STABILITYSOFT: A new online program to calculate parametric and non‐parametric stability statistics for crop traits

Abstract

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 fitness, 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 (θ i ), Plaisted's GE variance component (θ (i) ), Wricke's ecovalence stability index (W i 2 ), regression coefficient (b i ), deviation from regression (S di 2 ), Shukla's stability variance (σ i 2 ), environmental coefficient of variance (CV i ), 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 identification 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 different statistics with yield performance through a heat map plot. The software is available at https://mohsenyousefian.com/stabilitysoft/.

Full text

1 of 6
Genotype- by- environment interactions (GEI) refer to changes
in genotypic performance across dierent environments. e
presence of GEI in multi- environment trials is expressed either
as inconsistent responses of dierent genotypes (relative to oth-
ers) due to changes in genotypic rank, or as the absolute dier-
ence between genotypes without rank change (Crossa, 2012).
is eect can be used to assess quantitative traits of economic
importance—oen investigated in plant and animal breeding,
pharmacogenomics, genetic epidemiology, and conservation
biology research—including longevity, weight, height, biomass,
yield, and even disease resistance. e identication and subse-
quent selection of superior crop varieties in target environments
are important goals of agronomic and plant breeding studies
(Ahmadi etal., 2015; Vaezi etal., 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 eect 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 eect in multi- environment
Applications in Plant Sciences 2019 7(1): e1211; http://www.wileyonlinelibrary.com/journal/AppsPlantSci © 2019 Pour- Aboughadareh etal. 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 Yousean2, 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. Yousean, 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
coecient (bi), deviation from regression (Sdi
2), Shukla’s stability variance (σi
2), environmental
coecient 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 identication 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 dierent statistics with yield performance through a heat map
plot. The software is available at https://mohsenyousean.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 etal., 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 etal., 1998). ere are two
major statistical groups for interpreting GEI by numerical analysis.
e rst group contains parametric methods such as the regression
coecient (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 coecient 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 eects.
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 etal., 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 dierent 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 etal., 2016; Dia etal., 2016) or R (Branco, 2015; Yaseen
and Eskridge, 2018) to calculate some of the stability indices. Table1
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
soware 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 diculties 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://mohsenyousean.com/stabilityso/. Alternately, users can
access the source codes and data sets in GitHub (https://github.com/
pour-aboughadareh/stabilityso). Figure1 shows the information
ow in the STABILITYSOFT program. e soware can be used
online and is available in R programming language for advanced
users, which oers more exibility. e data used for testing the
soware 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 soware. 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 soware 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 coecient (bi), deviation from regression (Sdi
2), Shukla’s
stability variance (σi
2), environmental coecient 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 Appendix1. e
program also calculates ranking patterns of the genotypes, based on
each index. Aer 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 coecient (bi) is not
calculated because a signicance 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 coecients (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 etal. (2015), Khalili and
Pour- Aboughadareh (2016), and Vaezi etal. (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 etal., 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 signicance 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- signicant dierences 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 signicant dierences

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between tested lines in terms of grain yield, and ve lines (G3, G9,
G5, G7, and G12) could be identied 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 dierent 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 soware 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,
TABLE1. Statistical capacity and available features of STABILITYSOFT relative to other codes and packages.
Statistical capacity/
Features
SAS codes R packages
STABILITYSOFTPiepho (1999)
Hussein etal.
(2000)
Akbarpour
etal. (2016)
Dia etal.
(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 signicantly correlated
with each other and with NP(1), NP(3), and NP(4) (Appendix S5), and
grain yield had a signicant 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 identied as low- yielding genotypes,
hence these genotypes can be introduced to marginal cultivation
environments.
CONCLUSIONS
We developed an online soware to calculate several parametric
and non- parametric stability statistics that are important in the
identication 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 dierent parametric and
non- parametric statistics along with Pearson’s correlation with
high accuracy; (2) it is a cross- platform soware 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 soware 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
dierent 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 soware 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 soware.
DATA ACCESSIBILITY
e source code used to develop STABILITYSOFT is available
on GitHub (https://github.com/pour-aboughadareh/stabilityso).
STABILITYSOFT is available at https://mohsenyousean.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 dierent 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 dierent environments in Iran.
APPENDIX S3. Heat map plot rendered based on Pearson’s corre-
lation analysis for Example 1. See Appendix 1 for full denitions of
statistics. θi = mean variance component; θ(i) = GE variance com-
ponent; Wi
2 = Wricke’s ecovalence stability index; bi = regression
coecient; Sdi
2 = deviation from regression; σi
2 = Shukla’s stability
variance; CVi = environmental coecient 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 dierent environments in Iran.
APPENDIX S5. Heat map plot rendered based on Pearson’s corre-
lation analysis for Example 2. See Appendix 1 for full denitions of
statistics. θi = mean variance component; θ(i) = GE variance com-
ponent; Wi
2 = Wricke’s ecovalence stability index; bi = regression
coecient; Sdi
2 = deviation from regression; σi
2 = Shukla’s stability
variance; CVi = environmental coecient 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 dierent environments in Iran.
LITERATURE CITED
Ahmadi, J., B. Vaezi, A. Shaabani, K. Khademi, S. Fabriki-Ourang, and A. Pour-
Aboughadareh. 2015. Non- parametric measures for yield stability in grass
pea (Lathyrus sativus L.) advanced lines in semi warm regions. Journal of
Agricultural Science and Technology 17: 1825–1838.
Akbarpour, O. A., H. Dehghani, B. Dorkhi-Lalelo, and M. S. Kang. 2016. A SAS
macro for computing statistical tests for two- way table and stability indices
of nonparametric method from genotype- by- environment interaction. Acta
Scientiarum. Agronomy 38: 35–50.
Becker, H. C., and J. Leon. 1988. Stability analysis in plant breeding. Plant
Breeding 101: 1–23.
Branco, L. C. 2015. Nonparametric stability analysis (phenability R package).
Website https://cran.r-project.org/web/packages/phenability/phenability.
pdf [accessed 12 August 2018].
Crossa, J. 2012. From genotype × environment interaction to gene × environ-
ment interaction. Current Genomics 13: 225–244.
Dia, M., T. C. Wehner, and C. Arellano. 2016. Analysis of genotype × environment
interaction (GE) using SAS programming. Agronomy Journal 108: 1838–1852.
Ebdon, J. S., and H. G. Gauch. 2002. Additive main eect and multiplicative in-
teraction analysis of national turf grass performance trials: I. Interpretation
of genotype × environment interaction. Crop Science 42: 489–496.
Eberhart, S. A. T., and W. A. Russell. 1966. Stability parameters for comparing
varieties. Crop Science 6: 36–40.
Finlay, K. W., and G. N. Wilkinson. 1963. Adaptation in a plant breeding pro-
gramme. Australian Journal of Agricultural Research 14: 742–754.
Flores, F., M. T. Moreno, and J. I. Cubero. 1998. A comparison of univariate
and multivariate methods to analyze environments. Field Crops Research 56:
271–286.
Fox, P., B. Skovmand, B. ompson, H. I. Braun, and R. Cormier. 1990. Yield and
adaptation of hexaploid spring triticale. Euphytica 47: 57–64.
Francis, T. R., and L. W. Kannenberg. 1978. Yield stability studies in short- season
maize: I. A descriptive method for grouping genotypes. Canadian Journal of
Plant Science 58: 1029–1034.
Huhn, M. 1990. Nonparametric measures of phenotypic stability. Part 1: eory.
Euphytica 47: 189–194.
Hussein, M. A., A. Bjornstad, and H. Aastveit. 2000. SASG×ESTAB: A SAS pro-
gram for computing genotype × environment stability statistics. Agronomy
Journal 92: 454–459.
Kang, M. S. 1988. A rank- sum method for selecting high- yielding, stable corn
genotypes. Cereal Research Communication 16: 113–115.
Kang, M. S. 1991. Modied rank- sum method for selecting high yielding, stable
crop genotypes. Cereal Research Communication 19: 361–364.
Khalili, M., and A. Pour-Aboughadareh. 2016. Parametric and non- parametric
measures for evaluating yield stability and adaptability in barley doubled
haploid lines. Journal of Agricultural Science and Technology 18: 789–803.
Nassar, R., and M. Huhn. 1987. Studies on estimation of phenotypic stability:
Tests of signicance for nonparametric measures of phenotypic stability.
Biometrics 43: 45–53.
Pearson, K. 1895. Notes on regression and inheritance in the case of two parents.
Proceedings of the Royal Society of London 58: 240–242.
Piepho, H. S. 1999. Stability analysis using the SAS system. Agronomy Journal
91: 154–160.
Plaisted, R. L. 1960. A shorter method for evaluating the ability of selections to
yield consistently over locations. American Potato Journal 37: 166–172.
Plaisted, R. I., and L. C. Peterson. 1959. A technique for evaluating the ability
of selection to yield consistently in dierent locations or seasons. American
Potato Journal 36: 381–385.
Shukla, G. K. 1972. Some statistical aspects of partitioning genotype-
environmental components of variability. Heredity 29: 237–245.
ennarasu, K. 1995. On certain non-parametric procedures for studying gen-
otype-environment interactions and yield stability. PhD thesis, PJ School,
Indian Agricultural Research Institute, New Delhi, India.
Vaezi, B., A. Pour-Aboughadareh, R. Mohammadi, M. Armion, A. Mehraban, T.
Hossein-Pour, and M. Dorri. 2017. GGE biplot and AMMI analysis of barley
yield performance in Iran. Cereal Research Communications 45: 500–511.
Vaezi, B., A. Pour-Aboughadareh, A. Mehraban, T. Hossein-Pour, R.
Mohammadi, M. Armion, and M. Dorri. 2018. e use of parametric and
non- parametric measures for selecting stable and adapted barley lines.
Archives of Agronomy and Soil Science 64: 597–611.
Wricke, G. 1962. Übereine Methode zur Erfassung der ökologischen Streubreite
in Feldversuchen. Zeitschri für Panzenzüchtung 47: 92–96.
Yaseen, M., and K. M. Eskridge. 2018. Stability analysis of genotype by environ-
ment interaction (GEI) (stability R package). Website https://cran.r-project.
org/web/packages/stability/stability.pdf [accessed 12 August 2018].

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APPENDIX 1. Description of stability statistics calculated for the crop traits by STABILITYSOFT.
Statistic Symbol Denition
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.