Comparing Relationships Among Yield and Its Related Traits in Mycorrhizal and Nonmycorrhizal Inoculated Wheat Cultivars Under Different Water Regimes Using Multivariate Statistics

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Research ArticleComparing Relationships among Yield and Its Related Traitsin Mycorrhizal and Nonmycorrhizal Inoculated Wheat Cultivarsunder Different Water Regimes Using Multivariate Statistics

Armin Saed-Moucheshi, 1 Mohammad Pessarakli, 2 and Bahram Heidari 1

Department of Crop Production and Plant Breeding, Shiraz University, Shiraz , IranSchool of Plant Sciences, Te University of Arizona, uscan, AZ , USA

Correspondence should be addressed to Mohammad Pessarakli; [email protected]

Received October ; Accepted December

Academic Editor: Ravindra N. Chibbar

Copyright © Armin Saed-Moucheshi et al. Tis is an openaccess article distributed under the CreativeCommons AttributionLicense, whichpermitsunrestricted use,distribution,andreproduction in anymedium,providedthe originalworkis properlycited.

Multivariate statistical techniques were used to compare the relationship between yield and its related traits under noninoculatedand inoculated cultivars with mycorrhizal ungus ( Glomus intraradices); each one consisted o three wheat cultivars and our waterregimes. Results showedthat,underinoculationconditions, spikeweight perplantand total chlorophyll contento the ag lea werethe most important variables contributing to wheat grain yield variation, while, under noninoculated condition, in addition to twomentioned traits, grain weight per spike and lea area were also important variables accounting or wheat grain yield variation.Tere ore, spikeweight per plant andchlorophyll content o ag lea can be used as selectioncriteria in breeding programs or bothinoculated and noninoculated wheat cultivars under different water regimes, and also grain weight per spike and lea area can beconsidered or noninoculated condition. Furthermore, inoculation o wheat cultivars showed higher value in the most measuredtraits, and the results indicated that inoculation treatment could change the relationship among morphological traits o wheatcultivars under drought stress. Also, it seems that the results o stepwise regression as a selecting method together with principalcomponent and actor analysis are stronger methods to be applied in breeding programs or screening important traits.

1. Introduction

Bread wheat ( riticum aestivum L.) is one o the most widely cultivated and important ood crop in the world. Develop-ment o high yielding wheat cultivars is the major objectiveo breeding programs [ ]. On the other hand, targeted effortsto breed genotypes or improved mycorrhizal symbiosisresult in increased yield in crops under a wide range o environmental conditions and contribute toward sustainabil-ity o agricultural ecosystems in which soil-plant-microbeinteractions will be better exploited. Screening genotypes viamolecular biology and traditional breeding techniques canincrease productivity o symbioses and eventually result inincreased economic yield o crop plants [ ].

Arbuscular mycorrhizal (AM) ungi colonize the rootso most monocotyledons and dicotyledons, including impor-tant crops such as rice, maize, and wheat despite theirdifferent root architecture and cell patterning. In nature,mineral nutrient acquisition and water uptake by plant roots

are ofen assisted by symbioses with bene cial AM ungi.During this intimate association, the extraradical hyphalmycelium acquires minerals rom the soil beyond the zoneaccessible by the roots. Inside the root, a considerableproportiono theminerals isdelivered to thehost inexchange

or carbohydrates [ ]. However, a ew breeding programsand physiological researches have examined the morpho-physiological effects o mycorrhizal inoculation on wheatcultivars under drought stress. Te bene t arising rom themycorrhizal symbiosis was not proportional to the extent o the root colonization in durum wheat genotypes; because various genotypes showed various responses to mycorrhizalinoculation [ , ].

Aiming to providing methods in order to attain higherproduction, breeders have used important yield componentsas selection criteria to per orm higher yields via indirectselection [ , ]. Kumbhar et al. [ ] illustrated high effi-ciency o tiller and kernel production on wheat yield. Grainweight/spike has been reported as the most closely variable

http://dx.doi.org/10.1155/2013/682781

http://dx.doi.org/10.1155/2013/682781



International Journal o Agronomy

contributing to grain yield, and it has ofen been used inselecting high yielding wheat genotypes [ ]. -grainweight has been shown as the main yield component or %o variation in wheat grain yield. Moghaddam et al. [ ] ounda negative correlation between plant height andgrain yield o wheat due to the lower number o grains/spike. Te results

o Leilah and Al-Khateeb [ ] showed that number o spikeper square meter, -grain weight, grain weight/spike, andbiological yield were the most effective variables in uencinggrain yield. Te study o O. Alizadeh and A. Alizadeh [ ]showed that using mycorrhizal inoculation caused betternutrient elements uptake in plant andgeneratedplant growthregulators or increasing yield and yield components in corn.When Azospirillum and Mycorrhiza were used as bio ertil-izers in study conducted by Ardakani et al. [ ], signi canteffects on wheat yield and its related traits were ound.Statistical techniques have important roles in detecting rela-tionship among plants’ traits and between the yield and itsrelated components. One o the basic statistical methods tostudy the relationships between traits is simple correlationcoefficient analysis [ ]. Estimatingcorrelation coefficientso different variables with grain yield is a suitable technique todecisions about the relative importance o these charactersand their values as selection criteria [ ]. On the other hand,the correlation coefficient may not give enough in ormationabout the relationship between different variables as muchas statistical multivariate methods give. Tere ore, otherstatistical techniques such as multiple regressions, actoranalysis, principal component analysis, cluster analysis, andpath coefficient analysis have been de ned as appropriatetechniques or interpreting these relationships in crop plants[ , ]. Te multivariate statistical analyses canprovide moreinsights on thedeep structureo data andtraits’ relationships.

Attempts to identi ying an ideal model or producinghigh-yielding wheat plants under different water regimesusing mycorrhizal symbiosis in wheat breeding have rarely been made. Tis studywas conducted to clari yand interpret-ing the relationship between wheat grain yield and its relatedcomponents under drought conditions and mycorrhizalsymbiosis with aiming to provide theoretical oundationsguiding wheat breeders or researching the association o themain yield components and their in uences on wheat plantproductivity.

2. Materials and Methods

. . Experimental Procedures. Te experiment was carriedout in the greenhouse o Crop Production and Plant Breed-ing Department, College o Agriculture, Shiraz University,Shiraz, Iran, in . Maximum, minimum, and the meantemperatures o this area were . , . , and ∘C, respectively,with . % relative humidity and mm annual rain all.A actorial experiment based on completely randomizeddesign with three replications was used. Te studied actorswere our water regimes ( %, %, %, and % o eldcapacity), three wheat cultivars (Darab as a semi-resistantcultivar; Shiraz and Falat as sensitive cultivars), and mycor-rhizal inoculation, including inoculated and noninoculated

(control) treatments. Te ungus used in this experimentwas Glomus intraradices Schenck and Smith, provided by the Department o Soil Science, Shiraz University, Shiraz,Iran. Mycorrhizal inoculums were prepared through the trapculture in maize ( Zea mays L.) with spores o G. intraradices.Te mixture o trap culture medium was obtained rom

autoclaved soil/quartz sand ( < mm) ( : , v/v).Te soil samples used or planting were collected romBajgah, Fars, Iran ( m asl; longitude ∘ and latitude

∘ ). Te soil samples were air-dried, passed throughmm sieve,and mixed uni ormly. Tephysicochemical prop-

erties o the soil were sandy loam, ne, mixed, mesic, cal-cixerollic xerochrepts, eld capacity . %, pH . (soil:distilled water, : ), electrical conductivity . d S m−1 , car-bonate calcium equivalent . %, total organic matter . %,total Kjeldahl nitrogen . %, Olsen phosphorus mg kg−1 ,extractable potassium mg kg−1 , and D PA-extractableFe, Cu, Mn, and Zn were , , . , and . mg kg−1 , respec-tively [ ]. Te day/night air temperature o the greenhouse

was / .Te pots were lled with kg washed and sieved soil(mentioned previously) without puri cation or sterilizationto simulate the real soil eld properties. mg N kg−1 soil(urea %) and some micronutrient elements such as Zn,Fe, Ca, and K up to mgkg−1 were applied in each pot.Te seeds were treated with ethanol % or about s,washed three times with distilled water, and kept at ∘C ora week. About cm o sur ace soil o each pot was removedand in mycorrhizal treatments, g inoculums (containingspore numbers o g−1 substrate and root colonization o percent) were placed and incorporated with the remainingsoil. Ten, cm o the removed soils was added to each pot;

aferwards eight seeds were planted at equal distances in eachpot. Finally, the rest o the removed soils were added to thepots. Afer germination, seedlings were thinned to our plantsper pot.

Pots were daily weighed and based on the decreasingweight o each pot; decalci ed water was added to each potup to desired eld capacity (FC) until the date o applyingwater regimes’ treatments. Te water regimes were started atthe tillering stage. Te temperature during the experimentranged rom to ∘C, with a / h light/dark period.

. . Leaf Area Measurements. Plants’ leaves diameter weremeasured with a ruler, and leaves areas (X ) were calculated

using the ollowing equation [ , ]:Leaves area cm

2 = maximum lea length

× lea width × 0.75.( )

. . otal Chlorophyll Content. otal chlorophyll contents o the ag leaves (X ) were determined according to Iqbal etal. [ ] procedure. otal chlorophyll content was extracted in

% cold acetone, and the absorbance o the extractions wasmeasured spectrophotometrically at and nm. otalchlorophyll was determined based on the ollowing standard

ormula [ ]:

Chl mgmL−1 = 20.2 × 645 + 8.02 × 663 , ( )




where, is the spectrophotometer reading at and wavelengths (nm), and Chl is total chlorophyll content.

. . Agronomic raits. Grain yield (Y), tiller numbers (X ),spike length (X ), spikelet/spike (X ), spike weight/plant(X ), grains/spike (X ), grain weight/spike (X ), -grain

weight (X ), biologicalyield (X ), androot weight (X ) weredetermined afer the plants were harvested.

. . Statistical Analyses

. . . Simple Correlation Coefficients. Pearson simple corre-lation coefficients were calculated, and the matrix o thesecorrelations was studied [ ].

. . . Multiple Linear Regressions. A multiple linear regres-sion model was used or determining relative contributiono related components to the grain yield (Y) variations by applying the ollowing equation [ ]:

= + 1 1 + 2 2 + 3 3 + ⋅⋅ ⋅ + , ( )

where, is the dependent variable (yield), the ’s areindependent variables (measured traits) affecting dependentone, is the intercept coefficient, and the ’s are the relatedcoefficients o independent variables in predicting thedepen-dent variable.

. . . Stepwise Regression. Stepwise regression [ ] was usedin order to determine the most important variables signi -cantly contributed to total yield variability.

. . .FactorAnalysis. Te actoranalysismethodis consistedo the reduction o a large number o correlated variablesto a much smaller number o uncorrelated variables. Aferextracting main actors, the matrix o actor loading wasused to a varimax orthogonal rotation, and the communality or variance o uncorrelated variables was estimated by thehighest correlation coefficient in each array as suggested by Seiller and Stafford [ ].

. . . Principal Components Analysis. Principal componentsanalysis is a mathematical procedure used to classi y a largenumber o variables (items) into major components anddetermine their contribution to the total variation. Te rst

principal component is accounted or the highest variability in the data, and each succeeding component accounts or thehighest remaining variability as possible [ ].

. . . Path Analysis. Path coefficient analysis was per ormedusing simple Pearson correlation coefficients using grainyield/plant as dependent variable and the other charactersas in uential variables. Te direct and indirect effects o in uential variables on grain yield were calculated accordingto proposed method o Dewey and Lu [ ].

. . . Cluster Analysis. Cluster analysis was used or arrang-ing variables into different clusters to nd the clusters that

their cases within are more similar and correlated to oneanother comparing to other clusters. Tis procedure wasper ormed using a measure o similarity levels and Euclideandistance [ , ].

All statistical analyses were per ormed using SAS- . [ ]and Minitab- packages.

3. Results

. . Simple Correlations. able shows the minimum andmaximum values, arithmetic mean, standard deviation, andstandard error o means or all the estimated variables o wheat, separately or the inoculated and noninoculatedplants. Results o simple correlation analysis ( able ) show that all variables or either inoculated or noninoculatedcultivars have a signi cant positive correlation with grainyield. Te highest correlation with yield under both inocu-lated and noninoculated conditions was recorded or spikeweight/plant ( = 0.998 or inoculated and . or non-

inoculated conditions). Overall, correlation coefficients withgrain yield were higher in the inoculated plants than that o the noninoculated ones.

. . Path Coefficients. Te correlation coefficients were par-titioned into direct and indirect effects in both inoculatedand noninoculated plants ( ables and ). Te highestdirect effect ( . or the inoculation and . or thenoninoculation) on yields or both conditions belonged tothe spike weight/plant, while direct effects o the other variables were relatively low. Te indirect effects o the spikeweight/plant or both conditions were negative. Except orthe spike weight/plant, the other variables had high indirect

effects on the grain yield. Spikelets/spike showed the lowestdirect contribution to the grain yield variations or bothconditions but the highest indirect contribution throughother variables.

. . Multiple Linear Regressions. Regression coefficients andthe probability o the estimated variables in predicting thewheat grain yield separately or the inoculated and non-inoculated conditions are presented in able . Based onthese results, the predicting model equations or the grainyield/plant (Y) are ormulated as ollows.

Model for Inoculated Condition

Y = 0.539 − 0.116X1 − 0.0202X2 − 0.0081X3 + 0.962X4+ 0.0109X5 − 0.780X6 − 0.00698X7 − 0.00423X8+ 0.0131X9 + 0.0840X10 − 0.00080X11,

( )

where, Y is the grain yield, X is the tiller numbers, Xis the spike length, X is the spikelet/spike, X is thespike weight/plant, X is the grains/spike, X is the grainweight/spike, X is the -grain weight, X is the totalchlorophyll contents o the ag leaves, X is the biologicalyield, X is the root weight, and X is the lea area.




: Basic statistics (minimum and maximum values, arithmetic mean, standard deviation (SD) and standard error o mean (SE mean))or the measured variables o wheat under inoculation (In) and noninoculation (non-In) conditions and different water levels.

Variables Situation Mean SE mean SD Minimum Maximum

X In . . . . .Non-In . . . . .

X In . . . . .

Non-In . . . . .

X In . . . . .Non-In . . . . .

X In . . . . .Non-In . . . . .

X In . . . . .Non-In . . . . .

X In . . . . .Non-In . . . . .

X In . . . . .Non-In . . . . .

X In . . . . .

Non-In . . . . .

X In . . . . .Non-In . . . . .

X In . . . . .Non-In . . . . .

X In . . . . .Non-In . . . . .

Y In . . . . .Non-In . . . . .

X : tiller numbers/plant, X : spike length, X : spikelets/spike, X : spike weight/plant, X : grains/spike, X : grain weight/spike, X : -grain weight, X : totalchlorophyll content o ag lea , X : biological yield/plant, X : root weight, X : leaves area, and Y: grain yield.

Model for Noninoculated Condition

Y = − 0.089 − 0.0061X1 − 0.0103X2 + 0.0032X3 + 0.978X4+ 0.0119X5 − 1.51X6 − 0.00451X7 − 0.00316X8− 0.0109X9 + 0.119X10 + 0.00486X11,

( )

where, Y is grain yield,X is the tiller numbers, X is the spikelength, X is the spikelet/spike, X is the spike weight/plant,X is the grains/spike, X is the grain weight/spike, X is the

-grain weight, X is the total chlorophyll contents o the

ag leaves, X is the biological yield, X is the root weight,and X is the lea area. Te ormulas explained . % and

. % ( 2 ) o the total variations o the grain yields or theinoculated and noninoculated conditions, respectively, andthe remaining . % and . % are probably due to residualeffects. Te t -test or the variables revealed that the spikeweight/plant andgrainweight/spike contributed signi cantly in grain yields o both conditions, while the grains/spike,lea area and root weight were signi cant only or thenoninoculated condition.

. . Stepwise Regression. ables and show the entered orremoved variables rom the established model by stepwise

regression separately rom inoculated and noninoculatedconditions. Te partial and cumulative determination coe -

cient ( 2 ), the probability value o entered variables to themodel or removed variables rom models, andstandard erroro the variables are also presented in these ables ( ables and ). Under the inoculated condition, spike weight/plant,grains/spike, grain weight/spike, and total chlorophyll con-tent o the ag lea were entered into the model, and nonewere removed; while, under the noninoculated condition,seven variables, including spike weight/plant, grains/spike,grain weight/spike, total chlorophyll content o the ag lea ,biological yield, root weight, and the lea area were entered

into the model, and there were no variables to be removed.According to the results, . % and . % o the total variations in the grain yields were explained by the selected variablesunder the inoculated and noninoculatedconditions,respectively. Due to their lowrelative contributions, the other variables were not included in the models. Tere ore, basedon the nal step o stepwise regression analyses, theequations

or prediction o grain yield (Y) were computed as ollows.

Final Model under Inoculated Condition

Y = 0.07776 + 0.95104X4 + 0.01332X5 − 0.99926X6− 0.00472X8,

( )




: A matrix o simple correlation coefficients () or the measured variables o wheat under inoculation (In) and noninoculation(non-In) conditions and different water levels.

X X X X X X X X X X X

X In . ∗∗

Non-In . ∗∗

X In . ∗∗ . ∗∗

Non-In . ∗∗ . ∗∗

X In . ∗∗ . ∗∗ . ∗∗

Non-In . ∗∗ . ∗∗ . ∗∗

X In . ∗∗ . ∗∗ . ∗∗ . ∗∗

Non-In . ∗∗ . ∗∗ . ∗∗ . ∗∗

X In . ∗∗ . ∗∗ . ∗∗ . ∗∗ . ∗∗

Non-In . ∗∗ . ∗ . ∗ . ∗∗ . ∗∗

X In . ∗∗ . ∗∗ . ∗∗ . ∗∗ . ∗∗ . ∗

Non-In . ∗∗ . ∗∗ . ∗∗ . ∗∗ . ∗∗ . ∗

X In . ∗∗ . ∗∗ . ∗∗ . ∗∗ . ∗∗ . ∗∗ . ∗∗

Non-In . ∗∗ . ∗∗ . ∗∗ . ∗∗ . ∗∗ . ∗ . ∗∗

X In . ∗∗ . ∗∗ . ∗∗ . ∗∗ . ∗∗ . ∗∗ . ∗∗ . ∗∗

Non-In . ∗∗ . ∗∗ . ∗∗ . ∗∗ . ∗∗ . ∗∗ . ∗∗ . ∗∗

X In .∗∗

.∗∗

.∗∗

.∗∗

.∗∗

.∗∗

.∗∗

.∗∗

.∗∗

Non-In . ∗∗ . ∗∗ . ∗∗ . ∗∗ . ∗∗ . ∗∗ . ∗∗ . ∗∗ . ∗∗

X In . ∗ . ∗∗ . ns . ∗∗ . ∗∗ . ∗ . ∗ . ns . ns . ∗

Non-In . ∗ . ns . ∗∗ . ∗∗ . ∗∗ . ∗∗ . ∗∗ . ∗ . ∗∗ . ∗∗

Y In . ∗∗ . ∗∗ . ∗∗ . ∗∗ . ∗∗ . ∗∗ . ∗∗ . ∗∗ . ∗∗ . ∗∗ . ∗∗

Non-In . ∗∗ . ∗∗ . ∗∗ . ∗∗ . ∗∗ . ∗∗ . ∗∗ . ∗∗ . ∗∗ . ∗∗ . ∗∗

∗ and ∗∗ : Signi cant at % , % level o probability. ns: not signi cant.X : tiller numbers/plant, X : spike length, X : spikelets/spike, X : spike weight/plant, X : grains/spike, X : grain weight/spike, X : -grain weight, X : totalchlorophyll content o ag lea , X : biological yield/plant, X : root weight, X : leaves area, and Y: grain yield.

: Path coefficient (direct and indirect effects) o the measured variables attributed on grain yield variation o wheat in inoculationcondition and different water levels.

Variables Effects viaDirect effect Indirect effect Y

X X X X X X X X X X XX − . − . − . . . − . − . − . . . − . − . . .X − . − . − . . . − . − . − . . . − . − . . .X − . − . − . . . − . − . − . . . − . − . . .X − . − . − . . . − . − . − . . . − . . − . .X − . − . − . . . − . − . − . . . − . . . .X − . − . − . . . − . − . − . . . − . − . . .X − . − . − . . . − . − . − . . . − . − . . .X − . − . − . . . − . − . − . . . − . − . . .X − . − . − . . . − . − . − . . . − . . . .X − . − . − . . . − . − . − . . . − . . . .X − . − . − . . . − . − . − . . . − . − . . .

X : tiller numbers/plant, X : spike length, X : spikelets/spike, X : spike weight/plant, X : grains/spike, X : grain weight/spike, X : -grain weight, X : total

chlorophyll content o ag lea , X : biological yield/plant, X : root weight, and X : leaves area.

where, Y is grain yield, X is the spike weight/plant, X is thegrains/spike, X is the grain weight/spike, and X is the totalchlorophyll contents o the ag leaves.

Final Model under Noninoculated Condition

Y = − 0.19463 + 0.9767X4 + 0.01208X5 − 1.54441X6− 0.00407X8 − 0.01094X9 + 0.09707X10 + 0.00505X11,

( )

where, Y is grain yield, X is the spike weight/plant, X isthe grains/spike, X is the grain weight/spike, X is the total

chlorophyll contents o the ag leaves, X is the biologicalyield, X is the root weight, and X is the lea area.

. . Factor Analysis. Te rst two o the twelve actors ac-counted or . % and . % o the total variations o the inoculated and noninoculated conditions, respectively ( able ). Te rst actor was included or yield and spikeweight/plant or both conditions, and it could explain . %and . % o the total variations in the dependent structure

or the inoculated and noninoculated conditions, respec-tively; there ore, it can be named as grain yield actor. Te




: Path coefficient (direct and indirect effects) o the measured variables attributed on grain yield variation o wheat in noninoculationcondition and different water levels.

Variables Effects viaDirect effect Indirect effect Y

X X X X X X X X X X XX − . − . . . . − . − . − . − . . . − . . .X − . − . . . . − . − . − . − . . . − . . .X − . − . . . . − . − . − . − . . . . . .X − . − . . . . − . − . − . − . . . . − . .X − . − . . . . − . − . − . − . . . . . .X − . − . . . . − . − . − . − . . . − . . .X − . − . . . . − . − . − . − . . . − . . .X − . − . . . . − . − . − . − . . . − . . .X − . − . . . . − . − . − . − . . . − . . .X − . − . . . . − . − . − . − . . . . . .X − . − . . . . − . − . − . − . . . . . .

X : tiller numbers/plant, X : spike length, X : spikelets/spike, X : spike weight/plant, X : grains/spike, X : grain weight/spike, X : -grain weight, X : totalchlorophyll content o ag lea , X : biological yield/plant, X : root weight, and X : leaves area.

: Te regression coefficient ( ), standard error (SE), value, and probabilityo the estimated variables in predicting wheat grain yieldby the multiple linear regression analysis under inoculation (In) and noninoculation (non-In) conditions and different water levels.

Predictor DF SE Constant In . . . .

Non-In − . . − . .

X In − . . − . .Non-In − . . − . .

X In − . . − . .Non-In − . . − . .

X In − . . − . .Non-In . . . .

X In . . . .Non-In . . . .

X In . . . .Non-In . . . .

X In − . . − . .Non-In − . . − . .

X In − . . − . .Non-In − . . − . .

X In − . . − . .Non-In − . . − . .

X In . . . .Non-In − . . − . .

X In . . . .Non-In . . . .

X In − . . − . .Non-In . . . .

X : tiller numbers/plant, X : spike length, X : spikelets/spike, X : spike weight/plant, X : grains/spike, X : grain weight/spike, X : -grain weight, X : totalchlorophyll content o ag lea , X : biological yield/plant, X : root weight, and X : leaves area.

second actor included spike length and biological yieldor the inoculated condition which accounted or . % o

the total variability in the dependent structure, and it wasconsidered as the spike length ( able ). Under the noninoc-ulated condition, the second actor accounted or . % o

the total variability and was consisted o total chlorophyllcontent o the ag lea ; there ore it could be named as totalchlorophyll actor. Te rst two actors o the inoculated andnoninoculated conditions are graphically depicted in Figures

(a) and (b).




: Relative contribution (partial and model 2 ), value, and probability in predicting wheat grain yield by the stepwise procedureanalysis under inoculation condition and different water levels.

Step Variables entered Variable removed Partial 2 Model 2 value ER Parameter estimate Standard error value 4 — . . <. . . <. 6 — . . . − . . .

5 — . . . . . . 8 — . . . − . . .X : spike weight/plant, X : grains/spike, X : grain weight/spike and X : total chlorophyll content o ag lea .

2 : coefficient o determination, value ER: value or entered or removed variables, and value : value or nal model.

: Relative contribution (partial and model 2 ), value, and probability in predicting wheat grain yield by the stepwise procedureanalysis under noninoculation condition and different water levels.

Step Variables entered Variable removed Partial 2 Model 2 value ER Parameter estimate Standard error value 4 — . . <. . . <. 6 — . . . − . . <. 9 — . . . − . . . 5 — . . . . . .

11 — . . . . . . 8 — . . . − . . . 10 — . . . . . .

X : spike weight/plant, X : grains/spike, X : grain weight/spike, X : total chlorophyll content o ag lea , X : biological yield/plant, X : root weight, and X :leaves area.

2 : coefficient o determination, value ER: value or entered or removed variables, and value : value or nal model.

. .Principal Component. Tedata presented in able andFigures (a) and (b) demonstrated that the increase in thenumber o components was associated with a decrease ineigenvalues. According to the results, the estimated wheat variables grouped into two main components that accounted

or . % and . % o the total variations o the grainyields or the inoculated and noninoculated conditions,respectively. PC was moderatelycorrelated with spike length( = −0.311), spike weight/plant ( = −0.33), grains/spike( = −0.316), biological yield ( = −0.305), and grainyield ( = −0.325) in the inoculated plants and with spikeweight/plant ( = −0.315), biological yield ( = −0.324), andyield ( = −0.309) under the noninoculated condition. PC

or the inoculated condition was moderately correlated withspikelets/spike ( = −0.373) and total chlorophyll content( = −0.371), while it was highly correlated with the lea area ( = 0.737). In the noninoculated plants PC wasmoderately correlated with the spike length ( = −0.329),grain weight/spike ( = 0.382), total chlorophyll ( =−0.355), lea area ( = 0.477), and yield ( = 0.307).PC accounted or about . % and % o the variationsin the grain yields; while PC explained . % and . %o the variations in the grain yields under the inoculatedand noninoculated conditions, respectively. Te rst twocomponents and their contributions in the variables or bothconditions are graphically presented in Figures (a) and (b).

. . Cluster Analysis. Hierarchical cluster analysis showedthe similarity distance ranged between %– % under theinoculated condition and %– % under the noninoculatedcondition. Te examined variables o wheat cultivars couldbe agglomerated into our and three clusters, respectively

(Figures (a) and (b)). As the important variables affectingwheat grain yield, spike weight/plant, and -grain yieldunder the inoculated condition and the spike weight/plant,grain weight/spike, andthe lea area under thenoninoculatedcondition were grouped together with the wheat grain yieldinto the third cluster.

ables (a) and (b) outline the overall results o deter-mining the most important variables affecting wheat grainyield or separately inoculatedand noninoculated conditions.

4. Discussion

Grain yield o wheat is the integration o many variables thataffect plant growth throughout the growing period. Greatefforts have been made to develop proper models that canpredict wheat grain yield and distinguish the ideal- andhigh-yielding crop plants (ideotype). Te knowledge o associationand relationship between grain yield and its componentsunder water de cit conditions would improve the efficiency o breeding programs by identi ying appropriate indices toselectwheat cultivars [ ]. Becauseo wide variations in grainyield under normal and water stress conditions, simulatingper ormance o wheat under soil moisture de cit representsspecial challenges or wheat modelers [ ]. Te results o thepresent study showed that spike weight/plant had the highestpositive correlation with grain yield o wheat genotypesunderboth inoculated andnoninoculated conditions. Aswellas spike weight/plant, other variables showed high positivecorrelations with yield. Based on the correlation coefficientanalysis, all the variables had a high contribution with thewheat grain yield, but spike weight/plant was the mosteffective variable or both conditions. Moghaddam et al. [ ]




0.90.80.70.60.50.40.30.20.10

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First factor

S e c o n

d f a c t o r

Y

X11X10

X9

X8

X7X6

X5

X4X3

X2

X1

−0.8−0.7−0.6−0.5−0.4−0.3−0.2−0.1

(a)

0.90.80.70.60.50.40.30.20.10

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

First factor

S e c o n

d f a c t o r

YX11X10

X9

X8

X7

X6

X5

X4X3

X2

X1

(b)

F : (a) Variables loading by actor analysis and varimax rotation with rst two actors under inoculation condition and different waterlevels. X : tiller numbers/plant, X : spike length, X : spikelets/spike, X : spike weight/plant, X : grain number/spike, X : grain weight/spike,X : -grain weight, X : total chlorophyll content o ag lea , X : biological yield/plant, X : root weight, X : leaves area, and Y: grain yield(b) Variables loading by actor analysis andvarimax rotation with rst two actors under noninoculationcondition and different water levels.

X : tiller numbers/plant, X : spike length, X : spikelets/spike, X : spike weight/plant, X : grain number/spike, X : grain weight/spike, X :-grain weight, X : total chlorophyll content o ag lea , X : biological yield/plant, X : root weight, X : leaves area, and Y: grain yield.

121110987654321

8

7

6

5

4

3

2

1

0

Factor number

E i g e n v a l u e

(a)

121110987654321

8

7

6

5

4

3

2

1

0

Factor number

E i g e n v a l u e

(b)

F : (a) Scree plot showing eigenvaluesin response to thenumber o components or theestimatedvariables o wheat under inoculationcondition and different water levels. (b) Scree plot showing eigenvalues in response to the number o components or the estimated variableso wheat under noninoculatin condition and different water level.

showed a negative correlation between the plant height andthegrain yield.Tese investigators [ ] attributed that increasein stem height caused the lower number o grains/spike.

Kumbhar et al. [ ] and Mohamed [ ] had shown that grainweight/spike, biological yield, and the number o spikes wereclosely related to grain yield. In the study o Leilah andAl-Khateeb [ ] grain yield had a high positive correlationwith the number o spikes, number o grains/spike, -grainweight, weight o grains/spike, and the biological yield. In thestudy o Heidari et al. [ ], grain yield wascorrelatedpositively with each o the biological yield, spikes/m2 , harvest index,and the grain weight/spike, while there was no correlationbetween the grain yield and the heading date or maturity. Tedifferential relations o yield components to the grain yieldmay be attributed to environmental effects on plant growth[ , ].

Since simple correlation coefficient can only determinethe linear relationship between two related variables, but itcannotshowhow multiplevariablesare related tooneanother

contributing to dependent variable (yield); path analysis wasused or dividing the correlation coefficient o variables withyield into their direct and indirect effects via other variables.Spike weight/plant had the highest direct effect on grain yieldunder either condition. Path analysis shows that direct effecto biological yield, under inoculation condition, is positive,while, under noninoculated condition, it is negative,which isprobably due to the effect o AM symbiosis on higher uptakeo nutrient elements. Te results also show that biologicalyield o the inoculated plants is signi cantly higher thanthose in noninoculated ones. Higher biological yield, undernoninoculated condition, causes more consumption o plantenergy and nutrient elements or more vegetative growth,




: Rotated(Varimax rotation) actor loadingsandcommunalities or theestimatedvariables o wheatbased on actoranalysis techniqueor inoculation and noninoculation conditions and different water levels.

Variables Inoculation NoninoculationFactor Factor

Communality Factor Factor

Communality

X . − . . . . .

X . − . − . . . .X . − . . . . .X . − . . . . .X . − . . . . .X . − . . . . .X . − . . . . .X . − . . . . .X . − . − . . . .X . − . . . . .X . − . . . . .Y . − . . . . .Latent roots . . . . . .Factor variance (%) . . . . . .

X : tiller numbers/plant, X : spike length, X : spikelets/spike, X : spike weight/plant, X : grains/spike, X : grain weight/spike, X : -grain weight, X : totalchlorophyll content o ag lea , X : biological yield/plant, X : root weight, X : leaves area, and Y: grain yield.

: Summary o actors loading or the estimated variables o wheat with mycorrhiza inoculation or noninoculation under differentwater levels.

Characters Loading % totalcommunality

Factor name Characters Loading % totalcommunality

Factor name

InoculationFactor . . % Yield Factor . . % Spike length

X . X − .Y . X − .

Noninoculation Factor . . % Yield Factor . . %X . X . Ch ag

Y . — —

X : spike length, X : spike weight/plant, X : total chlorophyll content o ag lea , X : biological yield/plant, and Y: grain yield.

resulting in decreasing grain yield, but inoculation o themycorrhizal ungus compensated this problem by highernutrient elements uptake rom the soil. Based on the pathcoefficient analysis o wheat grain yield, Kumbhar et al. [ ],Mohamed [ ], and Leilah and Al-Khateeb [ ] reportedthat the biological yield, harvest index, grains weight/spike,number o spikes/m2 , and -grain weight have the greatestimpact in relation to the wheat grain yield. In the study o Heidari et al. [ ], numbero grains/spikehadthe largest directand positive effect on the grain yield.

Linear regression analysis revealed that spike weight/plant and grain weight/spike are variables that signi cantly contributed in grain yield or both conditions, while thegrains/spike, leaves area, and root weight were signi cantonly or the noninoculated condition, so, these are variablesdetermined as the most effective variables contributing to thegrain yield by this statistical method. Tese results show thatinoculation can affect relationship between the traits, and itcan be use ul or the breeding programs. Results o this study

or regression analysis, under the noninoculated condition,

are relative similar to the other studies such as Kumbharet al. [ ] and Leilah and Al-Khateeb [ ] which showedthat spike length, number o spikes/m 2 , grain weights/spike,and the biological yield have contributed signi cantly to thegrain yield. Asseng et al. [ ] reported that increased kernelnumber had improved the potential yield o wheat undercertain environmental conditions limited by water supply.

Stepwise regression analysis is a multiple statisticalmethod that canscreenor select themost important variablesthrough a dependent variable such as the grain yield. Basedon this method, spike weight/plant, number o grains/spike,grain weight/spike, and total chlorophyll content o the aglea are the most important variablescontributing to theyieldunder the inoculated condition. Under the noninoculatedcondition, in addition to the our mentioned variables orthe inoculated condition, three other variables, includingthe biological yield, root weight, and the leaves area areimportant.Relatively differences between the selected modelsby stepwise regression or the inoculated and noninoculatedconditions show effectiveness o the root colonization on




: (a) Eigenvaluesandthe correlation matrix or theestimated variableso wheat using principal component procedure or inoculatedwheat cultivars under different water levels. (b) Eigenvalues and the correlation matrix or the estimated variables o wheat using principalcomponent procedure or noninoculated wheat cultivars under different water levels.

(a)

Variables PC PC PC PC PC PC PC PC PC PC PC PC

X − . − . − . − . − . − . − . . − . . − . .X − . − . . − . . − . . . − . − . − . .X − . − . . − . . . − . − . . − . − . .X − . . . . − . − . − . . . − . − . − .X − . . . − . − . − . . − . . . − . − .X − . . − . . − . . . . − . . . .X − . . . . − . . − . − . − . . . .X − . − . − . . − . − . . − . − . − . . .X − . − . − . − . . − . − . . − . . . − .X − . . − . . . − . . . . − . . − .X − . . − . − . . . − . − . − . − . . .

Y − . . . . − . − . − . . . − . − . .Eigenvalue . . . . . . . . . . . Proportion . . . . . . . . . . . .Cumulative . . . . . . . . . . .

X : tiller numbers/plant, X : spike length, X : spikelets/spike, X : Spike weight/plant, X : grains/spike, X : grain weight/spike, X : -grain weight, X :total chlorophyll content o ag lea , X : biological yield/plant, X : root weight, X : leaves area, and Y: grain yield.

(b)

Variable PC PC PC PC PC PC PC PC PC PC PC PC

X − . − . . − . . − . − . . . . − . .X − . − . . . − . . − . − . − . . . .X − . − . − . . . . . . . − . . − .

X − . . − . . − . − . − . . − . . . − .X − . − . . . . − . . . − . . − . − .X − . . . − . − . . − . . − . − . . .X − . − . − . − . . . . − . − . − . − . .X − . − . . − . . − . . − . . − . . .X − . − . . . − . − . − . . . − . − . .X − . . − . − . − . . . . . − . . − .X − . . . − . . − . − . − . . . − . − .Y − . . − . . − . − . − . . − . . . .

Eigenvalue . . . . . . . . . . . Proportion . . . . . . . . . . . .

Cumulative . . . . . . . . . . . X : tiller numbers/plant, X : spike length, X : spikelets/spike, X : spike weight/plant, X : grains/spike, X : grain weight/spike, X : -grain weight, X :total chlorophyll content o ag lea , X : biological yield/plant, X : root weight, X : leaves area, and Y: grain yield.

interrelationship o the variables. Leilah and Al-Khateeb[ ] reported that the weight o grains/spike, harvest index,biological yield, number o spikes/m2 , and lastly spike lengthcan explain . % o the grain yield variations o wheat.Also, Mohamed [ ] ound that spike length, spike number,grain numbers/spike, spike weight, and straw yield are asso-ciated signi cantly with wheat grain yield. Heidari et al. [ ]showed that the most important components or grain yield

based on this method are grain weight/spike, spikes/m 2 , andspikelets/spike.

Factor analysis showed that spike weight/plant underboth inoculated and noninoculated conditions, spike length,and biological yield or the inoculated condition, and totalchlorophyll content o the ag lea or the noninoculatedconditionhadthehighest relativecontribution to wheat grainyield ( able ). Such results can be recognized by means




: (a) Wheatcharacteristics identi ed as crucial in wheat grain yield with each oneo theused statistical techniques under inoculationcondition and different water levels. (b) Wheat characteristics identi ed as crucial in wheat grain yield with each one o the used statisticaltechniques under noninoculation condition and different water levels.

(a)

Variables Reg Step FA PC Path Cluster otal score

X x X x x x X x x X x x x x x x x X x x x X x x x X x x X x x x x X x x X x X x x

X : tiller numbers/plant, X : spike length, X : spikelets/spike, X : spike weight/plant, X : grains/spike, X : grain weight/spike, X : -grain weight, X :

total chlorophyll content o ag lea , X : biological yield/plant, X : root weight, X : leaves area and Y: grain yield.: correlation analysis, Reg: multiple linear regression, Step: stepwise multiple regression, FA: actor analysis, PC: principal component analysis, path:path coefficient analysis, and cluster: cluster analysis.

(b)

Variables Reg Step FA PC Path Cluster otal score1 x x 2 x x 3 x 4 x x x x x x x 5 x x x 6 x x x x x 7 x

8 x x x x 9 x x x 10 x x x 11 x x x x x

1 = iller numbers/plant, 2 = Spike length, 3 = Spikelets/spike, 4 = Spike weight/plant, 5 = Grains/spike, 6 = Grain weight/spike, 7 = −

Grain weight, 8 = otal chlorophyll content o ag lea , 9 = Biological yield/plant, 10 = Root weight, 11 = Leaves area, Y = Grain yield.= Correlation analysis,Reg = Multiple linear regression, Step= Stepwise multipleregression, FA = Factor analysis,PC = Principal component analysis,

Path = Path coefficient analysis, and Cluster = Cluster analysis.

o Figures (a) and (b). Similar results were obtained by Mohamed [ ] who stated that actor analysis had classi-

ed the ten wheat variables into two main groups whichaccounted or . % o the total variability in the depen-

dence structure. Leilah and Al-Khateeb [ ] showed thatbiological yield, harvest index, weight o grains/spike, spikelength, and number o spikes/m 2 had a high relative contri-bution to wheat grain yield.

Results o the principal component analysis revealedthat, under the inoculated condition, spike length, spikeweight/plant, grains/spike, biological yield, number o spike-lets/spike, and total chlorophyll are important variablesa ectinggrain yield, andunder the noninoculatedcondition,spike length, spike weight/plant, biological yield, grainweight/spike, total chlorophyll, and leaves area are the mostimportant actors. Harvest index, biological yield, spikediameter, number o spikes/m 2 , spike length, grain

weights/spike, and -grain weight in the study o Leilahand Al-Khateeb [ ] were the most important actors in con-tributing to the yield. Also, Yin et al. [ ] stated that the grainyield was divided into three components, namely, number o

spikes/m2

, number o kernels/spike, and -kernel weight.Hierarchical cluster analysis showed that, under the inoc-

ulated condition, grain yield, spike weight/plant, and -grain yield are highly important variables or contributingto yield, while, under the noninoculated condition grainyield, spike weight/plant, grain weight/spike, and leaves areaare highly important variables. Hierarchical cluster analysismethod starts with the calculation o the distance o each variable in relation to other variables.Groupsare then ormedby the process o agglomeration division. In this process, all variables start individually in groups o one. Te close groupsare then gradually merged until nally all variables come to asingle group. Repeated splitting o the groups will result in all




0.350.30.250.20.150.10.050

0.5

0.25

0

First component

S e c o n d

c o m p o n e n

t

Y

X11

X10

X9X8

X7

X6

X5

X4

X3

X2

X1

−0.75

−0.5

−0.25

(a)

0.350.30.250.20.150.10.050

0.4

0.3

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0.1

0

Y

X11

X10

X9

X8

X7

X6

X5

X4

X3

X2X1

First component

S e c o n d c o m

p o n e n

t

−0.5−0.4−0.3−0.2−0.1

(b)

F : (a) Variables loading by principal component analysis with rst two components under inoculation condition and different waterlevels. X : tiller numbers/plant, X : spike length, X : spikelets/spike, X : spike weight/plant, X : grain number/spike, X : grain weight/spike,X : -grain weight, X : total chlorophyll content o ag lea , X : biological yield/plant, X : root weight, X : leaves area and Y: grain yield(b) Variables loading by principal component analysis with rst two components under noninoculation condition and different water levels.

X : tiller numbers/plant, X : spike length, X : spikelets/spike, X : spike weight/plant, X : grain number/spike, X : grain weight/spike, X :-grain weight, X : total chlorophyll content o ag lea , X : biological yield/plant, X : root weight, X : leaves area and Y: grain yield.

X11X7YX4X3X5X9X2X10X6X8X1

58.96

72.64

86.32

100

Variables

First clusterSecond cluster

Tird cluster

Fourth cluster

S i m i l a r i t y

(a)

X11X6YX4X10X7X3X9X5X2X8X1

47.49

64.99

82.5

100

Variables

First cluster Second cluster Tird cluster S i m i l a r i t y

(b)

F : (a) Similarity levels o theestimatedtwelve wheatvariablesusing the hierarchical cluster analysisundermycorrhizal inoculation anddifferentwater levels. X : tiller numbers/plant, X : spike length, X : spikelets/spike, X : spikeweight/plant, X : grain number/spike, X : grainweight/spike, X : -grain weight, X : total chlorophyll content o aglea ,X :biological yield/plant, X : root weight, X : leavesarea and Y:grain yield. (b) Similarity levels o the estimated twelve wheatvariables usingthe hierarchical cluster analysis under noninoculationconditionand different water levels. X : tiller numbers/plant, X : spike length, X : spikelets/spike, X : spike weight/plant, X : grain number/spike, X :grain weight/spike, X : -grainweight, X : total chlorophyll content o ag lea , X : biological yield/plant,X : root weight, X : leavesareaand Y: grain yield.

the evaluated variables being in groups o their own. In thestudy o Leilah and Al-Khateeb [ ] results proved that -grain weight, weight o grains/spike, harvest index, and thebiological yield were the variables most closely related to thegrain yield.

It has been well established that AM symbiosis protectshost plants against negative effects o drought stress dueto nutritional, physical, and cellular improvements [ ]. Inaddition, the AM symbiosis increases host plant growth dueto improved plant nutrient and water uptakes via externalhyphae in inoculated roots [ ]. Te bene cial effects o different mycorrhizal ungi on plant growth, under drought

conditions, have been demonstrated in wheat [ ] and otherplant species [ , ]. Mouchesi et al. [ ] showed higherproduction o yield and its related traits under inoculatedcondition in compare to noninoculated one due to higheruptake o nutrient elements and water by mycorrhizal roots.

5. Conclusions

Te multiple statistical procedures which have been usedin this study showed that, under water stress conditionand mycorrhizal inoculation, spike weight/plant and totalchlorophyll content o the ag lea are the most important




variables contributing to wheat grain yield, while or thenoninoculated condition, grain weight/spike and chlorophyllcontent o the ag lea , grain weight/plant, and leaves areaare also important. Tere ore, spike weight per plant andchlorophyll content o the ag lea can be used as selectioncriteria in the breeding programs or both the inoculated

and the noninoculated wheat cultivars under different waterregimes, and also grain weight per spike and lea area canbe considered or the noninoculated condition. Furthermore,the results indicated that root inoculation with the mycor-rhizal ungus changed the relationship among morphologicaltraits o wheat cultivars under drought stress.

Overall, the results indicate that mycorrhizal symbiosiscan relatively change the impact o important yield-relatedtraits through production o wheat grain yield which is dueto the effect o mycorrhizal symbiosis on water and nutrientelements uptakes by root. Also, plant breeders can consider

ewer variables as selection criteria under mycorrhizal sym-biosis than nonmycorrhizal condition to nd higher yieldingcultivars in their breeding programs.

Also, using different statistical techniques or determin-ing important traits contributing to grain yield o wheatshowed that simple correlation cannot distinguish important variables. On the other hand, since path analysis uses resultso simple correlation, it is not suitable or using it in selectingimportant variables. Similar to the results o correlation andpathanalysis, cluster analysis andmultiple regression analysiscould not clearly distinguish important traits either. It seemsthat the results o stepwise regression as a selecting methodtogether with principal component and actor analysis arestronger statistical methods to be applied in breeding pro-grams or screening important traits.

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Comparing Relationships Among Yield and Its Related Traits in Mycorrhizal and Nonmycorrhizal Inoculated Wheat Cultivars Under Different Water Regimes Using Multivariate Statistics

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