Revista Mexicana Ciencias Agrícolas   volume 11   number 4   May 16 - June 29, 2020

DOI: https://doi.org/10.29312/remexca.v11i4.2249

Article

SAS code to analyze a complete dialelic and heterosis. An environment

Delfina de Jesús Pérez López

Claudia Saavedra Guevara

Martín Rubí Arriaga

J. Ramón Pascual Franco Martínez

Francisco Gutiérrez Rodríguez

Andrés González Huerta§

Center for Research and Advanced Studies in Phytomeroration-Faculty of Agricultural Sciences-Autonomous University of the State of Mexico-University Campus ‘El Cerrillo’. El Cerrillo Piedras Blancas, Toluca, State of Mexico, Mexico. AP. 435. Tel. 722 2965531, ext. 148. (djperezl@uaemex.mx; csg1003@yahoo.com; m-rubi65@yahoo.com.mx; jrfrancom@uaemex.mx; fgrfca@hotmail.com.

§Corresponding author: agonzalezh@uaemex.mx.

Abstract

The development of statistical analysis system (SAS) programs and their validation with freely available software is essential when there are no financial resources to acquire the license of an appropriate statistical package. In this study a code for SAS is presented and its validation is performed with the program proposed by Zhang and Kang (1997), modified by Saavedra (2019). The code generates an analysis of variance with partition of the effects of treatments on parents (P), direct crosses (CD), reciprocal crosses (CR), P vs crosses, and CD vs CR. In addition to generating the comparison of treatment means with the Tukey test, the genetic effects for parents or for their crosses are estimated (Gi, Sij, Rij, Mi); as well as, those of heterosis with the average of both parents or with the best of them. Since both codes only coincide in the calculation of the previously indicated genetic effects, their simultaneous application is suggested to carry out a complete analysis of Griffing’s method 1 (1956a, b). The code that has been proposed will be especially useful for plant breeders and geneticists and especially for undergraduate and graduate level biological and agricultural science students with little training in the programming language at SAS.

Keywords: Griffing method 1, model 1, randomized complete blocks, Tukey test.

Reception date: February 2020

Acceptance date: April 2020

Introduction

Dialectic crosses were designed before the 1950’s, but soon became a powerful tool for plant and animal breeders, who to recognize the merit of various parents evaluated their progenies through the effects and variances of general combinatorial aptitude (ACG) and specific (ACE) (Sprague and Tatum, 1942; Griffing, 1956a, b; González et al., 2007a, b). These define new heterotic patterns or a segregating population from which it is possible to isolate again outstanding plants, predict the response to the selection or the behavior of hybrids or synthetics formed with new lines (Hallauer and Miranda, 1988; Christie and Shattuck, 1992; González et al., 2007a, b).

Analysis of a complete diallel crosses experiment without a personal computer (PC) is laborious and to save time, there are several statistical packages such as SAS (https://www.sas.com/store/index.ep), Excel (Microsoft Office), Indostat (https://www.indostat.org), AGD-R (https://data.cimmyt.org/dataset.xhtml?persistentld= hdl:11529/10202), Agrobase II, generation (http://www.agronomix.com), PB Tools (https://pbtools.software.informer.com/2.0/), TNAUSTAT (https:// sites. google.com/site/tnaustat) and GSCA (https://bioseqdata.com/gsca/gsca. htm), among others; of these, only Agrobase II generation and Indostat must be purchased under license with a cost higher than $1 000.00 USD, because at least three modules are required to properly operate both softwares. Although SAS is the best statistical package, it is common for breeders and geneticists to use various software to analyze data from experiments designed in the agricultural and biological sciences (Padilla et al., 2019a; Padilla et al., 2019b; Saavedra, 2019).

Also, for many users it is difficult to download free software because there is an incompatibility problem between it and their PCs, there are technical problems during the downloads, the necessary permission is not obtained, the researchers do not respond to the requests or the program does not work in versions old or recent Windows. In this context, it would be desirable to elaborate and validate some codes for SAS, for versions 6.01 or higher (SAS, 1989), that allow complementing the genetic-statistical analysis for experiments of complete dialectic crosses.

Materials and methods

Full dialectic

In methodology 1, described in Saavedra (2019), the analysis of variance (ANOVA) for a single environment contains repetitions (R), treatments (Trat) and experimental error, its statistical model corresponds to a randomized complete block design. In ANOVA, the effects of Trat are divided into progenitors (P), direct crosses (CD), reciprocal crosses (CR), P vs crosses and CD vs CR, as suggested by González et al. (2007b), both contrasts estimate average heterosis and maternal and non-maternal effects.

The program calculates the differences between Trat with the Tukey test (SAS, 1989). This code can be easily modified if the user requires other means comparison tests, or various regression and correlation analyzes, these analyzes can be extended to series of experiments in time and space (Saavedra, 2019).

In methodology 2, which corresponds to  method 1 of Griffing (1956a, b), the ANOVA for a single trial has repetitions (R), general combinatorial aptitude (ACG), specific combinatorial aptitude (ACE), maternal effects (EM) and reciprocal effects (ER); in the series of experiments the interactions of these with only two environments could be estimated.

Also, in both cases, the effects of gi for each parent or of sij for each cross, the reciprocal and maternal effects would be estimated (Zhang and Kang, 1997). The variance and heritability components, and the prediction of hybrids and synthetics could be estimated with other programs for SAS (Martínez, 1983; González et al., 2007a, b; Montesinos et al., 2007).

Defining variables in code

In the database called “diallel” female, male, YH, YP, YM, X, Y, A, B, C, D and M are defined, in the female and male variables the combinations of each female with each male, YH, YP and YM correspond to the cross, female and male means, respectively. In X, Y the totals for each pair of CD and CR are captured. After the sum over repetitions has been done. In A, B, C, D, each line of the CD or the CR appears twice, as female and as male (Yi. or Y.i.; Yj.. or Y.j.)M is the great arithmetic mean, GI, SIJ, RIJ and MI are the same genetic effects that are estimated with the formulas proposed in method 1 of Griffing (1956a, b).

Values used in the code

In this study, 96 data were used, corresponding to four parents, their six direct crosses and their six reciprocal crosses, registered in six repetitions (Saavedra, 2019).

Results and discussion

Since its creation in 1972, SAS programs for the analysis of diallelic cross experiments have been implemented on personal computers PC’s by several researchers. The great achievements that have been obtained for PC’s are attributed to Schaffer and Usanis (1989); Burow and Coors (1994); Magari and Kang (1994); Zhang and Kang (1997); Martínez (1983, 1991), among others. More recently, Mastache and Martínez (1998a, 1998b, 1999a, 1999b), they refined their algorithms to obtain the best empirical linear and unbiased predictors (MPLI) of the effects of the parents, to help users with little training in programming, when using completely random designs (DCA) and complete random blocks (BCA).

Also, Mastache and Martínez (2003) obtained an integrated algorithm for its simultaneous analysis in balanced experiments for fixed or random effects models. These and other programs could also be used to validate and complement the outputs that were obtained with the code proposed in the present study (Zhang et al., 2005; Montesinos et al., 2007).

Zhang et al. (2005) modified the codes of Zhang and Kang (1997); in Diallel-SAS05, they discussed a more efficient program for the genetic-statistical analysis four methods of Griffing’s (1956a, b), including those corresponding to designs II and III of Gardner and Eberhart (1966). This program is friendlier and easier to modify than Diallel-SAS, when parents vary from 4 to 12, when there is no restriction on the number of environments, and when the effects and variances of ACG and ACE for parents and crosses are estimated, as well as their interactions with environments. As with other statistical packages, there are problems in deploying on personal computers with recent versions of Windows (Padilla et al., 2019a, b).

With program 1a the ANOVA and the comparison of means (Tukey, p= 0.01) are calculated. Since Trat and its components are considered as fixed effects, the F tests are tested with the mean square of the experimental or residual error of the model. In your code, Data, SET, IF-THEN, ANOVA, and GLM are used to define subsets of data. The user will be careful to respect the correct order in the database: P, CD and CR, the signs and the coefficients of the contrasts, as for other statistical packages, must be captured within the program. If there is any doubt to design this type of contrasts, it is suggested to consult Padilla et al. (2019a).

At the SAS output, if R= 6 and Trat= 4, the ANOVA corresponds to parents; your hypothesis test is not correct because it was constructed as a subset and its mean square of the residual is a fraction of the 96 data. In this context, a table of F should be consulted at this stage there are no restrictions regarding the number of variables to analyze. The code can be modified to include tests for the least significant difference (DMS or LSD), Dunnett, or mutually orthogonal contrasts, among others. With two or more variables, it is possible to modify the program to perform regression and correlation, estimate simple statistics and apply multivariate methodologies, among others.

The code corresponding to program 1a is presented below:

Data corn; Input rep trat PVG;Cards;

1 01 758

1 02 761

6 15 768

6 16 758;

DATA PARENTS;SET CORN;IF TRAT>4 THEN DELETE;*parents only;

DATA CD;SET CORN;IF TRAT<5 OR TRAT>10 THEN DELETE;* only direct crosses;

DATA CR; SET CORN; IF TRAT<11 THEN DELETE; *only reciprocal crosses;

PROC ANOVA DATA= CORN; CLASS REP TRAT; MODEL PVG=REP TRAT; MEANS TRAT/TUKEY LINES ALPHA=0.01;* Analysis with 96 data;

PROC GLM DATA= CORN; CLASS REP TRAT; MODEL PVG=REP TRAT;

CONTRAST "P VS CROSSES"TRAT 12 12 12 12 -4 -4 -4 -4 -4 -4 -4 -4 -4 -4 -4 -4;

CONTRAST "CD VS CR" TRAT 0 0 0 0 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1;

PROC ANOVA DATA= PARENTS; CLASS REP TRAT; MODEL PVG=REP TRAT;*Analysis of variance for parents;

PROC ANOVA DATA=CD; CLASS REP TRAT; MODEL PVG=REP TRAT;* Analysis of variance for direct crosses;

PROC ANOVA DATA=CR; CLASS REP TRAT; MODEL PVG=REP TRAT;*Analysis of variance for reciprocal crosses; RUN;

With program 1b, estimates of genetic effects (Gi, Sij, Rij, MI) and heterosis (%) are obtained. The definition of variables before CARDS must be correctly indicated using the data in Tables 1 and 2 (Saavedra, 2019), but the denominator values of the GI, SIJ, RIJ and MI formulas should be

corrected, if R, P or both of them. At this stage it is essential to resort to the devices that Martínez (1983) used establishing a logical way of relating formulas Griffing (1956a, b) with the programming language in SAS (SAS Institute, 1989).

Table 1. Volumetric weight of the grain (g L-1) of 16 crosses formed with four lines.

Table 2. Values used to estimate genetic effects and heterosis.

Note: added over repetitions and row or column totals are the contribution of each female or male line, respectively.

In some columns, such as for the large arithmetic mean (M), which is a constant for the 12 mattings, there are duplicate values, but it is easy to establish which parent or cross they correspond to because the data is shown in descending order (González et al., 2007a, b; Saavedra, 2019).

The code for program 1b is presented below:

DATA HETERO; INPUT FEMALE MALE YH YP YM X Y A B C D M;

MP= YP+YM)/2;*to calculate the mean of the parents (MP);

BP= MAX (YP,YM);*to choose the best parent (BP);

DMP= YH-MP;* to estimate the numerator of the heterosis formula with MP;

HMP= (DMP/MP)*100;*to estimate heterosis with the mean of the parents, in %;

DBP= YH-BP;*calculate the numerator of the heterosis formula with BP;

HBP= (DBP/BP)*100;*calculates heterosis with the best father, in %;

GI= (A+B)/48 - M;*estimate the effects of gi;

SIJ= (X+Y)/12 -(A+B+C+D)/48 + M;*calculate the effects of Sij;

RIJ= (X-Y)/12;*determines the effects of rij;

MI= (A-B)/48;* calculate the effects mi;

CARDS;

1 2 781.1 759.1 762.5 4687 4645 18834 18891 18717 18636 792.01

1 3 813.8 759.1 804.8 4883 4851 18834 18891 19496 19481 792.01

1 4 784.8 759.1 778.0 4709 4840 18834 18891 18986 19025 792.01

2 3 807.6 762.5 804.8 4846 4819 18717 18636 19496 19481 792.01

2 4 775.1 762.5 778.0 4651 4555 18717 18636 18986 19025 792.01

3 4 832.8 804.8 778.0 4997 4923 19496 19481 18986 19025 792.01

2 1 774.1 762.5 759.1 4645 4687 18636 18717 18891 18834 792.01

3 1 808.5 804.8 759.1 4851 4883 19481 19496 18891 18834 792.01

4 1 806.6 778.0 759.1 4840 4709 19025 18986 18891 18834 792.01

3 2 803.1 804.8 762.5 4819 4846 19481 19496 18636 18717 792.01

4 2 759.1 778.0 762.5 4555 4651 19025 18986 18636 18717 792.01

4 3 820.5 778.0 804.8 4923 4997 19025 18986 19481 19496 792.01

TITLE ‘Effects of gi, sij, rij, mi and heterosis for the general dialectic’;

DATA DOS; SET HETERO; PROC PRINT; RUN;

                             ANOVA procedure

Dependent variable: PVG

                                           Sum of          Square of

Source                     DF      square            the mean           F-Value   Pr > F

Model                     20     51191.16667     2559.55833        9.69       <.0001

Error                        75      19801.82292      264.02431

Total correct          95      70992.98958

             R-square        Coef Var        Root MSE     PVG Mean

               0.721074      2.051592        16.24882      792.0104

                                                                  Square of

Source                  DF      ANOVA SS       the mean      F-Value   Pr > F

rep                         5         3365.67708      673.13542      2.55        0.0347

trat                       15      47825.48958     3188.36597     12.08      <.0001

            Tukey studentized range test (HSD) for PVG

Note: This test controls the rate of the probability of making an experimentwise Type I error, but usually has a higher Type II error rate than REGWQ.

                Alpha                                                        0.01

                Degrees of freedom error                         75

                Mean square error                                    264.0243

                Critical value of the studentized range     5.76634

                Minimal significant difference                 38.251

       Means with the same letter are not significantly different.

              Tukey   Grouping                  Mean        N    trat

                              A                           832.833     6     10

                B           A                           820.500     6     16

                B           A     C                   813.833     6     6

                B    D    A     C                   808.500     6     12

                B    D     A    C                   807.667     6     8

                B    D     A    C                   806.667     6     13

                B    D     A    C                  804.833      6      3

                B    D     A    C                  803.167      6     14

                B    D     E     C                 784.833      6      7

                     D       E     C                 781.167      6      5

                     D       E     C                 778.000      6      4

                     D       E                         775.167      6      9

                     D       E                         774.167      6      11

                               E                         762.500      6      2

                               E                         759.167      6      1

                               E                         759.167      6      15

                                                                       Square of

Contrast                      DF    Contrast SS       the mean         F-Value     Pr > F

P VS CRUZAS             1    8075.086806     8075.086806        30.58       <.0001

CD VS CR                    1     272.222222        272.222222          1.03        0.3132      

Dependent variable: PVG

                                                                    Square of

Source                 DF       ANOVA SS       the mean       F-Value    Pr > F

rep                        5       1952.875000      390.575000      2.00         0.1376

trat                        3        7805.458333    2601.819444     13.30       0.0002      

                                                                   Square of

Source                  DF       ANOVA SS       the mean        F-Value     Pr > F

rep                          5        2869.25000       573.85000        3.57         0.0143

trat                          5       15157.25000      3031.45000     18.84        <.0001  

                                                                   Square of

Source                  DF       ANOVA SS      the mean           F-Valor     Pr > F

rep                         5        1741.80556       348.36111             0.90         0.4948

trat                         5      16515.47222      3303.09444            8.56         <.000

            Effects of Gi, Sij, Rij, Mi and heterosis for methodology 1

Obs FEMALE MALE  YH  YP   YM       X      Y        A        B         C          D         M         MP

1         1            2    781.1  759.1  762.5  4687  4645  18834  18891  18717  18636  792.01  760.80

2         1            3   813.8  759.1  804.8  4883  4851  18834  18891  19496  19481  792.01  781.95

3         1            4   784.8  759.1  778.0  4709  4840  18834  18891  18986  19025  792.01  768.55

4         2            3   807.6  762.5  804.8  4846  4819  18717  18636  19496  19481  792.01  783.65

5         2            4   775.1  762.5  778.0  4651  4555  18717  18636  18986  19025  792.01  770.25

6         3            4   832.8  804.8  778.0  4997  4923  19496  19481  18986  19025  792.01  791.40

7         2            1   774.1  762.5  759.1  4645  4687  18636  18717  18891  18834  792.01  760.80

8         3            1   808.5  804.8  759.1  4851  4883  19481  19496  18891  18834  792.01  781.95

9         4            1   806.6  778.0  759.1  4840  4709  19025  18986  18891  18834  792.01  768.55

10       3            2   803.1  804.8  762.5  4819  4846  19481  19496  18636  18717  792.01  783.65

11       4            2   759.1  778.0  762.5  4555  4651  19025  18986  18636  18717  792.01  770.25

12       4            3   820.5  778.0  804.8  4923  4997  19025  18986  19481  19496  792.01  791.40

Obs    BP      DMP       HMP      DBP       HBP        GI            SIJ          RIJ         MI

  1     762.5    20.30    2.66824    18.6    2.43934    -6.0725     5.5517     3.5000  -1.1875

  2     804.8    31.85    4.07315     9.0    1.11829    -6.0725     5.2183     2.6667  -1.1875

  3     778.0    16.25    2.11437     6.8    0.87404    -6.0725     9.9267   -10.9167  -1.1875

  4     804.8    23.95    3.05621     2.8    0.34791   -13.8225     7.2183     2.2500   1.6875

  5     778.0     4.85    0.62967    -2.9   -0.37275   -13.8225   -10.9067     8.0000   1.6875

  6     804.8    41.40    5.23124    28.0    3.47913    20.0108    14.7600     6.1667   0.3125

  7     762.5    13.30    1.74816    11.6    1.52131   -13.8225     5.5517    -3.5000   1.6875

  8     804.8    26.55    3.39536     3.7    0.45974    20.0108     5.2183    -2.6667   0.3125

  9    778.0    38.05    4.95088    28.6    3.67609    -0.1142     9.9267    10.9167  -0.8125

 10   804.8    19.45    2.48198    -1.7   -0.21123    20.0108     7.2183    -2.2500   0.3125

 11   778.0   -11.15   -1.44758   -18.9   -2.42931    -0.1142   -10.9067    -8.0000  -0.8125

 12   804.8    29.10    3.67703    15.7    1.95080    -0.1142    14.7600    -6.1667  -0.8125

The previous results were validated with the program developed by Zhang and Kang (1997). In ANOVA the code allows the partitioning of possible cross effects in ACG, ACE, ER and EM, when SORT, BY, GLM, IF-THEN, DROP, ARRAY, ELSE, GLM, CONTRAST, ESTIMATE and some MACROS were implemented. In Martínez (1991) these and other components are presented to elaborate the reference code.

The program of Zhang and Kang (1997) applies to the four methods of Griffing (1956a, b), for method 1 m variables are analyzed in two environments. In the present study, this was adjusted to a single environment by implementing the restriction I IF ENV> 1 THEN DELETE or IF ENV< 2 THEN DELETE, captured before DROP and after INPUT. Modifying it is more laborious for users with little training in programming and, especially when the analysis extends to series of experiments (Singh, 1973; Mastache and Martínez, 2003; Zhang et al., 2005).

TNAUSTAT software, in addition to calculating the genetic effects related to parents and their crosses in method 1 of Griffing (1956a, b) also, simultaneously, allows the calculation of hybrid vigor with the mean of both parents, with the best of them and additionally, based on commercial heterosis. This has the additional advantage of estimating the genetic parameters corresponding to the mating design I, proposed by Hayman (1954). However, this software was designed to work properly on a platform with MS Dos, so DOSBox software must be downloaded in advance.

The Zhang and Kang program (1997), modified by Saavedra (2019), is presented below:

OPTIONS PS=56 LS=78; TITLE 'METHOD 1'; DATA METHOD1;

INPUT I J REP HYBRID YIELD ENV; IF ENV>1 THEN DELETE;DROP N NI NJ P;

P=4;*NUMBER OF PARENTAL LINES? ; ARRAY GCA (N) G1 G2 G3;DO N=1 TO (P-1);

GCA= ((I=N)-(I=P)) + ((J=N)-(J=P)); END;ARRAY SCA(N) S11 S12 S13 S22 S23 S33;

N=0; DO NI=1 TO (P-1); DO NJ=NI TO (P-1); N+1; IF NI=NJ THEN DO;

SCA=(I=NI)*((J=NJ)-(J=P))+(I=P)*((J=P)-(J=NI));END;ELSE DO;

SCA=(I=NI)*(J=NJ)-(J=P)*((I=NI)+(I=NJ)-(I=P)*2)+(I=NJ)*(J=NI)

-(I=P)*((J=NI)+(J=NJ));END;END;END;

ARRAY REC (N) R12 R13 R14 R23 R24 R34; N=0; DO NI=1 TO (P-1);

DO NJ= (NI+1) TO P; N+1; REC= (I=NI)*(J=NJ)-(j=NI)*(I=NJ); END;END;

ARRAY MAT (N) M1 M2 M3; DO N=1 TO (P-1); MAT= (I=N) + (J=P)-(J=N)-(I=P);

END;ARRAY NONM (N) N12 N13 N23;N=0;DO NI=1 TO (P-2);DO NJ=(NI+1) TO (P-1);N+1;NONM=((I=NI)*(J=NJ))-(I=NJ)*(J=NI)-((I=NI)*(J=P))+(I=NJ)*(J=P)

+ ((I=P)*((J=NI)-(J=NJ))); END;END;CARDS;

1 1 1 01 758 1

1 2 1 02 814 1

1 3 1 03 805 1

4 3 6 15 758 1

4 4 6 16 775 1;

PROC SORT; BY REP ENV I J; PROC GLM;CLASS REP ENV HYBRID;MODEL YIELD=ENV REP(ENV) HYBRID HYBRID*ENV;TEST H=HYBRID E=HYBRID*ENV;LSMEANS HYBRID;

RUN; TITLE 'DIALLEL-SAS 1'; PROC GLM; CLASS REP ENV HYBRID;

MODEL YIELD= ENV REP (ENV) G1 G2 G3 S11 S12 S13 S22 S23 S33 R12 R13 R14 R23 R24 R34 G1*ENV G2*ENV G3*ENV S11*ENV S12*ENV S13*ENV S22*ENV S23*ENV S33*ENV R12*ENV R13*ENV R14*ENV R23*ENV R24*ENV R34*ENV;

%MACRO GCASCA; CONTRAST 'GCA' G1 1, G2 1, G3 1;

CONTRAST 'SCA' S11 1, S12 1, S13 1, S22 1, S23 1, S33 1;

ESTIMATE 'G1' G1 1; ESTIMATE 'G2' G2 1; ESTIMATE 'G3' G3 1;

Estimate 'G4' G1 -1 G2 -1 G3 -1;

ESTIMATE 'S11' S11 1; ESTIMATE 'S12' S12 1; ESTIMATE 'S13' S13 1;

ESTIMATE 'S22' S22 1; ESTIMATE 'S23' S23 1; ESTIMATE 'S33' S33 1;

Estimate 'S14' S11 -1 S12 -1 S13 -1;

Estimate 'S24' S12 -1 S22 -1 S23 -1;

Estimate 'S34' S13 -1 S23 -1 S33 -1;

Estimate 'S44' S11 1 S12 2 S13 2 S22 1 S23 2 S33 1;

%MEND GCASCA; %GCASCA %MACRO INTERACT;

CONTRAST 'GCA*ENV' G1*ENV 1 -1, G2*ENV 1 -1, G3*ENV 1 -1;

CONTRAST 'SCA*ENV' S11*ENV 1 -1, S12*ENV 1 -1, S13*ENV 1 -1, S22*ENV 1 -1, S23*ENV 1 -1, S33*ENV 1 -1; %MEND INTERACT; %INTERACT

CONTRAST 'REC' R12 1, R13 1, R14 1, R23 1, R24 1, R34 1;

ESTIMATE 'R12' R12 1; ESTIMATE 'R13' R13 1; ESTIMATE 'R14' R14 1;

ESTIMATE 'R23' R23 1; Estimate 'R24' R24 1; ESTIMATE 'R34' R34 1;

CONTRAST 'REC*ENV' R12*ENV 1 -1,R13*ENV 1 -1,R14*ENV 1 -1,R23*ENV 1 -1,R24*ENV 1 -1,R34*ENV 1 -1;

CONTRAST 'MAT SS' R12 1 R13 1 R14 1, R12 -1 R23 1 R24 1, R13 -1 R23 -1 R34 1, R14 -1 R24 -1 R34 -1; ESTIMATE 'MAT1' R12 1 R13 1 R14 1/DIVISOR=3;

ESTIMATE 'MAT2' R12 -1 R23 1 R24 1/DIVISOR=3;

ESTIMATE 'MAT3' R13 -1 R23 -1 R34 1/DIVISOR=3;

ESTIMATE 'MAT4' R14 -1 R24 -1 R34 -1/DIVISOR=3; RUN;

TITLE 'DIALLEL-SAS 2'; PROC GLM; CLASS REP ENV HYBRID;

MODEL YIELD= ENV REP (ENV) G1 G2 G3 S11 S12 S13 S22 S23 S33

M1 M2 M3 N12 N13 N23 G1*ENV G2*ENV G3*ENV

S11*ENV S12*ENV S13*ENV S22*ENV S23*ENV S33*ENV

M1*ENV M2*ENV M3*ENV N12*ENV N13*ENV N23*ENV;

%GCASCA %INTERACT

CONTRAST 'MAT SS' M1 1, M2 1, M3 1;

CONTRAST 'NONM SS' N12 1, N13 1, N23 1;

CONTRAST 'MAT*ENV' M1*ENV 1 -1, M2*ENV 1 -1, M3*ENV 1 -1;

CONTRAST 'NONM*ENV' N12*ENV 1 -1, N13*ENV 1 -1, N23*ENV 1- 1;

ESTIMATE 'M1' M1 1; ESTIMATE 'M2' M2 1; ESTIMATE 'M3' M3 1;

Estimate 'M4' M1 -1 M2 -1 M3 -1;

ESTIMATE 'N12' N12 1; ESTIMATE 'N13' N13 1; ESTIMATE 'N23' N23 1;

Estimate 'N14' N12 -1 N13 -1;

Estimate 'N24' N12 1 N23 -1;

Estimate 'N34' N13 1 N23 1; RUN;

To validate the code presented in program 1a, some results are shown that are generated by the program of Zhang and Kang (1997).

                              GLM procedure

Dependent variable: YIELD

                                            Sum of     Square of

Source                     DF      Square            The mean      F-Value   Pr > F

Model                     20    51191.16667     2559.55833      9.69      <.0001

Error                         75    19801.82292      264.02431

Total correct            95    70992.98958        

            R-square        Coef Var      Root MSE    YIELD mean

              0.721074      2.051592      16.24882       792.0104

                                                             Square of

Source                     DF      Type I SS        The mean         F-Value     Pr > F

ENV                         0        0.00000         .            .      .

REP(ENV)               5     3365.67708      673.13542         2.55        0.0347

HYBRID                15    47825.48958     3188.36597     12.08       <.0001

ENV*HYBRID                  0        0.00000         .            .      .

                                                                    Square of

Contrast                  DF   Contrast SS         The mean            F-Value        Pr > F

GCA                         3    30162.39583      10054.13194         38.08          <.0001

SCA                         6    14715.59375         2452.59896          9.29           <.0001

REC                         6      2947.50000           491.25000          1.86            0.0988

(MAT SS)              (3)     (240.75000)            80.25000        0.30            0.8224

(NONM SS)          (3)    (2706.75000)          902.25000        3.42            0.0216

                                                               Error

 Parameter               Estimate          Standard         Value t     Pr > |t|

 G1                        -6.0729167       2.03110309      -2.99      0.0038

 G2                       -13.8229167      2.03110309      -6.81      <.0001

 G3                        20.0104167      2.03110309       9.85      <.0001

 G4                        -0.1145833      2.03110309      -0.06      0.9552

 S12                        5.5520833      3.70826994       1.50      0.1385

 S13                        5.2187500      3.70826994       1.41      0.1635

 S23                        7.2187500      3.70826994       1.95      0.0553

 S14                        9.9270833      3.70826994       2.68      0.0091

 S24                      -10.9062500     3.70826994      -2.94      0.0043

 S34                       14.7604167     3.70826994       3.98      0.0002

 M1                        -1.1875000     2.03110309      -0.58      0.5605

 M2                         1.6875000     2.03110309       0.83      0.4087

 M3                         0.3125000     2.03110309       0.15      0.8781

 M4                        -0.8125000     2.03110309      -0.40      0.6903

 R12                        3.5000000     4.69063167       0.75      0.4579

 R13                        2.6666667    4.69063167       0.57      0.5714

 R14                     -10.9166667    4.69063167      -2.33      0.0226

 R23                        2.2500000     4.69063167       0.48      0.6329

 R24                        8.0000000     4.69063167       1.71      0.0922

 R34                        6.1666667     4.69063167       1.31      0.1926

Conclusions

The programs ‘1a’ and ‘1b’ are easy to use and modify to carry out an analysis of variance in a single environment, with the subdivision of the effects of the treatments in parents (P), direct crosses (CD), reciprocal crosses (CR), P versus crosses and CD versus CR. It is also useful for comparing treatment means (Tukey, p= 0.01) and for estimating heterosis with the parents’ mean and with the best of these when analyzing a variable.

Zhang and Kang’s (1997) program was designed to analyze ‘m’ variables, but it is more difficult to manipulate when parents and environments are different from 5 and 2, respectively. Due to this restriction, it was necessary to modify the code with P= 4. The code proposed by Zhang and Kang estimates general and specific combinatorial aptitude, reciprocal and maternal effects, but does not include the Tukey test or the estimation of heterosis.

All three codes for SAS run on versions over 10 years from their commercial release and on the most recent academic proofs. The program of Zhang and Kang (1997) allowed the reliable validation of the code proposed in the present study when the genetic effects were estimated, but the three codes must be used to carry out a more complete diallelic analysis.

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