Computes the dissimilarity between environments based on several approaches. See the section details for more details.

env_dissimilarity(.data, env, gen, rep, resp)

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. Available at: http://www.ceres.ufv.br/ojs/index.php/ceres/article/view/2165/.

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{ mod <- env_dissimilarity(data_ge, ENV, GEN, REP, GY) 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 #> ---------------------------------------------------------------------- #> #> #>
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