The Use of the Generalized Linear Model to Assess the ...

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The Use of the Generalized Linear Model to Assess the Speedand Uniformity of Germination of Corn and Soybean Seeds

Deoclecio Jardim Amorim 1 Amanda Rithieli Pereira dos Santos 2 Gabriela Nunes da Piedade 2 Rute Quelvia de Faria 3 Edvaldo Aparecido Amaral da Silva 2 and Maria Maacutercia Pereira Sartori 2

Citation Jardim Amorim D

Pereira dos Santos AR

Nunes da Piedade G

Quelvia de Faria R

Amaral da Silva EA

Pereira Sartori MM The Use of the

Generalized Linear Model to Assess

the Speed and Uniformity of

Germination of Corn and Soybean

Seeds Agronomy 2021 11 588

httpsdoiorg103390

agronomy11030588

Academic Editors Petr Smyacutekal and

Juan Pablo Renzi

Received 19 February 2021

Accepted 16 March 2021

Published 19 March 2021

Publisherrsquos Note MDPI stays neutral

with regard to jurisdictional claims in

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Copyright copy 2021 by the authors

Licensee MDPI Basel Switzerland

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conditions of the Creative Commons

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40)

1 Department of Exact Sciences ESALQmdashUniversity of Satildeo Paulo Av Padua Dias 11 PO Box 9 PiracicabaSP 13418-900 Brazil deocleciojardimhotmailcom

2 Department of Plant Production School of Agriculture UNESPmdashSatildeo Paulo State University AvUniversitaacuteria 3780 PO Box Botucatu SP 18610-034 Brazil amandarithielihotmailcom (ARPdS)gabrielapiedadeunespbr (GNdP) amaralsilvaunespbr (EAAdS)

3 Department of Agricultural Engineering Goiano Federal Institute Rod Geraldo Silva Nascimento Km-25PO Box Urutaiacute GO 75790-00 Brazil rutefariaifgoianoedubr

Correspondence mariampsartoriunespbr

Abstract The use of seeds with high physiological quality allows rapid growth and establishmentof seedlings in the field to be obtained Therefore the accuracy of the information obtained duringthe determination of the physiological quality of seeds is of great importance The objective was touse generalized linear models investigating which link function (Probit Logit and Complementarylog-log) is suitable to predict T50 and uniformity during germination of soybean and corn seedsTo perform the experiments we used seeds from five commercial hybrids andor cultivars of cornand soybean The germination speed was calculated by counting the germinated seeds and theresults were expressed in the form of proportions Germination uniformity was calculated by thedifference in the times required for germination The best model was selected according to the criteriaof the test of Deviance AIC and BIC The Logit model showed accurate results for most cultivarsThe evaluation of germination in the form of proportions considering the assumption of binomialresponse is satisfactory and the choice of the link function is dependent on the characteristics ofeach lot andor species evaluated The use of this methodology makes it possible to estimate anygermination time and uniformity

Keywords physiological quality vigor Zea mays L Glycine max (L) Merrill link functions

1 Introduction

Physiological seed quality is the ability of the seed to perform vital functions charac-terized by germination vigor and longevity which directly affects the implantation of aculture under field conditions High-potential seeds guarantee the growth and develop-ment of plants and the eventual yield of crops [1ndash3]

The correct identification of lots andor cultivars with seeds of high physiological po-tential is one of the main tasks of researchers and professionals working in seed physiologyand technology For this two basic physiological components are taken into accountmdashgermination and vigormdashthese being the factors that theoretically govern the ability of seedsto express their vital functions under biotic and abiotic conditions [45]

There are several ways to assess the physiological quality of a seed lot however themost common method is the germination test [26] As a result the germination test isperformed to determine the final germination percentage of the seed lots However thetime for 50 of the seeds to germinate (T50) and the germination uniformity which is thetime difference between two percentage germinations and other defined parameters [7ndash10]complement the germination data and can indicate the performance of seeds in the field

To assess which seed lot has superior physiological quality the response variable(percentage of germinated seeds) is commonly assessed by non-linear regressions such as

Agronomy 2021 11 588 httpsdoiorg103390agronomy11030588 httpswwwmdpicomjournalagronomy

Agronomy 2021 11 588 2 of 16

the Hill function [71011] Another way used to analyze the germination data is throughlinearization in which a link function is used highlighting the Probit function as the mostused [12ndash14]

However such approaches are imprecise as they consider the response variableto be continuous For instance in the use of non-linear regressions the proportions ofgerminated seeds are cumulative and residual autocorrelation may occur [15] whereasin the use of linearization the germination percentages are transformed into Probit unitsconsidering that the data follow normal distribution which ends up generating inaccuratemodels or simply a lack of linearization [1416]

As the germination process is qualitative with a binary resultmdashthat is the seed doesor not germinatemdasherrors are not normally distributed Thus the classic regression analysisapproach is not indicated [15] An alternative for analyzing this type of data is the theoryof generalized linear models with the binomial distribution being a particular case andindicated for proportion data [131718] Therefore our hypothesis is that the generalizedlinear models are more indicative since it may provide the most accurate informationabout the problem exposed [19]

In this context the objective of this work was to use the generalized linear modelsinvestigating which link function (Probit Logit and Complementary log-log) is suitable topredict T50 and uniformity during germination of soybean and corn seeds

2 Materials and Methods21 Plant material

The commercial corn seeds used were AS 1633 PRO3 2B587 RR 2A401PW ALBandeirante and BRS 4103 The first three refer to hybrid corn seeds while the last two arecultivars The commercial soybean cultivars used were DS59716 IPRO CD2737 RR CD251RR CD2820 IPRO and CD2857 RR Corn seeds were produced in the center of southernBrazil and soybean seeds were produced in the central region of Brazil (Goiaacutes Province)grown in the crop season of 201617

22 Germination T50 and Uniformity Study

The corn and soybean seeds were distributed on sheets of paper towels moistenedwith an amount of water equivalent to 25 times the dry paper mass in Petri dishes For eachhybrid andor cultivar 20 seeds were used with four replications at 15 independent pointsin time Then the Petri dishes were transferred to a BOD (Biochemical Oxygen Demand)germinator type set at a constant temperature of 25 C In Table 1 the average watercontent of seeds for each hybrid andor cultivar used in this research is demonstrated

Table 1 Average water content for corn and soybean hybrids andor cultivars

Corn Soybean

HybridsCultivars (U) Cultivars (U)

AS 1633 PRO3 1072 DS59716 IPRO 11732B587 RR 1136 CD2737 RR 11822A401PW 1200 CD251 RR 1200

AL Bandeirante 1115 CD2820 IPRO 1226BRS 4103 1142 CD2857 RR 1260

(U) = average water content calculated based on wet weight [20]

The counting of the germinated seeds was carried out at regular intervals of 6 12 and24 h and continued until 204 h (15 independent points in time) with the protrusion of theprimary root ge2 mm being adopted as the germination criterion [20] The results wereexpressed by the percentage of the number of seeds germinated in each time interval andthe number of viable seeds obtained at the end of the experiment given by a sequence ofBernoulli tests

Agronomy 2021 11 588 3 of 16

23 Binomial Regression Models and Selection Criteria

Since the response variable that is the proportion of seeds germinated over time hasan exponential distribution the use of the generalized linear models proposed by [21] wasconsidered These models are made up of three parts a random component of the modelin which the response variable has a distribution belonging to the exponential familya systematic component formed by a set of independent variables and the link functionwhich makes the link between the random component and the systematic component

The default distribution assumed for the random variable Yi i = 1n which is thenumber of seeds germinated is the binomial with parameter mi and probability of successπimdashthat is Yi ~ Binomial (mi πi) Thus the link functions used for binomial regressionwere Probit Logit and Complementary log-log The canonical forms of these models arepresented below and according to [17] the use of these functions in canonical form hasas advantages an adequate scale for modeling with practical interpretation of the modelparameters and the simplification of the estimation algorithms Thus these models incanonical form are

g(microi) = Φminus1 (microimi) = Φminus1(πi) (1)

g(microi) = log(

microimi minus microi

)= log

(πi

1minus πi

)(2)

g(microi) = logminuslog

(1minus microi

mi

)= logminuslog(1minus πi) (3)

in which microi is the mean and Φminus1 is the standard normal cumulative distribution functionThe model parameters were obtained using the maximum likelihood method It is

recommended to use the maximum likelihood method due to its excellent consistentand asymptotic properties [1721] When the parameters β0 and β1 were obtained theadjustment was verified by the Deviance criteria and Akaike (AIC) and Bayesian (BIC)information criteria

The Deviance criterion is used as a measure of discrepancy measuring the quality offit of the models for this reason the log likelihood rate statistic is used By this criteriona model is considered ideal when it results in a significantly small value of the deviationthat is generating evidence that for a small number of parameters an adjustment as goodas the saturated model is obtained [2122] With regard to binomial distribution Deviancewas defined by

DB = 2n

sumi=1

[yi log

(yimicroi

)+ (mi minus yi)log

(mi minus yimi minus microi

)](4)

in which yi represents the realization of the random variable mi = n sample size microi i = 12 n are the adjusted values for the model of interest

Thus when Deviance divided by the number of degrees of freedom is not close to 1there is an indication that the model may be poorly adjusted since the binomial modelshave a dispersion parameter ψ = 1 which is fixed Values with parameter dispersion ψ lt 1and ψ gt 1 indicate underdispersion and overdispersion respectively

The checked sub-effect or overdispersion is incorporated into a constant parameterdispersion (ψ) using the maximum estimation method of ldquoquasi-likelihoodrdquo The disper-sion parameter ψ was estimated from the square root of the Deviance quotient by thedegrees of freedom Thus with this new dispersion parameter the standard errors of theparameters (β0 and β1) were corrected and the inferences in the significance tests werereformulated Such correction was performed as described by Equation (5)

SEcorrected = ψ times SE (5)

in which SE and SEcorrected is the standard error and standard error corrected respectively

Agronomy 2021 11 588 4 of 16

Among the more specific criteria and those used in the literature to assess qualitysetting are the Akaike (AIC) [23] and Bayesian (BIC) information criteria [24] Both criteriapenalize the lack of adjustment to the data and the complexity of the model so that thelowest values are preferred [19] The expressions are shown in (6) and (7) respectively

AIC = minus2LL + 2p (6)

BIC = minus2LL + p log(n) (7)

in which p is the number of parameters estimated in the model LL is the log likelihoodevaluated at the value of the estimated parameters and n is the total number of observa-tions used

24 Germination Times and Germination Uniformity

After selecting the most parsimonious model the times needed to germinate werecalculated at 10 20 25 30 40 50 60 70 75 80 90 and 99 for each corn and soybeanhybrid andor cultivar by repetition Germination uniformity was calculated by thedifference in germination times of 75 and 25 (U7525)

The following formulas and Table 2 were used to calculate each time already men-tioned depending on the model selected

Probit(θp)=

1β1

[Φminus1(p)minus β0

](8)

Logit(θp)=

1β1

[log(

p1minus p

)minus β0

](9)

CLL(θp)=

1β1

log[minus log(1minus p)]minus β0

(10)

in which θp is specific time for a determined p-value and (β0 β1) is the pair of estimates fora simple linear regression model

Table 2 Standard table for calculating the germination probabilities obtained by the Probit Logit and Complementarylog-log (CLL) functions

GerminationProbability Probit Logit CLL

p = (Germination100) Φminus1(p) log(p(1minusp)) log[minuslog(1minusp)]

1 00100 minus23263 minus45951 minus460012 00200 minus20537 minus38918 minus390193 00300 minus18808 minus34761 minus349144 00400 minus17507 minus31781 minus319855 00500 minus16449 minus29444 minus297026 00600 minus155478 minus27515 minus278267 00700 minus14758 minus25867 minus262328 00800 minus14051 minus24423 minus248439 00900 minus13408 minus23136 minus23612

10 01000 minus12816 minus21972 minus2250416 01600 minus09945 minus16582 minus1746720 02000 minus08416 minus13863 minus1499925 02500 minus06745 minus10986 minus1245930 03000 minus05244 minus08473 minus1030940 04000 minus02533 minus04055 minus0671750 05000 00000 0000 minus0366560 06000 02533 04055 minus0087470 07000 05244 08473 0185675 07500 06745 10986 03266

Agronomy 2021 11 588 5 of 16

Table 2 Cont



80 08000 08416 13863 0475984 08400 09945 16582 0605790 09000 12816 21972 0834091 09100 13408 23136 0878892 09200 14051 24423 0926593 09300 14758 25867 0978094 09400 15548 27515 1034495 09500 16449 29444 1097296 09600 17507 31781 1169097 09700 18808 34761 1254698 09800 20537 38918 1364199 09900 23263 45951 15272

Values in Probit units Values in Logit units Values in CLL units

25 Statistical Analysis of Germination Times

The germination times T10 T50 T99 and U7525 (uniformity) were submitted to theShapirondashWilk (modified) normality test [25] followed by univariate analysis considering thecompletely randomized design with the application of Fisherrsquos LSD test at 5 probability

Subsequently aiming to know the germination behavior of corn and soybean hybridsandor cultivars globally the germination times (T10 T20 T30 T40 T50 T60 T70 T80T90 and T99) and uniformity (U7525) were submitted to the multivariate classificatory tech-nique of grouping by the Ward method using the Euclidean distance by the standardizeddata matrix for each variable by the formula

Z =Xminus X

S(11)

in which Z is the standardized value observed X is the observed value X is the average ofthe observed values and S is the standard deviation of the observed values

26 Computational Aspects

The work was carried out using SAS Software (Version 94 Cary NC USA) throughGENMOD procedures for model adjustments and selection and GLM for univariate analy-ses For multivariate analysis and preparation of graphics we used MINITAB StatisticalSoftware (Version 17 State College PA USA)

3 Results and Discussion

In Figure 1 (experimental data) we present the representations of the germinationprocess for the different hybrids andor cultivars of corn and soybeans Initially germi-nation is slow with a low proportion then there is a period of acceleration and finallystabilization with all viable seeds germinating

Agronomy 2021 11 588 6 of 16

Figure 1 Germination process of corn and soybean hybrids andor cultivars (mean plusmn standard deviation of germinationproportions at 15 independent points in time)

Agronomy 2021 11 588 7 of 16

When adjusting the Probit Logit and Probit and Logit and Complementary log-loglink functions for the 10 hybrids andor cultivars tested it was observed that no cultivarpresented adequate adjustment simultaneously by the link functions when consideringthe Deviance criterion The corn hybrid and soybean cultivars with dispersion parameterclosest to 1 were AS 1633 PRO3 and CD251 RR both adjusted by the Logit link function Theoverdispersion phenomenon was observed in six cultivars simultaneously with functionsby link values to Deviance from 13 whereas only the 4103 corn cultivar BRS presentedunderdispersion indicated by three functions being used (Table 3)

Table 3 Criteria for adjustment and selection of models for corn and soybean hybrids andor cultivars

Corn

Cultivars Functions Deviance AIC BIC

AS 1633 PRO3Probit 12323 9497 9916Logit 10959 8924 9281 CLL 23024 13992 14349

2B587 RRProbit 21019 17506 17911Logit 17032 15353 15758 CLL 42072 28875 2928

2A401PWProbit 06858 637 6727Logit 05467 5786 6143 CLL 17637 10897 11254

AL BandeiranteProbit 18101 10283 10599Logit 18553 10436 10753 CLL 22246 11692 12009

BRS 4103Probit 03884 7705 8043Logit 04170 7814 8152 CLL 03350 7502 784

Soybean

HybridsCultivars Functions Deviance AIC BIC

DS59716 IPROProbit 15779 10476 10793Logit 16267 10642 10959 CLL 20302 12014 12331

CD2737 RRProbit 14961 10038 10355Logit 13030 9381 9698 CLL 28422 52507 52918


CD2820 IPROProbit 18319 13317 13683Logit 17514 12947 13321 CLL 31479 19371 19745


Complementary log-log Akaike information criterion (AIC) and Bayesian information criterion (BIC)

The phenomena of under- and overdispersion were defined by [17] as a varianceof the response variable above or below the variance expected by the model adoptedThe main consequences of these phenomena are the estimation of standard errors whichconsequently can induce an inappropriate choice of models potentially compromising theconclusions [26] Even in the face of researchersrsquo efforts to control experimental conditionsthe occurrence of phenomena such as overdispersion is common for agricultural systemsas there is great variability [2728]

Agronomy 2021 11 588 8 of 16

Among the tested link functions the complementary log-log was the one that gavethe highest values for Deviancemdashin other words most models formulated with that linkfunction are overdispersed except BRS 4103 While functions Probit and Logit showed thesmallest deviations the latter being closer the Logit function was the one that providedthe best adjustments presenting the appropriate adjustment in 7 of the 10 hybrids andorcultivars used in this research (Table 3)

These results demonstrate the importance of considering the choice of the correctlink function since the use of inaccurate models is potentially generating misleadingconclusions [2628] Although the logit model is currently preferred in some areasmdashforexample in biometrics [222930]mdashin this study smaller deviances were obtained for mosthybrid andor cultivar studied it is necessary to study this by comparing the link seekingfunctions that best describe the probability of interest [31]

For all hybrids andor cultivars tested there was agreement between the Deviancecriterion and the AIC and BIC information criteriamdashthat is those functions with the leastdeviations were also those with the lowest AIC and BIC values (Table 3) This agreementfacilitated the selection of the most parsimonious models to evaluate the germination ofcorn and soybean seeds Thus the Probit model was chosen to evaluate the germination oftwo cultivars the Logit model of seven cultivars and the Complementary log-log of onecultivar (Table 4)

Table 4 Estimation of the parameters of the binomial regression models adjusted to the proportion data in the germinationof corn and soybeans

Corn

HybridsCultivars Functions Parameter Estimated SE SEcorrected p Value p

Valuecorrected

AS 1633PRO3

Logitβ0 minus86418 07731 08093 lt00001 lt00001β1 01653 00158 00165 lt00001 lt00001ψ 10468 - - - -

2B587 RR Logitβ0 minus59099 03861 05039 lt00001 lt00001β1 01009 00074 00096 lt00001 lt00001ψ 13051 - - - -

2A401PW Logitβ0 minus129499 12264 09068 lt00001 lt00001β1 02417 00237 00175 lt00001 lt00001ψ 07394 - - - -

ALBandeirante Probit

β0 minus58063 04596 06183 lt00001 lt00001β1 01616 00126 00170 lt00001 lt00001ψ 13454 - - - -

BRS 4103 CLLβ0 minus60826 04315 02497 lt00001 lt00001β1 01521 00108 00063 lt00001 lt00001ψ 05788 - - - -

Soybean

Cultivars Functions Parameter Estimated SE SEcorrected p value pvaluecorrected

DS59716IPRO Probit


CD2737 RR Logitβ0 minus71362 05913 06749 lt00001 lt00001β1 02666 00214 00245 lt00001 lt00001ψ 11415 - - - -


Agronomy 2021 11 588 9 of 16

Table 4 Cont

Corn


Valuecorrected

CD2820IPRO



Estimated parameters at the 5 probability level β0 = intercept β1 = slope ψ = scale parameter calculated by the deviation divided by thedegrees of freedom SE = standard error and SEcorrected = standard error corrected

The information criteria presented penalize the lack of adjustment to the data andthe complexity of the model therefore models with lower values were chosen [1932]According to these criteria the Logit function stands out as a good alternative to evaluatethe germination of corn and soybean seeds generating theoretical bases for other areassuch as for example in seed science and technology countering the idea that the modelProbit should always be used to assess physiological quality from germination to longevityin thermal models [1214]

Keeping the focus on the estimation of the dispersion parameter the selected modelshad their standard errors of the estimates corrected by quasi-likelihood using Devianceto estimate the constant dispersion parameter where it was used in the procedure in (5)With the application of this correction as expected standard errors showed an increase formodels with overdispersion and a decrease for models with subdispersion however thesignificance of the parameters was not affected (Table 4)

The use of quasi-likelihood to correct estimated standard errors is recommendedby [33] and has been adopted in seed germination studies [1829] in entomology data [3435]in the assessment of ecological data [26] and in the modeling of the number and dry mat-ter mass of Rhizobium nodules in bean culture [28] Therefore there is a solid body ofliterature on the use of this methodology

With the selected models (Table 4) it is possible to estimate the germination times ofinterest to the researcher using the formulas presented in (8) (9) and (10) The averagegermination time or time required for 50 of the seeds used in the germination experiments(T50) is considered to be the preferred one to describe the germination and physiologicalquality of the seeds submitted to different treatments or to compare different batches ofseeds [7ndash91114]

In the case of the Probit and Logit models the T50 can be obtained easily since theparameters β0 and β1 form a linear equation of the type y = a plusmn bx where upon equalingthe terms of the equation to zero the T50 is obtained because both models have symmetryaround zero Thus to calculate the T50 we can use the following formula

T50 = minus β0

β1(12)

in which β0 is the intercept and β1 the slope angleTable 5 shows the values for T50 obtained in the 10 hybrids andor cultivars adopting

the models provided in Table 4 and the expected interval for this parameter obtainedin an experimental way Thus we can consider the methodology of generalized linearmodels adopting the efficient binomial distribution to evaluate the germination of cornand soybeans since all the results estimated by the chosen functions are contained in theexperimental intervals

Agronomy 2021 11 588 10 of 16

Table 5 Estimates of the T50 obtained from the equations in Table 4 and the experimental interval inwhich the T50 is contained

HybridsCultivars T50 (95 CI)T50 (Experimental

Interval)

Corn

AS 1633 PRO3 5223 (4890 5676) h 48ndash60 h2B587 RR 5857 (5442 6227) h 48ndash60 h2A401PW 5357 (4967 5752) h 48ndash60 h

AL Bandeirante 3593 (3202 3987) h 30ndash36 hBRS 4103 3759 (3365 4150) h 36ndash42 h

Cultivars T50 (95 CI)T50 (Experimental

Interval)

Soybean

DS59716 IPRO 3466 (2956 3970) h 30ndash36 hCD2737 RR 2677 (2173 3187) h 24ndash30 hCD251 RR 2692 (2186 3201) h 24ndash30 h

CD2820 IPRO 5312 (4831 5845) h 48ndash60 hCD2857 RR 3344 (2838 3852) h 30ndash36 h

95 CI = 95 confidence interval

As much as authors defend the use of linear models to estimate germination times con-sidering the assumption of normality of the data [121436] often a simple transformationof the percentages of germination using a certain link function such as the Probit model(inv Norm function in Microsoft Excel) does not allow the dataset to be linearized [1416]Thus an approach considering germination as a binary variable in which seeds may ormay not germinate has been more indicated [1318]

It is worth mentioning that another differential of the work is that the calculatedgermination times are obtained based on the number of viable seedsmdashthat is the correctdefinition for the T50 in this research is the time required for 50 of the viable seedsto germinate not requiring additional formulas to calculate the actual amount of germi-nated seeds

In addition to the traditional T50 other parameters can be used to evaluate thegermination of a seed batch for example it is possible to calculate the time for 10 ofviable seeds to germinate or it is also necessary to identify whether two batches withfinal germinations have the same germination uniformity or even understand germinationas a global process not being restricted to just a few parameters that can lead to falseconclusions about the physiological quality of a seed lot

As an example of using other parameters to assess germination we have the workof [711] using Hillrsquos nonlinear function of four parameters to estimate beyond T50 themaximum germination time and germination uniformity which is the time interval be-tween two predefined germinations The germination times of 10 and 90 of the seedshave also been calculated [1437] to evaluate the physiological quality of seeds Howeverthe two most widespread statistics for evaluating the germination of a seed lot are the T50and germination uniformities [71037]

For uniformity of germination in contrast to the T50 there is no standardization beingadopted in several ways U9010 (time for 90 germinationmdashtime for 10 germination) [37]U8416 (time for 84 germinationmdashtime for 16 germination) [10] U7525 (time for 75germinationmdashtime for 25 germination) [7] the latter being the most traditional

Thus seed lots or cultivars that exhibit the lowest values of T50 or any other germina-tion time can be considered of higher physiological quality the same reasoning is valid forgermination uniformity [7837]

Currently research involving the evaluation of seed germination to determine previ-ously mentioned parameters largely uses non-linear models or some link function directlyon the percentage data without paying attention to the type of variable studied and itsprobability distribution which often causes convergence problems or even severe errors inparameter estimation [71014] However when we use generalized linear models these

Agronomy 2021 11 588 11 of 16

difficulties are overcome as we are working with a simple linear equation As a demonstra-tion the germination of the corn cultivar BRS 4103 was modeled by the Complementarylog-log function showing the T50 and the germination uniformity (see Figure 2) The sub-stitution of T50 = 3759 in the equation shown in Figure 2 will return the value of ~ minus03665corresponding to 50 germination as indicated in Table 2

Figure 2 Germination times of BRS 4103 corn cultivar estimated by the Complementary log-log link function T25 = 3180 hT50 = 3759 h T75 = 4214 h and uniformity of germination U7525 At 5 probability

Following selection of link functions better suited to evaluate the germination ofeach plot germination times T10 T50 T99 and U7525 were determined for all samplingdata following which analysis of variance was performed complemented with the meanstest (LSD) in order to compare the physiological potential of corn and soybean cultivarsAccording to the (modified) ShapirondashWilk test [25] the four parameters evaluated havea normal distribution The results of the analysis of variance revealed that the F testwas significant for all corn parameters whereas for soybean cultivars only germinationuniformity was not significant at 5 probability

When evaluating T10 it was possible to observe that the corn cultivar 2A401PW wasthe one that showed the slowest germination while the cultivars AL Bandeirante and BRS4103 showed faster germinations For evaluated soybean varieties cultivating CD2820IPRO showed slower germination different to other cultivars using twice the time to reach10 germination compared with cultivars CD251 RR and CD2737 RR (Table 7)

Table 6 Germination times and uniformity for corn and soybean hybrids andor cultivars

HybridsCultivars T10(95 IC) T50(95 IC) T99(95 IC) U7525(95 IC)

Corn

2A401PW 4483 (4143 4822) a 5357 (4967 5752) a 7194 (5973 8414) b 877 (433 1321) bAS 1633 PRO3 4015 (3676 4355) ab 5223 (4890 5676) a 7934 (6714 9155) b 1268 (824 1712) b

2B587 RR 3744 (3404 4083) b 5857 (5442 6227) a 10207 (899 1143) a 2091 (1647 2535) aAL Bandeirante 2945 (2606 3285) c 3593 (3202 3987) b 4773 (3553 5994) c 683 (240 1127) b

BRS 4103 2526 (2186 2865) c 3759 (3365 4150) b 4996 (3775 6216) c 1028 (584 1472) b

Agronomy 2021 11 588 12 of 16


Cultivars T10(95 IC) T50(95 IC) T99(95 IC) U7525(95 IC)

Soybean

CD2820 IPRO 4030 (3469 4590) a 5312 (4831 5845) a 8074 (7117 9030) a 1308 (959 1658) nsDS59716 IPRO 2573 (2012 3133) b 3466 (2956 3970) b 5079 (4122 6036) bc 937 (588 1286) ns

CD2857 RR 2205 (1644 2766) b 3344 (2838 3852) bc 5729 (4773 6686) b 1140 (791 1490) nsCD251 RR 1944 (1384 2505) b 2692 (2186 3201) c 4262 (3305 5218) c 750 (400 1099) nsCD2737 RR 1901 (1340 2461) b 2677 (2173 3187) c 4311 (3355 5268) c 780 (430 1129) ns

T10(95 CI) T50(95 CI) and T99(95 CI) = time required for germination of 10 50 and 99 of viable seeds and 95 confidence interval

U7525(95 CI) = germination uniformity given by the difference between the 75th and 25 percentiles and 95 confidence interval ns = notsignificant at the 5 probability level averages followed by equal lowercase letters in the columns do not differ between themselves byFisherrsquos LSD test at 5

The behavior of cultivars at T50 was altered in relation to T10 only for cultivar 2B587RR the corn cultivars AL Bandeirante and BRS 4103 were also faster in reaching 50germination in approximately 16 h For soybeans the cultivar CD2820 IPRO continued tobe less vigorous whereas cultivars CD251 RR and CD2737 RR continued to exhibit greaterphysiological quality (Table 7)

The time for 99 of germinated seeds was calculated in order to determine thebehavior of hybrids andor cultivars when they are near to complete 100 germinationThus it is observed that the corn hybrid 2B587 RR which did not present statisticaldifference in the previous times with the cultivar AS 1633 PRO3 showed difference inmore than 22 h This differentiation may be due to uniformity since the corn hybrid 2B587RR proved to be less uniform The best performing corn cultivar in time T99 was ALBandeirante also being the most uniform For soybean cultivars at time T99 it was provedthat CD2820 IPRO is the least vigorous and the CD251 RR and CD2737 RR cultivars havethe highest physiological quality

The lower or higher speed of germination of one cultivar in relation to the other is dueto the time spent in the restoration of the damaged organelles and tissues before beginningthe development of the embryonic axis during the germination process [838] Accordingto [38] cultivars or seed lots with higher germination speed and uniformity are consideredthe most vigorous

The effect of a seed lot can be defined as the sum of the properties that determinethe activity and performance of seed lots as acceptable in germination in a wide range ofenvironments [45] Thus the identification of high-performance seed lots or cultivars is animportant initiative for the success of agricultural production [2]

Under these assumptions we list the corn cultivars AL Bandeirante and BRS 4103and the soybean cultivars CD251 RR and CD2737 RR as those of greater vigor based ongermination and uniformity times Several authors who using a simple radicle countmanaged to predict the vigor of several species [83940] support this statement

The higher vigor of hybrids andor cultivars is evidenced when analyzing germinationin a broader context considering various germination times (T10 T20 T30 T40 T50 T60T70 T80 T90 and T99) and uniformity standard (U7525) through multivariate classificatoryanalysis In general the cophenetic coefficient was above 090 indicating little distortionwith the original data matrix [41] It was possible to verify the existence of three groups inthe dendrogram for both corn and soybeans (Figure 3)

Agronomy 2021 11 588 13 of 16

Figure 3 Dendrogram including germination and uniformity times for corn (A) and soybean (B) seeds I II and III = groupsformed are after multivariate analysis by the Ward method using the Euclidean distance

The corn plants with smaller distance were AL Bandeirante and BRS 4103 withEuclidean distance of 096 (Table 8) or had similar physiological quality confirming theresults for T10 T50 and T99 (Table 7) The greatest difference in physiological qualitywas observed between the cultivars BRS 4103 and 2B587 RR with Euclidean distancegreater than 7 (Table 8) Regarding soybean cultivars the closest or less distant werecultivars CD2737 and CD251 RR with Euclidean distance equal to 015 (Table 8) confirmingthe results introduced previously (Table 5) Additionally the most distant physiologicalpotential was observed for the cultivar CD2820 IPRO with cultivars CD251 RR and CD2737RR with Euclidean distance equal to 802 (Table 8)

Agronomy 2021 11 588 14 of 16

Table 8 Euclidean distances between corn and soybean hybrids andor cultivars obtained using Wardrsquos method

Corn

HybridsCultivars 2A401PW 2B587 RR AL Bandeirante AS 1633 PRO3 BRS 4103

2A401PW 000 000 000 000 0002B587 RR 334 000 000 000 000

AL Bandeirante 526 715 000 000 000AS 1633 PRO3 113 253 507 000 000

BRS 4103 522 671 096 485 000

Soybean

Cultivars CD251 RR CD2737 RR CD2820 IPRO CD2857 RR DS59716 IPRO

CD251 RR 000 000 000 000 000CD2737 RR 015 000 000 000 000

CD2820 IPRO 802 802 000 000 000CD2857 RR 261 254 579 000 000

DS59716 IPRO 232 231 572 111 000

Smallest and largest distance obtained

4 Conclusions

Germination evaluation in the form of proportions considering the assumption ofbinomial response is satisfactory and the choice of the link function will depend on thecharacteristics of each lot andor species evaluated The presented methodology allowscalculation of any germination time and uniformity in a more robust way

Author Contributions Conceptualization DJA and MMPS methodology DJA ARPdSGNdP and RQdF software DJA validation MMPS ARPdS and RQdF formal analysisDJA ARPdS RQdF and MMPS investigation DJA ARPdS RQdF and MMPSwritingmdashoriginal draft preparation DJA MMPS and EAAdS writingmdashreview and editingARPdS GNdP MMPS EAAdS supervision MMPS and EAAdS project administra-tion DJA ARPdS MMPS and EAAdS funding acquisition MMPS and EAAdS Allauthors have read and agreed to the published version of the manuscript

Funding This research was funded by the National Council for Scientific and Technological De-velopment (CNPq-Brazil) finance code 1307732017-4 and the scholarship of the first author thefellowship granted to EA Amaral da Silva under the grant number 309718-2018-0 and Maria MarciaPereira Sartori under the grant number 3055242015-1 Was also funded by the FAPESP-Satildeo PauloResearch Foundation (Proc n 201825698-4) as financial support

Data Availability Statement Data sharing not applicable

Conflicts of Interest The authors declare no conflict of interest

References1 Franccedila-Neto JB Krzyzanowski FC Henning AA Paacutedua GP Tecnologia de produccedilatildeo de soja de alta qualidade Inf ABRATES

2010 20 26ndash322 Marcos Filho J Seed vigor testing An overview of the past present and future perspective Sci Agric 2015 72 363ndash374

[CrossRef]3 Pizaacute MCP Prevosto L Zili C Cejas E Kelly H Baleastrasse K Effects of nonndashthermal plasmas on seed-borne Dia-

porthePhomopsis complex and germination parameters of soybean seeds Innov Food Sci Emerg Technol 2018 49 82ndash91[CrossRef]

4 Association of Official Seed AnalystsmdashAOSA Seed Vigor Testing Handbook AOSA Ithaca NY USA 1983 p 935 Baalbaki R Elias S Marcos-Filho J McDonald MB Seed Vigor Testing Handbook Contribution to the Handbook on Seed

Testing AOSA Ithaca NY USA 2009 Volume 326 Diniz FO Reis MS Dias LAS Arauacutejo EF Sediyama T Sediyama CA Physiological quality of soybean seeds of cultivars

submitted to harvesting delay and its association with seedling emergence in the field J Seed Sci 2013 35 147ndash152 [CrossRef]7 Joosen RVL Kodde J Willems LAJ Ligterink W van der Plas LHW Hilhorst HWM Germinator A software package

for high-throughput scoring and curve fitting of Arabidopsis seed germination Plant J 2010 62 148ndash159 [CrossRef]

Agronomy 2021 11 588 15 of 16

8 Matthews S Noli E Demir I Khajeh-Hosseini MM-H Wagner Evaluation of seed quality From physiology to internationalstandardization Seed Sci Res 2012 22 S69ndashS73 [CrossRef]

9 Hatzig SV Matthias F Breuer F Nesi N Ducournau S Wagner M-H Leckband G Abbadi A Snowdon RJ Genome-wide association mapping unravels the genetic control of seed germination and vigor in Brassica napus Front Plant Sci 20156 221 [CrossRef]

10 Neto VG Ribeiroa PR Del-Bema LE Bernal DT Lima CST Ligterinke W Fernandez LG Castro RD Characterizationof the superoxide dismutase gene family in seeds of two Ricinus communis L genotypes submitted to germination under waterrestriction conditions Environ Exp Bot 2018 155 453ndash463 [CrossRef]

11 El-Kassaby YA Moss I Kolotelo D Stoehr M Seed germination Mathematical representation and parameters extractionFor Sci 2008 54 220ndash227

12 Ellis RH Roberts EH Improved equations for the prediction of seed longevity Ann Bot 1980 45 13ndash30 [CrossRef]13 Hay FR Mead A Bloomberg M Modelling seed germination in response to continuous variables Use and limitations of

Probit analysis and alternative approaches Seed Sci Res 2014 24 165ndash186 [CrossRef]14 Daibes LF Cardoso VJM Seed germination of a South American forest tree described by linear thermal time models

J Therm Biol 2018 76 156ndash164 [CrossRef] [PubMed]15 Onofri A Gresta F Tei F A new method for the analysis of germination and emergence data of weed species Weed Res 2010

50 187ndash198 [CrossRef]16 Gazola S Scapim CA Guedes TA Braccini AL Proposta de modelagem natildeo-linear do desempenho germinativo de

sementes de milho hiacutebrido Ciecircncia Rural 2011 41 551ndash556 [CrossRef]17 McCullagh P Nelder JA Generalized Linear Models Chapman and Hall London UK 1989 p 51118 Murphey M Kovach K Elnacash T He H Bentsink L Donohue K DOG1-imposed dormancy mediates germination

responses to temperature cues Environ Exp Bot 2015 112 33ndash43 [CrossRef]19 Emiliano PC Vivanco MJF Menezes FS Information criteria How do they behave in different models Comput Stat

Data Anal 2014 69 141ndash153 [CrossRef]20 Brasil Ministeacuterio da Agricultura Pesca e Abastecimento Regras Para Anaacutelise de Sementes Secretaria Nacional de Defesa Agropecuaacuteria

Brasiacutelia Brazil 2009 p 39921 Nelder JA Wedderburn RWM Generalized linear models J R Stat Soc A 1972 135 370ndash384 [CrossRef]22 Demeacutetrio CGB Hinde J Moral RA Models for overdispersed data in entomology In Ecological Modeling Applied to Entomology

Springer Cham Switzerland 2014 pp 219ndash25923 Akaike H A new look at the statistical model identification Trans Autom Control 1974 19 716ndash723 [CrossRef]24 Schwarz G Estimating the dimension of a model Ann Stat 1978 6 461ndash464 [CrossRef]25 Rahman MM Govindarajulu ZA Modification of the test of Shapiro and Wilk for normality J Appl Stat 1997 24 219ndash236

[CrossRef]26 Harrison XAA Comparison of observation-level random effect and Beta-Binomial models for modelling overdispersion in

Binomial data in ecology amp evolution PeerJ 2015 3 e1114 [PubMed]27 Suriyagoda LDB Ryan MH Lambers H Renton M Comparison of novel and standard methods for analysing patterns of

plant death in designed field experiments J Agric Sci 2012 150 319ndash334 [CrossRef]28 Rizzardi DA Contreras-Soto RI Figueredo AST Andrade CAB Santana RG Sacapim CA Generalized mixed linear

modeling approach to analyze nodulation in common bean inbred lines Pesquisa Agropecuaacuteria Brasileira 2017 52 1178ndash1184[CrossRef]

29 Nunes JAR Morais AR Bueno Filho JSS Modelagem da superdispersatildeo em dados por um modelo linear generalizadomisto Rev Mat Estat 2004 22 55ndash70

30 Nattino G Lu B Model assisted sensitivity analyses for hidden bias with binary outcomes Biometrics 2018 [CrossRef]31 Freitas L Filho S Juacutenior J Silva F Comparaccedilatildeo das funccedilotildees de ligaccedilatildeo Probit e Logit em regressatildeo binaacuteria considerando

diferentes tamanhos amostrais Encicl Biosf 2013 9 1632 Resende MDV Matemaacutetica e Estatiacutestica na Anaacutelise de Experimentos e no Melhoramento Geneacutetico 1st ed Embrapa Florestas Colombo

Brazil 2007 p 36233 Hinde J Demeacutetrio CGB Overdispersion Models and estimation Comput Stat Data Anal 1998 27 151ndash170 [CrossRef]34 Ribeiro LP Vendramim JD Bicalho KU Andrade MS Fernandes JB Moral RA Demeacutetrio CGB Annona mucosa Jacq

(Annonaceae) A promising source of bioactive compounds against Sitophilus zeamais Mots (Coleoptera) J Stored Prod Res 201355 6ndash14 [CrossRef]

35 Liska GR Silveira EC Reis PR Cirillo MAcirc Gonzalez GGH Seleccedilatildeo de um modelo de regressatildeo binomial para taxa depredaccedilatildeo de Euseius concordis (Chant 1959) Coffee Sci 2015 10 113ndash121

36 Bradford KJ Applications of hydrothermal time to quantifying and modeling seed germination and dormancy Weed Sci 200250 248ndash260 [CrossRef]

37 Coolbear P Mcgill CR Effects of a low-temperature pre-sowing treatment on the germination of tomato seed under temperatureand osmotic stress Sci Hortic 1990 44 43ndash54 [CrossRef]

38 Villiers TA Ageing and longevity of seeds infield conditions In Seed Ecology Heydecker W Ed The Pennsylvania StateUniversity London PA USA 1973 pp 265ndash288

Agronomy 2021 11 588 16 of 16

39 Khajeh-Hosseini M Lomholt A Matthews S Mean germination time in the laboratory estimates the relative vigour and fieldperformance of commercial seed lots of maize (Zea mays L) Seed Sci Technol 2009 37 446ndash456 [CrossRef]

40 Khajeh-Hosseini M Nasehzadeh M Matthews S Rate of physiological germination relates to the percentage of normalseedlings in standard germination tests of naturally aged seed lots of oilseed rape Seed Sci Technol 2010 38 602ndash611 [CrossRef]

41 Silva AR Dias CTSA Cophenetic correlation coefficient for Tocherrsquos method Pesquisa Agropecuaacuteria Brasileira 2013 48 589ndash596[CrossRef]

Introduction

Materials and Methods

Plant material

Germination T50 and Uniformity Study

Binomial Regression Models and Selection Criteria

Germination Times and Germination Uniformity

Statistical Analysis of Germination Times

Computational Aspects

Results

Conclusions

References

Agronomy 2021 11 588 2 of 16

the Hill function [71011] Another way used to analyze the germination data is throughlinearization in which a link function is used highlighting the Probit function as the mostused [12ndash14]

However such approaches are imprecise as they consider the response variableto be continuous For instance in the use of non-linear regressions the proportions ofgerminated seeds are cumulative and residual autocorrelation may occur [15] whereasin the use of linearization the germination percentages are transformed into Probit unitsconsidering that the data follow normal distribution which ends up generating inaccuratemodels or simply a lack of linearization [1416]

As the germination process is qualitative with a binary resultmdashthat is the seed doesor not germinatemdasherrors are not normally distributed Thus the classic regression analysisapproach is not indicated [15] An alternative for analyzing this type of data is the theoryof generalized linear models with the binomial distribution being a particular case andindicated for proportion data [131718] Therefore our hypothesis is that the generalizedlinear models are more indicative since it may provide the most accurate informationabout the problem exposed [19]

In this context the objective of this work was to use the generalized linear modelsinvestigating which link function (Probit Logit and Complementary log-log) is suitable topredict T50 and uniformity during germination of soybean and corn seeds

2 Materials and Methods21 Plant material

The commercial corn seeds used were AS 1633 PRO3 2B587 RR 2A401PW ALBandeirante and BRS 4103 The first three refer to hybrid corn seeds while the last two arecultivars The commercial soybean cultivars used were DS59716 IPRO CD2737 RR CD251RR CD2820 IPRO and CD2857 RR Corn seeds were produced in the center of southernBrazil and soybean seeds were produced in the central region of Brazil (Goiaacutes Province)grown in the crop season of 201617

22 Germination T50 and Uniformity Study

The corn and soybean seeds were distributed on sheets of paper towels moistenedwith an amount of water equivalent to 25 times the dry paper mass in Petri dishes For eachhybrid andor cultivar 20 seeds were used with four replications at 15 independent pointsin time Then the Petri dishes were transferred to a BOD (Biochemical Oxygen Demand)germinator type set at a constant temperature of 25 C In Table 1 the average watercontent of seeds for each hybrid andor cultivar used in this research is demonstrated

Table 1 Average water content for corn and soybean hybrids andor cultivars

Corn Soybean

HybridsCultivars (U) Cultivars (U)

AS 1633 PRO3 1072 DS59716 IPRO 11732B587 RR 1136 CD2737 RR 11822A401PW 1200 CD251 RR 1200

AL Bandeirante 1115 CD2820 IPRO 1226BRS 4103 1142 CD2857 RR 1260

(U) = average water content calculated based on wet weight [20]

The counting of the germinated seeds was carried out at regular intervals of 6 12 and24 h and continued until 204 h (15 independent points in time) with the protrusion of theprimary root ge2 mm being adopted as the germination criterion [20] The results wereexpressed by the percentage of the number of seeds germinated in each time interval andthe number of viable seeds obtained at the end of the experiment given by a sequence ofBernoulli tests

Agronomy 2021 11 588 3 of 16





g(microi) = log(


)= log

(πi

1minus πi

)(2)


(1minus microi

mi





DB = 2n

sumi=1

[yi log

(yimicroi

)+ (mi minus yi)log


)](4)






Agronomy 2021 11 588 4 of 16








Probit(θp)=

1β1


](8)

Logit(θp)=

1β1

[log(

p1minus p

)minus β0

](9)

CLL(θp)=

1β1


(10)







Agronomy 2021 11 588 5 of 16

Table 2 Cont



80 08000 08416 13863 0475984 08400 09945 16582 0605790 09000 12816 21972 0834091 09100 13408 23136 0878892 09200 14051 24423 0926593 09300 14758 25867 0978094 09400 15548 27515 1034495 09500 16449 29444 1097296 09600 17507 31781 1169097 09700 18808 34761 1254698 09800 20537 38918 1364199 09900 23263 45951 15272





Z =Xminus X

S(11)






Agronomy 2021 11 588 6 of 16


Agronomy 2021 11 588 7 of 16



Corn







Soybean









Agronomy 2021 11 588 8 of 16





Corn


Valuecorrected

AS 1633PRO3







Soybean


DS59716IPRO Probit




Agronomy 2021 11 588 9 of 16

Table 4 Cont

Corn


Valuecorrected

CD2820IPRO









T50 = minus β0

β1(12)



Agronomy 2021 11 588 10 of 16



Interval)

Corn




Interval)

Soybean











Agronomy 2021 11 588 11 of 16







Corn



BRS 4103 2526 (2186 2865) c 3759 (3365 4150) b 4996 (3775 6216) c 1028 (584 1472) b

Agronomy 2021 11 588 12 of 16



Soybean











Agronomy 2021 11 588 13 of 16



Agronomy 2021 11 588 14 of 16


Corn


2A401PW 000 000 000 000 0002B587 RR 334 000 000 000 000


BRS 4103 522 671 096 485 000

Soybean


CD251 RR 000 000 000 000 000CD2737 RR 015 000 000 000 000

CD2820 IPRO 802 802 000 000 000CD2857 RR 261 254 579 000 000

DS59716 IPRO 232 231 572 111 000


4 Conclusions














Agronomy 2021 11 588 15 of 16



























Agronomy 2021 11 588 16 of 16




Introduction


Plant material






Results

Conclusions

References

Agronomy 2021 11 588 3 of 16





g(microi) = log(


)= log

(πi

1minus πi

)(2)


(1minus microi

mi





DB = 2n

sumi=1

[yi log

(yimicroi

)+ (mi minus yi)log


)](4)






Agronomy 2021 11 588 4 of 16








Probit(θp)=

1β1


](8)

Logit(θp)=

1β1

[log(

p1minus p

)minus β0

](9)

CLL(θp)=

1β1


(10)







Agronomy 2021 11 588 5 of 16

Table 2 Cont



80 08000 08416 13863 0475984 08400 09945 16582 0605790 09000 12816 21972 0834091 09100 13408 23136 0878892 09200 14051 24423 0926593 09300 14758 25867 0978094 09400 15548 27515 1034495 09500 16449 29444 1097296 09600 17507 31781 1169097 09700 18808 34761 1254698 09800 20537 38918 1364199 09900 23263 45951 15272





Z =Xminus X

S(11)






Agronomy 2021 11 588 6 of 16


Agronomy 2021 11 588 7 of 16



Corn







Soybean









Agronomy 2021 11 588 8 of 16





Corn


Valuecorrected

AS 1633PRO3







Soybean


DS59716IPRO Probit




Agronomy 2021 11 588 9 of 16

Table 4 Cont

Corn


Valuecorrected

CD2820IPRO









T50 = minus β0

β1(12)



Agronomy 2021 11 588 10 of 16



Interval)

Corn




Interval)

Soybean











Agronomy 2021 11 588 11 of 16







Corn



BRS 4103 2526 (2186 2865) c 3759 (3365 4150) b 4996 (3775 6216) c 1028 (584 1472) b

Agronomy 2021 11 588 12 of 16



Soybean











Agronomy 2021 11 588 13 of 16



Agronomy 2021 11 588 14 of 16


Corn


2A401PW 000 000 000 000 0002B587 RR 334 000 000 000 000


BRS 4103 522 671 096 485 000

Soybean


CD251 RR 000 000 000 000 000CD2737 RR 015 000 000 000 000

CD2820 IPRO 802 802 000 000 000CD2857 RR 261 254 579 000 000

DS59716 IPRO 232 231 572 111 000


4 Conclusions














Agronomy 2021 11 588 15 of 16



























Agronomy 2021 11 588 16 of 16




Introduction


Plant material






Results

Conclusions

References

Agronomy 2021 11 588 4 of 16








Probit(θp)=

1β1


](8)

Logit(θp)=

1β1

[log(

p1minus p

)minus β0

](9)

CLL(θp)=

1β1


(10)







Agronomy 2021 11 588 5 of 16

Table 2 Cont



80 08000 08416 13863 0475984 08400 09945 16582 0605790 09000 12816 21972 0834091 09100 13408 23136 0878892 09200 14051 24423 0926593 09300 14758 25867 0978094 09400 15548 27515 1034495 09500 16449 29444 1097296 09600 17507 31781 1169097 09700 18808 34761 1254698 09800 20537 38918 1364199 09900 23263 45951 15272





Z =Xminus X

S(11)






Agronomy 2021 11 588 6 of 16


Agronomy 2021 11 588 7 of 16



Corn







Soybean









Agronomy 2021 11 588 8 of 16





Corn


Valuecorrected

AS 1633PRO3







Soybean


DS59716IPRO Probit




Agronomy 2021 11 588 9 of 16

Table 4 Cont

Corn


Valuecorrected

CD2820IPRO









T50 = minus β0

β1(12)



Agronomy 2021 11 588 10 of 16



Interval)

Corn




Interval)

Soybean











Agronomy 2021 11 588 11 of 16







Corn



BRS 4103 2526 (2186 2865) c 3759 (3365 4150) b 4996 (3775 6216) c 1028 (584 1472) b

Agronomy 2021 11 588 12 of 16



Soybean











Agronomy 2021 11 588 13 of 16



Agronomy 2021 11 588 14 of 16


Corn


2A401PW 000 000 000 000 0002B587 RR 334 000 000 000 000


BRS 4103 522 671 096 485 000

Soybean


CD251 RR 000 000 000 000 000CD2737 RR 015 000 000 000 000

CD2820 IPRO 802 802 000 000 000CD2857 RR 261 254 579 000 000

DS59716 IPRO 232 231 572 111 000


4 Conclusions














Agronomy 2021 11 588 15 of 16



























Agronomy 2021 11 588 16 of 16




Introduction


Plant material






Results

Conclusions

References

Agronomy 2021 11 588 5 of 16

Table 2 Cont



80 08000 08416 13863 0475984 08400 09945 16582 0605790 09000 12816 21972 0834091 09100 13408 23136 0878892 09200 14051 24423 0926593 09300 14758 25867 0978094 09400 15548 27515 1034495 09500 16449 29444 1097296 09600 17507 31781 1169097 09700 18808 34761 1254698 09800 20537 38918 1364199 09900 23263 45951 15272





Z =Xminus X

S(11)






Agronomy 2021 11 588 6 of 16


Agronomy 2021 11 588 7 of 16



Corn







Soybean









Agronomy 2021 11 588 8 of 16





Corn


Valuecorrected

AS 1633PRO3







Soybean


DS59716IPRO Probit




Agronomy 2021 11 588 9 of 16

Table 4 Cont

Corn


Valuecorrected

CD2820IPRO









T50 = minus β0

β1(12)



Agronomy 2021 11 588 10 of 16



Interval)

Corn




Interval)

Soybean











Agronomy 2021 11 588 11 of 16







Corn



BRS 4103 2526 (2186 2865) c 3759 (3365 4150) b 4996 (3775 6216) c 1028 (584 1472) b

Agronomy 2021 11 588 12 of 16



Soybean











Agronomy 2021 11 588 13 of 16



Agronomy 2021 11 588 14 of 16


Corn


2A401PW 000 000 000 000 0002B587 RR 334 000 000 000 000


BRS 4103 522 671 096 485 000

Soybean


CD251 RR 000 000 000 000 000CD2737 RR 015 000 000 000 000

CD2820 IPRO 802 802 000 000 000CD2857 RR 261 254 579 000 000

DS59716 IPRO 232 231 572 111 000


4 Conclusions














Agronomy 2021 11 588 15 of 16



























Agronomy 2021 11 588 16 of 16




Introduction


Plant material






Results

Conclusions

References

Agronomy 2021 11 588 6 of 16


Agronomy 2021 11 588 7 of 16



Corn







Soybean









Agronomy 2021 11 588 8 of 16





Corn


Valuecorrected

AS 1633PRO3







Soybean


DS59716IPRO Probit




Agronomy 2021 11 588 9 of 16

Table 4 Cont

Corn


Valuecorrected

CD2820IPRO









T50 = minus β0

β1(12)



Agronomy 2021 11 588 10 of 16



Interval)

Corn




Interval)

Soybean











Agronomy 2021 11 588 11 of 16







Corn



BRS 4103 2526 (2186 2865) c 3759 (3365 4150) b 4996 (3775 6216) c 1028 (584 1472) b

Agronomy 2021 11 588 12 of 16



Soybean











Agronomy 2021 11 588 13 of 16



Agronomy 2021 11 588 14 of 16


Corn


2A401PW 000 000 000 000 0002B587 RR 334 000 000 000 000


BRS 4103 522 671 096 485 000

Soybean


CD251 RR 000 000 000 000 000CD2737 RR 015 000 000 000 000

CD2820 IPRO 802 802 000 000 000CD2857 RR 261 254 579 000 000

DS59716 IPRO 232 231 572 111 000


4 Conclusions














Agronomy 2021 11 588 15 of 16



























Agronomy 2021 11 588 16 of 16




Introduction


Plant material






Results

Conclusions

References

Agronomy 2021 11 588 7 of 16



Corn







Soybean









Agronomy 2021 11 588 8 of 16





Corn


Valuecorrected

AS 1633PRO3







Soybean


DS59716IPRO Probit




Agronomy 2021 11 588 9 of 16

Table 4 Cont

Corn


Valuecorrected

CD2820IPRO









T50 = minus β0

β1(12)



Agronomy 2021 11 588 10 of 16



Interval)

Corn




Interval)

Soybean











Agronomy 2021 11 588 11 of 16







Corn



BRS 4103 2526 (2186 2865) c 3759 (3365 4150) b 4996 (3775 6216) c 1028 (584 1472) b

Agronomy 2021 11 588 12 of 16



Soybean











Agronomy 2021 11 588 13 of 16



Agronomy 2021 11 588 14 of 16


Corn


2A401PW 000 000 000 000 0002B587 RR 334 000 000 000 000


BRS 4103 522 671 096 485 000

Soybean


CD251 RR 000 000 000 000 000CD2737 RR 015 000 000 000 000

CD2820 IPRO 802 802 000 000 000CD2857 RR 261 254 579 000 000

DS59716 IPRO 232 231 572 111 000


4 Conclusions














Agronomy 2021 11 588 15 of 16



























Agronomy 2021 11 588 16 of 16




Introduction


Plant material






Results

Conclusions

References

Agronomy 2021 11 588 8 of 16





Corn


Valuecorrected

AS 1633PRO3







Soybean


DS59716IPRO Probit




Agronomy 2021 11 588 9 of 16

Table 4 Cont

Corn


Valuecorrected

CD2820IPRO









T50 = minus β0

β1(12)



Agronomy 2021 11 588 10 of 16



Interval)

Corn




Interval)

Soybean











Agronomy 2021 11 588 11 of 16







Corn



BRS 4103 2526 (2186 2865) c 3759 (3365 4150) b 4996 (3775 6216) c 1028 (584 1472) b

Agronomy 2021 11 588 12 of 16



Soybean











Agronomy 2021 11 588 13 of 16



Agronomy 2021 11 588 14 of 16


Corn


2A401PW 000 000 000 000 0002B587 RR 334 000 000 000 000


BRS 4103 522 671 096 485 000

Soybean


CD251 RR 000 000 000 000 000CD2737 RR 015 000 000 000 000

CD2820 IPRO 802 802 000 000 000CD2857 RR 261 254 579 000 000

DS59716 IPRO 232 231 572 111 000


4 Conclusions














Agronomy 2021 11 588 15 of 16



























Agronomy 2021 11 588 16 of 16




Introduction


Plant material






Results

Conclusions

References

Agronomy 2021 11 588 9 of 16

Table 4 Cont

Corn


Valuecorrected

CD2820IPRO









T50 = minus β0

β1(12)



Agronomy 2021 11 588 10 of 16



Interval)

Corn




Interval)

Soybean











Agronomy 2021 11 588 11 of 16







Corn



BRS 4103 2526 (2186 2865) c 3759 (3365 4150) b 4996 (3775 6216) c 1028 (584 1472) b

Agronomy 2021 11 588 12 of 16



Soybean











Agronomy 2021 11 588 13 of 16



Agronomy 2021 11 588 14 of 16


Corn


2A401PW 000 000 000 000 0002B587 RR 334 000 000 000 000


BRS 4103 522 671 096 485 000

Soybean


CD251 RR 000 000 000 000 000CD2737 RR 015 000 000 000 000

CD2820 IPRO 802 802 000 000 000CD2857 RR 261 254 579 000 000

DS59716 IPRO 232 231 572 111 000


4 Conclusions














Agronomy 2021 11 588 15 of 16



























Agronomy 2021 11 588 16 of 16




Introduction


Plant material






Results

Conclusions

References

Agronomy 2021 11 588 10 of 16



Interval)

Corn




Interval)

Soybean











Agronomy 2021 11 588 11 of 16







Corn



BRS 4103 2526 (2186 2865) c 3759 (3365 4150) b 4996 (3775 6216) c 1028 (584 1472) b

Agronomy 2021 11 588 12 of 16



Soybean











Agronomy 2021 11 588 13 of 16



Agronomy 2021 11 588 14 of 16


Corn


2A401PW 000 000 000 000 0002B587 RR 334 000 000 000 000


BRS 4103 522 671 096 485 000

Soybean


CD251 RR 000 000 000 000 000CD2737 RR 015 000 000 000 000

CD2820 IPRO 802 802 000 000 000CD2857 RR 261 254 579 000 000

DS59716 IPRO 232 231 572 111 000


4 Conclusions














Agronomy 2021 11 588 15 of 16



























Agronomy 2021 11 588 16 of 16




Introduction


Plant material






Results

Conclusions

References

Agronomy 2021 11 588 11 of 16







Corn



BRS 4103 2526 (2186 2865) c 3759 (3365 4150) b 4996 (3775 6216) c 1028 (584 1472) b

Agronomy 2021 11 588 12 of 16



Soybean











Agronomy 2021 11 588 13 of 16



Agronomy 2021 11 588 14 of 16


Corn


2A401PW 000 000 000 000 0002B587 RR 334 000 000 000 000


BRS 4103 522 671 096 485 000

Soybean


CD251 RR 000 000 000 000 000CD2737 RR 015 000 000 000 000

CD2820 IPRO 802 802 000 000 000CD2857 RR 261 254 579 000 000

DS59716 IPRO 232 231 572 111 000


4 Conclusions














Agronomy 2021 11 588 15 of 16



























Agronomy 2021 11 588 16 of 16




Introduction


Plant material






Results

Conclusions

References

Agronomy 2021 11 588 12 of 16



Soybean











Agronomy 2021 11 588 13 of 16



Agronomy 2021 11 588 14 of 16


Corn


2A401PW 000 000 000 000 0002B587 RR 334 000 000 000 000


BRS 4103 522 671 096 485 000

Soybean


CD251 RR 000 000 000 000 000CD2737 RR 015 000 000 000 000

CD2820 IPRO 802 802 000 000 000CD2857 RR 261 254 579 000 000

DS59716 IPRO 232 231 572 111 000


4 Conclusions














Agronomy 2021 11 588 15 of 16



























Agronomy 2021 11 588 16 of 16




Introduction


Plant material






Results

Conclusions

References

Agronomy 2021 11 588 13 of 16



Agronomy 2021 11 588 14 of 16


Corn


2A401PW 000 000 000 000 0002B587 RR 334 000 000 000 000


BRS 4103 522 671 096 485 000

Soybean


CD251 RR 000 000 000 000 000CD2737 RR 015 000 000 000 000

CD2820 IPRO 802 802 000 000 000CD2857 RR 261 254 579 000 000

DS59716 IPRO 232 231 572 111 000


4 Conclusions














Agronomy 2021 11 588 15 of 16



























Agronomy 2021 11 588 16 of 16




Introduction


Plant material






Results

Conclusions

References

Agronomy 2021 11 588 14 of 16


Corn


2A401PW 000 000 000 000 0002B587 RR 334 000 000 000 000


BRS 4103 522 671 096 485 000

Soybean


CD251 RR 000 000 000 000 000CD2737 RR 015 000 000 000 000

CD2820 IPRO 802 802 000 000 000CD2857 RR 261 254 579 000 000

DS59716 IPRO 232 231 572 111 000


4 Conclusions














Agronomy 2021 11 588 15 of 16



























Agronomy 2021 11 588 16 of 16




Introduction


Plant material






Results

Conclusions

References

Agronomy 2021 11 588 15 of 16



























Agronomy 2021 11 588 16 of 16




Introduction


Plant material






Results

Conclusions

References

Agronomy 2021 11 588 16 of 16




Introduction


Plant material






Results

Conclusions

References

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