Dominant Deviation effect

Description

DD effect to fit Hayman2 model with lm function

Usage

DD(P1, P2, type = "fix", data)

Arguments

Details

a design matrix of n-1 parentals

Value

A design matrix for the DD effect

Author(s)

Andrea Onofri, Niccolo' Terzaroli , Luigi Russi

References

Onofri, A., Terzaroli, N. & Russi, L. Linear models for diallel crosses: a review with R functions. Theor Appl Genet (2020). https://doi.org/10.1007/s00122-020-03716-8

Examples

data("hayman54")
contrasts(hayman54$Block) <- "contr.sum"
dMod <- lm(Ftime ~ Block + GCA(Par1, Par2) + MDD(Par1, Par2) +
             DD(Par1, Par2) + SCA(Par1, Par2) +
             RGCA(Par1, Par2) + RSCA(Par1, Par2), data = hayman54)
summary(dMod)

General Combining Ability effect

Description

GCA effect to fit Hayman1 & 2 and Griffing 1 & 2 models with lm function

Usage

GCA(P1,P2,type = "fix", data)

Arguments

Details

a design matrix of n-1 parentals

Value

A design matrix for the GCA effect

Author(s)

Andrea Onofri, Niccolo' Terzaroli , Luigi Russi

References

Onofri, A., Terzaroli, N. & Russi, L. Linear models for diallel crosses: a review with R functions. Theor Appl Genet (2020). https://doi.org/10.1007/s00122-020-03716-8

Examples

data("hayman54")
contrasts(hayman54$Block) <- "contr.sum"
dMod<-lm(Ftime ~ Block + GCA(Par1,Par2)
         + tSCA(Par1, Par2) + RGCA(Par1, Par2)
         + RSCA(Par1,Par2), data = hayman54)
anova(dMod)

General Combining Ability without considering the selfed parents

Description

Design matrix for GCAC, useful to fit Gardner & Eberhart model 3 (GE3) with lm function

Usage

GCAC(P1,P2,type = "fix", data)

Arguments

Details

a design matrix of n-1 parentals

Value

A design matrix for the GCAC effect

Author(s)

Andrea Onofri, Niccolo' Terzaroli, Luigi Russi

References

Onofri, A., Terzaroli, N. & Russi, L. Linear models for diallel crosses: a review with R functions. Theor Appl Genet (2020). https://doi.org/10.1007/s00122-020-03716-8

Examples

data("hayman54")
GCAC(Par1,Par2, data=hayman54)

Average heterosis effect

Description

H.BAR effect to fit GE2 and GE3 models with lm function

Usage

H.BAR(P1, P2, type = "fix", data)

Arguments

Value

A design matrix for the H.BAR effect

Author(s)

Andrea Onofri, Niccolo' Terzaroli , Luigi Russi

References

Onofri, A., Terzaroli, N. & Russi, L. Linear models for diallel crosses: a review with R functions. Theor Appl Genet (2020). https://doi.org/10.1007/s00122-020-03716-8

Examples

data("zhang05")
dMod <- lm(Yield ~ Env/Block + H.BAR(Par1, Par2) + VEi(Par1, Par2) +
                   Hi(Par1, Par2) + SCA(Par1, Par2) +
                   H.BAR(Par1, Par2):Env + VEi(Par1, Par2):Env +
                   Hi(Par1, Par2):Env + SCA(Par1, Par2):Env, data = zhang05)
anova(dMod)

Average heterosis effect

Description

H.i effect to fit GE2 Model with lm function

Usage

Hi(P1, P2, type = "fix", data)

Arguments

Details

a design matrix of n-1 parentals

Value

A design matrix for the Hi effect

Author(s)

Andrea Onofri, Niccolo' Terzaroli , Luigi Russi

References

Onofri, A., Terzaroli, N. & Russi, L. Linear models for diallel crosses: a review with R functions. Theor Appl Genet (2020). https://doi.org/10.1007/s00122-020-03716-8

Examples

data("zhang05")
dMod <- lm(Yield ~ Env/Block + H.BAR(Par1, Par2) + VEi(Par1, Par2) +
                   Hi(Par1, Par2) + SCA(Par1, Par2) +
                   H.BAR(Par1, Par2):Env + VEi(Par1, Par2):Env +
                   Hi(Par1, Par2):Env + SCA(Par1, Par2):Env, data = zhang05)
anova(dMod)

Mean Dominance Deviation effect

Description

It relates to the difference between the average yield of selfed parents and the average yield of crosses. DD effect to fit Hayman2 model with lm function

Usage

MDD(P1, P2, type = "fix", data)

Arguments

Value

A design matrix for the MDD effect

Author(s)

Andrea Onofri, Niccolo' Terzaroli, Luigi Russi

References

Onofri, A., Terzaroli, N. & Russi, L. Linear models for diallel crosses: a review with R functions. Theor Appl Genet (2020). https://doi.org/10.1007/s00122-020-03716-8

Examples

data("hayman54")
MDD(Par1, Par2, data = hayman54)

Reciprocal Effect not parted into RGCA and RSCA

Description

Build incidence matrix to fit reciprocal effects in Griffing's model 1, 2, 4 (REC) and 3 (REC.G3) with lm function

Usage

REC(P1, P2, type = "fix", data)

Arguments

Details

a design matrix of n-1 parentals

Value

A design matrix for the reciprocal (REC) effect

Author(s)

Andrea Onofri, Niccolo' Terzaroli, Luigi Russi

References

Onofri, A., Terzaroli, N. & Russi, L. Linear models for diallel crosses: a review with R functions. Theor Appl Genet (2020). https://doi.org/10.1007/s00122-020-03716-8

Examples

data("hayman54")
dMod<-lm(Ftime~ Block + GCA(Par1,Par2)
         +tSCA(Par1, Par2)+REC(Par1, Par2)
         , data = hayman54)
anova(dMod)

Reciprocal General Combining Ability

Description

RGCA effect to fit Hayman1 & 2 models with lm function

Usage

RGCA(P1,P2,type = "fix", data)

Arguments

Details

a design matrix of n-1 parentals

Value

A design matrix for the RGCA effect

Author(s)

Andrea Onofri, Niccolo' Terzaroli, Luigi Russi

References

Onofri, A., Terzaroli, N. & Russi, L. Linear models for diallel crosses: a review with R functions. Theor Appl Genet (2020). https://doi.org/10.1007/s00122-020-03716-8

Examples

data("hayman54")
dMod<-lm(Ftime~ Block + GCA(Par1,Par2)
         + tSCA(Par1, Par2) + RGCA(Par1, Par2)
         + RSCA(Par1,Par2), data = hayman54)
anova(dMod)

Reciprocal Specific Combining Ability

Description

RSCA effect to fit Hayman 1 & 2 models with lm function

Usage

RSCA(P1,P2,type = "fix",data)

Arguments

Details

a design matrix of all possible combinations between parentals with no selfs and no reciprocals

Value

A design matrix for the RSCA effect

Author(s)

Andrea Onofri, Niccolo' Terzaroli, Luigi Russi

References

Onofri, A., Terzaroli, N. & Russi, L. Linear models for diallel crosses: a review with R functions. Theor Appl Genet (2020). https://doi.org/10.1007/s00122-020-03716-8

Examples

data("hayman54")
dMod<-lm(Ftime~ Block + GCA(Par1,Par2)
         + tSCA(Par1, Par2) + RGCA(Par1, Par2)
         + RSCA(Par1,Par2), data = hayman54)
anova(dMod)

Specific Combining Ability

Description

SCA effect to fit Hayman2, Griffing3 (SCA.G3), GE2 and GE3 (SCA.GE) models with lm function

Usage

SCA(P1, P2, type = "fix", data)
SCA.G3(P1, P2,  type = "fix", data)

Arguments

Details

a design matrix of all possible combinations between parentals with no selfs and no reciprocals

Value

A design matrix for the SCA effect

Author(s)

Andrea Onofri, Niccolo' Terzaroli, Luigi Russi

References

Onofri, A., Terzaroli, N. & Russi, L. Linear models for diallel crosses: a review with R functions. Theor Appl Genet (2020). https://doi.org/10.1007/s00122-020-03716-8

Examples

data("zhang05")
dMod <- lm(Yield ~ Env/Block + H.BAR(Par1, Par2) + VEi(Par1, Par2) +
                   Hi(Par1, Par2) + SCA(Par1, Par2) +
                   H.BAR(Par1, Par2):Env + VEi(Par1, Par2):Env +
                   Hi(Par1, Par2):Env + SCA(Par1, Par2):Env, data = zhang05)
anova(dMod)

Selfed Parents effect

Description

SP effect to fit GE3 model with lm function

Usage

SP(P1, P2, type = "fix", data)

Arguments

Details

a design matrix of n-1 parentals

Value

A design matrix for the SP effect

Author(s)

Andrea Onofri, Niccolo' Terzaroli, Luigi Russi

References

Onofri, A., Terzaroli, N. & Russi, L. Linear models for diallel crosses: a review with R functions. Theor Appl Genet (2020). https://doi.org/10.1007/s00122-020-03716-8

Examples

data("hayman54")
SP(Par1,Par2, data=hayman54)

Variety Effect

Description

VE.i effect to fit GE2 model with lm function

Usage

VEi(P1, P2, type = "fix", data)

Arguments

Details

a design matrix of n-1 parentals

Value

A design matrix for the VEi effect

Author(s)

Andrea Onofri, Niccolo' Terzaroli, Luigi Russi

References

Onofri, A., Terzaroli, N. & Russi, L. Linear models for diallel crosses: a review with R functions. Theor Appl Genet (2020). https://doi.org/10.1007/s00122-020-03716-8

Examples

data("zhang05")
dMod <- lm(Yield ~ Env/Block + H.BAR(Par1, Par2) + VEi(Par1, Par2) +
                   Hi(Par1, Par2) + SCA(Par1, Par2) +
                   H.BAR(Par1, Par2):Env + VEi(Par1, Par2):Env +
                   Hi(Par1, Par2):Env + SCA(Par1, Par2):Env, data = zhang05)
anova(dMod)

Creates block diagonal matrix. It is used internally.

Description

This function takes a list of matrices and creates a block diagonal matrix. It is used to fit multi-environment diallel models

Usage

blockMatrixDiagonal(matList)

Arguments

Value

Returns a matrix object

Author(s)

Andrea Onofri, Niccolo' Terzaroli, Luigi Russi

References

Onofri, A., Terzaroli, N. & Russi, L. Linear models for diallel crosses: a review with R functions. Theoretical Applied Genetics (2020). https://doi.org/10.1007/s00122-020-03716-8

Examples

a <- matrix(1:16, 8, 2)
b <- matrix(1:9, 3, 3)
c <- list(a, b)
blockMatrixDiagonal(c)

Factitious dataset for Diallel analysis

Description

Multi-environment half-diallel dataset with six parentals, in five blocks and ten environments; the dataset is factitious and was obtained by Monte Carlo simulation.

Usage

data("diallelMET")

Format

A data.frame with 1050 observations on the following 5 variables.

Env

environment, a factor with 10 levels

Block

block, a factor with 5 levels

Par1

male parent, a factor with 6 levels

Par2

female parent, a factor with 6 levels

Yield

yield, a numeric vector

Author(s)

Andrea Onofri, Niccolo' Terzaroli, Luigi Russi

Source

Onofri, A., Terzaroli, N. & Russi, L. Linear models for diallel crosses: a review with R functions. Theor Appl Genet (2020). https://doi.org/10.1007/s00122-020-03716-8

References

Onofri, A., Terzaroli, N. & Russi, L. Linear models for diallel crosses: a review with R functions. Theor Appl Genet (2020). https://doi.org/10.1007/s00122-020-03716-8

Examples

data("diallelMET")

Functions to retreive full list of genetical effects

Description

Diallel model parameters are estimated under a set of restrictions and, therefore, the methods 'coef' and 'summary' do not return the full list of genetical parameters. Therefore, the 'glht.diallelMod' method can be used, which works by way of a series of helper functions, providing the necessary contrast matrices.

Usage

## S3 method for class 'diallelMod'
glht(model, linfct, ...)

Arguments

Details

...

Value

summary Returns the full list of genetical parameters

References

Onofri, A., Terzaroli, N. & Russi, L. Linear models for diallel crosses: a review with R functions. Theor Appl Genet (2020). https://doi.org/10.1007/s00122-020-03716-8

Examples

library(lmDiallel)
library(multcomp)

# Data with replicates
data("hayman54")

fit <- lm.diallel(Ftime ~ Par1 + Par2, data = hayman54,
                  fct = "HAYMAN1")
summary(fit)
anova(fit)
gh <- glht(linfct = diallel.eff(fit))

Create a Data Frame from All Combinations of Parentals

Description

This is a modification of the 'expand.grid()' function working specifically with diallel experiments. It creates a data frame from all combinations of the supplied vector of parents, depending on the mating scheme.

Usage

expand.diallel(pars, mating = 1)

Arguments

Value

returns a data.frame object

Author(s)

Andrea Onofri, Niccolo' Terzaroli, Luigi Russi

References

Onofri, A., Terzaroli, N. & Russi, L. Linear models for diallel crosses: a review with R functions. Theor Appl Genet (2020). https://doi.org/10.1007/s00122-020-03716-8

Examples

pars <- LETTERS[1:4]
expand.diallel(pars, mating = 3)

Griffing's dataset for diallel analysis

Description

Data for a diallel in maize, with no selfs and no selfed parents. Data are the means of several replicates.

Usage

data("griffing56")

Format

A data.frame with 36 observations on the following 5 variables

Par1

male parent, a factor with 8 levels

Par2

female parent, a factor with 8 levels

Yield

Maize Yield

Cob

Cob weight

Shelled

Shelled corn weight

Author(s)

Andrea Onofri, Niccolo' Terzaroli, Luigi Russi

Source

Griffing, B., 1956. Concept of general and specific combining ability in relation to diallel crossing systems. Australian Journal of Biological Science 9, 463–493.

References

Onofri, A., Terzaroli, N. & Russi, L. Linear models for diallel crosses: a review with R functions. Theor Appl Genet (2020). https://doi.org/10.1007/s00122-020-03716-8

Examples

data("griffing56")
dMod2 <- lm.diallel(Yield ~ Par1 + Par2,
                    data = griffing56, fct = "GRIFFING4")
anova(dMod2, MSE = 21.05, dfr = 2558)
summary(dMod2, MSE = 21.05, dfr = 2558)

Hayman dataset for diallel analysis

Description

Data for a diallel in tobacco with 2 reps

Usage

data(hayman54)

Format

A data.frame with 128 observations on the following 4 variables

Block

block, a factor with 2 levels

Par1

male parent, a factor with 8 levels

Par2

female parent, a factor with 8 levels

Ftime

mean flowering time (days), a numeric vector

Author(s)

Andrea Onofri, Niccolo' Terzaroli, Luigi Russi

Source

B. I. Hayman (1954a). The Analysis of Variance of Diallel Tables. Biometrics, 10, 235-244. Table 5, page 241. http://doi.org/10.2307/3001877

References

Onofri, A., Terzaroli, N. & Russi, L. Linear models for diallel crosses: a review with R functions. Theor Appl Genet (2020). https://doi.org/10.1007/s00122-020-03716-8

Examples

data("hayman54")

contrasts(hayman54$Block) <- c("contr.sum")
dMod <- lm(Ftime ~ Block  + GCA(Par1, Par2)
             + tSCA(Par1, Par2) + RGCA(Par1, Par2)
             + RSCA(Par1, Par2), data = hayman54)
anova(dMod)
#or
dMod2 <- lm.diallel(Ftime ~ Par1 + Par2, Block = Block,
                  data = hayman54,
                  fct = "HAYMAN1")
anova(dMod2)

Utilities for fitting diallel models.

Description

These functions are used internally by the package, but they can also called from the outside, to fit specific needs

Usage

int.matrix(Xa, Xb)
checkScheme(P1, P2)
emm.diallel(obj)

Arguments

Details

The function 'int.matrix()' produces the incidence matrix for the interaction between two main effects; 'Xa' and 'Xb' are two incidence matrices for two main effects. The function 'checkScheme()' takes two vectors containing the codings for parentals (P1 and P2), retrieves the mating scheme and detects whether there are missing crosses. The function 'emm.diallel()' is used with multi-environment diallel experiments to obtain the expected marginal means for genetic effects across environments.

Value

The function 'int.matrix()' returns an incidence matrix. The function 'checkScheme()' returns a list, containing the main traits of the mating scheme. The function 'emm.diallel()' retrns a data.frame with the marginal means, standard errors and t-test statistics.

Note

No further notes

Author(s)

Andrea Onofri

References

Onofri, A., Terzaroli, N. & Russi, L. Linear models for diallel crosses: a review with R functions. Theor Appl Genet (2020). https://doi.org/10.1007/s00122-020-03716-8

Examples

data(griffing56)
head(griffing56)
checkScheme(griffing56$Par1, griffing56$Par2)

Fitting diallel linear models

Description

Wrapper function for lm.fit and diallel models. It can be used to carry out several powerful methods for linear models, such as 'summary()', anova() or 'glht()' in the 'multcomp' package.

Usage

lm.diallel(formula, Block, Env, fct = "GRIFFING2", data)

Arguments

Details

Notations for the 8 models

Value

lm.diallel returns an object of class c("diallel", "lm"), that is a list containing at least the following components:

coefficients

a named vector of coefficients

residuals

the residuals, that is response minus fitted values

fitted.values

the fitted mean values

rank

the numeric rank of the fitted linear models

weights

(only for weighted fits) the specified weights

df.residual

the residual degrees of freedom

call

the matched call

terms

the terms object used

contrasts

(only where relevant) the contrasts used

xlevels

(only where relevant) a record of the levels of the factors used in fitting

call

the matched call

offset

the offset used (missing if none were used)

y

if requested, the response used

x

if requested, the model matrix used

model

if requested (the default), the model frame used

na.action

(where relevant) information returned by model.frame on the special handling of NAs

Author(s)

Andrea Onofri, Niccolo' Terzaroli, Luigi Russi

References

Onofri, A., Terzaroli, N. & Russi, L. Linear models for diallel crosses: a review with R functions. Theor Appl Genet (2020). https://doi.org/10.1007/s00122-020-03716-8

Examples

data("hayman54")
dMod <- lm.diallel(Ftime ~ Par1 + Par2, Block = Block,
                  data = hayman54,
                  fct = "HAYMAN1")
anova(dMod)

#or
data("zhang05")
contrasts(zhang05$Block) <- c("contr.sum")
dMod2 <- lm.diallel(Yield ~ Par1 + Par2, Env = Env, Block = Block,
            data = zhang05, fct = "GE2")

#or
data("lonnquist61")
dMod3 <- lm.diallel(Yield ~ Par1 + Par2,
                  data = lonnquist61,
                  fct = "GE2")
summary(dMod3, MSE = 7.10, dfr = 60)
anova(dMod3, MSE = 7.10, dfr = 60)

Methods for diallel model fitting

Description

The object returned by the 'lm.diallel()' function is of classes 'lm' and 'diallel'. Specific methods were devised to explore the 'diallel' object.

Usage

## S3 method for class 'diallel'
summary(object, MSE, dfr, ...)
## S3 method for class 'diallel'
vcov(object, MSE, ...)
## S3 method for class 'diallel'
anova(object, MSE, dfr, type = 1, ...)
## S3 method for class 'diallel'
model.matrix(object, ...)

Arguments

Details

To be defined

Value

vcov.diallel: a variance-covariance matrix summary.diallel: a data.frame of estimated parameters with standard errors anova.diallel: an ANOVA table predict.diallel: a vector of predictions from a diallel model model.matrix.diallel: a design matrix for the fitted diallel model

References

Onofri, A., Terzaroli, N. & Russi, L. Linear models for diallel crosses: a review with R functions. Theor Appl Genet (2020). https://doi.org/10.1007/s00122-020-03716-8

Examples

library(lmDiallel)
library(multcomp)
# Data with replicates
data("hayman54")

fit <- lm.diallel(Ftime ~ Par1 + Par2, data = hayman54,
                  fct = "HAYMAN1")
summary(fit)
anova(fit)
gh <- glht(linfct = diallel.eff(fit), adjust = "none")

Half diallel of maize dataset

Description

Diallel experiment with six maize varieties and no reciprocals. The data here are means adjusted for block effects.

Usage

data("lonnquist61")

Format

A data.frame with 21 observations on the following 3 variables.

Par1

male parent, a factor with 6 levels

Par2

female parent, a factor with 6 levels

Yield

mean across blocks, a numeric vector

Author(s)

Andrea Onofri, Niccolo' Terzaroli, Luigi Russi

Source

J. H. Lonnquist, C. O. Gardner. (1961) Heterosis in Intervarietal Crosses in Maize and Its Implication in Breeding Procedures. Crop Science, 1, 179-183. Table 1.

References

Onofri, A., Terzaroli, N. & Russi, L. Linear models for diallel crosses: a review with R functions. Theor Appl Genet (2020). https://doi.org/10.1007/s00122-020-03716-8

Mohring, Melchinger, Piepho. (2011). REML-Based Diallel Analysis. Crop Science, 51, 470-478. http://doi.org/10.2135/cropsci2010.05.0272

C. O. Gardner and S. A. Eberhart. 1966. Analysis and Interpretation of the Variety Cross Diallel and Related Populations. Biometrics, 22, 439-452. http://doi.org/10.2307/2528181

Examples

data("lonnquist61")
dMod <- lm(Yield ~ H.BAR(Par1, Par2) + VEi(Par1, Par2) +
             Hi(Par1, Par2) + SCA(Par1, Par2),
                  data = lonnquist61)
summary.diallel(dMod, MSE = 7.10, dfr = 60)
anova.diallel(dMod, MSE = 7.10, dfr = 60)

Design matrix for blocks

Description

It creates a disign matrix for block effects (with sum-to-zero constraint). It is used internally

Usage

matBlock(formula)

Arguments

Value

A design matrix for the block effect

Author(s)

Andrea Onofri, Niccolo' Terzaroli, Luigi Russi

References

Onofri, A., Terzaroli, N. & Russi, L. Linear models for diallel crosses: a review with R functions. Theor Appl Genet (2020). https://doi.org/10.1007/s00122-020-03716-8

Examples

data("hayman54")
matBlock(~hayman54$Block)

Fitting random diallel linear models

Description

Wrapper function for the function 'mmer()' in the 'sommer' package. It can be used to fit random diallel models and retreive variance components for main effects.

Usage

mmer.diallel(formula, Block, Env, fct, data, type = "all")

Arguments

Value

Returns a data frame of variance components with standard errors

Author(s)

Andrea Onofri, Niccolo' Terzaroli, Luigi Russi

References

Covarrubias-Pazaran, G., 2016. Genome-Assisted Prediction of Quantitative Traits Using the R Package sommer. PLOS ONE 11, e0156744. https://doi.org/10.1371/journal.pone.0156744

Examples

data("hayman54")
rMod <- mmer.diallel(Ftime ~ Par1 + Par2, Block = Block,
                  data = hayman54,
                  fct = "HAYMAN1")
rMod

Incidence matrices for Diallel model parametrisation

Description

model.matrixDiallel is useful to build design matrices, according to the user-defined (or default) parameterisation for lm function. It shares the same syntax of the lm.diallel function.

Arguments

Details

model.matrixDiallel creates a design matrix for a diallel model, as specified in the 'fct' argument.

Value

The design matrix for a diallel model as specified in the 'fct' argument.

Author(s)

Andrea Onofri, Niccolo' Terzaroli, Luigi Russi

References

Onofri, A., Terzaroli, N. & Russi, L. Linear models for diallel crosses: a review with R functions. Theor Appl Genet (2020). https://doi.org/10.1007/s00122-020-03716-8

Examples

data("diallelMET")
ModMat <- model.matrixDiallel(Yield ~ Par1 + Par2,
                   Env, Block, fct= "GE3",
                   data = diallelMET)

Total Specific Combining Ability

Description

Total SCA to fit Hayman1, Griffing1 and Griffing2 models with lm function

Usage

tSCA(P1,P2,type = "fix", data)

Arguments

Details

a design matrix of all possible combinations between parentals with selfs but no reciprocals

Value

A design matrix for the tSCA effect

Author(s)

Andrea Onofri, Niccolo' Terzaroli, Luigi Russi

References

Onofri, A., Terzaroli, N. & Russi, L. Linear models for diallel crosses: a review with R functions. Theor Appl Genet (2020). https://doi.org/10.1007/s00122-020-03716-8

Examples

data("hayman54")
dMod<-lm(Ftime~ Block + GCA(Par1,Par2)
         + tSCA(Par1, Par2) + RGCA(Par1, Par2)
         + RSCA(Par1,Par2), data = hayman54)
anova(dMod)

Data for diallel analysis from Zhang (2005)

Description

Data collected in XXX with 5 parents, 2 reps and 2 environments

Usage

data("zhang05")

Format

A data.frame with 60 observations on the following 6 variables.

Par1

male parent, a factor with 5 levels

Par2

female parent, a factor with 5 levels

Block

block, a factor with 2 levels

Combination

combination between environment and block, an integer vector

Env

environment, a factor with 2 levels

Yield

yield, a numeric vector

Author(s)

Andrea Onofri, Niccolo' Terzaroli, Luigi Russi

Source

Zhang, Y., Kang, M.S. and Lamkey, K.R. (2005), DIALLEL-SAS05: A Comprehensive Program for Griffing's and Gardner&Eberhart Analyses. Agron. J., 97: 1097-1106. https://doi.org/10.2134/agronj2004.0260

References

Onofri, A., Terzaroli, N. & Russi, L. Linear models for diallel crosses: a review with R functions. Theor Appl Genet (2020). https://doi.org/10.1007/s00122-020-03716-8

Examples

data("zhang05")
contrasts(zhang05$Block) <- c("contr.sum")
contrasts(zhang05$Env) <- c("contr.sum")
dMod <- lm(Yield ~ Env/Block + H.BAR(Par1, Par2) + VEi(Par1, Par2) +
                   Hi(Par1, Par2) + SCA(Par1, Par2) +
                   H.BAR(Par1, Par2):Env + GCA(Par1, Par2):Env +
                   Hi(Par1, Par2):Env + SCA(Par1, Par2):Env, data = zhang05)
anova(dMod)
#or
dMod2 <- lm(Yield ~ Env/Block + H.BAR(Par1, Par2) + VEi(Par1, Par2) +
                   Hi(Par1, Par2) + SCA(Par1, Par2), data = zhang05)
summary(dMod2)$coefficients