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Genotype- by- environment interactions (GEI) refer to changes

in genotypic performance across dierent environments. e

presence of GEI in multi- environment trials is expressed either

as inconsistent responses of dierent genotypes (relative to oth-

ers) due to changes in genotypic rank, or as the absolute dier-

ence between genotypes without rank change (Crossa, 2012).

is eect can be used to assess quantitative traits of economic

importance—oen investigated in plant and animal breeding,

pharmacogenomics, genetic epidemiology, and conservation

biology research—including longevity, weight, height, biomass,

yield, and even disease resistance. e identication and subse-

quent selection of superior crop varieties in target environments

are important goals of agronomic and plant breeding studies

(Ahmadi etal., 2015; Vaezi etal., 2018). To identify superior va-

rieties across multiple environments, plant breeders undertake

trials across several years and locations, usually during the nal

developmental stages of a crop variety. e GEI eect reduces

the association observed between genotypic and phenotypic val-

ues and complicates the selection of the best variety (Ebdon and

Gauch, 2002). Interpreting the GEI eect in multi- environment

Applications in Plant Sciences 2019 7(1): e1211; http://www.wileyonlinelibrary.com/journal/AppsPlantSci © 2019 Pour- Aboughadareh etal. Applications

in Plant Sciences is published by Wiley Periodicals, Inc. on behalf of the Botanical Society of America. This is an open access article under the terms of the

Creative Commons Attribution-NonCommercial License, which permits use, distribution and reproduction in any medium, provided the original work is

properly cited and is not used for commercial purposes.

STABILITYSOFT: A new online program to calculate

parametric and non- parametric stability statistics for

crop traits

Alireza Pour-Aboughadareh1, Mohsen Yousean2, Hoda Moradkhani3, Peter Poczai4,6 , and Kadambot H. M. Siddique5

SOFTWARE NOTE

Manuscript received 15 August 2018; revision accepted 18

November 2018.

1 Department of Agronomy and Plant Breeding,College of

Agriculture and Natural Resources,University of Tehran, Karaj,

Iran

2 Dr. Hashtroudi Pre-University Center, Tehran, Iran

3 Department of Biotechnology and Plant Breeding,Kermanshah

Branch,Islamic Azad University, Kermanshah, Iran

4 Botany Unit,Finnish Museum of Natural History,University of

Helsinki, P.O. Box 7, Helsinki FI-00014, Finland

5 e UWA Institute of Agriculture,e University of Western

Australia, LB 5005, Perth, Western Australia 6001, Australia

6 Author for correspondence: peter.poczai@helsinki.

Citation: Pour-Aboughadareh, A., M. Yousean, H. Moradkhani,

P. Poczai, and K. H. M. Siddique. 2019. STABILITYSOFT: A

new online program to calculate parametric and non- parametric

stability statistics for crop traits. Applications in Plant Sciences

7(1): e1211.

doi:10.1002/aps3.1211

PREMISE OF THE STUDY: Access to improved crop cultivars is the foundation for successful

agriculture. New cultivars must have improved yields that are determined by quantitative

and qualitative traits. Genotype- by- environment interactions (GEI) occur for quantitative

traits such as reproductive tness, longevity, height, weight, yield, and disease resistance.

The stability of genotypes across a range of environments can be analyzed using GEI analysis.

GEI analysis includes univariate and multivariate analyses with both parametric and non-

parametric models.

METHODS AND RESULTS: The program STABILITYSOFT is online software based on JavaScript

and R to calculate several univariate parametric and non- parametric statistics for various

crop traits. These statistics include Plaisted and Peterson’s mean variance component (θi),

Plaisted’s GE variance component (θ(i)), Wricke’s ecovalence stability index (Wi

2), regression

coecient (bi), deviation from regression (Sdi

2), Shukla’s stability variance (σi

2), environmental

coecient of variance (CVi), Nassar and Huhn’s statistics (S(1), S(2)), Huhn’s equation (S(3) and

S(6)), Thennarasu’s non- parametric statistics (NP(i)), and Kang’s rank- sum. These statistics

are important in the identication of stable genotypes; hence, this program can compare

and select genotypes across multiple environment trials for a given data set. This program

supports both the repeated data across environments and matrix data types. The accuracy of

the results obtained from this software was tested on several crop plants.

CONCLUSIONS: This new software provides a user- friendly interface to estimate stability

statistics accurately for plant scientists, agronomists, and breeders who deal with large

volumes of quantitative data. This software can also show ranking patterns of genotypes and

describe associations among dierent statistics with yield performance through a heat map

plot. The software is available at https://mohsenyousean.com/stabilitysoft/.

KEY WORDS adaptability; phenotypic stability; quantitative traits; ranking method;

STABILITYSOFT.

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trials assists in the selection of stable varieties for a wide range of

environments (Vaezi etal., 2017).

Many statistical approaches have been proposed for using stabil-

ity analyses to interpret GEI, all of which have been based on uni-

variate and multivariate models (Flores etal., 1998). ere are two

major statistical groups for interpreting GEI by numerical analysis.

e rst group contains parametric methods such as the regression

coecient (bi; Finlay and Wilkinson, 1963), variance of deviations

from the regression (Sdi

2; Eberhart and Russell, 1966), Wricke’s eco-

valence stability index (Wi

2; Wricke, 1962), Shukla’s stability vari-

ance (σi

2; Shukla, 1972), environmental coecient of variance (CVi;

Francis and Kannenberg, 1978), Plaisted and Peterson’s mean vari-

ance component (θi; Plaisted and Peterson, 1959), Plaisted’s GE var-

iance component (θ(i); Plaisted, 1960), and the yield- stability index

(YSi; Kang, 1991). ese parametric statistics are primarily used to

assess genotype stability by relating observed genotypic responses

(e.g., yield, plant height, seed oil content) to a sample of environ-

mental conditions (e.g., rainfall, temperature, osmotic stress, soil

type). Parametric stability statistics have suitable properties under

certain statistical assumptions, including a normal distribution and

homogeneity of variance of the errors and their interaction eects.

However, parametric statistics may not be the best method for as-

sessing genotype stability if the assumptions are not met (Huhn,

1990). e second group of analytical methods includes non-

parametric methods such as Nassar and Huhn’s statistics (S(1), S(2);

Nassar and Huhn, 1987), Huhn’s equation (S(3) and S(6); Huhn, 1990),

ennarasu’s statistics (NP(i); ennarasu, 1995), Kang’s rank- sum

(KR or Kang; Kang, 1988), and Fox’s top rank (FOX or Top- rank;

Fox etal., 1990). Non- parametric statistics explain environments

and phenotypes relative to both biotic and abiotic factors. Non-

parametric statistics are a feasible alternative to parametric statis-

tics because their performance is based on ranked data (Nassar and

Huhn, 1987) and no assumptions are needed about the distribution

and homogeneity of the variance of the errors. Because each method

has its own merits and weaknesses, most breeding programs now

incorporate both parametric and non- parametric methods for the

selection of stable genotypes (Becker and Leon, 1988).

Parametric and non- parametric statistics are used by researchers

from dierent elds, but the lack of a user- friendly statistical package

makes these methods unavailable for agronomists and plant breed-

ers. A literature review revealed that other studies have attempted

to introduce codes for SAS (Piepho, 1999; Hussein et al., 2000;

Akbarpour etal., 2016; Dia etal., 2016) or R (Branco, 2015; Yaseen

and Eskridge, 2018) to calculate some of the stability indices. Table1

compares the available features and capabilities of these codes and

packages. Currently, researchers interested in applying stability statis-

tics are required to use several programs to obtain the desired results,

and further applications are needed to describe and visualize the

correlations between these parameters, which are crucial for the se-

lection of stable varieties. e general lack of platform- independent

soware capable of calculating all parametric and nonparametric sta-

tistics in one package motivated our work to create an online tool

(STABILITYSOFT) that is able to overcome these diculties by pro-

viding a user- friendly interface for the non- specialist.

METHODS AND RESULTS

STABLITYSOFT is written in JavaScript at the browser- side and

PHP at the server- side and is available as a Web application at

https://mohsenyousean.com/stabilityso/. Alternately, users can

access the source codes and data sets in GitHub (https://github.com/

pour-aboughadareh/stabilityso). Figure1 shows the information

ow in the STABILITYSOFT program. e soware can be used

online and is available in R programming language for advanced

users, which oers more exibility. e data used for testing the

soware are available online and can be used as example les to run

the program. e input le is in a standard Excel le format, which

is widely supported by other well- known soware. Our program

supports two data types: (1) repeated data across environments

(year, location, and year × location), with genotype i in year n and

location m (or environment j for one year or one location) and rep-

lication k, and (2) matrix data that includes genotypes (rows) and

environments (columns). e program rst calculates the average of

the objective trait for each genotype and then provides a data matrix

by environment. Based on the data matrix, the soware calculates

several univariate parametric and non- parametric statistics, namely

Plaisted and Peterson’s mean variance component (θi), Plaisted’s GE

variance component (θ(i)), Wricke’s ecovalence stability index (Wi

2),

regression coecient (bi), deviation from regression (Sdi

2), Shukla’s

stability variance (σi

2), environmental coecient of variance (CVi),

Nassar and Huhn’s non- parametric statistics (S(1), Z1, S(2), and Z2),

Huhn’s nonparametric statistics (S(3) and S(6)), ennarasu’s non-

parametric statistics (NP(i)), and Kang’s rank- sum. For further

description and details about these statistics see Appendix1. e

program also calculates ranking patterns of the genotypes, based on

each index. Aer following the instructions outlined on the website,

STABILITYSOFT produces a simple Excel output on two separate

sheets. e rst sheet (named “Statistics”) includes the average of

crop yield along with 16 parametric and non- parametric statistics,

and the second sheet (“Ranks”) consists of the ranking of each gen-

otype for each statistic along with sum of ranks (SR), average of sum

of ranks (ASR), and standard deviation (SD). It is important to note

that the rank of genotypes for the regression coecient (bi) is not

calculated because a signicance test (H0: B ≠ 1) must be conducted

to determine the stability using this parameter. For further details,

see Finlay and Wilkinson (1963). STABILITYSOFT also renders a

heat map plot, based on Pearson’s correlation coecients (Pearson,

1895), using Canvas tools (W3C, Cambridge, Massachusetts, USA)

to display the interrelationships between the stability statistics and

yield performance.

To test the program, we are providing two examples and data sets

gathered from ve yield trials in grass pea and barley (advanced and

doubled haploid lines) taken from Ahmadi etal. (2015), Khalili and

Pour- Aboughadareh (2016), and Vaezi etal. (2018). In the rst ex-

ample, we used grain yield (kg ha−1) for 14 advanced grass pea lines

grown in three Iranian semi- arid regions (Kermanshah, Gachsaran,

and Lorestan) during four consecutive years (2005–2008) (see

Ahmadi etal., 2015 for further details on growing conditions and

experimental design). In this example, only the averages of grain

yield across replications were used for calculations. e averages of

grain yield, along with 16 parametric and non- parametric statistics,

are shown in Appendices S1 and S2 together with signicance tests

for S(1) and S(2) statistics, Z1 and Z2, respectively. According to Nassar

and Huhn (1987), if Z1 and Z2 are less than the critical value of χ2, the

results show non- signicant dierences in rank stability among the

studied genotypes grown in the test environments (Huhn, 1990).

In the second sheet of the output le, which is named “Ranks,” the

rank of each genotype for each statistic is calculated (Appendix

S2). e calculated values indicate there are signicant dierences

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between tested lines in terms of grain yield, and ve lines (G3, G9,

G5, G7, and G12) could be identied with high- yield performance

across nine diverse environments. e calculated S(1), S(2), S(3), S(6),

NP(3), NP(4), and θi statistics showed G3 to be the most stable line,

but according to other parameters (S(3), S(6), NP(1), NP(2), NP(3), NP(4),

θ(i), Wi

2, bi, Sdi

2, σi

2, and CVi), line G6 was also shown to possess

desired stability traits. In these cases, the heat map plot function

of STABILITYSOFT based on Pearson’s correlation can be used to

further investigate the interrelationships among dierent stability

statistics. is showed that yield performance only positively cor-

relates with the regression slope (bi) (Appendix S3). Because iden-

tifying stable lines based on grain yield and sole parameters could

be problematic, as shown in this example, our program provides an

estimation of the average of the sum ranks (ASR) for all statistics to

select potentially superior stable lines. Accordingly, a genotype with

low ASR value can be selected as a superior stable genotype. Based

on our results (Appendix S2), lines G6 (ASR = 3.44; SD = 3.01) fol-

lowed by G3 (ASR = 5.69; SD = 5.13) and G11 (ASR = 4.50; SD =

4.50) could be selected as stable lines for cultivation in the semi- arid

regions of Iran.

In the second example, we tested the soware using grain yield

data from a two- year (2016–2017) barley trial using 18 genotypes

grown at four semi- arid regions in Iran (Gonbad, Gachsaran,

Moghan, and Lorestan). At each location, the experimental layout

was a randomized complete block design with four replications.

Each experimental plot consisted of six rows with 17.5- cm row

spacing. Each location received optimal agricultural practices, with

total grain yield for each genotype estimated at harvest. e data le

is available on GitHub as “Example5.xlsx,” and the results are sum-

marized in Appendix S4. Grain yield (Y) ranged from 1820 to 2415

kg ha−1 (average 1985 kg ha−1), which was used as the rst statis-

tic for assessing genotypes. G2 had the highest yield performance,

TABLE1. Statistical capacity and available features of STABILITYSOFT relative to other codes and packages.

Statistical capacity/

Features

SAS codes R packages

STABILITYSOFTPiepho (1999)

Hussein etal.

(2000)

Akbarpour

etal. (2016)

Dia etal.

(2016) Branco (2015)

Yaseen and

Eskridge (2018)

Statistic

Mean variance

component

X X

GE variance

component

X X

Wricke’s ecovalence

stability index

X X X X

Regression coeﬃcient X X X

Deviation from

regression

X X X X

Shukla’s stability

variance

X X X X X

Environmental

coeﬃcient of

variance

X X X X

Nassar and Huhn’s

non- parametric

statistics and Huhn’s

statistics

X X X X

Thennarasu’s non-

parametric statistics

X X X

Kang’s rank- sum X X X X

Correlation

coeﬃcients

X

Ranking pattern of

genotypes through

all statistics

X

Calculation of

statistics based on

both types of data

(row data and matrix

mean data)

X

Features

Windows support X X X X X X X

Unix/Linux support X X X X X X X

Mac OS support X X X

Portable (without

installation)

X

GUI (graphical user

interface)

X

Oﬄine usage

capability

X X X X X X

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followed by G13, G5, G1, and G18 (2415, 2246, 2125, 2054, and

2053 kg ha−1, respectively). Two parametric statistics (Wi

2 and σi

2)

showed that genotypes G6 and G18 had the lowest values and are,

therefore, deemed stable lines. According to S(1), S(2), S(3), and S(6),

genotypes G2, G6, G7, and G13 were selected as desirable geno-

types. Two statistics (NP(3) and NP(4)) showed a similar trend, such

that G2 and G13 were selected as stable genotypes. Selection based

on the KR statistic orders the remaining genotypes as G18 > G13 >

G1 > G16. e heat map plot based on Pearson’s correlation revealed

that S(1), S(2), S(3), and S(6) were positively and signicantly correlated

with each other and with NP(1), NP(3), and NP(4) (Appendix S5), and

grain yield had a signicant positive correlation with bi and CVi.

Moreover, grain yield also had a positive association with θi, Wi

2,

and σi

2, but a negative association with NP(2), NP(3), NP(4), S(1), S(2),

S(3), S(6), and KR. Two statistics (Wi

2 and σi

2) were negatively associ-

ated with θ(i). Based on these associations and the use of the ranking

method integrated in STABILITYSOFT, we were able to identify the

six most stable genotypes (G18, G13, G12, G6, G2, and G1), which

had the lowest ASR values (4.81, 4.88, 5.13, 5.63, 6.75, and 7.69,

respectively; Appendix S6). With respect to yield performance, two

high- yielding genotypes (G1 [2054 kg ha−1] and G2 [2415 kg ha−1])

with relatively low ASR values are ideally suited for introduction

to desirable growth environments, whereas two genotypes (G13

[2246 kg ha−1] and G18 [2053 kg ha−1]) with high and middle yield

performance along with low ASR values can be introduced to semi-

arid or similar regions of Iran. Furthermore, genotypes G6 (1840

kg ha−1) and G12 (1923 kg ha−1), which have acceptable ASR val-

ues and low grain yields, were identied as low- yielding genotypes,

hence these genotypes can be introduced to marginal cultivation

environments.

CONCLUSIONS

We developed an online soware to calculate several parametric

and non- parametric stability statistics that are important in the

identication of stable crop genotypes. Some statistical programs

are available for stability analyses, but unlike our program they are

not platform independent and cannot calculate all the required

statistics. In addition to the favorable features listed in Table 1,

STABILITYSOFT has the following advantages over other R and

SAS packages: (1) it directly calculates dierent parametric and

non- parametric statistics along with Pearson’s correlation with

high accuracy; (2) it is a cross- platform soware that needs no

additional downloads or installation, calculations are performed

on PHP servers, and users are not limited to the processing power

of their computers when using large data sets; (3) unlike other

codes based on SAS and R packages, which require additional user

knowledge of these packages, STABILITYSOFT has a web- based

user interface; and (4) it is compatible with all major browsers

(e.g., Google Chrome, Mozilla Firefox). In conclusion, we expect

that this soware will be useful for analyzing essential data for

stability studies related to agronomy and plant breeding. Our

program is also able to visualize the interrelationships between

dierent indices, which is crucial for selecting stable varieties.

STABILITYSOFT will be helpful for agronomists and plant breed-

ers who deal with large volumes of quantitative data and require

user- friendly soware to explore GEI and accurately calculate sta-

bility parameters.

ACKNOWLEDGMENTS

e authors thank Dr. Mohsen Shekarbaigi (Department of

Mathematics, Imam Khomeini International University) for his as-

sistance with the dissection of mathematical formulae, Prof. Jafar

Ahmadi and Dr. Valiollah Youse (Department of Genetics and

Plant Breeding, Imam Khomeini International University) for their

suggestions, and Dr. Behroz Vaezi and Dr. Marouf Khalili for pro-

viding the data sets for testing this soware.

DATA ACCESSIBILITY

e source code used to develop STABILITYSOFT is available

on GitHub (https://github.com/pour-aboughadareh/stabilityso).

STABILITYSOFT is available at https://mohsenyousean.com/

stabilityso/.

SUPPORTING INFORMATION

Additional Supporting Information may be found online in the

supporting information tab for this article.

FIGURE 1. Information ow diagram for the STABILITYSOFT software

tool.

PHP (server-side)

Extract data and genotype labels from input file

Make Excel file from statistical analysis section

Draw heatmap plot from correlation matrix using Canvas tools

Download output file as an Excel file

Display correlation plot

To start calculating, the data file should be provided in Excel format

Calculation of parametric and non-parametric statistics for each genotype

Calculation of ranks of all statistics except bi statistics for each genotype

Calculation of correlation matrix from input data file

Data Input:

Statistical analysis:

JavaScript (client-side)

JavaScript (client-side)

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APPENDIX S1. Parametric and non- parametric stability statistics

calculated with STABILITYSOFT for grain yield (kg ha−1) of 14

grass pea advanced lines across nine dierent environments in Iran.

APPENDIX S2. Ranks of parametric and non- parametric stability

statistics calculated with STABILITYSOFT for grain yield (kg ha−1) of

14 grass pea advanced lines across nine dierent environments in Iran.

APPENDIX S3. Heat map plot rendered based on Pearson’s corre-

lation analysis for Example 1. See Appendix 1 for full denitions of

statistics. θi = mean variance component; θ(i) = GE variance com-

ponent; Wi

2 = Wricke’s ecovalence stability index; bi = regression

coecient; Sdi

2 = deviation from regression; σi

2 = Shukla’s stability

variance; CVi = environmental coecient of variance; S(1) and S(2) =

Nassar and Huhn’s non- parametric statistics; S(3) and S(6) = Huhn’s

non- parametric statistics; NP(1–4) = ennarasu’s non- parametric

statistics; KR = Kang’s rank- sum; Y = yield.

APPENDIX S4. Parametric and non- parametric stability statistics

calculated with STABILITYSOFT for grain yield (kg ha−1) of 18

barley genotypes across four dierent environments in Iran.

APPENDIX S5. Heat map plot rendered based on Pearson’s corre-

lation analysis for Example 2. See Appendix 1 for full denitions of

statistics. θi = mean variance component; θ(i) = GE variance com-

ponent; Wi

2 = Wricke’s ecovalence stability index; bi = regression

coecient; Sdi

2 = deviation from regression; σi

2 = Shukla’s stability

variance; CVi = environmental coecient of variance; S(1) and S(2) =

Nassar and Huhn’s non- parametric statistics; S(3) and S(6) = Huhn’s

non- parametric statistics; NP(1–4) = ennarasu’s non- parametric

statistics; KR = Kang’s rank- sum; Y = yield.

APPENDIX S6. Ranks of parametric and non- parametric stability sta-

tistics calculated with STABILITYSOFT for grain yield grain yield (kg

ha−1) of 18 barley genotypes across four dierent environments in Iran.

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Applications in Plant Sciences 2019 7(1): e1211 Pour- Aboughadareh etal.—STABILITYSOFT: Online stability statistical software • 6 of 6

http://www.wileyonlinelibrary.com/journal/AppsPlantSci © 2019 Pour- Aboughadareh etal.

APPENDIX 1. Description of stability statistics calculated for the crop traits by STABILITYSOFT.

Statistic Symbol Denition

Mean variance component θiPlaisted and Peterson (1959) proposed the variance component of genotype- by- environment

interactions (GEI) for interactions between each of the possible pairs of genotypes. This

statistic considers the average of the estimate for all combinations with a common genotype

to be a measure of stability. Accordingly, the genotypes that show a lower value for θi are

considered more stable.

GE variance component θ(i) This statistic is a modiﬁed measure of stability parameter. In this approach, the ith genotype is

deleted from the entire set of data and the GEI variance from this subset is the stability index

for the ith genotype. According to this statistic, the genotypes that show higher values for

the (i) are considered more stable.

Wricke’s ecovalence stability index Wi

2Wricke (1962) proposed the concept of ecovalence as the contribution of each genotype to

the GEI sum of squares. The ecovalence (Wi) of the ith genotype is its interaction with the

environments, squared and summed across environments. Thus, genotypes with low values

have smaller deviations from the mean across environments and are more stable.

Regression coeﬃcientabiThe regression coeﬃcient (bi) is the response of the genotype to the environmental index

that is derived from the average performance of all genotypes in each environment (Finlay

and Wilkinson, 1963). If bi does not signiﬁcantly diﬀer from 1, then the genotype is adapted

to all environments. A bi > 1 indicates genotypes with higher sensitivity to environmental

change and greater speciﬁcity of adaptability to high- yielding environments, whereas a bi <

1 describes a measure of greater resistance to environmental change, thereby increasing the

speciﬁcity of adaptability to low- yielding environments.

Deviation from regression Sdi

2In addition to the regression coeﬃcient, variance of deviations from the regression (Sdi

2) has

been suggested as one of the most- used parameters for the selection of stable genotypes.

Genotypes with an Sdi

2 = 0 would be most stable, while an Sdi

2 > 0 would indicate lower

stability across all environments. Hence, genotypes with lower values are the most desirable

(Eberhart and Russell, 1966).

Shukla’s stability variance σi

2Shukla (1972) suggested the stability variance of genotype i as its variance across environments

after the main eﬀects of environmental means have been removed. According to this statistic,

genotypes with minimum values are intended to be more stable.

Environmental coeﬃcient of variance CViThe coeﬃcient of variation is suggested by Francis and Kannenberg (1978) as a stability statistic

through the combination of the coeﬃcient of variation, mean yield, and environmental

variance. Genotypes with low CVi, low environmental variance (EV), and high mean yield are

considered to be the most desirable.

Nassar and Huhn’s non- parametric

statistics and Huhn’s statisticsb

S(1)

S(2)

S(3)

S(6)

Huhn (1990) and Nassar and Huhn (1987) suggested four non- parametric statistics: (1) S(1), the

mean of the absolute rank diﬀerences of a genotype over all tested environments; (2) S(2),

the variance among the ranks over all tested environments; (3) S(3), the sum of the absolute

deviations for each genotype relative to the mean of ranks; and (4) S(6), the sum of squares of

rank for each genotype relative to the mean of ranks. To compute these statistics, the mean

yield data have to be transformed into ranks for each genotype and environment, and the

genotypes are considered stable if their ranks are similar across environments. The lowest

value for each of these statistics reveals high stability for a certain genotype.

Thennarasu’s non- parametric statistics NP(1)

NP(2)

NP(3)

NP(4)

Four NP(1–4) statistics are a set of alternative non- parametric stability statistics deﬁned by

Thennarasu (1995). These parameters are based on the ranks of adjusted means of the

genotypes in each environment. Low values of these statistics reﬂect high stability.

Kang’s rank- sum Kang or KR Kang’s rank- sum (Kang, 1988) uses both yield and σi

2 as selection criteria. This parameter gives a

weight of 1 to both yield and stability statistics to identify high- yielding and stable genotypes.

The genotype with the highest yield and lower σi

2 is assigned a rank of 1. Then, the ranks of

yield and stability variance are added for each genotype, and the genotypes with the lowest

rank- sum are the most desirable.

aTo determine stability using this parameter, the signiﬁcance test (H0: B ≠ 1) must be conducted. For more detail, see Finlay and Wilkinson (1963).

bIn addition to S(i) statistics, two signiﬁcance tests for S(1) and S(2), namely Z1 and Z2, are calculated.