Use of AMMIWINS

Before using AMMIWINS, first run MATMODEL in fitting mode to perform AMMI analysis. Be sure to request at least as many axes as have any likelihood of contributing to predictive accuracy. Also, request the machine-readable output file from MATMODEL, which becomes the input file for AMMIWINS. If the yield trial is replicated, one may also run MATMODEL in validation mode to diagnose the most predictively accurate member of the AMMI family for a given dataset. One way or another, the best AMMI model must be diagnosed, ordinarily by the criterion of greatest predictive accuracy, because AMMIWINS will ask the user which AMMI model to use in its calculations. After producing the MATMODEL machine-readable file and diagnosing the best AMMI model, one is ready to use AMMIWINS.

This program is invoked from a DOS prompt by typing "AMMIWINS" and hitting the enter key. It first asks for the name of the input file, which had been produced previously as a machine-readable output file from MATMODEL. It then asks for the name of the output file. If the intended directory for the input or output file is not the current default directory, include the necessary path with the filename.

Incidentally, some nice conventions for these filenames are as follows. For the yield data, use the name data.DAT where "data" stands for a distinctive four-character name for a given dataset and the extension "DAT" signifies a dataset in MATMODEL input format, such as NY88.DAT. Then use the name data.MRn for the MATMODEL machine-readable output file with n AMMI axes, such as NY88.MR5 for the machine-readable results for the AMMI-5 model applied to dataset NY88.DAT. Finally, use the name data.WNS for the AMMIWINS output file, such as NY88.WNS for the AMMIWINS analysis of NY88.DAT.

The program then reads the beginning of the input file and reminds the user how many AMMI axes have been supplied by this file. The user is then asked whether to perform mega-environment analysis for each of the possible AMMI models from 1 to the maximum possible. For example, supplied 5 AMMI axes, the user is offered each and every possibility from 1 to 5. The response to each question is either "Y" for yes or "N" for no. Ordinarily, the user selects only one model, the one diagnosed previously to be the most predictively accurate member of the AMMI family for the data at hand. However, if desired, other possibilities can also be explored.

AMMIWINS then undertakes analysis of each requested model. For each and every model, the input requested from the user is the same, as explained momentarily. However, the amount of output differs, depending on which model has been requested. For AMMI-1 and AMMI-2, some extensive results or graphs are possible that are not possible for higher models. The AMMIWINS interactions with the user may be explained by saying in turn what happens for AMMI-1, for AMMI-2, and for higher-order models.

For AMMI-1, the analysis proceeds as follows. The list of mega-environments is written to the screen. Each mega-environment is characterized by its winning genotype, which is identified by the genotype's number and four-character brief name. For each mega-environment, its number of wins is given, as well as its expected yield averaged over the environments it wins. Yields are calculated according to the AMMI-1 model, rather than using the raw data. For comparison, the average expected yield for the overall main-effect winner is given and the yield boost of the mega-environment winner over the overall winner is expressed as a percentage.

After this table appears on the screen, the user is invited to request elimination of minor winners. A winner could be deemed minor because of one or both of two potential problems: (1) it wins very few environments, or (2) its yield boost over the overall main-effect winner is negligible. There are two methods for specifying which genotypes to eliminate, if any. The genotypes can be identified by number, one at a time, ending the list with 0; merely entering 0 eliminates none. Or, enter a negative number -N to signal automatic elimination of all genotypes with N or fewer wins. Incidentally, in the unlikely event that so many winners are present that some disappear off the top of the screen, to see the entire list, the user may need to finish the analysis, go to the output file that preserves this list of winners in its entirety, make these decisions about which minor winners to eliminate, and then run AMMIWINS again with these decisions already noted.

If any minor genotypes are eliminated, each environment whose original winning genotype was eliminated is reassigned to that genotype among the remaining winners that gives the highest yield according to the AMMI model. This method precludes the possibility of annoying emergence of further minor winners that could happen were all remaining genotypes considered, rather than just the roster of remaining winners. The revised, shorter table of mega-environments then appears on the screen.

During AMMIWINS analysis, only the table of mega-environments goes to the screen as just explained. For the AMMI-1 model, however, more extensive results are written to the output file.

The output file first identifies the input and output filenames. Then results are given for genotypes, starting with listing the genotype winners and their nominal yields at three values of the environment IPCA 1 scores: the positive extreme, zero, and the negative extreme. Then all genotype winners are listed that win anywhere in the environment IPCA 1 parameter space, anywhere from minus infinity to plus infinity, whether or not the dataset actually contains any environments with IPCA 1 scores in the domain of a given winner. This list begins with the genotype that wins for extremely large positive values for the environment IPCA 1 score, which is automatically that genotype with the largest IPCA 1 score. Likewise, this list ends with the genotype that wins for extremely large negative values for the environment IPCA 1 score, which is automatically that genotype with the smallest IPCA 1 score. Necessarily, these are two different genotypes, so this roster of genotype winners over this entire mathematical space must have at least two entries. AMMIWINS finds all of these winners and calculates the environment IPCA 1 switch value at which each winner gives way to the next winner. The nominal yield is also given at each switch value. In addition, nominal yields are also listed at the positive and negative extremes (of the actual environments) and at zero. At this environment IPCA 1 score of 0, the automatic winner is the overall main-effect winner. Again, the two genotypes with the positive and negative extremes of IPCA 1 scores are automatic winners, and the genotype with the largest main effect is an automatic winner, but the main effect winner may possibly be the same genotype as a genotype with either the positive or negative extreme of IPCA 1 scores, so there must always be at least two genotype winners over the entire mathematical space (although it is also possible to have all actual environments in the domain of only one genotype winner).

Next the AMMI-1 output gives results for mega-environments. This table is identical to the one that appeared on screen and was explained above. Then the output identifies genotypes eliminated by the user's requests, either listing such genotypes, or else noting that none were eliminated. If any winners were eliminated, the results for genotypes and results for mega-environments are repeated after eliminations.

Finally, the AMMI-1 output gives results for environments (after eliminations, if any). Each mega-environment is identified by its genotype winner, giving its number of wins and its yield boost over the main-effect winner. Then each environment in the mega-environment is listed, giving its number and four-character brief name, IPCA 1 score, expected yield, and yield boost. The entire list includes every environment and is ordered by IPCA 1 scores, running from the largest to the smallest environment IPCA 1 score. Of course, if that genotype with the highest main effect is among the winners, as is usually the case, then its yield boost over the main-effect winner (namely, itself) is zero.

After the above information has been written to the output file, the user is informed that AMMI-1 analysis has been completed. If this was the only analysis requested, AMMIWINS also terminates. If not, the program progresses to the next analysis.

If AMMI-2 analysis is requested, its output is as follows. The sorts of results that can be calculated for genotypes in AMMI-2 analysis are rather different than in AMMI-1 analysis. AMMIWINS notes the minimum and maximum environment scores for axis 1 and for axis 2, and places a 70x70 grid of points over this space (rather than over the entire mathematical space from minus infinity to plus infinity on both axes). For each of these 4900 pixels, AMMIWINS computes the AMMI-2 expected yield for every genotype and determines the winner. The winners are then listed in order from most to fewest wins. Expected yields and yield boosts over the main-effect winner are tabulated. The AMMI-2 model is also shown by a grid of 70x70 pixels, showing the winning genotype in each pixel. Each winner's domain has the shape of an irregular polygon (Gauch 1992:222). Next, results are given for mega-environments. This table is just the same as described previously for AMMI-1, and this table goes to both the output file and the screen. Then just like before, the user is allowed to eliminate minor winners, and if any winners are eliminated, then results for mega-environments are repeated after eliminations. Finally, results are given for each mega-environment, listing its environments with their expected yields and yield boosts.

If AMMI-3 or any higher models is requested, its output is as follows. Unlike AMMI-1 and AMMI-2 outputs, no results are presented for genotypes because no lists or two-dimensional graphs can convey the required high-dimensional information. The mega-environment results are like those for AMMI-2, listing the mega-environments in order from those with the most to the fewest wins, and writing results to both the output file and the screen. As usual, the user is allowed to request elimination of minor winners, and if any winners are eliminated, then the mega-environment results are repeated after eliminations. Finally, results are tabulated for each mega-environment, listing its environments and their expected yields and yield boosts.

After completing all requested analyses, the AMMIWINS program terminates. The following sample output exemplifies the above description of program utilization.