Calculates stability coefficients for genotype-by-environment data (R.W. Payne).

### Options

`PRINT` = string tokens |
Controls printed output (`means` , `stability` , `sortedstability` , `quantiles` ); default `stab` , `quan` |
---|---|

`METHOD` = string tokens |
Methods to use to calculate stability (`superiority` , `static` , `wricke` , `ranks` ); default `supe` |

`BESTMETHOD` = string token |
How to define the best genotype (`minimum` , `maximum` ); default `maxi` |

`PLOT` = string tokens |
What graphs to plot (`stability` ); default `*` i.e. none |

`NBEST` = string tokens |
Number of best genotypes to print in tables of sorted stability coefficients; default `*` i.e. print all of them |

`DIRECTION` = string token |
Direction to sort tables of sorted stability coefficients (`ascending` , `descending` ); default `asce` |

`PERCENTQUANTILES` = scalar or variate |
Percentage points for which quantiles are required; default `!(50,5,1,0.1)` |

`NTIMES` = scalar |
Number of permutations to make; default 999 |

`BLOCKSTRUCTURE` = formula |
Model formula defining any blocking to consider during the permutation test; default none |

`EXCLUDE` = factors |
Factors in the block formula whose levels are not to be andomized in the permutation test |

### Parameters

`Y` = variates |
Yields (or other measurements) made on the genotypes in the environments |
---|---|

`GENOTYPES` = factors |
Genotype corresponding to each yield |

`ENVIRONMENTS` = factors |
Environment where each yield was recorded |

`SEED` = scalar |
Seed for the random number generator used to make the permutations; default 0 continues from the previous generation or (if none) initializes the seed automatically |

`STABILITY` = tables or pointers |
Saves stability coefficients |

`QUANTILES` = tables or pointers |
Saves quantiles of the stability coefficients |

`TITLE` = texts |
Overall title for the graphs; default `*` i.e. none |

### Description

To assess new genotypes of plants, trials are often carried out in a range of environments. Yields and other measurements will then be made, and analyses carried out (e.g. using `REML`

) to see how well the genotypes perform. These analyses allow you to determine which genotypes are best overall, or at a specific site. However, they do not consider how reliable, or stable, their yields may be overall. `GESTABILITY`

allows you to calculate several stability coefficients to assess this. These are selected using the `METHOD`

option.

The `superiority`

setting of the `METHOD`

option calculates the cultivar-superiority measure of Lin & Binns (1988). For each genotype, this is the sum of the squares of the differences between its mean in each environment and the mean of the best genotype there, divided by twice the number of environments. The `BESTMETHOD`

option specifies whether the best genotype is defined to be the one with the maximum mean yield or the one with the minumum mean yield. (You would want to take the minimum as best, for example, if the “yields” were disease scores.) Genotypes with the smallest values of the superiority measure tend to have better yields and to be more stable.

The `ranks`

setting gives the mean and variance of the ranks of each genotype across the environments where it occurs, as well as the rank-difference coefficient of Nassar & Huehn (1987). For each genotype, this is the sum of the absolute differences between its ranks in all the pairs of environments where it occurs. This assesses the consistency of the response of each genotype with respect to the other genotypes.

The `static`

setting calculates the static stability coefficient. For each genotype, this is defined as the variance between its means in the various environments. This provides a measure of the consistency of the genotype (but without taking account of how good it is).

The `wricke`

setting gives Wricke’s (1962, 1964) ecovalence stability coefficient. This is the contribution of each genotype, to the genotype-by-environment sum of squares, in an unweighted analysis of the genotype-by-environment means. A low value indicates that the genotype responds in a consistent manner to changes in environment.

The yields (or other measurements) are specified, in a variate, using the `Y`

parameter. The `GENOTYPES`

parameter specifies a factor to indicate the genotype that supplied each yield, and the `ENVIRONMENTS`

parameter specifies a factor to indicate the environment where it was grown. `GESTABILITY`

prefers to be given all the data, not just the mean yield. It can then do some permutation tests to help you assess the coefficients.

In the permutation tests, `GESTABILITY`

randomly permutes the original data within each environment, and calculates and stores the coefficients. The `NTIMES`

option controls how many permutations are done; so its default of 999 gives 1000 sets of coefficients (the set from the original unpermuted data, plus the 999 permuted data sets). `GESTABILITY`

constructs a variate `Group`

to indicate genotypes that occurred in exactly the same sets of environments: you cannot make comparisons between genotypes that occurred at different sites as these will have been competing with different genotypes across their environments. `GESTABILITY`

combines the permuted and original coefficients within each group, and calculates quantiles over the combined set of values. A coefficient can then be taken as significant at a particular level if its coefficient is greater than the corresponding quantile. The `PERCENTQUANTILES`

option specifies a variate or scalar to define which quantiles are calculated; the default gives 50%, 5%, 1% and 0.1%. The `SEED`

parameter defines the seed used to generate the random numbers used to generate the permutations for each `Y`

variate. The default value of zero initializes the seed at random if this is the first time that the Genstat randomization routines have been used in the current job; otherwise it continues the existing sequence of random numbers.

If the data come from a designed experiment, you may need to use the `BLOCKSTRUCTURE`

option to specify a block model to define how to do the randomization. The `EXCLUDE`

option can then restrict the randomization so that one or more of the factors in the block model is not randomized. See the `RANDOMIZE`

directive for further details.

The `PRINT`

option controls the printed output. The `means`

setting prints the overall means of the genotypes. The `stability`

setting prints the stability coefficients. These are accompanied by the quantiles from the permutation tests if the `quantiles`

setting is also specified. The `sortedstability`

setting prints the stability coefficients in a sorted order, as specified by the the `DIRECTION`

option. The default, ascending, order prints the most stable genotypes first. The `NBEST`

option can be set to control the number of genotypes that are included; by default they are all printed.

The `PLOT`

option can be set to `stability`

to plot the stabilities against the mean responses. This provides a way of simultaneously assessing the general effectiveness and stability of the genotypes. You can supply a title for the plots using the `TITLE`

parameter.

The `STABILITY`

parameter allows you to save the coefficients selected by the `METHOD`

option. If only the cultivar-superiority measure has been selected, these are saved in a table. Otherwise a pointer of tables is saved with elements labelled by their names: `'superiority'`

, `'static'`

, `'wricke'`

, `'rankmeandifference'`

, `'rankmean'`

and `'rankvariance'`

. Similarly the `QUANTILES`

parameter can save the quantiles. If there is a single percentile, a table is saved for each coefficient. If there are several, a pointer of tables is saved for each one.

Options: `PRINT`

, `METHOD`

, `BESTMETHOD`

, `PLOT`

, `NBEST`

, `DIRECTION`

, `PERCENTQUANTILES`

, `NTIMES`

, `BLOCKSTRUCTURE`

, `EXCLUDE`

.

Parameters: `Y`

, `GENOTYPES`

, `ENVIRONMENTS`

, `SEED`

, `STABILITY`

, `QUANTILES`

. `TITLE`

.

### Action with `RESTRICT`

`GESTABILITY`

takes account of any restrictions on `Y`

, `GENOTYPES`

or `ENVIRONMENTS`

.

### References

Lin, C.S. & Binns, M.R. (1988). A superiority performance measure of cultivar performance for cultivar x location data. *Canadian Journal of Plant Science*, 68, 193-198.

Nassar, R. & Huehn, M. (1987). Studies on estimation of phenotype stability: tests of significance for nonparametric measures of phenotype stability. *Biometrics*, 43, 45-53.

Wricke, G. (1962). Uber eine methode zur erfassung der okologischen streubreite in feldversuchen. *Zeitschrift Fur Pflanzenzuchtung*, 47, 92-96.

Wricke, G (1964) Zur berechnung der okovalenz bei sommerweizen und hafer. *Zeitschrift Fur Pflanzenzuchtung*, 52, 127-138.

### See also

Procedures: `AMMI`

, `GGEBIPLOT`

, `RFINLAYWILKINSON`

, `DBIPLOT`

.

Commands for: REML analysis of linear mixed models.

### Example

CAPTION 'GESTABILITY example'; STYLE=meta FACTOR [NVALUES=72; LEVELS=6] Site FACTOR [NVALUES=72; LABELS=!t(a,b,c,d)] Variety GENERATE Site,Variety VARIATE [NVALUES=72] Y READ Y 7.268 7.132 8.735 11.461 9.736 10.760 6.684 7.344 8.580 9.141 8.625 8.272 8.781 8.103 8.064 8.885 10.703 9.884 10.740 10.067 8.489 8.549 11.046 8.775 7.037 7.026 7.084 10.745 9.577 8.923 7.735 9.263 7.410 8.660 8.331 7.171 8.916 7.418 8.61 11.861 11.294 11.969 9.061 9.186 9.241 10.751 9.528 9.438 6.646 2.092 5.652 6.691 6.644 7.728 5.983 5.047 4.655 6.962 5.614 6.530 1.370 2.213 0.689 0.476 2.836 2.121 4.048 1.766 2.868 1.702 4.116 2.775 : GESTABILITY [METHOD=superiority,ranks] Y; GENOTYPES=Variety;\ ENVIRONMENTS=Site; SEED=475739