![[Stable]](figures/lifecycle-stable.svg)
Computes the dissimilarity between environments based on several approaches. See the section details for more details.
Arguments
- .data
The dataset containing the columns related to Environments, Genotypes, replication/block and response variable(s).
- env
The name of the column that contains the levels of the environments.
- gen
The name of the column that contains the levels of the genotypes.
- rep
The name of the column that contains the levels of the replications/blocks.
- resp
The response variable(s). To analyze multiple variables in a single procedure a vector of variables may be used. For example
resp = c(var1, var2, var3). Select helpers are also allowed.
Value
A list with the following matrices:
SPART_CC: The percentage of the single (non cross-over) part of the interaction between genotypes and pairs of environments according to the method proposed by Cruz and Castoldi (1991).CPART_CC: The percentage of the complex (cross-over) part of the interaction between genotypes and pairs of environments according to the method proposed by Cruz and Castoldi (1991).SPART_RO: The percentage of the single (non cross-over) part of the interaction between genotypes and pairs of environments according to the method proposed by Robertson (1959).CPART_RO: The percentage of the complex (cross-over) part of the interaction between genotypes and pairs of environments according to the method proposed by Robertson (1959).MSGE: Interaction mean square between genotypes and pairs of environments.SSGE: Interaction sum of square between genotypes and pairs of environments.correlation: Correlation coefficients between genotypes's average in each pair of environment.
Details
Roberteson (1959) proposed the partition of the mean square of the genotype-environment interaction (MS_GE) into single (S) and complex (C) parts, where \(S = \frac{1}{2}(\sqrt{Q1}-\sqrt{Q2})^2)\) and \(C = (1-r)\sqrt{Q1-Q2}\), being r the correlation between the genotype's average in the two environments; and Q1 and Q2 the genotype mean square in the environments 1 and 2, respectively. Cruz and Castoldi (1991) proposed a new decomposition of the MS_GE, in which the complex part is given by \(C = \sqrt{(1-r)^3\times Q1\times Q2}\).
References
Cruz, C.D., Castoldi, F. (1991). Decomposicao da interacao genotipos x ambientes em partes simples e complexa. Ceres, 38:422-430.
Robertson, A. (1959). Experimental design on the measurement of heritabilities and genetic correlations. biometrical genetics. New York: Pergamon Press.
Author
Tiago Olivoto tiagoolivoto@gmail.com
Examples
# \donttest{
library(metan)
mod <- env_dissimilarity(data_ge, ENV, GEN, REP, GY)
#> Evaluating trait Y |=============================================| 100% 00:00:00
print(mod)
#> Variable GY
#> ----------------------------------------------------------------------
#> Pearson's correlation coefficient
#> ----------------------------------------------------------------------
#> E1 E10 E11 E12 E13 E14 E2 E3 E4 E5
#> E1 1.000 0.783 0.782 0.869 0.825 0.197 0.227 0.357 -0.011 0.704
#> E10 0.783 1.000 0.917 0.797 0.812 0.232 0.101 -0.136 -0.342 0.676
#> E11 0.782 0.917 1.000 0.749 0.840 0.234 0.438 -0.165 -0.130 0.635
#> E12 0.869 0.797 0.749 1.000 0.740 0.155 0.053 0.249 -0.190 0.567
#> E13 0.825 0.812 0.840 0.740 1.000 0.161 0.246 0.183 -0.045 0.814
#> E14 0.197 0.232 0.234 0.155 0.161 1.000 0.247 -0.427 0.149 0.218
#> E2 0.227 0.101 0.438 0.053 0.246 0.247 1.000 -0.069 0.661 0.210
#> E3 0.357 -0.136 -0.165 0.249 0.183 -0.427 -0.069 1.000 0.409 0.310
#> E4 -0.011 -0.342 -0.130 -0.190 -0.045 0.149 0.661 0.409 1.000 0.206
#> E5 0.704 0.676 0.635 0.567 0.814 0.218 0.210 0.310 0.206 1.000
#> E6 0.580 0.368 0.349 0.315 0.637 0.274 0.289 0.446 0.358 0.810
#> E7 0.454 0.394 0.188 0.350 0.152 0.566 -0.166 0.046 0.028 0.325
#> E8 -0.053 0.025 0.077 0.034 0.122 0.821 0.317 -0.293 0.417 0.216
#> E9 0.219 0.281 0.241 0.216 -0.184 0.323 0.119 -0.375 -0.276 -0.281
#> E6 E7 E8 E9
#> E1 0.580 0.454 -0.053 0.219
#> E10 0.368 0.394 0.025 0.281
#> E11 0.349 0.188 0.077 0.241
#> E12 0.315 0.350 0.034 0.216
#> E13 0.637 0.152 0.122 -0.184
#> E14 0.274 0.566 0.821 0.323
#> E2 0.289 -0.166 0.317 0.119
#> E3 0.446 0.046 -0.293 -0.375
#> E4 0.358 0.028 0.417 -0.276
#> E5 0.810 0.325 0.216 -0.281
#> E6 1.000 0.241 0.240 -0.237
#> E7 0.241 1.000 0.265 0.456
#> E8 0.240 0.265 1.000 -0.106
#> E9 -0.237 0.456 -0.106 1.000
#> ----------------------------------------------------------------------
#> Minimum correlation = -0.427 between environments 8 and 6
#> Maximum correlation = 0.917 between environments 3 and 2
#> ----------------------------------------------------------------------
#> Mean square GxEjj'
#> ----------------------------------------------------------------------
#> E1 E10 E11 E12 E13 E14 E2 E3 E4 E5 E6 E7
#> E1 0.000 0.023 0.023 0.014 0.040 0.064 0.071 0.072 0.146 0.045 0.037 0.061
#> E10 0.023 0.000 0.010 0.021 0.044 0.056 0.075 0.119 0.183 0.048 0.047 0.064
#> E11 0.023 0.010 0.000 0.024 0.052 0.036 0.034 0.093 0.126 0.053 0.031 0.067
#> E12 0.014 0.021 0.024 0.000 0.054 0.065 0.083 0.082 0.168 0.063 0.054 0.071
#> E13 0.040 0.044 0.052 0.054 0.000 0.124 0.122 0.145 0.217 0.040 0.075 0.150
#> E14 0.064 0.056 0.036 0.065 0.124 0.000 0.043 0.107 0.097 0.090 0.032 0.038
#> E2 0.071 0.075 0.034 0.083 0.122 0.043 0.000 0.096 0.050 0.099 0.041 0.105
#> E3 0.072 0.119 0.093 0.082 0.145 0.107 0.096 0.000 0.087 0.100 0.047 0.107
#> E4 0.146 0.183 0.126 0.168 0.217 0.097 0.050 0.087 0.000 0.140 0.079 0.141
#> E5 0.045 0.048 0.053 0.063 0.040 0.090 0.099 0.100 0.140 0.000 0.038 0.098
#> E6 0.037 0.047 0.031 0.054 0.075 0.032 0.041 0.047 0.079 0.038 0.000 0.062
#> E7 0.061 0.064 0.067 0.071 0.150 0.038 0.105 0.107 0.141 0.098 0.062 0.000
#> E8 0.097 0.083 0.056 0.086 0.139 0.012 0.048 0.118 0.077 0.099 0.045 0.068
#> E9 0.134 0.120 0.113 0.133 0.275 0.103 0.133 0.229 0.257 0.257 0.160 0.097
#> E8 E9
#> E1 0.097 0.134
#> E10 0.083 0.120
#> E11 0.056 0.113
#> E12 0.086 0.133
#> E13 0.139 0.275
#> E14 0.012 0.103
#> E2 0.048 0.133
#> E3 0.118 0.229
#> E4 0.077 0.257
#> E5 0.099 0.257
#> E6 0.045 0.160
#> E7 0.068 0.097
#> E8 0.000 0.163
#> E9 0.163 0.000
#> ----------------------------------------------------------------------
#> Total mean square = 8.091
#> Minimum = 0.01 between environments 3 and 2
#> Maximum = 0.275 between environments 14 and 5
#> ----------------------------------------------------------------------
#> % Of the single part of MS GxEjj' (Robertson, 1959)
#> ----------------------------------------------------------------------
#> E1 E10 E11 E12 E13 E14 E2 E3 E4 E5
#> E1 0.000 0.986 27.318 0.261 28.828 12.522 3.762 0.001 2.496 7.731
#> E10 0.986 0.000 40.737 0.385 34.423 9.953 1.763 0.171 3.118 11.398
#> E11 27.318 40.737 0.000 22.188 66.463 0.344 2.154 6.468 15.337 35.530
#> E12 0.261 0.385 22.188 0.000 23.835 10.808 2.477 0.034 2.638 6.684
#> E13 28.828 34.423 66.463 23.835 0.000 31.325 20.821 8.123 1.030 5.877
#> E14 12.522 9.953 0.344 10.808 31.325 0.000 3.400 7.351 23.171 24.437
#> E2 3.762 1.763 2.154 2.477 20.821 3.400 0.000 2.671 25.107 12.340
#> E3 0.001 0.171 6.468 0.034 8.123 7.351 2.671 0.000 4.323 3.574
#> E4 2.496 3.118 15.337 2.638 1.030 23.171 25.107 4.323 0.000 0.002
#> E5 7.731 11.398 35.530 6.684 5.877 24.437 12.340 3.574 0.002 0.000
#> E6 20.351 11.047 0.250 12.211 50.386 0.017 3.137 16.015 27.630 55.978
#> E7 0.000 0.349 9.145 0.050 7.742 20.888 2.510 0.000 2.611 3.560
#> E8 2.382 1.304 1.656 2.035 17.463 14.768 0.026 1.890 15.194 11.532
#> E9 7.339 10.869 28.075 8.369 0.025 34.705 17.152 4.388 0.588 0.634
#> E6 E7 E8 E9
#> E1 20.351 0.000 2.382 7.339
#> E10 11.047 0.349 1.304 10.869
#> E11 0.250 9.145 1.656 28.075
#> E12 12.211 0.050 2.035 8.369
#> E13 50.386 7.742 17.463 0.025
#> E14 0.017 20.888 14.768 34.705
#> E2 3.137 2.510 0.026 17.152
#> E3 16.015 0.000 1.890 4.388
#> E4 27.630 2.611 15.194 0.588
#> E5 55.978 3.560 11.532 0.634
#> E6 0.000 12.350 3.465 21.839
#> E7 12.350 0.000 3.358 10.237
#> E8 3.465 3.358 0.000 13.356
#> E9 21.839 10.237 13.356 0.000
#> ----------------------------------------------------------------------
#> Average = 11.464
#> Minimum = 0 between environments 12 and 12
#> Maximum = 66.463 between environments 5 and 3
#> ----------------------------------------------------------------------
#> % Of the complex part of MS GxEjj' (Robertson, 1959)
#> ----------------------------------------------------------------------
#> E1 E10 E11 E12 E13 E14 E2 E3 E4 E5
#> E1 0.000 99.014 72.682 99.739 71.172 87.478 96.238 99.999 97.504 92.269
#> E10 99.014 0.000 59.263 99.615 65.577 90.047 98.237 99.829 96.882 88.602
#> E11 72.682 59.263 0.000 77.812 33.537 99.656 97.846 93.532 84.663 64.470
#> E12 99.739 99.615 77.812 0.000 76.165 89.192 97.523 99.966 97.362 93.316
#> E13 71.172 65.577 33.537 76.165 0.000 68.675 79.179 91.877 98.970 94.123
#> E14 87.478 90.047 99.656 89.192 68.675 0.000 96.600 92.649 76.829 75.563
#> E2 96.238 98.237 97.846 97.523 79.179 96.600 0.000 97.329 74.893 87.660
#> E3 99.999 99.829 93.532 99.966 91.877 92.649 97.329 0.000 95.677 96.426
#> E4 97.504 96.882 84.663 97.362 98.970 76.829 74.893 95.677 0.000 99.998
#> E5 92.269 88.602 64.470 93.316 94.123 75.563 87.660 96.426 99.998 0.000
#> E6 79.649 88.953 99.750 87.789 49.614 99.983 96.863 83.985 72.370 44.022
#> E7 100.000 99.651 90.855 99.950 92.258 79.112 97.490 100.000 97.389 96.440
#> E8 97.618 98.696 98.344 97.965 82.537 85.232 99.974 98.110 84.806 88.468
#> E9 92.661 89.131 71.925 91.631 99.975 65.295 82.848 95.612 99.412 99.366
#> E6 E7 E8 E9
#> E1 79.649 100.000 97.618 92.661
#> E10 88.953 99.651 98.696 89.131
#> E11 99.750 90.855 98.344 71.925
#> E12 87.789 99.950 97.965 91.631
#> E13 49.614 92.258 82.537 99.975
#> E14 99.983 79.112 85.232 65.295
#> E2 96.863 97.490 99.974 82.848
#> E3 83.985 100.000 98.110 95.612
#> E4 72.370 97.389 84.806 99.412
#> E5 44.022 96.440 88.468 99.366
#> E6 0.000 87.650 96.535 78.161
#> E7 87.650 0.000 96.642 89.763
#> E8 96.535 96.642 0.000 86.644
#> E9 78.161 89.763 86.644 0.000
#> ----------------------------------------------------------------------
#> Average = 88.536
#> Minimum = 33.537 between environments 5 and 3
#> Maximum = 100 between environments 12 and 12
#> ----------------------------------------------------------------------
#> % Of the single part of MS GxEjj' (Cruz and Castoldi, 1991)
#> ----------------------------------------------------------------------
#> E1 E10 E11 E12 E13 E14 E2 E3 E4 E5
#> E1 0.000 53.838 66.053 63.833 70.220 21.623 15.404 19.783 1.938 49.824
#> E10 53.838 0.000 82.915 55.158 71.598 21.096 6.873 -6.386 -12.243 49.530
#> E11 66.053 82.915 0.000 61.028 86.585 12.789 26.675 -0.957 10.015 61.032
#> E12 63.833 55.158 61.028 0.000 61.171 18.020 5.082 13.394 -6.217 38.609
#> E13 70.220 71.598 86.585 61.171 0.000 37.079 31.266 16.941 -1.174 59.404
#> E14 21.623 21.096 12.789 18.020 37.079 0.000 16.166 -10.671 29.120 33.173
#> E2 15.404 6.873 26.675 5.082 31.266 16.166 0.000 -0.651 56.404 22.091
#> E3 19.783 -6.386 -0.957 13.394 16.941 -10.671 -0.651 0.000 26.463 19.926
#> E4 1.938 -12.243 10.015 -6.217 -1.174 29.120 56.404 26.463 0.000 10.922
#> E5 49.824 49.530 61.032 38.609 59.404 33.173 22.091 19.926 10.922 0.000
#> E6 48.374 29.311 19.513 27.350 70.128 14.796 18.342 37.471 42.032 80.822
#> E7 26.095 22.442 18.142 19.396 15.031 47.887 -5.293 2.351 3.998 20.747
#> E8 -0.157 2.521 5.536 3.726 22.646 63.892 17.366 -11.548 35.236 21.672
#> E9 18.128 24.437 37.322 18.890 -8.784 46.272 22.252 -12.098 -12.287 -12.467
#> E6 E7 E8 E9
#> E1 48.374 26.095 -0.157 18.128
#> E10 29.311 22.442 2.521 24.437
#> E11 19.513 18.142 5.536 37.322
#> E12 27.350 19.396 3.726 18.890
#> E13 70.128 15.031 22.646 -8.784
#> E14 14.796 47.887 63.892 46.272
#> E2 18.342 -5.293 17.366 22.252
#> E3 37.471 2.351 -11.548 -12.098
#> E4 42.032 3.998 35.236 -12.287
#> E5 80.822 20.747 21.672 -12.467
#> E6 0.000 23.614 15.820 13.068
#> E7 23.614 0.000 17.172 33.771
#> E8 15.820 17.172 0.000 8.861
#> E9 13.068 33.771 8.861 0.000
#> ----------------------------------------------------------------------
#> Average = 25.478
#> Minimum = -12.467 between environments 14 and 10
#> Maximum = 86.585 between environments 5 and 3
#> ----------------------------------------------------------------------
#> % Of the complex part of MS GxEjj' (Cruz and Castoldi, 1991)
#> ----------------------------------------------------------------------
#> E1 E10 E11 E12 E13 E14 E2 E3 E4
#> E1 0.000 46.162 33.947 36.167 29.780 78.377 84.596 80.217 98.062
#> E10 46.162 0.000 17.085 44.842 28.402 78.904 93.127 106.386 112.243
#> E11 33.947 17.085 0.000 38.972 13.415 87.211 73.325 100.957 89.985
#> E12 36.167 44.842 38.972 0.000 38.829 81.980 94.918 86.606 106.217
#> E13 29.780 28.402 13.415 38.829 0.000 62.921 68.734 83.059 101.174
#> E14 78.377 78.904 87.211 81.980 62.921 0.000 83.834 110.671 70.880
#> E2 84.596 93.127 73.325 94.918 68.734 83.834 0.000 100.651 43.596
#> E3 80.217 106.386 100.957 86.606 83.059 110.671 100.651 0.000 73.537
#> E4 98.062 112.243 89.985 106.217 101.174 70.880 43.596 73.537 0.000
#> E5 50.176 50.470 38.968 61.391 40.596 66.827 77.909 80.074 89.078
#> E6 51.626 70.689 80.487 72.650 29.872 85.204 81.658 62.529 57.968
#> E7 73.905 77.558 81.858 80.604 84.969 52.113 105.293 97.649 96.002
#> E8 100.157 97.479 94.464 96.274 77.354 36.108 82.634 111.548 64.764
#> E9 81.872 75.563 62.678 81.110 108.784 53.728 77.748 112.098 112.287
#> E5 E6 E7 E8 E9
#> E1 50.176 51.626 73.905 100.157 81.872
#> E10 50.470 70.689 77.558 97.479 75.563
#> E11 38.968 80.487 81.858 94.464 62.678
#> E12 61.391 72.650 80.604 96.274 81.110
#> E13 40.596 29.872 84.969 77.354 108.784
#> E14 66.827 85.204 52.113 36.108 53.728
#> E2 77.909 81.658 105.293 82.634 77.748
#> E3 80.074 62.529 97.649 111.548 112.098
#> E4 89.078 57.968 96.002 64.764 112.287
#> E5 0.000 19.178 79.253 78.328 112.467
#> E6 19.178 0.000 76.386 84.180 86.932
#> E7 79.253 76.386 0.000 82.828 66.229
#> E8 78.328 84.180 82.828 0.000 91.139
#> E9 112.467 86.932 66.229 91.139 0.000
#> ----------------------------------------------------------------------
#> Average = 74.522
#> Minimum = 13.415 between environments 5 and 3
#> Maximum = 112.467 between environments 14 and 10
#> ----------------------------------------------------------------------
#>
#>
#>
# }