AMMI based Stability Indices

Though,  AMMI biplots helps in visualizing the data, it does not provide a quantitative measure of stability, which is much suited for precise ranking of hybrids, in terms of yield stability. Hence, two quantitative inidices were introduced by Purchase et al. (2000) and Kang (1993) namely, AMMI stability value (ASV) and yield stability index (YSI). ASV is based on both IPCA 1 and IPCA2 scores, whereas the YSI is based on the sum of yield ranking and ASV ranking.

AMMI stability value

• IPCA1 SS/IPCA2 SS is the weight given to the IPCA1 value by dividing the IPCA1 sum of squares by the IPCA2 sum of squares.

• Irrespective of the sign, higher IPCA score means adaption of genotypes to a specific environment. Lower ASV scores indicate a more stable genotype across environments.

Yield stability index

• RASV is the rank of AMMI stability value and RY is the rank of the mean grain yield of genotypes across environments.

Estimation of ASV and YSI using RStudio

1. Data file format

• Type in the data as shown above. A minimum of three environment or season data is required. Here, I am taking a sample data for five genotypes with three replications grown across three environments.

• Save the file in the normal excel file format itself. Give an easy file name.

2. Import data file

• The procedure for data import has been given in the previous blog about RStudio. Please do refer to that if you have any sorts of doubts.

3. R Commands for AMMI quantification

3.1. Install package agricolae

install.packages(agricolae)

Note: We can put in the above command or just go directly to the install option ans search for the particular package. Upon selecting from the options, RStudio will automatically install the package.

3.2. Specifying the function AMMI along with the columns in excel file.

model<-with(stab,AMMI(env, geno, rep, ypp, console = FALSE))

• Type in the above command and make sure that the names specifying your columns are accurate without any spelling mistakes. The function is also saved in the name "model" for our convenience. "stab" is the file name given to the data file.

3.3. ANOVA for AMMI

model$ANOVA

• This gives you an ANOVA showing sources of variations namely, environment, genotypes, G*E and error along with their probability values.

3.4. Indexing AMMI

index.AMMI(model)

idx<-index.AMMI(model)

names(idx)

print(idx[order(idx[,3]),])

print(idx[order(idx[,4]),])

• index.AMMI function will calculate the values based on the formula discussed earlier. Those values are saved as "idx" for our convenience.

• names(idx) command will list out column names (Genotype number, ASV, YSI, rank of ASV, rank of YSI and mean value) whose data will be shown upon giving the next commands.

• To get crops with improved stability according to AMMI, "print(idx[order(idx[,3]),])" command is used. Here, the number "3" arranges the ASV index value in ascending order.

• To get crops with both better response and improved stability, "print(idx[order(idx[,4]),])" command is used. Here, the number "4" arranges the ASV index in descending order.

Note:

To select genotypes with better stability and better response for the character under consideration, we need to look into YSI in particular. 

"Hope it was useful for someone. Hoping to see you soon in next blog. Any improvisations in the commands are well received along with any criticism"