 605540 338179 872902 63 3277 983371 228766 350333 107199 64 3133 1816959 275811 348815 202807 200 3633 5624771 490714 341883 639546 300 3339 1869743 278790 348719 208862 -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- I I I I I 200. I 1.20 I 16. 13. I I 59. I I I I 33. I I I I 39. I 1.14 I I I 61. I I 3455. I I 1. I I 60. 45. I I 30. 40.22. I 1.08 I I I 51. I I 46. I I 28. 43. 15. 47. 49. I I 44. 38. 300. 56. I I 26. 12.36. I 1.02 I 48. I I 62. 63. 52. I I 6. 50. I I 23. 27. 18. I I 20. I I I 0.96 I 35. 4. I I 8. I I 25. 17. I I 24. 14. I I 10. I I 31. 42. I 0.90 I 5. 7. 29. 9. 32. I I 37. 64. 58. I I 21. I I I I I I I 0.84 I 19. I I I I I I I I 53. I I I 0.78 I I I I I 54. 41. I I I I 11. I I I 0.72 I I -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- 2400.0 2550.0 2700.0 2850.0 3000.0 3150.0 3300.0 3450.0 3600.0 3750.0 3900.0 Slope v. GenoMean using factor GenoNum Points coinciding with 48. 57. -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- I I I I I I 95.0 I I I I I 23. I I I I I I I 90.0 I I I I I I I 30. I I I I 33. I 85.0 I I I 28. I I 16. I I I I 25. 35. I I I 80.0 I 26. I I 1. 13. I I I I 43.46. 200. I I 6. 45. 39. I I 44. I 75.0 I I I 54. 31. 5. 61. I I 24. 50. 15. 51. 34. 59. I I 10. 47. 49. 22. I I 17. 20. 300. 40. 55. I I 827. 18. I 70.0 I 21. 48. I I 7. 9. 4. 56. I I 29. 12.36. I I 58. I I 14. 52. I I 64. I 65.0 I I I 53. I I I I 11. 32. I I 19. I I I 60.0 I I I I I I I 41. I I I I I 55.0 I I -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- 2400.0 2550.0 2700.0 2850.0 3000.0 3150.0 3300.0 3450.0 3600.0 3750.0 3900.0 GenoCV v. GenoMean using factor GenoNum Points coinciding with 7. 37. Points coinciding with 5. 38. Points coinciding with 14. 42. Points coinciding with 48. 57. Points coinciding with 1. 60. Points coinciding with 6. 62. Points coinciding with 18. 63. -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- I I I I I I 960000.0 I 62. I I I I I I I I I I I 840000.0 I I I I I I I I I I I I 720000.0 I I I I I I I I I 11. 9. I I I 600000.0 I I I 30. I I 5. 58. 34. I I I I I I 26. I 480000.0 I 17. 18. 45. 56. I I 35. 53. I I 8. 49. 200. I I I I 20. 22. I I 61. 55. I 360000.0 I 54. 4. I I 21. 47. 13. I I 25. 16. I I 19. I I 41. 38. I I 29. 43.46. 60. I 240000.0 I 23. 33. 52. I I 4851. 12. I I 28. 44. 1. I I 31. 24. 6. 14.15. 36. 59. I I 37. 64. I I I 120000.0 I 10. 7. 63. 32. I I 57. 40. I I 27. 39. I I I I I I I 0.0 I I -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- 2400.0 2550.0 2700.0 2850.0 3000.0 3150.0 3300.0 3450.0 3600.0 3750.0 3900.0 DeviMS v. GenoMean using factor GenoNum Points coinciding with 4. 42. Points coinciding with 41. 50. Points coinciding with 4851 300. -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- I I I 11. I I I 8000000.0 I I I I I 62. I I I I I I I 7000000.0 I I I I I I I I I I I I 6000000.0 I I I I I 54. 9. 200. I I 53. I I I I 34. I 5000000.0 I 5. 30. 58. I I 41. I I I I 16. 13. I I 45. I I I 4000000.0 I 26. 17. I I 18. 56.61. I I 35. 8.19. 49. 22. 55. I I 21. I I 42. I I 33. 20. I 3000000.0 I 4. 59. I I 47. I I 25. 29. I I 60. I I 46. 1. 38. I I 43. I 2000000.0 I 51. I I 23. 37. 64. 48. 12. I I 28.24. 44. 14. I I 7. 15. 32. 36. I I 6. I I 10. 40. I 1000000.0 I 63. I I I I 27. 57. I I I I I I I 0.0 I I -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- 2400.0 2550.0 2700.0 2850.0 3000.0 3150.0 3300.0 3450.0 3600.0 3750.0 3900.0 Wricke v. GenoMean using factor GenoNum Points coinciding with 28. 31. Points coinciding with 12. 39. Points coinciding with 46. 50. Points coinciding with 2. 52. Points coinciding with 48. 300. -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- I I I I I I 0.200 I I I I I 9. I I I I I I I 0.175 I I I I I I I I I I I I 0.150 I I I 33. I I I I I I I I I 0.125 I I I I I I I I I I I 23. I 0.100 I 62. 56. I I 30. I I 20. 18. I I I I I I I 0.075 I 25. 11. 17. I I 64. I I 21. 42. I I 45. 200. I I 19. I I 28.24. 58. 22. I 0.050 I 38. 16. I I 54. 29. 8. 12.13. I I 35. 60. 52. I I 41. 48. 49. 55. I I 5. 6. 32. 61. I I 31. 46. 15. 39. I 0.025 I 53. 27. 1. 4751. 34. I I 37. 26. 44. I I 10. 36. 59. I I 7. 4.63. 40. I I 300. I I I 0.000 I I -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- 2400.0 2550.0 2700.0 2850.0 3000.0 3150.0 3300.0 3450.0 3600.0 3750.0 3900.0 YauH v. GenoMean using factor GenoNum Points coinciding with 4. 14. Points coinciding with 41 43. Points coinciding with 27 50. Points coinciding with 475 57. 6.2 Stability indices under heterogeneous error-variances GenoNum GenoMean SlopeW SeSlopW Probb1W DeviSSW ProbDevW RSqW% 1 3240 0.978 0.07743 0.7818 8.87 0.3535 94.63 4 3246 1.010 0.06227 0.8823 5.74 0.6767 96.68 5 2890 0.910 0.08834 0.3362 11.55 0.1727 92.11 6 3006 0.968 0.08445 0.7133 10.55 0.2285 93.54 7 2998 0.920 0.05388 0.1738 4.29 0.8296 96.99 8 3165 0.995 0.08610 0.9528 10.97 0.2035 93.64 9 3153 0.834 0.15452 0.3150 35.32 0.0000 75.78 10 2915 0.944 0.07127 0.4564 7.52 0.4822 95.10 11 2931 0.902 0.14034 0.5028 29.14 0.0003 81.73 12 3456 1.014 0.08426 0.8739 10.50 0.2315 94.11 13 3501 1.049 0.10882 0.6664 17.52 0.0251 91.08 14 3224 0.971 0.04606 0.5492 3.14 0.9254 98.01 15 3268 0.991 0.08902 0.9240 11.72 0.1640 93.18 16 3341 1.029 0.12215 0.8177 22.07 0.0048 88.60 17 3122 0.913 0.13091 0.5240 25.35 0.0014 84.11 18 3290 0.933 0.13499 0.6308 26.96 0.0007 83.85 19 3192 0.897 0.09349 0.3019 12.93 0.1143 91.00 20 3212 0.875 0.13525 0.3822 27.06 0.0007 81.94 21 2935 0.857 0.10472 0.2101 16.22 0.0393 88.00 22 3509 1.052 0.11338 0.6568 19.02 0.0148 90.44 23 2459 0.914 0.09259 0.3782 12.68 0.1233 91.46 24 2900 1.023 0.07081 0.7554 7.42 0.4924 95.85 25 2684 0.938 0.09322 0.5234 12.86 0.1169 91.76 26 3045 0.969 0.07408 0.6842 8.12 0.4221 94.97 27 3180 0.930 0.06642 0.3230 6.53 0.5884 95.59 28 2855 0.983 0.08183 0.8379 9.91 0.2716 94.09 29 3047 0.968 0.10679 0.7694 16.87 0.0315 90.01 30 2955 1.037 0.10501 0.7368 16.31 0.0381 91.46 31 2834 0.969 0.06719 0.6564 6.68 0.5717 95.83 32 3323 1.002 0.07663 0.9827 8.69 0.3694 94.97 33 3136 1.141 0.09082 0.1584 12.20 0.1424 94.58 34 3588 1.162 0.07881 0.0738 9.19 0.3266 96.01 35 2769 0.947 0.07547 0.5038 8.43 0.3930 94.56 36 3488 1.066 0.05652 0.2770 4.73 0.7864 97.52 37 2963 0.947 0.07128 0.4764 7.52 0.4820 95.12 38 3288 1.083 0.10760 0.4641 17.13 0.0288 91.76 39 3431 1.163 0.05345 0.0157 4.23 0.8362 98.13 40 3467 1.093 0.04334 0.0636 2.78 0.9474 98.60 41 3154 1.005 0.10213 0.9630 15.43 0.0513 91.41 42 3206 1.060 0.10000 0.5636 14.79 0.0633 92.53 43 3120 0.990 0.09238 0.9157 12.62 0.1255 92.67 44 3151 1.039 0.05475 0.4986 4.43 0.8160 97.55 45 3368 0.985 0.10754 0.8929 17.11 0.0290 90.21 46 3164 1.013 0.07616 0.8716 8.58 0.3790 95.13 47 3349 1.040 0.08091 0.6309 9.69 0.2878 94.81 48 3341 1.098 0.09520 0.3323 13.41 0.0985 93.62 49 3425 1.110 0.08193 0.2147 9.93 0.2699 95.30 50 3154 0.953 0.06762 0.5075 6.76 0.5622 95.64 51 3380 1.043 0.07490 0.5828 8.30 0.4049 95.54 52 3470 1.107 0.08437 0.2396 10.53 0.2298 95.01 53 3011 0.914 0.07766 0.3027 8.92 0.3489 93.86 54 2443 0.859 0.07085 0.0812 7.43 0.4914 94.19 55 3620 1.125 0.09079 0.2074 12.19 0.1428 94.42 56 3517 0.982 0.12419 0.8878 22.82 0.0036 87.24 57 3325 1.078 0.08370 0.3803 10.37 0.2403 94.82 58 3194 0.933 0.09274 0.4879 12.72 0.1217 91.75 59 3706 1.188 0.06003 0.0141 5.33 0.7217 97.75 60 3220 1.034 0.09415 0.7250 13.11 0.1080 93.01 61 3556 1.069 0.07066 0.3590 7.39 0.4955 96.20 62 3175 0.861 0.11564 0.2651 19.78 0.0112 85.82 63 3277 1.002 0.04151 0.9542 2.55 0.9594 98.48 64 3133 0.881 0.08201 0.1849 9.95 0.2686 92.71 200 3633 1.240 0.10927 0.0596 17.66 0.0239 93.42 300 3339 1.018 0.05075 0.7327 3.81 0.8738 97.81 -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- I I I I I I 1.26 I I I I I 200. I I I I I I I 1.20 I I I 59. I I I I I I 39. 34. I I I 1.14 I 33. I I I I 55. I I 49.52. I I 48. I I 40. I 1.08 I 38.57. I I 36. 61. I I 42. I I 13. I I 30. 44. 4751. I I 60. 16. I 1.02 I 24. 300. I I 46. 4. 12. I I 41. 63. 32. I I 43.8. 15. 45. I I 28. 1. 56. I I 31. 6. 26. 14. I 0.96 I I I 35. 37. 50. I I 25. 10. I I 27. 18. I I 7. I I 23. 5. 53. 17. I 0.90 I 11. 19. I I I I 64. I I 20. I I 54. 21. 62. I I I 0.84 I I I 9. I I I I I I I I I 0.78 I I -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+- 2400.0 2550.0 2700.0 2850.0 3000.0 3150.0 3300.0 3450.0 3600.0 3750.0 3900.0 SlopeW v. GenoMean using factor GenoNum Points coinciding with 3. 22. Points coinciding with 26. 29. Points coinciding with 7. 58. 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 3240 79.09 1028086 827854 200232 31.29 28.08 13.81 4 3246 69.45 1228250 820630 407620 34.14 27.91 19.67 5 2890 74.55 1950426 1339533 610893 48.32 40.05 27.04 6 3006 76.29 1459620 1156830 302790 40.19 35.78 18.31 7 2998 68.82 1507425 1168672 338752 40.95 36.06 19.41 8 3165 70.63 1241947 927061 314886 35.21 30.42 17.73 9 3153 68.94 1455751 944199 511552 38.27 30.82 22.69 10 2915 72.63 1612736 1299234 313502 43.57 39.10 19.21 11 2931 62.76 2084226 1274297 809929 49.26 38.52 30.71 12 3456 68.46 797345 573232 224113 25.84 21.91 13.70 13 3501 79.47 753582 525862 227721 24.79 20.71 13.63 14 3224 66.30 1091378 848946 242432 32.40 28.58 15.27 15 3268 73.57 1045825 792774 253051 31.30 27.25 15.39 16 3341 83.33 956794 703281 253513 29.28 25.10 15.07 17 3122 71.46 1514196 987547 526649 39.42 31.83 23.25 18 3290 71.20 1236593 765203 471390 33.80 26.59 20.87 19 3192 61.69 1334020 890744 443275 36.18 29.57 20.86 20 3212 71.80 1238561 863932 374629 34.64 28.93 19.05 21 2935 70.28 1767141 1266878 500263 45.29 38.35 24.10 22 3509 72.35 763573 518213 245360 24.90 20.52 14.12 23 2459 93.55 2418940 2137938 281003 63.25 59.46 21.56 24 2900 73.66 1646521 1323396 323124 44.25 39.67 19.60 25 2684 81.94 2112461 1699038 413424 54.16 48.57 23.96 26 3045 79.76 1514051 1098799 415253 40.42 34.43 21.17 27 3180 71.20 1138103 907507 230596 33.55 29.96 15.10 28 2855 84.35 1606846 1397957 208889 44.40 41.42 16.01 29 3047 68.45 1485774 1094435 391338 40.00 34.33 20.53 30 2955 87.18 1665695 1235209 430486 43.67 37.61 22.20 31 2834 74.14 1746336 1432493 313842 46.62 42.23 19.77 32 3323 62.17 1073253 724598 348655 31.17 25.62 17.77 33 3136 85.66 1097554 967792 129761 33.41 31.37 11.49 34 3588 73.36 616126 441049 175077 21.88 18.51 11.66 35 2769 81.84 1917460 1545761 371699 50.01 44.91 22.02 36 3488 67.98 677435 539882 137553 23.60 21.07 10.63 37 2963 69.54 1561609 1222431 339177 42.17 37.31 19.65 38 3288 73.11 988329 767649 220680 30.24 26.65 14.29 39 3431 76.74 677944 601046 76898 24.00 22.60 8.08 40 3467 71.76 690149 561449 128700 23.96 21.61 10.35 41 3154 57.18 1601004 942221 658783 40.11 30.77 25.73 42 3206 67.01 1241473 873038 368435 34.76 29.15 18.94 43 3120 77.53 1203076 990202 212874 35.16 31.90 14.79 44 3151 76.21 1102541 946675 155865 33.32 30.88 12.53 45 3368 76.79 890682 672106 218577 28.03 24.34 13.88 46 3164 77.34 1167379 929037 238342 34.15 30.46 15.43 47 3349 72.76 850785 693684 157101 27.54 24.87 11.83 48 3341 70.22 926402 703106 223296 28.81 25.10 14.14 49 3425 72.16 851175 607318 243857 26.94 22.75 14.42 50 3154 73.73 1281228 943124 338104 35.89 30.80 18.44 51 3380 73.25 782724 657602 125122 26.17 23.99 10.46 52 3470 67.08 772392 558214 214178 25.32 21.53 13.34 53 3011 64.02 1693744 1148445 545299 43.22 35.59 24.52 54 2443 74.26 2796897 2172219 624678 68.47 60.34 32.36 55 3620 71.97 535137 410920 124217 20.21 17.71 9.73 56 3517 69.43 721733 509557 212177 24.15 20.29 13.10 57 3325 69.86 898335 722537 175797 28.51 25.57 12.61 58 3194 67.27 1497618 888413 609204 38.31 29.51 24.44 59 3706 73.39 381411 337221 44190 16.67 15.67 5.67 60 3220 78.88 989235 854493 134741 30.89 28.71 11.40 61 3556 73.88 712730 471634 241095 23.74 19.31 13.81 62 3175 77.70 1561505 914491 647014 39.36 30.12 25.34 63 3277 70.70 954460 781136 173324 29.81 26.97 12.70 64 3133 65.42 1349220 971264 377956 37.07 31.45 19.62 200 3633 77.66 512401 399975 112426 19.71 17.41 9.23 300 3339 71.58 971955 706032 265923 29.53 25.17 15.45 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 3240 79.09 1493272 941942 551330 37.71 29.95 22.92 4 3246 69.45 1280230 949681 330548 34.86 30.02 17.71 5 2890 74.55 1010567 522758 487809 34.78 25.02 24.17 6 3006 76.29 951362 647770 303592 32.45 26.78 18.33 7 2998 68.82 877566 638961 238605 31.25 26.66 16.29 8 3165 70.63 1117762 841920 275842 33.40 28.99 16.59 9 3153 68.94 1317144 825741 491403 36.40 28.82 22.23 10 2915 72.63 763040 548433 214607 29.97 25.41 15.89 11 2931 62.76 955217 564834 390383 33.35 25.65 21.32 12 3456 68.46 1593554 1261760 331794 36.52 32.50 16.67 13 3501 79.47 1936805 1334576 602228 39.75 32.99 22.16 14 3224 66.30 1072226 919718 152507 32.12 29.75 12.11 15 3268 73.57 1319407 980146 339260 35.15 30.30 17.82 16 3341 83.33 1774895 1085313 689582 39.88 31.18 24.86 17 3122 71.46 1101211 786145 315067 33.62 28.40 17.98 18 3290 71.20 1415251 1011318 403933 36.16 30.57 19.32 19 3192 61.69 1010837 877238 133599 31.50 29.34 11.45 20 3212 71.80 1162066 904253 257812 33.56 29.60 15.81 21 2935 70.28 841889 569791 272097 31.26 25.72 17.77 22 3509 72.35 1809586 1346834 462752 38.34 33.07 19.39 23 2459 93.55 387733 174919 212814 25.32 17.01 18.76 24 2900 73.66 781467 532918 248549 30.48 25.17 17.19 25 2684 81.94 556668 332849 223819 27.80 21.50 17.63 26 3045 79.76 1278362 692500 585861 37.14 27.33 25.14 27 3180 71.20 1066454 860758 205696 32.48 29.18 14.26 28 2855 84.35 828411 487274 341138 31.88 24.45 20.46 29 3047 68.45 919771 695972 223799 31.47 27.38 15.52 30 2955 87.18 1177583 591365 586218 36.72 26.02 25.91 31 2834 74.14 652466 467219 185247 28.50 24.12 15.19 32 3323 62.17 1204136 1059188 144948 33.02 30.97 11.46 33 3136 85.66 1319964 803959 516005 36.64 28.59 22.91 34 3588 73.36 2021737 1479354 542384 39.63 33.90 20.53 35 2769 81.84 646147 405917 240231 29.03 23.01 17.70 36 3488 67.98 1627626 1312481 315145 36.58 32.85 16.10 37 2963 69.54 842943 600262 242681 30.98 26.14 16.62 38 3288 73.11 1465637 1008510 457126 36.82 30.54 20.56 39 3431 76.74 1765667 1221314 544353 38.73 32.21 21.51 40 3467 71.76 1693822 1279394 414428 37.54 32.62 18.57 41 3154 57.18 1045984 827593 218391 32.42 28.84 14.82 42 3206 67.01 1107994 894986 213008 32.84 29.51 14.40 43 3120 77.53 1121653 783779 337874 33.95 28.38 18.63 44 3151 76.21 1114905 823428 291477 33.51 28.80 17.13 45 3368 76.79 1565603 1124833 440769 37.16 31.49 19.71 46 3164 77.34 1351647 840039 511607 36.75 28.97 22.61 47 3349 72.76 1446074 1097309 348765 35.91 31.28 17.63 48 3341 70.22 1488360 1085531 402829 36.51 31.18 19.00 49 3425 72.16 1591820 1212412 379408 36.84 32.15 17.99 50 3154 73.73 1197269 826747 370522 34.70 28.83 19.30 51 3380 73.25 1498419 1143777 354642 36.21 31.64 17.62 52 3470 67.08 1635484 1284289 351194 36.85 32.66 17.08 53 3011 64.02 782572 654071 128501 29.38 26.86 11.90 54 2443 74.26 240945 165289 75656 20.10 16.64 11.26 55 3620 71.97 2132268 1536042 596226 40.33 34.23 21.33 56 3517 69.43 1784394 1360885 423510 37.98 33.17 18.50 57 3325 69.86 1304746 1061683 243063 34.36 30.99 14.83 58 3194 67.27 1270842 879554 391288 35.29 29.36 19.58 59 3706 73.39 2254443 1689207 565236 40.52 35.07 20.29 60 3220 78.88 1446203 913963 532240 37.35 29.69 22.66 61 3556 73.88 2114420 1424790 689630 40.89 33.57 23.35 62 3175 77.70 1691996 853983 838014 40.97 29.11 28.84 63 3277 70.70 1252299 993178 259121 34.15 30.41 15.53 64 3133 65.42 979660 800801 178859 31.59 28.56 13.50 200 3633 77.66 2268446 1557421 711025 41.46 34.35 23.21 300 3339 71.58 1490514 1081902 408612 36.57 31.15 19.15 6.4 Correlations between various indices GenoMean 1.0000 Slope 0.6171 1.0000 DeviMS -0.0290 -0.0982 1.0000 GenoCV -0.2712 0.5772 0.0643 1.0000 Wricke -0.0362 -0.1521 0.8972 -0.0197 1.0000 Pla_Pet -0.0362 -0.1521 0.8972 -0.0197 1.0000 1.0000 Plaisted 0.0362 0.1521 -0.8972 0.0197 -1.0000 -1.0000 1.0000 Shukla -0.0362 -0.1521 0.8972 -0.0197 1.0000 1.0000 -1.0000 1.0000 YauH -0.1959 -0.0627 0.5077 0.2187 0.4565 0.4565 -0.4565 0.4565 1.0000 SlopeW 0.6708 0.7062 -0.2596 0.1439 -0.1852 -0.1852 0.1852 -0.1852 -0.2871 1.0000 DeviSSW 0.0089 -0.0893 0.6179 -0.0222 0.6007 0.6007 -0.6007 0.6007 0.7671 -0.2944 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 0.5255 1.0000 RDeviMS -0.0690 -0.1384 1.0000 RGenoCV -0.0971 0.2298 -0.0264 1.0000 RWricke -0.0712 -0.1120 0.5939 -0.0197 1.0000 RPla_Pet -0.0712 -0.1120 0.5939 -0.0197 1.0000 1.0000 RPlaist 0.0756 0.6181 -0.3625 0.0473 -0.4143 -0.4143 1.0000 RShukla -0.0712 -0.1120 0.5939 -0.0197 1.0000 1.0000 -0.4143 1.0000 RYauH -0.1432 -0.1112 0.1682 0.0093 0.1798 0.1798 -0.2490 0.1798 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 ---------------- 12 61 99.1 5 8 99.0 2 64 98.8 15 16 98.8 13 14 98.6 32 45 98.5 37 38 98.4 57 63 98.3 12 25 98.2 44 58 98.1 34 49 98.1 37 55 98.0 27 41 97.9 48 56 97.9 3 5 97.7 27 36 97.7 22 26 97.7 37 46 97.6 30 39 97.1 19 62 97.1 4 35 96.9 12 37 96.8 13 15 96.8 34 43 96.7 10 54 96.7 53 57 96.7 1 44 96.5 3 24 96.4 32 42 96.4 6 12 96.3 17 20 96.3 21 23 96.1 30 48 96.0 3 29 95.9 2 4 95.9 1 27 95.8 11 34 95.8 13 18 95.7 33 52 95.7 30 50 95.6 11 47 95.4 59 60 95.4 6 32 95.2 28 31 95.0 30 40 94.7 2 51 94.6 10 53 94.5 1 6 94.4 13 19 94.3 22 33 94.1 17 30 93.6 1 10 93.6 2 11 93.4 21 22 93.4 2 17 92.2 3 59 92.1 21 28 91.9 3 13 91.2 1 2 90.1 1 3 89.8 1 9 86.9 1 21 83.4 1 7 77.5 Hierarchical clusters --------------------- Level 95.0 1 44 58 27 41 36 6 12 61 25 37 38 55 46 32 45 42 10 54 53 57 63 2 64 4 35 11 34 49 43 47 17 20 30 39 48 56 50 3 5 8 24 29 59 60 13 14 15 16 18 19 62 21 23 22 26 33 52 Ungrouped 51 40 9 28 31 7 Level 90.0 1 44 58 27 41 36 6 12 61 25 37 38 55 46 32 45 42 10 54 53 57 63 2 64 4 35 51 11 34 49 43 47 17 20 30 39 48 56 50 40 3 5 8 24 29 59 60 13 14 15 16 18 19 62 21 23 22 26 33 52 28 31 Ungrouped 9 7 Level 85.0 1 44 58 27 41 36 6 12 61 25 37 38 55 46 32 45 42 10 54 53 57 63 2 64 4 35 51 11 34 49 43 47 17 20 30 39 48 56 50 40 3 5 8 24 29 59 60 13 14 15 16 18 19 62 9 21 23 22 26 33 52 28 31 Ungrouped 7 Level 80.0 1 44 58 27 41 36 6 12 61 25 37 38 55 46 32 45 42 10 54 53 57 63 2 64 4 35 51 11 34 49 43 47 17 20 30 39 48 56 50 40 3 5 8 24 29 59 60 13 14 15 16 18 19 62 9 21 23 22 26 33 52 28 31 Ungrouped 7 Level 75.0 1 44 58 27 41 36 6 12 61 25 37 38 55 46 32 45 42 10 54 53 57 63 2 64 4 35 51 11 34 49 43 47 17 20 30 39 48 56 50 40 3 5 8 24 29 59 60 13 14 15 16 18 19 62 9 21 23 22 26 33 52 28 31 7 Dendrogram ---------- ** Levels 100.0 90.0 80.0 1.00 1 .. 46.00 44 ..) 60.00 58 ..) 29.00 27 ..) 43.00 41 ..) 38.00 36 ..).. 8.00 6 .. ) 14.00 12 ..) ) 63.00 61 ..) ) 27.00 25 ..) ) 39.00 37 ..) ) 40.00 38 ..) ) 57.00 55 ..) ) 48.00 46 ..) ) 34.00 32 ..) ) 47.00 45 ..) ) 44.00 42 ..)..) 12.00 10 .. ) 56.00 54 ..)..) 55.00 53 .. ) 59.00 57 ..) ) 200.00 63 ..)..) 4.00 2 .. ) 300.00 64 ..) ) 6.00 4 ..) ) 37.00 35 ..)..) 53.00 51 .....) 13.00 11 .. ) 36.00 34 ..) ) 51.00 49 ..) ) 45.00 43 ..) ) 49.00 47 ..)..) 19.00 17 .. ) 22.00 20 ..)..) 32.00 30 .. ) 41.00 39 ..) ) 50.00 48 ..) ) 58.00 56 ..) ) 52.00 50 ..)..) 42.00 40 .....).. 5.00 3 .. ) 7.00 5 ..) ) 10.00 8 ..) ) 26.00 24 ..) ) 31.00 29 ..).. ) 61.00 59 .. ) ) 62.00 60 ..)..) ) 15.00 13 .. ) ) 16.00 14 ..) ) ) 17.00 15 ..) ) ) 18.00 16 ..) ) ) 20.00 18 ..)..) ) 21.00 19 .. ) ) 64.00 62 ..)..)..) 11.00 9 ........).. 23.00 21 .. ) 25.00 23 ..).. ) 24.00 22 .. ) ) 28.00 26 ..)..) ) 35.00 33 .. ) ) 54.00 52 ..)..) ) 30.00 28 .. ) ) 33.00 31 ..)..).....).. 9.00 7 ..............)........ ===================================================================================================== ................................................................................... 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 9 99.2 3 6 98.9 8 10 98.7 2 8 97.9 1 3 97.7 5 7 95.4 1 2 93.2 4 5 91.0 1 4 63.4 Hierarchical clusters --------------------- Level 95.0 1 9 3 6 2 8 10 5 7 Ungrouped 4 Level 90.0 1 9 3 6 2 8 10 4 5 7 Level 85.0 1 9 3 6 2 8 10 4 5 7 Level 80.0 1 9 3 6 2 8 10 4 5 7 Level 75.0 1 9 3 6 2 8 10 4 5 7 Level 70.0 1 9 3 6 2 8 10 4 5 7 Level 65.0 1 9 3 6 2 8 10 4 5 7 Level 60.0 1 9 3 6 2 8 10 4 5 7 Dendrogram ---------- ** Levels 100.0 90.0 80.0 70.0 60.0 1.00 1 .. 20.00 9 ..) 4.00 3 ..) 7.00 6 ..).. 3.00 2 .. ) 9.00 8 ..) ) 100.00 10 ..)..)................. 5.00 4 ..... ) 6.00 5 .. ) ) 8.00 7 ..)..).................)........... =====================================================================================================